TSTP Solution File: SET686+3 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET686+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 : n010.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 15:11:55 EDT 2024
% Result : Theorem 1.28s 0.53s
% Output : Refutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 366
% Syntax : Number of formulae : 1312 ( 57 unt; 0 def)
% Number of atoms : 7427 ( 156 equ)
% Maximal formula atoms : 32 ( 5 avg)
% Number of connectives : 10951 (4836 ~;5414 |; 263 &)
% ( 353 <=>; 83 =>; 0 <=; 2 <~>)
% Maximal formula depth : 19 ( 8 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 333 ( 331 usr; 324 prp; 0-2 aty)
% Number of functors : 29 ( 29 usr; 9 con; 0-4 aty)
% Number of variables : 2123 (2009 !; 114 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3283,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,f371,f375,f380,f384,f388,f390,f394,f398,f402,f406,f434,f438,f447,f456,f464,f466,f470,f480,f487,f491,f495,f508,f517,f519,f529,f595,f601,f603,f613,f622,f626,f636,f638,f642,f647,f651,f660,f665,f678,f687,f693,f697,f701,f709,f713,f719,f724,f728,f734,f742,f746,f750,f754,f755,f778,f782,f786,f803,f818,f823,f827,f837,f842,f846,f872,f876,f892,f896,f900,f909,f917,f922,f928,f932,f947,f962,f968,f972,f978,f982,f989,f994,f1006,f1011,f1026,f1028,f1030,f1034,f1043,f1049,f1073,f1078,f1083,f1102,f1106,f1110,f1114,f1145,f1146,f1153,f1168,f1172,f1184,f1188,f1193,f1209,f1217,f1221,f1257,f1266,f1285,f1289,f1295,f1299,f1303,f1307,f1324,f1329,f1333,f1337,f1341,f1345,f1387,f1406,f1410,f1416,f1420,f1425,f1430,f1453,f1457,f1461,f1471,f1475,f1479,f1483,f1487,f1491,f1495,f1503,f1529,f1533,f1537,f1545,f1549,f1555,f1560,f1564,f1572,f1576,f1586,f1591,f1595,f1599,f1616,f1620,f1624,f1628,f1632,f1636,f1642,f1646,f1650,f1654,f1662,f1666,f1672,f1677,f1681,f1695,f1699,f1705,f1709,f1713,f1720,f1724,f1728,f1734,f1739,f1743,f1768,f1773,f1782,f1784,f1792,f1794,f1798,f1814,f1828,f1830,f1834,f1840,f1869,f1881,f1885,f1905,f1909,f1913,f1924,f1928,f1933,f1950,f1958,f1970,f1982,f1986,f1991,f1996,f2000,f2004,f2008,f2017,f2079,f2083,f2087,f2105,f2109,f2129,f2133,f2137,f2141,f2173,f2205,f2209,f2213,f2217,f2247,f2251,f2256,f2259,f2263,f2267,f2271,f2275,f2379,f2383,f2387,f2394,f2399,f2404,f2408,f2412,f2416,f2420,f2424,f2428,f2432,f2696,f2700,f2704,f2716,f2720,f2724,f2728,f2775,f2777,f2781,f2785,f2789,f2793,f2797,f2818,f2862,f2866,f2870,f2874,f2878,f2955,f2959,f2963,f2967,f3108,f3117,f3121,f3127,f3131,f3135,f3181,f3186,f3190,f3194,f3203,f3207,f3211,f3213,f3217,f3221,f3225,f3229,f3241,f3282]) ).
fof(f3282,plain,
( ~ spl21_7
| ~ spl21_219
| spl21_120
| ~ spl21_221 ),
inference(avatar_split_clause,[],[f1848,f1796,f1003,f1776,f222]) ).
fof(f222,plain,
( spl21_7
<=> member(sK9,sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_7])]) ).
fof(f1776,plain,
( spl21_219
<=> ilf_type(sK5,set_type) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_219])]) ).
fof(f1003,plain,
( spl21_120
<=> member(sK8,inverse2(sK7,sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_120])]) ).
fof(f1796,plain,
( spl21_221
<=> ! [X0] :
( ~ member(sK9,X0)
| ~ ilf_type(X0,set_type)
| member(sK8,inverse2(sK7,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_221])]) ).
fof(f1848,plain,
( ~ ilf_type(sK5,set_type)
| ~ member(sK9,sK5)
| spl21_120
| ~ spl21_221 ),
inference(resolution,[],[f1797,f1005]) ).
fof(f1005,plain,
( ~ member(sK8,inverse2(sK7,sK5))
| spl21_120 ),
inference(avatar_component_clause,[],[f1003]) ).
fof(f1797,plain,
( ! [X0] :
( member(sK8,inverse2(sK7,X0))
| ~ ilf_type(X0,set_type)
| ~ member(sK9,X0) )
| ~ spl21_221 ),
inference(avatar_component_clause,[],[f1796]) ).
fof(f3241,plain,
( ~ spl21_219
| ~ spl21_37
| ~ spl21_74
| ~ spl21_120
| ~ spl21_50
| spl21_307 ),
inference(avatar_split_clause,[],[f3182,f3110,f454,f1003,f654,f358,f1776]) ).
fof(f358,plain,
( spl21_37
<=> ilf_type(sK8,set_type) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_37])]) ).
fof(f654,plain,
( spl21_74
<=> ilf_type(sK7,binary_relation_type) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_74])]) ).
fof(f454,plain,
( spl21_50
<=> ! [X2,X0,X1] :
( member(sK16(X0,X1,X2),X0)
| ~ member(X1,inverse2(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_50])]) ).
fof(f3110,plain,
( spl21_307
<=> member(sK16(sK5,sK8,sK7),sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_307])]) ).
fof(f3182,plain,
( ~ member(sK8,inverse2(sK7,sK5))
| ~ ilf_type(sK7,binary_relation_type)
| ~ ilf_type(sK8,set_type)
| ~ ilf_type(sK5,set_type)
| ~ spl21_50
| spl21_307 ),
inference(resolution,[],[f3112,f455]) ).
fof(f455,plain,
( ! [X2,X0,X1] :
( member(sK16(X0,X1,X2),X0)
| ~ member(X1,inverse2(X2,X0))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_50 ),
inference(avatar_component_clause,[],[f454]) ).
fof(f3112,plain,
( ~ member(sK16(sK5,sK8,sK7),sK5)
| spl21_307 ),
inference(avatar_component_clause,[],[f3110]) ).
fof(f3229,plain,
( spl21_323
| ~ spl21_29
| ~ spl21_154 ),
inference(avatar_split_clause,[],[f1356,f1327,f321,f3227]) ).
fof(f3227,plain,
( spl21_323
<=> ! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ ilf_type(ordered_pair(X2,X0),set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(power_set(ordered_pair(X2,X0)),binary_relation_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ empty(inverse2(power_set(ordered_pair(X2,X0)),X1))
| ~ ilf_type(inverse2(power_set(ordered_pair(X2,X0)),X1),set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_323])]) ).
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(f1327,plain,
( spl21_154
<=> ! [X2,X0,X1] :
( ~ ilf_type(ordered_pair(X0,X1),set_type)
| ~ member(X1,X2)
| member(X0,inverse2(power_set(ordered_pair(X0,X1)),X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(power_set(ordered_pair(X0,X1)),binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X2,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_154])]) ).
fof(f1356,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ ilf_type(ordered_pair(X2,X0),set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(power_set(ordered_pair(X2,X0)),binary_relation_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ empty(inverse2(power_set(ordered_pair(X2,X0)),X1))
| ~ ilf_type(inverse2(power_set(ordered_pair(X2,X0)),X1),set_type) )
| ~ spl21_29
| ~ spl21_154 ),
inference(duplicate_literal_removal,[],[f1350]) ).
fof(f1350,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ ilf_type(ordered_pair(X2,X0),set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(power_set(ordered_pair(X2,X0)),binary_relation_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ empty(inverse2(power_set(ordered_pair(X2,X0)),X1))
| ~ ilf_type(inverse2(power_set(ordered_pair(X2,X0)),X1),set_type) )
| ~ spl21_29
| ~ spl21_154 ),
inference(resolution,[],[f1328,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(f1328,plain,
( ! [X2,X0,X1] :
( member(X0,inverse2(power_set(ordered_pair(X0,X1)),X2))
| ~ member(X1,X2)
| ~ ilf_type(ordered_pair(X0,X1),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(power_set(ordered_pair(X0,X1)),binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X2,set_type) )
| ~ spl21_154 ),
inference(avatar_component_clause,[],[f1327]) ).
fof(f3225,plain,
( spl21_322
| ~ spl21_127
| ~ spl21_151 ),
inference(avatar_split_clause,[],[f1320,f1301,f1047,f3223]) ).
fof(f3223,plain,
( spl21_322
<=> ! [X0,X3,X2,X1] :
( member(sK19(inverse2(X0,X1)),X2)
| ~ ilf_type(sK19(inverse2(X0,X1)),set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,relation_type(X2,X3))
| ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,set_type)
| empty(inverse2(X0,X1))
| ~ ilf_type(inverse2(X0,X1),set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_322])]) ).
fof(f1047,plain,
( spl21_127
<=> ! [X0] :
( ~ ilf_type(X0,set_type)
| empty(X0)
| member(sK19(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_127])]) ).
fof(f1301,plain,
( spl21_151
<=> ! [X4,X0,X3,X2,X1] :
( ~ ilf_type(X0,relation_type(X1,X2))
| member(X3,X1)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(X3,inverse2(X0,X4))
| ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X4,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_151])]) ).
fof(f1320,plain,
( ! [X2,X3,X0,X1] :
( member(sK19(inverse2(X0,X1)),X2)
| ~ ilf_type(sK19(inverse2(X0,X1)),set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,relation_type(X2,X3))
| ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,set_type)
| empty(inverse2(X0,X1))
| ~ ilf_type(inverse2(X0,X1),set_type) )
| ~ spl21_127
| ~ spl21_151 ),
inference(resolution,[],[f1302,f1048]) ).
fof(f1048,plain,
( ! [X0] :
( member(sK19(X0),X0)
| empty(X0)
| ~ ilf_type(X0,set_type) )
| ~ spl21_127 ),
inference(avatar_component_clause,[],[f1047]) ).
fof(f1302,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ member(X3,inverse2(X0,X4))
| member(X3,X1)
| ~ ilf_type(X3,set_type)
| ~ 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_151 ),
inference(avatar_component_clause,[],[f1301]) ).
fof(f3221,plain,
( spl21_321
| ~ spl21_24
| ~ spl21_151 ),
inference(avatar_split_clause,[],[f1311,f1301,f300,f3219]) ).
fof(f3219,plain,
( spl21_321
<=> ! [X0,X3,X2,X1] :
( member(sK13(inverse2(X0,X1)),X2)
| ~ ilf_type(sK13(inverse2(X0,X1)),set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,relation_type(X2,X3))
| ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,set_type)
| empty(inverse2(X0,X1))
| ~ ilf_type(inverse2(X0,X1),set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_321])]) ).
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(f1311,plain,
( ! [X2,X3,X0,X1] :
( member(sK13(inverse2(X0,X1)),X2)
| ~ ilf_type(sK13(inverse2(X0,X1)),set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,relation_type(X2,X3))
| ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,set_type)
| empty(inverse2(X0,X1))
| ~ ilf_type(inverse2(X0,X1),set_type) )
| ~ spl21_24
| ~ spl21_151 ),
inference(resolution,[],[f1302,f301]) ).
fof(f301,plain,
( ! [X0] :
( member(sK13(X0),X0)
| empty(X0)
| ~ ilf_type(X0,set_type) )
| ~ spl21_24 ),
inference(avatar_component_clause,[],[f300]) ).
fof(f3217,plain,
( spl21_320
| ~ spl21_47
| ~ spl21_142 ),
inference(avatar_split_clause,[],[f1210,f1207,f432,f3215]) ).
fof(f3215,plain,
( spl21_320
<=> ! [X0,X1] :
( empty(power_set(cross_product(X0,X1)))
| ~ ilf_type(sK13(power_set(cross_product(X0,X1))),set_type)
| ~ ilf_type(power_set(cross_product(X0,X1)),set_type)
| ~ ilf_type(cross_product(X0,X1),set_type)
| ilf_type(sK13(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_320])]) ).
fof(f432,plain,
( spl21_47
<=> ! [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_47])]) ).
fof(f1207,plain,
( spl21_142
<=> ! [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_142])]) ).
fof(f1210,plain,
( ! [X0,X1] :
( empty(power_set(cross_product(X0,X1)))
| ~ ilf_type(sK13(power_set(cross_product(X0,X1))),set_type)
| ~ ilf_type(power_set(cross_product(X0,X1)),set_type)
| ~ ilf_type(cross_product(X0,X1),set_type)
| ilf_type(sK13(power_set(cross_product(X0,X1))),relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_47
| ~ spl21_142 ),
inference(resolution,[],[f1208,f433]) ).
fof(f433,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_47 ),
inference(avatar_component_clause,[],[f432]) ).
fof(f1208,plain,
( ! [X0] :
( ilf_type(sK13(power_set(X0)),subset_type(X0))
| empty(power_set(X0))
| ~ ilf_type(sK13(power_set(X0)),set_type)
| ~ ilf_type(power_set(X0),set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_142 ),
inference(avatar_component_clause,[],[f1207]) ).
fof(f3213,plain,
( ~ spl21_9
| spl21_308 ),
inference(avatar_contradiction_clause,[],[f3212]) ).
fof(f3212,plain,
( $false
| ~ spl21_9
| spl21_308 ),
inference(resolution,[],[f3116,f233]) ).
fof(f233,plain,
( ! [X0] : ilf_type(X0,set_type)
| ~ spl21_9 ),
inference(avatar_component_clause,[],[f232]) ).
fof(f232,plain,
( spl21_9
<=> ! [X0] : ilf_type(X0,set_type) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_9])]) ).
fof(f3116,plain,
( ~ ilf_type(sK16(sK5,sK8,sK7),set_type)
| spl21_308 ),
inference(avatar_component_clause,[],[f3114]) ).
fof(f3114,plain,
( spl21_308
<=> ilf_type(sK16(sK5,sK8,sK7),set_type) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_308])]) ).
fof(f3211,plain,
( spl21_319
| ~ spl21_105
| ~ spl21_130 ),
inference(avatar_split_clause,[],[f1094,f1081,f894,f3209]) ).
fof(f3209,plain,
( spl21_319
<=> ! [X0,X3,X2,X1] :
( ~ ilf_type(sK16(X0,X1,X2),set_type)
| ~ ilf_type(X3,set_type)
| ~ empty(sK16(X0,X1,X2))
| member(X1,inverse2(X2,power_set(X3)))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(power_set(X3),set_type)
| ~ member(X1,inverse2(X2,X0))
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_319])]) ).
fof(f894,plain,
( spl21_105
<=> ! [X0,X3,X2,X1] :
( ~ member(sK16(X0,X1,X2),X3)
| member(X1,inverse2(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,inverse2(X2,X0))
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_105])]) ).
fof(f1081,plain,
( spl21_130
<=> ! [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_130])]) ).
fof(f1094,plain,
( ! [X2,X3,X0,X1] :
( ~ ilf_type(sK16(X0,X1,X2),set_type)
| ~ ilf_type(X3,set_type)
| ~ empty(sK16(X0,X1,X2))
| member(X1,inverse2(X2,power_set(X3)))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(power_set(X3),set_type)
| ~ member(X1,inverse2(X2,X0))
| ~ ilf_type(X0,set_type) )
| ~ spl21_105
| ~ spl21_130 ),
inference(duplicate_literal_removal,[],[f1093]) ).
fof(f1093,plain,
( ! [X2,X3,X0,X1] :
( ~ ilf_type(sK16(X0,X1,X2),set_type)
| ~ ilf_type(X3,set_type)
| ~ empty(sK16(X0,X1,X2))
| member(X1,inverse2(X2,power_set(X3)))
| ~ ilf_type(sK16(X0,X1,X2),set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(power_set(X3),set_type)
| ~ member(X1,inverse2(X2,X0))
| ~ ilf_type(X0,set_type) )
| ~ spl21_105
| ~ spl21_130 ),
inference(resolution,[],[f1082,f895]) ).
fof(f895,plain,
( ! [X2,X3,X0,X1] :
( ~ member(sK16(X0,X1,X2),X3)
| member(X1,inverse2(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,inverse2(X2,X0))
| ~ ilf_type(X0,set_type) )
| ~ spl21_105 ),
inference(avatar_component_clause,[],[f894]) ).
fof(f1082,plain,
( ! [X0,X1] :
( member(X1,power_set(X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ empty(X1) )
| ~ spl21_130 ),
inference(avatar_component_clause,[],[f1081]) ).
fof(f3207,plain,
( spl21_318
| ~ spl21_100
| ~ spl21_127 ),
inference(avatar_split_clause,[],[f1064,f1047,f840,f3205]) ).
fof(f3205,plain,
( spl21_318
<=> ! [X0,X1] :
( empty(sK14(X0,power_set(X1)))
| ~ ilf_type(sK14(X0,power_set(X1)),set_type)
| ~ ilf_type(sK19(sK14(X0,power_set(X1))),set_type)
| member(sK19(sK14(X0,power_set(X1))),X1)
| ~ ilf_type(X1,set_type)
| member(sK14(X0,power_set(X1)),X0)
| sP2(X0,power_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_318])]) ).
fof(f840,plain,
( spl21_100
<=> ! [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_100])]) ).
fof(f1064,plain,
( ! [X0,X1] :
( empty(sK14(X0,power_set(X1)))
| ~ ilf_type(sK14(X0,power_set(X1)),set_type)
| ~ ilf_type(sK19(sK14(X0,power_set(X1))),set_type)
| member(sK19(sK14(X0,power_set(X1))),X1)
| ~ ilf_type(X1,set_type)
| member(sK14(X0,power_set(X1)),X0)
| sP2(X0,power_set(X1)) )
| ~ spl21_100
| ~ spl21_127 ),
inference(duplicate_literal_removal,[],[f1057]) ).
fof(f1057,plain,
( ! [X0,X1] :
( empty(sK14(X0,power_set(X1)))
| ~ ilf_type(sK14(X0,power_set(X1)),set_type)
| ~ ilf_type(sK19(sK14(X0,power_set(X1))),set_type)
| member(sK19(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)) )
| ~ spl21_100
| ~ spl21_127 ),
inference(resolution,[],[f1048,f841]) ).
fof(f841,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_100 ),
inference(avatar_component_clause,[],[f840]) ).
fof(f3203,plain,
( spl21_317
| ~ spl21_101
| ~ spl21_127 ),
inference(avatar_split_clause,[],[f1063,f1047,f844,f3201]) ).
fof(f3201,plain,
( spl21_317
<=> ! [X0,X1] :
( empty(sK14(power_set(X0),X1))
| ~ ilf_type(sK14(power_set(X0),X1),set_type)
| ~ ilf_type(sK19(sK14(power_set(X0),X1)),set_type)
| member(sK19(sK14(power_set(X0),X1)),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_317])]) ).
fof(f844,plain,
( spl21_101
<=> ! [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_101])]) ).
fof(f1063,plain,
( ! [X0,X1] :
( empty(sK14(power_set(X0),X1))
| ~ ilf_type(sK14(power_set(X0),X1),set_type)
| ~ ilf_type(sK19(sK14(power_set(X0),X1)),set_type)
| member(sK19(sK14(power_set(X0),X1)),X0)
| ~ ilf_type(X0,set_type)
| member(sK14(power_set(X0),X1),X1)
| sP2(power_set(X0),X1) )
| ~ spl21_101
| ~ spl21_127 ),
inference(duplicate_literal_removal,[],[f1058]) ).
fof(f1058,plain,
( ! [X0,X1] :
( empty(sK14(power_set(X0),X1))
| ~ ilf_type(sK14(power_set(X0),X1),set_type)
| ~ ilf_type(sK19(sK14(power_set(X0),X1)),set_type)
| member(sK19(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) )
| ~ spl21_101
| ~ spl21_127 ),
inference(resolution,[],[f1048,f845]) ).
fof(f845,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_101 ),
inference(avatar_component_clause,[],[f844]) ).
fof(f3194,plain,
( spl21_316
| ~ spl21_9
| ~ spl21_187 ),
inference(avatar_split_clause,[],[f1582,f1574,f232,f3192]) ).
fof(f3192,plain,
( spl21_316
<=> ! [X2,X0,X1] :
( 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_316])]) ).
fof(f1574,plain,
( spl21_187
<=> ! [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_187])]) ).
fof(f1582,plain,
( ! [X2,X0,X1] :
( 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_9
| ~ spl21_187 ),
inference(resolution,[],[f1575,f233]) ).
fof(f1575,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_187 ),
inference(avatar_component_clause,[],[f1574]) ).
fof(f3190,plain,
( spl21_315
| ~ spl21_9
| ~ spl21_184 ),
inference(avatar_split_clause,[],[f1581,f1562,f232,f3188]) ).
fof(f3188,plain,
( spl21_315
<=> ! [X2,X0,X1] :
( 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_315])]) ).
fof(f1562,plain,
( spl21_184
<=> ! [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_184])]) ).
fof(f1581,plain,
( ! [X2,X0,X1] :
( 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_9
| ~ spl21_184 ),
inference(resolution,[],[f1563,f233]) ).
fof(f1563,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_184 ),
inference(avatar_component_clause,[],[f1562]) ).
fof(f3186,plain,
( spl21_314
| ~ spl21_40
| ~ spl21_154 ),
inference(avatar_split_clause,[],[f1357,f1327,f378,f3184]) ).
fof(f3184,plain,
( spl21_314
<=> ! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ ilf_type(ordered_pair(X2,X0),set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(power_set(ordered_pair(X2,X0)),binary_relation_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ordered_pair(sK11(X2),sK12(X2)) = X2
| ~ sP0(inverse2(power_set(ordered_pair(X2,X0)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_314])]) ).
fof(f378,plain,
( spl21_40
<=> ! [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_40])]) ).
fof(f1357,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ ilf_type(ordered_pair(X2,X0),set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(power_set(ordered_pair(X2,X0)),binary_relation_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ordered_pair(sK11(X2),sK12(X2)) = X2
| ~ sP0(inverse2(power_set(ordered_pair(X2,X0)),X1)) )
| ~ spl21_40
| ~ spl21_154 ),
inference(duplicate_literal_removal,[],[f1349]) ).
fof(f1349,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ ilf_type(ordered_pair(X2,X0),set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(power_set(ordered_pair(X2,X0)),binary_relation_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ordered_pair(sK11(X2),sK12(X2)) = X2
| ~ ilf_type(X2,set_type)
| ~ sP0(inverse2(power_set(ordered_pair(X2,X0)),X1)) )
| ~ spl21_40
| ~ spl21_154 ),
inference(resolution,[],[f1328,f379]) ).
fof(f379,plain,
( ! [X0,X4] :
( ~ member(X4,X0)
| ordered_pair(sK11(X4),sK12(X4)) = X4
| ~ ilf_type(X4,set_type)
| ~ sP0(X0) )
| ~ spl21_40 ),
inference(avatar_component_clause,[],[f378]) ).
fof(f3181,plain,
( spl21_313
| ~ spl21_50
| ~ spl21_140 ),
inference(avatar_split_clause,[],[f1204,f1186,f454,f3179]) ).
fof(f3179,plain,
( spl21_313
<=> ! [X0,X3,X2,X1] :
( ~ ilf_type(sK16(inverse2(X0,X1),X2,X3),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type)
| ~ member(X2,inverse2(X3,inverse2(X0,X1)))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(inverse2(X0,X1),set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_313])]) ).
fof(f1186,plain,
( spl21_140
<=> ! [X2,X0,X1] :
( ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X1,inverse2(X0,X2))
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_140])]) ).
fof(f1204,plain,
( ! [X2,X3,X0,X1] :
( ~ ilf_type(sK16(inverse2(X0,X1),X2,X3),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type)
| ~ member(X2,inverse2(X3,inverse2(X0,X1)))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(inverse2(X0,X1),set_type) )
| ~ spl21_50
| ~ spl21_140 ),
inference(resolution,[],[f1187,f455]) ).
fof(f1187,plain,
( ! [X2,X0,X1] :
( ~ member(X1,inverse2(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_140 ),
inference(avatar_component_clause,[],[f1186]) ).
fof(f3135,plain,
( spl21_312
| ~ spl21_9
| ~ spl21_182 ),
inference(avatar_split_clause,[],[f1556,f1553,f232,f3133]) ).
fof(f3133,plain,
( spl21_312
<=> ! [X2,X0,X1] :
( 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,inverse2(X2,sK13(power_set(X0))))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_312])]) ).
fof(f1553,plain,
( spl21_182
<=> ! [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,inverse2(X2,sK13(power_set(X0))))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_182])]) ).
fof(f1556,plain,
( ! [X2,X0,X1] :
( 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,inverse2(X2,sK13(power_set(X0))))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type) )
| ~ spl21_9
| ~ spl21_182 ),
inference(resolution,[],[f1554,f233]) ).
fof(f1554,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,inverse2(X2,sK13(power_set(X0))))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type) )
| ~ spl21_182 ),
inference(avatar_component_clause,[],[f1553]) ).
fof(f3131,plain,
( spl21_311
| ~ spl21_17
| ~ spl21_158 ),
inference(avatar_split_clause,[],[f1372,f1343,f267,f3129]) ).
fof(f3129,plain,
( spl21_311
<=> ! [X0,X3,X2,X1] :
( member(sK16(X0,sK10(inverse2(X1,X0)),X1),X2)
| ~ ilf_type(sK10(inverse2(X1,X0)),set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X1,relation_type(X3,X2))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type)
| sP0(inverse2(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_311])]) ).
fof(f267,plain,
( spl21_17
<=> ! [X0] :
( sP0(X0)
| member(sK10(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_17])]) ).
fof(f1343,plain,
( spl21_158
<=> ! [X4,X0,X3,X2,X1] :
( ~ ilf_type(X0,relation_type(X1,X2))
| member(sK16(X3,X4,X0),X2)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(X4,inverse2(X0,X3))
| ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X3,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_158])]) ).
fof(f1372,plain,
( ! [X2,X3,X0,X1] :
( member(sK16(X0,sK10(inverse2(X1,X0)),X1),X2)
| ~ ilf_type(sK10(inverse2(X1,X0)),set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X1,relation_type(X3,X2))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type)
| sP0(inverse2(X1,X0)) )
| ~ spl21_17
| ~ spl21_158 ),
inference(resolution,[],[f1344,f268]) ).
fof(f268,plain,
( ! [X0] :
( member(sK10(X0),X0)
| sP0(X0) )
| ~ spl21_17 ),
inference(avatar_component_clause,[],[f267]) ).
fof(f1344,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ member(X4,inverse2(X0,X3))
| member(sK16(X3,X4,X0),X2)
| ~ ilf_type(X4,set_type)
| ~ 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(X3,set_type) )
| ~ spl21_158 ),
inference(avatar_component_clause,[],[f1343]) ).
fof(f3127,plain,
( spl21_310
| ~ spl21_51
| ~ spl21_136 ),
inference(avatar_split_clause,[],[f1154,f1151,f462,f3125]) ).
fof(f3125,plain,
( spl21_310
<=> ! [X0,X3,X2,X1] :
( ~ ilf_type(ordered_pair(X0,sK16(X1,X0,inverse2(X2,X3))),set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ empty(X3)
| ~ member(X0,inverse2(inverse2(X2,X3),X1))
| ~ ilf_type(inverse2(X2,X3),binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_310])]) ).
fof(f462,plain,
( spl21_51
<=> ! [X2,X0,X1] :
( member(ordered_pair(X1,sK16(X0,X1,X2)),X2)
| ~ member(X1,inverse2(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(f1151,plain,
( spl21_136
<=> ! [X2,X0,X1] :
( ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X1,inverse2(X0,X2))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_136])]) ).
fof(f1154,plain,
( ! [X2,X3,X0,X1] :
( ~ ilf_type(ordered_pair(X0,sK16(X1,X0,inverse2(X2,X3))),set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ empty(X3)
| ~ member(X0,inverse2(inverse2(X2,X3),X1))
| ~ ilf_type(inverse2(X2,X3),binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type) )
| ~ spl21_51
| ~ spl21_136 ),
inference(resolution,[],[f1152,f463]) ).
fof(f463,plain,
( ! [X2,X0,X1] :
( member(ordered_pair(X1,sK16(X0,X1,X2)),X2)
| ~ member(X1,inverse2(X2,X0))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_51 ),
inference(avatar_component_clause,[],[f462]) ).
fof(f1152,plain,
( ! [X2,X0,X1] :
( ~ member(X1,inverse2(X0,X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ empty(X2) )
| ~ spl21_136 ),
inference(avatar_component_clause,[],[f1151]) ).
fof(f3121,plain,
( spl21_309
| ~ spl21_39
| ~ spl21_142 ),
inference(avatar_split_clause,[],[f1211,f1207,f373,f3119]) ).
fof(f3119,plain,
( spl21_309
<=> ! [X0,X1] :
( empty(power_set(cross_product(X0,X1)))
| ~ ilf_type(sK13(power_set(cross_product(X0,X1))),set_type)
| ~ ilf_type(power_set(cross_product(X0,X1)),set_type)
| ~ ilf_type(cross_product(X0,X1),set_type)
| relation_like(sK13(power_set(cross_product(X0,X1))))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_309])]) ).
fof(f373,plain,
( spl21_39
<=> ! [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_39])]) ).
fof(f1211,plain,
( ! [X0,X1] :
( empty(power_set(cross_product(X0,X1)))
| ~ ilf_type(sK13(power_set(cross_product(X0,X1))),set_type)
| ~ ilf_type(power_set(cross_product(X0,X1)),set_type)
| ~ ilf_type(cross_product(X0,X1),set_type)
| relation_like(sK13(power_set(cross_product(X0,X1))))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_39
| ~ spl21_142 ),
inference(resolution,[],[f1208,f374]) ).
fof(f374,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_39 ),
inference(avatar_component_clause,[],[f373]) ).
fof(f3117,plain,
( ~ spl21_120
| ~ spl21_219
| ~ spl21_307
| ~ spl21_308
| ~ spl21_119
| ~ spl21_233 ),
inference(avatar_split_clause,[],[f1972,f1921,f992,f3114,f3110,f1776,f1003]) ).
fof(f992,plain,
( spl21_119
<=> ! [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,inverse2(sK7,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_119])]) ).
fof(f1921,plain,
( spl21_233
<=> member(sK16(sK5,sK8,sK7),sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_233])]) ).
fof(f1972,plain,
( ~ ilf_type(sK16(sK5,sK8,sK7),set_type)
| ~ member(sK16(sK5,sK8,sK7),sK5)
| ~ ilf_type(sK5,set_type)
| ~ member(sK8,inverse2(sK7,sK5))
| ~ spl21_119
| ~ spl21_233 ),
inference(resolution,[],[f1923,f993]) ).
fof(f993,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,inverse2(sK7,X0)) )
| ~ spl21_119 ),
inference(avatar_component_clause,[],[f992]) ).
fof(f1923,plain,
( member(sK16(sK5,sK8,sK7),sK6)
| ~ spl21_233 ),
inference(avatar_component_clause,[],[f1921]) ).
fof(f3108,plain,
( spl21_306
| ~ spl21_92
| ~ spl21_133 ),
inference(avatar_split_clause,[],[f1122,f1108,f776,f3106]) ).
fof(f3106,plain,
( spl21_306
<=> ! [X0,X1] :
( sP2(sK10(power_set(X0)),X1)
| ~ empty(X1)
| ~ ilf_type(X1,set_type)
| ~ 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)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_306])]) ).
fof(f776,plain,
( spl21_92
<=> ! [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_92])]) ).
fof(f1108,plain,
( spl21_133
<=> ! [X0,X1] :
( sP2(X0,X1)
| member(sK14(X0,X1),X0)
| ~ empty(X1)
| ~ ilf_type(X1,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_133])]) ).
fof(f1122,plain,
( ! [X0,X1] :
( sP2(sK10(power_set(X0)),X1)
| ~ empty(X1)
| ~ ilf_type(X1,set_type)
| ~ 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)) )
| ~ spl21_92
| ~ spl21_133 ),
inference(resolution,[],[f1109,f777]) ).
fof(f777,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_92 ),
inference(avatar_component_clause,[],[f776]) ).
fof(f1109,plain,
( ! [X0,X1] :
( member(sK14(X0,X1),X0)
| sP2(X0,X1)
| ~ empty(X1)
| ~ ilf_type(X1,set_type) )
| ~ spl21_133 ),
inference(avatar_component_clause,[],[f1108]) ).
fof(f2967,plain,
( spl21_305
| ~ spl21_9
| ~ spl21_181 ),
inference(avatar_split_clause,[],[f1551,f1547,f232,f2965]) ).
fof(f2965,plain,
( spl21_305
<=> ! [X0,X1] :
( 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_305])]) ).
fof(f1547,plain,
( spl21_181
<=> ! [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_181])]) ).
fof(f1551,plain,
( ! [X0,X1] :
( 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_9
| ~ spl21_181 ),
inference(resolution,[],[f1548,f233]) ).
fof(f1548,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_181 ),
inference(avatar_component_clause,[],[f1547]) ).
fof(f2963,plain,
( spl21_304
| ~ spl21_9
| ~ spl21_180 ),
inference(avatar_split_clause,[],[f1550,f1543,f232,f2961]) ).
fof(f2961,plain,
( spl21_304
<=> ! [X0,X1] :
( 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_304])]) ).
fof(f1543,plain,
( spl21_180
<=> ! [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_180])]) ).
fof(f1550,plain,
( ! [X0,X1] :
( 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_9
| ~ spl21_180 ),
inference(resolution,[],[f1544,f233]) ).
fof(f1544,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_180 ),
inference(avatar_component_clause,[],[f1543]) ).
fof(f2959,plain,
( spl21_303
| ~ spl21_50
| ~ spl21_136 ),
inference(avatar_split_clause,[],[f1163,f1151,f454,f2957]) ).
fof(f2957,plain,
( spl21_303
<=> ! [X0,X3,X2,X1] :
( ~ ilf_type(sK16(inverse2(X0,X1),X2,X3),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ empty(X1)
| ~ member(X2,inverse2(X3,inverse2(X0,X1)))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(inverse2(X0,X1),set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_303])]) ).
fof(f1163,plain,
( ! [X2,X3,X0,X1] :
( ~ ilf_type(sK16(inverse2(X0,X1),X2,X3),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ empty(X1)
| ~ member(X2,inverse2(X3,inverse2(X0,X1)))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(inverse2(X0,X1),set_type) )
| ~ spl21_50
| ~ spl21_136 ),
inference(resolution,[],[f1152,f455]) ).
fof(f2955,plain,
( spl21_302
| ~ spl21_54
| ~ spl21_130 ),
inference(avatar_split_clause,[],[f1090,f1081,f485,f2953]) ).
fof(f2953,plain,
( spl21_302
<=> ! [X0,X3,X2,X1] :
( ~ ilf_type(ordered_pair(X0,X1),set_type)
| ~ ilf_type(X2,set_type)
| ~ empty(ordered_pair(X0,X1))
| ~ member(X1,X3)
| member(X0,inverse2(power_set(X2),X3))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(power_set(X2),binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X3,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_302])]) ).
fof(f485,plain,
( spl21_54
<=> ! [X0,X3,X2,X1] :
( member(X1,inverse2(X2,X0))
| ~ member(X3,X0)
| ~ member(ordered_pair(X1,X3),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_54])]) ).
fof(f1090,plain,
( ! [X2,X3,X0,X1] :
( ~ ilf_type(ordered_pair(X0,X1),set_type)
| ~ ilf_type(X2,set_type)
| ~ empty(ordered_pair(X0,X1))
| ~ member(X1,X3)
| member(X0,inverse2(power_set(X2),X3))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(power_set(X2),binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X3,set_type) )
| ~ spl21_54
| ~ spl21_130 ),
inference(resolution,[],[f1082,f486]) ).
fof(f486,plain,
( ! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X1,X3),X2)
| ~ member(X3,X0)
| member(X1,inverse2(X2,X0))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_54 ),
inference(avatar_component_clause,[],[f485]) ).
fof(f2878,plain,
( spl21_301
| ~ spl21_9
| ~ spl21_179 ),
inference(avatar_split_clause,[],[f1541,f1535,f232,f2876]) ).
fof(f2876,plain,
( spl21_301
<=> ! [X0,X1] :
( 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_301])]) ).
fof(f1535,plain,
( spl21_179
<=> ! [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_179])]) ).
fof(f1541,plain,
( ! [X0,X1] :
( 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_9
| ~ spl21_179 ),
inference(resolution,[],[f1536,f233]) ).
fof(f1536,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_179 ),
inference(avatar_component_clause,[],[f1535]) ).
fof(f2874,plain,
( spl21_300
| ~ spl21_9
| ~ spl21_178 ),
inference(avatar_split_clause,[],[f1540,f1531,f232,f2872]) ).
fof(f2872,plain,
( spl21_300
<=> ! [X0,X1] :
( 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_300])]) ).
fof(f1531,plain,
( spl21_178
<=> ! [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_178])]) ).
fof(f1540,plain,
( ! [X0,X1] :
( 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_9
| ~ spl21_178 ),
inference(resolution,[],[f1532,f233]) ).
fof(f1532,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_178 ),
inference(avatar_component_clause,[],[f1531]) ).
fof(f2870,plain,
( spl21_299
| ~ spl21_17
| ~ spl21_151 ),
inference(avatar_split_clause,[],[f1310,f1301,f267,f2868]) ).
fof(f2868,plain,
( spl21_299
<=> ! [X0,X3,X2,X1] :
( member(sK10(inverse2(X0,X1)),X2)
| ~ ilf_type(sK10(inverse2(X0,X1)),set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,relation_type(X2,X3))
| ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,set_type)
| sP0(inverse2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_299])]) ).
fof(f1310,plain,
( ! [X2,X3,X0,X1] :
( member(sK10(inverse2(X0,X1)),X2)
| ~ ilf_type(sK10(inverse2(X0,X1)),set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,relation_type(X2,X3))
| ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,set_type)
| sP0(inverse2(X0,X1)) )
| ~ spl21_17
| ~ spl21_151 ),
inference(resolution,[],[f1302,f268]) ).
fof(f2866,plain,
( spl21_298
| ~ spl21_55
| ~ spl21_130 ),
inference(avatar_split_clause,[],[f1089,f1081,f489,f2864]) ).
fof(f2864,plain,
( spl21_298
<=> ! [X4,X0,X3,X2,X1] :
( ~ ilf_type(ordered_pair(X0,X1),set_type)
| ~ ilf_type(X2,set_type)
| ~ empty(ordered_pair(X0,X1))
| member(X0,X3)
| ~ ilf_type(power_set(X2),relation_type(X3,X4))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_298])]) ).
fof(f489,plain,
( spl21_55
<=> ! [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_55])]) ).
fof(f1089,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ ilf_type(ordered_pair(X0,X1),set_type)
| ~ ilf_type(X2,set_type)
| ~ empty(ordered_pair(X0,X1))
| member(X0,X3)
| ~ ilf_type(power_set(X2),relation_type(X3,X4))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type) )
| ~ spl21_55
| ~ spl21_130 ),
inference(resolution,[],[f1082,f490]) ).
fof(f490,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_55 ),
inference(avatar_component_clause,[],[f489]) ).
fof(f2862,plain,
( spl21_297
| ~ spl21_56
| ~ spl21_130 ),
inference(avatar_split_clause,[],[f1088,f1081,f493,f2860]) ).
fof(f2860,plain,
( spl21_297
<=> ! [X4,X0,X3,X2,X1] :
( ~ ilf_type(ordered_pair(X0,X1),set_type)
| ~ ilf_type(X2,set_type)
| ~ empty(ordered_pair(X0,X1))
| member(X1,X3)
| ~ ilf_type(power_set(X2),relation_type(X4,X3))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_297])]) ).
fof(f493,plain,
( spl21_56
<=> ! [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_56])]) ).
fof(f1088,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ ilf_type(ordered_pair(X0,X1),set_type)
| ~ ilf_type(X2,set_type)
| ~ empty(ordered_pair(X0,X1))
| member(X1,X3)
| ~ ilf_type(power_set(X2),relation_type(X4,X3))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,set_type) )
| ~ spl21_56
| ~ spl21_130 ),
inference(resolution,[],[f1082,f494]) ).
fof(f494,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_56 ),
inference(avatar_component_clause,[],[f493]) ).
fof(f2818,plain,
( ~ spl21_9
| spl21_286 ),
inference(avatar_contradiction_clause,[],[f2817]) ).
fof(f2817,plain,
( $false
| ~ spl21_9
| spl21_286 ),
inference(resolution,[],[f2712,f233]) ).
fof(f2712,plain,
( ~ ilf_type(sK12(sK13(sK7)),set_type)
| spl21_286 ),
inference(avatar_component_clause,[],[f2710]) ).
fof(f2710,plain,
( spl21_286
<=> ilf_type(sK12(sK13(sK7)),set_type) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_286])]) ).
fof(f2797,plain,
( spl21_296
| ~ spl21_9
| ~ spl21_177 ),
inference(avatar_split_clause,[],[f1538,f1527,f232,f2795]) ).
fof(f2795,plain,
( spl21_296
<=> ! [X2,X0,X1] :
( 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,inverse2(X2,sK10(power_set(X0))))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_296])]) ).
fof(f1527,plain,
( spl21_177
<=> ! [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,inverse2(X2,sK10(power_set(X0))))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_177])]) ).
fof(f1538,plain,
( ! [X2,X0,X1] :
( 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,inverse2(X2,sK10(power_set(X0))))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type) )
| ~ spl21_9
| ~ spl21_177 ),
inference(resolution,[],[f1528,f233]) ).
fof(f1528,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,inverse2(X2,sK10(power_set(X0))))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type) )
| ~ spl21_177 ),
inference(avatar_component_clause,[],[f1527]) ).
fof(f2793,plain,
( spl21_295
| ~ spl21_91
| ~ spl21_146 ),
inference(avatar_split_clause,[],[f1281,f1264,f752,f2791]) ).
fof(f2791,plain,
( spl21_295
<=> ! [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)
| ~ ilf_type(power_set(X1),set_type)
| empty(power_set(X1))
| ilf_type(X0,subset_type(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_295])]) ).
fof(f752,plain,
( spl21_91
<=> ! [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_91])]) ).
fof(f1264,plain,
( spl21_146
<=> ! [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_146])]) ).
fof(f1281,plain,
( ! [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)
| ~ ilf_type(power_set(X1),set_type)
| empty(power_set(X1))
| ilf_type(X0,subset_type(X1)) )
| ~ spl21_91
| ~ spl21_146 ),
inference(duplicate_literal_removal,[],[f1267]) ).
fof(f1267,plain,
( ! [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)
| ~ 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_91
| ~ spl21_146 ),
inference(resolution,[],[f1265,f753]) ).
fof(f753,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_91 ),
inference(avatar_component_clause,[],[f752]) ).
fof(f1265,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_146 ),
inference(avatar_component_clause,[],[f1264]) ).
fof(f2789,plain,
( spl21_294
| ~ spl21_41
| ~ spl21_140 ),
inference(avatar_split_clause,[],[f1203,f1186,f382,f2787]) ).
fof(f2787,plain,
( spl21_294
<=> ! [X2,X0,X1] :
( ~ ilf_type(sK15(inverse2(X0,X1),X2),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type)
| member(inverse2(X0,X1),power_set(X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(inverse2(X0,X1),set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_294])]) ).
fof(f382,plain,
( spl21_41
<=> ! [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_41])]) ).
fof(f1203,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(sK15(inverse2(X0,X1),X2),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type)
| member(inverse2(X0,X1),power_set(X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(inverse2(X0,X1),set_type) )
| ~ spl21_41
| ~ spl21_140 ),
inference(resolution,[],[f1187,f383]) ).
fof(f383,plain,
( ! [X0,X1] :
( member(sK15(X0,X1),X0)
| member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_41 ),
inference(avatar_component_clause,[],[f382]) ).
fof(f2785,plain,
( spl21_293
| ~ spl21_52
| ~ spl21_138 ),
inference(avatar_split_clause,[],[f1180,f1170,f468,f2783]) ).
fof(f2783,plain,
( spl21_293
<=> ! [X0,X3,X2,X1] :
( empty(power_set(X0))
| ~ ilf_type(inverse4(X0,X1,X2,X3),set_type)
| member(inverse4(X0,X1,X2,X3),power_set(X0))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_293])]) ).
fof(f468,plain,
( spl21_52
<=> ! [X0,X3,X2,X1] :
( ilf_type(inverse4(X0,X1,X2,X3),subset_type(X0))
| ~ 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_52])]) ).
fof(f1170,plain,
( spl21_138
<=> ! [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_138])]) ).
fof(f1180,plain,
( ! [X2,X3,X0,X1] :
( empty(power_set(X0))
| ~ ilf_type(inverse4(X0,X1,X2,X3),set_type)
| member(inverse4(X0,X1,X2,X3),power_set(X0))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type) )
| ~ spl21_52
| ~ spl21_138 ),
inference(duplicate_literal_removal,[],[f1175]) ).
fof(f1175,plain,
( ! [X2,X3,X0,X1] :
( empty(power_set(X0))
| ~ ilf_type(inverse4(X0,X1,X2,X3),set_type)
| member(inverse4(X0,X1,X2,X3),power_set(X0))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_52
| ~ spl21_138 ),
inference(resolution,[],[f1171,f469]) ).
fof(f469,plain,
( ! [X2,X3,X0,X1] :
( ilf_type(inverse4(X0,X1,X2,X3),subset_type(X0))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_52 ),
inference(avatar_component_clause,[],[f468]) ).
fof(f1171,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_138 ),
inference(avatar_component_clause,[],[f1170]) ).
fof(f2781,plain,
( spl21_292
| ~ spl21_91
| ~ spl21_133 ),
inference(avatar_split_clause,[],[f1120,f1108,f752,f2779]) ).
fof(f2779,plain,
( spl21_292
<=> ! [X0,X1] :
( sP2(power_set(X0),X1)
| ~ empty(X1)
| ~ ilf_type(X1,set_type)
| ~ 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) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_292])]) ).
fof(f1120,plain,
( ! [X0,X1] :
( sP2(power_set(X0),X1)
| ~ empty(X1)
| ~ ilf_type(X1,set_type)
| ~ 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) )
| ~ spl21_91
| ~ spl21_133 ),
inference(resolution,[],[f1109,f753]) ).
fof(f2777,plain,
( ~ spl21_9
| spl21_285 ),
inference(avatar_contradiction_clause,[],[f2776]) ).
fof(f2776,plain,
( $false
| ~ spl21_9
| spl21_285 ),
inference(resolution,[],[f2708,f233]) ).
fof(f2708,plain,
( ~ ilf_type(sK11(sK13(sK7)),set_type)
| spl21_285 ),
inference(avatar_component_clause,[],[f2706]) ).
fof(f2706,plain,
( spl21_285
<=> ilf_type(sK11(sK13(sK7)),set_type) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_285])]) ).
fof(f2775,plain,
( spl21_291
| ~ spl21_102
| ~ spl21_117 ),
inference(avatar_split_clause,[],[f985,f980,f870,f2773]) ).
fof(f2773,plain,
( spl21_291
<=> ! [X4,X0,X3,X2,X1] :
( sP0(inverse4(cross_product(X0,X1),X2,X3,X4))
| ~ ilf_type(X3,relation_type(cross_product(X0,X1),X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(cross_product(X0,X1),set_type)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_291])]) ).
fof(f870,plain,
( spl21_102
<=> ! [X4,X0,X3,X2,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,relation_type(cross_product(X2,X3),X4))
| ~ ilf_type(X4,set_type)
| ~ ilf_type(cross_product(X2,X3),set_type)
| relation_like(inverse4(cross_product(X2,X3),X4,X1,X0))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_102])]) ).
fof(f980,plain,
( spl21_117
<=> ! [X0] :
( ~ relation_like(X0)
| sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_117])]) ).
fof(f985,plain,
( ! [X2,X3,X0,X1,X4] :
( sP0(inverse4(cross_product(X0,X1),X2,X3,X4))
| ~ ilf_type(X3,relation_type(cross_product(X0,X1),X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(cross_product(X0,X1),set_type)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_102
| ~ spl21_117 ),
inference(resolution,[],[f981,f871]) ).
fof(f871,plain,
( ! [X2,X3,X0,X1,X4] :
( relation_like(inverse4(cross_product(X2,X3),X4,X1,X0))
| ~ ilf_type(X1,relation_type(cross_product(X2,X3),X4))
| ~ ilf_type(X4,set_type)
| ~ ilf_type(cross_product(X2,X3),set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type) )
| ~ spl21_102 ),
inference(avatar_component_clause,[],[f870]) ).
fof(f981,plain,
( ! [X0] :
( ~ relation_like(X0)
| sP0(X0) )
| ~ spl21_117 ),
inference(avatar_component_clause,[],[f980]) ).
fof(f2728,plain,
( spl21_290
| ~ spl21_9
| ~ spl21_174 ),
inference(avatar_split_clause,[],[f1508,f1489,f232,f2726]) ).
fof(f2726,plain,
( spl21_290
<=> ! [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_290])]) ).
fof(f1489,plain,
( spl21_174
<=> ! [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_174])]) ).
fof(f1508,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_174 ),
inference(resolution,[],[f1490,f233]) ).
fof(f1490,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_174 ),
inference(avatar_component_clause,[],[f1489]) ).
fof(f2724,plain,
( spl21_289
| ~ spl21_9
| ~ spl21_173 ),
inference(avatar_split_clause,[],[f1507,f1485,f232,f2722]) ).
fof(f2722,plain,
( spl21_289
<=> ! [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_289])]) ).
fof(f1485,plain,
( spl21_173
<=> ! [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_173])]) ).
fof(f1507,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_173 ),
inference(resolution,[],[f1486,f233]) ).
fof(f1486,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_173 ),
inference(avatar_component_clause,[],[f1485]) ).
fof(f2720,plain,
( spl21_288
| ~ spl21_9
| ~ spl21_172 ),
inference(avatar_split_clause,[],[f1506,f1481,f232,f2718]) ).
fof(f2718,plain,
( spl21_288
<=> ! [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_288])]) ).
fof(f1481,plain,
( spl21_172
<=> ! [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_172])]) ).
fof(f1506,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_172 ),
inference(resolution,[],[f1482,f233]) ).
fof(f1482,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_172 ),
inference(avatar_component_clause,[],[f1481]) ).
fof(f2716,plain,
( ~ spl21_285
| ~ spl21_286
| spl21_287
| ~ spl21_38
| ~ spl21_264 ),
inference(avatar_split_clause,[],[f2279,f2253,f369,f2714,f2710,f2706]) ).
fof(f2714,plain,
( spl21_287
<=> ! [X0] :
( sK10(X0) != sK13(sK7)
| sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_287])]) ).
fof(f369,plain,
( spl21_38
<=> ! [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_38])]) ).
fof(f2253,plain,
( spl21_264
<=> sK13(sK7) = ordered_pair(sK11(sK13(sK7)),sK12(sK13(sK7))) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_264])]) ).
fof(f2279,plain,
( ! [X0] :
( sK10(X0) != sK13(sK7)
| sP0(X0)
| ~ ilf_type(sK12(sK13(sK7)),set_type)
| ~ ilf_type(sK11(sK13(sK7)),set_type) )
| ~ spl21_38
| ~ spl21_264 ),
inference(superposition,[],[f370,f2255]) ).
fof(f2255,plain,
( sK13(sK7) = ordered_pair(sK11(sK13(sK7)),sK12(sK13(sK7)))
| ~ spl21_264 ),
inference(avatar_component_clause,[],[f2253]) ).
fof(f370,plain,
( ! [X2,X3,X0] :
( ordered_pair(X2,X3) != sK10(X0)
| sP0(X0)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type) )
| ~ spl21_38 ),
inference(avatar_component_clause,[],[f369]) ).
fof(f2704,plain,
( spl21_284
| ~ spl21_9
| ~ spl21_171 ),
inference(avatar_split_clause,[],[f1505,f1477,f232,f2702]) ).
fof(f2702,plain,
( spl21_284
<=> ! [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_284])]) ).
fof(f1477,plain,
( spl21_171
<=> ! [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_171])]) ).
fof(f1505,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_171 ),
inference(resolution,[],[f1478,f233]) ).
fof(f1478,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_171 ),
inference(avatar_component_clause,[],[f1477]) ).
fof(f2700,plain,
( spl21_283
| ~ spl21_9
| ~ spl21_170 ),
inference(avatar_split_clause,[],[f1504,f1473,f232,f2698]) ).
fof(f2698,plain,
( spl21_283
<=> ! [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_283])]) ).
fof(f1473,plain,
( spl21_170
<=> ! [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_170])]) ).
fof(f1504,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_170 ),
inference(resolution,[],[f1474,f233]) ).
fof(f1474,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_170 ),
inference(avatar_component_clause,[],[f1473]) ).
fof(f2696,plain,
( spl21_282
| ~ spl21_95
| ~ spl21_127 ),
inference(avatar_split_clause,[],[f1065,f1047,f801,f2694]) ).
fof(f2694,plain,
( spl21_282
<=> ! [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_282])]) ).
fof(f801,plain,
( spl21_95
<=> ! [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_95])]) ).
fof(f1065,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_95
| ~ spl21_127 ),
inference(duplicate_literal_removal,[],[f1056]) ).
fof(f1056,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_95
| ~ spl21_127 ),
inference(resolution,[],[f1048,f802]) ).
fof(f802,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_95 ),
inference(avatar_component_clause,[],[f801]) ).
fof(f2432,plain,
( spl21_281
| ~ spl21_9
| ~ spl21_168 ),
inference(avatar_split_clause,[],[f1467,f1459,f232,f2430]) ).
fof(f2430,plain,
( spl21_281
<=> ! [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_281])]) ).
fof(f1459,plain,
( spl21_168
<=> ! [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_168])]) ).
fof(f1467,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_168 ),
inference(resolution,[],[f1460,f233]) ).
fof(f1460,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_168 ),
inference(avatar_component_clause,[],[f1459]) ).
fof(f2428,plain,
( spl21_280
| ~ spl21_9
| ~ spl21_167 ),
inference(avatar_split_clause,[],[f1466,f1455,f232,f2426]) ).
fof(f2426,plain,
( spl21_280
<=> ! [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_280])]) ).
fof(f1455,plain,
( spl21_167
<=> ! [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_167])]) ).
fof(f1466,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_167 ),
inference(resolution,[],[f1456,f233]) ).
fof(f1456,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_167 ),
inference(avatar_component_clause,[],[f1455]) ).
fof(f2424,plain,
( spl21_279
| ~ spl21_49
| ~ spl21_146 ),
inference(avatar_split_clause,[],[f1280,f1264,f445,f2422]) ).
fof(f2422,plain,
( spl21_279
<=> ! [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_279])]) ).
fof(f445,plain,
( spl21_49
<=> ! [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_49])]) ).
fof(f1280,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_49
| ~ spl21_146 ),
inference(duplicate_literal_removal,[],[f1268]) ).
fof(f1268,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_49
| ~ spl21_146 ),
inference(resolution,[],[f1265,f446]) ).
fof(f446,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_49 ),
inference(avatar_component_clause,[],[f445]) ).
fof(f2420,plain,
( spl21_278
| ~ spl21_32
| ~ spl21_140 ),
inference(avatar_split_clause,[],[f1202,f1186,f338,f2418]) ).
fof(f2418,plain,
( spl21_278
<=> ! [X2,X0,X1] :
( ~ ilf_type(sK14(inverse2(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(inverse2(X0,X1),X2),X2)
| sP2(inverse2(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_278])]) ).
fof(f338,plain,
( spl21_32
<=> ! [X0,X1] :
( sP2(X0,X1)
| member(sK14(X0,X1),X0)
| member(sK14(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_32])]) ).
fof(f1202,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(sK14(inverse2(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(inverse2(X0,X1),X2),X2)
| sP2(inverse2(X0,X1),X2) )
| ~ spl21_32
| ~ spl21_140 ),
inference(resolution,[],[f1187,f339]) ).
fof(f339,plain,
( ! [X0,X1] :
( member(sK14(X0,X1),X1)
| member(sK14(X0,X1),X0)
| sP2(X0,X1) )
| ~ spl21_32 ),
inference(avatar_component_clause,[],[f338]) ).
fof(f2416,plain,
( spl21_277
| ~ spl21_32
| ~ spl21_140 ),
inference(avatar_split_clause,[],[f1200,f1186,f338,f2414]) ).
fof(f2414,plain,
( spl21_277
<=> ! [X2,X0,X1] :
( ~ ilf_type(sK14(X0,inverse2(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,inverse2(X1,X2)),X0)
| sP2(X0,inverse2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_277])]) ).
fof(f1200,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(sK14(X0,inverse2(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,inverse2(X1,X2)),X0)
| sP2(X0,inverse2(X1,X2)) )
| ~ spl21_32
| ~ spl21_140 ),
inference(resolution,[],[f1187,f339]) ).
fof(f2412,plain,
( spl21_276
| ~ spl21_48
| ~ spl21_138 ),
inference(avatar_split_clause,[],[f1174,f1170,f436,f2410]) ).
fof(f2410,plain,
( spl21_276
<=> ! [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_276])]) ).
fof(f436,plain,
( spl21_48
<=> ! [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_48])]) ).
fof(f1174,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_48
| ~ spl21_138 ),
inference(resolution,[],[f1171,f437]) ).
fof(f437,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_48 ),
inference(avatar_component_clause,[],[f436]) ).
fof(f2408,plain,
( spl21_275
| ~ spl21_49
| ~ spl21_134 ),
inference(avatar_split_clause,[],[f1134,f1112,f445,f2406]) ).
fof(f2406,plain,
( spl21_275
<=> ! [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_275])]) ).
fof(f1112,plain,
( spl21_134
<=> ! [X0,X1] :
( sP2(X0,X1)
| member(sK14(X0,X1),X1)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_134])]) ).
fof(f1134,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_49
| ~ spl21_134 ),
inference(resolution,[],[f1113,f446]) ).
fof(f1113,plain,
( ! [X0,X1] :
( member(sK14(X0,X1),X1)
| sP2(X0,X1)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) )
| ~ spl21_134 ),
inference(avatar_component_clause,[],[f1112]) ).
fof(f2404,plain,
( spl21_274
| ~ spl21_49
| ~ spl21_133 ),
inference(avatar_split_clause,[],[f1121,f1108,f445,f2402]) ).
fof(f2402,plain,
( spl21_274
<=> ! [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_274])]) ).
fof(f1121,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_49
| ~ spl21_133 ),
inference(resolution,[],[f1109,f446]) ).
fof(f2399,plain,
( ~ spl21_273
| ~ spl21_37
| spl21_67
| ~ spl21_40
| ~ spl21_223 ),
inference(avatar_split_clause,[],[f1893,f1817,f378,f619,f358,f2396]) ).
fof(f2396,plain,
( spl21_273
<=> sP0(inverse2(sK7,sK6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_273])]) ).
fof(f619,plain,
( spl21_67
<=> sK8 = ordered_pair(sK11(sK8),sK12(sK8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_67])]) ).
fof(f1817,plain,
( spl21_223
<=> member(sK8,inverse2(sK7,sK6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_223])]) ).
fof(f1893,plain,
( sK8 = ordered_pair(sK11(sK8),sK12(sK8))
| ~ ilf_type(sK8,set_type)
| ~ sP0(inverse2(sK7,sK6))
| ~ spl21_40
| ~ spl21_223 ),
inference(resolution,[],[f1818,f379]) ).
fof(f1818,plain,
( member(sK8,inverse2(sK7,sK6))
| ~ spl21_223 ),
inference(avatar_component_clause,[],[f1817]) ).
fof(f2394,plain,
( spl21_272
| ~ spl21_41
| ~ spl21_136 ),
inference(avatar_split_clause,[],[f1162,f1151,f382,f2392]) ).
fof(f2392,plain,
( spl21_272
<=> ! [X2,X0,X1] :
( ~ ilf_type(sK15(inverse2(X0,X1),X2),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ empty(X1)
| member(inverse2(X0,X1),power_set(X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(inverse2(X0,X1),set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_272])]) ).
fof(f1162,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(sK15(inverse2(X0,X1),X2),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ empty(X1)
| member(inverse2(X0,X1),power_set(X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(inverse2(X0,X1),set_type) )
| ~ spl21_41
| ~ spl21_136 ),
inference(resolution,[],[f1152,f383]) ).
fof(f2387,plain,
( spl21_271
| ~ spl21_9
| ~ spl21_164 ),
inference(avatar_split_clause,[],[f1426,f1423,f232,f2385]) ).
fof(f2385,plain,
( spl21_271
<=> ! [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_271])]) ).
fof(f1423,plain,
( spl21_164
<=> ! [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_164])]) ).
fof(f1426,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_164 ),
inference(resolution,[],[f1424,f233]) ).
fof(f1424,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_164 ),
inference(avatar_component_clause,[],[f1423]) ).
fof(f2383,plain,
( spl21_270
| ~ spl21_133
| ~ spl21_140 ),
inference(avatar_split_clause,[],[f1201,f1186,f1108,f2381]) ).
fof(f2381,plain,
( spl21_270
<=> ! [X2,X0,X1] :
( ~ ilf_type(sK14(inverse2(X0,X1),X2),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type)
| sP2(inverse2(X0,X1),X2)
| ~ empty(X2)
| ~ ilf_type(X2,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_270])]) ).
fof(f1201,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(sK14(inverse2(X0,X1),X2),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type)
| sP2(inverse2(X0,X1),X2)
| ~ empty(X2)
| ~ ilf_type(X2,set_type) )
| ~ spl21_133
| ~ spl21_140 ),
inference(resolution,[],[f1187,f1109]) ).
fof(f2379,plain,
( spl21_269
| ~ spl21_134
| ~ spl21_140 ),
inference(avatar_split_clause,[],[f1199,f1186,f1112,f2377]) ).
fof(f2377,plain,
( spl21_269
<=> ! [X2,X0,X1] :
( ~ ilf_type(sK14(X0,inverse2(X1,X2)),set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ empty(X1)
| ~ ilf_type(X1,set_type)
| sP2(X0,inverse2(X1,X2))
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_269])]) ).
fof(f1199,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(sK14(X0,inverse2(X1,X2)),set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ empty(X1)
| ~ ilf_type(X1,set_type)
| sP2(X0,inverse2(X1,X2))
| ~ empty(X0)
| ~ ilf_type(X0,set_type) )
| ~ spl21_134
| ~ spl21_140 ),
inference(resolution,[],[f1187,f1113]) ).
fof(f2275,plain,
( spl21_268
| ~ spl21_9
| ~ spl21_163 ),
inference(avatar_split_clause,[],[f1421,f1418,f232,f2273]) ).
fof(f2273,plain,
( spl21_268
<=> ! [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_268])]) ).
fof(f1418,plain,
( spl21_163
<=> ! [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_163])]) ).
fof(f1421,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_163 ),
inference(resolution,[],[f1419,f233]) ).
fof(f1419,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_163 ),
inference(avatar_component_clause,[],[f1418]) ).
fof(f2271,plain,
( spl21_267
| ~ spl21_9
| ~ spl21_161 ),
inference(avatar_split_clause,[],[f1412,f1408,f232,f2269]) ).
fof(f2269,plain,
( spl21_267
<=> ! [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_267])]) ).
fof(f1408,plain,
( spl21_161
<=> ! [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_161])]) ).
fof(f1412,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_161 ),
inference(resolution,[],[f1409,f233]) ).
fof(f1409,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_161 ),
inference(avatar_component_clause,[],[f1408]) ).
fof(f2267,plain,
( spl21_266
| ~ spl21_9
| ~ spl21_160 ),
inference(avatar_split_clause,[],[f1411,f1404,f232,f2265]) ).
fof(f2265,plain,
( spl21_266
<=> ! [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_266])]) ).
fof(f1404,plain,
( spl21_160
<=> ! [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_160])]) ).
fof(f1411,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_160 ),
inference(resolution,[],[f1405,f233]) ).
fof(f1405,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_160 ),
inference(avatar_component_clause,[],[f1404]) ).
fof(f2263,plain,
( spl21_265
| ~ spl21_32
| ~ spl21_136 ),
inference(avatar_split_clause,[],[f1161,f1151,f338,f2261]) ).
fof(f2261,plain,
( spl21_265
<=> ! [X2,X0,X1] :
( ~ ilf_type(sK14(inverse2(X0,X1),X2),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ empty(X1)
| member(sK14(inverse2(X0,X1),X2),X2)
| sP2(inverse2(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_265])]) ).
fof(f1161,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(sK14(inverse2(X0,X1),X2),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ empty(X1)
| member(sK14(inverse2(X0,X1),X2),X2)
| sP2(inverse2(X0,X1),X2) )
| ~ spl21_32
| ~ spl21_136 ),
inference(resolution,[],[f1152,f339]) ).
fof(f2259,plain,
( ~ spl21_122
| ~ spl21_123
| ~ spl21_74
| ~ spl21_219
| ~ spl21_37
| ~ spl21_120
| ~ spl21_140 ),
inference(avatar_split_clause,[],[f1876,f1186,f1003,f358,f1776,f654,f1019,f1015]) ).
fof(f1015,plain,
( spl21_122
<=> ilf_type(sK7,set_type) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_122])]) ).
fof(f1019,plain,
( spl21_123
<=> empty(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_123])]) ).
fof(f1876,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_120
| ~ spl21_140 ),
inference(resolution,[],[f1004,f1187]) ).
fof(f1004,plain,
( member(sK8,inverse2(sK7,sK5))
| ~ spl21_120 ),
inference(avatar_component_clause,[],[f1003]) ).
fof(f2256,plain,
( spl21_264
| spl21_123
| ~ spl21_121
| ~ spl21_236 ),
inference(avatar_split_clause,[],[f1951,f1948,f1008,f1019,f2253]) ).
fof(f1008,plain,
( spl21_121
<=> sP0(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_121])]) ).
fof(f1948,plain,
( spl21_236
<=> ! [X0] :
( ~ sP0(X0)
| empty(X0)
| sK13(X0) = ordered_pair(sK11(sK13(X0)),sK12(sK13(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_236])]) ).
fof(f1951,plain,
( empty(sK7)
| sK13(sK7) = ordered_pair(sK11(sK13(sK7)),sK12(sK13(sK7)))
| ~ spl21_121
| ~ spl21_236 ),
inference(resolution,[],[f1949,f1010]) ).
fof(f1010,plain,
( sP0(sK7)
| ~ spl21_121 ),
inference(avatar_component_clause,[],[f1008]) ).
fof(f1949,plain,
( ! [X0] :
( ~ sP0(X0)
| empty(X0)
| sK13(X0) = ordered_pair(sK11(sK13(X0)),sK12(sK13(X0))) )
| ~ spl21_236 ),
inference(avatar_component_clause,[],[f1948]) ).
fof(f2251,plain,
( spl21_263
| ~ spl21_32
| ~ spl21_136 ),
inference(avatar_split_clause,[],[f1159,f1151,f338,f2249]) ).
fof(f2249,plain,
( spl21_263
<=> ! [X2,X0,X1] :
( ~ ilf_type(sK14(X0,inverse2(X1,X2)),set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ empty(X2)
| member(sK14(X0,inverse2(X1,X2)),X0)
| sP2(X0,inverse2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_263])]) ).
fof(f1159,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(sK14(X0,inverse2(X1,X2)),set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ empty(X2)
| member(sK14(X0,inverse2(X1,X2)),X0)
| sP2(X0,inverse2(X1,X2)) )
| ~ spl21_32
| ~ spl21_136 ),
inference(resolution,[],[f1152,f339]) ).
fof(f2247,plain,
( spl21_262
| ~ spl21_92
| ~ spl21_127 ),
inference(avatar_split_clause,[],[f1066,f1047,f776,f2245]) ).
fof(f2245,plain,
( spl21_262
<=> ! [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_262])]) ).
fof(f1066,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_92
| ~ spl21_127 ),
inference(duplicate_literal_removal,[],[f1055]) ).
fof(f1055,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_92
| ~ spl21_127 ),
inference(resolution,[],[f1048,f777]) ).
fof(f2217,plain,
( spl21_261
| ~ spl21_127
| ~ spl21_140 ),
inference(avatar_split_clause,[],[f1205,f1186,f1047,f2215]) ).
fof(f2215,plain,
( spl21_261
<=> ! [X0,X1] :
( ~ ilf_type(sK19(inverse2(X0,X1)),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type)
| empty(inverse2(X0,X1))
| ~ ilf_type(inverse2(X0,X1),set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_261])]) ).
fof(f1205,plain,
( ! [X0,X1] :
( ~ ilf_type(sK19(inverse2(X0,X1)),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type)
| empty(inverse2(X0,X1))
| ~ ilf_type(inverse2(X0,X1),set_type) )
| ~ spl21_127
| ~ spl21_140 ),
inference(resolution,[],[f1187,f1048]) ).
fof(f2213,plain,
( spl21_260
| ~ spl21_24
| ~ spl21_140 ),
inference(avatar_split_clause,[],[f1198,f1186,f300,f2211]) ).
fof(f2211,plain,
( spl21_260
<=> ! [X0,X1] :
( ~ ilf_type(sK13(inverse2(X0,X1)),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type)
| empty(inverse2(X0,X1))
| ~ ilf_type(inverse2(X0,X1),set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_260])]) ).
fof(f1198,plain,
( ! [X0,X1] :
( ~ ilf_type(sK13(inverse2(X0,X1)),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type)
| empty(inverse2(X0,X1))
| ~ ilf_type(inverse2(X0,X1),set_type) )
| ~ spl21_24
| ~ spl21_140 ),
inference(resolution,[],[f1187,f301]) ).
fof(f2209,plain,
( spl21_259
| ~ spl21_42
| ~ spl21_130 ),
inference(avatar_split_clause,[],[f1092,f1081,f386,f2207]) ).
fof(f2207,plain,
( spl21_259
<=> ! [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_259])]) ).
fof(f386,plain,
( spl21_42
<=> ! [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_42])]) ).
fof(f1092,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_42
| ~ spl21_130 ),
inference(resolution,[],[f1082,f387]) ).
fof(f387,plain,
( ! [X0,X1] :
( ~ member(sK15(X0,X1),X1)
| member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_42 ),
inference(avatar_component_clause,[],[f386]) ).
fof(f2205,plain,
( spl21_258
| ~ spl21_49
| ~ spl21_127 ),
inference(avatar_split_clause,[],[f1054,f1047,f445,f2203]) ).
fof(f2203,plain,
( spl21_258
<=> ! [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_258])]) ).
fof(f1054,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_49
| ~ spl21_127 ),
inference(resolution,[],[f1048,f446]) ).
fof(f2173,plain,
( ~ spl21_9
| spl21_247 ),
inference(avatar_contradiction_clause,[],[f2172]) ).
fof(f2172,plain,
( $false
| ~ spl21_9
| spl21_247 ),
inference(resolution,[],[f2012,f233]) ).
fof(f2012,plain,
( ~ ilf_type(inverse2(sK7,sK6),set_type)
| spl21_247 ),
inference(avatar_component_clause,[],[f2010]) ).
fof(f2010,plain,
( spl21_247
<=> ilf_type(inverse2(sK7,sK6),set_type) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_247])]) ).
fof(f2141,plain,
( spl21_257
| ~ spl21_9
| ~ spl21_157 ),
inference(avatar_split_clause,[],[f1368,f1339,f232,f2139]) ).
fof(f2139,plain,
( spl21_257
<=> ! [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_257])]) ).
fof(f1339,plain,
( spl21_157
<=> ! [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_157])]) ).
fof(f1368,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_157 ),
inference(resolution,[],[f1340,f233]) ).
fof(f1340,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_157 ),
inference(avatar_component_clause,[],[f1339]) ).
fof(f2137,plain,
( spl21_256
| ~ spl21_9
| ~ spl21_156 ),
inference(avatar_split_clause,[],[f1367,f1335,f232,f2135]) ).
fof(f2135,plain,
( spl21_256
<=> ! [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_256])]) ).
fof(f1335,plain,
( spl21_156
<=> ! [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_156])]) ).
fof(f1367,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_156 ),
inference(resolution,[],[f1336,f233]) ).
fof(f1336,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_156 ),
inference(avatar_component_clause,[],[f1335]) ).
fof(f2133,plain,
( spl21_255
| ~ spl21_133
| ~ spl21_136 ),
inference(avatar_split_clause,[],[f1160,f1151,f1108,f2131]) ).
fof(f2131,plain,
( spl21_255
<=> ! [X2,X0,X1] :
( ~ ilf_type(sK14(inverse2(X0,X1),X2),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ empty(X1)
| sP2(inverse2(X0,X1),X2)
| ~ empty(X2)
| ~ ilf_type(X2,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_255])]) ).
fof(f1160,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(sK14(inverse2(X0,X1),X2),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ empty(X1)
| sP2(inverse2(X0,X1),X2)
| ~ empty(X2)
| ~ ilf_type(X2,set_type) )
| ~ spl21_133
| ~ spl21_136 ),
inference(resolution,[],[f1152,f1109]) ).
fof(f2129,plain,
( spl21_254
| ~ spl21_134
| ~ spl21_136 ),
inference(avatar_split_clause,[],[f1158,f1151,f1112,f2127]) ).
fof(f2127,plain,
( spl21_254
<=> ! [X2,X0,X1] :
( ~ ilf_type(sK14(X0,inverse2(X1,X2)),set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ empty(X2)
| sP2(X0,inverse2(X1,X2))
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_254])]) ).
fof(f1158,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(sK14(X0,inverse2(X1,X2)),set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ empty(X2)
| sP2(X0,inverse2(X1,X2))
| ~ empty(X0)
| ~ ilf_type(X0,set_type) )
| ~ spl21_134
| ~ spl21_136 ),
inference(resolution,[],[f1152,f1113]) ).
fof(f2109,plain,
( spl21_253
| ~ spl21_9
| ~ spl21_153 ),
inference(avatar_split_clause,[],[f1325,f1322,f232,f2107]) ).
fof(f2107,plain,
( spl21_253
<=> ! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| inverse4(X0,X1,sK18(cross_product(X0,X1)),X2) = inverse2(sK18(cross_product(X0,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_253])]) ).
fof(f1322,plain,
( spl21_153
<=> ! [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)
| inverse4(X1,X0,sK18(cross_product(X1,X0)),X2) = inverse2(sK18(cross_product(X1,X0)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_153])]) ).
fof(f1325,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| inverse4(X0,X1,sK18(cross_product(X0,X1)),X2) = inverse2(sK18(cross_product(X0,X1)),X2) )
| ~ spl21_9
| ~ spl21_153 ),
inference(resolution,[],[f1323,f233]) ).
fof(f1323,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)
| inverse4(X1,X0,sK18(cross_product(X1,X0)),X2) = inverse2(sK18(cross_product(X1,X0)),X2) )
| ~ spl21_153 ),
inference(avatar_component_clause,[],[f1322]) ).
fof(f2105,plain,
( spl21_252
| ~ spl21_33
| ~ spl21_130 ),
inference(avatar_split_clause,[],[f1091,f1081,f342,f2103]) ).
fof(f2103,plain,
( spl21_252
<=> ! [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_252])]) ).
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(f1091,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_33
| ~ spl21_130 ),
inference(resolution,[],[f1082,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(f2087,plain,
( spl21_251
| ~ spl21_33
| ~ spl21_144 ),
inference(avatar_split_clause,[],[f1253,f1219,f342,f2085]) ).
fof(f2085,plain,
( spl21_251
<=> ! [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_251])]) ).
fof(f1219,plain,
( spl21_144
<=> ! [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_144])]) ).
fof(f1253,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_33
| ~ spl21_144 ),
inference(duplicate_literal_removal,[],[f1238]) ).
fof(f1238,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_33
| ~ spl21_144 ),
inference(resolution,[],[f1220,f343]) ).
fof(f1220,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_144 ),
inference(avatar_component_clause,[],[f1219]) ).
fof(f2083,plain,
( spl21_250
| ~ spl21_127
| ~ spl21_136 ),
inference(avatar_split_clause,[],[f1164,f1151,f1047,f2081]) ).
fof(f2081,plain,
( spl21_250
<=> ! [X0,X1] :
( ~ ilf_type(sK19(inverse2(X0,X1)),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ empty(X1)
| empty(inverse2(X0,X1))
| ~ ilf_type(inverse2(X0,X1),set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_250])]) ).
fof(f1164,plain,
( ! [X0,X1] :
( ~ ilf_type(sK19(inverse2(X0,X1)),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ empty(X1)
| empty(inverse2(X0,X1))
| ~ ilf_type(inverse2(X0,X1),set_type) )
| ~ spl21_127
| ~ spl21_136 ),
inference(resolution,[],[f1152,f1048]) ).
fof(f2079,plain,
( spl21_249
| ~ spl21_24
| ~ spl21_136 ),
inference(avatar_split_clause,[],[f1157,f1151,f300,f2077]) ).
fof(f2077,plain,
( spl21_249
<=> ! [X0,X1] :
( ~ ilf_type(sK13(inverse2(X0,X1)),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ empty(X1)
| empty(inverse2(X0,X1))
| ~ ilf_type(inverse2(X0,X1),set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_249])]) ).
fof(f1157,plain,
( ! [X0,X1] :
( ~ ilf_type(sK13(inverse2(X0,X1)),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ empty(X1)
| empty(inverse2(X0,X1))
| ~ ilf_type(inverse2(X0,X1),set_type) )
| ~ spl21_24
| ~ spl21_136 ),
inference(resolution,[],[f1152,f301]) ).
fof(f2017,plain,
( ~ spl21_247
| ~ spl21_248
| ~ spl21_37
| ~ spl21_29
| ~ spl21_223 ),
inference(avatar_split_clause,[],[f1894,f1817,f321,f358,f2014,f2010]) ).
fof(f2014,plain,
( spl21_248
<=> empty(inverse2(sK7,sK6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_248])]) ).
fof(f1894,plain,
( ~ ilf_type(sK8,set_type)
| ~ empty(inverse2(sK7,sK6))
| ~ ilf_type(inverse2(sK7,sK6),set_type)
| ~ spl21_29
| ~ spl21_223 ),
inference(resolution,[],[f1818,f322]) ).
fof(f2008,plain,
( spl21_246
| ~ spl21_9
| ~ spl21_148 ),
inference(avatar_split_clause,[],[f1291,f1287,f232,f2006]) ).
fof(f2006,plain,
( spl21_246
<=> ! [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_246])]) ).
fof(f1287,plain,
( spl21_148
<=> ! [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_148])]) ).
fof(f1291,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_148 ),
inference(resolution,[],[f1288,f233]) ).
fof(f1288,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_148 ),
inference(avatar_component_clause,[],[f1287]) ).
fof(f2004,plain,
( spl21_245
| ~ spl21_9
| ~ spl21_147 ),
inference(avatar_split_clause,[],[f1290,f1283,f232,f2002]) ).
fof(f2002,plain,
( spl21_245
<=> ! [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_245])]) ).
fof(f1283,plain,
( spl21_147
<=> ! [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_147])]) ).
fof(f1290,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_147 ),
inference(resolution,[],[f1284,f233]) ).
fof(f1284,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_147 ),
inference(avatar_component_clause,[],[f1283]) ).
fof(f2000,plain,
( spl21_244
| ~ spl21_17
| ~ spl21_140 ),
inference(avatar_split_clause,[],[f1197,f1186,f267,f1998]) ).
fof(f1998,plain,
( spl21_244
<=> ! [X0,X1] :
( ~ ilf_type(sK10(inverse2(X0,X1)),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type)
| sP0(inverse2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_244])]) ).
fof(f1197,plain,
( ! [X0,X1] :
( ~ ilf_type(sK10(inverse2(X0,X1)),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type)
| sP0(inverse2(X0,X1)) )
| ~ spl21_17
| ~ spl21_140 ),
inference(resolution,[],[f1187,f268]) ).
fof(f1996,plain,
( spl21_243
| ~ spl21_40
| ~ spl21_127 ),
inference(avatar_split_clause,[],[f1050,f1047,f378,f1994]) ).
fof(f1994,plain,
( spl21_243
<=> ! [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_243])]) ).
fof(f1050,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_40
| ~ spl21_127 ),
inference(resolution,[],[f1048,f379]) ).
fof(f1991,plain,
( spl21_242
| ~ spl21_91
| ~ spl21_130 ),
inference(avatar_split_clause,[],[f1098,f1081,f752,f1989]) ).
fof(f1989,plain,
( spl21_242
<=> ! [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_242])]) ).
fof(f1098,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_91
| ~ spl21_130 ),
inference(duplicate_literal_removal,[],[f1084]) ).
fof(f1084,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_91
| ~ spl21_130 ),
inference(resolution,[],[f1082,f753]) ).
fof(f1986,plain,
( spl21_241
| ~ spl21_17
| ~ spl21_136 ),
inference(avatar_split_clause,[],[f1156,f1151,f267,f1984]) ).
fof(f1984,plain,
( spl21_241
<=> ! [X0,X1] :
( ~ ilf_type(sK10(inverse2(X0,X1)),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ empty(X1)
| sP0(inverse2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_241])]) ).
fof(f1156,plain,
( ! [X0,X1] :
( ~ ilf_type(sK10(inverse2(X0,X1)),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ empty(X1)
| sP0(inverse2(X0,X1)) )
| ~ spl21_17
| ~ spl21_136 ),
inference(resolution,[],[f1152,f268]) ).
fof(f1982,plain,
( spl21_239
| spl21_240
| ~ spl21_40
| ~ spl21_130 ),
inference(avatar_split_clause,[],[f1096,f1081,f378,f1980,f1977]) ).
fof(f1977,plain,
( spl21_239
<=> ! [X1] :
( ~ ilf_type(X1,set_type)
| ~ sP0(power_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_239])]) ).
fof(f1980,plain,
( spl21_240
<=> ! [X0] :
( ~ ilf_type(X0,set_type)
| ordered_pair(sK11(X0),sK12(X0)) = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_240])]) ).
fof(f1096,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_40
| ~ spl21_130 ),
inference(duplicate_literal_removal,[],[f1086]) ).
fof(f1086,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_40
| ~ spl21_130 ),
inference(resolution,[],[f1082,f379]) ).
fof(f1970,plain,
( spl21_238
| ~ spl21_9
| ~ spl21_139 ),
inference(avatar_split_clause,[],[f1194,f1182,f232,f1968]) ).
fof(f1968,plain,
( spl21_238
<=> ! [X2,X0,X1] :
( inverse4(X0,X1,sK17(X1,X0),X2) = inverse2(sK17(X1,X0),X2)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_238])]) ).
fof(f1182,plain,
( spl21_139
<=> ! [X2,X0,X1] :
( inverse4(X0,X1,sK17(X1,X0),X2) = inverse2(sK17(X1,X0),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_139])]) ).
fof(f1194,plain,
( ! [X2,X0,X1] :
( inverse4(X0,X1,sK17(X1,X0),X2) = inverse2(sK17(X1,X0),X2)
| ~ ilf_type(X0,set_type) )
| ~ spl21_9
| ~ spl21_139 ),
inference(resolution,[],[f1183,f233]) ).
fof(f1183,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(X2,set_type)
| inverse4(X0,X1,sK17(X1,X0),X2) = inverse2(sK17(X1,X0),X2)
| ~ ilf_type(X0,set_type) )
| ~ spl21_139 ),
inference(avatar_component_clause,[],[f1182]) ).
fof(f1958,plain,
( spl21_237
| ~ spl21_22
| ~ spl21_138 ),
inference(avatar_split_clause,[],[f1179,f1170,f288,f1956]) ).
fof(f1956,plain,
( spl21_237
<=> ! [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_237])]) ).
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(f1179,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_138 ),
inference(duplicate_literal_removal,[],[f1176]) ).
fof(f1176,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_138 ),
inference(resolution,[],[f1171,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(f1950,plain,
( spl21_236
| ~ spl21_9
| ~ spl21_137 ),
inference(avatar_split_clause,[],[f1173,f1166,f232,f1948]) ).
fof(f1166,plain,
( spl21_137
<=> ! [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_137])]) ).
fof(f1173,plain,
( ! [X0] :
( ~ sP0(X0)
| empty(X0)
| sK13(X0) = ordered_pair(sK11(sK13(X0)),sK12(sK13(X0))) )
| ~ spl21_9
| ~ spl21_137 ),
inference(resolution,[],[f1167,f233]) ).
fof(f1167,plain,
( ! [X0] :
( ~ ilf_type(X0,set_type)
| ~ sP0(X0)
| empty(X0)
| sK13(X0) = ordered_pair(sK11(sK13(X0)),sK12(sK13(X0))) )
| ~ spl21_137 ),
inference(avatar_component_clause,[],[f1166]) ).
fof(f1933,plain,
( spl21_235
| ~ spl21_33
| ~ spl21_134 ),
inference(avatar_split_clause,[],[f1141,f1112,f342,f1931]) ).
fof(f1931,plain,
( spl21_235
<=> ! [X0,X1] :
( sP2(X0,X1)
| ~ empty(X0)
| ~ ilf_type(X0,set_type)
| ~ member(sK14(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_235])]) ).
fof(f1141,plain,
( ! [X0,X1] :
( sP2(X0,X1)
| ~ empty(X0)
| ~ ilf_type(X0,set_type)
| ~ member(sK14(X0,X1),X0) )
| ~ spl21_33
| ~ spl21_134 ),
inference(duplicate_literal_removal,[],[f1129]) ).
fof(f1129,plain,
( ! [X0,X1] :
( sP2(X0,X1)
| ~ empty(X0)
| ~ ilf_type(X0,set_type)
| ~ member(sK14(X0,X1),X0)
| sP2(X0,X1) )
| ~ spl21_33
| ~ spl21_134 ),
inference(resolution,[],[f1113,f343]) ).
fof(f1928,plain,
( spl21_234
| ~ spl21_117
| ~ spl21_129 ),
inference(avatar_split_clause,[],[f1079,f1076,f980,f1926]) ).
fof(f1926,plain,
( spl21_234
<=> ! [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_234])]) ).
fof(f1076,plain,
( spl21_129
<=> ! [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_129])]) ).
fof(f1079,plain,
( ! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| sP0(sK18(cross_product(X0,X1))) )
| ~ spl21_117
| ~ spl21_129 ),
inference(resolution,[],[f1077,f981]) ).
fof(f1077,plain,
( ! [X0,X1] :
( relation_like(sK18(cross_product(X1,X0)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_129 ),
inference(avatar_component_clause,[],[f1076]) ).
fof(f1924,plain,
( ~ spl21_62
| spl21_233
| ~ spl21_57
| ~ spl21_5
| ~ spl21_226 ),
inference(avatar_split_clause,[],[f1835,f1832,f213,f501,f1921,f588]) ).
fof(f588,plain,
( spl21_62
<=> ilf_type(sK6,set_type) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_62])]) ).
fof(f501,plain,
( spl21_57
<=> ilf_type(sK4,set_type) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_57])]) ).
fof(f213,plain,
( spl21_5
<=> ilf_type(sK7,relation_type(sK4,sK6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_5])]) ).
fof(f1832,plain,
( spl21_226
<=> ! [X0,X1] :
( member(sK16(sK5,sK8,sK7),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK7,relation_type(X1,X0))
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_226])]) ).
fof(f1835,plain,
( ~ ilf_type(sK4,set_type)
| member(sK16(sK5,sK8,sK7),sK6)
| ~ ilf_type(sK6,set_type)
| ~ spl21_5
| ~ spl21_226 ),
inference(resolution,[],[f1833,f215]) ).
fof(f215,plain,
( ilf_type(sK7,relation_type(sK4,sK6))
| ~ spl21_5 ),
inference(avatar_component_clause,[],[f213]) ).
fof(f1833,plain,
( ! [X0,X1] :
( ~ ilf_type(sK7,relation_type(X1,X0))
| ~ ilf_type(X1,set_type)
| member(sK16(sK5,sK8,sK7),X0)
| ~ ilf_type(X0,set_type) )
| ~ spl21_226 ),
inference(avatar_component_clause,[],[f1832]) ).
fof(f1913,plain,
( spl21_232
| ~ spl21_9
| ~ spl21_135 ),
inference(avatar_split_clause,[],[f1149,f1143,f232,f1911]) ).
fof(f1911,plain,
( spl21_232
<=> ! [X0] :
( empty(power_set(X0))
| ~ ilf_type(X0,set_type)
| ilf_type(X0,subset_type(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_232])]) ).
fof(f1143,plain,
( spl21_135
<=> ! [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_135])]) ).
fof(f1149,plain,
( ! [X0] :
( empty(power_set(X0))
| ~ ilf_type(X0,set_type)
| ilf_type(X0,subset_type(X0)) )
| ~ spl21_9
| ~ spl21_135 ),
inference(resolution,[],[f1144,f233]) ).
fof(f1144,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_135 ),
inference(avatar_component_clause,[],[f1143]) ).
fof(f1909,plain,
( spl21_231
| ~ spl21_9
| ~ spl21_132 ),
inference(avatar_split_clause,[],[f1115,f1104,f232,f1907]) ).
fof(f1907,plain,
( spl21_231
<=> ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_231])]) ).
fof(f1104,plain,
( spl21_132
<=> ! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_132])]) ).
fof(f1115,plain,
( ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0))
| ~ spl21_9
| ~ spl21_132 ),
inference(resolution,[],[f1105,f233]) ).
fof(f1105,plain,
( ! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)) )
| ~ spl21_132 ),
inference(avatar_component_clause,[],[f1104]) ).
fof(f1905,plain,
( spl21_230
| ~ spl21_117
| ~ spl21_128 ),
inference(avatar_split_clause,[],[f1074,f1071,f980,f1903]) ).
fof(f1903,plain,
( spl21_230
<=> ! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| sP0(sK17(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_230])]) ).
fof(f1071,plain,
( spl21_128
<=> ! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| relation_like(sK17(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_128])]) ).
fof(f1074,plain,
( ! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| sP0(sK17(X1,X0)) )
| ~ spl21_117
| ~ spl21_128 ),
inference(resolution,[],[f1072,f981]) ).
fof(f1072,plain,
( ! [X0,X1] :
( relation_like(sK17(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_128 ),
inference(avatar_component_clause,[],[f1071]) ).
fof(f1885,plain,
( ~ spl21_37
| spl21_229
| ~ spl21_29
| ~ spl21_221 ),
inference(avatar_split_clause,[],[f1857,f1796,f321,f1883,f358]) ).
fof(f1883,plain,
( spl21_229
<=> ! [X0] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(inverse2(sK7,X0),set_type)
| ~ empty(inverse2(sK7,X0))
| ~ member(sK9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_229])]) ).
fof(f1857,plain,
( ! [X0] :
( ~ ilf_type(X0,set_type)
| ~ member(sK9,X0)
| ~ ilf_type(sK8,set_type)
| ~ empty(inverse2(sK7,X0))
| ~ ilf_type(inverse2(sK7,X0),set_type) )
| ~ spl21_29
| ~ spl21_221 ),
inference(resolution,[],[f1797,f322]) ).
fof(f1881,plain,
( ~ spl21_63
| ~ spl21_62
| ~ spl21_221
| spl21_223 ),
inference(avatar_split_clause,[],[f1847,f1817,f1796,f588,f592]) ).
fof(f592,plain,
( spl21_63
<=> member(sK9,sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_63])]) ).
fof(f1847,plain,
( ~ ilf_type(sK6,set_type)
| ~ member(sK9,sK6)
| ~ spl21_221
| spl21_223 ),
inference(resolution,[],[f1797,f1819]) ).
fof(f1819,plain,
( ~ member(sK8,inverse2(sK7,sK6))
| spl21_223 ),
inference(avatar_component_clause,[],[f1817]) ).
fof(f1869,plain,
( ~ spl21_121
| ~ spl21_124
| spl21_228
| ~ spl21_12
| ~ spl21_40 ),
inference(avatar_split_clause,[],[f1000,f378,f245,f1866,f1023,f1008]) ).
fof(f1023,plain,
( spl21_124
<=> ilf_type(ordered_pair(sK8,sK9),set_type) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_124])]) ).
fof(f1866,plain,
( spl21_228
<=> ordered_pair(sK8,sK9) = ordered_pair(sK11(ordered_pair(sK8,sK9)),sK12(ordered_pair(sK8,sK9))) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_228])]) ).
fof(f245,plain,
( spl21_12
<=> member(ordered_pair(sK8,sK9),sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_12])]) ).
fof(f1000,plain,
( ordered_pair(sK8,sK9) = ordered_pair(sK11(ordered_pair(sK8,sK9)),sK12(ordered_pair(sK8,sK9)))
| ~ ilf_type(ordered_pair(sK8,sK9),set_type)
| ~ sP0(sK7)
| ~ spl21_12
| ~ spl21_40 ),
inference(resolution,[],[f247,f379]) ).
fof(f247,plain,
( member(ordered_pair(sK8,sK9),sK7)
| ~ spl21_12 ),
inference(avatar_component_clause,[],[f245]) ).
fof(f1840,plain,
( ~ spl21_121
| ~ spl21_74
| spl21_227
| ~ spl21_219
| ~ spl21_37
| ~ spl21_120
| ~ spl21_175 ),
inference(avatar_split_clause,[],[f1512,f1493,f1003,f358,f1776,f1837,f654,f1008]) ).
fof(f1837,plain,
( spl21_227
<=> ordered_pair(sK8,sK16(sK5,sK8,sK7)) = ordered_pair(sK11(ordered_pair(sK8,sK16(sK5,sK8,sK7))),sK12(ordered_pair(sK8,sK16(sK5,sK8,sK7)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_227])]) ).
fof(f1493,plain,
( spl21_175
<=> ! [X2,X0,X1] :
( ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ordered_pair(X1,sK16(X2,X1,X0)) = ordered_pair(sK11(ordered_pair(X1,sK16(X2,X1,X0))),sK12(ordered_pair(X1,sK16(X2,X1,X0))))
| ~ member(X1,inverse2(X0,X2))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_175])]) ).
fof(f1512,plain,
( ~ ilf_type(sK8,set_type)
| ~ ilf_type(sK5,set_type)
| ordered_pair(sK8,sK16(sK5,sK8,sK7)) = ordered_pair(sK11(ordered_pair(sK8,sK16(sK5,sK8,sK7))),sK12(ordered_pair(sK8,sK16(sK5,sK8,sK7))))
| ~ ilf_type(sK7,binary_relation_type)
| ~ sP0(sK7)
| ~ spl21_120
| ~ spl21_175 ),
inference(resolution,[],[f1494,f1004]) ).
fof(f1494,plain,
( ! [X2,X0,X1] :
( ~ member(X1,inverse2(X0,X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ordered_pair(X1,sK16(X2,X1,X0)) = ordered_pair(sK11(ordered_pair(X1,sK16(X2,X1,X0))),sK12(ordered_pair(X1,sK16(X2,X1,X0))))
| ~ ilf_type(X0,binary_relation_type)
| ~ sP0(X0) )
| ~ spl21_175 ),
inference(avatar_component_clause,[],[f1493]) ).
fof(f1834,plain,
( ~ spl21_219
| ~ spl21_74
| ~ spl21_37
| spl21_226
| ~ spl21_120
| ~ spl21_158 ),
inference(avatar_split_clause,[],[f1371,f1343,f1003,f1832,f358,f654,f1776]) ).
fof(f1371,plain,
( ! [X0,X1] :
( member(sK16(sK5,sK8,sK7),X0)
| ~ ilf_type(sK8,set_type)
| ~ 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_120
| ~ spl21_158 ),
inference(resolution,[],[f1344,f1004]) ).
fof(f1830,plain,
( ~ spl21_9
| spl21_225 ),
inference(avatar_contradiction_clause,[],[f1829]) ).
fof(f1829,plain,
( $false
| ~ spl21_9
| spl21_225 ),
inference(resolution,[],[f1827,f233]) ).
fof(f1827,plain,
( ~ ilf_type(sK16(sK6,sK8,sK7),set_type)
| spl21_225 ),
inference(avatar_component_clause,[],[f1825]) ).
fof(f1825,plain,
( spl21_225
<=> ilf_type(sK16(sK6,sK8,sK7),set_type) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_225])]) ).
fof(f1828,plain,
( ~ spl21_37
| ~ spl21_74
| ~ spl21_223
| ~ spl21_62
| ~ spl21_224
| ~ spl21_225
| ~ spl21_50
| ~ spl21_119 ),
inference(avatar_split_clause,[],[f1045,f992,f454,f1825,f1821,f588,f1817,f654,f358]) ).
fof(f1821,plain,
( spl21_224
<=> member(sK16(sK6,sK8,sK7),sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_224])]) ).
fof(f1045,plain,
( ~ ilf_type(sK16(sK6,sK8,sK7),set_type)
| ~ member(sK16(sK6,sK8,sK7),sK5)
| ~ ilf_type(sK6,set_type)
| ~ member(sK8,inverse2(sK7,sK6))
| ~ ilf_type(sK7,binary_relation_type)
| ~ ilf_type(sK8,set_type)
| ~ spl21_50
| ~ spl21_119 ),
inference(duplicate_literal_removal,[],[f1044]) ).
fof(f1044,plain,
( ~ ilf_type(sK16(sK6,sK8,sK7),set_type)
| ~ member(sK16(sK6,sK8,sK7),sK5)
| ~ ilf_type(sK6,set_type)
| ~ member(sK8,inverse2(sK7,sK6))
| ~ member(sK8,inverse2(sK7,sK6))
| ~ ilf_type(sK7,binary_relation_type)
| ~ ilf_type(sK8,set_type)
| ~ ilf_type(sK6,set_type)
| ~ spl21_50
| ~ spl21_119 ),
inference(resolution,[],[f993,f455]) ).
fof(f1814,plain,
( spl21_222
| ~ spl21_25
| ~ spl21_115 ),
inference(avatar_split_clause,[],[f974,f970,f304,f1812]) ).
fof(f1812,plain,
( spl21_222
<=> ! [X0,X1] :
( ~ sP2(X0,X1)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_222])]) ).
fof(f304,plain,
( spl21_25
<=> ! [X0,X1] :
( X0 = X1
| ~ sP2(X1,X0)
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_25])]) ).
fof(f970,plain,
( spl21_115
<=> ! [X0,X1] : sP3(X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_115])]) ).
fof(f974,plain,
( ! [X0,X1] :
( ~ sP2(X0,X1)
| X0 = X1 )
| ~ spl21_25
| ~ spl21_115 ),
inference(resolution,[],[f971,f305]) ).
fof(f305,plain,
( ! [X0,X1] :
( ~ sP3(X0,X1)
| ~ sP2(X1,X0)
| X0 = X1 )
| ~ spl21_25 ),
inference(avatar_component_clause,[],[f304]) ).
fof(f971,plain,
( ! [X0,X1] : sP3(X0,X1)
| ~ spl21_115 ),
inference(avatar_component_clause,[],[f970]) ).
fof(f1798,plain,
( ~ spl21_37
| ~ spl21_74
| ~ spl21_61
| spl21_221
| ~ spl21_12
| ~ spl21_54 ),
inference(avatar_split_clause,[],[f999,f485,f245,f1796,f584,f654,f358]) ).
fof(f584,plain,
( spl21_61
<=> ilf_type(sK9,set_type) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_61])]) ).
fof(f999,plain,
( ! [X0] :
( ~ member(sK9,X0)
| member(sK8,inverse2(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_54 ),
inference(resolution,[],[f247,f486]) ).
fof(f1794,plain,
( ~ spl21_37
| ~ spl21_61
| spl21_220
| ~ spl21_12
| ~ spl21_55 ),
inference(avatar_split_clause,[],[f998,f489,f245,f1780,f584,f358]) ).
fof(f1780,plain,
( spl21_220
<=> ! [X0,X1] :
( member(sK8,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_220])]) ).
fof(f998,plain,
( ! [X0,X1] :
( member(sK8,X0)
| ~ ilf_type(sK7,relation_type(X0,X1))
| ~ ilf_type(sK9,set_type)
| ~ ilf_type(sK8,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_12
| ~ spl21_55 ),
inference(resolution,[],[f247,f490]) ).
fof(f1792,plain,
( ~ spl21_7
| ~ spl21_8
| ~ spl21_11
| ~ spl21_12 ),
inference(avatar_split_clause,[],[f1786,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(sK8,X5),sK7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_11])]) ).
fof(f1786,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(sK8,X5),sK7)
| ~ ilf_type(X5,member_type(sK6))
| ~ member(X5,sK5) )
| ~ spl21_11 ),
inference(avatar_component_clause,[],[f241]) ).
fof(f1784,plain,
( ~ spl21_9
| spl21_219 ),
inference(avatar_contradiction_clause,[],[f1783]) ).
fof(f1783,plain,
( $false
| ~ spl21_9
| spl21_219 ),
inference(resolution,[],[f1778,f233]) ).
fof(f1778,plain,
( ~ ilf_type(sK5,set_type)
| spl21_219 ),
inference(avatar_component_clause,[],[f1776]) ).
fof(f1782,plain,
( ~ spl21_219
| ~ spl21_74
| ~ spl21_37
| spl21_220
| ~ spl21_120
| ~ spl21_151 ),
inference(avatar_split_clause,[],[f1309,f1301,f1003,f1780,f358,f654,f1776]) ).
fof(f1309,plain,
( ! [X0,X1] :
( member(sK8,X0)
| ~ ilf_type(sK8,set_type)
| ~ 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_120
| ~ spl21_151 ),
inference(resolution,[],[f1302,f1004]) ).
fof(f1773,plain,
( spl21_218
| ~ spl21_51
| ~ spl21_112 ),
inference(avatar_split_clause,[],[f948,f945,f462,f1771]) ).
fof(f1771,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,inverse2(power_set(X0),X2))
| ~ ilf_type(ordered_pair(X3,sK16(X4,X3,ordered_pair(X1,sK16(X2,X1,power_set(X0))))),set_type)
| member(ordered_pair(X3,sK16(X4,X3,ordered_pair(X1,sK16(X2,X1,power_set(X0))))),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(ordered_pair(X1,sK16(X2,X1,power_set(X0))),set_type)
| ~ member(X3,inverse2(ordered_pair(X1,sK16(X2,X1,power_set(X0))),X4))
| ~ ilf_type(ordered_pair(X1,sK16(X2,X1,power_set(X0))),binary_relation_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_218])]) ).
fof(f945,plain,
( spl21_112
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,inverse2(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(X0,sK16(X2,X0,power_set(X1))))
| ~ ilf_type(X3,set_type)
| member(X3,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(ordered_pair(X0,sK16(X2,X0,power_set(X1))),set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_112])]) ).
fof(f948,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,inverse2(power_set(X0),X2))
| ~ ilf_type(ordered_pair(X3,sK16(X4,X3,ordered_pair(X1,sK16(X2,X1,power_set(X0))))),set_type)
| member(ordered_pair(X3,sK16(X4,X3,ordered_pair(X1,sK16(X2,X1,power_set(X0))))),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(ordered_pair(X1,sK16(X2,X1,power_set(X0))),set_type)
| ~ member(X3,inverse2(ordered_pair(X1,sK16(X2,X1,power_set(X0))),X4))
| ~ ilf_type(ordered_pair(X1,sK16(X2,X1,power_set(X0))),binary_relation_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,set_type) )
| ~ spl21_51
| ~ spl21_112 ),
inference(resolution,[],[f946,f463]) ).
fof(f946,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X3,ordered_pair(X0,sK16(X2,X0,power_set(X1))))
| ~ ilf_type(power_set(X1),binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X0,inverse2(power_set(X1),X2))
| ~ ilf_type(X3,set_type)
| member(X3,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(ordered_pair(X0,sK16(X2,X0,power_set(X1))),set_type) )
| ~ spl21_112 ),
inference(avatar_component_clause,[],[f945]) ).
fof(f1768,plain,
( spl21_217
| ~ spl21_51
| ~ spl21_111 ),
inference(avatar_split_clause,[],[f933,f930,f462,f1766]) ).
fof(f1766,plain,
( spl21_217
<=> ! [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,inverse2(X0,power_set(X2)))
| ~ ilf_type(ordered_pair(X3,sK16(X4,X3,sK16(power_set(X2),X1,X0))),set_type)
| member(ordered_pair(X3,sK16(X4,X3,sK16(power_set(X2),X1,X0))),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(sK16(power_set(X2),X1,X0),set_type)
| ~ member(X3,inverse2(sK16(power_set(X2),X1,X0),X4))
| ~ ilf_type(sK16(power_set(X2),X1,X0),binary_relation_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_217])]) ).
fof(f930,plain,
( spl21_111
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,inverse2(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_111])]) ).
fof(f933,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,inverse2(X0,power_set(X2)))
| ~ ilf_type(ordered_pair(X3,sK16(X4,X3,sK16(power_set(X2),X1,X0))),set_type)
| member(ordered_pair(X3,sK16(X4,X3,sK16(power_set(X2),X1,X0))),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(sK16(power_set(X2),X1,X0),set_type)
| ~ member(X3,inverse2(sK16(power_set(X2),X1,X0),X4))
| ~ ilf_type(sK16(power_set(X2),X1,X0),binary_relation_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,set_type) )
| ~ spl21_51
| ~ spl21_111 ),
inference(resolution,[],[f931,f463]) ).
fof(f931,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,inverse2(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_111 ),
inference(avatar_component_clause,[],[f930]) ).
fof(f1743,plain,
( spl21_216
| ~ spl21_32
| ~ spl21_112 ),
inference(avatar_split_clause,[],[f952,f945,f338,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,inverse2(power_set(X0),X2))
| ~ ilf_type(sK14(ordered_pair(X1,sK16(X2,X1,power_set(X0))),X3),set_type)
| member(sK14(ordered_pair(X1,sK16(X2,X1,power_set(X0))),X3),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(ordered_pair(X1,sK16(X2,X1,power_set(X0))),set_type)
| member(sK14(ordered_pair(X1,sK16(X2,X1,power_set(X0))),X3),X3)
| sP2(ordered_pair(X1,sK16(X2,X1,power_set(X0))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_216])]) ).
fof(f952,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,inverse2(power_set(X0),X2))
| ~ ilf_type(sK14(ordered_pair(X1,sK16(X2,X1,power_set(X0))),X3),set_type)
| member(sK14(ordered_pair(X1,sK16(X2,X1,power_set(X0))),X3),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(ordered_pair(X1,sK16(X2,X1,power_set(X0))),set_type)
| member(sK14(ordered_pair(X1,sK16(X2,X1,power_set(X0))),X3),X3)
| sP2(ordered_pair(X1,sK16(X2,X1,power_set(X0))),X3) )
| ~ spl21_32
| ~ spl21_112 ),
inference(resolution,[],[f946,f339]) ).
fof(f1739,plain,
( spl21_215
| ~ spl21_32
| ~ spl21_112 ),
inference(avatar_split_clause,[],[f951,f945,f338,f1737]) ).
fof(f1737,plain,
( spl21_215
<=> ! [X0,X3,X2,X1] :
( ~ ilf_type(power_set(X0),binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X1,inverse2(power_set(X0),X2))
| ~ ilf_type(sK14(X3,ordered_pair(X1,sK16(X2,X1,power_set(X0)))),set_type)
| member(sK14(X3,ordered_pair(X1,sK16(X2,X1,power_set(X0)))),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(ordered_pair(X1,sK16(X2,X1,power_set(X0))),set_type)
| member(sK14(X3,ordered_pair(X1,sK16(X2,X1,power_set(X0)))),X3)
| sP2(X3,ordered_pair(X1,sK16(X2,X1,power_set(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_215])]) ).
fof(f951,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,inverse2(power_set(X0),X2))
| ~ ilf_type(sK14(X3,ordered_pair(X1,sK16(X2,X1,power_set(X0)))),set_type)
| member(sK14(X3,ordered_pair(X1,sK16(X2,X1,power_set(X0)))),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(ordered_pair(X1,sK16(X2,X1,power_set(X0))),set_type)
| member(sK14(X3,ordered_pair(X1,sK16(X2,X1,power_set(X0)))),X3)
| sP2(X3,ordered_pair(X1,sK16(X2,X1,power_set(X0)))) )
| ~ spl21_32
| ~ spl21_112 ),
inference(resolution,[],[f946,f339]) ).
fof(f1734,plain,
( spl21_214
| ~ spl21_50
| ~ spl21_112 ),
inference(avatar_split_clause,[],[f956,f945,f454,f1732]) ).
fof(f1732,plain,
( spl21_214
<=> ! [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,inverse2(power_set(X0),X2))
| ~ ilf_type(sK16(ordered_pair(X1,sK16(X2,X1,power_set(X0))),X3,X4),set_type)
| member(sK16(ordered_pair(X1,sK16(X2,X1,power_set(X0))),X3,X4),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(ordered_pair(X1,sK16(X2,X1,power_set(X0))),set_type)
| ~ member(X3,inverse2(X4,ordered_pair(X1,sK16(X2,X1,power_set(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(power_set(X0),binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X1,inverse2(power_set(X0),X2))
| ~ ilf_type(sK16(ordered_pair(X1,sK16(X2,X1,power_set(X0))),X3,X4),set_type)
| member(sK16(ordered_pair(X1,sK16(X2,X1,power_set(X0))),X3,X4),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(ordered_pair(X1,sK16(X2,X1,power_set(X0))),set_type)
| ~ member(X3,inverse2(X4,ordered_pair(X1,sK16(X2,X1,power_set(X0)))))
| ~ ilf_type(X4,binary_relation_type)
| ~ ilf_type(X3,set_type) )
| ~ spl21_50
| ~ spl21_112 ),
inference(duplicate_literal_removal,[],[f955]) ).
fof(f955,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,inverse2(power_set(X0),X2))
| ~ ilf_type(sK16(ordered_pair(X1,sK16(X2,X1,power_set(X0))),X3,X4),set_type)
| member(sK16(ordered_pair(X1,sK16(X2,X1,power_set(X0))),X3,X4),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(ordered_pair(X1,sK16(X2,X1,power_set(X0))),set_type)
| ~ member(X3,inverse2(X4,ordered_pair(X1,sK16(X2,X1,power_set(X0)))))
| ~ ilf_type(X4,binary_relation_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(ordered_pair(X1,sK16(X2,X1,power_set(X0))),set_type) )
| ~ spl21_50
| ~ spl21_112 ),
inference(resolution,[],[f946,f455]) ).
fof(f1728,plain,
( spl21_213
| ~ spl21_41
| ~ spl21_112 ),
inference(avatar_split_clause,[],[f957,f945,f382,f1726]) ).
fof(f1726,plain,
( spl21_213
<=> ! [X0,X3,X2,X1] :
( ~ ilf_type(power_set(X0),binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X1,inverse2(power_set(X0),X2))
| ~ ilf_type(sK15(ordered_pair(X1,sK16(X2,X1,power_set(X0))),X3),set_type)
| member(sK15(ordered_pair(X1,sK16(X2,X1,power_set(X0))),X3),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(ordered_pair(X1,sK16(X2,X1,power_set(X0))),set_type)
| member(ordered_pair(X1,sK16(X2,X1,power_set(X0))),power_set(X3))
| ~ ilf_type(X3,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_213])]) ).
fof(f957,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,inverse2(power_set(X0),X2))
| ~ ilf_type(sK15(ordered_pair(X1,sK16(X2,X1,power_set(X0))),X3),set_type)
| member(sK15(ordered_pair(X1,sK16(X2,X1,power_set(X0))),X3),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(ordered_pair(X1,sK16(X2,X1,power_set(X0))),set_type)
| member(ordered_pair(X1,sK16(X2,X1,power_set(X0))),power_set(X3))
| ~ ilf_type(X3,set_type) )
| ~ spl21_41
| ~ spl21_112 ),
inference(duplicate_literal_removal,[],[f954]) ).
fof(f954,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,inverse2(power_set(X0),X2))
| ~ ilf_type(sK15(ordered_pair(X1,sK16(X2,X1,power_set(X0))),X3),set_type)
| member(sK15(ordered_pair(X1,sK16(X2,X1,power_set(X0))),X3),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(ordered_pair(X1,sK16(X2,X1,power_set(X0))),set_type)
| member(ordered_pair(X1,sK16(X2,X1,power_set(X0))),power_set(X3))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(ordered_pair(X1,sK16(X2,X1,power_set(X0))),set_type) )
| ~ spl21_41
| ~ spl21_112 ),
inference(resolution,[],[f946,f383]) ).
fof(f1724,plain,
( spl21_212
| ~ spl21_51
| ~ spl21_103 ),
inference(avatar_split_clause,[],[f877,f874,f462,f1722]) ).
fof(f1722,plain,
( spl21_212
<=> ! [X0,X3,X2,X1] :
( ~ ilf_type(ordered_pair(X0,sK16(X1,X0,sK15(power_set(X2),X3))),set_type)
| member(ordered_pair(X0,sK16(X1,X0,sK15(power_set(X2),X3))),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(X0,inverse2(sK15(power_set(X2),X3),X1))
| ~ ilf_type(sK15(power_set(X2),X3),binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_212])]) ).
fof(f874,plain,
( spl21_103
<=> ! [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_103])]) ).
fof(f877,plain,
( ! [X2,X3,X0,X1] :
( ~ ilf_type(ordered_pair(X0,sK16(X1,X0,sK15(power_set(X2),X3))),set_type)
| member(ordered_pair(X0,sK16(X1,X0,sK15(power_set(X2),X3))),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(X0,inverse2(sK15(power_set(X2),X3),X1))
| ~ ilf_type(sK15(power_set(X2),X3),binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type) )
| ~ spl21_51
| ~ spl21_103 ),
inference(resolution,[],[f875,f463]) ).
fof(f875,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_103 ),
inference(avatar_component_clause,[],[f874]) ).
fof(f1720,plain,
( ~ spl21_57
| spl21_211
| ~ spl21_49
| ~ spl21_186 ),
inference(avatar_split_clause,[],[f1690,f1570,f445,f1718,f501]) ).
fof(f1718,plain,
( spl21_211
<=> ! [X0,X1] :
( ~ ilf_type(X0,set_type)
| member(X1,sK4)
| ~ ilf_type(X1,set_type)
| ~ member(X1,inverse2(sK7,X0))
| ~ ilf_type(inverse2(sK7,X0),set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_211])]) ).
fof(f1570,plain,
( spl21_186
<=> ! [X0] :
( ~ ilf_type(X0,set_type)
| member(inverse2(sK7,X0),power_set(sK4))
| ~ ilf_type(inverse2(sK7,X0),set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_186])]) ).
fof(f1690,plain,
( ! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(inverse2(sK7,X0),set_type)
| ~ member(X1,inverse2(sK7,X0))
| ~ ilf_type(X1,set_type)
| member(X1,sK4)
| ~ ilf_type(sK4,set_type) )
| ~ spl21_49
| ~ spl21_186 ),
inference(duplicate_literal_removal,[],[f1685]) ).
fof(f1685,plain,
( ! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(inverse2(sK7,X0),set_type)
| ~ member(X1,inverse2(sK7,X0))
| ~ ilf_type(X1,set_type)
| member(X1,sK4)
| ~ ilf_type(sK4,set_type)
| ~ ilf_type(inverse2(sK7,X0),set_type) )
| ~ spl21_49
| ~ spl21_186 ),
inference(resolution,[],[f1571,f446]) ).
fof(f1571,plain,
( ! [X0] :
( member(inverse2(sK7,X0),power_set(sK4))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(inverse2(sK7,X0),set_type) )
| ~ spl21_186 ),
inference(avatar_component_clause,[],[f1570]) ).
fof(f1713,plain,
( spl21_210
| ~ spl21_50
| ~ spl21_111 ),
inference(avatar_split_clause,[],[f941,f930,f454,f1711]) ).
fof(f1711,plain,
( spl21_210
<=> ! [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,inverse2(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,inverse2(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_210])]) ).
fof(f941,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,inverse2(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,inverse2(X4,sK16(power_set(X2),X1,X0)))
| ~ ilf_type(X4,binary_relation_type)
| ~ ilf_type(X3,set_type) )
| ~ spl21_50
| ~ spl21_111 ),
inference(duplicate_literal_removal,[],[f940]) ).
fof(f940,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,inverse2(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,inverse2(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_50
| ~ spl21_111 ),
inference(resolution,[],[f931,f455]) ).
fof(f1709,plain,
( spl21_209
| ~ spl21_51
| ~ spl21_101 ),
inference(avatar_split_clause,[],[f858,f844,f462,f1707]) ).
fof(f1707,plain,
( spl21_209
<=> ! [X0,X3,X2,X1] :
( ~ ilf_type(ordered_pair(X0,sK16(X1,X0,sK14(power_set(X2),X3))),set_type)
| member(ordered_pair(X0,sK16(X1,X0,sK14(power_set(X2),X3))),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(X0,inverse2(sK14(power_set(X2),X3),X1))
| ~ ilf_type(sK14(power_set(X2),X3),binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_209])]) ).
fof(f858,plain,
( ! [X2,X3,X0,X1] :
( ~ ilf_type(ordered_pair(X0,sK16(X1,X0,sK14(power_set(X2),X3))),set_type)
| member(ordered_pair(X0,sK16(X1,X0,sK14(power_set(X2),X3))),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(X0,inverse2(sK14(power_set(X2),X3),X1))
| ~ ilf_type(sK14(power_set(X2),X3),binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type) )
| ~ spl21_51
| ~ spl21_101 ),
inference(resolution,[],[f845,f463]) ).
fof(f1705,plain,
( spl21_208
| ~ spl21_51
| ~ spl21_100 ),
inference(avatar_split_clause,[],[f847,f840,f462,f1703]) ).
fof(f1703,plain,
( spl21_208
<=> ! [X0,X3,X2,X1] :
( ~ ilf_type(ordered_pair(X0,sK16(X1,X0,sK14(X2,power_set(X3)))),set_type)
| member(ordered_pair(X0,sK16(X1,X0,sK14(X2,power_set(X3)))),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(X0,inverse2(sK14(X2,power_set(X3)),X1))
| ~ ilf_type(sK14(X2,power_set(X3)),binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_208])]) ).
fof(f847,plain,
( ! [X2,X3,X0,X1] :
( ~ ilf_type(ordered_pair(X0,sK16(X1,X0,sK14(X2,power_set(X3)))),set_type)
| member(ordered_pair(X0,sK16(X1,X0,sK14(X2,power_set(X3)))),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(X0,inverse2(sK14(X2,power_set(X3)),X1))
| ~ ilf_type(sK14(X2,power_set(X3)),binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type) )
| ~ spl21_51
| ~ spl21_100 ),
inference(resolution,[],[f841,f463]) ).
fof(f1699,plain,
( spl21_207
| ~ spl21_32
| ~ spl21_111 ),
inference(avatar_split_clause,[],[f937,f930,f338,f1697]) ).
fof(f1697,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,inverse2(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_207])]) ).
fof(f937,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,inverse2(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_32
| ~ spl21_111 ),
inference(resolution,[],[f931,f339]) ).
fof(f1695,plain,
( spl21_206
| ~ spl21_32
| ~ spl21_111 ),
inference(avatar_split_clause,[],[f936,f930,f338,f1693]) ).
fof(f1693,plain,
( spl21_206
<=> ! [X0,X3,X2,X1] :
( ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(power_set(X2),set_type)
| ~ member(X1,inverse2(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_206])]) ).
fof(f936,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,inverse2(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_32
| ~ spl21_111 ),
inference(resolution,[],[f931,f339]) ).
fof(f1681,plain,
( spl21_205
| ~ spl21_24
| ~ spl21_112 ),
inference(avatar_split_clause,[],[f958,f945,f300,f1679]) ).
fof(f1679,plain,
( spl21_205
<=> ! [X2,X0,X1] :
( ~ ilf_type(power_set(X0),binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X1,inverse2(power_set(X0),X2))
| ~ ilf_type(sK13(ordered_pair(X1,sK16(X2,X1,power_set(X0)))),set_type)
| member(sK13(ordered_pair(X1,sK16(X2,X1,power_set(X0)))),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(ordered_pair(X1,sK16(X2,X1,power_set(X0))),set_type)
| empty(ordered_pair(X1,sK16(X2,X1,power_set(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_205])]) ).
fof(f958,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(power_set(X0),binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X1,inverse2(power_set(X0),X2))
| ~ ilf_type(sK13(ordered_pair(X1,sK16(X2,X1,power_set(X0)))),set_type)
| member(sK13(ordered_pair(X1,sK16(X2,X1,power_set(X0)))),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(ordered_pair(X1,sK16(X2,X1,power_set(X0))),set_type)
| empty(ordered_pair(X1,sK16(X2,X1,power_set(X0)))) )
| ~ spl21_24
| ~ spl21_112 ),
inference(duplicate_literal_removal,[],[f950]) ).
fof(f950,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(power_set(X0),binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X1,inverse2(power_set(X0),X2))
| ~ ilf_type(sK13(ordered_pair(X1,sK16(X2,X1,power_set(X0)))),set_type)
| member(sK13(ordered_pair(X1,sK16(X2,X1,power_set(X0)))),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(ordered_pair(X1,sK16(X2,X1,power_set(X0))),set_type)
| empty(ordered_pair(X1,sK16(X2,X1,power_set(X0))))
| ~ ilf_type(ordered_pair(X1,sK16(X2,X1,power_set(X0))),set_type) )
| ~ spl21_24
| ~ spl21_112 ),
inference(resolution,[],[f946,f301]) ).
fof(f1677,plain,
( spl21_204
| ~ spl21_17
| ~ spl21_112 ),
inference(avatar_split_clause,[],[f949,f945,f267,f1675]) ).
fof(f1675,plain,
( spl21_204
<=> ! [X2,X0,X1] :
( ~ ilf_type(power_set(X0),binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X1,inverse2(power_set(X0),X2))
| ~ ilf_type(sK10(ordered_pair(X1,sK16(X2,X1,power_set(X0)))),set_type)
| member(sK10(ordered_pair(X1,sK16(X2,X1,power_set(X0)))),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(ordered_pair(X1,sK16(X2,X1,power_set(X0))),set_type)
| sP0(ordered_pair(X1,sK16(X2,X1,power_set(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_204])]) ).
fof(f949,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(power_set(X0),binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X1,inverse2(power_set(X0),X2))
| ~ ilf_type(sK10(ordered_pair(X1,sK16(X2,X1,power_set(X0)))),set_type)
| member(sK10(ordered_pair(X1,sK16(X2,X1,power_set(X0)))),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(ordered_pair(X1,sK16(X2,X1,power_set(X0))),set_type)
| sP0(ordered_pair(X1,sK16(X2,X1,power_set(X0)))) )
| ~ spl21_17
| ~ spl21_112 ),
inference(resolution,[],[f946,f268]) ).
fof(f1672,plain,
( spl21_203
| ~ spl21_41
| ~ spl21_111 ),
inference(avatar_split_clause,[],[f942,f930,f382,f1670]) ).
fof(f1670,plain,
( spl21_203
<=> ! [X0,X3,X2,X1] :
( ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(power_set(X2),set_type)
| ~ member(X1,inverse2(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_203])]) ).
fof(f942,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,inverse2(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_41
| ~ spl21_111 ),
inference(duplicate_literal_removal,[],[f939]) ).
fof(f939,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,inverse2(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_41
| ~ spl21_111 ),
inference(resolution,[],[f931,f383]) ).
fof(f1666,plain,
( spl21_202
| ~ spl21_50
| ~ spl21_103 ),
inference(avatar_split_clause,[],[f885,f874,f454,f1664]) ).
fof(f1664,plain,
( spl21_202
<=> ! [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,inverse2(X3,sK15(power_set(X0),X1)))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_202])]) ).
fof(f885,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,inverse2(X3,sK15(power_set(X0),X1)))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,set_type) )
| ~ spl21_50
| ~ spl21_103 ),
inference(duplicate_literal_removal,[],[f884]) ).
fof(f884,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,inverse2(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_50
| ~ spl21_103 ),
inference(resolution,[],[f875,f455]) ).
fof(f1662,plain,
( spl21_201
| ~ spl21_51
| ~ spl21_95 ),
inference(avatar_split_clause,[],[f804,f801,f462,f1660]) ).
fof(f1660,plain,
( spl21_201
<=> ! [X2,X0,X1] :
( ~ ilf_type(ordered_pair(X0,sK16(X1,X0,sK13(power_set(X2)))),set_type)
| member(ordered_pair(X0,sK16(X1,X0,sK13(power_set(X2)))),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(X0,inverse2(sK13(power_set(X2)),X1))
| ~ ilf_type(sK13(power_set(X2)),binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_201])]) ).
fof(f804,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(ordered_pair(X0,sK16(X1,X0,sK13(power_set(X2)))),set_type)
| member(ordered_pair(X0,sK16(X1,X0,sK13(power_set(X2)))),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(X0,inverse2(sK13(power_set(X2)),X1))
| ~ ilf_type(sK13(power_set(X2)),binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type) )
| ~ spl21_51
| ~ spl21_95 ),
inference(resolution,[],[f802,f463]) ).
fof(f1654,plain,
( spl21_200
| ~ spl21_32
| ~ spl21_103 ),
inference(avatar_split_clause,[],[f881,f874,f338,f1652]) ).
fof(f1652,plain,
( spl21_200
<=> ! [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_200])]) ).
fof(f881,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_32
| ~ spl21_103 ),
inference(resolution,[],[f875,f339]) ).
fof(f1650,plain,
( spl21_199
| ~ spl21_32
| ~ spl21_103 ),
inference(avatar_split_clause,[],[f880,f874,f338,f1648]) ).
fof(f1648,plain,
( spl21_199
<=> ! [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_199])]) ).
fof(f880,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_32
| ~ spl21_103 ),
inference(resolution,[],[f875,f339]) ).
fof(f1646,plain,
( spl21_198
| ~ spl21_50
| ~ spl21_101 ),
inference(avatar_split_clause,[],[f866,f844,f454,f1644]) ).
fof(f1644,plain,
( spl21_198
<=> ! [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,inverse2(X3,sK14(power_set(X0),X1)))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_198])]) ).
fof(f866,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,inverse2(X3,sK14(power_set(X0),X1)))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,set_type) )
| ~ spl21_50
| ~ spl21_101 ),
inference(duplicate_literal_removal,[],[f865]) ).
fof(f865,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,inverse2(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_50
| ~ spl21_101 ),
inference(resolution,[],[f845,f455]) ).
fof(f1642,plain,
( spl21_197
| ~ spl21_50
| ~ spl21_100 ),
inference(avatar_split_clause,[],[f855,f840,f454,f1640]) ).
fof(f1640,plain,
( spl21_197
<=> ! [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,inverse2(X3,sK14(X0,power_set(X1))))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_197])]) ).
fof(f855,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,inverse2(X3,sK14(X0,power_set(X1))))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,set_type) )
| ~ spl21_50
| ~ spl21_100 ),
inference(duplicate_literal_removal,[],[f854]) ).
fof(f854,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,inverse2(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_50
| ~ spl21_100 ),
inference(resolution,[],[f841,f455]) ).
fof(f1636,plain,
( ~ spl21_57
| ~ spl21_14
| ~ spl21_185 ),
inference(avatar_split_clause,[],[f1608,f1566,f255,f501]) ).
fof(f255,plain,
( spl21_14
<=> ! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_14])]) ).
fof(f1566,plain,
( spl21_185
<=> empty(power_set(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_185])]) ).
fof(f1608,plain,
( ~ ilf_type(sK4,set_type)
| ~ spl21_14
| ~ spl21_185 ),
inference(resolution,[],[f1568,f256]) ).
fof(f256,plain,
( ! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) )
| ~ spl21_14 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f1568,plain,
( empty(power_set(sK4))
| ~ spl21_185 ),
inference(avatar_component_clause,[],[f1566]) ).
fof(f1632,plain,
( spl21_196
| ~ spl21_32
| ~ spl21_101 ),
inference(avatar_split_clause,[],[f862,f844,f338,f1630]) ).
fof(f1630,plain,
( spl21_196
<=> ! [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_196])]) ).
fof(f862,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_32
| ~ spl21_101 ),
inference(resolution,[],[f845,f339]) ).
fof(f1628,plain,
( spl21_195
| ~ spl21_32
| ~ spl21_101 ),
inference(avatar_split_clause,[],[f861,f844,f338,f1626]) ).
fof(f1626,plain,
( spl21_195
<=> ! [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_195])]) ).
fof(f861,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_32
| ~ spl21_101 ),
inference(resolution,[],[f845,f339]) ).
fof(f1624,plain,
( spl21_194
| ~ spl21_32
| ~ spl21_100 ),
inference(avatar_split_clause,[],[f851,f840,f338,f1622]) ).
fof(f1622,plain,
( spl21_194
<=> ! [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_194])]) ).
fof(f851,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_32
| ~ spl21_100 ),
inference(resolution,[],[f841,f339]) ).
fof(f1620,plain,
( spl21_193
| ~ spl21_32
| ~ spl21_100 ),
inference(avatar_split_clause,[],[f850,f840,f338,f1618]) ).
fof(f1618,plain,
( spl21_193
<=> ! [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_193])]) ).
fof(f850,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_32
| ~ spl21_100 ),
inference(resolution,[],[f841,f339]) ).
fof(f1616,plain,
( spl21_192
| ~ spl21_51
| ~ spl21_92 ),
inference(avatar_split_clause,[],[f787,f776,f462,f1614]) ).
fof(f1614,plain,
( spl21_192
<=> ! [X2,X0,X1] :
( ~ ilf_type(ordered_pair(X0,sK16(X1,X0,sK10(power_set(X2)))),set_type)
| member(ordered_pair(X0,sK16(X1,X0,sK10(power_set(X2)))),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(sK10(power_set(X2)),set_type)
| sP0(power_set(X2))
| ~ member(X0,inverse2(sK10(power_set(X2)),X1))
| ~ ilf_type(sK10(power_set(X2)),binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_192])]) ).
fof(f787,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(ordered_pair(X0,sK16(X1,X0,sK10(power_set(X2)))),set_type)
| member(ordered_pair(X0,sK16(X1,X0,sK10(power_set(X2)))),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(sK10(power_set(X2)),set_type)
| sP0(power_set(X2))
| ~ member(X0,inverse2(sK10(power_set(X2)),X1))
| ~ ilf_type(sK10(power_set(X2)),binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type) )
| ~ spl21_51
| ~ spl21_92 ),
inference(resolution,[],[f777,f463]) ).
fof(f1599,plain,
( spl21_191
| ~ spl21_24
| ~ spl21_111 ),
inference(avatar_split_clause,[],[f943,f930,f300,f1597]) ).
fof(f1597,plain,
( spl21_191
<=> ! [X2,X0,X1] :
( ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(power_set(X2),set_type)
| ~ member(X1,inverse2(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_191])]) ).
fof(f943,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(power_set(X2),set_type)
| ~ member(X1,inverse2(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_111 ),
inference(duplicate_literal_removal,[],[f935]) ).
fof(f935,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(power_set(X2),set_type)
| ~ member(X1,inverse2(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_111 ),
inference(resolution,[],[f931,f301]) ).
fof(f1595,plain,
( spl21_190
| ~ spl21_17
| ~ spl21_111 ),
inference(avatar_split_clause,[],[f934,f930,f267,f1593]) ).
fof(f1593,plain,
( spl21_190
<=> ! [X2,X0,X1] :
( ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(power_set(X2),set_type)
| ~ member(X1,inverse2(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_190])]) ).
fof(f934,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(power_set(X2),set_type)
| ~ member(X1,inverse2(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_111 ),
inference(resolution,[],[f931,f268]) ).
fof(f1591,plain,
( spl21_189
| ~ spl21_53
| ~ spl21_107 ),
inference(avatar_split_clause,[],[f912,f907,f478,f1589]) ).
fof(f1589,plain,
( spl21_189
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ ilf_type(X0,relation_type(cross_product(X1,X2),X3))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(cross_product(X1,X2),set_type)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X5,set_type)
| inverse4(X1,X2,inverse4(cross_product(X1,X2),X3,X0,X4),X5) = inverse2(inverse4(cross_product(X1,X2),X3,X0,X4),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_189])]) ).
fof(f478,plain,
( spl21_53
<=> ! [X0,X3,X2,X1] :
( inverse4(X0,X1,X2,X3) = inverse2(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_53])]) ).
fof(f907,plain,
( spl21_107
<=> ! [X4,X0,X3,X2,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,relation_type(cross_product(X2,X3),X4))
| ~ ilf_type(X4,set_type)
| ~ ilf_type(cross_product(X2,X3),set_type)
| ilf_type(inverse4(cross_product(X2,X3),X4,X1,X0),relation_type(X2,X3))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_107])]) ).
fof(f912,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ ilf_type(X0,relation_type(cross_product(X1,X2),X3))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(cross_product(X1,X2),set_type)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X5,set_type)
| inverse4(X1,X2,inverse4(cross_product(X1,X2),X3,X0,X4),X5) = inverse2(inverse4(cross_product(X1,X2),X3,X0,X4),X5) )
| ~ spl21_53
| ~ spl21_107 ),
inference(duplicate_literal_removal,[],[f911]) ).
fof(f911,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ ilf_type(X0,relation_type(cross_product(X1,X2),X3))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(cross_product(X1,X2),set_type)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X5,set_type)
| inverse4(X1,X2,inverse4(cross_product(X1,X2),X3,X0,X4),X5) = inverse2(inverse4(cross_product(X1,X2),X3,X0,X4),X5)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) )
| ~ spl21_53
| ~ spl21_107 ),
inference(resolution,[],[f908,f479]) ).
fof(f479,plain,
( ! [X2,X3,X0,X1] :
( ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X3,set_type)
| inverse4(X0,X1,X2,X3) = inverse2(X2,X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_53 ),
inference(avatar_component_clause,[],[f478]) ).
fof(f908,plain,
( ! [X2,X3,X0,X1,X4] :
( ilf_type(inverse4(cross_product(X2,X3),X4,X1,X0),relation_type(X2,X3))
| ~ ilf_type(X1,relation_type(cross_product(X2,X3),X4))
| ~ ilf_type(X4,set_type)
| ~ ilf_type(cross_product(X2,X3),set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type) )
| ~ spl21_107 ),
inference(avatar_component_clause,[],[f907]) ).
fof(f1586,plain,
( spl21_188
| ~ spl21_41
| ~ spl21_103 ),
inference(avatar_split_clause,[],[f886,f874,f382,f1584]) ).
fof(f1584,plain,
( spl21_188
<=> ! [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_188])]) ).
fof(f886,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_41
| ~ spl21_103 ),
inference(duplicate_literal_removal,[],[f883]) ).
fof(f883,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_41
| ~ spl21_103 ),
inference(resolution,[],[f875,f383]) ).
fof(f1576,plain,
( spl21_187
| ~ spl21_41
| ~ spl21_101 ),
inference(avatar_split_clause,[],[f867,f844,f382,f1574]) ).
fof(f867,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_41
| ~ spl21_101 ),
inference(duplicate_literal_removal,[],[f864]) ).
fof(f864,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_41
| ~ spl21_101 ),
inference(resolution,[],[f845,f383]) ).
fof(f1572,plain,
( ~ spl21_57
| spl21_185
| spl21_186
| ~ spl21_138
| ~ spl21_176 ),
inference(avatar_split_clause,[],[f1539,f1501,f1170,f1570,f1566,f501]) ).
fof(f1501,plain,
( spl21_176
<=> ! [X0] :
( ilf_type(inverse2(sK7,X0),subset_type(sK4))
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_176])]) ).
fof(f1539,plain,
( ! [X0] :
( ~ ilf_type(X0,set_type)
| empty(power_set(sK4))
| ~ ilf_type(inverse2(sK7,X0),set_type)
| member(inverse2(sK7,X0),power_set(sK4))
| ~ ilf_type(sK4,set_type) )
| ~ spl21_138
| ~ spl21_176 ),
inference(resolution,[],[f1502,f1171]) ).
fof(f1502,plain,
( ! [X0] :
( ilf_type(inverse2(sK7,X0),subset_type(sK4))
| ~ ilf_type(X0,set_type) )
| ~ spl21_176 ),
inference(avatar_component_clause,[],[f1501]) ).
fof(f1564,plain,
( spl21_184
| ~ spl21_41
| ~ spl21_100 ),
inference(avatar_split_clause,[],[f856,f840,f382,f1562]) ).
fof(f856,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_41
| ~ spl21_100 ),
inference(duplicate_literal_removal,[],[f853]) ).
fof(f853,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_41
| ~ spl21_100 ),
inference(resolution,[],[f841,f383]) ).
fof(f1560,plain,
( spl21_183
| ~ spl21_51
| ~ spl21_91 ),
inference(avatar_split_clause,[],[f763,f752,f462,f1558]) ).
fof(f1558,plain,
( spl21_183
<=> ! [X2,X0,X1] :
( ~ ilf_type(power_set(X0),set_type)
| empty(power_set(X0))
| ~ ilf_type(ordered_pair(X1,sK16(X2,X1,power_set(X0))),set_type)
| ilf_type(ordered_pair(X1,sK16(X2,X1,power_set(X0))),subset_type(X0))
| ~ ilf_type(X0,set_type)
| ~ member(X1,inverse2(power_set(X0),X2))
| ~ ilf_type(power_set(X0),binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_183])]) ).
fof(f763,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(power_set(X0),set_type)
| empty(power_set(X0))
| ~ ilf_type(ordered_pair(X1,sK16(X2,X1,power_set(X0))),set_type)
| ilf_type(ordered_pair(X1,sK16(X2,X1,power_set(X0))),subset_type(X0))
| ~ ilf_type(X0,set_type)
| ~ member(X1,inverse2(power_set(X0),X2))
| ~ ilf_type(power_set(X0),binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) )
| ~ spl21_51
| ~ spl21_91 ),
inference(resolution,[],[f753,f463]) ).
fof(f1555,plain,
( spl21_182
| ~ spl21_50
| ~ spl21_95 ),
inference(avatar_split_clause,[],[f812,f801,f454,f1553]) ).
fof(f812,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,inverse2(X2,sK13(power_set(X0))))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type) )
| ~ spl21_50
| ~ spl21_95 ),
inference(duplicate_literal_removal,[],[f811]) ).
fof(f811,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,inverse2(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_50
| ~ spl21_95 ),
inference(resolution,[],[f802,f455]) ).
fof(f1549,plain,
( spl21_181
| ~ spl21_32
| ~ spl21_95 ),
inference(avatar_split_clause,[],[f808,f801,f338,f1547]) ).
fof(f808,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_32
| ~ spl21_95 ),
inference(resolution,[],[f802,f339]) ).
fof(f1545,plain,
( spl21_180
| ~ spl21_32
| ~ spl21_95 ),
inference(avatar_split_clause,[],[f807,f801,f338,f1543]) ).
fof(f807,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_32
| ~ spl21_95 ),
inference(resolution,[],[f802,f339]) ).
fof(f1537,plain,
( spl21_179
| ~ spl21_24
| ~ spl21_103 ),
inference(avatar_split_clause,[],[f887,f874,f300,f1535]) ).
fof(f887,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_103 ),
inference(duplicate_literal_removal,[],[f879]) ).
fof(f879,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_103 ),
inference(resolution,[],[f875,f301]) ).
fof(f1533,plain,
( spl21_178
| ~ spl21_17
| ~ spl21_103 ),
inference(avatar_split_clause,[],[f878,f874,f267,f1531]) ).
fof(f878,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_103 ),
inference(resolution,[],[f875,f268]) ).
fof(f1529,plain,
( spl21_177
| ~ spl21_50
| ~ spl21_92 ),
inference(avatar_split_clause,[],[f795,f776,f454,f1527]) ).
fof(f795,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,inverse2(X2,sK10(power_set(X0))))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type) )
| ~ spl21_50
| ~ spl21_92 ),
inference(duplicate_literal_removal,[],[f794]) ).
fof(f794,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,inverse2(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_50
| ~ spl21_92 ),
inference(resolution,[],[f777,f455]) ).
fof(f1503,plain,
( ~ spl21_57
| ~ spl21_62
| ~ spl21_5
| spl21_176
| ~ spl21_52
| ~ spl21_72 ),
inference(avatar_split_clause,[],[f833,f645,f468,f1501,f213,f588,f501]) ).
fof(f645,plain,
( spl21_72
<=> ! [X0] : inverse2(sK7,X0) = inverse4(sK4,sK6,sK7,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_72])]) ).
fof(f833,plain,
( ! [X0] :
( ilf_type(inverse2(sK7,X0),subset_type(sK4))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK7,relation_type(sK4,sK6))
| ~ ilf_type(sK6,set_type)
| ~ ilf_type(sK4,set_type) )
| ~ spl21_52
| ~ spl21_72 ),
inference(superposition,[],[f469,f646]) ).
fof(f646,plain,
( ! [X0] : inverse2(sK7,X0) = inverse4(sK4,sK6,sK7,X0)
| ~ spl21_72 ),
inference(avatar_component_clause,[],[f645]) ).
fof(f1495,plain,
( spl21_175
| ~ spl21_9
| ~ spl21_113 ),
inference(avatar_split_clause,[],[f963,f960,f232,f1493]) ).
fof(f960,plain,
( spl21_113
<=> ! [X2,X0,X1] :
( ~ member(X0,inverse2(X1,X2))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X2,set_type)
| ordered_pair(X0,sK16(X2,X0,X1)) = ordered_pair(sK11(ordered_pair(X0,sK16(X2,X0,X1))),sK12(ordered_pair(X0,sK16(X2,X0,X1))))
| ~ ilf_type(ordered_pair(X0,sK16(X2,X0,X1)),set_type)
| ~ sP0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_113])]) ).
fof(f963,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ordered_pair(X1,sK16(X2,X1,X0)) = ordered_pair(sK11(ordered_pair(X1,sK16(X2,X1,X0))),sK12(ordered_pair(X1,sK16(X2,X1,X0))))
| ~ member(X1,inverse2(X0,X2))
| ~ sP0(X0) )
| ~ spl21_9
| ~ spl21_113 ),
inference(resolution,[],[f961,f233]) ).
fof(f961,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(ordered_pair(X0,sK16(X2,X0,X1)),set_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X2,set_type)
| ordered_pair(X0,sK16(X2,X0,X1)) = ordered_pair(sK11(ordered_pair(X0,sK16(X2,X0,X1))),sK12(ordered_pair(X0,sK16(X2,X0,X1))))
| ~ member(X0,inverse2(X1,X2))
| ~ sP0(X1) )
| ~ spl21_113 ),
inference(avatar_component_clause,[],[f960]) ).
fof(f1491,plain,
( spl21_174
| ~ spl21_24
| ~ spl21_101 ),
inference(avatar_split_clause,[],[f868,f844,f300,f1489]) ).
fof(f868,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_101 ),
inference(duplicate_literal_removal,[],[f860]) ).
fof(f860,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_101 ),
inference(resolution,[],[f845,f301]) ).
fof(f1487,plain,
( spl21_173
| ~ spl21_17
| ~ spl21_101 ),
inference(avatar_split_clause,[],[f859,f844,f267,f1485]) ).
fof(f859,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_101 ),
inference(resolution,[],[f845,f268]) ).
fof(f1483,plain,
( spl21_172
| ~ spl21_24
| ~ spl21_100 ),
inference(avatar_split_clause,[],[f857,f840,f300,f1481]) ).
fof(f857,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_100 ),
inference(duplicate_literal_removal,[],[f849]) ).
fof(f849,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_100 ),
inference(resolution,[],[f841,f301]) ).
fof(f1479,plain,
( spl21_171
| ~ spl21_17
| ~ spl21_100 ),
inference(avatar_split_clause,[],[f848,f840,f267,f1477]) ).
fof(f848,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_100 ),
inference(resolution,[],[f841,f268]) ).
fof(f1475,plain,
( spl21_170
| ~ spl21_41
| ~ spl21_95 ),
inference(avatar_split_clause,[],[f813,f801,f382,f1473]) ).
fof(f813,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_41
| ~ spl21_95 ),
inference(duplicate_literal_removal,[],[f810]) ).
fof(f810,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_41
| ~ spl21_95 ),
inference(resolution,[],[f802,f383]) ).
fof(f1471,plain,
( spl21_169
| ~ spl21_47
| ~ spl21_89 ),
inference(avatar_split_clause,[],[f759,f744,f432,f1469]) ).
fof(f1469,plain,
( spl21_169
<=> ! [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_169])]) ).
fof(f744,plain,
( spl21_89
<=> ! [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_89])]) ).
fof(f759,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_47
| ~ spl21_89 ),
inference(resolution,[],[f745,f433]) ).
fof(f745,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_89 ),
inference(avatar_component_clause,[],[f744]) ).
fof(f1461,plain,
( spl21_168
| ~ spl21_32
| ~ spl21_92 ),
inference(avatar_split_clause,[],[f791,f776,f338,f1459]) ).
fof(f791,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_32
| ~ spl21_92 ),
inference(resolution,[],[f777,f339]) ).
fof(f1457,plain,
( spl21_167
| ~ spl21_32
| ~ spl21_92 ),
inference(avatar_split_clause,[],[f790,f776,f338,f1455]) ).
fof(f790,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_32
| ~ spl21_92 ),
inference(resolution,[],[f777,f339]) ).
fof(f1453,plain,
( spl21_166
| ~ spl21_50
| ~ spl21_91 ),
inference(avatar_split_clause,[],[f771,f752,f454,f1451]) ).
fof(f1451,plain,
( spl21_166
<=> ! [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,inverse2(X2,power_set(X0)))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_166])]) ).
fof(f771,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,inverse2(X2,power_set(X0)))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type) )
| ~ spl21_50
| ~ spl21_91 ),
inference(duplicate_literal_removal,[],[f770]) ).
fof(f770,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,inverse2(X2,power_set(X0)))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(power_set(X0),set_type) )
| ~ spl21_50
| ~ spl21_91 ),
inference(resolution,[],[f753,f455]) ).
fof(f1430,plain,
( spl21_165
| ~ spl21_76
| ~ spl21_105 ),
inference(avatar_split_clause,[],[f903,f894,f663,f1428]) ).
fof(f1428,plain,
( spl21_165
<=> ! [X2,X0,X1] :
( member(X0,inverse2(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,inverse2(X1,X2))
| ~ ilf_type(X2,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_165])]) ).
fof(f663,plain,
( spl21_76
<=> ! [X0] :
( member(X0,power_set(X0))
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_76])]) ).
fof(f903,plain,
( ! [X2,X0,X1] :
( member(X0,inverse2(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,inverse2(X1,X2))
| ~ ilf_type(X2,set_type) )
| ~ spl21_76
| ~ spl21_105 ),
inference(duplicate_literal_removal,[],[f902]) ).
fof(f902,plain,
( ! [X2,X0,X1] :
( member(X0,inverse2(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,inverse2(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(sK16(X2,X0,X1),set_type) )
| ~ spl21_76
| ~ spl21_105 ),
inference(resolution,[],[f895,f664]) ).
fof(f664,plain,
( ! [X0] :
( member(X0,power_set(X0))
| ~ ilf_type(X0,set_type) )
| ~ spl21_76 ),
inference(avatar_component_clause,[],[f663]) ).
fof(f1425,plain,
( spl21_164
| ~ spl21_39
| ~ spl21_89 ),
inference(avatar_split_clause,[],[f760,f744,f373,f1423]) ).
fof(f760,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_39
| ~ spl21_89 ),
inference(resolution,[],[f745,f374]) ).
fof(f1420,plain,
( spl21_163
| ~ spl21_41
| ~ spl21_92 ),
inference(avatar_split_clause,[],[f796,f776,f382,f1418]) ).
fof(f796,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_41
| ~ spl21_92 ),
inference(duplicate_literal_removal,[],[f793]) ).
fof(f793,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_41
| ~ spl21_92 ),
inference(resolution,[],[f777,f383]) ).
fof(f1416,plain,
( spl21_162
| ~ spl21_9
| ~ spl21_118 ),
inference(avatar_split_clause,[],[f990,f987,f232,f1414]) ).
fof(f1414,plain,
( spl21_162
<=> ! [X0] :
( ~ empty(X0)
| sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_162])]) ).
fof(f987,plain,
( spl21_118
<=> ! [X0] :
( ~ empty(X0)
| ~ ilf_type(X0,set_type)
| sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_118])]) ).
fof(f990,plain,
( ! [X0] :
( ~ empty(X0)
| sP0(X0) )
| ~ spl21_9
| ~ spl21_118 ),
inference(resolution,[],[f988,f233]) ).
fof(f988,plain,
( ! [X0] :
( ~ ilf_type(X0,set_type)
| ~ empty(X0)
| sP0(X0) )
| ~ spl21_118 ),
inference(avatar_component_clause,[],[f987]) ).
fof(f1410,plain,
( spl21_161
| ~ spl21_32
| ~ spl21_91 ),
inference(avatar_split_clause,[],[f767,f752,f338,f1408]) ).
fof(f767,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_32
| ~ spl21_91 ),
inference(resolution,[],[f753,f339]) ).
fof(f1406,plain,
( spl21_160
| ~ spl21_32
| ~ spl21_91 ),
inference(avatar_split_clause,[],[f766,f752,f338,f1404]) ).
fof(f766,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_32
| ~ spl21_91 ),
inference(resolution,[],[f753,f339]) ).
fof(f1387,plain,
( spl21_159
| ~ spl21_9
| ~ spl21_109 ),
inference(avatar_split_clause,[],[f923,f920,f232,f1385]) ).
fof(f1385,plain,
( spl21_159
<=> ! [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,inverse2(X0,X2))
| ~ sP0(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_159])]) ).
fof(f920,plain,
( spl21_109
<=> ! [X2,X0,X1] :
( ~ member(X0,inverse2(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_109])]) ).
fof(f923,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,inverse2(X0,X2))
| ~ sP0(X2) )
| ~ spl21_9
| ~ spl21_109 ),
inference(resolution,[],[f921,f233]) ).
fof(f921,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,inverse2(X1,X2))
| ~ sP0(X2) )
| ~ spl21_109 ),
inference(avatar_component_clause,[],[f920]) ).
fof(f1345,plain,
( spl21_158
| ~ spl21_9
| ~ spl21_108 ),
inference(avatar_split_clause,[],[f918,f915,f232,f1343]) ).
fof(f915,plain,
( spl21_108
<=> ! [X4,X0,X3,X2,X1] :
( member(sK16(X0,X1,X2),X3)
| ~ ilf_type(X2,relation_type(X4,X3))
| ~ ilf_type(sK16(X0,X1,X2),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,set_type)
| ~ member(X1,inverse2(X2,X0))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_108])]) ).
fof(f918,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ ilf_type(X0,relation_type(X1,X2))
| member(sK16(X3,X4,X0),X2)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(X4,inverse2(X0,X3))
| ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X3,set_type) )
| ~ spl21_9
| ~ spl21_108 ),
inference(resolution,[],[f916,f233]) ).
fof(f916,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ ilf_type(sK16(X0,X1,X2),set_type)
| ~ ilf_type(X2,relation_type(X4,X3))
| member(sK16(X0,X1,X2),X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,set_type)
| ~ member(X1,inverse2(X2,X0))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_108 ),
inference(avatar_component_clause,[],[f915]) ).
fof(f1341,plain,
( spl21_157
| ~ spl21_24
| ~ spl21_95 ),
inference(avatar_split_clause,[],[f814,f801,f300,f1339]) ).
fof(f814,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_95 ),
inference(duplicate_literal_removal,[],[f806]) ).
fof(f806,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_95 ),
inference(resolution,[],[f802,f301]) ).
fof(f1337,plain,
( spl21_156
| ~ spl21_17
| ~ spl21_95 ),
inference(avatar_split_clause,[],[f805,f801,f267,f1335]) ).
fof(f805,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_95 ),
inference(resolution,[],[f802,f268]) ).
fof(f1333,plain,
( spl21_155
| ~ spl21_41
| ~ spl21_91 ),
inference(avatar_split_clause,[],[f772,f752,f382,f1331]) ).
fof(f1331,plain,
( spl21_155
<=> ! [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_155])]) ).
fof(f772,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_41
| ~ spl21_91 ),
inference(duplicate_literal_removal,[],[f769]) ).
fof(f769,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_41
| ~ spl21_91 ),
inference(resolution,[],[f753,f383]) ).
fof(f1329,plain,
( spl21_154
| ~ spl21_54
| ~ spl21_76 ),
inference(avatar_split_clause,[],[f671,f663,f485,f1327]) ).
fof(f671,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(ordered_pair(X0,X1),set_type)
| ~ member(X1,X2)
| member(X0,inverse2(power_set(ordered_pair(X0,X1)),X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(power_set(ordered_pair(X0,X1)),binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X2,set_type) )
| ~ spl21_54
| ~ spl21_76 ),
inference(resolution,[],[f664,f486]) ).
fof(f1324,plain,
( spl21_153
| ~ spl21_53
| ~ spl21_87 ),
inference(avatar_split_clause,[],[f737,f732,f478,f1322]) ).
fof(f732,plain,
( spl21_87
<=> ! [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_87])]) ).
fof(f737,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)
| inverse4(X1,X0,sK18(cross_product(X1,X0)),X2) = inverse2(sK18(cross_product(X1,X0)),X2) )
| ~ spl21_53
| ~ spl21_87 ),
inference(duplicate_literal_removal,[],[f736]) ).
fof(f736,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)
| inverse4(X1,X0,sK18(cross_product(X1,X0)),X2) = inverse2(sK18(cross_product(X1,X0)),X2)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type) )
| ~ spl21_53
| ~ spl21_87 ),
inference(resolution,[],[f733,f479]) ).
fof(f733,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_87 ),
inference(avatar_component_clause,[],[f732]) ).
fof(f1307,plain,
( spl21_152
| ~ spl21_18
| ~ spl21_115 ),
inference(avatar_split_clause,[],[f973,f970,f271,f1305]) ).
fof(f1305,plain,
( spl21_152
<=> ! [X0] : sP2(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_152])]) ).
fof(f271,plain,
( spl21_18
<=> ! [X1] :
( sP2(X1,X1)
| ~ sP3(X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_18])]) ).
fof(f973,plain,
( ! [X0] : sP2(X0,X0)
| ~ spl21_18
| ~ spl21_115 ),
inference(resolution,[],[f971,f272]) ).
fof(f272,plain,
( ! [X1] :
( ~ sP3(X1,X1)
| sP2(X1,X1) )
| ~ spl21_18 ),
inference(avatar_component_clause,[],[f271]) ).
fof(f1303,plain,
( spl21_151
| ~ spl21_9
| ~ spl21_106 ),
inference(avatar_split_clause,[],[f905,f898,f232,f1301]) ).
fof(f898,plain,
( spl21_106
<=> ! [X4,X0,X3,X2,X1] :
( member(X0,X1)
| ~ ilf_type(X2,relation_type(X1,X3))
| ~ ilf_type(sK16(X4,X0,X2),set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(X0,inverse2(X2,X4))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X4,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_106])]) ).
fof(f905,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ ilf_type(X0,relation_type(X1,X2))
| member(X3,X1)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(X3,inverse2(X0,X4))
| ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X4,set_type) )
| ~ spl21_9
| ~ spl21_106 ),
inference(resolution,[],[f899,f233]) ).
fof(f899,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ ilf_type(sK16(X4,X0,X2),set_type)
| ~ ilf_type(X2,relation_type(X1,X3))
| member(X0,X1)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(X0,inverse2(X2,X4))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X4,set_type) )
| ~ spl21_106 ),
inference(avatar_component_clause,[],[f898]) ).
fof(f1299,plain,
( spl21_150
| ~ spl21_55
| ~ spl21_76 ),
inference(avatar_split_clause,[],[f670,f663,f489,f1297]) ).
fof(f1297,plain,
( spl21_150
<=> ! [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_150])]) ).
fof(f670,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_55
| ~ spl21_76 ),
inference(resolution,[],[f664,f490]) ).
fof(f1295,plain,
( spl21_149
| ~ spl21_56
| ~ spl21_76 ),
inference(avatar_split_clause,[],[f669,f663,f493,f1293]) ).
fof(f1293,plain,
( spl21_149
<=> ! [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_149])]) ).
fof(f669,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_56
| ~ spl21_76 ),
inference(resolution,[],[f664,f494]) ).
fof(f1289,plain,
( spl21_148
| ~ spl21_24
| ~ spl21_92 ),
inference(avatar_split_clause,[],[f797,f776,f300,f1287]) ).
fof(f797,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_92 ),
inference(duplicate_literal_removal,[],[f789]) ).
fof(f789,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_92 ),
inference(resolution,[],[f777,f301]) ).
fof(f1285,plain,
( spl21_147
| ~ spl21_17
| ~ spl21_92 ),
inference(avatar_split_clause,[],[f788,f776,f267,f1283]) ).
fof(f788,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_92 ),
inference(resolution,[],[f777,f268]) ).
fof(f1266,plain,
( spl21_146
| ~ spl21_9
| ~ spl21_99 ),
inference(avatar_split_clause,[],[f838,f835,f232,f1264]) ).
fof(f835,plain,
( spl21_99
<=> ! [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_99])]) ).
fof(f838,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_99 ),
inference(resolution,[],[f836,f233]) ).
fof(f836,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_99 ),
inference(avatar_component_clause,[],[f835]) ).
fof(f1257,plain,
( spl21_145
| ~ spl21_17
| ~ spl21_91 ),
inference(avatar_split_clause,[],[f764,f752,f267,f1255]) ).
fof(f1255,plain,
( spl21_145
<=> ! [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_145])]) ).
fof(f764,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_91 ),
inference(resolution,[],[f753,f268]) ).
fof(f1221,plain,
( spl21_144
| ~ spl21_9
| ~ spl21_98 ),
inference(avatar_split_clause,[],[f829,f825,f232,f1219]) ).
fof(f825,plain,
( spl21_98
<=> ! [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_98])]) ).
fof(f829,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_98 ),
inference(resolution,[],[f826,f233]) ).
fof(f826,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_98 ),
inference(avatar_component_clause,[],[f825]) ).
fof(f1217,plain,
( spl21_143
| ~ spl21_9
| ~ spl21_97 ),
inference(avatar_split_clause,[],[f828,f821,f232,f1215]) ).
fof(f1215,plain,
( spl21_143
<=> ! [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_143])]) ).
fof(f821,plain,
( spl21_97
<=> ! [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_97])]) ).
fof(f828,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_97 ),
inference(resolution,[],[f822,f233]) ).
fof(f822,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_97 ),
inference(avatar_component_clause,[],[f821]) ).
fof(f1209,plain,
( spl21_142
| ~ spl21_24
| ~ spl21_91 ),
inference(avatar_split_clause,[],[f773,f752,f300,f1207]) ).
fof(f773,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_91 ),
inference(duplicate_literal_removal,[],[f765]) ).
fof(f765,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_91 ),
inference(resolution,[],[f753,f301]) ).
fof(f1193,plain,
( spl21_141
| ~ spl21_70
| ~ spl21_117 ),
inference(avatar_split_clause,[],[f983,f980,f633,f1190]) ).
fof(f1190,plain,
( spl21_141
<=> sP0(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_141])]) ).
fof(f633,plain,
( spl21_70
<=> relation_like(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_70])]) ).
fof(f983,plain,
( sP0(sK20)
| ~ spl21_70
| ~ spl21_117 ),
inference(resolution,[],[f981,f635]) ).
fof(f635,plain,
( relation_like(sK20)
| ~ spl21_70 ),
inference(avatar_component_clause,[],[f633]) ).
fof(f1188,plain,
( spl21_140
| ~ spl21_9
| ~ spl21_96 ),
inference(avatar_split_clause,[],[f819,f816,f232,f1186]) ).
fof(f816,plain,
( spl21_96
<=> ! [X2,X0,X1] :
( ~ member(X0,inverse2(X1,X2))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(ordered_pair(X0,sK16(X2,X0,X1)),set_type)
| ~ empty(X1)
| ~ ilf_type(X1,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_96])]) ).
fof(f819,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X1,inverse2(X0,X2))
| ~ empty(X0)
| ~ ilf_type(X0,set_type) )
| ~ spl21_9
| ~ spl21_96 ),
inference(resolution,[],[f817,f233]) ).
fof(f817,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(ordered_pair(X0,sK16(X2,X0,X1)),set_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X0,inverse2(X1,X2))
| ~ empty(X1)
| ~ ilf_type(X1,set_type) )
| ~ spl21_96 ),
inference(avatar_component_clause,[],[f816]) ).
fof(f1184,plain,
( spl21_139
| ~ spl21_9
| ~ spl21_94 ),
inference(avatar_split_clause,[],[f799,f784,f232,f1182]) ).
fof(f784,plain,
( spl21_94
<=> ! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| inverse4(X1,X2,sK17(X2,X1),X0) = inverse2(sK17(X2,X1),X0)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_94])]) ).
fof(f799,plain,
( ! [X2,X0,X1] :
( inverse4(X0,X1,sK17(X1,X0),X2) = inverse2(sK17(X1,X0),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_9
| ~ spl21_94 ),
inference(resolution,[],[f785,f233]) ).
fof(f785,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(X2,set_type)
| inverse4(X1,X2,sK17(X2,X1),X0) = inverse2(sK17(X2,X1),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type) )
| ~ spl21_94 ),
inference(avatar_component_clause,[],[f784]) ).
fof(f1172,plain,
( spl21_138
| ~ spl21_9
| ~ spl21_90 ),
inference(avatar_split_clause,[],[f761,f748,f232,f1170]) ).
fof(f748,plain,
( spl21_90
<=> ! [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_90])]) ).
fof(f761,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_90 ),
inference(resolution,[],[f749,f233]) ).
fof(f749,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_90 ),
inference(avatar_component_clause,[],[f748]) ).
fof(f1168,plain,
( spl21_137
| ~ spl21_9
| ~ spl21_88 ),
inference(avatar_split_clause,[],[f758,f740,f232,f1166]) ).
fof(f740,plain,
( spl21_88
<=> ! [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_88])]) ).
fof(f758,plain,
( ! [X0] :
( sK13(X0) = ordered_pair(sK11(sK13(X0)),sK12(sK13(X0)))
| ~ sP0(X0)
| empty(X0)
| ~ ilf_type(X0,set_type) )
| ~ spl21_9
| ~ spl21_88 ),
inference(resolution,[],[f741,f233]) ).
fof(f741,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_88 ),
inference(avatar_component_clause,[],[f740]) ).
fof(f1153,plain,
( spl21_136
| ~ spl21_9
| ~ spl21_93 ),
inference(avatar_split_clause,[],[f798,f780,f232,f1151]) ).
fof(f780,plain,
( spl21_93
<=> ! [X2,X0,X1] :
( ~ member(X0,inverse2(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_93])]) ).
fof(f798,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X1,inverse2(X0,X2))
| ~ empty(X2) )
| ~ spl21_9
| ~ spl21_93 ),
inference(resolution,[],[f781,f233]) ).
fof(f781,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,inverse2(X1,X2))
| ~ empty(X2) )
| ~ spl21_93 ),
inference(avatar_component_clause,[],[f780]) ).
fof(f1146,plain,
( spl21_120
| ~ spl21_6
| ~ spl21_72 ),
inference(avatar_split_clause,[],[f832,f645,f218,f1003]) ).
fof(f218,plain,
( spl21_6
<=> member(sK8,inverse4(sK4,sK6,sK7,sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_6])]) ).
fof(f832,plain,
( member(sK8,inverse2(sK7,sK5))
| ~ spl21_6
| ~ spl21_72 ),
inference(superposition,[],[f220,f646]) ).
fof(f220,plain,
( member(sK8,inverse4(sK4,sK6,sK7,sK5))
| ~ spl21_6 ),
inference(avatar_component_clause,[],[f218]) ).
fof(f1145,plain,
( spl21_135
| ~ spl21_76
| ~ spl21_91 ),
inference(avatar_split_clause,[],[f774,f752,f663,f1143]) ).
fof(f774,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_76
| ~ spl21_91 ),
inference(duplicate_literal_removal,[],[f762]) ).
fof(f762,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_76
| ~ spl21_91 ),
inference(resolution,[],[f753,f664]) ).
fof(f1114,plain,
( spl21_134
| ~ spl21_9
| ~ spl21_86 ),
inference(avatar_split_clause,[],[f730,f726,f232,f1112]) ).
fof(f726,plain,
( spl21_86
<=> ! [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_86])]) ).
fof(f730,plain,
( ! [X0,X1] :
( sP2(X0,X1)
| member(sK14(X0,X1),X1)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) )
| ~ spl21_9
| ~ spl21_86 ),
inference(resolution,[],[f727,f233]) ).
fof(f727,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_86 ),
inference(avatar_component_clause,[],[f726]) ).
fof(f1110,plain,
( spl21_133
| ~ spl21_9
| ~ spl21_85 ),
inference(avatar_split_clause,[],[f729,f722,f232,f1108]) ).
fof(f722,plain,
( spl21_85
<=> ! [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_85])]) ).
fof(f729,plain,
( ! [X0,X1] :
( sP2(X0,X1)
| member(sK14(X0,X1),X0)
| ~ empty(X1)
| ~ ilf_type(X1,set_type) )
| ~ spl21_9
| ~ spl21_85 ),
inference(resolution,[],[f723,f233]) ).
fof(f723,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_85 ),
inference(avatar_component_clause,[],[f722]) ).
fof(f1106,plain,
( spl21_132
| ~ spl21_9
| ~ spl21_83 ),
inference(avatar_split_clause,[],[f715,f711,f232,f1104]) ).
fof(f711,plain,
( spl21_83
<=> ! [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_83])]) ).
fof(f715,plain,
( ! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)) )
| ~ spl21_9
| ~ spl21_83 ),
inference(resolution,[],[f712,f233]) ).
fof(f712,plain,
( ! [X0,X1] :
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)) )
| ~ spl21_83 ),
inference(avatar_component_clause,[],[f711]) ).
fof(f1102,plain,
( spl21_131
| ~ spl21_40
| ~ spl21_76 ),
inference(avatar_split_clause,[],[f673,f663,f378,f1100]) ).
fof(f1100,plain,
( spl21_131
<=> ! [X0] :
( ~ ilf_type(X0,set_type)
| ordered_pair(sK11(X0),sK12(X0)) = X0
| ~ sP0(power_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_131])]) ).
fof(f673,plain,
( ! [X0] :
( ~ ilf_type(X0,set_type)
| ordered_pair(sK11(X0),sK12(X0)) = X0
| ~ sP0(power_set(X0)) )
| ~ spl21_40
| ~ spl21_76 ),
inference(duplicate_literal_removal,[],[f667]) ).
fof(f667,plain,
( ! [X0] :
( ~ ilf_type(X0,set_type)
| ordered_pair(sK11(X0),sK12(X0)) = X0
| ~ ilf_type(X0,set_type)
| ~ sP0(power_set(X0)) )
| ~ spl21_40
| ~ spl21_76 ),
inference(resolution,[],[f664,f379]) ).
fof(f1083,plain,
( spl21_130
| ~ spl21_9
| ~ spl21_84 ),
inference(avatar_split_clause,[],[f720,f717,f232,f1081]) ).
fof(f717,plain,
( spl21_84
<=> ! [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_84])]) ).
fof(f720,plain,
( ! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| member(X1,power_set(X0))
| ~ empty(X1) )
| ~ spl21_9
| ~ spl21_84 ),
inference(resolution,[],[f718,f233]) ).
fof(f718,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_84 ),
inference(avatar_component_clause,[],[f717]) ).
fof(f1078,plain,
( spl21_129
| ~ spl21_9
| ~ spl21_82 ),
inference(avatar_split_clause,[],[f714,f707,f232,f1076]) ).
fof(f707,plain,
( spl21_82
<=> ! [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_82])]) ).
fof(f714,plain,
( ! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| relation_like(sK18(cross_product(X1,X0))) )
| ~ spl21_9
| ~ spl21_82 ),
inference(resolution,[],[f708,f233]) ).
fof(f708,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_82 ),
inference(avatar_component_clause,[],[f707]) ).
fof(f1073,plain,
( spl21_128
| ~ spl21_34
| ~ spl21_81 ),
inference(avatar_split_clause,[],[f705,f699,f346,f1071]) ).
fof(f346,plain,
( spl21_34
<=> ! [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_34])]) ).
fof(f699,plain,
( spl21_81
<=> ! [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_81])]) ).
fof(f705,plain,
( ! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| relation_like(sK17(X0,X1)) )
| ~ spl21_34
| ~ spl21_81 ),
inference(duplicate_literal_removal,[],[f704]) ).
fof(f704,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_34
| ~ spl21_81 ),
inference(resolution,[],[f700,f347]) ).
fof(f347,plain,
( ! [X0,X1] :
( ilf_type(sK17(X0,X1),relation_type(X1,X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_34 ),
inference(avatar_component_clause,[],[f346]) ).
fof(f700,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_81 ),
inference(avatar_component_clause,[],[f699]) ).
fof(f1049,plain,
( spl21_127
| ~ spl21_9
| ~ spl21_80 ),
inference(avatar_split_clause,[],[f702,f695,f232,f1047]) ).
fof(f695,plain,
( spl21_80
<=> ! [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_80])]) ).
fof(f702,plain,
( ! [X0] :
( ~ ilf_type(X0,set_type)
| empty(X0)
| member(sK19(X0),X0) )
| ~ spl21_9
| ~ spl21_80 ),
inference(resolution,[],[f696,f233]) ).
fof(f696,plain,
( ! [X0] :
( ~ ilf_type(sK19(X0),set_type)
| ~ ilf_type(X0,set_type)
| empty(X0)
| member(sK19(X0),X0) )
| ~ spl21_80 ),
inference(avatar_component_clause,[],[f695]) ).
fof(f1043,plain,
( ~ spl21_126
| ~ spl21_61
| spl21_65
| ~ spl21_40
| ~ spl21_63 ),
inference(avatar_split_clause,[],[f1012,f592,f378,f610,f584,f1040]) ).
fof(f1040,plain,
( spl21_126
<=> sP0(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_126])]) ).
fof(f610,plain,
( spl21_65
<=> sK9 = ordered_pair(sK11(sK9),sK12(sK9)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_65])]) ).
fof(f1012,plain,
( sK9 = ordered_pair(sK11(sK9),sK12(sK9))
| ~ ilf_type(sK9,set_type)
| ~ sP0(sK6)
| ~ spl21_40
| ~ spl21_63 ),
inference(resolution,[],[f594,f379]) ).
fof(f594,plain,
( member(sK9,sK6)
| ~ spl21_63 ),
inference(avatar_component_clause,[],[f592]) ).
fof(f1034,plain,
( ~ spl21_37
| ~ spl21_61
| spl21_125
| ~ spl21_12
| ~ spl21_56 ),
inference(avatar_split_clause,[],[f997,f493,f245,f1032,f584,f358]) ).
fof(f1032,plain,
( spl21_125
<=> ! [X0,X1] :
( member(sK9,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_125])]) ).
fof(f997,plain,
( ! [X0,X1] :
( member(sK9,X0)
| ~ ilf_type(sK7,relation_type(X1,X0))
| ~ ilf_type(sK9,set_type)
| ~ ilf_type(sK8,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type) )
| ~ spl21_12
| ~ spl21_56 ),
inference(resolution,[],[f247,f494]) ).
fof(f1030,plain,
( ~ spl21_9
| spl21_124 ),
inference(avatar_contradiction_clause,[],[f1029]) ).
fof(f1029,plain,
( $false
| ~ spl21_9
| spl21_124 ),
inference(resolution,[],[f1025,f233]) ).
fof(f1025,plain,
( ~ ilf_type(ordered_pair(sK8,sK9),set_type)
| spl21_124 ),
inference(avatar_component_clause,[],[f1023]) ).
fof(f1028,plain,
( ~ spl21_9
| spl21_122 ),
inference(avatar_contradiction_clause,[],[f1027]) ).
fof(f1027,plain,
( $false
| ~ spl21_9
| spl21_122 ),
inference(resolution,[],[f1017,f233]) ).
fof(f1017,plain,
( ~ ilf_type(sK7,set_type)
| spl21_122 ),
inference(avatar_component_clause,[],[f1015]) ).
fof(f1026,plain,
( ~ spl21_122
| ~ spl21_123
| ~ spl21_124
| ~ spl21_12
| ~ spl21_29 ),
inference(avatar_split_clause,[],[f1001,f321,f245,f1023,f1019,f1015]) ).
fof(f1001,plain,
( ~ ilf_type(ordered_pair(sK8,sK9),set_type)
| ~ empty(sK7)
| ~ ilf_type(sK7,set_type)
| ~ spl21_12
| ~ spl21_29 ),
inference(resolution,[],[f247,f322]) ).
fof(f1011,plain,
( spl21_121
| ~ spl21_79
| ~ spl21_117 ),
inference(avatar_split_clause,[],[f984,f980,f690,f1008]) ).
fof(f690,plain,
( spl21_79
<=> relation_like(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_79])]) ).
fof(f984,plain,
( sP0(sK7)
| ~ spl21_79
| ~ spl21_117 ),
inference(resolution,[],[f981,f691]) ).
fof(f691,plain,
( relation_like(sK7)
| ~ spl21_79 ),
inference(avatar_component_clause,[],[f690]) ).
fof(f1006,plain,
( ~ spl21_120
| spl21_6
| ~ spl21_72 ),
inference(avatar_split_clause,[],[f995,f645,f218,f1003]) ).
fof(f995,plain,
( ~ member(sK8,inverse2(sK7,sK5))
| spl21_6
| ~ spl21_72 ),
inference(forward_demodulation,[],[f219,f646]) ).
fof(f219,plain,
( ~ member(sK8,inverse4(sK4,sK6,sK7,sK5))
| spl21_6 ),
inference(avatar_component_clause,[],[f218]) ).
fof(f994,plain,
( spl21_3
| ~ spl21_62
| spl21_119
| ~ spl21_46
| ~ spl21_75 ),
inference(avatar_split_clause,[],[f757,f658,f404,f992,f588,f203]) ).
fof(f203,plain,
( spl21_3
<=> empty(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_3])]) ).
fof(f404,plain,
( spl21_46
<=> ! [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_46])]) ).
fof(f658,plain,
( spl21_75
<=> ! [X0] :
( ~ member(sK8,inverse2(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_75])]) ).
fof(f757,plain,
( ! [X0] :
( ~ member(sK16(X0,sK8,sK7),sK5)
| ~ member(sK8,inverse2(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_46
| ~ spl21_75 ),
inference(resolution,[],[f659,f405]) ).
fof(f405,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,[],[f404]) ).
fof(f659,plain,
( ! [X0] :
( ~ ilf_type(sK16(X0,sK8,sK7),member_type(sK6))
| ~ member(sK16(X0,sK8,sK7),sK5)
| ~ member(sK8,inverse2(sK7,X0))
| ~ ilf_type(X0,set_type) )
| ~ spl21_75 ),
inference(avatar_component_clause,[],[f658]) ).
fof(f989,plain,
( spl21_118
| ~ spl21_9
| ~ spl21_78 ),
inference(avatar_split_clause,[],[f688,f685,f232,f987]) ).
fof(f685,plain,
( spl21_78
<=> ! [X0] :
( ~ ilf_type(sK10(X0),set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type)
| sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_78])]) ).
fof(f688,plain,
( ! [X0] :
( ~ empty(X0)
| ~ ilf_type(X0,set_type)
| sP0(X0) )
| ~ spl21_9
| ~ spl21_78 ),
inference(resolution,[],[f686,f233]) ).
fof(f686,plain,
( ! [X0] :
( ~ ilf_type(sK10(X0),set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type)
| sP0(X0) )
| ~ spl21_78 ),
inference(avatar_component_clause,[],[f685]) ).
fof(f982,plain,
( spl21_117
| ~ spl21_15
| ~ spl21_19 ),
inference(avatar_split_clause,[],[f296,f275,f259,f980]) ).
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(f978,plain,
( spl21_116
| ~ spl21_16
| ~ spl21_19 ),
inference(avatar_split_clause,[],[f295,f275,f263,f976]) ).
fof(f976,plain,
( spl21_116
<=> ! [X0] :
( ~ sP0(X0)
| relation_like(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_116])]) ).
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(f972,plain,
( spl21_115
| ~ spl21_9
| ~ spl21_73 ),
inference(avatar_split_clause,[],[f652,f649,f232,f970]) ).
fof(f649,plain,
( spl21_73
<=> ! [X0,X1] :
( sP3(X0,X1)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_73])]) ).
fof(f652,plain,
( ! [X0,X1] : sP3(X0,X1)
| ~ spl21_9
| ~ spl21_73 ),
inference(resolution,[],[f650,f233]) ).
fof(f650,plain,
( ! [X0,X1] :
( ~ ilf_type(X0,set_type)
| sP3(X0,X1) )
| ~ spl21_73 ),
inference(avatar_component_clause,[],[f649]) ).
fof(f968,plain,
( ~ spl21_114
| ~ spl21_37
| spl21_67
| ~ spl21_40
| ~ spl21_58 ),
inference(avatar_split_clause,[],[f551,f505,f378,f619,f358,f965]) ).
fof(f965,plain,
( spl21_114
<=> sP0(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_114])]) ).
fof(f505,plain,
( spl21_58
<=> member(sK8,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_58])]) ).
fof(f551,plain,
( sK8 = ordered_pair(sK11(sK8),sK12(sK8))
| ~ ilf_type(sK8,set_type)
| ~ sP0(sK4)
| ~ spl21_40
| ~ spl21_58 ),
inference(resolution,[],[f507,f379]) ).
fof(f507,plain,
( member(sK8,sK4)
| ~ spl21_58 ),
inference(avatar_component_clause,[],[f505]) ).
fof(f962,plain,
( spl21_113
| ~ spl21_40
| ~ spl21_51 ),
inference(avatar_split_clause,[],[f472,f462,f378,f960]) ).
fof(f472,plain,
( ! [X2,X0,X1] :
( ~ member(X0,inverse2(X1,X2))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X2,set_type)
| ordered_pair(X0,sK16(X2,X0,X1)) = ordered_pair(sK11(ordered_pair(X0,sK16(X2,X0,X1))),sK12(ordered_pair(X0,sK16(X2,X0,X1))))
| ~ ilf_type(ordered_pair(X0,sK16(X2,X0,X1)),set_type)
| ~ sP0(X1) )
| ~ spl21_40
| ~ spl21_51 ),
inference(resolution,[],[f463,f379]) ).
fof(f947,plain,
( spl21_112
| ~ spl21_49
| ~ spl21_51 ),
inference(avatar_split_clause,[],[f474,f462,f445,f945]) ).
fof(f474,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,inverse2(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(X0,sK16(X2,X0,power_set(X1))))
| ~ ilf_type(X3,set_type)
| member(X3,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(ordered_pair(X0,sK16(X2,X0,power_set(X1))),set_type) )
| ~ spl21_49
| ~ spl21_51 ),
inference(resolution,[],[f463,f446]) ).
fof(f932,plain,
( spl21_111
| ~ spl21_49
| ~ spl21_50 ),
inference(avatar_split_clause,[],[f459,f454,f445,f930]) ).
fof(f459,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,inverse2(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_49
| ~ spl21_50 ),
inference(resolution,[],[f455,f446]) ).
fof(f928,plain,
( ~ spl21_110
| spl21_36
| ~ spl21_72 ),
inference(avatar_split_clause,[],[f831,f645,f354,f925]) ).
fof(f925,plain,
( spl21_110
<=> empty(inverse2(sK7,sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_110])]) ).
fof(f354,plain,
( spl21_36
<=> empty(inverse4(sK4,sK6,sK7,sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_36])]) ).
fof(f831,plain,
( ~ empty(inverse2(sK7,sK5))
| spl21_36
| ~ spl21_72 ),
inference(superposition,[],[f356,f646]) ).
fof(f356,plain,
( ~ empty(inverse4(sK4,sK6,sK7,sK5))
| spl21_36 ),
inference(avatar_component_clause,[],[f354]) ).
fof(f922,plain,
( spl21_109
| ~ spl21_40
| ~ spl21_50 ),
inference(avatar_split_clause,[],[f457,f454,f378,f920]) ).
fof(f457,plain,
( ! [X2,X0,X1] :
( ~ member(X0,inverse2(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_40
| ~ spl21_50 ),
inference(resolution,[],[f455,f379]) ).
fof(f917,plain,
( spl21_108
| ~ spl21_51
| ~ spl21_56 ),
inference(avatar_split_clause,[],[f510,f493,f462,f915]) ).
fof(f510,plain,
( ! [X2,X3,X0,X1,X4] :
( member(sK16(X0,X1,X2),X3)
| ~ ilf_type(X2,relation_type(X4,X3))
| ~ ilf_type(sK16(X0,X1,X2),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,set_type)
| ~ member(X1,inverse2(X2,X0))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_51
| ~ spl21_56 ),
inference(duplicate_literal_removal,[],[f509]) ).
fof(f509,plain,
( ! [X2,X3,X0,X1,X4] :
( member(sK16(X0,X1,X2),X3)
| ~ ilf_type(X2,relation_type(X4,X3))
| ~ ilf_type(sK16(X0,X1,X2),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,set_type)
| ~ member(X1,inverse2(X2,X0))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_51
| ~ spl21_56 ),
inference(resolution,[],[f494,f463]) ).
fof(f909,plain,
( spl21_107
| ~ spl21_47
| ~ spl21_52 ),
inference(avatar_split_clause,[],[f475,f468,f432,f907]) ).
fof(f475,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,relation_type(cross_product(X2,X3),X4))
| ~ ilf_type(X4,set_type)
| ~ ilf_type(cross_product(X2,X3),set_type)
| ilf_type(inverse4(cross_product(X2,X3),X4,X1,X0),relation_type(X2,X3))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type) )
| ~ spl21_47
| ~ spl21_52 ),
inference(resolution,[],[f469,f433]) ).
fof(f900,plain,
( spl21_106
| ~ spl21_51
| ~ spl21_55 ),
inference(avatar_split_clause,[],[f499,f489,f462,f898]) ).
fof(f499,plain,
( ! [X2,X3,X0,X1,X4] :
( member(X0,X1)
| ~ ilf_type(X2,relation_type(X1,X3))
| ~ ilf_type(sK16(X4,X0,X2),set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(X0,inverse2(X2,X4))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X4,set_type) )
| ~ spl21_51
| ~ spl21_55 ),
inference(duplicate_literal_removal,[],[f498]) ).
fof(f498,plain,
( ! [X2,X3,X0,X1,X4] :
( member(X0,X1)
| ~ ilf_type(X2,relation_type(X1,X3))
| ~ ilf_type(sK16(X4,X0,X2),set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(X0,inverse2(X2,X4))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X4,set_type) )
| ~ spl21_51
| ~ spl21_55 ),
inference(resolution,[],[f490,f463]) ).
fof(f896,plain,
( spl21_105
| ~ spl21_51
| ~ spl21_54 ),
inference(avatar_split_clause,[],[f497,f485,f462,f894]) ).
fof(f497,plain,
( ! [X2,X3,X0,X1] :
( ~ member(sK16(X0,X1,X2),X3)
| member(X1,inverse2(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,inverse2(X2,X0))
| ~ ilf_type(X0,set_type) )
| ~ spl21_51
| ~ spl21_54 ),
inference(duplicate_literal_removal,[],[f496]) ).
fof(f496,plain,
( ! [X2,X3,X0,X1] :
( ~ member(sK16(X0,X1,X2),X3)
| member(X1,inverse2(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,inverse2(X2,X0))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_51
| ~ spl21_54 ),
inference(resolution,[],[f486,f463]) ).
fof(f892,plain,
( ~ spl21_104
| spl21_66
| ~ spl21_72 ),
inference(avatar_split_clause,[],[f830,f645,f615,f889]) ).
fof(f889,plain,
( spl21_104
<=> sP0(inverse2(sK7,sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_104])]) ).
fof(f615,plain,
( spl21_66
<=> sP0(inverse4(sK4,sK6,sK7,sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_66])]) ).
fof(f830,plain,
( ~ sP0(inverse2(sK7,sK5))
| spl21_66
| ~ spl21_72 ),
inference(superposition,[],[f617,f646]) ).
fof(f617,plain,
( ~ sP0(inverse4(sK4,sK6,sK7,sK5))
| spl21_66 ),
inference(avatar_component_clause,[],[f615]) ).
fof(f876,plain,
( spl21_103
| ~ spl21_41
| ~ spl21_49 ),
inference(avatar_split_clause,[],[f452,f445,f382,f874]) ).
fof(f452,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_41
| ~ spl21_49 ),
inference(resolution,[],[f446,f383]) ).
fof(f872,plain,
( spl21_102
| ~ spl21_39
| ~ spl21_52 ),
inference(avatar_split_clause,[],[f476,f468,f373,f870]) ).
fof(f476,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,relation_type(cross_product(X2,X3),X4))
| ~ ilf_type(X4,set_type)
| ~ ilf_type(cross_product(X2,X3),set_type)
| relation_like(inverse4(cross_product(X2,X3),X4,X1,X0))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type) )
| ~ spl21_39
| ~ spl21_52 ),
inference(resolution,[],[f469,f374]) ).
fof(f846,plain,
( spl21_101
| ~ spl21_32
| ~ spl21_49 ),
inference(avatar_split_clause,[],[f451,f445,f338,f844]) ).
fof(f451,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_32
| ~ spl21_49 ),
inference(resolution,[],[f446,f339]) ).
fof(f842,plain,
( spl21_100
| ~ spl21_32
| ~ spl21_49 ),
inference(avatar_split_clause,[],[f450,f445,f338,f840]) ).
fof(f450,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_32
| ~ spl21_49 ),
inference(resolution,[],[f446,f339]) ).
fof(f837,plain,
( spl21_99
| ~ spl21_40
| ~ spl21_41 ),
inference(avatar_split_clause,[],[f413,f382,f378,f835]) ).
fof(f413,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_40
| ~ spl21_41 ),
inference(resolution,[],[f383,f379]) ).
fof(f827,plain,
( spl21_98
| ~ spl21_32
| ~ spl21_40 ),
inference(avatar_split_clause,[],[f412,f378,f338,f825]) ).
fof(f412,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_32
| ~ spl21_40 ),
inference(resolution,[],[f379,f339]) ).
fof(f823,plain,
( spl21_97
| ~ spl21_32
| ~ spl21_40 ),
inference(avatar_split_clause,[],[f411,f378,f338,f821]) ).
fof(f411,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_32
| ~ spl21_40 ),
inference(resolution,[],[f379,f339]) ).
fof(f818,plain,
( spl21_96
| ~ spl21_29
| ~ spl21_51 ),
inference(avatar_split_clause,[],[f473,f462,f321,f816]) ).
fof(f473,plain,
( ! [X2,X0,X1] :
( ~ member(X0,inverse2(X1,X2))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(ordered_pair(X0,sK16(X2,X0,X1)),set_type)
| ~ empty(X1)
| ~ ilf_type(X1,set_type) )
| ~ spl21_29
| ~ spl21_51 ),
inference(resolution,[],[f463,f322]) ).
fof(f803,plain,
( spl21_95
| ~ spl21_24
| ~ spl21_49 ),
inference(avatar_split_clause,[],[f449,f445,f300,f801]) ).
fof(f449,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_49 ),
inference(resolution,[],[f446,f301]) ).
fof(f786,plain,
( spl21_94
| ~ spl21_34
| ~ spl21_53 ),
inference(avatar_split_clause,[],[f483,f478,f346,f784]) ).
fof(f483,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| inverse4(X1,X2,sK17(X2,X1),X0) = inverse2(sK17(X2,X1),X0)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) )
| ~ spl21_34
| ~ spl21_53 ),
inference(duplicate_literal_removal,[],[f482]) ).
fof(f482,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| inverse4(X1,X2,sK17(X2,X1),X0) = inverse2(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_34
| ~ spl21_53 ),
inference(resolution,[],[f479,f347]) ).
fof(f782,plain,
( spl21_93
| ~ spl21_29
| ~ spl21_50 ),
inference(avatar_split_clause,[],[f460,f454,f321,f780]) ).
fof(f460,plain,
( ! [X2,X0,X1] :
( ~ member(X0,inverse2(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_50 ),
inference(duplicate_literal_removal,[],[f458]) ).
fof(f458,plain,
( ! [X2,X0,X1] :
( ~ member(X0,inverse2(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_50 ),
inference(resolution,[],[f455,f322]) ).
fof(f778,plain,
( spl21_92
| ~ spl21_17
| ~ spl21_49 ),
inference(avatar_split_clause,[],[f448,f445,f267,f776]) ).
fof(f448,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_49 ),
inference(resolution,[],[f446,f268]) ).
fof(f755,plain,
( spl21_79
| ~ spl21_57
| ~ spl21_62
| ~ spl21_5
| ~ spl21_81 ),
inference(avatar_split_clause,[],[f703,f699,f213,f588,f501,f690]) ).
fof(f703,plain,
( ~ ilf_type(sK6,set_type)
| ~ ilf_type(sK4,set_type)
| relation_like(sK7)
| ~ spl21_5
| ~ spl21_81 ),
inference(resolution,[],[f700,f215]) ).
fof(f754,plain,
( spl21_91
| ~ spl21_44
| ~ spl21_46 ),
inference(avatar_split_clause,[],[f430,f404,f396,f752]) ).
fof(f396,plain,
( spl21_44
<=> ! [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_44])]) ).
fof(f430,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,[],[f427]) ).
fof(f427,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,[],[f405,f397]) ).
fof(f397,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,[],[f396]) ).
fof(f750,plain,
( spl21_90
| ~ spl21_43
| ~ spl21_45 ),
inference(avatar_split_clause,[],[f426,f400,f392,f748]) ).
fof(f392,plain,
( spl21_43
<=> ! [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_43])]) ).
fof(f400,plain,
( spl21_45
<=> ! [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_45])]) ).
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(X1,set_type) )
| ~ spl21_43
| ~ spl21_45 ),
inference(duplicate_literal_removal,[],[f421]) ).
fof(f421,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_43
| ~ spl21_45 ),
inference(resolution,[],[f401,f393]) ).
fof(f393,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_43 ),
inference(avatar_component_clause,[],[f392]) ).
fof(f401,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_45 ),
inference(avatar_component_clause,[],[f400]) ).
fof(f746,plain,
( spl21_89
| ~ spl21_27
| ~ spl21_44 ),
inference(avatar_split_clause,[],[f419,f396,f313,f744]) ).
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(f419,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_44 ),
inference(resolution,[],[f397,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(f742,plain,
( spl21_88
| ~ spl21_24
| ~ spl21_40 ),
inference(avatar_split_clause,[],[f410,f378,f300,f740]) ).
fof(f410,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_40 ),
inference(resolution,[],[f379,f301]) ).
fof(f734,plain,
( spl21_87
| ~ spl21_22
| ~ spl21_47 ),
inference(avatar_split_clause,[],[f439,f432,f288,f732]) ).
fof(f439,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_47 ),
inference(resolution,[],[f433,f289]) ).
fof(f728,plain,
( spl21_86
| ~ spl21_29
| ~ spl21_32 ),
inference(avatar_split_clause,[],[f363,f338,f321,f726]) ).
fof(f363,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_32 ),
inference(resolution,[],[f339,f322]) ).
fof(f724,plain,
( spl21_85
| ~ spl21_29
| ~ spl21_32 ),
inference(avatar_split_clause,[],[f362,f338,f321,f722]) ).
fof(f362,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_32 ),
inference(resolution,[],[f339,f322]) ).
fof(f719,plain,
( spl21_84
| ~ spl21_29
| ~ spl21_41 ),
inference(avatar_split_clause,[],[f415,f382,f321,f717]) ).
fof(f415,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_41 ),
inference(duplicate_literal_removal,[],[f414]) ).
fof(f414,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_41 ),
inference(resolution,[],[f383,f322]) ).
fof(f713,plain,
( spl21_83
| ~ spl21_9
| ~ spl21_60 ),
inference(avatar_split_clause,[],[f571,f515,f232,f711]) ).
fof(f515,plain,
( spl21_60
<=> ! [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_60])]) ).
fof(f571,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_60 ),
inference(resolution,[],[f516,f233]) ).
fof(f516,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_60 ),
inference(avatar_component_clause,[],[f515]) ).
fof(f709,plain,
( spl21_82
| ~ spl21_22
| ~ spl21_39 ),
inference(avatar_split_clause,[],[f376,f373,f288,f707]) ).
fof(f376,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_39 ),
inference(resolution,[],[f374,f289]) ).
fof(f701,plain,
( spl21_81
| ~ spl21_39
| ~ spl21_48 ),
inference(avatar_split_clause,[],[f442,f436,f373,f699]) ).
fof(f442,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_39
| ~ spl21_48 ),
inference(duplicate_literal_removal,[],[f441]) ).
fof(f441,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_39
| ~ spl21_48 ),
inference(resolution,[],[f437,f374]) ).
fof(f697,plain,
( spl21_80
| ~ spl21_27
| ~ spl21_45 ),
inference(avatar_split_clause,[],[f425,f400,f313,f695]) ).
fof(f425,plain,
( ! [X0] :
( member(sK19(X0),X0)
| ~ ilf_type(X0,set_type)
| empty(X0)
| ~ ilf_type(sK19(X0),set_type) )
| ~ spl21_27
| ~ spl21_45 ),
inference(duplicate_literal_removal,[],[f424]) ).
fof(f424,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_45 ),
inference(resolution,[],[f401,f314]) ).
fof(f693,plain,
( ~ spl21_79
| ~ spl21_71
| spl21_74 ),
inference(avatar_split_clause,[],[f661,f654,f640,f690]) ).
fof(f640,plain,
( spl21_71
<=> ! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_71])]) ).
fof(f661,plain,
( ~ relation_like(sK7)
| ~ spl21_71
| spl21_74 ),
inference(resolution,[],[f656,f641]) ).
fof(f641,plain,
( ! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) )
| ~ spl21_71 ),
inference(avatar_component_clause,[],[f640]) ).
fof(f656,plain,
( ~ ilf_type(sK7,binary_relation_type)
| spl21_74 ),
inference(avatar_component_clause,[],[f654]) ).
fof(f687,plain,
( spl21_78
| ~ spl21_17
| ~ spl21_29 ),
inference(avatar_split_clause,[],[f326,f321,f267,f685]) ).
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(f678,plain,
( spl21_77
| ~ spl21_32 ),
inference(avatar_split_clause,[],[f364,f338,f676]) ).
fof(f676,plain,
( spl21_77
<=> ! [X0] :
( member(sK14(X0,X0),X0)
| sP2(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_77])]) ).
fof(f364,plain,
( ! [X0] :
( member(sK14(X0,X0),X0)
| sP2(X0,X0) )
| ~ spl21_32 ),
inference(factoring,[],[f339]) ).
fof(f665,plain,
( spl21_76
| ~ spl21_41
| ~ spl21_42 ),
inference(avatar_split_clause,[],[f417,f386,f382,f663]) ).
fof(f417,plain,
( ! [X0] :
( member(X0,power_set(X0))
| ~ ilf_type(X0,set_type) )
| ~ spl21_41
| ~ spl21_42 ),
inference(duplicate_literal_removal,[],[f416]) ).
fof(f416,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_41
| ~ spl21_42 ),
inference(resolution,[],[f387,f383]) ).
fof(f660,plain,
( ~ spl21_37
| ~ spl21_74
| spl21_75
| ~ spl21_11
| ~ spl21_51 ),
inference(avatar_split_clause,[],[f471,f462,f241,f658,f654,f358]) ).
fof(f471,plain,
( ! [X0] :
( ~ member(sK8,inverse2(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_51 ),
inference(resolution,[],[f463,f242]) ).
fof(f651,plain,
( spl21_73
| ~ spl21_9
| ~ spl21_26 ),
inference(avatar_split_clause,[],[f311,f308,f232,f649]) ).
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(f647,plain,
( spl21_72
| ~ spl21_9
| ~ spl21_68 ),
inference(avatar_split_clause,[],[f627,f624,f232,f645]) ).
fof(f624,plain,
( spl21_68
<=> ! [X0] :
( ~ ilf_type(X0,set_type)
| inverse2(sK7,X0) = inverse4(sK4,sK6,sK7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_68])]) ).
fof(f627,plain,
( ! [X0] : inverse2(sK7,X0) = inverse4(sK4,sK6,sK7,X0)
| ~ spl21_9
| ~ spl21_68 ),
inference(resolution,[],[f625,f233]) ).
fof(f625,plain,
( ! [X0] :
( ~ ilf_type(X0,set_type)
| inverse2(sK7,X0) = inverse4(sK4,sK6,sK7,X0) )
| ~ spl21_68 ),
inference(avatar_component_clause,[],[f624]) ).
fof(f642,plain,
( spl21_71
| ~ spl21_9
| ~ spl21_23 ),
inference(avatar_split_clause,[],[f298,f292,f232,f640]) ).
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(f638,plain,
( ~ spl21_9
| spl21_69 ),
inference(avatar_contradiction_clause,[],[f637]) ).
fof(f637,plain,
( $false
| ~ spl21_9
| spl21_69 ),
inference(resolution,[],[f631,f233]) ).
fof(f631,plain,
( ~ ilf_type(sK20,set_type)
| spl21_69 ),
inference(avatar_component_clause,[],[f629]) ).
fof(f629,plain,
( spl21_69
<=> ilf_type(sK20,set_type) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_69])]) ).
fof(f636,plain,
( ~ spl21_69
| spl21_70
| ~ spl21_10
| ~ spl21_21 ),
inference(avatar_split_clause,[],[f297,f284,f236,f633,f629]) ).
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(f626,plain,
( ~ spl21_57
| ~ spl21_62
| spl21_68
| ~ spl21_5
| ~ spl21_53 ),
inference(avatar_split_clause,[],[f481,f478,f213,f624,f588,f501]) ).
fof(f481,plain,
( ! [X0] :
( ~ ilf_type(X0,set_type)
| inverse2(sK7,X0) = inverse4(sK4,sK6,sK7,X0)
| ~ ilf_type(sK6,set_type)
| ~ ilf_type(sK4,set_type) )
| ~ spl21_5
| ~ spl21_53 ),
inference(resolution,[],[f479,f215]) ).
fof(f622,plain,
( ~ spl21_66
| ~ spl21_37
| spl21_67
| ~ spl21_6
| ~ spl21_40 ),
inference(avatar_split_clause,[],[f407,f378,f218,f619,f358,f615]) ).
fof(f407,plain,
( sK8 = ordered_pair(sK11(sK8),sK12(sK8))
| ~ ilf_type(sK8,set_type)
| ~ sP0(inverse4(sK4,sK6,sK7,sK5))
| ~ spl21_6
| ~ spl21_40 ),
inference(resolution,[],[f379,f220]) ).
fof(f613,plain,
( ~ spl21_64
| ~ spl21_61
| spl21_65
| ~ spl21_7
| ~ spl21_40 ),
inference(avatar_split_clause,[],[f408,f378,f222,f610,f584,f606]) ).
fof(f606,plain,
( spl21_64
<=> sP0(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_64])]) ).
fof(f408,plain,
( sK9 = ordered_pair(sK11(sK9),sK12(sK9))
| ~ ilf_type(sK9,set_type)
| ~ sP0(sK5)
| ~ spl21_7
| ~ spl21_40 ),
inference(resolution,[],[f379,f224]) ).
fof(f224,plain,
( member(sK9,sK5)
| ~ spl21_7 ),
inference(avatar_component_clause,[],[f222]) ).
fof(f603,plain,
( ~ spl21_9
| spl21_62 ),
inference(avatar_contradiction_clause,[],[f602]) ).
fof(f602,plain,
( $false
| ~ spl21_9
| spl21_62 ),
inference(resolution,[],[f590,f233]) ).
fof(f590,plain,
( ~ ilf_type(sK6,set_type)
| spl21_62 ),
inference(avatar_component_clause,[],[f588]) ).
fof(f601,plain,
( ~ spl21_9
| spl21_61 ),
inference(avatar_contradiction_clause,[],[f600]) ).
fof(f600,plain,
( $false
| ~ spl21_9
| spl21_61 ),
inference(resolution,[],[f586,f233]) ).
fof(f586,plain,
( ~ ilf_type(sK9,set_type)
| spl21_61 ),
inference(avatar_component_clause,[],[f584]) ).
fof(f595,plain,
( ~ spl21_61
| spl21_3
| ~ spl21_62
| spl21_63
| ~ spl21_8
| ~ spl21_45 ),
inference(avatar_split_clause,[],[f423,f400,f227,f592,f588,f203,f584]) ).
fof(f423,plain,
( member(sK9,sK6)
| ~ ilf_type(sK6,set_type)
| empty(sK6)
| ~ ilf_type(sK9,set_type)
| ~ spl21_8
| ~ spl21_45 ),
inference(resolution,[],[f401,f229]) ).
fof(f229,plain,
( ilf_type(sK9,member_type(sK6))
| ~ spl21_8 ),
inference(avatar_component_clause,[],[f227]) ).
fof(f529,plain,
( ~ spl21_9
| spl21_57 ),
inference(avatar_contradiction_clause,[],[f528]) ).
fof(f528,plain,
( $false
| ~ spl21_9
| spl21_57 ),
inference(resolution,[],[f503,f233]) ).
fof(f503,plain,
( ~ ilf_type(sK4,set_type)
| spl21_57 ),
inference(avatar_component_clause,[],[f501]) ).
fof(f519,plain,
( ~ spl21_9
| ~ spl21_59 ),
inference(avatar_contradiction_clause,[],[f518]) ).
fof(f518,plain,
( $false
| ~ spl21_9
| ~ spl21_59 ),
inference(resolution,[],[f513,f233]) ).
fof(f513,plain,
( ! [X0] : ~ ilf_type(X0,set_type)
| ~ spl21_59 ),
inference(avatar_component_clause,[],[f512]) ).
fof(f512,plain,
( spl21_59
<=> ! [X0] : ~ ilf_type(X0,set_type) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_59])]) ).
fof(f517,plain,
( spl21_59
| spl21_59
| spl21_60 ),
inference(avatar_split_clause,[],[f190,f515,f512,f512]) ).
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/sandbox2/benchmark/theBenchmark.p',p3) ).
fof(f508,plain,
( ~ spl21_37
| spl21_1
| ~ spl21_57
| spl21_58
| ~ spl21_4
| ~ spl21_45 ),
inference(avatar_split_clause,[],[f422,f400,f208,f505,f501,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(f422,plain,
( member(sK8,sK4)
| ~ ilf_type(sK4,set_type)
| empty(sK4)
| ~ ilf_type(sK8,set_type)
| ~ spl21_4
| ~ spl21_45 ),
inference(resolution,[],[f401,f210]) ).
fof(f210,plain,
( ilf_type(sK8,member_type(sK4))
| ~ spl21_4 ),
inference(avatar_component_clause,[],[f208]) ).
fof(f495,plain,
spl21_56,
inference(avatar_split_clause,[],[f177,f493]) ).
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/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(f491,plain,
spl21_55,
inference(avatar_split_clause,[],[f176,f489]) ).
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(f487,plain,
spl21_54,
inference(avatar_split_clause,[],[f173,f485]) ).
fof(f173,plain,
! [X2,X3,X0,X1] :
( member(X1,inverse2(X2,X0))
| ~ member(X3,X0)
| ~ member(ordered_pair(X1,X3),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,inverse2(X2,X0))
| ! [X3] :
( ~ member(X3,X0)
| ~ member(ordered_pair(X1,X3),X2)
| ~ ilf_type(X3,set_type) ) )
& ( ( member(sK16(X0,X1,X2),X0)
& member(ordered_pair(X1,sK16(X0,X1,X2)),X2)
& ilf_type(sK16(X0,X1,X2),set_type) )
| ~ member(X1,inverse2(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(X1,X4),X2)
& ilf_type(X4,set_type) )
=> ( member(sK16(X0,X1,X2),X0)
& member(ordered_pair(X1,sK16(X0,X1,X2)),X2)
& ilf_type(sK16(X0,X1,X2),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f105,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( member(X1,inverse2(X2,X0))
| ! [X3] :
( ~ member(X3,X0)
| ~ member(ordered_pair(X1,X3),X2)
| ~ ilf_type(X3,set_type) ) )
& ( ? [X4] :
( member(X4,X0)
& member(ordered_pair(X1,X4),X2)
& ilf_type(X4,set_type) )
| ~ member(X1,inverse2(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,inverse2(X2,X0))
| ! [X3] :
( ~ member(X3,X0)
| ~ member(ordered_pair(X1,X3),X2)
| ~ ilf_type(X3,set_type) ) )
& ( ? [X3] :
( member(X3,X0)
& member(ordered_pair(X1,X3),X2)
& ilf_type(X3,set_type) )
| ~ member(X1,inverse2(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,inverse2(X2,X0))
<=> ? [X3] :
( member(X3,X0)
& member(ordered_pair(X1,X3),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,inverse2(X2,X0))
<=> ? [X3] :
( member(X3,X0)
& member(ordered_pair(X1,X3),X2)
& ilf_type(X3,set_type) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(f480,plain,
spl21_53,
inference(avatar_split_clause,[],[f179,f478]) ).
fof(f179,plain,
! [X2,X3,X0,X1] :
( inverse4(X0,X1,X2,X3) = inverse2(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] :
( inverse4(X0,X1,X2,X3) = inverse2(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)
=> inverse4(X0,X1,X2,X3) = inverse2(X2,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p25) ).
fof(f470,plain,
spl21_52,
inference(avatar_split_clause,[],[f178,f468]) ).
fof(f178,plain,
! [X2,X3,X0,X1] :
( ilf_type(inverse4(X0,X1,X2,X3),subset_type(X0))
| ~ 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(inverse4(X0,X1,X2,X3),subset_type(X0))
| ~ 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(inverse4(X0,X1,X2,X3),subset_type(X0)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p26) ).
fof(f466,plain,
( ~ spl21_9
| spl21_35 ),
inference(avatar_contradiction_clause,[],[f465]) ).
fof(f465,plain,
( $false
| ~ spl21_9
| spl21_35 ),
inference(resolution,[],[f352,f233]) ).
fof(f352,plain,
( ~ ilf_type(inverse4(sK4,sK6,sK7,sK5),set_type)
| spl21_35 ),
inference(avatar_component_clause,[],[f350]) ).
fof(f350,plain,
( spl21_35
<=> ilf_type(inverse4(sK4,sK6,sK7,sK5),set_type) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_35])]) ).
fof(f464,plain,
spl21_51,
inference(avatar_split_clause,[],[f171,f462]) ).
fof(f171,plain,
! [X2,X0,X1] :
( member(ordered_pair(X1,sK16(X0,X1,X2)),X2)
| ~ member(X1,inverse2(X2,X0))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f107]) ).
fof(f456,plain,
spl21_50,
inference(avatar_split_clause,[],[f172,f454]) ).
fof(f172,plain,
! [X2,X0,X1] :
( member(sK16(X0,X1,X2),X0)
| ~ member(X1,inverse2(X2,X0))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f107]) ).
fof(f447,plain,
spl21_49,
inference(avatar_split_clause,[],[f164,f445]) ).
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/sandbox2/benchmark/theBenchmark.p',p20) ).
fof(f438,plain,
spl21_48,
inference(avatar_split_clause,[],[f155,f436]) ).
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/sandbox2/benchmark/theBenchmark.p',p5) ).
fof(f434,plain,
spl21_47,
inference(avatar_split_clause,[],[f154,f432]) ).
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(f406,plain,
spl21_46,
inference(avatar_split_clause,[],[f183,f404]) ).
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/sandbox2/benchmark/theBenchmark.p',p7) ).
fof(f402,plain,
spl21_45,
inference(avatar_split_clause,[],[f182,f400]) ).
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(f398,plain,
spl21_44,
inference(avatar_split_clause,[],[f169,f396]) ).
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/sandbox2/benchmark/theBenchmark.p',p17) ).
fof(f394,plain,
spl21_43,
inference(avatar_split_clause,[],[f168,f392]) ).
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(f390,plain,
( ~ spl21_9
| spl21_37 ),
inference(avatar_contradiction_clause,[],[f389]) ).
fof(f389,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(f388,plain,
spl21_42,
inference(avatar_split_clause,[],[f167,f386]) ).
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(f384,plain,
spl21_41,
inference(avatar_split_clause,[],[f166,f382]) ).
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(f380,plain,
spl21_40,
inference(avatar_split_clause,[],[f139,f378]) ).
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(f375,plain,
spl21_39,
inference(avatar_split_clause,[],[f180,f373]) ).
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/sandbox2/benchmark/theBenchmark.p',p24) ).
fof(f371,plain,
spl21_38,
inference(avatar_split_clause,[],[f142,f369]) ).
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(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(inverse4(sK4,sK6,sK7,sK5))
| ~ ilf_type(inverse4(sK4,sK6,sK7,sK5),set_type)
| ~ spl21_6
| ~ spl21_29 ),
inference(resolution,[],[f322,f220]) ).
fof(f348,plain,
spl21_34,
inference(avatar_split_clause,[],[f181,f346]) ).
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/sandbox2/benchmark/theBenchmark.p',p6) ).
fof(f344,plain,
spl21_33,
inference(avatar_split_clause,[],[f162,f342]) ).
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(f340,plain,
spl21_32,
inference(avatar_split_clause,[],[f161,f338]) ).
fof(f161,plain,
! [X0,X1] :
( sP2(X0,X1)
| member(sK14(X0,X1),X0)
| member(sK14(X0,X1),X1) ),
inference(cnf_transformation,[],[f98]) ).
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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',p22) ).
fof(f248,plain,
( spl21_6
| spl21_12 ),
inference(avatar_split_clause,[],[f127,f245,f218]) ).
fof(f127,plain,
( member(ordered_pair(sK8,sK9),sK7)
| member(sK8,inverse4(sK4,sK6,sK7,sK5)) ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
( ( ! [X5] :
( ~ member(X5,sK5)
| ~ member(ordered_pair(sK8,X5),sK7)
| ~ ilf_type(X5,member_type(sK6)) )
| ~ member(sK8,inverse4(sK4,sK6,sK7,sK5)) )
& ( ( member(sK9,sK5)
& member(ordered_pair(sK8,sK9),sK7)
& ilf_type(sK9,member_type(sK6)) )
| member(sK8,inverse4(sK4,sK6,sK7,sK5)) )
& ilf_type(sK8,member_type(sK4))
& ilf_type(sK7,relation_type(sK4,sK6))
& 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(X4,X5),X3)
| ~ ilf_type(X5,member_type(X2)) )
| ~ member(X4,inverse4(X0,X2,X3,X1)) )
& ( ? [X6] :
( member(X6,X1)
& member(ordered_pair(X4,X6),X3)
& ilf_type(X6,member_type(X2)) )
| member(X4,inverse4(X0,X2,X3,X1)) )
& ilf_type(X4,member_type(X0)) )
& ilf_type(X3,relation_type(X0,X2)) )
& 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(X4,X5),X3)
| ~ ilf_type(X5,member_type(X2)) )
| ~ member(X4,inverse4(sK4,X2,X3,X1)) )
& ( ? [X6] :
( member(X6,X1)
& member(ordered_pair(X4,X6),X3)
& ilf_type(X6,member_type(X2)) )
| member(X4,inverse4(sK4,X2,X3,X1)) )
& ilf_type(X4,member_type(sK4)) )
& ilf_type(X3,relation_type(sK4,X2)) )
& 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(X4,X5),X3)
| ~ ilf_type(X5,member_type(X2)) )
| ~ member(X4,inverse4(sK4,X2,X3,X1)) )
& ( ? [X6] :
( member(X6,X1)
& member(ordered_pair(X4,X6),X3)
& ilf_type(X6,member_type(X2)) )
| member(X4,inverse4(sK4,X2,X3,X1)) )
& ilf_type(X4,member_type(sK4)) )
& ilf_type(X3,relation_type(sK4,X2)) )
& ilf_type(X2,set_type)
& ~ empty(X2) )
& ilf_type(X1,set_type)
& ~ empty(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( ! [X5] :
( ~ member(X5,sK5)
| ~ member(ordered_pair(X4,X5),X3)
| ~ ilf_type(X5,member_type(X2)) )
| ~ member(X4,inverse4(sK4,X2,X3,sK5)) )
& ( ? [X6] :
( member(X6,sK5)
& member(ordered_pair(X4,X6),X3)
& ilf_type(X6,member_type(X2)) )
| member(X4,inverse4(sK4,X2,X3,sK5)) )
& ilf_type(X4,member_type(sK4)) )
& ilf_type(X3,relation_type(sK4,X2)) )
& 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(X4,X5),X3)
| ~ ilf_type(X5,member_type(X2)) )
| ~ member(X4,inverse4(sK4,X2,X3,sK5)) )
& ( ? [X6] :
( member(X6,sK5)
& member(ordered_pair(X4,X6),X3)
& ilf_type(X6,member_type(X2)) )
| member(X4,inverse4(sK4,X2,X3,sK5)) )
& ilf_type(X4,member_type(sK4)) )
& ilf_type(X3,relation_type(sK4,X2)) )
& ilf_type(X2,set_type)
& ~ empty(X2) )
=> ( ? [X3] :
( ? [X4] :
( ( ! [X5] :
( ~ member(X5,sK5)
| ~ member(ordered_pair(X4,X5),X3)
| ~ ilf_type(X5,member_type(sK6)) )
| ~ member(X4,inverse4(sK4,sK6,X3,sK5)) )
& ( ? [X6] :
( member(X6,sK5)
& member(ordered_pair(X4,X6),X3)
& ilf_type(X6,member_type(sK6)) )
| member(X4,inverse4(sK4,sK6,X3,sK5)) )
& ilf_type(X4,member_type(sK4)) )
& ilf_type(X3,relation_type(sK4,sK6)) )
& ilf_type(sK6,set_type)
& ~ empty(sK6) ) ),
introduced(choice_axiom,[]) ).
fof(f76,plain,
( ? [X3] :
( ? [X4] :
( ( ! [X5] :
( ~ member(X5,sK5)
| ~ member(ordered_pair(X4,X5),X3)
| ~ ilf_type(X5,member_type(sK6)) )
| ~ member(X4,inverse4(sK4,sK6,X3,sK5)) )
& ( ? [X6] :
( member(X6,sK5)
& member(ordered_pair(X4,X6),X3)
& ilf_type(X6,member_type(sK6)) )
| member(X4,inverse4(sK4,sK6,X3,sK5)) )
& ilf_type(X4,member_type(sK4)) )
& ilf_type(X3,relation_type(sK4,sK6)) )
=> ( ? [X4] :
( ( ! [X5] :
( ~ member(X5,sK5)
| ~ member(ordered_pair(X4,X5),sK7)
| ~ ilf_type(X5,member_type(sK6)) )
| ~ member(X4,inverse4(sK4,sK6,sK7,sK5)) )
& ( ? [X6] :
( member(X6,sK5)
& member(ordered_pair(X4,X6),sK7)
& ilf_type(X6,member_type(sK6)) )
| member(X4,inverse4(sK4,sK6,sK7,sK5)) )
& ilf_type(X4,member_type(sK4)) )
& ilf_type(sK7,relation_type(sK4,sK6)) ) ),
introduced(choice_axiom,[]) ).
fof(f77,plain,
( ? [X4] :
( ( ! [X5] :
( ~ member(X5,sK5)
| ~ member(ordered_pair(X4,X5),sK7)
| ~ ilf_type(X5,member_type(sK6)) )
| ~ member(X4,inverse4(sK4,sK6,sK7,sK5)) )
& ( ? [X6] :
( member(X6,sK5)
& member(ordered_pair(X4,X6),sK7)
& ilf_type(X6,member_type(sK6)) )
| member(X4,inverse4(sK4,sK6,sK7,sK5)) )
& ilf_type(X4,member_type(sK4)) )
=> ( ( ! [X5] :
( ~ member(X5,sK5)
| ~ member(ordered_pair(sK8,X5),sK7)
| ~ ilf_type(X5,member_type(sK6)) )
| ~ member(sK8,inverse4(sK4,sK6,sK7,sK5)) )
& ( ? [X6] :
( member(X6,sK5)
& member(ordered_pair(sK8,X6),sK7)
& ilf_type(X6,member_type(sK6)) )
| member(sK8,inverse4(sK4,sK6,sK7,sK5)) )
& ilf_type(sK8,member_type(sK4)) ) ),
introduced(choice_axiom,[]) ).
fof(f78,plain,
( ? [X6] :
( member(X6,sK5)
& member(ordered_pair(sK8,X6),sK7)
& ilf_type(X6,member_type(sK6)) )
=> ( member(sK9,sK5)
& member(ordered_pair(sK8,sK9),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(X4,X5),X3)
| ~ ilf_type(X5,member_type(X2)) )
| ~ member(X4,inverse4(X0,X2,X3,X1)) )
& ( ? [X6] :
( member(X6,X1)
& member(ordered_pair(X4,X6),X3)
& ilf_type(X6,member_type(X2)) )
| member(X4,inverse4(X0,X2,X3,X1)) )
& ilf_type(X4,member_type(X0)) )
& ilf_type(X3,relation_type(X0,X2)) )
& 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(X4,X5),X3)
| ~ ilf_type(X5,member_type(X2)) )
| ~ member(X4,inverse4(X0,X2,X3,X1)) )
& ( ? [X5] :
( member(X5,X1)
& member(ordered_pair(X4,X5),X3)
& ilf_type(X5,member_type(X2)) )
| member(X4,inverse4(X0,X2,X3,X1)) )
& ilf_type(X4,member_type(X0)) )
& ilf_type(X3,relation_type(X0,X2)) )
& 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(X4,X5),X3)
| ~ ilf_type(X5,member_type(X2)) )
| ~ member(X4,inverse4(X0,X2,X3,X1)) )
& ( ? [X5] :
( member(X5,X1)
& member(ordered_pair(X4,X5),X3)
& ilf_type(X5,member_type(X2)) )
| member(X4,inverse4(X0,X2,X3,X1)) )
& ilf_type(X4,member_type(X0)) )
& ilf_type(X3,relation_type(X0,X2)) )
& 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,inverse4(X0,X2,X3,X1))
<~> ? [X5] :
( member(X5,X1)
& member(ordered_pair(X4,X5),X3)
& ilf_type(X5,member_type(X2)) ) )
& ilf_type(X4,member_type(X0)) )
& ilf_type(X3,relation_type(X0,X2)) )
& 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,inverse4(X0,X2,X3,X1))
<~> ? [X5] :
( member(X5,X1)
& member(ordered_pair(X4,X5),X3)
& ilf_type(X5,member_type(X2)) ) )
& ilf_type(X4,member_type(X0)) )
& ilf_type(X3,relation_type(X0,X2)) )
& 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(X0,X2))
=> ! [X4] :
( ilf_type(X4,member_type(X0))
=> ( member(X4,inverse4(X0,X2,X3,X1))
<=> ? [X5] :
( member(X5,X1)
& member(ordered_pair(X4,X5),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(X0,X2))
=> ! [X4] :
( ilf_type(X4,member_type(X0))
=> ( member(X4,inverse4(X0,X2,X3,X1))
<=> ? [X5] :
( member(X5,X1)
& member(ordered_pair(X4,X5),X3)
& ilf_type(X5,member_type(X2)) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_53) ).
fof(f243,plain,
( ~ spl21_6
| spl21_11 ),
inference(avatar_split_clause,[],[f129,f241,f218]) ).
fof(f129,plain,
! [X5] :
( ~ member(X5,sK5)
| ~ member(ordered_pair(sK8,X5),sK7)
| ~ ilf_type(X5,member_type(sK6))
| ~ member(sK8,inverse4(sK4,sK6,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/sandbox2/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/sandbox2/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,inverse4(sK4,sK6,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,inverse4(sK4,sK6,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(sK4,sK6)),
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
% 0.07/0.12 % Problem : SET686+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n010.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Apr 30 01:02:35 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (21118)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37 % (21121)WARNING: value z3 for option sas not known
% 0.14/0.37 % (21122)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.37 % (21120)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.37 % (21124)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)
% 0.14/0.37 % (21119)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.37 % (21123)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)
% 0.14/0.37 % (21125)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)
% 0.14/0.37 % (21121)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)
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [2]
% 0.20/0.39 TRYING [3]
% 0.20/0.39 TRYING [1]
% 0.20/0.40 TRYING [2]
% 0.20/0.43 TRYING [4]
% 0.20/0.44 TRYING [3]
% 0.20/0.51 % (21123)First to succeed.
% 1.28/0.53 % (21123)Refutation found. Thanks to Tanya!
% 1.28/0.53 % SZS status Theorem for theBenchmark
% 1.28/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 1.28/0.54 % (21123)------------------------------
% 1.28/0.54 % (21123)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 1.28/0.54 % (21123)Termination reason: Refutation
% 1.28/0.54
% 1.28/0.54 % (21123)Memory used [KB]: 3297
% 1.28/0.54 % (21123)Time elapsed: 0.161 s
% 1.28/0.54 % (21123)Instructions burned: 347 (million)
% 1.28/0.54 % (21123)------------------------------
% 1.28/0.54 % (21123)------------------------------
% 1.28/0.54 % (21118)Success in time 0.174 s
%------------------------------------------------------------------------------