TSTP Solution File: SEU291+1 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU291+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 09:32:36 EDT 2024
% Result : Theorem 0.21s 0.44s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 380
% Syntax : Number of formulae : 1309 ( 128 unt; 0 def)
% Number of atoms : 4004 ( 317 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 4857 (2162 ~;2190 |; 134 &)
% ( 327 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 331 ( 329 usr; 318 prp; 0-3 aty)
% Number of functors : 26 ( 26 usr; 15 con; 0-3 aty)
% Number of variables : 1392 (1341 !; 51 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2609,plain,
$false,
inference(avatar_sat_refutation,[],[f224,f229,f234,f239,f248,f253,f258,f263,f268,f273,f278,f283,f288,f293,f298,f303,f308,f313,f318,f323,f328,f333,f338,f343,f348,f353,f362,f366,f370,f374,f378,f382,f386,f390,f394,f398,f402,f418,f422,f427,f431,f435,f439,f443,f461,f465,f471,f475,f479,f483,f487,f491,f495,f499,f504,f510,f514,f518,f523,f527,f531,f553,f557,f561,f565,f569,f573,f594,f599,f609,f613,f628,f632,f636,f640,f651,f662,f666,f673,f680,f688,f692,f696,f701,f706,f711,f715,f722,f730,f735,f741,f746,f751,f756,f760,f761,f769,f774,f781,f798,f806,f811,f817,f821,f825,f832,f839,f840,f841,f842,f843,f844,f863,f868,f900,f904,f908,f912,f916,f920,f924,f928,f932,f936,f940,f957,f986,f990,f995,f999,f1011,f1015,f1019,f1047,f1051,f1055,f1059,f1063,f1084,f1088,f1092,f1096,f1110,f1114,f1118,f1122,f1147,f1151,f1168,f1172,f1176,f1187,f1191,f1202,f1211,f1220,f1224,f1228,f1245,f1250,f1272,f1277,f1281,f1288,f1292,f1296,f1307,f1314,f1323,f1328,f1333,f1337,f1341,f1345,f1359,f1376,f1380,f1384,f1388,f1392,f1410,f1421,f1446,f1458,f1462,f1466,f1470,f1474,f1502,f1506,f1510,f1514,f1518,f1568,f1574,f1578,f1582,f1595,f1599,f1603,f1607,f1611,f1615,f1619,f1623,f1627,f1656,f1660,f1688,f1692,f1696,f1700,f1705,f1709,f1726,f1730,f1734,f1738,f1748,f1752,f1756,f1760,f1767,f1781,f1785,f1789,f1793,f1807,f1811,f1815,f1819,f1841,f1846,f1851,f1855,f1859,f1863,f1872,f1876,f1880,f1884,f1889,f1891,f1896,f1902,f1915,f1916,f1920,f1930,f1935,f1942,f1947,f1953,f1958,f1963,f1965,f1969,f1978,f1987,f1991,f1998,f2005,f2026,f2031,f2035,f2049,f2053,f2054,f2058,f2066,f2070,f2074,f2098,f2103,f2107,f2111,f2115,f2119,f2123,f2127,f2131,f2135,f2139,f2144,f2149,f2195,f2202,f2206,f2210,f2214,f2218,f2222,f2226,f2230,f2231,f2299,f2304,f2305,f2335,f2340,f2402,f2408,f2414,f2419,f2424,f2434,f2440,f2445,f2456,f2458,f2475,f2480,f2485,f2490,f2500,f2506,f2508,f2519,f2524,f2552,f2557,f2561,f2565,f2570,f2575,f2580,f2584,f2588,f2592,f2607,f2608]) ).
fof(f2608,plain,
( spl22_294
| ~ spl22_56
| ~ spl22_301 ),
inference(avatar_split_clause,[],[f2491,f2482,f497,f2421]) ).
fof(f2421,plain,
( spl22_294
<=> sK13 = relation_dom(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_294])]) ).
fof(f497,plain,
( spl22_56
<=> ! [X0] :
( ~ subset(X0,sK13)
| sK13 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_56])]) ).
fof(f2482,plain,
( spl22_301
<=> subset(relation_dom(sK4),sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_301])]) ).
fof(f2491,plain,
( sK13 = relation_dom(sK4)
| ~ spl22_56
| ~ spl22_301 ),
inference(resolution,[],[f2484,f498]) ).
fof(f498,plain,
( ! [X0] :
( ~ subset(X0,sK13)
| sK13 = X0 )
| ~ spl22_56 ),
inference(avatar_component_clause,[],[f497]) ).
fof(f2484,plain,
( subset(relation_dom(sK4),sK13)
| ~ spl22_301 ),
inference(avatar_component_clause,[],[f2482]) ).
fof(f2607,plain,
( spl22_317
| ~ spl22_160
| ~ spl22_166 ),
inference(avatar_split_clause,[],[f2253,f1311,f1275,f2605]) ).
fof(f2605,plain,
( spl22_317
<=> ! [X0] :
( element(X0,cartesian_product2(sK13,sK3))
| ~ in(X0,sK4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_317])]) ).
fof(f1275,plain,
( spl22_160
<=> ! [X0] :
( ~ in(X0,sK4)
| element(X0,cartesian_product2(sK1,sK3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_160])]) ).
fof(f1311,plain,
( spl22_166
<=> sK1 = sK13 ),
introduced(avatar_definition,[new_symbols(naming,[spl22_166])]) ).
fof(f2253,plain,
( ! [X0] :
( element(X0,cartesian_product2(sK13,sK3))
| ~ in(X0,sK4) )
| ~ spl22_160
| ~ spl22_166 ),
inference(superposition,[],[f1276,f1313]) ).
fof(f1313,plain,
( sK1 = sK13
| ~ spl22_166 ),
inference(avatar_component_clause,[],[f1311]) ).
fof(f1276,plain,
( ! [X0] :
( element(X0,cartesian_product2(sK1,sK3))
| ~ in(X0,sK4) )
| ~ spl22_160 ),
inference(avatar_component_clause,[],[f1275]) ).
fof(f2592,plain,
( spl22_316
| ~ spl22_166
| ~ spl22_249 ),
inference(avatar_split_clause,[],[f2307,f1951,f1311,f2590]) ).
fof(f2590,plain,
( spl22_316
<=> ! [X0] :
( element(X0,sK13)
| ~ in(X0,relation_dom(sK4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_316])]) ).
fof(f1951,plain,
( spl22_249
<=> ! [X0] :
( ~ in(X0,relation_dom(sK4))
| element(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_249])]) ).
fof(f2307,plain,
( ! [X0] :
( element(X0,sK13)
| ~ in(X0,relation_dom(sK4)) )
| ~ spl22_166
| ~ spl22_249 ),
inference(forward_demodulation,[],[f1952,f1313]) ).
fof(f1952,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sK4))
| element(X0,sK1) )
| ~ spl22_249 ),
inference(avatar_component_clause,[],[f1951]) ).
fof(f2588,plain,
( spl22_315
| ~ spl22_101
| ~ spl22_166
| ~ spl22_192 ),
inference(avatar_split_clause,[],[f2289,f1572,f1311,f795,f2586]) ).
fof(f2586,plain,
( spl22_315
<=> ! [X0] :
( ~ subset(sK13,X0)
| ~ empty(cartesian_product2(sK13,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_315])]) ).
fof(f795,plain,
( spl22_101
<=> sK2 = sK13 ),
introduced(avatar_definition,[new_symbols(naming,[spl22_101])]) ).
fof(f1572,plain,
( spl22_192
<=> ! [X0] :
( ~ empty(cartesian_product2(sK1,X0))
| ~ subset(sK2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_192])]) ).
fof(f2289,plain,
( ! [X0] :
( ~ subset(sK13,X0)
| ~ empty(cartesian_product2(sK13,X0)) )
| ~ spl22_101
| ~ spl22_166
| ~ spl22_192 ),
inference(forward_demodulation,[],[f2255,f796]) ).
fof(f796,plain,
( sK2 = sK13
| ~ spl22_101 ),
inference(avatar_component_clause,[],[f795]) ).
fof(f2255,plain,
( ! [X0] :
( ~ empty(cartesian_product2(sK13,X0))
| ~ subset(sK2,X0) )
| ~ spl22_166
| ~ spl22_192 ),
inference(superposition,[],[f1573,f1313]) ).
fof(f1573,plain,
( ! [X0] :
( ~ empty(cartesian_product2(sK1,X0))
| ~ subset(sK2,X0) )
| ~ spl22_192 ),
inference(avatar_component_clause,[],[f1572]) ).
fof(f2584,plain,
( spl22_314
| ~ spl22_101
| ~ spl22_121
| ~ spl22_166 ),
inference(avatar_split_clause,[],[f2279,f1311,f955,f795,f2582]) ).
fof(f2582,plain,
( spl22_314
<=> ! [X0] :
( ~ subset(sK13,X0)
| sP0(sK13,sK4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_314])]) ).
fof(f955,plain,
( spl22_121
<=> ! [X0] :
( ~ subset(sK2,X0)
| sP0(sK1,sK4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_121])]) ).
fof(f2279,plain,
( ! [X0] :
( ~ subset(sK13,X0)
| sP0(sK13,sK4,X0) )
| ~ spl22_101
| ~ spl22_121
| ~ spl22_166 ),
inference(forward_demodulation,[],[f2246,f796]) ).
fof(f2246,plain,
( ! [X0] :
( sP0(sK13,sK4,X0)
| ~ subset(sK2,X0) )
| ~ spl22_121
| ~ spl22_166 ),
inference(superposition,[],[f956,f1313]) ).
fof(f956,plain,
( ! [X0] :
( sP0(sK1,sK4,X0)
| ~ subset(sK2,X0) )
| ~ spl22_121 ),
inference(avatar_component_clause,[],[f955]) ).
fof(f2580,plain,
( ~ spl22_313
| ~ spl22_101
| spl22_220 ),
inference(avatar_split_clause,[],[f2325,f1764,f795,f2577]) ).
fof(f2577,plain,
( spl22_313
<=> in(sK6(sK13),sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_313])]) ).
fof(f1764,plain,
( spl22_220
<=> in(sK6(sK2),sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_220])]) ).
fof(f2325,plain,
( ~ in(sK6(sK13),sK3)
| ~ spl22_101
| spl22_220 ),
inference(forward_demodulation,[],[f1765,f796]) ).
fof(f1765,plain,
( ~ in(sK6(sK2),sK3)
| spl22_220 ),
inference(avatar_component_clause,[],[f1764]) ).
fof(f2575,plain,
( spl22_312
| ~ spl22_101
| ~ spl22_112
| ~ spl22_166 ),
inference(avatar_split_clause,[],[f2278,f1311,f906,f795,f2573]) ).
fof(f2573,plain,
( spl22_312
<=> ! [X0] :
( ~ subset(sK13,X0)
| relation_of2(sK4,sK13,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_312])]) ).
fof(f906,plain,
( spl22_112
<=> ! [X0] :
( ~ subset(sK2,X0)
| relation_of2(sK4,sK1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_112])]) ).
fof(f2278,plain,
( ! [X0] :
( ~ subset(sK13,X0)
| relation_of2(sK4,sK13,X0) )
| ~ spl22_101
| ~ spl22_112
| ~ spl22_166 ),
inference(forward_demodulation,[],[f2245,f796]) ).
fof(f2245,plain,
( ! [X0] :
( relation_of2(sK4,sK13,X0)
| ~ subset(sK2,X0) )
| ~ spl22_112
| ~ spl22_166 ),
inference(superposition,[],[f907,f1313]) ).
fof(f907,plain,
( ! [X0] :
( relation_of2(sK4,sK1,X0)
| ~ subset(sK2,X0) )
| ~ spl22_112 ),
inference(avatar_component_clause,[],[f906]) ).
fof(f2570,plain,
( spl22_311
| ~ spl22_101
| ~ spl22_109
| ~ spl22_166 ),
inference(avatar_split_clause,[],[f2275,f1311,f865,f795,f2567]) ).
fof(f2567,plain,
( spl22_311
<=> relation_dom(sK4) = relation_dom_as_subset(sK13,sK13,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_311])]) ).
fof(f865,plain,
( spl22_109
<=> relation_dom_as_subset(sK1,sK2,sK4) = relation_dom(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_109])]) ).
fof(f2275,plain,
( relation_dom(sK4) = relation_dom_as_subset(sK13,sK13,sK4)
| ~ spl22_101
| ~ spl22_109
| ~ spl22_166 ),
inference(forward_demodulation,[],[f2244,f796]) ).
fof(f2244,plain,
( relation_dom(sK4) = relation_dom_as_subset(sK13,sK2,sK4)
| ~ spl22_109
| ~ spl22_166 ),
inference(superposition,[],[f867,f1313]) ).
fof(f867,plain,
( relation_dom_as_subset(sK1,sK2,sK4) = relation_dom(sK4)
| ~ spl22_109 ),
inference(avatar_component_clause,[],[f865]) ).
fof(f2565,plain,
( spl22_310
| ~ spl22_164
| ~ spl22_166 ),
inference(avatar_split_clause,[],[f2254,f1311,f1294,f2563]) ).
fof(f2563,plain,
( spl22_310
<=> ! [X0] :
( ~ empty(cartesian_product2(sK13,X0))
| ~ subset(sK3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_310])]) ).
fof(f1294,plain,
( spl22_164
<=> ! [X0] :
( ~ empty(cartesian_product2(sK1,X0))
| ~ subset(sK3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_164])]) ).
fof(f2254,plain,
( ! [X0] :
( ~ empty(cartesian_product2(sK13,X0))
| ~ subset(sK3,X0) )
| ~ spl22_164
| ~ spl22_166 ),
inference(superposition,[],[f1295,f1313]) ).
fof(f1295,plain,
( ! [X0] :
( ~ empty(cartesian_product2(sK1,X0))
| ~ subset(sK3,X0) )
| ~ spl22_164 ),
inference(avatar_component_clause,[],[f1294]) ).
fof(f2561,plain,
( spl22_309
| ~ spl22_155
| ~ spl22_166 ),
inference(avatar_split_clause,[],[f2249,f1311,f1226,f2559]) ).
fof(f2559,plain,
( spl22_309
<=> ! [X0] :
( sP0(sK13,sK4,X0)
| ~ subset(sK3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_309])]) ).
fof(f1226,plain,
( spl22_155
<=> ! [X0] :
( ~ subset(sK3,X0)
| sP0(sK1,sK4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_155])]) ).
fof(f2249,plain,
( ! [X0] :
( sP0(sK13,sK4,X0)
| ~ subset(sK3,X0) )
| ~ spl22_155
| ~ spl22_166 ),
inference(superposition,[],[f1227,f1313]) ).
fof(f1227,plain,
( ! [X0] :
( sP0(sK1,sK4,X0)
| ~ subset(sK3,X0) )
| ~ spl22_155 ),
inference(avatar_component_clause,[],[f1226]) ).
fof(f2557,plain,
( spl22_308
| ~ spl22_154
| ~ spl22_166 ),
inference(avatar_split_clause,[],[f2248,f1311,f1222,f2555]) ).
fof(f2555,plain,
( spl22_308
<=> ! [X0] :
( relation_of2(sK4,sK13,X0)
| ~ subset(sK3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_308])]) ).
fof(f1222,plain,
( spl22_154
<=> ! [X0] :
( ~ subset(sK3,X0)
| relation_of2(sK4,sK1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_154])]) ).
fof(f2248,plain,
( ! [X0] :
( relation_of2(sK4,sK13,X0)
| ~ subset(sK3,X0) )
| ~ spl22_154
| ~ spl22_166 ),
inference(superposition,[],[f1223,f1313]) ).
fof(f1223,plain,
( ! [X0] :
( relation_of2(sK4,sK1,X0)
| ~ subset(sK3,X0) )
| ~ spl22_154 ),
inference(avatar_component_clause,[],[f1222]) ).
fof(f2552,plain,
( spl22_307
| ~ spl22_151
| ~ spl22_166 ),
inference(avatar_split_clause,[],[f2247,f1311,f1208,f2549]) ).
fof(f2549,plain,
( spl22_307
<=> relation_dom(sK4) = relation_dom_as_subset(sK13,sK3,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_307])]) ).
fof(f1208,plain,
( spl22_151
<=> relation_dom(sK4) = relation_dom_as_subset(sK1,sK3,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_151])]) ).
fof(f2247,plain,
( relation_dom(sK4) = relation_dom_as_subset(sK13,sK3,sK4)
| ~ spl22_151
| ~ spl22_166 ),
inference(superposition,[],[f1210,f1313]) ).
fof(f1210,plain,
( relation_dom(sK4) = relation_dom_as_subset(sK1,sK3,sK4)
| ~ spl22_151 ),
inference(avatar_component_clause,[],[f1208]) ).
fof(f2524,plain,
( spl22_306
| ~ spl22_199
| ~ spl22_290 ),
inference(avatar_split_clause,[],[f2460,f2399,f1609,f2521]) ).
fof(f2521,plain,
( spl22_306
<=> sK13 = relation_dom_as_subset(sK13,sK3,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_306])]) ).
fof(f1609,plain,
( spl22_199
<=> ! [X0,X1] :
( ~ relation_of2(X0,sK13,X1)
| sK13 = relation_dom_as_subset(sK13,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_199])]) ).
fof(f2399,plain,
( spl22_290
<=> relation_of2(sK4,sK13,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_290])]) ).
fof(f2460,plain,
( sK13 = relation_dom_as_subset(sK13,sK3,sK4)
| ~ spl22_199
| ~ spl22_290 ),
inference(resolution,[],[f2401,f1610]) ).
fof(f1610,plain,
( ! [X0,X1] :
( ~ relation_of2(X0,sK13,X1)
| sK13 = relation_dom_as_subset(sK13,X1,X0) )
| ~ spl22_199 ),
inference(avatar_component_clause,[],[f1609]) ).
fof(f2401,plain,
( relation_of2(sK4,sK13,sK3)
| ~ spl22_290 ),
inference(avatar_component_clause,[],[f2399]) ).
fof(f2519,plain,
( spl22_305
| ~ spl22_199
| ~ spl22_293 ),
inference(avatar_split_clause,[],[f2428,f2416,f1609,f2516]) ).
fof(f2516,plain,
( spl22_305
<=> sK13 = relation_dom_as_subset(sK13,sK13,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_305])]) ).
fof(f2416,plain,
( spl22_293
<=> relation_of2(sK4,sK13,sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_293])]) ).
fof(f2428,plain,
( sK13 = relation_dom_as_subset(sK13,sK13,sK4)
| ~ spl22_199
| ~ spl22_293 ),
inference(resolution,[],[f2418,f1610]) ).
fof(f2418,plain,
( relation_of2(sK4,sK13,sK13)
| ~ spl22_293 ),
inference(avatar_component_clause,[],[f2416]) ).
fof(f2508,plain,
( ~ spl22_10
| ~ spl22_166
| spl22_210 ),
inference(avatar_split_clause,[],[f2258,f1702,f1311,f265]) ).
fof(f265,plain,
( spl22_10
<=> empty(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_10])]) ).
fof(f1702,plain,
( spl22_210
<=> empty(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_210])]) ).
fof(f2258,plain,
( ~ empty(sK13)
| ~ spl22_166
| spl22_210 ),
inference(superposition,[],[f1704,f1313]) ).
fof(f1704,plain,
( ~ empty(sK1)
| spl22_210 ),
inference(avatar_component_clause,[],[f1702]) ).
fof(f2506,plain,
( spl22_304
| ~ spl22_166
| ~ spl22_240 ),
inference(avatar_split_clause,[],[f2311,f1893,f1311,f2503]) ).
fof(f2503,plain,
( spl22_304
<=> element(relation_dom(sK4),powerset(sK13)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_304])]) ).
fof(f1893,plain,
( spl22_240
<=> element(relation_dom(sK4),powerset(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_240])]) ).
fof(f2311,plain,
( element(relation_dom(sK4),powerset(sK13))
| ~ spl22_166
| ~ spl22_240 ),
inference(forward_demodulation,[],[f1895,f1313]) ).
fof(f1895,plain,
( element(relation_dom(sK4),powerset(sK1))
| ~ spl22_240 ),
inference(avatar_component_clause,[],[f1893]) ).
fof(f2500,plain,
( spl22_303
| ~ spl22_166
| ~ spl22_250 ),
inference(avatar_split_clause,[],[f2306,f1960,f1311,f2497]) ).
fof(f2497,plain,
( spl22_303
<=> in(relation_dom(sK4),powerset(sK13)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_303])]) ).
fof(f1960,plain,
( spl22_250
<=> in(relation_dom(sK4),powerset(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_250])]) ).
fof(f2306,plain,
( in(relation_dom(sK4),powerset(sK13))
| ~ spl22_166
| ~ spl22_250 ),
inference(forward_demodulation,[],[f1962,f1313]) ).
fof(f1962,plain,
( in(relation_dom(sK4),powerset(sK1))
| ~ spl22_250 ),
inference(avatar_component_clause,[],[f1960]) ).
fof(f2490,plain,
( ~ spl22_302
| ~ spl22_101
| spl22_153 ),
inference(avatar_split_clause,[],[f2459,f1217,f795,f2487]) ).
fof(f2487,plain,
( spl22_302
<=> element(sK6(sK13),sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_302])]) ).
fof(f1217,plain,
( spl22_153
<=> element(sK6(sK2),sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_153])]) ).
fof(f2459,plain,
( ~ element(sK6(sK13),sK3)
| ~ spl22_101
| spl22_153 ),
inference(forward_demodulation,[],[f1218,f796]) ).
fof(f1218,plain,
( ~ element(sK6(sK2),sK3)
| spl22_153 ),
inference(avatar_component_clause,[],[f1217]) ).
fof(f2485,plain,
( spl22_301
| ~ spl22_166
| ~ spl22_239 ),
inference(avatar_split_clause,[],[f2312,f1886,f1311,f2482]) ).
fof(f1886,plain,
( spl22_239
<=> subset(relation_dom(sK4),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_239])]) ).
fof(f2312,plain,
( subset(relation_dom(sK4),sK13)
| ~ spl22_166
| ~ spl22_239 ),
inference(forward_demodulation,[],[f1888,f1313]) ).
fof(f1888,plain,
( subset(relation_dom(sK4),sK1)
| ~ spl22_239 ),
inference(avatar_component_clause,[],[f1886]) ).
fof(f2480,plain,
( ~ spl22_300
| ~ spl22_101
| spl22_157
| ~ spl22_166 ),
inference(avatar_split_clause,[],[f2284,f1311,f1242,f795,f2477]) ).
fof(f2477,plain,
( spl22_300
<=> empty(cartesian_product2(sK13,sK13)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_300])]) ).
fof(f1242,plain,
( spl22_157
<=> empty(cartesian_product2(sK1,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_157])]) ).
fof(f2284,plain,
( ~ empty(cartesian_product2(sK13,sK13))
| ~ spl22_101
| spl22_157
| ~ spl22_166 ),
inference(forward_demodulation,[],[f2250,f796]) ).
fof(f2250,plain,
( ~ empty(cartesian_product2(sK13,sK2))
| spl22_157
| ~ spl22_166 ),
inference(superposition,[],[f1244,f1313]) ).
fof(f1244,plain,
( ~ empty(cartesian_product2(sK1,sK2))
| spl22_157 ),
inference(avatar_component_clause,[],[f1242]) ).
fof(f2475,plain,
( ~ spl22_299
| spl22_158
| ~ spl22_166 ),
inference(avatar_split_clause,[],[f2251,f1311,f1247,f2472]) ).
fof(f2472,plain,
( spl22_299
<=> empty(cartesian_product2(sK13,sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_299])]) ).
fof(f1247,plain,
( spl22_158
<=> empty(cartesian_product2(sK1,sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_158])]) ).
fof(f2251,plain,
( ~ empty(cartesian_product2(sK13,sK3))
| spl22_158
| ~ spl22_166 ),
inference(superposition,[],[f1249,f1313]) ).
fof(f1249,plain,
( ~ empty(cartesian_product2(sK1,sK3))
| spl22_158 ),
inference(avatar_component_clause,[],[f1247]) ).
fof(f2458,plain,
( spl22_256
| ~ spl22_106
| ~ spl22_134 ),
inference(avatar_split_clause,[],[f2357,f1078,f823,f2002]) ).
fof(f2002,plain,
( spl22_256
<=> sK3 = sK13 ),
introduced(avatar_definition,[new_symbols(naming,[spl22_256])]) ).
fof(f823,plain,
( spl22_106
<=> ! [X0] :
( sK13 = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_106])]) ).
fof(f1078,plain,
( spl22_134
<=> empty(sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_134])]) ).
fof(f2357,plain,
( sK3 = sK13
| ~ spl22_106
| ~ spl22_134 ),
inference(resolution,[],[f1079,f824]) ).
fof(f824,plain,
( ! [X0] :
( ~ empty(X0)
| sK13 = X0 )
| ~ spl22_106 ),
inference(avatar_component_clause,[],[f823]) ).
fof(f1079,plain,
( empty(sK3)
| ~ spl22_134 ),
inference(avatar_component_clause,[],[f1078]) ).
fof(f2456,plain,
( spl22_298
| ~ spl22_34
| ~ spl22_134 ),
inference(avatar_split_clause,[],[f2355,f1078,f380,f2453]) ).
fof(f2453,plain,
( spl22_298
<=> relation(sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_298])]) ).
fof(f380,plain,
( spl22_34
<=> ! [X0] :
( relation(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_34])]) ).
fof(f2355,plain,
( relation(sK3)
| ~ spl22_34
| ~ spl22_134 ),
inference(resolution,[],[f1079,f381]) ).
fof(f381,plain,
( ! [X0] :
( ~ empty(X0)
| relation(X0) )
| ~ spl22_34 ),
inference(avatar_component_clause,[],[f380]) ).
fof(f2445,plain,
( spl22_297
| ~ spl22_90
| ~ spl22_101
| ~ spl22_166 ),
inference(avatar_split_clause,[],[f2271,f1311,f795,f720,f2443]) ).
fof(f2443,plain,
( spl22_297
<=> ! [X0] :
( ~ subset(sK13,X0)
| relation_of2_as_subset(sK4,sK13,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_297])]) ).
fof(f720,plain,
( spl22_90
<=> ! [X0] :
( ~ subset(sK2,X0)
| relation_of2_as_subset(sK4,sK1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_90])]) ).
fof(f2271,plain,
( ! [X0] :
( ~ subset(sK13,X0)
| relation_of2_as_subset(sK4,sK13,X0) )
| ~ spl22_90
| ~ spl22_101
| ~ spl22_166 ),
inference(forward_demodulation,[],[f2240,f796]) ).
fof(f2240,plain,
( ! [X0] :
( relation_of2_as_subset(sK4,sK13,X0)
| ~ subset(sK2,X0) )
| ~ spl22_90
| ~ spl22_166 ),
inference(superposition,[],[f721,f1313]) ).
fof(f721,plain,
( ! [X0] :
( relation_of2_as_subset(sK4,sK1,X0)
| ~ subset(sK2,X0) )
| ~ spl22_90 ),
inference(avatar_component_clause,[],[f720]) ).
fof(f2440,plain,
( spl22_296
| ~ spl22_33
| ~ spl22_134 ),
inference(avatar_split_clause,[],[f2354,f1078,f376,f2437]) ).
fof(f2437,plain,
( spl22_296
<=> function(sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_296])]) ).
fof(f376,plain,
( spl22_33
<=> ! [X0] :
( function(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_33])]) ).
fof(f2354,plain,
( function(sK3)
| ~ spl22_33
| ~ spl22_134 ),
inference(resolution,[],[f1079,f377]) ).
fof(f377,plain,
( ! [X0] :
( ~ empty(X0)
| function(X0) )
| ~ spl22_33 ),
inference(avatar_component_clause,[],[f376]) ).
fof(f2434,plain,
( spl22_295
| ~ spl22_100
| ~ spl22_166 ),
inference(avatar_split_clause,[],[f2243,f1311,f779,f2432]) ).
fof(f2432,plain,
( spl22_295
<=> ! [X0] :
( relation_of2_as_subset(sK4,sK13,X0)
| ~ subset(sK3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_295])]) ).
fof(f779,plain,
( spl22_100
<=> ! [X0] :
( ~ subset(sK3,X0)
| relation_of2_as_subset(sK4,sK1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_100])]) ).
fof(f2243,plain,
( ! [X0] :
( relation_of2_as_subset(sK4,sK13,X0)
| ~ subset(sK3,X0) )
| ~ spl22_100
| ~ spl22_166 ),
inference(superposition,[],[f780,f1313]) ).
fof(f780,plain,
( ! [X0] :
( relation_of2_as_subset(sK4,sK1,X0)
| ~ subset(sK3,X0) )
| ~ spl22_100 ),
inference(avatar_component_clause,[],[f779]) ).
fof(f2424,plain,
( ~ spl22_294
| spl22_165
| ~ spl22_166 ),
inference(avatar_split_clause,[],[f2330,f1311,f1304,f2421]) ).
fof(f1304,plain,
( spl22_165
<=> sK1 = relation_dom(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_165])]) ).
fof(f2330,plain,
( sK13 != relation_dom(sK4)
| spl22_165
| ~ spl22_166 ),
inference(forward_demodulation,[],[f1305,f1313]) ).
fof(f1305,plain,
( sK1 != relation_dom(sK4)
| spl22_165 ),
inference(avatar_component_clause,[],[f1304]) ).
fof(f2419,plain,
( spl22_293
| ~ spl22_78
| ~ spl22_101
| ~ spl22_166 ),
inference(avatar_split_clause,[],[f2270,f1311,f795,f648,f2416]) ).
fof(f648,plain,
( spl22_78
<=> relation_of2(sK4,sK1,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_78])]) ).
fof(f2270,plain,
( relation_of2(sK4,sK13,sK13)
| ~ spl22_78
| ~ spl22_101
| ~ spl22_166 ),
inference(forward_demodulation,[],[f2239,f796]) ).
fof(f2239,plain,
( relation_of2(sK4,sK13,sK2)
| ~ spl22_78
| ~ spl22_166 ),
inference(superposition,[],[f650,f1313]) ).
fof(f650,plain,
( relation_of2(sK4,sK1,sK2)
| ~ spl22_78 ),
inference(avatar_component_clause,[],[f648]) ).
fof(f2414,plain,
( spl22_292
| ~ spl22_71
| ~ spl22_101
| ~ spl22_166 ),
inference(avatar_split_clause,[],[f2269,f1311,f795,f596,f2411]) ).
fof(f2411,plain,
( spl22_292
<=> sP0(sK13,sK4,sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_292])]) ).
fof(f596,plain,
( spl22_71
<=> sP0(sK1,sK4,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_71])]) ).
fof(f2269,plain,
( sP0(sK13,sK4,sK13)
| ~ spl22_71
| ~ spl22_101
| ~ spl22_166 ),
inference(forward_demodulation,[],[f2238,f796]) ).
fof(f2238,plain,
( sP0(sK13,sK4,sK2)
| ~ spl22_71
| ~ spl22_166 ),
inference(superposition,[],[f598,f1313]) ).
fof(f598,plain,
( sP0(sK1,sK4,sK2)
| ~ spl22_71 ),
inference(avatar_component_clause,[],[f596]) ).
fof(f2408,plain,
( spl22_291
| ~ spl22_99
| ~ spl22_166 ),
inference(avatar_split_clause,[],[f2242,f1311,f771,f2405]) ).
fof(f2405,plain,
( spl22_291
<=> sP0(sK13,sK4,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_291])]) ).
fof(f771,plain,
( spl22_99
<=> sP0(sK1,sK4,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_99])]) ).
fof(f2242,plain,
( sP0(sK13,sK4,sK3)
| ~ spl22_99
| ~ spl22_166 ),
inference(superposition,[],[f773,f1313]) ).
fof(f773,plain,
( sP0(sK1,sK4,sK3)
| ~ spl22_99 ),
inference(avatar_component_clause,[],[f771]) ).
fof(f2402,plain,
( spl22_290
| ~ spl22_98
| ~ spl22_166 ),
inference(avatar_split_clause,[],[f2241,f1311,f766,f2399]) ).
fof(f766,plain,
( spl22_98
<=> relation_of2(sK4,sK1,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_98])]) ).
fof(f2241,plain,
( relation_of2(sK4,sK13,sK3)
| ~ spl22_98
| ~ spl22_166 ),
inference(superposition,[],[f768,f1313]) ).
fof(f768,plain,
( relation_of2(sK4,sK1,sK3)
| ~ spl22_98 ),
inference(avatar_component_clause,[],[f766]) ).
fof(f2340,plain,
( spl22_289
| ~ spl22_29
| ~ spl22_166 ),
inference(avatar_split_clause,[],[f2237,f1311,f359,f2337]) ).
fof(f2337,plain,
( spl22_289
<=> relation_of2_as_subset(sK4,sK13,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_289])]) ).
fof(f359,plain,
( spl22_29
<=> relation_of2_as_subset(sK4,sK1,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_29])]) ).
fof(f2237,plain,
( relation_of2_as_subset(sK4,sK13,sK3)
| ~ spl22_29
| ~ spl22_166 ),
inference(superposition,[],[f360,f1313]) ).
fof(f360,plain,
( relation_of2_as_subset(sK4,sK1,sK3)
| ~ spl22_29 ),
inference(avatar_component_clause,[],[f359]) ).
fof(f2335,plain,
( ~ spl22_288
| spl22_28
| ~ spl22_166 ),
inference(avatar_split_clause,[],[f2236,f1311,f355,f2332]) ).
fof(f2332,plain,
( spl22_288
<=> quasi_total(sK4,sK13,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_288])]) ).
fof(f355,plain,
( spl22_28
<=> quasi_total(sK4,sK1,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_28])]) ).
fof(f2236,plain,
( ~ quasi_total(sK4,sK13,sK3)
| spl22_28
| ~ spl22_166 ),
inference(superposition,[],[f357,f1313]) ).
fof(f357,plain,
( ~ quasi_total(sK4,sK1,sK3)
| spl22_28 ),
inference(avatar_component_clause,[],[f355]) ).
fof(f2305,plain,
( ~ spl22_286
| spl22_28
| ~ spl22_166
| ~ spl22_256 ),
inference(avatar_split_clause,[],[f2267,f2002,f1311,f355,f2296]) ).
fof(f2296,plain,
( spl22_286
<=> quasi_total(sK4,sK13,sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_286])]) ).
fof(f2267,plain,
( ~ quasi_total(sK4,sK13,sK13)
| spl22_28
| ~ spl22_166
| ~ spl22_256 ),
inference(forward_demodulation,[],[f2236,f2004]) ).
fof(f2004,plain,
( sK3 = sK13
| ~ spl22_256 ),
inference(avatar_component_clause,[],[f2002]) ).
fof(f2304,plain,
( spl22_287
| ~ spl22_4
| ~ spl22_101
| ~ spl22_166 ),
inference(avatar_split_clause,[],[f2266,f1311,f795,f236,f2301]) ).
fof(f2301,plain,
( spl22_287
<=> relation_of2_as_subset(sK4,sK13,sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_287])]) ).
fof(f236,plain,
( spl22_4
<=> relation_of2_as_subset(sK4,sK1,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_4])]) ).
fof(f2266,plain,
( relation_of2_as_subset(sK4,sK13,sK13)
| ~ spl22_4
| ~ spl22_101
| ~ spl22_166 ),
inference(forward_demodulation,[],[f2235,f796]) ).
fof(f2235,plain,
( relation_of2_as_subset(sK4,sK13,sK2)
| ~ spl22_4
| ~ spl22_166 ),
inference(superposition,[],[f238,f1313]) ).
fof(f238,plain,
( relation_of2_as_subset(sK4,sK1,sK2)
| ~ spl22_4 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f2299,plain,
( spl22_286
| ~ spl22_3
| ~ spl22_101
| ~ spl22_166 ),
inference(avatar_split_clause,[],[f2265,f1311,f795,f231,f2296]) ).
fof(f231,plain,
( spl22_3
<=> quasi_total(sK4,sK1,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_3])]) ).
fof(f2265,plain,
( quasi_total(sK4,sK13,sK13)
| ~ spl22_3
| ~ spl22_101
| ~ spl22_166 ),
inference(forward_demodulation,[],[f2234,f796]) ).
fof(f2234,plain,
( quasi_total(sK4,sK13,sK2)
| ~ spl22_3
| ~ spl22_166 ),
inference(superposition,[],[f233,f1313]) ).
fof(f233,plain,
( quasi_total(sK4,sK1,sK2)
| ~ spl22_3 ),
inference(avatar_component_clause,[],[f231]) ).
fof(f2231,plain,
( spl22_101
| ~ spl22_106
| ~ spl22_152 ),
inference(avatar_split_clause,[],[f1259,f1213,f823,f795]) ).
fof(f1213,plain,
( spl22_152
<=> empty(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_152])]) ).
fof(f1259,plain,
( sK2 = sK13
| ~ spl22_106
| ~ spl22_152 ),
inference(resolution,[],[f1215,f824]) ).
fof(f1215,plain,
( empty(sK2)
| ~ spl22_152 ),
inference(avatar_component_clause,[],[f1213]) ).
fof(f2230,plain,
( spl22_285
| ~ spl22_116
| ~ spl22_199 ),
inference(avatar_split_clause,[],[f1643,f1609,f922,f2228]) ).
fof(f2228,plain,
( spl22_285
<=> ! [X0] : sK13 = relation_dom_as_subset(sK13,X0,sK9(sK13,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_285])]) ).
fof(f922,plain,
( spl22_116
<=> ! [X0,X1] : relation_of2(sK9(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_116])]) ).
fof(f1643,plain,
( ! [X0] : sK13 = relation_dom_as_subset(sK13,X0,sK9(sK13,X0))
| ~ spl22_116
| ~ spl22_199 ),
inference(resolution,[],[f1610,f923]) ).
fof(f923,plain,
( ! [X0,X1] : relation_of2(sK9(X0,X1),X0,X1)
| ~ spl22_116 ),
inference(avatar_component_clause,[],[f922]) ).
fof(f2226,plain,
( spl22_284
| ~ spl22_51
| ~ spl22_199 ),
inference(avatar_split_clause,[],[f1642,f1609,f477,f2224]) ).
fof(f2224,plain,
( spl22_284
<=> ! [X0] : sK13 = relation_dom_as_subset(sK13,X0,sK8(sK13,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_284])]) ).
fof(f477,plain,
( spl22_51
<=> ! [X0,X1] : relation_of2(sK8(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_51])]) ).
fof(f1642,plain,
( ! [X0] : sK13 = relation_dom_as_subset(sK13,X0,sK8(sK13,X0))
| ~ spl22_51
| ~ spl22_199 ),
inference(resolution,[],[f1610,f478]) ).
fof(f478,plain,
( ! [X0,X1] : relation_of2(sK8(X0,X1),X0,X1)
| ~ spl22_51 ),
inference(avatar_component_clause,[],[f477]) ).
fof(f2222,plain,
( spl22_283
| ~ spl22_113
| ~ spl22_191 ),
inference(avatar_split_clause,[],[f1590,f1516,f910,f2220]) ).
fof(f2220,plain,
( spl22_283
<=> ! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(sK11(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_283])]) ).
fof(f910,plain,
( spl22_113
<=> ! [X0] :
( empty(X0)
| in(sK6(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_113])]) ).
fof(f1516,plain,
( spl22_191
<=> ! [X2,X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| ~ in(X2,sK11(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_191])]) ).
fof(f1590,plain,
( ! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(sK11(X0,X1)) )
| ~ spl22_113
| ~ spl22_191 ),
inference(resolution,[],[f1517,f911]) ).
fof(f911,plain,
( ! [X0] :
( in(sK6(X0),X0)
| empty(X0) )
| ~ spl22_113 ),
inference(avatar_component_clause,[],[f910]) ).
fof(f1517,plain,
( ! [X2,X0,X1] :
( ~ in(X2,sK11(X0,X1))
| ~ empty(cartesian_product2(X0,X1)) )
| ~ spl22_191 ),
inference(avatar_component_clause,[],[f1516]) ).
fof(f2218,plain,
( spl22_282
| ~ spl22_113
| ~ spl22_190 ),
inference(avatar_split_clause,[],[f1589,f1512,f910,f2216]) ).
fof(f2216,plain,
( spl22_282
<=> ! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(sK10(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_282])]) ).
fof(f1512,plain,
( spl22_190
<=> ! [X2,X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| ~ in(X2,sK10(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_190])]) ).
fof(f1589,plain,
( ! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(sK10(X0,X1)) )
| ~ spl22_113
| ~ spl22_190 ),
inference(resolution,[],[f1513,f911]) ).
fof(f1513,plain,
( ! [X2,X0,X1] :
( ~ in(X2,sK10(X0,X1))
| ~ empty(cartesian_product2(X0,X1)) )
| ~ spl22_190 ),
inference(avatar_component_clause,[],[f1512]) ).
fof(f2214,plain,
( spl22_281
| ~ spl22_113
| ~ spl22_189 ),
inference(avatar_split_clause,[],[f1588,f1508,f910,f2212]) ).
fof(f2212,plain,
( spl22_281
<=> ! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(sK9(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_281])]) ).
fof(f1508,plain,
( spl22_189
<=> ! [X2,X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| ~ in(X2,sK9(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_189])]) ).
fof(f1588,plain,
( ! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(sK9(X0,X1)) )
| ~ spl22_113
| ~ spl22_189 ),
inference(resolution,[],[f1509,f911]) ).
fof(f1509,plain,
( ! [X2,X0,X1] :
( ~ in(X2,sK9(X0,X1))
| ~ empty(cartesian_product2(X0,X1)) )
| ~ spl22_189 ),
inference(avatar_component_clause,[],[f1508]) ).
fof(f2210,plain,
( spl22_280
| ~ spl22_113
| ~ spl22_188 ),
inference(avatar_split_clause,[],[f1587,f1504,f910,f2208]) ).
fof(f2208,plain,
( spl22_280
<=> ! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(sK8(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_280])]) ).
fof(f1504,plain,
( spl22_188
<=> ! [X2,X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| ~ in(X2,sK8(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_188])]) ).
fof(f1587,plain,
( ! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(sK8(X0,X1)) )
| ~ spl22_113
| ~ spl22_188 ),
inference(resolution,[],[f1505,f911]) ).
fof(f1505,plain,
( ! [X2,X0,X1] :
( ~ in(X2,sK8(X0,X1))
| ~ empty(cartesian_product2(X0,X1)) )
| ~ spl22_188 ),
inference(avatar_component_clause,[],[f1504]) ).
fof(f2206,plain,
( spl22_279
| ~ spl22_43
| ~ spl22_180 ),
inference(avatar_split_clause,[],[f1423,f1419,f429,f2204]) ).
fof(f2204,plain,
( spl22_279
<=> ! [X0] :
( sK13 = relation_dom(relation_dom(relation_dom(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_279])]) ).
fof(f429,plain,
( spl22_43
<=> ! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_43])]) ).
fof(f1419,plain,
( spl22_180
<=> ! [X0] :
( sK13 = relation_dom(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_180])]) ).
fof(f1423,plain,
( ! [X0] :
( sK13 = relation_dom(relation_dom(relation_dom(X0)))
| ~ empty(X0) )
| ~ spl22_43
| ~ spl22_180 ),
inference(resolution,[],[f1420,f430]) ).
fof(f430,plain,
( ! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) )
| ~ spl22_43 ),
inference(avatar_component_clause,[],[f429]) ).
fof(f1420,plain,
( ! [X0] :
( ~ empty(X0)
| sK13 = relation_dom(relation_dom(X0)) )
| ~ spl22_180 ),
inference(avatar_component_clause,[],[f1419]) ).
fof(f2202,plain,
( spl22_278
| ~ spl22_110
| ~ spl22_178 ),
inference(avatar_split_clause,[],[f1412,f1390,f898,f2200]) ).
fof(f2200,plain,
( spl22_278
<=> ! [X0] :
( ~ empty(X0)
| sK13 = relation_dom(sK6(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_278])]) ).
fof(f898,plain,
( spl22_110
<=> ! [X0] :
( relation_dom(X0) = sK13
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_110])]) ).
fof(f1390,plain,
( spl22_178
<=> ! [X0] :
( ~ empty(X0)
| empty(sK6(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_178])]) ).
fof(f1412,plain,
( ! [X0] :
( ~ empty(X0)
| sK13 = relation_dom(sK6(powerset(X0))) )
| ~ spl22_110
| ~ spl22_178 ),
inference(resolution,[],[f1391,f899]) ).
fof(f899,plain,
( ! [X0] :
( ~ empty(X0)
| relation_dom(X0) = sK13 )
| ~ spl22_110 ),
inference(avatar_component_clause,[],[f898]) ).
fof(f1391,plain,
( ! [X0] :
( empty(sK6(powerset(X0)))
| ~ empty(X0) )
| ~ spl22_178 ),
inference(avatar_component_clause,[],[f1390]) ).
fof(f2195,plain,
( ~ spl22_10
| ~ spl22_46
| ~ spl22_220
| ~ spl22_256 ),
inference(avatar_split_clause,[],[f2055,f2002,f1764,f441,f265]) ).
fof(f441,plain,
( spl22_46
<=> ! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_46])]) ).
fof(f2055,plain,
( ~ empty(sK13)
| ~ spl22_46
| ~ spl22_220
| ~ spl22_256 ),
inference(forward_demodulation,[],[f1801,f2004]) ).
fof(f1801,plain,
( ~ empty(sK3)
| ~ spl22_46
| ~ spl22_220 ),
inference(resolution,[],[f1766,f442]) ).
fof(f442,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) )
| ~ spl22_46 ),
inference(avatar_component_clause,[],[f441]) ).
fof(f1766,plain,
( in(sK6(sK2),sK3)
| ~ spl22_220 ),
inference(avatar_component_clause,[],[f1764]) ).
fof(f2149,plain,
( spl22_277
| ~ spl22_54
| ~ spl22_234 ),
inference(avatar_split_clause,[],[f1866,f1861,f489,f2147]) ).
fof(f2147,plain,
( spl22_277
<=> ! [X2,X0,X1] : relation(relation_dom(sK11(cartesian_product2(X0,X1),X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_277])]) ).
fof(f489,plain,
( spl22_54
<=> ! [X0,X1] : relation_of2(sK11(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_54])]) ).
fof(f1861,plain,
( spl22_234
<=> ! [X2,X0,X1] :
( relation(relation_dom(sK11(cartesian_product2(X0,X1),X2)))
| ~ relation_of2(sK11(cartesian_product2(X0,X1),X2),cartesian_product2(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_234])]) ).
fof(f1866,plain,
( ! [X2,X0,X1] : relation(relation_dom(sK11(cartesian_product2(X0,X1),X2)))
| ~ spl22_54
| ~ spl22_234 ),
inference(resolution,[],[f1862,f490]) ).
fof(f490,plain,
( ! [X0,X1] : relation_of2(sK11(X0,X1),X0,X1)
| ~ spl22_54 ),
inference(avatar_component_clause,[],[f489]) ).
fof(f1862,plain,
( ! [X2,X0,X1] :
( ~ relation_of2(sK11(cartesian_product2(X0,X1),X2),cartesian_product2(X0,X1),X2)
| relation(relation_dom(sK11(cartesian_product2(X0,X1),X2))) )
| ~ spl22_234 ),
inference(avatar_component_clause,[],[f1861]) ).
fof(f2144,plain,
( spl22_276
| ~ spl22_33
| ~ spl22_152 ),
inference(avatar_split_clause,[],[f1262,f1213,f376,f2141]) ).
fof(f2141,plain,
( spl22_276
<=> function(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_276])]) ).
fof(f1262,plain,
( function(sK2)
| ~ spl22_33
| ~ spl22_152 ),
inference(resolution,[],[f1215,f377]) ).
fof(f2139,plain,
( spl22_275
| ~ spl22_53
| ~ spl22_233 ),
inference(avatar_split_clause,[],[f1865,f1857,f485,f2137]) ).
fof(f2137,plain,
( spl22_275
<=> ! [X2,X0,X1] : relation(relation_dom(sK10(cartesian_product2(X0,X1),X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_275])]) ).
fof(f485,plain,
( spl22_53
<=> ! [X0,X1] : relation_of2(sK10(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_53])]) ).
fof(f1857,plain,
( spl22_233
<=> ! [X2,X0,X1] :
( relation(relation_dom(sK10(cartesian_product2(X0,X1),X2)))
| ~ relation_of2(sK10(cartesian_product2(X0,X1),X2),cartesian_product2(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_233])]) ).
fof(f1865,plain,
( ! [X2,X0,X1] : relation(relation_dom(sK10(cartesian_product2(X0,X1),X2)))
| ~ spl22_53
| ~ spl22_233 ),
inference(resolution,[],[f1858,f486]) ).
fof(f486,plain,
( ! [X0,X1] : relation_of2(sK10(X0,X1),X0,X1)
| ~ spl22_53 ),
inference(avatar_component_clause,[],[f485]) ).
fof(f1858,plain,
( ! [X2,X0,X1] :
( ~ relation_of2(sK10(cartesian_product2(X0,X1),X2),cartesian_product2(X0,X1),X2)
| relation(relation_dom(sK10(cartesian_product2(X0,X1),X2))) )
| ~ spl22_233 ),
inference(avatar_component_clause,[],[f1857]) ).
fof(f2135,plain,
( spl22_274
| ~ spl22_51
| ~ spl22_232 ),
inference(avatar_split_clause,[],[f1864,f1853,f477,f2133]) ).
fof(f2133,plain,
( spl22_274
<=> ! [X2,X0,X1] : relation(relation_dom(sK8(cartesian_product2(X0,X1),X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_274])]) ).
fof(f1853,plain,
( spl22_232
<=> ! [X2,X0,X1] :
( relation(relation_dom(sK8(cartesian_product2(X0,X1),X2)))
| ~ relation_of2(sK8(cartesian_product2(X0,X1),X2),cartesian_product2(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_232])]) ).
fof(f1864,plain,
( ! [X2,X0,X1] : relation(relation_dom(sK8(cartesian_product2(X0,X1),X2)))
| ~ spl22_51
| ~ spl22_232 ),
inference(resolution,[],[f1854,f478]) ).
fof(f1854,plain,
( ! [X2,X0,X1] :
( ~ relation_of2(sK8(cartesian_product2(X0,X1),X2),cartesian_product2(X0,X1),X2)
| relation(relation_dom(sK8(cartesian_product2(X0,X1),X2))) )
| ~ spl22_232 ),
inference(avatar_component_clause,[],[f1853]) ).
fof(f2131,plain,
( spl22_273
| ~ spl22_54
| ~ spl22_214 ),
inference(avatar_split_clause,[],[f1741,f1732,f489,f2129]) ).
fof(f2129,plain,
( spl22_273
<=> ! [X0,X1] : element(relation_dom(sK11(X0,X1)),powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_273])]) ).
fof(f1732,plain,
( spl22_214
<=> ! [X0,X1] :
( element(relation_dom(sK11(X0,X1)),powerset(X0))
| ~ relation_of2(sK11(X0,X1),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_214])]) ).
fof(f1741,plain,
( ! [X0,X1] : element(relation_dom(sK11(X0,X1)),powerset(X0))
| ~ spl22_54
| ~ spl22_214 ),
inference(resolution,[],[f1733,f490]) ).
fof(f1733,plain,
( ! [X0,X1] :
( ~ relation_of2(sK11(X0,X1),X0,X1)
| element(relation_dom(sK11(X0,X1)),powerset(X0)) )
| ~ spl22_214 ),
inference(avatar_component_clause,[],[f1732]) ).
fof(f2127,plain,
( spl22_272
| ~ spl22_53
| ~ spl22_213 ),
inference(avatar_split_clause,[],[f1740,f1728,f485,f2125]) ).
fof(f2125,plain,
( spl22_272
<=> ! [X0,X1] : element(relation_dom(sK10(X0,X1)),powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_272])]) ).
fof(f1728,plain,
( spl22_213
<=> ! [X0,X1] :
( element(relation_dom(sK10(X0,X1)),powerset(X0))
| ~ relation_of2(sK10(X0,X1),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_213])]) ).
fof(f1740,plain,
( ! [X0,X1] : element(relation_dom(sK10(X0,X1)),powerset(X0))
| ~ spl22_53
| ~ spl22_213 ),
inference(resolution,[],[f1729,f486]) ).
fof(f1729,plain,
( ! [X0,X1] :
( ~ relation_of2(sK10(X0,X1),X0,X1)
| element(relation_dom(sK10(X0,X1)),powerset(X0)) )
| ~ spl22_213 ),
inference(avatar_component_clause,[],[f1728]) ).
fof(f2123,plain,
( spl22_271
| ~ spl22_51
| ~ spl22_212 ),
inference(avatar_split_clause,[],[f1739,f1724,f477,f2121]) ).
fof(f2121,plain,
( spl22_271
<=> ! [X0,X1] : element(relation_dom(sK8(X0,X1)),powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_271])]) ).
fof(f1724,plain,
( spl22_212
<=> ! [X0,X1] :
( element(relation_dom(sK8(X0,X1)),powerset(X0))
| ~ relation_of2(sK8(X0,X1),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_212])]) ).
fof(f1739,plain,
( ! [X0,X1] : element(relation_dom(sK8(X0,X1)),powerset(X0))
| ~ spl22_51
| ~ spl22_212 ),
inference(resolution,[],[f1725,f478]) ).
fof(f1725,plain,
( ! [X0,X1] :
( ~ relation_of2(sK8(X0,X1),X0,X1)
| element(relation_dom(sK8(X0,X1)),powerset(X0)) )
| ~ spl22_212 ),
inference(avatar_component_clause,[],[f1724]) ).
fof(f2119,plain,
( spl22_270
| ~ spl22_177
| ~ spl22_181 ),
inference(avatar_split_clause,[],[f1453,f1444,f1386,f2117]) ).
fof(f2117,plain,
( spl22_270
<=> ! [X0] :
( sP0(X0,sK13,sK13)
| sK13 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_270])]) ).
fof(f1386,plain,
( spl22_177
<=> ! [X0,X1] : sP0(X0,sK11(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_177])]) ).
fof(f1444,plain,
( spl22_181
<=> ! [X0] :
( sK13 = X0
| sK13 = sK11(X0,sK13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_181])]) ).
fof(f1453,plain,
( ! [X0] :
( sP0(X0,sK13,sK13)
| sK13 = X0 )
| ~ spl22_177
| ~ spl22_181 ),
inference(superposition,[],[f1387,f1445]) ).
fof(f1445,plain,
( ! [X0] :
( sK13 = sK11(X0,sK13)
| sK13 = X0 )
| ~ spl22_181 ),
inference(avatar_component_clause,[],[f1444]) ).
fof(f1387,plain,
( ! [X0,X1] : sP0(X0,sK11(X0,X1),X1)
| ~ spl22_177 ),
inference(avatar_component_clause,[],[f1386]) ).
fof(f2115,plain,
( spl22_269
| ~ spl22_119
| ~ spl22_181 ),
inference(avatar_split_clause,[],[f1451,f1444,f934,f2113]) ).
fof(f2113,plain,
( spl22_269
<=> ! [X0] :
( relation_of2_as_subset(sK13,X0,sK13)
| sK13 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_269])]) ).
fof(f934,plain,
( spl22_119
<=> ! [X0,X1] : relation_of2_as_subset(sK11(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_119])]) ).
fof(f1451,plain,
( ! [X0] :
( relation_of2_as_subset(sK13,X0,sK13)
| sK13 = X0 )
| ~ spl22_119
| ~ spl22_181 ),
inference(superposition,[],[f935,f1445]) ).
fof(f935,plain,
( ! [X0,X1] : relation_of2_as_subset(sK11(X0,X1),X0,X1)
| ~ spl22_119 ),
inference(avatar_component_clause,[],[f934]) ).
fof(f2111,plain,
( spl22_268
| ~ spl22_55
| ~ spl22_181 ),
inference(avatar_split_clause,[],[f1450,f1444,f493,f2109]) ).
fof(f2109,plain,
( spl22_268
<=> ! [X0] :
( quasi_total(sK13,X0,sK13)
| sK13 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_268])]) ).
fof(f493,plain,
( spl22_55
<=> ! [X0,X1] : quasi_total(sK11(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_55])]) ).
fof(f1450,plain,
( ! [X0] :
( quasi_total(sK13,X0,sK13)
| sK13 = X0 )
| ~ spl22_55
| ~ spl22_181 ),
inference(superposition,[],[f494,f1445]) ).
fof(f494,plain,
( ! [X0,X1] : quasi_total(sK11(X0,X1),X0,X1)
| ~ spl22_55 ),
inference(avatar_component_clause,[],[f493]) ).
fof(f2107,plain,
( spl22_267
| ~ spl22_54
| ~ spl22_181 ),
inference(avatar_split_clause,[],[f1449,f1444,f489,f2105]) ).
fof(f2105,plain,
( spl22_267
<=> ! [X0] :
( relation_of2(sK13,X0,sK13)
| sK13 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_267])]) ).
fof(f1449,plain,
( ! [X0] :
( relation_of2(sK13,X0,sK13)
| sK13 = X0 )
| ~ spl22_54
| ~ spl22_181 ),
inference(superposition,[],[f490,f1445]) ).
fof(f2103,plain,
( spl22_266
| ~ spl22_106
| ~ spl22_178 ),
inference(avatar_split_clause,[],[f1413,f1390,f823,f2101]) ).
fof(f2101,plain,
( spl22_266
<=> ! [X0] :
( ~ empty(X0)
| sK13 = sK6(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_266])]) ).
fof(f1413,plain,
( ! [X0] :
( ~ empty(X0)
| sK13 = sK6(powerset(X0)) )
| ~ spl22_106
| ~ spl22_178 ),
inference(resolution,[],[f1391,f824]) ).
fof(f2098,plain,
( spl22_265
| ~ spl22_34
| ~ spl22_152 ),
inference(avatar_split_clause,[],[f1261,f1213,f380,f2095]) ).
fof(f2095,plain,
( spl22_265
<=> relation(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_265])]) ).
fof(f1261,plain,
( relation(sK2)
| ~ spl22_34
| ~ spl22_152 ),
inference(resolution,[],[f1215,f381]) ).
fof(f2074,plain,
( spl22_264
| ~ spl22_54
| ~ spl22_211 ),
inference(avatar_split_clause,[],[f1720,f1707,f489,f2072]) ).
fof(f2072,plain,
( spl22_264
<=> ! [X0,X1] : subset(relation_dom(sK11(X0,X1)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_264])]) ).
fof(f1707,plain,
( spl22_211
<=> ! [X0,X1] :
( subset(relation_dom(sK11(X0,X1)),X0)
| ~ relation_of2(sK11(X0,X1),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_211])]) ).
fof(f1720,plain,
( ! [X0,X1] : subset(relation_dom(sK11(X0,X1)),X0)
| ~ spl22_54
| ~ spl22_211 ),
inference(resolution,[],[f1708,f490]) ).
fof(f1708,plain,
( ! [X0,X1] :
( ~ relation_of2(sK11(X0,X1),X0,X1)
| subset(relation_dom(sK11(X0,X1)),X0) )
| ~ spl22_211 ),
inference(avatar_component_clause,[],[f1707]) ).
fof(f2070,plain,
( spl22_263
| ~ spl22_53
| ~ spl22_209 ),
inference(avatar_split_clause,[],[f1719,f1698,f485,f2068]) ).
fof(f2068,plain,
( spl22_263
<=> ! [X0,X1] : subset(relation_dom(sK10(X0,X1)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_263])]) ).
fof(f1698,plain,
( spl22_209
<=> ! [X0,X1] :
( subset(relation_dom(sK10(X0,X1)),X0)
| ~ relation_of2(sK10(X0,X1),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_209])]) ).
fof(f1719,plain,
( ! [X0,X1] : subset(relation_dom(sK10(X0,X1)),X0)
| ~ spl22_53
| ~ spl22_209 ),
inference(resolution,[],[f1699,f486]) ).
fof(f1699,plain,
( ! [X0,X1] :
( ~ relation_of2(sK10(X0,X1),X0,X1)
| subset(relation_dom(sK10(X0,X1)),X0) )
| ~ spl22_209 ),
inference(avatar_component_clause,[],[f1698]) ).
fof(f2066,plain,
( spl22_262
| ~ spl22_51
| ~ spl22_208 ),
inference(avatar_split_clause,[],[f1718,f1694,f477,f2064]) ).
fof(f2064,plain,
( spl22_262
<=> ! [X0,X1] : subset(relation_dom(sK8(X0,X1)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_262])]) ).
fof(f1694,plain,
( spl22_208
<=> ! [X0,X1] :
( subset(relation_dom(sK8(X0,X1)),X0)
| ~ relation_of2(sK8(X0,X1),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_208])]) ).
fof(f1718,plain,
( ! [X0,X1] : subset(relation_dom(sK8(X0,X1)),X0)
| ~ spl22_51
| ~ spl22_208 ),
inference(resolution,[],[f1695,f478]) ).
fof(f1695,plain,
( ! [X0,X1] :
( ~ relation_of2(sK8(X0,X1),X0,X1)
| subset(relation_dom(sK8(X0,X1)),X0) )
| ~ spl22_208 ),
inference(avatar_component_clause,[],[f1694]) ).
fof(f2058,plain,
( spl22_152
| ~ spl22_113
| ~ spl22_135 ),
inference(avatar_split_clause,[],[f2057,f1082,f910,f1213]) ).
fof(f1082,plain,
( spl22_135
<=> ! [X0] : ~ in(X0,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_135])]) ).
fof(f2057,plain,
( empty(sK2)
| ~ spl22_113
| ~ spl22_135 ),
inference(resolution,[],[f1083,f911]) ).
fof(f1083,plain,
( ! [X0] : ~ in(X0,sK2)
| ~ spl22_135 ),
inference(avatar_component_clause,[],[f1082]) ).
fof(f2054,plain,
( ~ spl22_10
| spl22_134
| ~ spl22_256 ),
inference(avatar_split_clause,[],[f2011,f2002,f1078,f265]) ).
fof(f2011,plain,
( ~ empty(sK13)
| spl22_134
| ~ spl22_256 ),
inference(superposition,[],[f1080,f2004]) ).
fof(f1080,plain,
( ~ empty(sK3)
| spl22_134 ),
inference(avatar_component_clause,[],[f1078]) ).
fof(f2053,plain,
( spl22_261
| ~ spl22_33
| ~ spl22_178 ),
inference(avatar_split_clause,[],[f1416,f1390,f376,f2051]) ).
fof(f2051,plain,
( spl22_261
<=> ! [X0] :
( ~ empty(X0)
| function(sK6(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_261])]) ).
fof(f1416,plain,
( ! [X0] :
( ~ empty(X0)
| function(sK6(powerset(X0))) )
| ~ spl22_33
| ~ spl22_178 ),
inference(resolution,[],[f1391,f377]) ).
fof(f2049,plain,
( spl22_260
| ~ spl22_34
| ~ spl22_178 ),
inference(avatar_split_clause,[],[f1415,f1390,f380,f2047]) ).
fof(f2047,plain,
( spl22_260
<=> ! [X0] :
( ~ empty(X0)
| relation(sK6(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_260])]) ).
fof(f1415,plain,
( ! [X0] :
( ~ empty(X0)
| relation(sK6(powerset(X0))) )
| ~ spl22_34
| ~ spl22_178 ),
inference(resolution,[],[f1391,f381]) ).
fof(f2035,plain,
( spl22_259
| ~ spl22_256
| ~ spl22_257 ),
inference(avatar_split_clause,[],[f2027,f2024,f2002,f2033]) ).
fof(f2033,plain,
( spl22_259
<=> ! [X0,X1] :
( ~ subset(sK13,X1)
| ~ in(X0,sK4)
| empty(cartesian_product2(sK1,X1))
| in(X0,cartesian_product2(sK1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_259])]) ).
fof(f2024,plain,
( spl22_257
<=> ! [X0,X1] :
( ~ in(X0,sK4)
| ~ subset(sK3,X1)
| empty(cartesian_product2(sK1,X1))
| in(X0,cartesian_product2(sK1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_257])]) ).
fof(f2027,plain,
( ! [X0,X1] :
( ~ subset(sK13,X1)
| ~ in(X0,sK4)
| empty(cartesian_product2(sK1,X1))
| in(X0,cartesian_product2(sK1,X1)) )
| ~ spl22_256
| ~ spl22_257 ),
inference(forward_demodulation,[],[f2025,f2004]) ).
fof(f2025,plain,
( ! [X0,X1] :
( ~ in(X0,sK4)
| ~ subset(sK3,X1)
| empty(cartesian_product2(sK1,X1))
| in(X0,cartesian_product2(sK1,X1)) )
| ~ spl22_257 ),
inference(avatar_component_clause,[],[f2024]) ).
fof(f2031,plain,
( spl22_258
| ~ spl22_64
| ~ spl22_194 ),
inference(avatar_split_clause,[],[f1584,f1580,f551,f2029]) ).
fof(f2029,plain,
( spl22_258
<=> ! [X0,X1] :
( ~ in(X0,sK4)
| ~ subset(sK2,X1)
| empty(cartesian_product2(sK1,X1))
| in(X0,cartesian_product2(sK1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_258])]) ).
fof(f551,plain,
( spl22_64
<=> ! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_64])]) ).
fof(f1580,plain,
( spl22_194
<=> ! [X0,X1] :
( ~ in(X0,sK4)
| element(X0,cartesian_product2(sK1,X1))
| ~ subset(sK2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_194])]) ).
fof(f1584,plain,
( ! [X0,X1] :
( ~ in(X0,sK4)
| ~ subset(sK2,X1)
| empty(cartesian_product2(sK1,X1))
| in(X0,cartesian_product2(sK1,X1)) )
| ~ spl22_64
| ~ spl22_194 ),
inference(resolution,[],[f1581,f552]) ).
fof(f552,plain,
( ! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) )
| ~ spl22_64 ),
inference(avatar_component_clause,[],[f551]) ).
fof(f1581,plain,
( ! [X0,X1] :
( element(X0,cartesian_product2(sK1,X1))
| ~ in(X0,sK4)
| ~ subset(sK2,X1) )
| ~ spl22_194 ),
inference(avatar_component_clause,[],[f1580]) ).
fof(f2026,plain,
( spl22_257
| ~ spl22_64
| ~ spl22_193 ),
inference(avatar_split_clause,[],[f1583,f1576,f551,f2024]) ).
fof(f1576,plain,
( spl22_193
<=> ! [X0,X1] :
( ~ in(X0,sK4)
| element(X0,cartesian_product2(sK1,X1))
| ~ subset(sK3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_193])]) ).
fof(f1583,plain,
( ! [X0,X1] :
( ~ in(X0,sK4)
| ~ subset(sK3,X1)
| empty(cartesian_product2(sK1,X1))
| in(X0,cartesian_product2(sK1,X1)) )
| ~ spl22_64
| ~ spl22_193 ),
inference(resolution,[],[f1577,f552]) ).
fof(f1577,plain,
( ! [X0,X1] :
( element(X0,cartesian_product2(sK1,X1))
| ~ in(X0,sK4)
| ~ subset(sK3,X1) )
| ~ spl22_193 ),
inference(avatar_component_clause,[],[f1576]) ).
fof(f2005,plain,
( ~ spl22_99
| spl22_256
| spl22_28
| ~ spl22_165
| ~ spl22_89
| ~ spl22_151 ),
inference(avatar_split_clause,[],[f1255,f1208,f713,f1304,f355,f2002,f771]) ).
fof(f713,plain,
( spl22_89
<=> ! [X2,X0,X1] :
( sK13 = X2
| quasi_total(X1,X0,X2)
| relation_dom_as_subset(X0,X2,X1) != X0
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_89])]) ).
fof(f1255,plain,
( sK1 != relation_dom(sK4)
| quasi_total(sK4,sK1,sK3)
| sK3 = sK13
| ~ sP0(sK1,sK4,sK3)
| ~ spl22_89
| ~ spl22_151 ),
inference(superposition,[],[f714,f1210]) ).
fof(f714,plain,
( ! [X2,X0,X1] :
( relation_dom_as_subset(X0,X2,X1) != X0
| quasi_total(X1,X0,X2)
| sK13 = X2
| ~ sP0(X0,X1,X2) )
| ~ spl22_89 ),
inference(avatar_component_clause,[],[f713]) ).
fof(f1998,plain,
( ~ spl22_255
| ~ spl22_49
| ~ spl22_242 ),
inference(avatar_split_clause,[],[f1957,f1908,f469,f1995]) ).
fof(f1995,plain,
( spl22_255
<=> in(powerset(sK1),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_255])]) ).
fof(f469,plain,
( spl22_49
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_49])]) ).
fof(f1908,plain,
( spl22_242
<=> in(sK1,powerset(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_242])]) ).
fof(f1957,plain,
( ~ in(powerset(sK1),sK1)
| ~ spl22_49
| ~ spl22_242 ),
inference(resolution,[],[f1910,f470]) ).
fof(f470,plain,
( ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) )
| ~ spl22_49 ),
inference(avatar_component_clause,[],[f469]) ).
fof(f1910,plain,
( in(sK1,powerset(sK1))
| ~ spl22_242 ),
inference(avatar_component_clause,[],[f1908]) ).
fof(f1991,plain,
( spl22_254
| ~ spl22_130
| ~ spl22_163 ),
inference(avatar_split_clause,[],[f1302,f1290,f1049,f1989]) ).
fof(f1989,plain,
( spl22_254
<=> ! [X2,X0,X1] :
( ~ subset(cartesian_product2(X0,X1),X2)
| relation_of2_as_subset(sK4,sK1,X2)
| ~ relation_of2_as_subset(sK3,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_254])]) ).
fof(f1049,plain,
( spl22_130
<=> ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| subset(X0,cartesian_product2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_130])]) ).
fof(f1290,plain,
( spl22_163
<=> ! [X0,X1] :
( ~ subset(sK3,X0)
| ~ subset(X0,X1)
| relation_of2_as_subset(sK4,sK1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_163])]) ).
fof(f1302,plain,
( ! [X2,X0,X1] :
( ~ subset(cartesian_product2(X0,X1),X2)
| relation_of2_as_subset(sK4,sK1,X2)
| ~ relation_of2_as_subset(sK3,X0,X1) )
| ~ spl22_130
| ~ spl22_163 ),
inference(resolution,[],[f1291,f1050]) ).
fof(f1050,plain,
( ! [X2,X0,X1] :
( subset(X0,cartesian_product2(X1,X2))
| ~ relation_of2_as_subset(X0,X1,X2) )
| ~ spl22_130 ),
inference(avatar_component_clause,[],[f1049]) ).
fof(f1291,plain,
( ! [X0,X1] :
( ~ subset(sK3,X0)
| ~ subset(X0,X1)
| relation_of2_as_subset(sK4,sK1,X1) )
| ~ spl22_163 ),
inference(avatar_component_clause,[],[f1290]) ).
fof(f1987,plain,
( spl22_253
| ~ spl22_130
| ~ spl22_162 ),
inference(avatar_split_clause,[],[f1300,f1286,f1049,f1985]) ).
fof(f1985,plain,
( spl22_253
<=> ! [X2,X0,X1] :
( ~ subset(cartesian_product2(X0,X1),X2)
| relation_of2_as_subset(sK4,sK1,X2)
| ~ relation_of2_as_subset(sK2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_253])]) ).
fof(f1286,plain,
( spl22_162
<=> ! [X0,X1] :
( ~ subset(sK2,X0)
| ~ subset(X0,X1)
| relation_of2_as_subset(sK4,sK1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_162])]) ).
fof(f1300,plain,
( ! [X2,X0,X1] :
( ~ subset(cartesian_product2(X0,X1),X2)
| relation_of2_as_subset(sK4,sK1,X2)
| ~ relation_of2_as_subset(sK2,X0,X1) )
| ~ spl22_130
| ~ spl22_162 ),
inference(resolution,[],[f1287,f1050]) ).
fof(f1287,plain,
( ! [X0,X1] :
( ~ subset(sK2,X0)
| ~ subset(X0,X1)
| relation_of2_as_subset(sK4,sK1,X1) )
| ~ spl22_162 ),
inference(avatar_component_clause,[],[f1286]) ).
fof(f1978,plain,
( spl22_158
| spl22_252
| ~ spl22_64
| ~ spl22_160 ),
inference(avatar_split_clause,[],[f1284,f1275,f551,f1976,f1247]) ).
fof(f1976,plain,
( spl22_252
<=> ! [X0] :
( ~ in(X0,sK4)
| in(X0,cartesian_product2(sK1,sK3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_252])]) ).
fof(f1284,plain,
( ! [X0] :
( ~ in(X0,sK4)
| empty(cartesian_product2(sK1,sK3))
| in(X0,cartesian_product2(sK1,sK3)) )
| ~ spl22_64
| ~ spl22_160 ),
inference(resolution,[],[f1276,f552]) ).
fof(f1969,plain,
( spl22_157
| spl22_251
| ~ spl22_64
| ~ spl22_159 ),
inference(avatar_split_clause,[],[f1283,f1270,f551,f1967,f1242]) ).
fof(f1967,plain,
( spl22_251
<=> ! [X0] :
( ~ in(X0,sK4)
| in(X0,cartesian_product2(sK1,sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_251])]) ).
fof(f1270,plain,
( spl22_159
<=> ! [X0] :
( ~ in(X0,sK4)
| element(X0,cartesian_product2(sK1,sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_159])]) ).
fof(f1283,plain,
( ! [X0] :
( ~ in(X0,sK4)
| empty(cartesian_product2(sK1,sK2))
| in(X0,cartesian_product2(sK1,sK2)) )
| ~ spl22_64
| ~ spl22_159 ),
inference(resolution,[],[f1271,f552]) ).
fof(f1271,plain,
( ! [X0] :
( element(X0,cartesian_product2(sK1,sK2))
| ~ in(X0,sK4) )
| ~ spl22_159 ),
inference(avatar_component_clause,[],[f1270]) ).
fof(f1965,plain,
( ~ spl22_98
| spl22_243
| spl22_250
| ~ spl22_148
| ~ spl22_151 ),
inference(avatar_split_clause,[],[f1251,f1208,f1185,f1960,f1912,f766]) ).
fof(f1912,plain,
( spl22_243
<=> empty(powerset(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_243])]) ).
fof(f1185,plain,
( spl22_148
<=> ! [X2,X0,X1] :
( ~ relation_of2(X0,X1,X2)
| empty(powerset(X1))
| in(relation_dom_as_subset(X1,X2,X0),powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_148])]) ).
fof(f1251,plain,
( in(relation_dom(sK4),powerset(sK1))
| empty(powerset(sK1))
| ~ relation_of2(sK4,sK1,sK3)
| ~ spl22_148
| ~ spl22_151 ),
inference(superposition,[],[f1186,f1210]) ).
fof(f1186,plain,
( ! [X2,X0,X1] :
( in(relation_dom_as_subset(X1,X2,X0),powerset(X1))
| empty(powerset(X1))
| ~ relation_of2(X0,X1,X2) )
| ~ spl22_148 ),
inference(avatar_component_clause,[],[f1185]) ).
fof(f1963,plain,
( ~ spl22_78
| spl22_243
| spl22_250
| ~ spl22_109
| ~ spl22_148 ),
inference(avatar_split_clause,[],[f1229,f1185,f865,f1960,f1912,f648]) ).
fof(f1229,plain,
( in(relation_dom(sK4),powerset(sK1))
| empty(powerset(sK1))
| ~ relation_of2(sK4,sK1,sK2)
| ~ spl22_109
| ~ spl22_148 ),
inference(superposition,[],[f1186,f867]) ).
fof(f1958,plain,
( ~ spl22_98
| spl22_249
| ~ spl22_145
| ~ spl22_151 ),
inference(avatar_split_clause,[],[f1252,f1208,f1166,f1951,f766]) ).
fof(f1166,plain,
( spl22_145
<=> ! [X0,X3,X2,X1] :
( ~ relation_of2(X0,X1,X2)
| element(X3,X1)
| ~ in(X3,relation_dom_as_subset(X1,X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_145])]) ).
fof(f1252,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sK4))
| element(X0,sK1)
| ~ relation_of2(sK4,sK1,sK3) )
| ~ spl22_145
| ~ spl22_151 ),
inference(superposition,[],[f1167,f1210]) ).
fof(f1167,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X3,relation_dom_as_subset(X1,X2,X0))
| element(X3,X1)
| ~ relation_of2(X0,X1,X2) )
| ~ spl22_145 ),
inference(avatar_component_clause,[],[f1166]) ).
fof(f1953,plain,
( ~ spl22_78
| spl22_249
| ~ spl22_109
| ~ spl22_145 ),
inference(avatar_split_clause,[],[f1230,f1166,f865,f1951,f648]) ).
fof(f1230,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sK4))
| element(X0,sK1)
| ~ relation_of2(sK4,sK1,sK2) )
| ~ spl22_109
| ~ spl22_145 ),
inference(superposition,[],[f1167,f867]) ).
fof(f1947,plain,
( spl22_248
| ~ spl22_165
| ~ spl22_247 ),
inference(avatar_split_clause,[],[f1943,f1940,f1304,f1945]) ).
fof(f1945,plain,
( spl22_248
<=> ! [X0] :
( sK1 = relation_dom_as_subset(sK1,X0,sK4)
| ~ subset(sK3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_248])]) ).
fof(f1940,plain,
( spl22_247
<=> ! [X0] :
( ~ subset(sK3,X0)
| relation_dom(sK4) = relation_dom_as_subset(sK1,X0,sK4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_247])]) ).
fof(f1943,plain,
( ! [X0] :
( sK1 = relation_dom_as_subset(sK1,X0,sK4)
| ~ subset(sK3,X0) )
| ~ spl22_165
| ~ spl22_247 ),
inference(forward_demodulation,[],[f1941,f1306]) ).
fof(f1306,plain,
( sK1 = relation_dom(sK4)
| ~ spl22_165 ),
inference(avatar_component_clause,[],[f1304]) ).
fof(f1941,plain,
( ! [X0] :
( ~ subset(sK3,X0)
| relation_dom(sK4) = relation_dom_as_subset(sK1,X0,sK4) )
| ~ spl22_247 ),
inference(avatar_component_clause,[],[f1940]) ).
fof(f1942,plain,
( spl22_247
| ~ spl22_74
| ~ spl22_154 ),
inference(avatar_split_clause,[],[f1266,f1222,f626,f1940]) ).
fof(f626,plain,
( spl22_74
<=> ! [X2,X0,X1] :
( relation_dom_as_subset(X0,X1,X2) = relation_dom(X2)
| ~ relation_of2(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_74])]) ).
fof(f1266,plain,
( ! [X0] :
( ~ subset(sK3,X0)
| relation_dom(sK4) = relation_dom_as_subset(sK1,X0,sK4) )
| ~ spl22_74
| ~ spl22_154 ),
inference(resolution,[],[f1223,f627]) ).
fof(f627,plain,
( ! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| relation_dom_as_subset(X0,X1,X2) = relation_dom(X2) )
| ~ spl22_74 ),
inference(avatar_component_clause,[],[f626]) ).
fof(f1935,plain,
( spl22_246
| ~ spl22_165
| ~ spl22_245 ),
inference(avatar_split_clause,[],[f1931,f1928,f1304,f1933]) ).
fof(f1933,plain,
( spl22_246
<=> ! [X0] :
( sK1 = relation_dom_as_subset(sK1,X0,sK4)
| ~ subset(sK2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_246])]) ).
fof(f1928,plain,
( spl22_245
<=> ! [X0] :
( ~ subset(sK2,X0)
| relation_dom(sK4) = relation_dom_as_subset(sK1,X0,sK4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_245])]) ).
fof(f1931,plain,
( ! [X0] :
( sK1 = relation_dom_as_subset(sK1,X0,sK4)
| ~ subset(sK2,X0) )
| ~ spl22_165
| ~ spl22_245 ),
inference(forward_demodulation,[],[f1929,f1306]) ).
fof(f1929,plain,
( ! [X0] :
( ~ subset(sK2,X0)
| relation_dom(sK4) = relation_dom_as_subset(sK1,X0,sK4) )
| ~ spl22_245 ),
inference(avatar_component_clause,[],[f1928]) ).
fof(f1930,plain,
( spl22_245
| ~ spl22_74
| ~ spl22_112 ),
inference(avatar_split_clause,[],[f1235,f906,f626,f1928]) ).
fof(f1235,plain,
( ! [X0] :
( ~ subset(sK2,X0)
| relation_dom(sK4) = relation_dom_as_subset(sK1,X0,sK4) )
| ~ spl22_74
| ~ spl22_112 ),
inference(resolution,[],[f907,f627]) ).
fof(f1920,plain,
( spl22_244
| ~ spl22_2
| ~ spl22_206 ),
inference(avatar_split_clause,[],[f1713,f1686,f226,f1918]) ).
fof(f1918,plain,
( spl22_244
<=> ! [X0,X1] :
( ~ subset(X0,sK2)
| relation_of2_as_subset(sK9(X1,X0),X1,sK3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_244])]) ).
fof(f226,plain,
( spl22_2
<=> subset(sK2,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_2])]) ).
fof(f1686,plain,
( spl22_206
<=> ! [X0,X3,X2,X1] :
( ~ subset(X0,X1)
| ~ subset(X1,X2)
| relation_of2_as_subset(sK9(X3,X0),X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_206])]) ).
fof(f1713,plain,
( ! [X0,X1] :
( ~ subset(X0,sK2)
| relation_of2_as_subset(sK9(X1,X0),X1,sK3) )
| ~ spl22_2
| ~ spl22_206 ),
inference(resolution,[],[f1687,f228]) ).
fof(f228,plain,
( subset(sK2,sK3)
| ~ spl22_2 ),
inference(avatar_component_clause,[],[f226]) ).
fof(f1687,plain,
( ! [X2,X3,X0,X1] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| relation_of2_as_subset(sK9(X3,X0),X3,X2) )
| ~ spl22_206 ),
inference(avatar_component_clause,[],[f1686]) ).
fof(f1916,plain,
( ~ spl22_98
| spl22_240
| ~ spl22_75
| ~ spl22_151 ),
inference(avatar_split_clause,[],[f1256,f1208,f630,f1893,f766]) ).
fof(f630,plain,
( spl22_75
<=> ! [X2,X0,X1] :
( element(relation_dom_as_subset(X0,X1,X2),powerset(X0))
| ~ relation_of2(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_75])]) ).
fof(f1256,plain,
( element(relation_dom(sK4),powerset(sK1))
| ~ relation_of2(sK4,sK1,sK3)
| ~ spl22_75
| ~ spl22_151 ),
inference(superposition,[],[f631,f1210]) ).
fof(f631,plain,
( ! [X2,X0,X1] :
( element(relation_dom_as_subset(X0,X1,X2),powerset(X0))
| ~ relation_of2(X2,X0,X1) )
| ~ spl22_75 ),
inference(avatar_component_clause,[],[f630]) ).
fof(f1915,plain,
( spl22_242
| spl22_243
| ~ spl22_64
| ~ spl22_241 ),
inference(avatar_split_clause,[],[f1906,f1899,f551,f1912,f1908]) ).
fof(f1899,plain,
( spl22_241
<=> element(sK1,powerset(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_241])]) ).
fof(f1906,plain,
( empty(powerset(sK1))
| in(sK1,powerset(sK1))
| ~ spl22_64
| ~ spl22_241 ),
inference(resolution,[],[f1901,f552]) ).
fof(f1901,plain,
( element(sK1,powerset(sK1))
| ~ spl22_241 ),
inference(avatar_component_clause,[],[f1899]) ).
fof(f1902,plain,
( spl22_241
| ~ spl22_165
| ~ spl22_240 ),
inference(avatar_split_clause,[],[f1897,f1893,f1304,f1899]) ).
fof(f1897,plain,
( element(sK1,powerset(sK1))
| ~ spl22_165
| ~ spl22_240 ),
inference(forward_demodulation,[],[f1895,f1306]) ).
fof(f1896,plain,
( ~ spl22_78
| spl22_240
| ~ spl22_75
| ~ spl22_109 ),
inference(avatar_split_clause,[],[f1234,f865,f630,f1893,f648]) ).
fof(f1234,plain,
( element(relation_dom(sK4),powerset(sK1))
| ~ relation_of2(sK4,sK1,sK2)
| ~ spl22_75
| ~ spl22_109 ),
inference(superposition,[],[f631,f867]) ).
fof(f1891,plain,
( ~ spl22_98
| spl22_239
| ~ spl22_138
| ~ spl22_151 ),
inference(avatar_split_clause,[],[f1254,f1208,f1094,f1886,f766]) ).
fof(f1094,plain,
( spl22_138
<=> ! [X2,X0,X1] :
( ~ relation_of2(X0,X1,X2)
| subset(relation_dom_as_subset(X1,X2,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_138])]) ).
fof(f1254,plain,
( subset(relation_dom(sK4),sK1)
| ~ relation_of2(sK4,sK1,sK3)
| ~ spl22_138
| ~ spl22_151 ),
inference(superposition,[],[f1095,f1210]) ).
fof(f1095,plain,
( ! [X2,X0,X1] :
( subset(relation_dom_as_subset(X1,X2,X0),X1)
| ~ relation_of2(X0,X1,X2) )
| ~ spl22_138 ),
inference(avatar_component_clause,[],[f1094]) ).
fof(f1889,plain,
( ~ spl22_78
| spl22_239
| ~ spl22_109
| ~ spl22_138 ),
inference(avatar_split_clause,[],[f1232,f1094,f865,f1886,f648]) ).
fof(f1232,plain,
( subset(relation_dom(sK4),sK1)
| ~ relation_of2(sK4,sK1,sK2)
| ~ spl22_109
| ~ spl22_138 ),
inference(superposition,[],[f1095,f867]) ).
fof(f1884,plain,
( spl22_238
| ~ spl22_89
| ~ spl22_141 ),
inference(avatar_split_clause,[],[f1137,f1116,f713,f1882]) ).
fof(f1882,plain,
( spl22_238
<=> ! [X0,X1] :
( relation_dom(sK10(X0,X1)) != X0
| quasi_total(sK10(X0,X1),X0,X1)
| sK13 = X1
| ~ sP0(X0,sK10(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_238])]) ).
fof(f1116,plain,
( spl22_141
<=> ! [X0,X1] : relation_dom_as_subset(X0,X1,sK10(X0,X1)) = relation_dom(sK10(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_141])]) ).
fof(f1137,plain,
( ! [X0,X1] :
( relation_dom(sK10(X0,X1)) != X0
| quasi_total(sK10(X0,X1),X0,X1)
| sK13 = X1
| ~ sP0(X0,sK10(X0,X1),X1) )
| ~ spl22_89
| ~ spl22_141 ),
inference(superposition,[],[f714,f1117]) ).
fof(f1117,plain,
( ! [X0,X1] : relation_dom_as_subset(X0,X1,sK10(X0,X1)) = relation_dom(sK10(X0,X1))
| ~ spl22_141 ),
inference(avatar_component_clause,[],[f1116]) ).
fof(f1880,plain,
( spl22_237
| ~ spl22_89
| ~ spl22_140 ),
inference(avatar_split_clause,[],[f1133,f1112,f713,f1878]) ).
fof(f1878,plain,
( spl22_237
<=> ! [X0,X1] :
( relation_dom(sK8(X0,X1)) != X0
| quasi_total(sK8(X0,X1),X0,X1)
| sK13 = X1
| ~ sP0(X0,sK8(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_237])]) ).
fof(f1112,plain,
( spl22_140
<=> ! [X0,X1] : relation_dom_as_subset(X0,X1,sK8(X0,X1)) = relation_dom(sK8(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_140])]) ).
fof(f1133,plain,
( ! [X0,X1] :
( relation_dom(sK8(X0,X1)) != X0
| quasi_total(sK8(X0,X1),X0,X1)
| sK13 = X1
| ~ sP0(X0,sK8(X0,X1),X1) )
| ~ spl22_89
| ~ spl22_140 ),
inference(superposition,[],[f714,f1113]) ).
fof(f1113,plain,
( ! [X0,X1] : relation_dom_as_subset(X0,X1,sK8(X0,X1)) = relation_dom(sK8(X0,X1))
| ~ spl22_140 ),
inference(avatar_component_clause,[],[f1112]) ).
fof(f1876,plain,
( spl22_236
| ~ spl22_83
| ~ spl22_141 ),
inference(avatar_split_clause,[],[f1139,f1116,f686,f1874]) ).
fof(f1874,plain,
( spl22_236
<=> ! [X0] :
( sK13 != relation_dom(sK10(sK13,X0))
| ~ sP0(sK13,sK10(sK13,X0),X0)
| quasi_total(sK10(sK13,X0),sK13,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_236])]) ).
fof(f686,plain,
( spl22_83
<=> ! [X2,X1] :
( ~ sP0(sK13,X1,X2)
| sK13 != relation_dom_as_subset(sK13,X2,X1)
| quasi_total(X1,sK13,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_83])]) ).
fof(f1139,plain,
( ! [X0] :
( sK13 != relation_dom(sK10(sK13,X0))
| ~ sP0(sK13,sK10(sK13,X0),X0)
| quasi_total(sK10(sK13,X0),sK13,X0) )
| ~ spl22_83
| ~ spl22_141 ),
inference(superposition,[],[f687,f1117]) ).
fof(f687,plain,
( ! [X2,X1] :
( sK13 != relation_dom_as_subset(sK13,X2,X1)
| ~ sP0(sK13,X1,X2)
| quasi_total(X1,sK13,X2) )
| ~ spl22_83 ),
inference(avatar_component_clause,[],[f686]) ).
fof(f1872,plain,
( spl22_235
| ~ spl22_83
| ~ spl22_140 ),
inference(avatar_split_clause,[],[f1135,f1112,f686,f1870]) ).
fof(f1870,plain,
( spl22_235
<=> ! [X0] :
( sK13 != relation_dom(sK8(sK13,X0))
| ~ sP0(sK13,sK8(sK13,X0),X0)
| quasi_total(sK8(sK13,X0),sK13,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_235])]) ).
fof(f1135,plain,
( ! [X0] :
( sK13 != relation_dom(sK8(sK13,X0))
| ~ sP0(sK13,sK8(sK13,X0),X0)
| quasi_total(sK8(sK13,X0),sK13,X0) )
| ~ spl22_83
| ~ spl22_140 ),
inference(superposition,[],[f687,f1113]) ).
fof(f1863,plain,
( spl22_234
| ~ spl22_142
| ~ spl22_146 ),
inference(avatar_split_clause,[],[f1183,f1170,f1120,f1861]) ).
fof(f1120,plain,
( spl22_142
<=> ! [X0,X1] : relation_dom_as_subset(X0,X1,sK11(X0,X1)) = relation_dom(sK11(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_142])]) ).
fof(f1170,plain,
( spl22_146
<=> ! [X0,X3,X2,X1] :
( ~ relation_of2(X0,cartesian_product2(X1,X2),X3)
| relation(relation_dom_as_subset(cartesian_product2(X1,X2),X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_146])]) ).
fof(f1183,plain,
( ! [X2,X0,X1] :
( relation(relation_dom(sK11(cartesian_product2(X0,X1),X2)))
| ~ relation_of2(sK11(cartesian_product2(X0,X1),X2),cartesian_product2(X0,X1),X2) )
| ~ spl22_142
| ~ spl22_146 ),
inference(superposition,[],[f1171,f1121]) ).
fof(f1121,plain,
( ! [X0,X1] : relation_dom_as_subset(X0,X1,sK11(X0,X1)) = relation_dom(sK11(X0,X1))
| ~ spl22_142 ),
inference(avatar_component_clause,[],[f1120]) ).
fof(f1171,plain,
( ! [X2,X3,X0,X1] :
( relation(relation_dom_as_subset(cartesian_product2(X1,X2),X3,X0))
| ~ relation_of2(X0,cartesian_product2(X1,X2),X3) )
| ~ spl22_146 ),
inference(avatar_component_clause,[],[f1170]) ).
fof(f1859,plain,
( spl22_233
| ~ spl22_141
| ~ spl22_146 ),
inference(avatar_split_clause,[],[f1182,f1170,f1116,f1857]) ).
fof(f1182,plain,
( ! [X2,X0,X1] :
( relation(relation_dom(sK10(cartesian_product2(X0,X1),X2)))
| ~ relation_of2(sK10(cartesian_product2(X0,X1),X2),cartesian_product2(X0,X1),X2) )
| ~ spl22_141
| ~ spl22_146 ),
inference(superposition,[],[f1171,f1117]) ).
fof(f1855,plain,
( spl22_232
| ~ spl22_140
| ~ spl22_146 ),
inference(avatar_split_clause,[],[f1181,f1170,f1112,f1853]) ).
fof(f1181,plain,
( ! [X2,X0,X1] :
( relation(relation_dom(sK8(cartesian_product2(X0,X1),X2)))
| ~ relation_of2(sK8(cartesian_product2(X0,X1),X2),cartesian_product2(X0,X1),X2) )
| ~ spl22_140
| ~ spl22_146 ),
inference(superposition,[],[f1171,f1113]) ).
fof(f1851,plain,
( ~ spl22_231
| ~ spl22_49
| ~ spl22_220 ),
inference(avatar_split_clause,[],[f1803,f1764,f469,f1848]) ).
fof(f1848,plain,
( spl22_231
<=> in(sK3,sK6(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_231])]) ).
fof(f1803,plain,
( ~ in(sK3,sK6(sK2))
| ~ spl22_49
| ~ spl22_220 ),
inference(resolution,[],[f1766,f470]) ).
fof(f1846,plain,
( spl22_230
| ~ spl22_204
| ~ spl22_229 ),
inference(avatar_split_clause,[],[f1842,f1839,f1654,f1844]) ).
fof(f1844,plain,
( spl22_230
<=> ! [X0,X1] :
( relation_dom(sK9(X0,X1)) = X0
| ~ quasi_total(sK9(X0,X1),X0,X1)
| sK13 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_230])]) ).
fof(f1654,plain,
( spl22_204
<=> ! [X0,X1] : relation_dom_as_subset(X0,X1,sK9(X0,X1)) = relation_dom(sK9(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_204])]) ).
fof(f1839,plain,
( spl22_229
<=> ! [X0,X1] :
( relation_dom_as_subset(X0,X1,sK9(X0,X1)) = X0
| ~ quasi_total(sK9(X0,X1),X0,X1)
| sK13 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_229])]) ).
fof(f1842,plain,
( ! [X0,X1] :
( relation_dom(sK9(X0,X1)) = X0
| ~ quasi_total(sK9(X0,X1),X0,X1)
| sK13 = X1 )
| ~ spl22_204
| ~ spl22_229 ),
inference(forward_demodulation,[],[f1840,f1655]) ).
fof(f1655,plain,
( ! [X0,X1] : relation_dom_as_subset(X0,X1,sK9(X0,X1)) = relation_dom(sK9(X0,X1))
| ~ spl22_204 ),
inference(avatar_component_clause,[],[f1654]) ).
fof(f1840,plain,
( ! [X0,X1] :
( relation_dom_as_subset(X0,X1,sK9(X0,X1)) = X0
| ~ quasi_total(sK9(X0,X1),X0,X1)
| sK13 = X1 )
| ~ spl22_229 ),
inference(avatar_component_clause,[],[f1839]) ).
fof(f1841,plain,
( spl22_229
| ~ spl22_88
| ~ spl22_114 ),
inference(avatar_split_clause,[],[f963,f914,f709,f1839]) ).
fof(f709,plain,
( spl22_88
<=> ! [X2,X0,X1] :
( sK13 = X2
| relation_dom_as_subset(X0,X2,X1) = X0
| ~ quasi_total(X1,X0,X2)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_88])]) ).
fof(f914,plain,
( spl22_114
<=> ! [X0,X1] : sP0(X0,sK9(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_114])]) ).
fof(f963,plain,
( ! [X0,X1] :
( relation_dom_as_subset(X0,X1,sK9(X0,X1)) = X0
| ~ quasi_total(sK9(X0,X1),X0,X1)
| sK13 = X1 )
| ~ spl22_88
| ~ spl22_114 ),
inference(resolution,[],[f915,f710]) ).
fof(f710,plain,
( ! [X2,X0,X1] :
( ~ sP0(X0,X1,X2)
| relation_dom_as_subset(X0,X2,X1) = X0
| ~ quasi_total(X1,X0,X2)
| sK13 = X2 )
| ~ spl22_88 ),
inference(avatar_component_clause,[],[f709]) ).
fof(f915,plain,
( ! [X0,X1] : sP0(X0,sK9(X0,X1),X1)
| ~ spl22_114 ),
inference(avatar_component_clause,[],[f914]) ).
fof(f1819,plain,
( spl22_228
| ~ spl22_142
| ~ spl22_148 ),
inference(avatar_split_clause,[],[f1197,f1185,f1120,f1817]) ).
fof(f1817,plain,
( spl22_228
<=> ! [X0,X1] :
( in(relation_dom(sK11(X0,X1)),powerset(X0))
| empty(powerset(X0))
| ~ relation_of2(sK11(X0,X1),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_228])]) ).
fof(f1197,plain,
( ! [X0,X1] :
( in(relation_dom(sK11(X0,X1)),powerset(X0))
| empty(powerset(X0))
| ~ relation_of2(sK11(X0,X1),X0,X1) )
| ~ spl22_142
| ~ spl22_148 ),
inference(superposition,[],[f1186,f1121]) ).
fof(f1815,plain,
( spl22_227
| ~ spl22_141
| ~ spl22_148 ),
inference(avatar_split_clause,[],[f1196,f1185,f1116,f1813]) ).
fof(f1813,plain,
( spl22_227
<=> ! [X0,X1] :
( in(relation_dom(sK10(X0,X1)),powerset(X0))
| empty(powerset(X0))
| ~ relation_of2(sK10(X0,X1),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_227])]) ).
fof(f1196,plain,
( ! [X0,X1] :
( in(relation_dom(sK10(X0,X1)),powerset(X0))
| empty(powerset(X0))
| ~ relation_of2(sK10(X0,X1),X0,X1) )
| ~ spl22_141
| ~ spl22_148 ),
inference(superposition,[],[f1186,f1117]) ).
fof(f1811,plain,
( spl22_226
| ~ spl22_140
| ~ spl22_148 ),
inference(avatar_split_clause,[],[f1195,f1185,f1112,f1809]) ).
fof(f1809,plain,
( spl22_226
<=> ! [X0,X1] :
( in(relation_dom(sK8(X0,X1)),powerset(X0))
| empty(powerset(X0))
| ~ relation_of2(sK8(X0,X1),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_226])]) ).
fof(f1195,plain,
( ! [X0,X1] :
( in(relation_dom(sK8(X0,X1)),powerset(X0))
| empty(powerset(X0))
| ~ relation_of2(sK8(X0,X1),X0,X1) )
| ~ spl22_140
| ~ spl22_148 ),
inference(superposition,[],[f1186,f1113]) ).
fof(f1807,plain,
( spl22_225
| ~ spl22_113
| ~ spl22_145 ),
inference(avatar_split_clause,[],[f1177,f1166,f910,f1805]) ).
fof(f1805,plain,
( spl22_225
<=> ! [X2,X0,X1] :
( element(sK6(relation_dom_as_subset(X0,X1,X2)),X0)
| ~ relation_of2(X2,X0,X1)
| empty(relation_dom_as_subset(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_225])]) ).
fof(f1177,plain,
( ! [X2,X0,X1] :
( element(sK6(relation_dom_as_subset(X0,X1,X2)),X0)
| ~ relation_of2(X2,X0,X1)
| empty(relation_dom_as_subset(X0,X1,X2)) )
| ~ spl22_113
| ~ spl22_145 ),
inference(resolution,[],[f1167,f911]) ).
fof(f1793,plain,
( spl22_224
| ~ spl22_49
| ~ spl22_150 ),
inference(avatar_split_clause,[],[f1205,f1200,f469,f1791]) ).
fof(f1791,plain,
( spl22_224
<=> ! [X2,X0,X1] :
( empty(powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1)
| ~ in(powerset(cartesian_product2(X0,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_224])]) ).
fof(f1200,plain,
( spl22_150
<=> ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| empty(powerset(cartesian_product2(X1,X2)))
| in(X0,powerset(cartesian_product2(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_150])]) ).
fof(f1205,plain,
( ! [X2,X0,X1] :
( empty(powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1)
| ~ in(powerset(cartesian_product2(X0,X1)),X2) )
| ~ spl22_49
| ~ spl22_150 ),
inference(resolution,[],[f1201,f470]) ).
fof(f1201,plain,
( ! [X2,X0,X1] :
( in(X0,powerset(cartesian_product2(X1,X2)))
| empty(powerset(cartesian_product2(X1,X2)))
| ~ relation_of2_as_subset(X0,X1,X2) )
| ~ spl22_150 ),
inference(avatar_component_clause,[],[f1200]) ).
fof(f1789,plain,
( spl22_223
| ~ spl22_142
| ~ spl22_145 ),
inference(avatar_split_clause,[],[f1180,f1166,f1120,f1787]) ).
fof(f1787,plain,
( spl22_223
<=> ! [X2,X0,X1] :
( ~ in(X2,relation_dom(sK11(X0,X1)))
| element(X2,X0)
| ~ relation_of2(sK11(X0,X1),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_223])]) ).
fof(f1180,plain,
( ! [X2,X0,X1] :
( ~ in(X2,relation_dom(sK11(X0,X1)))
| element(X2,X0)
| ~ relation_of2(sK11(X0,X1),X0,X1) )
| ~ spl22_142
| ~ spl22_145 ),
inference(superposition,[],[f1167,f1121]) ).
fof(f1785,plain,
( spl22_222
| ~ spl22_141
| ~ spl22_145 ),
inference(avatar_split_clause,[],[f1179,f1166,f1116,f1783]) ).
fof(f1783,plain,
( spl22_222
<=> ! [X2,X0,X1] :
( ~ in(X2,relation_dom(sK10(X0,X1)))
| element(X2,X0)
| ~ relation_of2(sK10(X0,X1),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_222])]) ).
fof(f1179,plain,
( ! [X2,X0,X1] :
( ~ in(X2,relation_dom(sK10(X0,X1)))
| element(X2,X0)
| ~ relation_of2(sK10(X0,X1),X0,X1) )
| ~ spl22_141
| ~ spl22_145 ),
inference(superposition,[],[f1167,f1117]) ).
fof(f1781,plain,
( spl22_221
| ~ spl22_140
| ~ spl22_145 ),
inference(avatar_split_clause,[],[f1178,f1166,f1112,f1779]) ).
fof(f1779,plain,
( spl22_221
<=> ! [X2,X0,X1] :
( ~ in(X2,relation_dom(sK8(X0,X1)))
| element(X2,X0)
| ~ relation_of2(sK8(X0,X1),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_221])]) ).
fof(f1178,plain,
( ! [X2,X0,X1] :
( ~ in(X2,relation_dom(sK8(X0,X1)))
| element(X2,X0)
| ~ relation_of2(sK8(X0,X1),X0,X1) )
| ~ spl22_140
| ~ spl22_145 ),
inference(superposition,[],[f1167,f1113]) ).
fof(f1767,plain,
( spl22_220
| spl22_134
| ~ spl22_64
| ~ spl22_153 ),
inference(avatar_split_clause,[],[f1649,f1217,f551,f1078,f1764]) ).
fof(f1649,plain,
( empty(sK3)
| in(sK6(sK2),sK3)
| ~ spl22_64
| ~ spl22_153 ),
inference(resolution,[],[f1219,f552]) ).
fof(f1219,plain,
( element(sK6(sK2),sK3)
| ~ spl22_153 ),
inference(avatar_component_clause,[],[f1217]) ).
fof(f1760,plain,
( spl22_219
| ~ spl22_49
| ~ spl22_148 ),
inference(avatar_split_clause,[],[f1194,f1185,f469,f1758]) ).
fof(f1758,plain,
( spl22_219
<=> ! [X2,X0,X1] :
( empty(powerset(X0))
| ~ relation_of2(X1,X0,X2)
| ~ in(powerset(X0),relation_dom_as_subset(X0,X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_219])]) ).
fof(f1194,plain,
( ! [X2,X0,X1] :
( empty(powerset(X0))
| ~ relation_of2(X1,X0,X2)
| ~ in(powerset(X0),relation_dom_as_subset(X0,X2,X1)) )
| ~ spl22_49
| ~ spl22_148 ),
inference(resolution,[],[f1186,f470]) ).
fof(f1756,plain,
( spl22_218
| ~ spl22_142
| ~ spl22_144 ),
inference(avatar_split_clause,[],[f1164,f1149,f1120,f1754]) ).
fof(f1754,plain,
( spl22_218
<=> ! [X2,X0,X1] :
( ~ in(X2,relation_dom(sK11(X0,X1)))
| ~ empty(X0)
| ~ relation_of2(sK11(X0,X1),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_218])]) ).
fof(f1149,plain,
( spl22_144
<=> ! [X2,X0,X1,X3] :
( ~ relation_of2(X0,X1,X2)
| ~ empty(X1)
| ~ in(X3,relation_dom_as_subset(X1,X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_144])]) ).
fof(f1164,plain,
( ! [X2,X0,X1] :
( ~ in(X2,relation_dom(sK11(X0,X1)))
| ~ empty(X0)
| ~ relation_of2(sK11(X0,X1),X0,X1) )
| ~ spl22_142
| ~ spl22_144 ),
inference(superposition,[],[f1150,f1121]) ).
fof(f1150,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X3,relation_dom_as_subset(X1,X2,X0))
| ~ empty(X1)
| ~ relation_of2(X0,X1,X2) )
| ~ spl22_144 ),
inference(avatar_component_clause,[],[f1149]) ).
fof(f1752,plain,
( spl22_217
| ~ spl22_141
| ~ spl22_144 ),
inference(avatar_split_clause,[],[f1163,f1149,f1116,f1750]) ).
fof(f1750,plain,
( spl22_217
<=> ! [X2,X0,X1] :
( ~ in(X2,relation_dom(sK10(X0,X1)))
| ~ empty(X0)
| ~ relation_of2(sK10(X0,X1),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_217])]) ).
fof(f1163,plain,
( ! [X2,X0,X1] :
( ~ in(X2,relation_dom(sK10(X0,X1)))
| ~ empty(X0)
| ~ relation_of2(sK10(X0,X1),X0,X1) )
| ~ spl22_141
| ~ spl22_144 ),
inference(superposition,[],[f1150,f1117]) ).
fof(f1748,plain,
( spl22_216
| ~ spl22_140
| ~ spl22_144 ),
inference(avatar_split_clause,[],[f1162,f1149,f1112,f1746]) ).
fof(f1746,plain,
( spl22_216
<=> ! [X2,X0,X1] :
( ~ in(X2,relation_dom(sK8(X0,X1)))
| ~ empty(X0)
| ~ relation_of2(sK8(X0,X1),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_216])]) ).
fof(f1162,plain,
( ! [X2,X0,X1] :
( ~ in(X2,relation_dom(sK8(X0,X1)))
| ~ empty(X0)
| ~ relation_of2(sK8(X0,X1),X0,X1) )
| ~ spl22_140
| ~ spl22_144 ),
inference(superposition,[],[f1150,f1113]) ).
fof(f1738,plain,
( spl22_215
| ~ spl22_133
| ~ spl22_143 ),
inference(avatar_split_clause,[],[f1158,f1145,f1061,f1736]) ).
fof(f1736,plain,
( spl22_215
<=> ! [X0,X3,X2,X1] :
( ~ in(X0,sK9(X1,X2))
| element(X0,cartesian_product2(X1,X3))
| ~ subset(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_215])]) ).
fof(f1061,plain,
( spl22_133
<=> ! [X2,X0,X1] :
( ~ subset(X0,X1)
| relation_of2_as_subset(sK9(X2,X0),X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_133])]) ).
fof(f1145,plain,
( spl22_143
<=> ! [X0,X3,X2,X1] :
( element(X0,cartesian_product2(X1,X2))
| ~ in(X0,X3)
| ~ relation_of2_as_subset(X3,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_143])]) ).
fof(f1158,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X0,sK9(X1,X2))
| element(X0,cartesian_product2(X1,X3))
| ~ subset(X2,X3) )
| ~ spl22_133
| ~ spl22_143 ),
inference(resolution,[],[f1146,f1062]) ).
fof(f1062,plain,
( ! [X2,X0,X1] :
( relation_of2_as_subset(sK9(X2,X0),X2,X1)
| ~ subset(X0,X1) )
| ~ spl22_133 ),
inference(avatar_component_clause,[],[f1061]) ).
fof(f1146,plain,
( ! [X2,X3,X0,X1] :
( ~ relation_of2_as_subset(X3,X1,X2)
| ~ in(X0,X3)
| element(X0,cartesian_product2(X1,X2)) )
| ~ spl22_143 ),
inference(avatar_component_clause,[],[f1145]) ).
fof(f1734,plain,
( spl22_214
| ~ spl22_75
| ~ spl22_142 ),
inference(avatar_split_clause,[],[f1142,f1120,f630,f1732]) ).
fof(f1142,plain,
( ! [X0,X1] :
( element(relation_dom(sK11(X0,X1)),powerset(X0))
| ~ relation_of2(sK11(X0,X1),X0,X1) )
| ~ spl22_75
| ~ spl22_142 ),
inference(superposition,[],[f631,f1121]) ).
fof(f1730,plain,
( spl22_213
| ~ spl22_75
| ~ spl22_141 ),
inference(avatar_split_clause,[],[f1138,f1116,f630,f1728]) ).
fof(f1138,plain,
( ! [X0,X1] :
( element(relation_dom(sK10(X0,X1)),powerset(X0))
| ~ relation_of2(sK10(X0,X1),X0,X1) )
| ~ spl22_75
| ~ spl22_141 ),
inference(superposition,[],[f631,f1117]) ).
fof(f1726,plain,
( spl22_212
| ~ spl22_75
| ~ spl22_140 ),
inference(avatar_split_clause,[],[f1134,f1112,f630,f1724]) ).
fof(f1134,plain,
( ! [X0,X1] :
( element(relation_dom(sK8(X0,X1)),powerset(X0))
| ~ relation_of2(sK8(X0,X1),X0,X1) )
| ~ spl22_75
| ~ spl22_140 ),
inference(superposition,[],[f631,f1113]) ).
fof(f1709,plain,
( spl22_211
| ~ spl22_138
| ~ spl22_142 ),
inference(avatar_split_clause,[],[f1140,f1120,f1094,f1707]) ).
fof(f1140,plain,
( ! [X0,X1] :
( subset(relation_dom(sK11(X0,X1)),X0)
| ~ relation_of2(sK11(X0,X1),X0,X1) )
| ~ spl22_138
| ~ spl22_142 ),
inference(superposition,[],[f1095,f1121]) ).
fof(f1705,plain,
( spl22_168
| ~ spl22_124
| ~ spl22_210
| ~ spl22_59
| ~ spl22_165 ),
inference(avatar_split_clause,[],[f1317,f1304,f512,f1702,f992,f1325]) ).
fof(f1325,plain,
( spl22_168
<=> empty(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_168])]) ).
fof(f992,plain,
( spl22_124
<=> relation(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_124])]) ).
fof(f512,plain,
( spl22_59
<=> ! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_59])]) ).
fof(f1317,plain,
( ~ empty(sK1)
| ~ relation(sK4)
| empty(sK4)
| ~ spl22_59
| ~ spl22_165 ),
inference(superposition,[],[f513,f1306]) ).
fof(f513,plain,
( ! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) )
| ~ spl22_59 ),
inference(avatar_component_clause,[],[f512]) ).
fof(f1700,plain,
( spl22_209
| ~ spl22_138
| ~ spl22_141 ),
inference(avatar_split_clause,[],[f1136,f1116,f1094,f1698]) ).
fof(f1136,plain,
( ! [X0,X1] :
( subset(relation_dom(sK10(X0,X1)),X0)
| ~ relation_of2(sK10(X0,X1),X0,X1) )
| ~ spl22_138
| ~ spl22_141 ),
inference(superposition,[],[f1095,f1117]) ).
fof(f1696,plain,
( spl22_208
| ~ spl22_138
| ~ spl22_140 ),
inference(avatar_split_clause,[],[f1132,f1112,f1094,f1694]) ).
fof(f1132,plain,
( ! [X0,X1] :
( subset(relation_dom(sK8(X0,X1)),X0)
| ~ relation_of2(sK8(X0,X1),X0,X1) )
| ~ spl22_138
| ~ spl22_140 ),
inference(superposition,[],[f1095,f1113]) ).
fof(f1692,plain,
( spl22_207
| ~ spl22_133
| ~ spl22_139 ),
inference(avatar_split_clause,[],[f1129,f1108,f1061,f1690]) ).
fof(f1690,plain,
( spl22_207
<=> ! [X0,X3,X2,X1] :
( ~ empty(cartesian_product2(X0,X1))
| ~ in(X2,sK9(X0,X3))
| ~ subset(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_207])]) ).
fof(f1108,plain,
( spl22_139
<=> ! [X2,X0,X1,X3] :
( ~ relation_of2_as_subset(X0,X1,X2)
| ~ empty(cartesian_product2(X1,X2))
| ~ in(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_139])]) ).
fof(f1129,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| ~ in(X2,sK9(X0,X3))
| ~ subset(X3,X1) )
| ~ spl22_133
| ~ spl22_139 ),
inference(resolution,[],[f1109,f1062]) ).
fof(f1109,plain,
( ! [X2,X3,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| ~ empty(cartesian_product2(X1,X2))
| ~ in(X3,X0) )
| ~ spl22_139 ),
inference(avatar_component_clause,[],[f1108]) ).
fof(f1688,plain,
( spl22_206
| ~ spl22_76
| ~ spl22_133 ),
inference(avatar_split_clause,[],[f1074,f1061,f634,f1686]) ).
fof(f634,plain,
( spl22_76
<=> ! [X0,X3,X2,X1] :
( relation_of2_as_subset(X3,X2,X1)
| ~ subset(X0,X1)
| ~ relation_of2_as_subset(X3,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_76])]) ).
fof(f1074,plain,
( ! [X2,X3,X0,X1] :
( ~ subset(X0,X1)
| ~ subset(X1,X2)
| relation_of2_as_subset(sK9(X3,X0),X3,X2) )
| ~ spl22_76
| ~ spl22_133 ),
inference(resolution,[],[f1062,f635]) ).
fof(f635,plain,
( ! [X2,X3,X0,X1] :
( ~ relation_of2_as_subset(X3,X2,X0)
| ~ subset(X0,X1)
| relation_of2_as_subset(X3,X2,X1) )
| ~ spl22_76 ),
inference(avatar_component_clause,[],[f634]) ).
fof(f1660,plain,
( spl22_205
| ~ spl22_113
| ~ spl22_144 ),
inference(avatar_split_clause,[],[f1161,f1149,f910,f1658]) ).
fof(f1658,plain,
( spl22_205
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ relation_of2(X1,X0,X2)
| empty(relation_dom_as_subset(X0,X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_205])]) ).
fof(f1161,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ relation_of2(X1,X0,X2)
| empty(relation_dom_as_subset(X0,X2,X1)) )
| ~ spl22_113
| ~ spl22_144 ),
inference(resolution,[],[f1150,f911]) ).
fof(f1656,plain,
( spl22_204
| ~ spl22_74
| ~ spl22_116 ),
inference(avatar_split_clause,[],[f964,f922,f626,f1654]) ).
fof(f964,plain,
( ! [X0,X1] : relation_dom_as_subset(X0,X1,sK9(X0,X1)) = relation_dom(sK9(X0,X1))
| ~ spl22_74
| ~ spl22_116 ),
inference(resolution,[],[f923,f627]) ).
fof(f1627,plain,
( spl22_203
| ~ spl22_119
| ~ spl22_143 ),
inference(avatar_split_clause,[],[f1160,f1145,f934,f1625]) ).
fof(f1625,plain,
( spl22_203
<=> ! [X2,X0,X1] :
( ~ in(X0,sK11(X1,X2))
| element(X0,cartesian_product2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_203])]) ).
fof(f1160,plain,
( ! [X2,X0,X1] :
( ~ in(X0,sK11(X1,X2))
| element(X0,cartesian_product2(X1,X2)) )
| ~ spl22_119
| ~ spl22_143 ),
inference(resolution,[],[f1146,f935]) ).
fof(f1623,plain,
( spl22_202
| ~ spl22_118
| ~ spl22_143 ),
inference(avatar_split_clause,[],[f1159,f1145,f930,f1621]) ).
fof(f1621,plain,
( spl22_202
<=> ! [X2,X0,X1] :
( ~ in(X0,sK10(X1,X2))
| element(X0,cartesian_product2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_202])]) ).
fof(f930,plain,
( spl22_118
<=> ! [X0,X1] : relation_of2_as_subset(sK10(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_118])]) ).
fof(f1159,plain,
( ! [X2,X0,X1] :
( ~ in(X0,sK10(X1,X2))
| element(X0,cartesian_product2(X1,X2)) )
| ~ spl22_118
| ~ spl22_143 ),
inference(resolution,[],[f1146,f931]) ).
fof(f931,plain,
( ! [X0,X1] : relation_of2_as_subset(sK10(X0,X1),X0,X1)
| ~ spl22_118 ),
inference(avatar_component_clause,[],[f930]) ).
fof(f1619,plain,
( spl22_201
| ~ spl22_52
| ~ spl22_143 ),
inference(avatar_split_clause,[],[f1157,f1145,f481,f1617]) ).
fof(f1617,plain,
( spl22_201
<=> ! [X2,X0,X1] :
( ~ in(X0,sK9(X1,X2))
| element(X0,cartesian_product2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_201])]) ).
fof(f481,plain,
( spl22_52
<=> ! [X0,X1] : relation_of2_as_subset(sK9(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_52])]) ).
fof(f1157,plain,
( ! [X2,X0,X1] :
( ~ in(X0,sK9(X1,X2))
| element(X0,cartesian_product2(X1,X2)) )
| ~ spl22_52
| ~ spl22_143 ),
inference(resolution,[],[f1146,f482]) ).
fof(f482,plain,
( ! [X0,X1] : relation_of2_as_subset(sK9(X0,X1),X0,X1)
| ~ spl22_52 ),
inference(avatar_component_clause,[],[f481]) ).
fof(f1615,plain,
( spl22_200
| ~ spl22_117
| ~ spl22_143 ),
inference(avatar_split_clause,[],[f1156,f1145,f926,f1613]) ).
fof(f1613,plain,
( spl22_200
<=> ! [X2,X0,X1] :
( ~ in(X0,sK8(X1,X2))
| element(X0,cartesian_product2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_200])]) ).
fof(f926,plain,
( spl22_117
<=> ! [X0,X1] : relation_of2_as_subset(sK8(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_117])]) ).
fof(f1156,plain,
( ! [X2,X0,X1] :
( ~ in(X0,sK8(X1,X2))
| element(X0,cartesian_product2(X1,X2)) )
| ~ spl22_117
| ~ spl22_143 ),
inference(resolution,[],[f1146,f927]) ).
fof(f927,plain,
( ! [X0,X1] : relation_of2_as_subset(sK8(X0,X1),X0,X1)
| ~ spl22_117 ),
inference(avatar_component_clause,[],[f926]) ).
fof(f1611,plain,
( spl22_199
| ~ spl22_56
| ~ spl22_138 ),
inference(avatar_split_clause,[],[f1103,f1094,f497,f1609]) ).
fof(f1103,plain,
( ! [X0,X1] :
( ~ relation_of2(X0,sK13,X1)
| sK13 = relation_dom_as_subset(sK13,X1,X0) )
| ~ spl22_56
| ~ spl22_138 ),
inference(resolution,[],[f1095,f498]) ).
fof(f1607,plain,
( spl22_198
| ~ spl22_49
| ~ spl22_137 ),
inference(avatar_split_clause,[],[f1102,f1090,f469,f1605]) ).
fof(f1605,plain,
( spl22_198
<=> ! [X0] :
( empty(powerset(X0))
| empty(X0)
| ~ in(powerset(X0),sK5(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_198])]) ).
fof(f1090,plain,
( spl22_137
<=> ! [X0] :
( empty(powerset(X0))
| in(sK5(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_137])]) ).
fof(f1102,plain,
( ! [X0] :
( empty(powerset(X0))
| empty(X0)
| ~ in(powerset(X0),sK5(X0)) )
| ~ spl22_49
| ~ spl22_137 ),
inference(resolution,[],[f1091,f470]) ).
fof(f1091,plain,
( ! [X0] :
( in(sK5(X0),powerset(X0))
| empty(powerset(X0))
| empty(X0) )
| ~ spl22_137 ),
inference(avatar_component_clause,[],[f1090]) ).
fof(f1603,plain,
( spl22_197
| ~ spl22_49
| ~ spl22_136 ),
inference(avatar_split_clause,[],[f1099,f1086,f469,f1601]) ).
fof(f1601,plain,
( spl22_197
<=> ! [X0,X1] :
( empty(powerset(X0))
| ~ subset(X1,X0)
| ~ in(powerset(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_197])]) ).
fof(f1086,plain,
( spl22_136
<=> ! [X0,X1] :
( empty(powerset(X0))
| in(X1,powerset(X0))
| ~ subset(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_136])]) ).
fof(f1099,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| ~ subset(X1,X0)
| ~ in(powerset(X0),X1) )
| ~ spl22_49
| ~ spl22_136 ),
inference(resolution,[],[f1087,f470]) ).
fof(f1087,plain,
( ! [X0,X1] :
( in(X1,powerset(X0))
| empty(powerset(X0))
| ~ subset(X1,X0) )
| ~ spl22_136 ),
inference(avatar_component_clause,[],[f1086]) ).
fof(f1599,plain,
( spl22_196
| ~ spl22_113
| ~ spl22_132 ),
inference(avatar_split_clause,[],[f1072,f1057,f910,f1597]) ).
fof(f1597,plain,
( spl22_196
<=> ! [X0] :
( element(sK6(sK5(X0)),X0)
| empty(X0)
| empty(sK5(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_196])]) ).
fof(f1057,plain,
( spl22_132
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK5(X1))
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_132])]) ).
fof(f1072,plain,
( ! [X0] :
( element(sK6(sK5(X0)),X0)
| empty(X0)
| empty(sK5(X0)) )
| ~ spl22_113
| ~ spl22_132 ),
inference(resolution,[],[f1058,f911]) ).
fof(f1058,plain,
( ! [X0,X1] :
( ~ in(X0,sK5(X1))
| element(X0,X1)
| empty(X1) )
| ~ spl22_132 ),
inference(avatar_component_clause,[],[f1057]) ).
fof(f1595,plain,
( spl22_195
| ~ spl22_113
| ~ spl22_128 ),
inference(avatar_split_clause,[],[f1043,f1017,f910,f1593]) ).
fof(f1593,plain,
( spl22_195
<=> ! [X0] :
( element(sK6(sK6(powerset(X0))),X0)
| empty(sK6(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_195])]) ).
fof(f1017,plain,
( spl22_128
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK6(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_128])]) ).
fof(f1043,plain,
( ! [X0] :
( element(sK6(sK6(powerset(X0))),X0)
| empty(sK6(powerset(X0))) )
| ~ spl22_113
| ~ spl22_128 ),
inference(resolution,[],[f1018,f911]) ).
fof(f1018,plain,
( ! [X0,X1] :
( ~ in(X0,sK6(powerset(X1)))
| element(X0,X1) )
| ~ spl22_128 ),
inference(avatar_component_clause,[],[f1017]) ).
fof(f1582,plain,
( spl22_194
| ~ spl22_90
| ~ spl22_143 ),
inference(avatar_split_clause,[],[f1154,f1145,f720,f1580]) ).
fof(f1154,plain,
( ! [X0,X1] :
( ~ in(X0,sK4)
| element(X0,cartesian_product2(sK1,X1))
| ~ subset(sK2,X1) )
| ~ spl22_90
| ~ spl22_143 ),
inference(resolution,[],[f1146,f721]) ).
fof(f1578,plain,
( spl22_193
| ~ spl22_100
| ~ spl22_143 ),
inference(avatar_split_clause,[],[f1153,f1145,f779,f1576]) ).
fof(f1153,plain,
( ! [X0,X1] :
( ~ in(X0,sK4)
| element(X0,cartesian_product2(sK1,X1))
| ~ subset(sK3,X1) )
| ~ spl22_100
| ~ spl22_143 ),
inference(resolution,[],[f1146,f780]) ).
fof(f1574,plain,
( spl22_156
| spl22_192
| ~ spl22_90
| ~ spl22_139 ),
inference(avatar_split_clause,[],[f1125,f1108,f720,f1572,f1239]) ).
fof(f1239,plain,
( spl22_156
<=> ! [X0] : ~ in(X0,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_156])]) ).
fof(f1125,plain,
( ! [X0,X1] :
( ~ empty(cartesian_product2(sK1,X0))
| ~ in(X1,sK4)
| ~ subset(sK2,X0) )
| ~ spl22_90
| ~ spl22_139 ),
inference(resolution,[],[f1109,f721]) ).
fof(f1568,plain,
( spl22_166
| ~ spl22_165
| ~ spl22_169
| ~ spl22_179 ),
inference(avatar_split_clause,[],[f1498,f1407,f1330,f1304,f1311]) ).
fof(f1330,plain,
( spl22_169
<=> sK13 = relation_dom(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_169])]) ).
fof(f1407,plain,
( spl22_179
<=> sK4 = sK13 ),
introduced(avatar_definition,[new_symbols(naming,[spl22_179])]) ).
fof(f1498,plain,
( sK1 = sK13
| ~ spl22_165
| ~ spl22_169
| ~ spl22_179 ),
inference(forward_demodulation,[],[f1494,f1332]) ).
fof(f1332,plain,
( sK13 = relation_dom(sK13)
| ~ spl22_169 ),
inference(avatar_component_clause,[],[f1330]) ).
fof(f1494,plain,
( sK1 = relation_dom(sK13)
| ~ spl22_165
| ~ spl22_179 ),
inference(superposition,[],[f1306,f1409]) ).
fof(f1409,plain,
( sK4 = sK13
| ~ spl22_179 ),
inference(avatar_component_clause,[],[f1407]) ).
fof(f1518,plain,
( spl22_191
| ~ spl22_119
| ~ spl22_139 ),
inference(avatar_split_clause,[],[f1131,f1108,f934,f1516]) ).
fof(f1131,plain,
( ! [X2,X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| ~ in(X2,sK11(X0,X1)) )
| ~ spl22_119
| ~ spl22_139 ),
inference(resolution,[],[f1109,f935]) ).
fof(f1514,plain,
( spl22_190
| ~ spl22_118
| ~ spl22_139 ),
inference(avatar_split_clause,[],[f1130,f1108,f930,f1512]) ).
fof(f1130,plain,
( ! [X2,X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| ~ in(X2,sK10(X0,X1)) )
| ~ spl22_118
| ~ spl22_139 ),
inference(resolution,[],[f1109,f931]) ).
fof(f1510,plain,
( spl22_189
| ~ spl22_52
| ~ spl22_139 ),
inference(avatar_split_clause,[],[f1128,f1108,f481,f1508]) ).
fof(f1128,plain,
( ! [X2,X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| ~ in(X2,sK9(X0,X1)) )
| ~ spl22_52
| ~ spl22_139 ),
inference(resolution,[],[f1109,f482]) ).
fof(f1506,plain,
( spl22_188
| ~ spl22_117
| ~ spl22_139 ),
inference(avatar_split_clause,[],[f1127,f1108,f926,f1504]) ).
fof(f1127,plain,
( ! [X2,X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| ~ in(X2,sK8(X0,X1)) )
| ~ spl22_117
| ~ spl22_139 ),
inference(resolution,[],[f1109,f927]) ).
fof(f1502,plain,
( spl22_187
| ~ spl22_66
| ~ spl22_133 ),
inference(avatar_split_clause,[],[f1076,f1061,f559,f1500]) ).
fof(f1500,plain,
( spl22_187
<=> ! [X2,X0,X1] :
( ~ subset(X0,X1)
| sP0(X2,sK9(X2,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_187])]) ).
fof(f559,plain,
( spl22_66
<=> ! [X2,X0,X1] :
( sP0(X0,X2,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_66])]) ).
fof(f1076,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X1)
| sP0(X2,sK9(X2,X0),X1) )
| ~ spl22_66
| ~ spl22_133 ),
inference(resolution,[],[f1062,f560]) ).
fof(f560,plain,
( ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| sP0(X0,X2,X1) )
| ~ spl22_66 ),
inference(avatar_component_clause,[],[f559]) ).
fof(f1474,plain,
( spl22_186
| ~ spl22_68
| ~ spl22_133 ),
inference(avatar_split_clause,[],[f1075,f1061,f567,f1472]) ).
fof(f1472,plain,
( spl22_186
<=> ! [X2,X0,X1] :
( ~ subset(X0,X1)
| relation_of2(sK9(X2,X0),X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_186])]) ).
fof(f567,plain,
( spl22_68
<=> ! [X2,X0,X1] :
( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_68])]) ).
fof(f1075,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X1)
| relation_of2(sK9(X2,X0),X2,X1) )
| ~ spl22_68
| ~ spl22_133 ),
inference(resolution,[],[f1062,f568]) ).
fof(f568,plain,
( ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| relation_of2(X2,X0,X1) )
| ~ spl22_68 ),
inference(avatar_component_clause,[],[f567]) ).
fof(f1470,plain,
( spl22_185
| ~ spl22_43
| ~ spl22_126 ),
inference(avatar_split_clause,[],[f1021,f1009,f429,f1468]) ).
fof(f1468,plain,
( spl22_185
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_dom(relation_dom(X1)) = X0
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_185])]) ).
fof(f1009,plain,
( spl22_126
<=> ! [X0,X1] :
( relation_dom(X1) = X0
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_126])]) ).
fof(f1021,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_dom(relation_dom(X1)) = X0
| ~ empty(X1) )
| ~ spl22_43
| ~ spl22_126 ),
inference(resolution,[],[f1010,f430]) ).
fof(f1010,plain,
( ! [X0,X1] :
( ~ empty(X1)
| ~ empty(X0)
| relation_dom(X1) = X0 )
| ~ spl22_126 ),
inference(avatar_component_clause,[],[f1009]) ).
fof(f1466,plain,
( spl22_184
| ~ spl22_76
| ~ spl22_119 ),
inference(avatar_split_clause,[],[f972,f934,f634,f1464]) ).
fof(f1464,plain,
( spl22_184
<=> ! [X2,X0,X1] :
( ~ subset(X0,X1)
| relation_of2_as_subset(sK11(X2,X0),X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_184])]) ).
fof(f972,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X1)
| relation_of2_as_subset(sK11(X2,X0),X2,X1) )
| ~ spl22_76
| ~ spl22_119 ),
inference(resolution,[],[f935,f635]) ).
fof(f1462,plain,
( spl22_183
| ~ spl22_76
| ~ spl22_118 ),
inference(avatar_split_clause,[],[f969,f930,f634,f1460]) ).
fof(f1460,plain,
( spl22_183
<=> ! [X2,X0,X1] :
( ~ subset(X0,X1)
| relation_of2_as_subset(sK10(X2,X0),X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_183])]) ).
fof(f969,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X1)
| relation_of2_as_subset(sK10(X2,X0),X2,X1) )
| ~ spl22_76
| ~ spl22_118 ),
inference(resolution,[],[f931,f635]) ).
fof(f1458,plain,
( spl22_182
| ~ spl22_76
| ~ spl22_117 ),
inference(avatar_split_clause,[],[f966,f926,f634,f1456]) ).
fof(f1456,plain,
( spl22_182
<=> ! [X2,X0,X1] :
( ~ subset(X0,X1)
| relation_of2_as_subset(sK8(X2,X0),X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_182])]) ).
fof(f966,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X1)
| relation_of2_as_subset(sK8(X2,X0),X2,X1) )
| ~ spl22_76
| ~ spl22_117 ),
inference(resolution,[],[f927,f635]) ).
fof(f1446,plain,
( spl22_181
| ~ spl22_119
| ~ spl22_149 ),
inference(avatar_split_clause,[],[f1198,f1189,f934,f1444]) ).
fof(f1189,plain,
( spl22_149
<=> ! [X0] :
( sK13 = X0
| ~ relation_of2_as_subset(sK11(X0,sK13),X0,sK13)
| sK13 = sK11(X0,sK13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_149])]) ).
fof(f1198,plain,
( ! [X0] :
( sK13 = X0
| sK13 = sK11(X0,sK13) )
| ~ spl22_119
| ~ spl22_149 ),
inference(resolution,[],[f1190,f935]) ).
fof(f1190,plain,
( ! [X0] :
( ~ relation_of2_as_subset(sK11(X0,sK13),X0,sK13)
| sK13 = X0
| sK13 = sK11(X0,sK13) )
| ~ spl22_149 ),
inference(avatar_component_clause,[],[f1189]) ).
fof(f1421,plain,
( spl22_180
| ~ spl22_43
| ~ spl22_110 ),
inference(avatar_split_clause,[],[f942,f898,f429,f1419]) ).
fof(f942,plain,
( ! [X0] :
( sK13 = relation_dom(relation_dom(X0))
| ~ empty(X0) )
| ~ spl22_43
| ~ spl22_110 ),
inference(resolution,[],[f899,f430]) ).
fof(f1410,plain,
( spl22_179
| ~ spl22_106
| ~ spl22_168 ),
inference(avatar_split_clause,[],[f1362,f1325,f823,f1407]) ).
fof(f1362,plain,
( sK4 = sK13
| ~ spl22_106
| ~ spl22_168 ),
inference(resolution,[],[f1327,f824]) ).
fof(f1327,plain,
( empty(sK4)
| ~ spl22_168 ),
inference(avatar_component_clause,[],[f1325]) ).
fof(f1392,plain,
( spl22_178
| ~ spl22_113
| ~ spl22_125 ),
inference(avatar_split_clause,[],[f1007,f997,f910,f1390]) ).
fof(f997,plain,
( spl22_125
<=> ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK6(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_125])]) ).
fof(f1007,plain,
( ! [X0] :
( ~ empty(X0)
| empty(sK6(powerset(X0))) )
| ~ spl22_113
| ~ spl22_125 ),
inference(resolution,[],[f998,f911]) ).
fof(f998,plain,
( ! [X0,X1] :
( ~ in(X1,sK6(powerset(X0)))
| ~ empty(X0) )
| ~ spl22_125 ),
inference(avatar_component_clause,[],[f997]) ).
fof(f1388,plain,
( spl22_177
| ~ spl22_66
| ~ spl22_119 ),
inference(avatar_split_clause,[],[f974,f934,f559,f1386]) ).
fof(f974,plain,
( ! [X0,X1] : sP0(X0,sK11(X0,X1),X1)
| ~ spl22_66
| ~ spl22_119 ),
inference(resolution,[],[f935,f560]) ).
fof(f1384,plain,
( spl22_176
| ~ spl22_66
| ~ spl22_118 ),
inference(avatar_split_clause,[],[f971,f930,f559,f1382]) ).
fof(f1382,plain,
( spl22_176
<=> ! [X0,X1] : sP0(X0,sK10(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_176])]) ).
fof(f971,plain,
( ! [X0,X1] : sP0(X0,sK10(X0,X1),X1)
| ~ spl22_66
| ~ spl22_118 ),
inference(resolution,[],[f931,f560]) ).
fof(f1380,plain,
( spl22_175
| ~ spl22_66
| ~ spl22_117 ),
inference(avatar_split_clause,[],[f968,f926,f559,f1378]) ).
fof(f1378,plain,
( spl22_175
<=> ! [X0,X1] : sP0(X0,sK8(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_175])]) ).
fof(f968,plain,
( ! [X0,X1] : sP0(X0,sK8(X0,X1),X1)
| ~ spl22_66
| ~ spl22_117 ),
inference(resolution,[],[f927,f560]) ).
fof(f1376,plain,
( spl22_174
| ~ spl22_49
| ~ spl22_113 ),
inference(avatar_split_clause,[],[f960,f910,f469,f1374]) ).
fof(f1374,plain,
( spl22_174
<=> ! [X0] :
( empty(X0)
| ~ in(X0,sK6(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_174])]) ).
fof(f960,plain,
( ! [X0] :
( empty(X0)
| ~ in(X0,sK6(X0)) )
| ~ spl22_49
| ~ spl22_113 ),
inference(resolution,[],[f911,f470]) ).
fof(f1359,plain,
( spl22_173
| ~ spl22_56
| ~ spl22_105 ),
inference(avatar_split_clause,[],[f889,f819,f497,f1356]) ).
fof(f1356,plain,
( spl22_173
<=> sK13 = sK6(powerset(sK13)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_173])]) ).
fof(f819,plain,
( spl22_105
<=> ! [X0] : subset(sK6(powerset(X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_105])]) ).
fof(f889,plain,
( sK13 = sK6(powerset(sK13))
| ~ spl22_56
| ~ spl22_105 ),
inference(resolution,[],[f820,f498]) ).
fof(f820,plain,
( ! [X0] : subset(sK6(powerset(X0)),X0)
| ~ spl22_105 ),
inference(avatar_component_clause,[],[f819]) ).
fof(f1345,plain,
( spl22_172
| ~ spl22_32
| ~ spl22_123 ),
inference(avatar_split_clause,[],[f1003,f988,f372,f1343]) ).
fof(f1343,plain,
( spl22_172
<=> ! [X0,X1] : relation(cartesian_product2(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_172])]) ).
fof(f372,plain,
( spl22_32
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_32])]) ).
fof(f988,plain,
( spl22_123
<=> ! [X2,X0,X1] :
( relation(X0)
| ~ subset(X0,cartesian_product2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_123])]) ).
fof(f1003,plain,
( ! [X0,X1] : relation(cartesian_product2(X0,X1))
| ~ spl22_32
| ~ spl22_123 ),
inference(resolution,[],[f989,f373]) ).
fof(f373,plain,
( ! [X0] : subset(X0,X0)
| ~ spl22_32 ),
inference(avatar_component_clause,[],[f372]) ).
fof(f989,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,cartesian_product2(X1,X2))
| relation(X0) )
| ~ spl22_123 ),
inference(avatar_component_clause,[],[f988]) ).
fof(f1341,plain,
( spl22_171
| ~ spl22_52
| ~ spl22_120 ),
inference(avatar_split_clause,[],[f980,f938,f481,f1339]) ).
fof(f1339,plain,
( spl22_171
<=> ! [X0,X1] : relation(sK9(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_171])]) ).
fof(f938,plain,
( spl22_120
<=> ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_120])]) ).
fof(f980,plain,
( ! [X0,X1] : relation(sK9(X0,X1))
| ~ spl22_52
| ~ spl22_120 ),
inference(resolution,[],[f939,f482]) ).
fof(f939,plain,
( ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| relation(X0) )
| ~ spl22_120 ),
inference(avatar_component_clause,[],[f938]) ).
fof(f1337,plain,
( spl22_170
| ~ spl22_117
| ~ spl22_120 ),
inference(avatar_split_clause,[],[f979,f938,f926,f1335]) ).
fof(f1335,plain,
( spl22_170
<=> ! [X0,X1] : relation(sK8(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_170])]) ).
fof(f979,plain,
( ! [X0,X1] : relation(sK8(X0,X1))
| ~ spl22_117
| ~ spl22_120 ),
inference(resolution,[],[f939,f927]) ).
fof(f1333,plain,
( spl22_169
| ~ spl22_7
| ~ spl22_93
| ~ spl22_110 ),
inference(avatar_split_clause,[],[f948,f898,f738,f250,f1330]) ).
fof(f250,plain,
( spl22_7
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_7])]) ).
fof(f738,plain,
( spl22_93
<=> empty_set = sK13 ),
introduced(avatar_definition,[new_symbols(naming,[spl22_93])]) ).
fof(f948,plain,
( sK13 = relation_dom(sK13)
| ~ spl22_7
| ~ spl22_93
| ~ spl22_110 ),
inference(forward_demodulation,[],[f941,f740]) ).
fof(f740,plain,
( empty_set = sK13
| ~ spl22_93 ),
inference(avatar_component_clause,[],[f738]) ).
fof(f941,plain,
( sK13 = relation_dom(empty_set)
| ~ spl22_7
| ~ spl22_110 ),
inference(resolution,[],[f899,f252]) ).
fof(f252,plain,
( empty(empty_set)
| ~ spl22_7 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f1328,plain,
( spl22_168
| ~ spl22_113
| ~ spl22_156 ),
inference(avatar_split_clause,[],[f1297,f1239,f910,f1325]) ).
fof(f1297,plain,
( empty(sK4)
| ~ spl22_113
| ~ spl22_156 ),
inference(resolution,[],[f1240,f911]) ).
fof(f1240,plain,
( ! [X0] : ~ in(X0,sK4)
| ~ spl22_156 ),
inference(avatar_component_clause,[],[f1239]) ).
fof(f1323,plain,
( spl22_167
| ~ spl22_45
| ~ spl22_103 ),
inference(avatar_split_clause,[],[f812,f809,f437,f1321]) ).
fof(f1321,plain,
( spl22_167
<=> ! [X0] : element(sK13,powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_167])]) ).
fof(f437,plain,
( spl22_45
<=> ! [X0] : element(sK7(X0),powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_45])]) ).
fof(f809,plain,
( spl22_103
<=> ! [X0] : sK7(X0) = sK13 ),
introduced(avatar_definition,[new_symbols(naming,[spl22_103])]) ).
fof(f812,plain,
( ! [X0] : element(sK13,powerset(X0))
| ~ spl22_45
| ~ spl22_103 ),
inference(superposition,[],[f438,f810]) ).
fof(f810,plain,
( ! [X0] : sK7(X0) = sK13
| ~ spl22_103 ),
inference(avatar_component_clause,[],[f809]) ).
fof(f438,plain,
( ! [X0] : element(sK7(X0),powerset(X0))
| ~ spl22_45 ),
inference(avatar_component_clause,[],[f437]) ).
fof(f1314,plain,
( spl22_166
| ~ spl22_6
| ~ spl22_101 ),
inference(avatar_split_clause,[],[f1308,f795,f245,f1311]) ).
fof(f245,plain,
( spl22_6
<=> sK1 = sK2 ),
introduced(avatar_definition,[new_symbols(naming,[spl22_6])]) ).
fof(f1308,plain,
( sK1 = sK13
| ~ spl22_6
| ~ spl22_101 ),
inference(forward_demodulation,[],[f247,f796]) ).
fof(f247,plain,
( sK1 = sK2
| ~ spl22_6 ),
inference(avatar_component_clause,[],[f245]) ).
fof(f1307,plain,
( spl22_101
| ~ spl22_3
| spl22_165
| ~ spl22_71
| ~ spl22_88
| ~ spl22_109 ),
inference(avatar_split_clause,[],[f1282,f865,f709,f596,f1304,f231,f795]) ).
fof(f1282,plain,
( sK1 = relation_dom(sK4)
| ~ quasi_total(sK4,sK1,sK2)
| sK2 = sK13
| ~ spl22_71
| ~ spl22_88
| ~ spl22_109 ),
inference(forward_demodulation,[],[f716,f867]) ).
fof(f716,plain,
( sK1 = relation_dom_as_subset(sK1,sK2,sK4)
| ~ quasi_total(sK4,sK1,sK2)
| sK2 = sK13
| ~ spl22_71
| ~ spl22_88 ),
inference(resolution,[],[f710,f598]) ).
fof(f1296,plain,
( spl22_156
| spl22_164
| ~ spl22_100
| ~ spl22_139 ),
inference(avatar_split_clause,[],[f1124,f1108,f779,f1294,f1239]) ).
fof(f1124,plain,
( ! [X0,X1] :
( ~ empty(cartesian_product2(sK1,X0))
| ~ in(X1,sK4)
| ~ subset(sK3,X0) )
| ~ spl22_100
| ~ spl22_139 ),
inference(resolution,[],[f1109,f780]) ).
fof(f1292,plain,
( spl22_163
| ~ spl22_76
| ~ spl22_100 ),
inference(avatar_split_clause,[],[f782,f779,f634,f1290]) ).
fof(f782,plain,
( ! [X0,X1] :
( ~ subset(sK3,X0)
| ~ subset(X0,X1)
| relation_of2_as_subset(sK4,sK1,X1) )
| ~ spl22_76
| ~ spl22_100 ),
inference(resolution,[],[f780,f635]) ).
fof(f1288,plain,
( spl22_162
| ~ spl22_76
| ~ spl22_90 ),
inference(avatar_split_clause,[],[f724,f720,f634,f1286]) ).
fof(f724,plain,
( ! [X0,X1] :
( ~ subset(sK2,X0)
| ~ subset(X0,X1)
| relation_of2_as_subset(sK4,sK1,X1) )
| ~ spl22_76
| ~ spl22_90 ),
inference(resolution,[],[f721,f635]) ).
fof(f1281,plain,
( spl22_161
| ~ spl22_106
| ~ spl22_152
| ~ spl22_159 ),
inference(avatar_split_clause,[],[f1273,f1270,f1213,f823,f1279]) ).
fof(f1279,plain,
( spl22_161
<=> ! [X0] :
( element(X0,cartesian_product2(sK1,sK13))
| ~ in(X0,sK4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_161])]) ).
fof(f1273,plain,
( ! [X0] :
( element(X0,cartesian_product2(sK1,sK13))
| ~ in(X0,sK4) )
| ~ spl22_106
| ~ spl22_152
| ~ spl22_159 ),
inference(forward_demodulation,[],[f1271,f1259]) ).
fof(f1277,plain,
( spl22_160
| ~ spl22_29
| ~ spl22_143 ),
inference(avatar_split_clause,[],[f1155,f1145,f359,f1275]) ).
fof(f1155,plain,
( ! [X0] :
( ~ in(X0,sK4)
| element(X0,cartesian_product2(sK1,sK3)) )
| ~ spl22_29
| ~ spl22_143 ),
inference(resolution,[],[f1146,f360]) ).
fof(f1272,plain,
( spl22_159
| ~ spl22_4
| ~ spl22_143 ),
inference(avatar_split_clause,[],[f1152,f1145,f236,f1270]) ).
fof(f1152,plain,
( ! [X0] :
( ~ in(X0,sK4)
| element(X0,cartesian_product2(sK1,sK2)) )
| ~ spl22_4
| ~ spl22_143 ),
inference(resolution,[],[f1146,f238]) ).
fof(f1250,plain,
( spl22_156
| ~ spl22_158
| ~ spl22_29
| ~ spl22_139 ),
inference(avatar_split_clause,[],[f1126,f1108,f359,f1247,f1239]) ).
fof(f1126,plain,
( ! [X0] :
( ~ empty(cartesian_product2(sK1,sK3))
| ~ in(X0,sK4) )
| ~ spl22_29
| ~ spl22_139 ),
inference(resolution,[],[f1109,f360]) ).
fof(f1245,plain,
( spl22_156
| ~ spl22_157
| ~ spl22_4
| ~ spl22_139 ),
inference(avatar_split_clause,[],[f1123,f1108,f236,f1242,f1239]) ).
fof(f1123,plain,
( ! [X0] :
( ~ empty(cartesian_product2(sK1,sK2))
| ~ in(X0,sK4) )
| ~ spl22_4
| ~ spl22_139 ),
inference(resolution,[],[f1109,f238]) ).
fof(f1228,plain,
( spl22_155
| ~ spl22_66
| ~ spl22_100 ),
inference(avatar_split_clause,[],[f784,f779,f559,f1226]) ).
fof(f784,plain,
( ! [X0] :
( ~ subset(sK3,X0)
| sP0(sK1,sK4,X0) )
| ~ spl22_66
| ~ spl22_100 ),
inference(resolution,[],[f780,f560]) ).
fof(f1224,plain,
( spl22_154
| ~ spl22_68
| ~ spl22_100 ),
inference(avatar_split_clause,[],[f783,f779,f567,f1222]) ).
fof(f783,plain,
( ! [X0] :
( ~ subset(sK3,X0)
| relation_of2(sK4,sK1,X0) )
| ~ spl22_68
| ~ spl22_100 ),
inference(resolution,[],[f780,f568]) ).
fof(f1220,plain,
( spl22_152
| spl22_153
| ~ spl22_113
| ~ spl22_147 ),
inference(avatar_split_clause,[],[f1206,f1174,f910,f1217,f1213]) ).
fof(f1174,plain,
( spl22_147
<=> ! [X0] :
( ~ in(X0,sK2)
| element(X0,sK3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_147])]) ).
fof(f1206,plain,
( element(sK6(sK2),sK3)
| empty(sK2)
| ~ spl22_113
| ~ spl22_147 ),
inference(resolution,[],[f1175,f911]) ).
fof(f1175,plain,
( ! [X0] :
( ~ in(X0,sK2)
| element(X0,sK3) )
| ~ spl22_147 ),
inference(avatar_component_clause,[],[f1174]) ).
fof(f1211,plain,
( spl22_151
| ~ spl22_74
| ~ spl22_98 ),
inference(avatar_split_clause,[],[f775,f766,f626,f1208]) ).
fof(f775,plain,
( relation_dom(sK4) = relation_dom_as_subset(sK1,sK3,sK4)
| ~ spl22_74
| ~ spl22_98 ),
inference(resolution,[],[f768,f627]) ).
fof(f1202,plain,
( spl22_150
| ~ spl22_64
| ~ spl22_72 ),
inference(avatar_split_clause,[],[f617,f607,f551,f1200]) ).
fof(f607,plain,
( spl22_72
<=> ! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_72])]) ).
fof(f617,plain,
( ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| empty(powerset(cartesian_product2(X1,X2)))
| in(X0,powerset(cartesian_product2(X1,X2))) )
| ~ spl22_64
| ~ spl22_72 ),
inference(resolution,[],[f608,f552]) ).
fof(f608,plain,
( ! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) )
| ~ spl22_72 ),
inference(avatar_component_clause,[],[f607]) ).
fof(f1191,plain,
( spl22_149
| ~ spl22_55
| ~ spl22_85 ),
inference(avatar_split_clause,[],[f697,f694,f493,f1189]) ).
fof(f694,plain,
( spl22_85
<=> ! [X2,X0] :
( ~ relation_of2_as_subset(X2,X0,sK13)
| sK13 = X0
| ~ quasi_total(X2,X0,sK13)
| sK13 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_85])]) ).
fof(f697,plain,
( ! [X0] :
( sK13 = X0
| ~ relation_of2_as_subset(sK11(X0,sK13),X0,sK13)
| sK13 = sK11(X0,sK13) )
| ~ spl22_55
| ~ spl22_85 ),
inference(resolution,[],[f695,f494]) ).
fof(f695,plain,
( ! [X2,X0] :
( ~ quasi_total(X2,X0,sK13)
| sK13 = X0
| ~ relation_of2_as_subset(X2,X0,sK13)
| sK13 = X2 )
| ~ spl22_85 ),
inference(avatar_component_clause,[],[f694]) ).
fof(f1187,plain,
( spl22_148
| ~ spl22_64
| ~ spl22_75 ),
inference(avatar_split_clause,[],[f656,f630,f551,f1185]) ).
fof(f656,plain,
( ! [X2,X0,X1] :
( ~ relation_of2(X0,X1,X2)
| empty(powerset(X1))
| in(relation_dom_as_subset(X1,X2,X0),powerset(X1)) )
| ~ spl22_64
| ~ spl22_75 ),
inference(resolution,[],[f631,f552]) ).
fof(f1176,plain,
( spl22_147
| ~ spl22_2
| ~ spl22_131 ),
inference(avatar_split_clause,[],[f1068,f1053,f226,f1174]) ).
fof(f1053,plain,
( spl22_131
<=> ! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_131])]) ).
fof(f1068,plain,
( ! [X0] :
( ~ in(X0,sK2)
| element(X0,sK3) )
| ~ spl22_2
| ~ spl22_131 ),
inference(resolution,[],[f1054,f228]) ).
fof(f1054,plain,
( ! [X2,X0,X1] :
( ~ subset(X2,X1)
| ~ in(X0,X2)
| element(X0,X1) )
| ~ spl22_131 ),
inference(avatar_component_clause,[],[f1053]) ).
fof(f1172,plain,
( spl22_146
| ~ spl22_67
| ~ spl22_75 ),
inference(avatar_split_clause,[],[f655,f630,f563,f1170]) ).
fof(f563,plain,
( spl22_67
<=> ! [X2,X0,X1] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_67])]) ).
fof(f655,plain,
( ! [X2,X3,X0,X1] :
( ~ relation_of2(X0,cartesian_product2(X1,X2),X3)
| relation(relation_dom_as_subset(cartesian_product2(X1,X2),X3,X0)) )
| ~ spl22_67
| ~ spl22_75 ),
inference(resolution,[],[f631,f564]) ).
fof(f564,plain,
( ! [X2,X0,X1] :
( ~ element(X2,powerset(cartesian_product2(X0,X1)))
| relation(X2) )
| ~ spl22_67 ),
inference(avatar_component_clause,[],[f563]) ).
fof(f1168,plain,
( spl22_145
| ~ spl22_73
| ~ spl22_75 ),
inference(avatar_split_clause,[],[f652,f630,f611,f1166]) ).
fof(f611,plain,
( spl22_73
<=> ! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_73])]) ).
fof(f652,plain,
( ! [X2,X3,X0,X1] :
( ~ relation_of2(X0,X1,X2)
| element(X3,X1)
| ~ in(X3,relation_dom_as_subset(X1,X2,X0)) )
| ~ spl22_73
| ~ spl22_75 ),
inference(resolution,[],[f631,f612]) ).
fof(f612,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| element(X0,X2)
| ~ in(X0,X1) )
| ~ spl22_73 ),
inference(avatar_component_clause,[],[f611]) ).
fof(f1151,plain,
( spl22_144
| ~ spl22_70
| ~ spl22_75 ),
inference(avatar_split_clause,[],[f653,f630,f592,f1149]) ).
fof(f592,plain,
( spl22_70
<=> ! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_70])]) ).
fof(f653,plain,
( ! [X2,X3,X0,X1] :
( ~ relation_of2(X0,X1,X2)
| ~ empty(X1)
| ~ in(X3,relation_dom_as_subset(X1,X2,X0)) )
| ~ spl22_70
| ~ spl22_75 ),
inference(resolution,[],[f631,f593]) ).
fof(f593,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X0,X1) )
| ~ spl22_70 ),
inference(avatar_component_clause,[],[f592]) ).
fof(f1147,plain,
( spl22_143
| ~ spl22_72
| ~ spl22_73 ),
inference(avatar_split_clause,[],[f619,f611,f607,f1145]) ).
fof(f619,plain,
( ! [X2,X3,X0,X1] :
( element(X0,cartesian_product2(X1,X2))
| ~ in(X0,X3)
| ~ relation_of2_as_subset(X3,X1,X2) )
| ~ spl22_72
| ~ spl22_73 ),
inference(resolution,[],[f612,f608]) ).
fof(f1122,plain,
( spl22_142
| ~ spl22_54
| ~ spl22_74 ),
inference(avatar_split_clause,[],[f646,f626,f489,f1120]) ).
fof(f646,plain,
( ! [X0,X1] : relation_dom_as_subset(X0,X1,sK11(X0,X1)) = relation_dom(sK11(X0,X1))
| ~ spl22_54
| ~ spl22_74 ),
inference(resolution,[],[f627,f490]) ).
fof(f1118,plain,
( spl22_141
| ~ spl22_53
| ~ spl22_74 ),
inference(avatar_split_clause,[],[f645,f626,f485,f1116]) ).
fof(f645,plain,
( ! [X0,X1] : relation_dom_as_subset(X0,X1,sK10(X0,X1)) = relation_dom(sK10(X0,X1))
| ~ spl22_53
| ~ spl22_74 ),
inference(resolution,[],[f627,f486]) ).
fof(f1114,plain,
( spl22_140
| ~ spl22_51
| ~ spl22_74 ),
inference(avatar_split_clause,[],[f644,f626,f477,f1112]) ).
fof(f644,plain,
( ! [X0,X1] : relation_dom_as_subset(X0,X1,sK8(X0,X1)) = relation_dom(sK8(X0,X1))
| ~ spl22_51
| ~ spl22_74 ),
inference(resolution,[],[f627,f478]) ).
fof(f1110,plain,
( spl22_139
| ~ spl22_70
| ~ spl22_72 ),
inference(avatar_split_clause,[],[f615,f607,f592,f1108]) ).
fof(f615,plain,
( ! [X2,X3,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| ~ empty(cartesian_product2(X1,X2))
| ~ in(X3,X0) )
| ~ spl22_70
| ~ spl22_72 ),
inference(resolution,[],[f608,f593]) ).
fof(f1096,plain,
( spl22_138
| ~ spl22_60
| ~ spl22_75 ),
inference(avatar_split_clause,[],[f654,f630,f516,f1094]) ).
fof(f516,plain,
( spl22_60
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_60])]) ).
fof(f654,plain,
( ! [X2,X0,X1] :
( ~ relation_of2(X0,X1,X2)
| subset(relation_dom_as_subset(X1,X2,X0),X1) )
| ~ spl22_60
| ~ spl22_75 ),
inference(resolution,[],[f631,f517]) ).
fof(f517,plain,
( ! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) )
| ~ spl22_60 ),
inference(avatar_component_clause,[],[f516]) ).
fof(f1092,plain,
( spl22_137
| ~ spl22_58
| ~ spl22_64 ),
inference(avatar_split_clause,[],[f575,f551,f508,f1090]) ).
fof(f508,plain,
( spl22_58
<=> ! [X0] :
( element(sK5(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_58])]) ).
fof(f575,plain,
( ! [X0] :
( empty(powerset(X0))
| in(sK5(X0),powerset(X0))
| empty(X0) )
| ~ spl22_58
| ~ spl22_64 ),
inference(resolution,[],[f552,f509]) ).
fof(f509,plain,
( ! [X0] :
( element(sK5(X0),powerset(X0))
| empty(X0) )
| ~ spl22_58 ),
inference(avatar_component_clause,[],[f508]) ).
fof(f1088,plain,
( spl22_136
| ~ spl22_62
| ~ spl22_64 ),
inference(avatar_split_clause,[],[f574,f551,f525,f1086]) ).
fof(f525,plain,
( spl22_62
<=> ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_62])]) ).
fof(f574,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| in(X1,powerset(X0))
| ~ subset(X1,X0) )
| ~ spl22_62
| ~ spl22_64 ),
inference(resolution,[],[f552,f526]) ).
fof(f526,plain,
( ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) )
| ~ spl22_62 ),
inference(avatar_component_clause,[],[f525]) ).
fof(f1084,plain,
( ~ spl22_134
| spl22_135
| ~ spl22_2
| ~ spl22_127 ),
inference(avatar_split_clause,[],[f1039,f1013,f226,f1082,f1078]) ).
fof(f1013,plain,
( spl22_127
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,X2)
| ~ subset(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_127])]) ).
fof(f1039,plain,
( ! [X0] :
( ~ in(X0,sK2)
| ~ empty(sK3) )
| ~ spl22_2
| ~ spl22_127 ),
inference(resolution,[],[f1014,f228]) ).
fof(f1014,plain,
( ! [X2,X0,X1] :
( ~ subset(X2,X0)
| ~ in(X1,X2)
| ~ empty(X0) )
| ~ spl22_127 ),
inference(avatar_component_clause,[],[f1013]) ).
fof(f1063,plain,
( spl22_133
| ~ spl22_52
| ~ spl22_76 ),
inference(avatar_split_clause,[],[f658,f634,f481,f1061]) ).
fof(f658,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X1)
| relation_of2_as_subset(sK9(X2,X0),X2,X1) )
| ~ spl22_52
| ~ spl22_76 ),
inference(resolution,[],[f635,f482]) ).
fof(f1059,plain,
( spl22_132
| ~ spl22_58
| ~ spl22_73 ),
inference(avatar_split_clause,[],[f620,f611,f508,f1057]) ).
fof(f620,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK5(X1))
| empty(X1) )
| ~ spl22_58
| ~ spl22_73 ),
inference(resolution,[],[f612,f509]) ).
fof(f1055,plain,
( spl22_131
| ~ spl22_62
| ~ spl22_73 ),
inference(avatar_split_clause,[],[f618,f611,f525,f1053]) ).
fof(f618,plain,
( ! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,X1) )
| ~ spl22_62
| ~ spl22_73 ),
inference(resolution,[],[f612,f526]) ).
fof(f1051,plain,
( spl22_130
| ~ spl22_60
| ~ spl22_72 ),
inference(avatar_split_clause,[],[f616,f607,f516,f1049]) ).
fof(f616,plain,
( ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| subset(X0,cartesian_product2(X1,X2)) )
| ~ spl22_60
| ~ spl22_72 ),
inference(resolution,[],[f608,f517]) ).
fof(f1047,plain,
( spl22_129
| ~ spl22_58
| ~ spl22_67 ),
inference(avatar_split_clause,[],[f583,f563,f508,f1045]) ).
fof(f1045,plain,
( spl22_129
<=> ! [X0,X1] :
( relation(sK5(cartesian_product2(X0,X1)))
| empty(cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_129])]) ).
fof(f583,plain,
( ! [X0,X1] :
( relation(sK5(cartesian_product2(X0,X1)))
| empty(cartesian_product2(X0,X1)) )
| ~ spl22_58
| ~ spl22_67 ),
inference(resolution,[],[f564,f509]) ).
fof(f1019,plain,
( spl22_128
| ~ spl22_35
| ~ spl22_73 ),
inference(avatar_split_clause,[],[f621,f611,f384,f1017]) ).
fof(f384,plain,
( spl22_35
<=> ! [X0] : element(sK6(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_35])]) ).
fof(f621,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK6(powerset(X1))) )
| ~ spl22_35
| ~ spl22_73 ),
inference(resolution,[],[f612,f385]) ).
fof(f385,plain,
( ! [X0] : element(sK6(X0),X0)
| ~ spl22_35 ),
inference(avatar_component_clause,[],[f384]) ).
fof(f1015,plain,
( spl22_127
| ~ spl22_62
| ~ spl22_70 ),
inference(avatar_split_clause,[],[f600,f592,f525,f1013]) ).
fof(f600,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,X2)
| ~ subset(X2,X0) )
| ~ spl22_62
| ~ spl22_70 ),
inference(resolution,[],[f593,f526]) ).
fof(f1011,plain,
( spl22_126
| ~ spl22_43
| ~ spl22_63 ),
inference(avatar_split_clause,[],[f540,f529,f429,f1009]) ).
fof(f529,plain,
( spl22_63
<=> ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_63])]) ).
fof(f540,plain,
( ! [X0,X1] :
( relation_dom(X1) = X0
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl22_43
| ~ spl22_63 ),
inference(resolution,[],[f530,f430]) ).
fof(f530,plain,
( ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) )
| ~ spl22_63 ),
inference(avatar_component_clause,[],[f529]) ).
fof(f999,plain,
( spl22_125
| ~ spl22_35
| ~ spl22_70 ),
inference(avatar_split_clause,[],[f602,f592,f384,f997]) ).
fof(f602,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK6(powerset(X0))) )
| ~ spl22_35
| ~ spl22_70 ),
inference(resolution,[],[f593,f385]) ).
fof(f995,plain,
( spl22_124
| ~ spl22_4
| ~ spl22_120 ),
inference(avatar_split_clause,[],[f975,f938,f236,f992]) ).
fof(f975,plain,
( relation(sK4)
| ~ spl22_4
| ~ spl22_120 ),
inference(resolution,[],[f939,f238]) ).
fof(f990,plain,
( spl22_123
| ~ spl22_62
| ~ spl22_67 ),
inference(avatar_split_clause,[],[f582,f563,f525,f988]) ).
fof(f582,plain,
( ! [X2,X0,X1] :
( relation(X0)
| ~ subset(X0,cartesian_product2(X1,X2)) )
| ~ spl22_62
| ~ spl22_67 ),
inference(resolution,[],[f564,f526]) ).
fof(f986,plain,
( spl22_122
| ~ spl22_10
| ~ spl22_31
| ~ spl22_41
| ~ spl22_45
| ~ spl22_64 ),
inference(avatar_split_clause,[],[f579,f551,f437,f420,f368,f265,f984]) ).
fof(f984,plain,
( spl22_122
<=> ! [X0] :
( in(sK13,powerset(X0))
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_122])]) ).
fof(f368,plain,
( spl22_31
<=> ! [X0] : empty(sK7(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_31])]) ).
fof(f420,plain,
( spl22_41
<=> ! [X0] :
( empty_set = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_41])]) ).
fof(f579,plain,
( ! [X0] :
( in(sK13,powerset(X0))
| empty(powerset(X0)) )
| ~ spl22_10
| ~ spl22_31
| ~ spl22_41
| ~ spl22_45
| ~ spl22_64 ),
inference(forward_demodulation,[],[f578,f446]) ).
fof(f446,plain,
( empty_set = sK13
| ~ spl22_10
| ~ spl22_41 ),
inference(resolution,[],[f421,f267]) ).
fof(f267,plain,
( empty(sK13)
| ~ spl22_10 ),
inference(avatar_component_clause,[],[f265]) ).
fof(f421,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = X0 )
| ~ spl22_41 ),
inference(avatar_component_clause,[],[f420]) ).
fof(f578,plain,
( ! [X0] :
( in(empty_set,powerset(X0))
| empty(powerset(X0)) )
| ~ spl22_31
| ~ spl22_41
| ~ spl22_45
| ~ spl22_64 ),
inference(forward_demodulation,[],[f577,f445]) ).
fof(f445,plain,
( ! [X0] : empty_set = sK7(X0)
| ~ spl22_31
| ~ spl22_41 ),
inference(resolution,[],[f421,f369]) ).
fof(f369,plain,
( ! [X0] : empty(sK7(X0))
| ~ spl22_31 ),
inference(avatar_component_clause,[],[f368]) ).
fof(f577,plain,
( ! [X0] :
( empty(powerset(X0))
| in(sK7(X0),powerset(X0)) )
| ~ spl22_45
| ~ spl22_64 ),
inference(resolution,[],[f552,f438]) ).
fof(f957,plain,
( spl22_121
| ~ spl22_66
| ~ spl22_90 ),
inference(avatar_split_clause,[],[f726,f720,f559,f955]) ).
fof(f726,plain,
( ! [X0] :
( ~ subset(sK2,X0)
| sP0(sK1,sK4,X0) )
| ~ spl22_66
| ~ spl22_90 ),
inference(resolution,[],[f721,f560]) ).
fof(f940,plain,
( spl22_120
| ~ spl22_67
| ~ spl22_72 ),
inference(avatar_split_clause,[],[f614,f607,f563,f938]) ).
fof(f614,plain,
( ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| relation(X0) )
| ~ spl22_67
| ~ spl22_72 ),
inference(resolution,[],[f608,f564]) ).
fof(f936,plain,
( spl22_119
| ~ spl22_54
| ~ spl22_69 ),
inference(avatar_split_clause,[],[f590,f571,f489,f934]) ).
fof(f571,plain,
( spl22_69
<=> ! [X2,X0,X1] :
( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_69])]) ).
fof(f590,plain,
( ! [X0,X1] : relation_of2_as_subset(sK11(X0,X1),X0,X1)
| ~ spl22_54
| ~ spl22_69 ),
inference(resolution,[],[f572,f490]) ).
fof(f572,plain,
( ! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| relation_of2_as_subset(X2,X0,X1) )
| ~ spl22_69 ),
inference(avatar_component_clause,[],[f571]) ).
fof(f932,plain,
( spl22_118
| ~ spl22_53
| ~ spl22_69 ),
inference(avatar_split_clause,[],[f589,f571,f485,f930]) ).
fof(f589,plain,
( ! [X0,X1] : relation_of2_as_subset(sK10(X0,X1),X0,X1)
| ~ spl22_53
| ~ spl22_69 ),
inference(resolution,[],[f572,f486]) ).
fof(f928,plain,
( spl22_117
| ~ spl22_51
| ~ spl22_69 ),
inference(avatar_split_clause,[],[f588,f571,f477,f926]) ).
fof(f588,plain,
( ! [X0,X1] : relation_of2_as_subset(sK8(X0,X1),X0,X1)
| ~ spl22_51
| ~ spl22_69 ),
inference(resolution,[],[f572,f478]) ).
fof(f924,plain,
( spl22_116
| ~ spl22_52
| ~ spl22_68 ),
inference(avatar_split_clause,[],[f587,f567,f481,f922]) ).
fof(f587,plain,
( ! [X0,X1] : relation_of2(sK9(X0,X1),X0,X1)
| ~ spl22_52
| ~ spl22_68 ),
inference(resolution,[],[f568,f482]) ).
fof(f920,plain,
( spl22_115
| ~ spl22_35
| ~ spl22_67 ),
inference(avatar_split_clause,[],[f584,f563,f384,f918]) ).
fof(f918,plain,
( spl22_115
<=> ! [X0,X1] : relation(sK6(powerset(cartesian_product2(X0,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_115])]) ).
fof(f584,plain,
( ! [X0,X1] : relation(sK6(powerset(cartesian_product2(X0,X1))))
| ~ spl22_35
| ~ spl22_67 ),
inference(resolution,[],[f564,f385]) ).
fof(f916,plain,
( spl22_114
| ~ spl22_52
| ~ spl22_66 ),
inference(avatar_split_clause,[],[f581,f559,f481,f914]) ).
fof(f581,plain,
( ! [X0,X1] : sP0(X0,sK9(X0,X1),X1)
| ~ spl22_52
| ~ spl22_66 ),
inference(resolution,[],[f560,f482]) ).
fof(f912,plain,
( spl22_113
| ~ spl22_35
| ~ spl22_64 ),
inference(avatar_split_clause,[],[f576,f551,f384,f910]) ).
fof(f576,plain,
( ! [X0] :
( empty(X0)
| in(sK6(X0),X0) )
| ~ spl22_35
| ~ spl22_64 ),
inference(resolution,[],[f552,f385]) ).
fof(f908,plain,
( spl22_112
| ~ spl22_68
| ~ spl22_90 ),
inference(avatar_split_clause,[],[f725,f720,f567,f906]) ).
fof(f725,plain,
( ! [X0] :
( ~ subset(sK2,X0)
| relation_of2(sK4,sK1,X0) )
| ~ spl22_68
| ~ spl22_90 ),
inference(resolution,[],[f721,f568]) ).
fof(f904,plain,
( spl22_111
| ~ spl22_58
| ~ spl22_60 ),
inference(avatar_split_clause,[],[f535,f516,f508,f902]) ).
fof(f902,plain,
( spl22_111
<=> ! [X0] :
( subset(sK5(X0),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_111])]) ).
fof(f535,plain,
( ! [X0] :
( subset(sK5(X0),X0)
| empty(X0) )
| ~ spl22_58
| ~ spl22_60 ),
inference(resolution,[],[f517,f509]) ).
fof(f900,plain,
( spl22_110
| ~ spl22_10
| ~ spl22_41
| ~ spl22_43 ),
inference(avatar_split_clause,[],[f456,f429,f420,f265,f898]) ).
fof(f456,plain,
( ! [X0] :
( relation_dom(X0) = sK13
| ~ empty(X0) )
| ~ spl22_10
| ~ spl22_41
| ~ spl22_43 ),
inference(forward_demodulation,[],[f453,f446]) ).
fof(f453,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = relation_dom(X0) )
| ~ spl22_41
| ~ spl22_43 ),
inference(resolution,[],[f430,f421]) ).
fof(f868,plain,
( spl22_109
| ~ spl22_74
| ~ spl22_78 ),
inference(avatar_split_clause,[],[f717,f648,f626,f865]) ).
fof(f717,plain,
( relation_dom_as_subset(sK1,sK2,sK4) = relation_dom(sK4)
| ~ spl22_74
| ~ spl22_78 ),
inference(resolution,[],[f650,f627]) ).
fof(f863,plain,
( spl22_106
| ~ spl22_41
| ~ spl22_93 ),
inference(avatar_split_clause,[],[f845,f738,f420,f823]) ).
fof(f845,plain,
( ! [X0] :
( sK13 = X0
| ~ empty(X0) )
| ~ spl22_41
| ~ spl22_93 ),
inference(forward_demodulation,[],[f421,f740]) ).
fof(f844,plain,
( ~ spl22_7
| ~ spl22_107 ),
inference(avatar_contradiction_clause,[],[f833]) ).
fof(f833,plain,
( $false
| ~ spl22_7
| ~ spl22_107 ),
inference(resolution,[],[f828,f252]) ).
fof(f828,plain,
( ! [X0] : ~ empty(X0)
| ~ spl22_107 ),
inference(avatar_component_clause,[],[f827]) ).
fof(f827,plain,
( spl22_107
<=> ! [X0] : ~ empty(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_107])]) ).
fof(f843,plain,
( ~ spl22_31
| ~ spl22_107 ),
inference(avatar_contradiction_clause,[],[f834]) ).
fof(f834,plain,
( $false
| ~ spl22_31
| ~ spl22_107 ),
inference(resolution,[],[f828,f369]) ).
fof(f842,plain,
( ~ spl22_10
| ~ spl22_107 ),
inference(avatar_contradiction_clause,[],[f835]) ).
fof(f835,plain,
( $false
| ~ spl22_10
| ~ spl22_107 ),
inference(resolution,[],[f828,f267]) ).
fof(f841,plain,
( ~ spl22_13
| ~ spl22_107 ),
inference(avatar_contradiction_clause,[],[f836]) ).
fof(f836,plain,
( $false
| ~ spl22_13
| ~ spl22_107 ),
inference(resolution,[],[f828,f282]) ).
fof(f282,plain,
( empty(sK15)
| ~ spl22_13 ),
inference(avatar_component_clause,[],[f280]) ).
fof(f280,plain,
( spl22_13
<=> empty(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_13])]) ).
fof(f840,plain,
( ~ spl22_24
| ~ spl22_107 ),
inference(avatar_contradiction_clause,[],[f837]) ).
fof(f837,plain,
( $false
| ~ spl22_24
| ~ spl22_107 ),
inference(resolution,[],[f828,f337]) ).
fof(f337,plain,
( empty(sK20)
| ~ spl22_24 ),
inference(avatar_component_clause,[],[f335]) ).
fof(f335,plain,
( spl22_24
<=> empty(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_24])]) ).
fof(f839,plain,
( ~ spl22_26
| ~ spl22_107 ),
inference(avatar_contradiction_clause,[],[f838]) ).
fof(f838,plain,
( $false
| ~ spl22_26
| ~ spl22_107 ),
inference(resolution,[],[f828,f347]) ).
fof(f347,plain,
( empty(sK21)
| ~ spl22_26 ),
inference(avatar_component_clause,[],[f345]) ).
fof(f345,plain,
( spl22_26
<=> empty(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_26])]) ).
fof(f832,plain,
( spl22_107
| spl22_108
| ~ spl22_10
| ~ spl22_31
| ~ spl22_41
| ~ spl22_45
| ~ spl22_70 ),
inference(avatar_split_clause,[],[f605,f592,f437,f420,f368,f265,f830,f827]) ).
fof(f830,plain,
( spl22_108
<=> ! [X1] : ~ in(X1,sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_108])]) ).
fof(f605,plain,
( ! [X0,X1] :
( ~ in(X1,sK13)
| ~ empty(X0) )
| ~ spl22_10
| ~ spl22_31
| ~ spl22_41
| ~ spl22_45
| ~ spl22_70 ),
inference(forward_demodulation,[],[f604,f446]) ).
fof(f604,plain,
( ! [X0,X1] :
( ~ in(X1,empty_set)
| ~ empty(X0) )
| ~ spl22_31
| ~ spl22_41
| ~ spl22_45
| ~ spl22_70 ),
inference(forward_demodulation,[],[f603,f445]) ).
fof(f603,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK7(X0)) )
| ~ spl22_45
| ~ spl22_70 ),
inference(resolution,[],[f593,f438]) ).
fof(f825,plain,
( spl22_106
| ~ spl22_10
| ~ spl22_63 ),
inference(avatar_split_clause,[],[f542,f529,f265,f823]) ).
fof(f542,plain,
( ! [X0] :
( sK13 = X0
| ~ empty(X0) )
| ~ spl22_10
| ~ spl22_63 ),
inference(resolution,[],[f530,f267]) ).
fof(f821,plain,
( spl22_105
| ~ spl22_35
| ~ spl22_60 ),
inference(avatar_split_clause,[],[f533,f516,f384,f819]) ).
fof(f533,plain,
( ! [X0] : subset(sK6(powerset(X0)),X0)
| ~ spl22_35
| ~ spl22_60 ),
inference(resolution,[],[f517,f385]) ).
fof(f817,plain,
( spl22_104
| ~ spl22_33
| ~ spl22_43 ),
inference(avatar_split_clause,[],[f455,f429,f376,f815]) ).
fof(f815,plain,
( spl22_104
<=> ! [X0] :
( ~ empty(X0)
| function(relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_104])]) ).
fof(f455,plain,
( ! [X0] :
( ~ empty(X0)
| function(relation_dom(X0)) )
| ~ spl22_33
| ~ spl22_43 ),
inference(resolution,[],[f430,f377]) ).
fof(f811,plain,
( spl22_103
| ~ spl22_93
| ~ spl22_102 ),
inference(avatar_split_clause,[],[f807,f804,f738,f809]) ).
fof(f804,plain,
( spl22_102
<=> ! [X0] : empty_set = sK7(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_102])]) ).
fof(f807,plain,
( ! [X0] : sK7(X0) = sK13
| ~ spl22_93
| ~ spl22_102 ),
inference(forward_demodulation,[],[f805,f740]) ).
fof(f805,plain,
( ! [X0] : empty_set = sK7(X0)
| ~ spl22_102 ),
inference(avatar_component_clause,[],[f804]) ).
fof(f806,plain,
( spl22_102
| ~ spl22_31
| ~ spl22_41 ),
inference(avatar_split_clause,[],[f445,f420,f368,f804]) ).
fof(f798,plain,
( ~ spl22_101
| spl22_5
| ~ spl22_93 ),
inference(avatar_split_clause,[],[f788,f738,f241,f795]) ).
fof(f241,plain,
( spl22_5
<=> empty_set = sK2 ),
introduced(avatar_definition,[new_symbols(naming,[spl22_5])]) ).
fof(f788,plain,
( sK2 != sK13
| spl22_5
| ~ spl22_93 ),
inference(superposition,[],[f243,f740]) ).
fof(f243,plain,
( empty_set != sK2
| spl22_5 ),
inference(avatar_component_clause,[],[f241]) ).
fof(f781,plain,
( spl22_100
| ~ spl22_29
| ~ spl22_76 ),
inference(avatar_split_clause,[],[f762,f634,f359,f779]) ).
fof(f762,plain,
( ! [X0] :
( ~ subset(sK3,X0)
| relation_of2_as_subset(sK4,sK1,X0) )
| ~ spl22_29
| ~ spl22_76 ),
inference(resolution,[],[f360,f635]) ).
fof(f774,plain,
( spl22_99
| ~ spl22_29
| ~ spl22_66 ),
inference(avatar_split_clause,[],[f764,f559,f359,f771]) ).
fof(f764,plain,
( sP0(sK1,sK4,sK3)
| ~ spl22_29
| ~ spl22_66 ),
inference(resolution,[],[f360,f560]) ).
fof(f769,plain,
( spl22_98
| ~ spl22_29
| ~ spl22_68 ),
inference(avatar_split_clause,[],[f763,f567,f359,f766]) ).
fof(f763,plain,
( relation_of2(sK4,sK1,sK3)
| ~ spl22_29
| ~ spl22_68 ),
inference(resolution,[],[f360,f568]) ).
fof(f761,plain,
( ~ spl22_2
| spl22_29
| ~ spl22_90 ),
inference(avatar_split_clause,[],[f723,f720,f359,f226]) ).
fof(f723,plain,
( ~ subset(sK2,sK3)
| spl22_29
| ~ spl22_90 ),
inference(resolution,[],[f721,f361]) ).
fof(f361,plain,
( ~ relation_of2_as_subset(sK4,sK1,sK3)
| spl22_29 ),
inference(avatar_component_clause,[],[f359]) ).
fof(f760,plain,
( spl22_97
| ~ spl22_10
| ~ spl22_31
| ~ spl22_41
| ~ spl22_45
| ~ spl22_60 ),
inference(avatar_split_clause,[],[f537,f516,f437,f420,f368,f265,f758]) ).
fof(f758,plain,
( spl22_97
<=> ! [X0] : subset(sK13,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_97])]) ).
fof(f537,plain,
( ! [X0] : subset(sK13,X0)
| ~ spl22_10
| ~ spl22_31
| ~ spl22_41
| ~ spl22_45
| ~ spl22_60 ),
inference(forward_demodulation,[],[f536,f446]) ).
fof(f536,plain,
( ! [X0] : subset(empty_set,X0)
| ~ spl22_31
| ~ spl22_41
| ~ spl22_45
| ~ spl22_60 ),
inference(forward_demodulation,[],[f534,f445]) ).
fof(f534,plain,
( ! [X0] : subset(sK7(X0),X0)
| ~ spl22_45
| ~ spl22_60 ),
inference(resolution,[],[f517,f438]) ).
fof(f756,plain,
( spl22_96
| ~ spl22_10
| ~ spl22_26
| ~ spl22_41 ),
inference(avatar_split_clause,[],[f452,f420,f345,f265,f753]) ).
fof(f753,plain,
( spl22_96
<=> sK13 = sK21 ),
introduced(avatar_definition,[new_symbols(naming,[spl22_96])]) ).
fof(f452,plain,
( sK13 = sK21
| ~ spl22_10
| ~ spl22_26
| ~ spl22_41 ),
inference(forward_demodulation,[],[f449,f446]) ).
fof(f449,plain,
( empty_set = sK21
| ~ spl22_26
| ~ spl22_41 ),
inference(resolution,[],[f421,f347]) ).
fof(f751,plain,
( spl22_95
| ~ spl22_10
| ~ spl22_24
| ~ spl22_41 ),
inference(avatar_split_clause,[],[f451,f420,f335,f265,f748]) ).
fof(f748,plain,
( spl22_95
<=> sK13 = sK20 ),
introduced(avatar_definition,[new_symbols(naming,[spl22_95])]) ).
fof(f451,plain,
( sK13 = sK20
| ~ spl22_10
| ~ spl22_24
| ~ spl22_41 ),
inference(forward_demodulation,[],[f448,f446]) ).
fof(f448,plain,
( empty_set = sK20
| ~ spl22_24
| ~ spl22_41 ),
inference(resolution,[],[f421,f337]) ).
fof(f746,plain,
( spl22_94
| ~ spl22_10
| ~ spl22_13
| ~ spl22_41 ),
inference(avatar_split_clause,[],[f450,f420,f280,f265,f743]) ).
fof(f743,plain,
( spl22_94
<=> sK13 = sK15 ),
introduced(avatar_definition,[new_symbols(naming,[spl22_94])]) ).
fof(f450,plain,
( sK13 = sK15
| ~ spl22_10
| ~ spl22_13
| ~ spl22_41 ),
inference(forward_demodulation,[],[f447,f446]) ).
fof(f447,plain,
( empty_set = sK15
| ~ spl22_13
| ~ spl22_41 ),
inference(resolution,[],[f421,f282]) ).
fof(f741,plain,
( spl22_93
| ~ spl22_10
| ~ spl22_41 ),
inference(avatar_split_clause,[],[f446,f420,f265,f738]) ).
fof(f735,plain,
( spl22_92
| ~ spl22_31
| ~ spl22_34 ),
inference(avatar_split_clause,[],[f410,f380,f368,f733]) ).
fof(f733,plain,
( spl22_92
<=> ! [X0] : relation(sK7(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_92])]) ).
fof(f410,plain,
( ! [X0] : relation(sK7(X0))
| ~ spl22_31
| ~ spl22_34 ),
inference(resolution,[],[f381,f369]) ).
fof(f730,plain,
( spl22_91
| ~ spl22_31
| ~ spl22_33 ),
inference(avatar_split_clause,[],[f404,f376,f368,f728]) ).
fof(f728,plain,
( spl22_91
<=> ! [X0] : function(sK7(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_91])]) ).
fof(f404,plain,
( ! [X0] : function(sK7(X0))
| ~ spl22_31
| ~ spl22_33 ),
inference(resolution,[],[f377,f369]) ).
fof(f722,plain,
( spl22_90
| ~ spl22_4
| ~ spl22_76 ),
inference(avatar_split_clause,[],[f657,f634,f236,f720]) ).
fof(f657,plain,
( ! [X0] :
( ~ subset(sK2,X0)
| relation_of2_as_subset(sK4,sK1,X0) )
| ~ spl22_4
| ~ spl22_76 ),
inference(resolution,[],[f635,f238]) ).
fof(f715,plain,
( spl22_89
| ~ spl22_10
| ~ spl22_41
| ~ spl22_87 ),
inference(avatar_split_clause,[],[f707,f704,f420,f265,f713]) ).
fof(f704,plain,
( spl22_87
<=> ! [X2,X0,X1] :
( quasi_total(X1,X0,X2)
| relation_dom_as_subset(X0,X2,X1) != X0
| empty_set = X2
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_87])]) ).
fof(f707,plain,
( ! [X2,X0,X1] :
( sK13 = X2
| quasi_total(X1,X0,X2)
| relation_dom_as_subset(X0,X2,X1) != X0
| ~ sP0(X0,X1,X2) )
| ~ spl22_10
| ~ spl22_41
| ~ spl22_87 ),
inference(forward_demodulation,[],[f705,f446]) ).
fof(f705,plain,
( ! [X2,X0,X1] :
( quasi_total(X1,X0,X2)
| relation_dom_as_subset(X0,X2,X1) != X0
| empty_set = X2
| ~ sP0(X0,X1,X2) )
| ~ spl22_87 ),
inference(avatar_component_clause,[],[f704]) ).
fof(f711,plain,
( spl22_88
| ~ spl22_10
| ~ spl22_41
| ~ spl22_86 ),
inference(avatar_split_clause,[],[f702,f699,f420,f265,f709]) ).
fof(f699,plain,
( spl22_86
<=> ! [X2,X0,X1] :
( relation_dom_as_subset(X0,X2,X1) = X0
| ~ quasi_total(X1,X0,X2)
| empty_set = X2
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_86])]) ).
fof(f702,plain,
( ! [X2,X0,X1] :
( sK13 = X2
| relation_dom_as_subset(X0,X2,X1) = X0
| ~ quasi_total(X1,X0,X2)
| ~ sP0(X0,X1,X2) )
| ~ spl22_10
| ~ spl22_41
| ~ spl22_86 ),
inference(forward_demodulation,[],[f700,f446]) ).
fof(f700,plain,
( ! [X2,X0,X1] :
( relation_dom_as_subset(X0,X2,X1) = X0
| ~ quasi_total(X1,X0,X2)
| empty_set = X2
| ~ sP0(X0,X1,X2) )
| ~ spl22_86 ),
inference(avatar_component_clause,[],[f699]) ).
fof(f706,plain,
spl22_87,
inference(avatar_split_clause,[],[f184,f704]) ).
fof(f184,plain,
! [X2,X0,X1] :
( quasi_total(X1,X0,X2)
| relation_dom_as_subset(X0,X2,X1) != X0
| empty_set = X2
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f112]) ).
fof(f112,plain,
! [X0,X1,X2] :
( ( ( quasi_total(X1,X0,X2)
| relation_dom_as_subset(X0,X2,X1) != X0 )
& ( relation_dom_as_subset(X0,X2,X1) = X0
| ~ quasi_total(X1,X0,X2) ) )
| ( empty_set != X0
& empty_set = X2 )
| ~ sP0(X0,X1,X2) ),
inference(rectify,[],[f111]) ).
fof(f111,plain,
! [X0,X2,X1] :
( ( ( quasi_total(X2,X0,X1)
| relation_dom_as_subset(X0,X1,X2) != X0 )
& ( relation_dom_as_subset(X0,X1,X2) = X0
| ~ quasi_total(X2,X0,X1) ) )
| ( empty_set != X0
& empty_set = X1 )
| ~ sP0(X0,X2,X1) ),
inference(nnf_transformation,[],[f92]) ).
fof(f92,plain,
! [X0,X2,X1] :
( ( quasi_total(X2,X0,X1)
<=> relation_dom_as_subset(X0,X1,X2) = X0 )
| ( empty_set != X0
& empty_set = X1 )
| ~ sP0(X0,X2,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f701,plain,
spl22_86,
inference(avatar_split_clause,[],[f182,f699]) ).
fof(f182,plain,
! [X2,X0,X1] :
( relation_dom_as_subset(X0,X2,X1) = X0
| ~ quasi_total(X1,X0,X2)
| empty_set = X2
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f112]) ).
fof(f696,plain,
( spl22_85
| ~ spl22_10
| ~ spl22_41
| ~ spl22_82 ),
inference(avatar_split_clause,[],[f684,f678,f420,f265,f694]) ).
fof(f678,plain,
( spl22_82
<=> ! [X2,X0] :
( empty_set = X2
| ~ quasi_total(X2,X0,empty_set)
| empty_set = X0
| ~ relation_of2_as_subset(X2,X0,empty_set) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_82])]) ).
fof(f684,plain,
( ! [X2,X0] :
( ~ relation_of2_as_subset(X2,X0,sK13)
| sK13 = X0
| ~ quasi_total(X2,X0,sK13)
| sK13 = X2 )
| ~ spl22_10
| ~ spl22_41
| ~ spl22_82 ),
inference(forward_demodulation,[],[f683,f446]) ).
fof(f683,plain,
( ! [X2,X0] :
( sK13 = X0
| ~ quasi_total(X2,X0,sK13)
| sK13 = X2
| ~ relation_of2_as_subset(X2,X0,empty_set) )
| ~ spl22_10
| ~ spl22_41
| ~ spl22_82 ),
inference(forward_demodulation,[],[f682,f446]) ).
fof(f682,plain,
( ! [X2,X0] :
( ~ quasi_total(X2,X0,sK13)
| sK13 = X2
| empty_set = X0
| ~ relation_of2_as_subset(X2,X0,empty_set) )
| ~ spl22_10
| ~ spl22_41
| ~ spl22_82 ),
inference(forward_demodulation,[],[f681,f446]) ).
fof(f681,plain,
( ! [X2,X0] :
( sK13 = X2
| ~ quasi_total(X2,X0,empty_set)
| empty_set = X0
| ~ relation_of2_as_subset(X2,X0,empty_set) )
| ~ spl22_10
| ~ spl22_41
| ~ spl22_82 ),
inference(forward_demodulation,[],[f679,f446]) ).
fof(f679,plain,
( ! [X2,X0] :
( empty_set = X2
| ~ quasi_total(X2,X0,empty_set)
| empty_set = X0
| ~ relation_of2_as_subset(X2,X0,empty_set) )
| ~ spl22_82 ),
inference(avatar_component_clause,[],[f678]) ).
fof(f692,plain,
( spl22_84
| ~ spl22_10
| ~ spl22_41
| ~ spl22_81 ),
inference(avatar_split_clause,[],[f676,f671,f420,f265,f690]) ).
fof(f690,plain,
( spl22_84
<=> ! [X2,X1] :
( ~ sP0(sK13,X1,X2)
| ~ quasi_total(X1,sK13,X2)
| sK13 = relation_dom_as_subset(sK13,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_84])]) ).
fof(f671,plain,
( spl22_81
<=> ! [X2,X1] :
( empty_set = relation_dom_as_subset(empty_set,X2,X1)
| ~ quasi_total(X1,empty_set,X2)
| ~ sP0(empty_set,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_81])]) ).
fof(f676,plain,
( ! [X2,X1] :
( ~ sP0(sK13,X1,X2)
| ~ quasi_total(X1,sK13,X2)
| sK13 = relation_dom_as_subset(sK13,X2,X1) )
| ~ spl22_10
| ~ spl22_41
| ~ spl22_81 ),
inference(forward_demodulation,[],[f675,f446]) ).
fof(f675,plain,
( ! [X2,X1] :
( ~ quasi_total(X1,sK13,X2)
| sK13 = relation_dom_as_subset(sK13,X2,X1)
| ~ sP0(empty_set,X1,X2) )
| ~ spl22_10
| ~ spl22_41
| ~ spl22_81 ),
inference(forward_demodulation,[],[f674,f446]) ).
fof(f674,plain,
( ! [X2,X1] :
( sK13 = relation_dom_as_subset(sK13,X2,X1)
| ~ quasi_total(X1,empty_set,X2)
| ~ sP0(empty_set,X1,X2) )
| ~ spl22_10
| ~ spl22_41
| ~ spl22_81 ),
inference(forward_demodulation,[],[f672,f446]) ).
fof(f672,plain,
( ! [X2,X1] :
( empty_set = relation_dom_as_subset(empty_set,X2,X1)
| ~ quasi_total(X1,empty_set,X2)
| ~ sP0(empty_set,X1,X2) )
| ~ spl22_81 ),
inference(avatar_component_clause,[],[f671]) ).
fof(f688,plain,
( spl22_83
| ~ spl22_10
| ~ spl22_41
| ~ spl22_80 ),
inference(avatar_split_clause,[],[f669,f664,f420,f265,f686]) ).
fof(f664,plain,
( spl22_80
<=> ! [X2,X1] :
( quasi_total(X1,empty_set,X2)
| empty_set != relation_dom_as_subset(empty_set,X2,X1)
| ~ sP0(empty_set,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_80])]) ).
fof(f669,plain,
( ! [X2,X1] :
( ~ sP0(sK13,X1,X2)
| sK13 != relation_dom_as_subset(sK13,X2,X1)
| quasi_total(X1,sK13,X2) )
| ~ spl22_10
| ~ spl22_41
| ~ spl22_80 ),
inference(forward_demodulation,[],[f668,f446]) ).
fof(f668,plain,
( ! [X2,X1] :
( sK13 != relation_dom_as_subset(sK13,X2,X1)
| quasi_total(X1,sK13,X2)
| ~ sP0(empty_set,X1,X2) )
| ~ spl22_10
| ~ spl22_41
| ~ spl22_80 ),
inference(forward_demodulation,[],[f667,f446]) ).
fof(f667,plain,
( ! [X2,X1] :
( quasi_total(X1,sK13,X2)
| empty_set != relation_dom_as_subset(empty_set,X2,X1)
| ~ sP0(empty_set,X1,X2) )
| ~ spl22_10
| ~ spl22_41
| ~ spl22_80 ),
inference(forward_demodulation,[],[f665,f446]) ).
fof(f665,plain,
( ! [X2,X1] :
( quasi_total(X1,empty_set,X2)
| empty_set != relation_dom_as_subset(empty_set,X2,X1)
| ~ sP0(empty_set,X1,X2) )
| ~ spl22_80 ),
inference(avatar_component_clause,[],[f664]) ).
fof(f680,plain,
spl22_82,
inference(avatar_split_clause,[],[f218,f678]) ).
fof(f218,plain,
! [X2,X0] :
( empty_set = X2
| ~ quasi_total(X2,X0,empty_set)
| empty_set = X0
| ~ relation_of2_as_subset(X2,X0,empty_set) ),
inference(equality_resolution,[],[f187]) ).
fof(f187,plain,
! [X2,X0,X1] :
( empty_set = X2
| ~ quasi_total(X2,X0,X1)
| empty_set = X0
| empty_set != X1
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f113]) ).
fof(f113,plain,
! [X0,X1,X2] :
( ( ( ( ( quasi_total(X2,X0,X1)
| empty_set != X2 )
& ( empty_set = X2
| ~ quasi_total(X2,X0,X1) ) )
| empty_set = X0
| empty_set != X1 )
& sP0(X0,X2,X1) )
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(nnf_transformation,[],[f93]) ).
fof(f93,plain,
! [X0,X1,X2] :
( ( ( ( quasi_total(X2,X0,X1)
<=> empty_set = X2 )
| empty_set = X0
| empty_set != X1 )
& sP0(X0,X2,X1) )
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(definition_folding,[],[f85,f92]) ).
fof(f85,plain,
! [X0,X1,X2] :
( ( ( ( quasi_total(X2,X0,X1)
<=> empty_set = X2 )
| empty_set = X0
| empty_set != X1 )
& ( ( quasi_total(X2,X0,X1)
<=> relation_dom_as_subset(X0,X1,X2) = X0 )
| ( empty_set != X0
& empty_set = X1 ) ) )
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(flattening,[],[f84]) ).
fof(f84,plain,
! [X0,X1,X2] :
( ( ( ( quasi_total(X2,X0,X1)
<=> empty_set = X2 )
| empty_set = X0
| empty_set != X1 )
& ( ( quasi_total(X2,X0,X1)
<=> relation_dom_as_subset(X0,X1,X2) = X0 )
| ( empty_set != X0
& empty_set = X1 ) ) )
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> ( ( empty_set = X1
=> ( ( quasi_total(X2,X0,X1)
<=> empty_set = X2 )
| empty_set = X0 ) )
& ( ( empty_set = X1
=> empty_set = X0 )
=> ( quasi_total(X2,X0,X1)
<=> relation_dom_as_subset(X0,X1,X2) = X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_funct_2) ).
fof(f673,plain,
spl22_81,
inference(avatar_split_clause,[],[f215,f671]) ).
fof(f215,plain,
! [X2,X1] :
( empty_set = relation_dom_as_subset(empty_set,X2,X1)
| ~ quasi_total(X1,empty_set,X2)
| ~ sP0(empty_set,X1,X2) ),
inference(equality_resolution,[],[f183]) ).
fof(f183,plain,
! [X2,X0,X1] :
( relation_dom_as_subset(X0,X2,X1) = X0
| ~ quasi_total(X1,X0,X2)
| empty_set != X0
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f112]) ).
fof(f666,plain,
spl22_80,
inference(avatar_split_clause,[],[f214,f664]) ).
fof(f214,plain,
! [X2,X1] :
( quasi_total(X1,empty_set,X2)
| empty_set != relation_dom_as_subset(empty_set,X2,X1)
| ~ sP0(empty_set,X1,X2) ),
inference(equality_resolution,[],[f185]) ).
fof(f185,plain,
! [X2,X0,X1] :
( quasi_total(X1,X0,X2)
| relation_dom_as_subset(X0,X2,X1) != X0
| empty_set != X0
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f112]) ).
fof(f662,plain,
( spl22_79
| ~ spl22_10
| ~ spl22_41
| ~ spl22_77 ),
inference(avatar_split_clause,[],[f643,f638,f420,f265,f660]) ).
fof(f660,plain,
( spl22_79
<=> ! [X0] :
( ~ relation_of2_as_subset(sK13,X0,sK13)
| sK13 = X0
| quasi_total(sK13,X0,sK13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_79])]) ).
fof(f638,plain,
( spl22_77
<=> ! [X0] :
( quasi_total(empty_set,X0,empty_set)
| empty_set = X0
| ~ relation_of2_as_subset(empty_set,X0,empty_set) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_77])]) ).
fof(f643,plain,
( ! [X0] :
( ~ relation_of2_as_subset(sK13,X0,sK13)
| sK13 = X0
| quasi_total(sK13,X0,sK13) )
| ~ spl22_10
| ~ spl22_41
| ~ spl22_77 ),
inference(forward_demodulation,[],[f642,f446]) ).
fof(f642,plain,
( ! [X0] :
( sK13 = X0
| quasi_total(sK13,X0,sK13)
| ~ relation_of2_as_subset(empty_set,X0,empty_set) )
| ~ spl22_10
| ~ spl22_41
| ~ spl22_77 ),
inference(forward_demodulation,[],[f641,f446]) ).
fof(f641,plain,
( ! [X0] :
( quasi_total(sK13,X0,sK13)
| empty_set = X0
| ~ relation_of2_as_subset(empty_set,X0,empty_set) )
| ~ spl22_10
| ~ spl22_41
| ~ spl22_77 ),
inference(forward_demodulation,[],[f639,f446]) ).
fof(f639,plain,
( ! [X0] :
( quasi_total(empty_set,X0,empty_set)
| empty_set = X0
| ~ relation_of2_as_subset(empty_set,X0,empty_set) )
| ~ spl22_77 ),
inference(avatar_component_clause,[],[f638]) ).
fof(f651,plain,
( spl22_78
| ~ spl22_4
| ~ spl22_68 ),
inference(avatar_split_clause,[],[f586,f567,f236,f648]) ).
fof(f586,plain,
( relation_of2(sK4,sK1,sK2)
| ~ spl22_4
| ~ spl22_68 ),
inference(resolution,[],[f568,f238]) ).
fof(f640,plain,
spl22_77,
inference(avatar_split_clause,[],[f217,f638]) ).
fof(f217,plain,
! [X0] :
( quasi_total(empty_set,X0,empty_set)
| empty_set = X0
| ~ relation_of2_as_subset(empty_set,X0,empty_set) ),
inference(equality_resolution,[],[f216]) ).
fof(f216,plain,
! [X0,X1] :
( quasi_total(empty_set,X0,X1)
| empty_set = X0
| empty_set != X1
| ~ relation_of2_as_subset(empty_set,X0,X1) ),
inference(equality_resolution,[],[f188]) ).
fof(f188,plain,
! [X2,X0,X1] :
( quasi_total(X2,X0,X1)
| empty_set != X2
| empty_set = X0
| empty_set != X1
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f113]) ).
fof(f636,plain,
spl22_76,
inference(avatar_split_clause,[],[f194,f634]) ).
fof(f194,plain,
! [X2,X3,X0,X1] :
( relation_of2_as_subset(X3,X2,X1)
| ~ subset(X0,X1)
| ~ relation_of2_as_subset(X3,X2,X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f91,plain,
! [X0,X1,X2,X3] :
( relation_of2_as_subset(X3,X2,X1)
| ~ subset(X0,X1)
| ~ relation_of2_as_subset(X3,X2,X0) ),
inference(flattening,[],[f90]) ).
fof(f90,plain,
! [X0,X1,X2,X3] :
( relation_of2_as_subset(X3,X2,X1)
| ~ subset(X0,X1)
| ~ relation_of2_as_subset(X3,X2,X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0,X1,X2,X3] :
( relation_of2_as_subset(X3,X2,X0)
=> ( subset(X0,X1)
=> relation_of2_as_subset(X3,X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_relset_1) ).
fof(f632,plain,
spl22_75,
inference(avatar_split_clause,[],[f180,f630]) ).
fof(f180,plain,
! [X2,X0,X1] :
( element(relation_dom_as_subset(X0,X1,X2),powerset(X0))
| ~ relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0,X1,X2] :
( element(relation_dom_as_subset(X0,X1,X2),powerset(X0))
| ~ relation_of2(X2,X0,X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0,X1,X2] :
( relation_of2(X2,X0,X1)
=> element(relation_dom_as_subset(X0,X1,X2),powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relset_1) ).
fof(f628,plain,
spl22_74,
inference(avatar_split_clause,[],[f179,f626]) ).
fof(f179,plain,
! [X2,X0,X1] :
( relation_dom_as_subset(X0,X1,X2) = relation_dom(X2)
| ~ relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0,X1,X2] :
( relation_dom_as_subset(X0,X1,X2) = relation_dom(X2)
| ~ relation_of2(X2,X0,X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f39,axiom,
! [X0,X1,X2] :
( relation_of2(X2,X0,X1)
=> relation_dom_as_subset(X0,X1,X2) = relation_dom(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_relset_1) ).
fof(f613,plain,
spl22_73,
inference(avatar_split_clause,[],[f190,f611]) ).
fof(f190,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f87]) ).
fof(f87,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f47]) ).
fof(f47,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f609,plain,
spl22_72,
inference(avatar_split_clause,[],[f181,f607]) ).
fof(f181,plain,
! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> element(X2,powerset(cartesian_product2(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(f599,plain,
( spl22_71
| ~ spl22_4
| ~ spl22_66 ),
inference(avatar_split_clause,[],[f580,f559,f236,f596]) ).
fof(f580,plain,
( sP0(sK1,sK4,sK2)
| ~ spl22_4
| ~ spl22_66 ),
inference(resolution,[],[f560,f238]) ).
fof(f594,plain,
spl22_70,
inference(avatar_split_clause,[],[f193,f592]) ).
fof(f193,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f48]) ).
fof(f48,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f573,plain,
spl22_69,
inference(avatar_split_clause,[],[f192,f571]) ).
fof(f192,plain,
! [X2,X0,X1] :
( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f114]) ).
fof(f114,plain,
! [X0,X1,X2] :
( ( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) )
& ( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f40]) ).
fof(f40,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
<=> relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f569,plain,
spl22_68,
inference(avatar_split_clause,[],[f191,f567]) ).
fof(f191,plain,
! [X2,X0,X1] :
( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f114]) ).
fof(f565,plain,
spl22_67,
inference(avatar_split_clause,[],[f189,f563]) ).
fof(f189,plain,
! [X2,X0,X1] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0,X1,X2] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
=> relation(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f561,plain,
spl22_66,
inference(avatar_split_clause,[],[f186,f559]) ).
fof(f186,plain,
! [X2,X0,X1] :
( sP0(X0,X2,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f113]) ).
fof(f557,plain,
spl22_65,
inference(avatar_split_clause,[],[f165,f555]) ).
fof(f555,plain,
( spl22_65
<=> ! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_65])]) ).
fof(f165,plain,
! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ),
inference(flattening,[],[f77]) ).
fof(f77,plain,
! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0,X1] :
( ( ~ empty(X1)
& ~ empty(X0) )
=> ~ empty(cartesian_product2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_subset_1) ).
fof(f553,plain,
spl22_64,
inference(avatar_split_clause,[],[f164,f551]) ).
fof(f164,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f75]) ).
fof(f75,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f44]) ).
fof(f44,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f531,plain,
spl22_63,
inference(avatar_split_clause,[],[f168,f529]) ).
fof(f168,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f51]) ).
fof(f51,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(f527,plain,
spl22_62,
inference(avatar_split_clause,[],[f167,f525]) ).
fof(f167,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f102,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f45]) ).
fof(f45,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f523,plain,
( spl22_61
| ~ spl22_10
| ~ spl22_34 ),
inference(avatar_split_clause,[],[f411,f380,f265,f520]) ).
fof(f520,plain,
( spl22_61
<=> relation(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_61])]) ).
fof(f411,plain,
( relation(sK13)
| ~ spl22_10
| ~ spl22_34 ),
inference(resolution,[],[f381,f267]) ).
fof(f518,plain,
spl22_60,
inference(avatar_split_clause,[],[f166,f516]) ).
fof(f166,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f102]) ).
fof(f514,plain,
spl22_59,
inference(avatar_split_clause,[],[f155,f512]) ).
fof(f155,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(flattening,[],[f69]) ).
fof(f69,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_dom(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(f510,plain,
spl22_58,
inference(avatar_split_clause,[],[f147,f508]) ).
fof(f147,plain,
! [X0] :
( element(sK5(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f97,plain,
! [X0] :
( ( ~ empty(sK5(X0))
& element(sK5(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f63,f96]) ).
fof(f96,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( ~ empty(sK5(X0))
& element(sK5(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f63,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f504,plain,
( spl22_57
| ~ spl22_13
| ~ spl22_33 ),
inference(avatar_split_clause,[],[f406,f376,f280,f501]) ).
fof(f501,plain,
( spl22_57
<=> function(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_57])]) ).
fof(f406,plain,
( function(sK15)
| ~ spl22_13
| ~ spl22_33 ),
inference(resolution,[],[f377,f282]) ).
fof(f499,plain,
( spl22_56
| ~ spl22_10
| ~ spl22_41
| ~ spl22_48 ),
inference(avatar_split_clause,[],[f467,f463,f420,f265,f497]) ).
fof(f463,plain,
( spl22_48
<=> ! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_48])]) ).
fof(f467,plain,
( ! [X0] :
( ~ subset(X0,sK13)
| sK13 = X0 )
| ~ spl22_10
| ~ spl22_41
| ~ spl22_48 ),
inference(forward_demodulation,[],[f466,f446]) ).
fof(f466,plain,
( ! [X0] :
( sK13 = X0
| ~ subset(X0,empty_set) )
| ~ spl22_10
| ~ spl22_41
| ~ spl22_48 ),
inference(forward_demodulation,[],[f464,f446]) ).
fof(f464,plain,
( ! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set) )
| ~ spl22_48 ),
inference(avatar_component_clause,[],[f463]) ).
fof(f495,plain,
spl22_55,
inference(avatar_split_clause,[],[f178,f493]) ).
fof(f178,plain,
! [X0,X1] : quasi_total(sK11(X0,X1),X0,X1),
inference(cnf_transformation,[],[f110]) ).
fof(f110,plain,
! [X0,X1] :
( quasi_total(sK11(X0,X1),X0,X1)
& function(sK11(X0,X1))
& relation(sK11(X0,X1))
& relation_of2(sK11(X0,X1),X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f26,f109]) ).
fof(f109,plain,
! [X0,X1] :
( ? [X2] :
( quasi_total(X2,X0,X1)
& function(X2)
& relation(X2)
& relation_of2(X2,X0,X1) )
=> ( quasi_total(sK11(X0,X1),X0,X1)
& function(sK11(X0,X1))
& relation(sK11(X0,X1))
& relation_of2(sK11(X0,X1),X0,X1) ) ),
introduced(choice_axiom,[]) ).
fof(f26,axiom,
! [X0,X1] :
? [X2] :
( quasi_total(X2,X0,X1)
& function(X2)
& relation(X2)
& relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_2) ).
fof(f491,plain,
spl22_54,
inference(avatar_split_clause,[],[f175,f489]) ).
fof(f175,plain,
! [X0,X1] : relation_of2(sK11(X0,X1),X0,X1),
inference(cnf_transformation,[],[f110]) ).
fof(f487,plain,
spl22_53,
inference(avatar_split_clause,[],[f172,f485]) ).
fof(f172,plain,
! [X0,X1] : relation_of2(sK10(X0,X1),X0,X1),
inference(cnf_transformation,[],[f108]) ).
fof(f108,plain,
! [X0,X1] :
( function(sK10(X0,X1))
& relation(sK10(X0,X1))
& relation_of2(sK10(X0,X1),X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f32,f107]) ).
fof(f107,plain,
! [X0,X1] :
( ? [X2] :
( function(X2)
& relation(X2)
& relation_of2(X2,X0,X1) )
=> ( function(sK10(X0,X1))
& relation(sK10(X0,X1))
& relation_of2(sK10(X0,X1),X0,X1) ) ),
introduced(choice_axiom,[]) ).
fof(f32,axiom,
! [X0,X1] :
? [X2] :
( function(X2)
& relation(X2)
& relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_partfun1) ).
fof(f483,plain,
spl22_52,
inference(avatar_split_clause,[],[f171,f481]) ).
fof(f171,plain,
! [X0,X1] : relation_of2_as_subset(sK9(X0,X1),X0,X1),
inference(cnf_transformation,[],[f106]) ).
fof(f106,plain,
! [X0,X1] : relation_of2_as_subset(sK9(X0,X1),X0,X1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f17,f105]) ).
fof(f105,plain,
! [X0,X1] :
( ? [X2] : relation_of2_as_subset(X2,X0,X1)
=> relation_of2_as_subset(sK9(X0,X1),X0,X1) ),
introduced(choice_axiom,[]) ).
fof(f17,axiom,
! [X0,X1] :
? [X2] : relation_of2_as_subset(X2,X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_relset_1) ).
fof(f479,plain,
spl22_51,
inference(avatar_split_clause,[],[f170,f477]) ).
fof(f170,plain,
! [X0,X1] : relation_of2(sK8(X0,X1),X0,X1),
inference(cnf_transformation,[],[f104]) ).
fof(f104,plain,
! [X0,X1] : relation_of2(sK8(X0,X1),X0,X1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f15,f103]) ).
fof(f103,plain,
! [X0,X1] :
( ? [X2] : relation_of2(X2,X0,X1)
=> relation_of2(sK8(X0,X1),X0,X1) ),
introduced(choice_axiom,[]) ).
fof(f15,axiom,
! [X0,X1] :
? [X2] : relation_of2(X2,X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_relset_1) ).
fof(f475,plain,
spl22_50,
inference(avatar_split_clause,[],[f163,f473]) ).
fof(f473,plain,
( spl22_50
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_50])]) ).
fof(f163,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f43]) ).
fof(f43,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f471,plain,
spl22_49,
inference(avatar_split_clause,[],[f162,f469]) ).
fof(f162,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f73,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f465,plain,
spl22_48,
inference(avatar_split_clause,[],[f154,f463]) ).
fof(f154,plain,
! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set) ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set) ),
inference(ennf_transformation,[],[f46]) ).
fof(f46,axiom,
! [X0] :
( subset(X0,empty_set)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
fof(f461,plain,
( spl22_47
| ~ spl22_10
| ~ spl22_33 ),
inference(avatar_split_clause,[],[f405,f376,f265,f458]) ).
fof(f458,plain,
( spl22_47
<=> function(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_47])]) ).
fof(f405,plain,
( function(sK13)
| ~ spl22_10
| ~ spl22_33 ),
inference(resolution,[],[f377,f267]) ).
fof(f443,plain,
spl22_46,
inference(avatar_split_clause,[],[f169,f441]) ).
fof(f169,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f50]) ).
fof(f50,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f439,plain,
spl22_45,
inference(avatar_split_clause,[],[f159,f437]) ).
fof(f159,plain,
! [X0] : element(sK7(X0),powerset(X0)),
inference(cnf_transformation,[],[f101]) ).
fof(f101,plain,
! [X0] :
( empty(sK7(X0))
& element(sK7(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f34,f100]) ).
fof(f100,plain,
! [X0] :
( ? [X1] :
( empty(X1)
& element(X1,powerset(X0)) )
=> ( empty(sK7(X0))
& element(sK7(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f34,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f435,plain,
spl22_44,
inference(avatar_split_clause,[],[f153,f433]) ).
fof(f433,plain,
( spl22_44
<=> ! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_44])]) ).
fof(f153,plain,
! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0] :
( ( relation(relation_dom(X0))
& empty(relation_dom(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(f431,plain,
spl22_43,
inference(avatar_split_clause,[],[f152,f429]) ).
fof(f152,plain,
! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f427,plain,
( spl22_42
| ~ spl22_7
| ~ spl22_33 ),
inference(avatar_split_clause,[],[f403,f376,f250,f424]) ).
fof(f424,plain,
( spl22_42
<=> function(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_42])]) ).
fof(f403,plain,
( function(empty_set)
| ~ spl22_7
| ~ spl22_33 ),
inference(resolution,[],[f377,f252]) ).
fof(f422,plain,
spl22_41,
inference(avatar_split_clause,[],[f151,f420]) ).
fof(f151,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f49]) ).
fof(f49,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f418,plain,
spl22_40,
inference(avatar_split_clause,[],[f148,f416]) ).
fof(f416,plain,
( spl22_40
<=> ! [X0] :
( ~ empty(sK5(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_40])]) ).
fof(f148,plain,
! [X0] :
( ~ empty(sK5(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f402,plain,
spl22_39,
inference(avatar_split_clause,[],[f177,f400]) ).
fof(f400,plain,
( spl22_39
<=> ! [X0,X1] : function(sK11(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_39])]) ).
fof(f177,plain,
! [X0,X1] : function(sK11(X0,X1)),
inference(cnf_transformation,[],[f110]) ).
fof(f398,plain,
spl22_38,
inference(avatar_split_clause,[],[f176,f396]) ).
fof(f396,plain,
( spl22_38
<=> ! [X0,X1] : relation(sK11(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_38])]) ).
fof(f176,plain,
! [X0,X1] : relation(sK11(X0,X1)),
inference(cnf_transformation,[],[f110]) ).
fof(f394,plain,
spl22_37,
inference(avatar_split_clause,[],[f174,f392]) ).
fof(f392,plain,
( spl22_37
<=> ! [X0,X1] : function(sK10(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_37])]) ).
fof(f174,plain,
! [X0,X1] : function(sK10(X0,X1)),
inference(cnf_transformation,[],[f108]) ).
fof(f390,plain,
spl22_36,
inference(avatar_split_clause,[],[f173,f388]) ).
fof(f388,plain,
( spl22_36
<=> ! [X0,X1] : relation(sK10(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_36])]) ).
fof(f173,plain,
! [X0,X1] : relation(sK10(X0,X1)),
inference(cnf_transformation,[],[f108]) ).
fof(f386,plain,
spl22_35,
inference(avatar_split_clause,[],[f158,f384]) ).
fof(f158,plain,
! [X0] : element(sK6(X0),X0),
inference(cnf_transformation,[],[f99]) ).
fof(f99,plain,
! [X0] : element(sK6(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f16,f98]) ).
fof(f98,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK6(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f16,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f382,plain,
spl22_34,
inference(avatar_split_clause,[],[f150,f380]) ).
fof(f150,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( empty(X0)
=> relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(f378,plain,
spl22_33,
inference(avatar_split_clause,[],[f149,f376]) ).
fof(f149,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( empty(X0)
=> function(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
fof(f374,plain,
spl22_32,
inference(avatar_split_clause,[],[f161,f372]) ).
fof(f161,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f41]) ).
fof(f41,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f370,plain,
spl22_31,
inference(avatar_split_clause,[],[f160,f368]) ).
fof(f160,plain,
! [X0] : empty(sK7(X0)),
inference(cnf_transformation,[],[f101]) ).
fof(f366,plain,
spl22_30,
inference(avatar_split_clause,[],[f146,f364]) ).
fof(f364,plain,
( spl22_30
<=> ! [X0] : ~ empty(powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_30])]) ).
fof(f146,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f362,plain,
( ~ spl22_1
| ~ spl22_28
| ~ spl22_29 ),
inference(avatar_split_clause,[],[f140,f359,f355,f221]) ).
fof(f221,plain,
( spl22_1
<=> function(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1])]) ).
fof(f140,plain,
( ~ relation_of2_as_subset(sK4,sK1,sK3)
| ~ quasi_total(sK4,sK1,sK3)
| ~ function(sK4) ),
inference(cnf_transformation,[],[f95]) ).
fof(f95,plain,
( ( ~ relation_of2_as_subset(sK4,sK1,sK3)
| ~ quasi_total(sK4,sK1,sK3)
| ~ function(sK4) )
& ( empty_set = sK1
| empty_set != sK2 )
& subset(sK2,sK3)
& relation_of2_as_subset(sK4,sK1,sK2)
& quasi_total(sK4,sK1,sK2)
& function(sK4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4])],[f62,f94]) ).
fof(f94,plain,
( ? [X0,X1,X2,X3] :
( ( ~ relation_of2_as_subset(X3,X0,X2)
| ~ quasi_total(X3,X0,X2)
| ~ function(X3) )
& ( empty_set = X0
| empty_set != X1 )
& subset(X1,X2)
& relation_of2_as_subset(X3,X0,X1)
& quasi_total(X3,X0,X1)
& function(X3) )
=> ( ( ~ relation_of2_as_subset(sK4,sK1,sK3)
| ~ quasi_total(sK4,sK1,sK3)
| ~ function(sK4) )
& ( empty_set = sK1
| empty_set != sK2 )
& subset(sK2,sK3)
& relation_of2_as_subset(sK4,sK1,sK2)
& quasi_total(sK4,sK1,sK2)
& function(sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f62,plain,
? [X0,X1,X2,X3] :
( ( ~ relation_of2_as_subset(X3,X0,X2)
| ~ quasi_total(X3,X0,X2)
| ~ function(X3) )
& ( empty_set = X0
| empty_set != X1 )
& subset(X1,X2)
& relation_of2_as_subset(X3,X0,X1)
& quasi_total(X3,X0,X1)
& function(X3) ),
inference(flattening,[],[f61]) ).
fof(f61,plain,
? [X0,X1,X2,X3] :
( ( ~ relation_of2_as_subset(X3,X0,X2)
| ~ quasi_total(X3,X0,X2)
| ~ function(X3) )
& ( empty_set = X0
| empty_set != X1 )
& subset(X1,X2)
& relation_of2_as_subset(X3,X0,X1)
& quasi_total(X3,X0,X1)
& function(X3) ),
inference(ennf_transformation,[],[f53]) ).
fof(f53,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( relation_of2_as_subset(X3,X0,X1)
& quasi_total(X3,X0,X1)
& function(X3) )
=> ( subset(X1,X2)
=> ( ( relation_of2_as_subset(X3,X0,X2)
& quasi_total(X3,X0,X2)
& function(X3) )
| ( empty_set != X0
& empty_set = X1 ) ) ) ),
inference(negated_conjecture,[],[f52]) ).
fof(f52,conjecture,
! [X0,X1,X2,X3] :
( ( relation_of2_as_subset(X3,X0,X1)
& quasi_total(X3,X0,X1)
& function(X3) )
=> ( subset(X1,X2)
=> ( ( relation_of2_as_subset(X3,X0,X2)
& quasi_total(X3,X0,X2)
& function(X3) )
| ( empty_set != X0
& empty_set = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_funct_2) ).
fof(f353,plain,
spl22_27,
inference(avatar_split_clause,[],[f213,f350]) ).
fof(f350,plain,
( spl22_27
<=> function(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_27])]) ).
fof(f213,plain,
function(sK21),
inference(cnf_transformation,[],[f134]) ).
fof(f134,plain,
( function(sK21)
& empty(sK21)
& relation(sK21) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f31,f133]) ).
fof(f133,plain,
( ? [X0] :
( function(X0)
& empty(X0)
& relation(X0) )
=> ( function(sK21)
& empty(sK21)
& relation(sK21) ) ),
introduced(choice_axiom,[]) ).
fof(f31,axiom,
? [X0] :
( function(X0)
& empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(f348,plain,
spl22_26,
inference(avatar_split_clause,[],[f212,f345]) ).
fof(f212,plain,
empty(sK21),
inference(cnf_transformation,[],[f134]) ).
fof(f343,plain,
spl22_25,
inference(avatar_split_clause,[],[f211,f340]) ).
fof(f340,plain,
( spl22_25
<=> relation(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_25])]) ).
fof(f211,plain,
relation(sK21),
inference(cnf_transformation,[],[f134]) ).
fof(f338,plain,
spl22_24,
inference(avatar_split_clause,[],[f210,f335]) ).
fof(f210,plain,
empty(sK20),
inference(cnf_transformation,[],[f132]) ).
fof(f132,plain,
( empty(sK20)
& function(sK20)
& relation(sK20) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f59,f131]) ).
fof(f131,plain,
( ? [X0] :
( empty(X0)
& function(X0)
& relation(X0) )
=> ( empty(sK20)
& function(sK20)
& relation(sK20) ) ),
introduced(choice_axiom,[]) ).
fof(f59,plain,
? [X0] :
( empty(X0)
& function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f27]) ).
fof(f27,axiom,
? [X0] :
( empty(X0)
& one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_partfun1) ).
fof(f333,plain,
spl22_23,
inference(avatar_split_clause,[],[f209,f330]) ).
fof(f330,plain,
( spl22_23
<=> function(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_23])]) ).
fof(f209,plain,
function(sK20),
inference(cnf_transformation,[],[f132]) ).
fof(f328,plain,
spl22_22,
inference(avatar_split_clause,[],[f208,f325]) ).
fof(f325,plain,
( spl22_22
<=> relation(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_22])]) ).
fof(f208,plain,
relation(sK20),
inference(cnf_transformation,[],[f132]) ).
fof(f323,plain,
spl22_21,
inference(avatar_split_clause,[],[f207,f320]) ).
fof(f320,plain,
( spl22_21
<=> function(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_21])]) ).
fof(f207,plain,
function(sK19),
inference(cnf_transformation,[],[f130]) ).
fof(f130,plain,
( function(sK19)
& relation(sK19) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f58,f129]) ).
fof(f129,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK19)
& relation(sK19) ) ),
introduced(choice_axiom,[]) ).
fof(f58,plain,
? [X0] :
( function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f36]) ).
fof(f36,axiom,
? [X0] :
( one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
fof(f318,plain,
spl22_20,
inference(avatar_split_clause,[],[f206,f315]) ).
fof(f315,plain,
( spl22_20
<=> relation(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_20])]) ).
fof(f206,plain,
relation(sK19),
inference(cnf_transformation,[],[f130]) ).
fof(f313,plain,
spl22_19,
inference(avatar_split_clause,[],[f205,f310]) ).
fof(f310,plain,
( spl22_19
<=> function(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_19])]) ).
fof(f205,plain,
function(sK18),
inference(cnf_transformation,[],[f128]) ).
fof(f128,plain,
( function(sK18)
& relation(sK18) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f25,f127]) ).
fof(f127,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK18)
& relation(sK18) ) ),
introduced(choice_axiom,[]) ).
fof(f25,axiom,
? [X0] :
( function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
fof(f308,plain,
spl22_18,
inference(avatar_split_clause,[],[f204,f305]) ).
fof(f305,plain,
( spl22_18
<=> relation(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_18])]) ).
fof(f204,plain,
relation(sK18),
inference(cnf_transformation,[],[f128]) ).
fof(f303,plain,
spl22_17,
inference(avatar_split_clause,[],[f203,f300]) ).
fof(f300,plain,
( spl22_17
<=> function(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_17])]) ).
fof(f203,plain,
function(sK17),
inference(cnf_transformation,[],[f126]) ).
fof(f126,plain,
( function(sK17)
& relation(sK17) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f55,f125]) ).
fof(f125,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK17)
& relation(sK17) ) ),
introduced(choice_axiom,[]) ).
fof(f55,plain,
? [X0] :
( function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f38]) ).
fof(f38,axiom,
? [X0] :
( function(X0)
& relation_empty_yielding(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_funct_1) ).
fof(f298,plain,
spl22_16,
inference(avatar_split_clause,[],[f202,f295]) ).
fof(f295,plain,
( spl22_16
<=> relation(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_16])]) ).
fof(f202,plain,
relation(sK17),
inference(cnf_transformation,[],[f126]) ).
fof(f293,plain,
spl22_15,
inference(avatar_split_clause,[],[f201,f290]) ).
fof(f290,plain,
( spl22_15
<=> relation(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_15])]) ).
fof(f201,plain,
relation(sK16),
inference(cnf_transformation,[],[f124]) ).
fof(f124,plain,
relation(sK16),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f57,f123]) ).
fof(f123,plain,
( ? [X0] : relation(X0)
=> relation(sK16) ),
introduced(choice_axiom,[]) ).
fof(f57,plain,
? [X0] : relation(X0),
inference(pure_predicate_removal,[],[f37]) ).
fof(f37,axiom,
? [X0] :
( relation_empty_yielding(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
fof(f288,plain,
spl22_14,
inference(avatar_split_clause,[],[f200,f285]) ).
fof(f285,plain,
( spl22_14
<=> relation(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_14])]) ).
fof(f200,plain,
relation(sK15),
inference(cnf_transformation,[],[f122]) ).
fof(f122,plain,
( relation(sK15)
& empty(sK15) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f28,f121]) ).
fof(f121,plain,
( ? [X0] :
( relation(X0)
& empty(X0) )
=> ( relation(sK15)
& empty(sK15) ) ),
introduced(choice_axiom,[]) ).
fof(f28,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f283,plain,
spl22_13,
inference(avatar_split_clause,[],[f199,f280]) ).
fof(f199,plain,
empty(sK15),
inference(cnf_transformation,[],[f122]) ).
fof(f278,plain,
spl22_12,
inference(avatar_split_clause,[],[f198,f275]) ).
fof(f275,plain,
( spl22_12
<=> relation(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_12])]) ).
fof(f198,plain,
relation(sK14),
inference(cnf_transformation,[],[f120]) ).
fof(f120,plain,
( relation(sK14)
& ~ empty(sK14) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f33,f119]) ).
fof(f119,plain,
( ? [X0] :
( relation(X0)
& ~ empty(X0) )
=> ( relation(sK14)
& ~ empty(sK14) ) ),
introduced(choice_axiom,[]) ).
fof(f33,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f273,plain,
~ spl22_11,
inference(avatar_split_clause,[],[f197,f270]) ).
fof(f270,plain,
( spl22_11
<=> empty(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_11])]) ).
fof(f197,plain,
~ empty(sK14),
inference(cnf_transformation,[],[f120]) ).
fof(f268,plain,
spl22_10,
inference(avatar_split_clause,[],[f196,f265]) ).
fof(f196,plain,
empty(sK13),
inference(cnf_transformation,[],[f118]) ).
fof(f118,plain,
empty(sK13),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f30,f117]) ).
fof(f117,plain,
( ? [X0] : empty(X0)
=> empty(sK13) ),
introduced(choice_axiom,[]) ).
fof(f30,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f263,plain,
~ spl22_9,
inference(avatar_split_clause,[],[f195,f260]) ).
fof(f260,plain,
( spl22_9
<=> empty(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_9])]) ).
fof(f195,plain,
~ empty(sK12),
inference(cnf_transformation,[],[f116]) ).
fof(f116,plain,
~ empty(sK12),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f35,f115]) ).
fof(f115,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK12) ),
introduced(choice_axiom,[]) ).
fof(f35,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f258,plain,
spl22_8,
inference(avatar_split_clause,[],[f143,f255]) ).
fof(f255,plain,
( spl22_8
<=> relation(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_8])]) ).
fof(f143,plain,
relation(empty_set),
inference(cnf_transformation,[],[f21]) ).
fof(f21,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f253,plain,
spl22_7,
inference(avatar_split_clause,[],[f141,f250]) ).
fof(f141,plain,
empty(empty_set),
inference(cnf_transformation,[],[f20]) ).
fof(f20,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f248,plain,
( ~ spl22_5
| spl22_6 ),
inference(avatar_split_clause,[],[f219,f245,f241]) ).
fof(f219,plain,
( sK1 = sK2
| empty_set != sK2 ),
inference(inner_rewriting,[],[f139]) ).
fof(f139,plain,
( empty_set = sK1
| empty_set != sK2 ),
inference(cnf_transformation,[],[f95]) ).
fof(f239,plain,
spl22_4,
inference(avatar_split_clause,[],[f137,f236]) ).
fof(f137,plain,
relation_of2_as_subset(sK4,sK1,sK2),
inference(cnf_transformation,[],[f95]) ).
fof(f234,plain,
spl22_3,
inference(avatar_split_clause,[],[f136,f231]) ).
fof(f136,plain,
quasi_total(sK4,sK1,sK2),
inference(cnf_transformation,[],[f95]) ).
fof(f229,plain,
spl22_2,
inference(avatar_split_clause,[],[f138,f226]) ).
fof(f138,plain,
subset(sK2,sK3),
inference(cnf_transformation,[],[f95]) ).
fof(f224,plain,
spl22_1,
inference(avatar_split_clause,[],[f135,f221]) ).
fof(f135,plain,
function(sK4),
inference(cnf_transformation,[],[f95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU291+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n011.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri May 3 11:22:04 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.35 % (19646)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37 % (19652)WARNING: value z3 for option sas not known
% 0.15/0.37 % (19651)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.37 % (19652)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.37 % (19650)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.37 % (19655)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.37 % (19653)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.37 % (19654)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.37 % (19656)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.38 TRYING [1]
% 0.15/0.38 TRYING [2]
% 0.15/0.38 TRYING [3]
% 0.15/0.38 TRYING [1]
% 0.15/0.38 TRYING [2]
% 0.15/0.39 TRYING [4]
% 0.21/0.40 TRYING [3]
% 0.21/0.40 TRYING [5]
% 0.21/0.42 % (19654)First to succeed.
% 0.21/0.43 % (19652)Also succeeded, but the first one will report.
% 0.21/0.44 % (19654)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-19646"
% 0.21/0.44 TRYING [4]
% 0.21/0.44 % (19654)Refutation found. Thanks to Tanya!
% 0.21/0.44 % SZS status Theorem for theBenchmark
% 0.21/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.46 % (19654)------------------------------
% 0.21/0.46 % (19654)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.46 % (19654)Termination reason: Refutation
% 0.21/0.46
% 0.21/0.46 % (19654)Memory used [KB]: 1867
% 0.21/0.46 % (19654)Time elapsed: 0.071 s
% 0.21/0.46 % (19654)Instructions burned: 97 (million)
% 0.21/0.46 % (19646)Success in time 0.089 s
%------------------------------------------------------------------------------