TSTP Solution File: SEU072+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU072+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n018.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 09:26:56 EDT 2024
% Result : Theorem 1.39s 0.58s
% Output : Refutation 1.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 490
% Syntax : Number of formulae : 1628 ( 113 unt; 0 def)
% Number of atoms : 5882 ( 566 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 7554 (3300 ~;3631 |; 134 &)
% ( 449 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 445 ( 443 usr; 432 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 10 con; 0-2 aty)
% Number of variables : 1696 (1648 !; 48 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5282,plain,
$false,
inference(avatar_sat_refutation,[],[f207,f212,f217,f221,f226,f231,f236,f241,f246,f251,f256,f261,f266,f271,f276,f281,f286,f291,f296,f301,f306,f310,f314,f318,f322,f326,f330,f334,f338,f353,f357,f361,f365,f369,f373,f377,f381,f385,f390,f409,f413,f418,f423,f427,f431,f435,f439,f476,f480,f484,f488,f492,f496,f500,f504,f508,f514,f543,f547,f551,f555,f585,f589,f601,f611,f615,f620,f627,f631,f636,f642,f646,f651,f655,f665,f670,f681,f685,f698,f702,f709,f714,f721,f726,f732,f737,f742,f746,f751,f765,f775,f784,f789,f796,f803,f810,f815,f824,f828,f834,f841,f845,f849,f853,f861,f865,f872,f878,f879,f880,f881,f882,f912,f967,f971,f975,f983,f992,f997,f1001,f1034,f1038,f1042,f1046,f1050,f1054,f1057,f1068,f1072,f1076,f1080,f1084,f1088,f1092,f1096,f1155,f1159,f1164,f1168,f1191,f1195,f1205,f1209,f1214,f1218,f1222,f1245,f1249,f1254,f1258,f1262,f1266,f1289,f1300,f1304,f1308,f1312,f1316,f1320,f1349,f1353,f1357,f1361,f1365,f1415,f1419,f1436,f1445,f1454,f1467,f1481,f1494,f1500,f1509,f1515,f1520,f1528,f1532,f1537,f1542,f1595,f1600,f1604,f1608,f1612,f1624,f1628,f1632,f1649,f1653,f1657,f1661,f1665,f1669,f1690,f1766,f1770,f1774,f1778,f1797,f1801,f1805,f1809,f1813,f1862,f1919,f1923,f1927,f1931,f1935,f1939,f1943,f1986,f1990,f1994,f1998,f2002,f2006,f2010,f2034,f2058,f2062,f2066,f2089,f2093,f2097,f2101,f2105,f2109,f2145,f2149,f2153,f2157,f2161,f2165,f2169,f2205,f2209,f2213,f2217,f2221,f2225,f2229,f2234,f2276,f2280,f2284,f2288,f2292,f2348,f2352,f2356,f2386,f2390,f2418,f2422,f2426,f2430,f2487,f2491,f2495,f2499,f2503,f2507,f2511,f2515,f2611,f2615,f2623,f2630,f2634,f2686,f2690,f2694,f2726,f2730,f2734,f2752,f2756,f2760,f2782,f2786,f2790,f2823,f2827,f2831,f2835,f2884,f2891,f2895,f2899,f2941,f2950,f2959,f2985,f2989,f2993,f3007,f3029,f3055,f3081,f3085,f3109,f3138,f3146,f3168,f3179,f3183,f3187,f3191,f3195,f3217,f3238,f3242,f3246,f3279,f3291,f3297,f3301,f3305,f3310,f3345,f3371,f3375,f3380,f3408,f3412,f3416,f3420,f3424,f3459,f3487,f3491,f3495,f3499,f3526,f3530,f3534,f3543,f3567,f3587,f3655,f3659,f3663,f3732,f3736,f3740,f3744,f3748,f3752,f3756,f3760,f3764,f3768,f3772,f3777,f3781,f3785,f3793,f3801,f3805,f4062,f4085,f4098,f4125,f4149,f4154,f4158,f4162,f4166,f4170,f4174,f4307,f4311,f4315,f4319,f4323,f4327,f4331,f4335,f4339,f4344,f4348,f4352,f4356,f4360,f4364,f4368,f4608,f4664,f4677,f4681,f4685,f4689,f4693,f4714,f4718,f4722,f4858,f4862,f4866,f4870,f4874,f4878,f4882,f4886,f4910,f5017,f5021,f5025,f5033,f5037,f5041,f5045,f5049,f5053,f5057,f5061,f5065,f5069,f5074,f5078,f5082,f5264,f5268,f5272,f5276,f5280,f5281]) ).
fof(f5281,plain,
( spl21_71
| ~ spl21_54
| ~ spl21_424 ),
inference(avatar_split_clause,[],[f5211,f5071,f498,f639]) ).
fof(f639,plain,
( spl21_71
<=> sP0(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_71])]) ).
fof(f498,plain,
( spl21_54
<=> ! [X0] :
( sP0(X0)
| sK6(X0) != sK7(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_54])]) ).
fof(f5071,plain,
( spl21_424
<=> sK6(sK4) = sK7(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_424])]) ).
fof(f5211,plain,
( sP0(sK4)
| ~ spl21_54
| ~ spl21_424 ),
inference(trivial_inequality_removal,[],[f5209]) ).
fof(f5209,plain,
( sK6(sK4) != sK6(sK4)
| sP0(sK4)
| ~ spl21_54
| ~ spl21_424 ),
inference(superposition,[],[f499,f5073]) ).
fof(f5073,plain,
( sK6(sK4) = sK7(sK4)
| ~ spl21_424 ),
inference(avatar_component_clause,[],[f5071]) ).
fof(f499,plain,
( ! [X0] :
( sK6(X0) != sK7(X0)
| sP0(X0) )
| ~ spl21_54 ),
inference(avatar_component_clause,[],[f498]) ).
fof(f5280,plain,
( spl21_431
| ~ spl21_139
| ~ spl21_207 ),
inference(avatar_split_clause,[],[f1954,f1925,f1189,f5278]) ).
fof(f5278,plain,
( spl21_431
<=> ! [X0,X1] :
( ~ subset(powerset(X0),X1)
| empty(powerset(X1))
| empty(powerset(X0))
| ~ subset(powerset(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_431])]) ).
fof(f1189,plain,
( spl21_139
<=> ! [X0,X1] :
( empty(powerset(X0))
| in(X1,powerset(X0))
| ~ subset(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_139])]) ).
fof(f1925,plain,
( spl21_207
<=> ! [X0,X1] :
( empty(powerset(X0))
| ~ subset(X1,X0)
| ~ in(powerset(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_207])]) ).
fof(f1954,plain,
( ! [X0,X1] :
( ~ subset(powerset(X0),X1)
| empty(powerset(X1))
| empty(powerset(X0))
| ~ subset(powerset(X1),X0) )
| ~ spl21_139
| ~ spl21_207 ),
inference(resolution,[],[f1926,f1190]) ).
fof(f1190,plain,
( ! [X0,X1] :
( in(X1,powerset(X0))
| empty(powerset(X0))
| ~ subset(X1,X0) )
| ~ spl21_139 ),
inference(avatar_component_clause,[],[f1189]) ).
fof(f1926,plain,
( ! [X0,X1] :
( ~ in(powerset(X0),X1)
| ~ subset(X1,X0)
| empty(powerset(X0)) )
| ~ spl21_207 ),
inference(avatar_component_clause,[],[f1925]) ).
fof(f5276,plain,
( spl21_430
| ~ spl21_63
| ~ spl21_205 ),
inference(avatar_split_clause,[],[f1944,f1917,f587,f5274]) ).
fof(f5274,plain,
( spl21_430
<=> ! [X0,X1] :
( empty(sK11(powerset(powerset(X0))))
| ~ empty(X0)
| ~ in(X1,sK11(sK11(powerset(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_430])]) ).
fof(f587,plain,
( spl21_63
<=> ! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_63])]) ).
fof(f1917,plain,
( spl21_205
<=> ! [X0] :
( element(sK11(sK11(powerset(X0))),X0)
| empty(sK11(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_205])]) ).
fof(f1944,plain,
( ! [X0,X1] :
( empty(sK11(powerset(powerset(X0))))
| ~ empty(X0)
| ~ in(X1,sK11(sK11(powerset(powerset(X0))))) )
| ~ spl21_63
| ~ spl21_205 ),
inference(resolution,[],[f1918,f588]) ).
fof(f588,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X0,X1) )
| ~ spl21_63 ),
inference(avatar_component_clause,[],[f587]) ).
fof(f1918,plain,
( ! [X0] :
( element(sK11(sK11(powerset(X0))),X0)
| empty(sK11(powerset(X0))) )
| ~ spl21_205 ),
inference(avatar_component_clause,[],[f1917]) ).
fof(f5272,plain,
( spl21_429
| ~ spl21_158
| ~ spl21_195 ),
inference(avatar_split_clause,[],[f1782,f1764,f1318,f5270]) ).
fof(f5270,plain,
( spl21_429
<=> ! [X0,X1] :
( ~ empty(X0)
| empty(relation_dom(X1))
| sK8(X1,X0) = apply(X1,sK9(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_429])]) ).
fof(f1318,plain,
( spl21_158
<=> ! [X0,X1] :
( sK8(X0,X1) = apply(X0,sK9(X0,X1))
| sP2(X0,X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_158])]) ).
fof(f1764,plain,
( spl21_195
<=> ! [X0,X1] :
( ~ sP2(X0,X1)
| ~ empty(X1)
| empty(relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_195])]) ).
fof(f1782,plain,
( ! [X0,X1] :
( ~ empty(X0)
| empty(relation_dom(X1))
| sK8(X1,X0) = apply(X1,sK9(X1,X0)) )
| ~ spl21_158
| ~ spl21_195 ),
inference(duplicate_literal_removal,[],[f1780]) ).
fof(f1780,plain,
( ! [X0,X1] :
( ~ empty(X0)
| empty(relation_dom(X1))
| sK8(X1,X0) = apply(X1,sK9(X1,X0))
| ~ empty(X0) )
| ~ spl21_158
| ~ spl21_195 ),
inference(resolution,[],[f1765,f1319]) ).
fof(f1319,plain,
( ! [X0,X1] :
( sP2(X0,X1)
| sK8(X0,X1) = apply(X0,sK9(X0,X1))
| ~ empty(X1) )
| ~ spl21_158 ),
inference(avatar_component_clause,[],[f1318]) ).
fof(f1765,plain,
( ! [X0,X1] :
( ~ sP2(X0,X1)
| ~ empty(X1)
| empty(relation_dom(X0)) )
| ~ spl21_195 ),
inference(avatar_component_clause,[],[f1764]) ).
fof(f5268,plain,
( spl21_428
| ~ spl21_76
| ~ spl21_188 ),
inference(avatar_split_clause,[],[f1683,f1647,f668,f5266]) ).
fof(f5266,plain,
( spl21_428
<=> ! [X0,X1] :
( ~ sP2(X0,sK14)
| in(sK9(X1,relation_dom(X0)),relation_dom(X1))
| sP2(X1,relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_428])]) ).
fof(f668,plain,
( spl21_76
<=> ! [X0,X1] :
( sP2(X0,X1)
| in(sK9(X0,X1),relation_dom(X0))
| in(sK8(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_76])]) ).
fof(f1647,plain,
( spl21_188
<=> ! [X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ sP2(X1,sK14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_188])]) ).
fof(f1683,plain,
( ! [X0,X1] :
( ~ sP2(X0,sK14)
| in(sK9(X1,relation_dom(X0)),relation_dom(X1))
| sP2(X1,relation_dom(X0)) )
| ~ spl21_76
| ~ spl21_188 ),
inference(resolution,[],[f1648,f669]) ).
fof(f669,plain,
( ! [X0,X1] :
( in(sK9(X0,X1),relation_dom(X0))
| in(sK8(X0,X1),X1)
| sP2(X0,X1) )
| ~ spl21_76 ),
inference(avatar_component_clause,[],[f668]) ).
fof(f1648,plain,
( ! [X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ sP2(X1,sK14) )
| ~ spl21_188 ),
inference(avatar_component_clause,[],[f1647]) ).
fof(f5264,plain,
( spl21_427
| ~ spl21_154
| ~ spl21_188 ),
inference(avatar_split_clause,[],[f1680,f1647,f1302,f5262]) ).
fof(f5262,plain,
( spl21_427
<=> ! [X0,X1] :
( ~ sP2(X0,sK14)
| element(sK9(X1,relation_dom(X0)),relation_dom(X1))
| sP2(X1,relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_427])]) ).
fof(f1302,plain,
( spl21_154
<=> ! [X0,X1] :
( in(sK8(X0,X1),X1)
| sP2(X0,X1)
| element(sK9(X0,X1),relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_154])]) ).
fof(f1680,plain,
( ! [X0,X1] :
( ~ sP2(X0,sK14)
| element(sK9(X1,relation_dom(X0)),relation_dom(X1))
| sP2(X1,relation_dom(X0)) )
| ~ spl21_154
| ~ spl21_188 ),
inference(resolution,[],[f1648,f1303]) ).
fof(f1303,plain,
( ! [X0,X1] :
( element(sK9(X0,X1),relation_dom(X0))
| in(sK8(X0,X1),X1)
| sP2(X0,X1) )
| ~ spl21_154 ),
inference(avatar_component_clause,[],[f1302]) ).
fof(f5082,plain,
( spl21_426
| ~ spl21_188
| ~ spl21_250 ),
inference(avatar_split_clause,[],[f2363,f2350,f1647,f5080]) ).
fof(f5080,plain,
( spl21_426
<=> ! [X0,X1] :
( subset(sK8(X0,powerset(X1)),X1)
| sP2(X0,powerset(X1))
| ~ sP2(X0,sK14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_426])]) ).
fof(f2350,plain,
( spl21_250
<=> ! [X0,X1] :
( in(sK9(X0,powerset(X1)),relation_dom(X0))
| sP2(X0,powerset(X1))
| subset(sK8(X0,powerset(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_250])]) ).
fof(f2363,plain,
( ! [X0,X1] :
( subset(sK8(X0,powerset(X1)),X1)
| sP2(X0,powerset(X1))
| ~ sP2(X0,sK14) )
| ~ spl21_188
| ~ spl21_250 ),
inference(resolution,[],[f2351,f1648]) ).
fof(f2351,plain,
( ! [X0,X1] :
( in(sK9(X0,powerset(X1)),relation_dom(X0))
| subset(sK8(X0,powerset(X1)),X1)
| sP2(X0,powerset(X1)) )
| ~ spl21_250 ),
inference(avatar_component_clause,[],[f2350]) ).
fof(f5078,plain,
( spl21_425
| ~ spl21_179
| ~ spl21_235 ),
inference(avatar_split_clause,[],[f2201,f2167,f1539,f5076]) ).
fof(f5076,plain,
( spl21_425
<=> ! [X0] :
( ~ in(sK14,sK9(sK14,X0))
| sP2(sK14,X0)
| element(sK8(sK14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_425])]) ).
fof(f1539,plain,
( spl21_179
<=> sK14 = relation_dom(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_179])]) ).
fof(f2167,plain,
( spl21_235
<=> ! [X0,X1] :
( element(sK8(X0,X1),X1)
| sP2(X0,X1)
| ~ in(relation_dom(X0),sK9(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_235])]) ).
fof(f2201,plain,
( ! [X0] :
( ~ in(sK14,sK9(sK14,X0))
| sP2(sK14,X0)
| element(sK8(sK14,X0),X0) )
| ~ spl21_179
| ~ spl21_235 ),
inference(superposition,[],[f2168,f1541]) ).
fof(f1541,plain,
( sK14 = relation_dom(sK14)
| ~ spl21_179 ),
inference(avatar_component_clause,[],[f1539]) ).
fof(f2168,plain,
( ! [X0,X1] :
( ~ in(relation_dom(X0),sK9(X0,X1))
| sP2(X0,X1)
| element(sK8(X0,X1),X1) )
| ~ spl21_235 ),
inference(avatar_component_clause,[],[f2167]) ).
fof(f5074,plain,
( spl21_424
| ~ spl21_61
| ~ spl21_410 ),
inference(avatar_split_clause,[],[f5026,f4907,f553,f5071]) ).
fof(f553,plain,
( spl21_61
<=> ! [X0,X1] :
( X0 = X1
| ~ subset(singleton(X0),singleton(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_61])]) ).
fof(f4907,plain,
( spl21_410
<=> subset(singleton(sK7(sK4)),singleton(sK6(sK4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_410])]) ).
fof(f5026,plain,
( sK6(sK4) = sK7(sK4)
| ~ spl21_61
| ~ spl21_410 ),
inference(resolution,[],[f4909,f554]) ).
fof(f554,plain,
( ! [X0,X1] :
( ~ subset(singleton(X0),singleton(X1))
| X0 = X1 )
| ~ spl21_61 ),
inference(avatar_component_clause,[],[f553]) ).
fof(f4909,plain,
( subset(singleton(sK7(sK4)),singleton(sK6(sK4)))
| ~ spl21_410 ),
inference(avatar_component_clause,[],[f4907]) ).
fof(f5069,plain,
( spl21_423
| ~ spl21_179
| ~ spl21_233 ),
inference(avatar_split_clause,[],[f2199,f2159,f1539,f5067]) ).
fof(f5067,plain,
( spl21_423
<=> ! [X0] :
( element(sK9(sK14,X0),sK14)
| element(sK8(sK14,X0),X0)
| sP2(sK14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_423])]) ).
fof(f2159,plain,
( spl21_233
<=> ! [X0,X1] :
( element(sK9(X0,X1),relation_dom(X0))
| sP2(X0,X1)
| element(sK8(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_233])]) ).
fof(f2199,plain,
( ! [X0] :
( element(sK9(sK14,X0),sK14)
| element(sK8(sK14,X0),X0)
| sP2(sK14,X0) )
| ~ spl21_179
| ~ spl21_233 ),
inference(superposition,[],[f2160,f1541]) ).
fof(f2160,plain,
( ! [X0,X1] :
( element(sK9(X0,X1),relation_dom(X0))
| element(sK8(X0,X1),X1)
| sP2(X0,X1) )
| ~ spl21_233 ),
inference(avatar_component_clause,[],[f2159]) ).
fof(f5065,plain,
( spl21_422
| ~ spl21_47
| ~ spl21_228 ),
inference(avatar_split_clause,[],[f2137,f2107,f437,f5063]) ).
fof(f5063,plain,
( spl21_422
<=> ! [X0,X1] :
( sP2(X0,X1)
| element(sK8(X0,X1),X1)
| ~ empty(relation_rng(X0))
| ~ sP3(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_422])]) ).
fof(f437,plain,
( spl21_47
<=> ! [X0] :
( sP2(X0,relation_rng(X0))
| ~ sP3(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_47])]) ).
fof(f2107,plain,
( spl21_228
<=> ! [X2,X0,X1] :
( element(sK8(X0,X1),X1)
| sP2(X0,X1)
| ~ sP2(X0,X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_228])]) ).
fof(f2137,plain,
( ! [X0,X1] :
( sP2(X0,X1)
| element(sK8(X0,X1),X1)
| ~ empty(relation_rng(X0))
| ~ sP3(X0) )
| ~ spl21_47
| ~ spl21_228 ),
inference(resolution,[],[f2108,f438]) ).
fof(f438,plain,
( ! [X0] :
( sP2(X0,relation_rng(X0))
| ~ sP3(X0) )
| ~ spl21_47 ),
inference(avatar_component_clause,[],[f437]) ).
fof(f2108,plain,
( ! [X2,X0,X1] :
( ~ sP2(X0,X2)
| sP2(X0,X1)
| element(sK8(X0,X1),X1)
| ~ empty(X2) )
| ~ spl21_228 ),
inference(avatar_component_clause,[],[f2107]) ).
fof(f5061,plain,
( spl21_421
| ~ spl21_47
| ~ spl21_224 ),
inference(avatar_split_clause,[],[f2124,f2091,f437,f5059]) ).
fof(f5059,plain,
( spl21_421
<=> ! [X0,X1] :
( ~ empty(relation_rng(X0))
| in(sK8(X0,X1),X1)
| sP2(X0,X1)
| ~ sP3(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_421])]) ).
fof(f2091,plain,
( spl21_224
<=> ! [X2,X0,X1] :
( ~ sP2(X0,X1)
| ~ empty(X1)
| in(sK8(X0,X2),X2)
| sP2(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_224])]) ).
fof(f2124,plain,
( ! [X0,X1] :
( ~ empty(relation_rng(X0))
| in(sK8(X0,X1),X1)
| sP2(X0,X1)
| ~ sP3(X0) )
| ~ spl21_47
| ~ spl21_224 ),
inference(resolution,[],[f2092,f438]) ).
fof(f2092,plain,
( ! [X2,X0,X1] :
( ~ sP2(X0,X1)
| ~ empty(X1)
| in(sK8(X0,X2),X2)
| sP2(X0,X2) )
| ~ spl21_224 ),
inference(avatar_component_clause,[],[f2091]) ).
fof(f5057,plain,
( spl21_420
| ~ spl21_55
| ~ spl21_213 ),
inference(avatar_split_clause,[],[f2016,f1988,f502,f5055]) ).
fof(f5055,plain,
( spl21_420
<=> ! [X0,X1] :
( ~ empty(relation_dom(X0))
| sP2(X0,powerset(X1))
| subset(sK8(X0,powerset(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_420])]) ).
fof(f502,plain,
( spl21_55
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_55])]) ).
fof(f1988,plain,
( spl21_213
<=> ! [X0,X1] :
( sP2(X0,X1)
| ~ empty(relation_dom(X0))
| element(sK8(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_213])]) ).
fof(f2016,plain,
( ! [X0,X1] :
( ~ empty(relation_dom(X0))
| sP2(X0,powerset(X1))
| subset(sK8(X0,powerset(X1)),X1) )
| ~ spl21_55
| ~ spl21_213 ),
inference(resolution,[],[f1989,f503]) ).
fof(f503,plain,
( ! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) )
| ~ spl21_55 ),
inference(avatar_component_clause,[],[f502]) ).
fof(f1989,plain,
( ! [X0,X1] :
( element(sK8(X0,X1),X1)
| ~ empty(relation_dom(X0))
| sP2(X0,X1) )
| ~ spl21_213 ),
inference(avatar_component_clause,[],[f1988]) ).
fof(f5053,plain,
( spl21_419
| ~ spl21_62
| ~ spl21_210 ),
inference(avatar_split_clause,[],[f1976,f1937,f583,f5051]) ).
fof(f5051,plain,
( spl21_419
<=> ! [X0,X1] :
( ~ empty(relation_dom(X0))
| ~ empty(X1)
| relation_rng(X0) = sK11(powerset(X1))
| ~ sP3(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_419])]) ).
fof(f583,plain,
( spl21_62
<=> ! [X0,X1] :
( relation_rng(X0) = X1
| ~ sP2(X0,X1)
| ~ sP3(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_62])]) ).
fof(f1937,plain,
( spl21_210
<=> ! [X0,X1] :
( sP2(X0,sK11(powerset(X1)))
| ~ empty(relation_dom(X0))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_210])]) ).
fof(f1976,plain,
( ! [X0,X1] :
( ~ empty(relation_dom(X0))
| ~ empty(X1)
| relation_rng(X0) = sK11(powerset(X1))
| ~ sP3(X0) )
| ~ spl21_62
| ~ spl21_210 ),
inference(resolution,[],[f1938,f584]) ).
fof(f584,plain,
( ! [X0,X1] :
( ~ sP2(X0,X1)
| relation_rng(X0) = X1
| ~ sP3(X0) )
| ~ spl21_62 ),
inference(avatar_component_clause,[],[f583]) ).
fof(f1938,plain,
( ! [X0,X1] :
( sP2(X0,sK11(powerset(X1)))
| ~ empty(relation_dom(X0))
| ~ empty(X1) )
| ~ spl21_210 ),
inference(avatar_component_clause,[],[f1937]) ).
fof(f5049,plain,
( spl21_418
| ~ spl21_55
| ~ spl21_206 ),
inference(avatar_split_clause,[],[f1950,f1921,f502,f5047]) ).
fof(f5047,plain,
( spl21_418
<=> ! [X0] :
( empty(powerset(X0))
| empty(sK5(powerset(X0)))
| subset(sK11(sK5(powerset(X0))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_418])]) ).
fof(f1921,plain,
( spl21_206
<=> ! [X0] :
( element(sK11(sK5(X0)),X0)
| empty(X0)
| empty(sK5(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_206])]) ).
fof(f1950,plain,
( ! [X0] :
( empty(powerset(X0))
| empty(sK5(powerset(X0)))
| subset(sK11(sK5(powerset(X0))),X0) )
| ~ spl21_55
| ~ spl21_206 ),
inference(resolution,[],[f1922,f503]) ).
fof(f1922,plain,
( ! [X0] :
( element(sK11(sK5(X0)),X0)
| empty(X0)
| empty(sK5(X0)) )
| ~ spl21_206 ),
inference(avatar_component_clause,[],[f1921]) ).
fof(f5045,plain,
( spl21_417
| ~ spl21_72
| ~ spl21_203 ),
inference(avatar_split_clause,[],[f1914,f1811,f644,f5043]) ).
fof(f5043,plain,
( spl21_417
<=> ! [X2,X0,X1] :
( ~ sP3(X0)
| ~ empty(relation_dom(X0))
| ~ in(X1,relation_dom(X2))
| ~ sP2(X2,relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_417])]) ).
fof(f644,plain,
( spl21_72
<=> ! [X6,X0,X1] :
( in(apply(X0,X6),X1)
| ~ in(X6,relation_dom(X0))
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_72])]) ).
fof(f1811,plain,
( spl21_203
<=> ! [X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ sP3(X1)
| ~ empty(relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_203])]) ).
fof(f1914,plain,
( ! [X2,X0,X1] :
( ~ sP3(X0)
| ~ empty(relation_dom(X0))
| ~ in(X1,relation_dom(X2))
| ~ sP2(X2,relation_rng(X0)) )
| ~ spl21_72
| ~ spl21_203 ),
inference(resolution,[],[f1812,f645]) ).
fof(f645,plain,
( ! [X0,X1,X6] :
( in(apply(X0,X6),X1)
| ~ in(X6,relation_dom(X0))
| ~ sP2(X0,X1) )
| ~ spl21_72 ),
inference(avatar_component_clause,[],[f644]) ).
fof(f1812,plain,
( ! [X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ sP3(X1)
| ~ empty(relation_dom(X1)) )
| ~ spl21_203 ),
inference(avatar_component_clause,[],[f1811]) ).
fof(f5041,plain,
( spl21_416
| ~ spl21_74
| ~ spl21_203 ),
inference(avatar_split_clause,[],[f1907,f1811,f653,f5039]) ).
fof(f5039,plain,
( spl21_416
<=> ! [X0,X1] :
( ~ sP3(X0)
| ~ empty(relation_dom(X0))
| sK14 = relation_inverse_image(X0,singleton(X1))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_416])]) ).
fof(f653,plain,
( spl21_74
<=> ! [X0,X1] :
( relation_inverse_image(X1,singleton(X0)) = sK14
| in(X0,relation_rng(X1))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_74])]) ).
fof(f1907,plain,
( ! [X0,X1] :
( ~ sP3(X0)
| ~ empty(relation_dom(X0))
| sK14 = relation_inverse_image(X0,singleton(X1))
| ~ relation(X0) )
| ~ spl21_74
| ~ spl21_203 ),
inference(resolution,[],[f1812,f654]) ).
fof(f654,plain,
( ! [X0,X1] :
( in(X0,relation_rng(X1))
| relation_inverse_image(X1,singleton(X0)) = sK14
| ~ relation(X1) )
| ~ spl21_74 ),
inference(avatar_component_clause,[],[f653]) ).
fof(f5037,plain,
( spl21_415
| ~ spl21_158
| ~ spl21_193 ),
inference(avatar_split_clause,[],[f1762,f1667,f1318,f5035]) ).
fof(f5035,plain,
( spl21_415
<=> ! [X0,X1] :
( ~ empty(X0)
| sP0(X1)
| sK8(X1,X0) = apply(X1,sK9(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_415])]) ).
fof(f1667,plain,
( spl21_193
<=> ! [X0,X1] :
( ~ sP2(X0,X1)
| ~ empty(X1)
| sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_193])]) ).
fof(f1762,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sP0(X1)
| sK8(X1,X0) = apply(X1,sK9(X1,X0)) )
| ~ spl21_158
| ~ spl21_193 ),
inference(duplicate_literal_removal,[],[f1760]) ).
fof(f1760,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sP0(X1)
| sK8(X1,X0) = apply(X1,sK9(X1,X0))
| ~ empty(X0) )
| ~ spl21_158
| ~ spl21_193 ),
inference(resolution,[],[f1668,f1319]) ).
fof(f1668,plain,
( ! [X0,X1] :
( ~ sP2(X0,X1)
| ~ empty(X1)
| sP0(X0) )
| ~ spl21_193 ),
inference(avatar_component_clause,[],[f1667]) ).
fof(f5033,plain,
( spl21_414
| ~ spl21_156
| ~ spl21_179 ),
inference(avatar_split_clause,[],[f1586,f1539,f1310,f5031]) ).
fof(f5031,plain,
( spl21_414
<=> ! [X0] :
( in(sK9(sK14,X0),sK14)
| element(sK8(sK14,X0),X0)
| sP2(sK14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_414])]) ).
fof(f1310,plain,
( spl21_156
<=> ! [X0,X1] :
( in(sK9(X0,X1),relation_dom(X0))
| sP2(X0,X1)
| element(sK8(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_156])]) ).
fof(f1586,plain,
( ! [X0] :
( in(sK9(sK14,X0),sK14)
| element(sK8(sK14,X0),X0)
| sP2(sK14,X0) )
| ~ spl21_156
| ~ spl21_179 ),
inference(superposition,[],[f1311,f1541]) ).
fof(f1311,plain,
( ! [X0,X1] :
( in(sK9(X0,X1),relation_dom(X0))
| element(sK8(X0,X1),X1)
| sP2(X0,X1) )
| ~ spl21_156 ),
inference(avatar_component_clause,[],[f1310]) ).
fof(f5025,plain,
( spl21_413
| ~ spl21_155
| ~ spl21_179 ),
inference(avatar_split_clause,[],[f1585,f1539,f1306,f5023]) ).
fof(f5023,plain,
( spl21_413
<=> ! [X0] :
( ~ in(sK14,sK9(sK14,X0))
| sP2(sK14,X0)
| in(sK8(sK14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_413])]) ).
fof(f1306,plain,
( spl21_155
<=> ! [X0,X1] :
( in(sK8(X0,X1),X1)
| sP2(X0,X1)
| ~ in(relation_dom(X0),sK9(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_155])]) ).
fof(f1585,plain,
( ! [X0] :
( ~ in(sK14,sK9(sK14,X0))
| sP2(sK14,X0)
| in(sK8(sK14,X0),X0) )
| ~ spl21_155
| ~ spl21_179 ),
inference(superposition,[],[f1307,f1541]) ).
fof(f1307,plain,
( ! [X0,X1] :
( ~ in(relation_dom(X0),sK9(X0,X1))
| sP2(X0,X1)
| in(sK8(X0,X1),X1) )
| ~ spl21_155 ),
inference(avatar_component_clause,[],[f1306]) ).
fof(f5021,plain,
( spl21_412
| ~ spl21_154
| ~ spl21_179 ),
inference(avatar_split_clause,[],[f1584,f1539,f1302,f5019]) ).
fof(f5019,plain,
( spl21_412
<=> ! [X0] :
( element(sK9(sK14,X0),sK14)
| in(sK8(sK14,X0),X0)
| sP2(sK14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_412])]) ).
fof(f1584,plain,
( ! [X0] :
( element(sK9(sK14,X0),sK14)
| in(sK8(sK14,X0),X0)
| sP2(sK14,X0) )
| ~ spl21_154
| ~ spl21_179 ),
inference(superposition,[],[f1303,f1541]) ).
fof(f5017,plain,
( spl21_411
| ~ spl21_76
| ~ spl21_179 ),
inference(avatar_split_clause,[],[f1573,f1539,f668,f5015]) ).
fof(f5015,plain,
( spl21_411
<=> ! [X0] :
( in(sK9(sK14,X0),sK14)
| in(sK8(sK14,X0),X0)
| sP2(sK14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_411])]) ).
fof(f1573,plain,
( ! [X0] :
( in(sK9(sK14,X0),sK14)
| in(sK8(sK14,X0),X0)
| sP2(sK14,X0) )
| ~ spl21_76
| ~ spl21_179 ),
inference(superposition,[],[f669,f1541]) ).
fof(f4910,plain,
( spl21_410
| ~ spl21_4
| ~ spl21_322 ),
inference(avatar_split_clause,[],[f4616,f3342,f219,f4907]) ).
fof(f219,plain,
( spl21_4
<=> ! [X1] : subset(relation_inverse_image(sK4,relation_image(sK4,X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_4])]) ).
fof(f3342,plain,
( spl21_322
<=> singleton(sK7(sK4)) = relation_inverse_image(sK4,relation_image(sK4,singleton(sK6(sK4)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_322])]) ).
fof(f4616,plain,
( subset(singleton(sK7(sK4)),singleton(sK6(sK4)))
| ~ spl21_4
| ~ spl21_322 ),
inference(superposition,[],[f220,f3344]) ).
fof(f3344,plain,
( singleton(sK7(sK4)) = relation_inverse_image(sK4,relation_image(sK4,singleton(sK6(sK4))))
| ~ spl21_322 ),
inference(avatar_component_clause,[],[f3342]) ).
fof(f220,plain,
( ! [X1] : subset(relation_inverse_image(sK4,relation_image(sK4,X1)),X1)
| ~ spl21_4 ),
inference(avatar_component_clause,[],[f219]) ).
fof(f4886,plain,
( spl21_409
| ~ spl21_138
| ~ spl21_236 ),
inference(avatar_split_clause,[],[f2236,f2203,f1166,f4884]) ).
fof(f4884,plain,
( spl21_409
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(X1,sK11(powerset(X0)))
| ~ sP2(X1,X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_409])]) ).
fof(f1166,plain,
( spl21_138
<=> ! [X2,X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ sP2(X1,X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_138])]) ).
fof(f2203,plain,
( spl21_236
<=> ! [X0,X1] :
( ~ empty(X0)
| in(sK9(X1,sK11(powerset(X0))),relation_dom(X1))
| sP2(X1,sK11(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_236])]) ).
fof(f2236,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP2(X1,sK11(powerset(X0)))
| ~ sP2(X1,X2)
| ~ empty(X2) )
| ~ spl21_138
| ~ spl21_236 ),
inference(resolution,[],[f2204,f1167]) ).
fof(f1167,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ sP2(X1,X2)
| ~ empty(X2) )
| ~ spl21_138 ),
inference(avatar_component_clause,[],[f1166]) ).
fof(f2204,plain,
( ! [X0,X1] :
( in(sK9(X1,sK11(powerset(X0))),relation_dom(X1))
| ~ empty(X0)
| sP2(X1,sK11(powerset(X0))) )
| ~ spl21_236 ),
inference(avatar_component_clause,[],[f2203]) ).
fof(f4882,plain,
( spl21_408
| ~ spl21_28
| ~ spl21_223 ),
inference(avatar_split_clause,[],[f2120,f2087,f332,f4880]) ).
fof(f4880,plain,
( spl21_408
<=> ! [X0] :
( element(singleton(X0),powerset(singleton(X0)))
| sK14 = sK11(powerset(singleton(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_408])]) ).
fof(f332,plain,
( spl21_28
<=> ! [X0] : element(sK11(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_28])]) ).
fof(f2087,plain,
( spl21_223
<=> ! [X0] :
( singleton(X0) = sK11(powerset(singleton(X0)))
| sK14 = sK11(powerset(singleton(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_223])]) ).
fof(f2120,plain,
( ! [X0] :
( element(singleton(X0),powerset(singleton(X0)))
| sK14 = sK11(powerset(singleton(X0))) )
| ~ spl21_28
| ~ spl21_223 ),
inference(superposition,[],[f333,f2088]) ).
fof(f2088,plain,
( ! [X0] :
( singleton(X0) = sK11(powerset(singleton(X0)))
| sK14 = sK11(powerset(singleton(X0))) )
| ~ spl21_223 ),
inference(avatar_component_clause,[],[f2087]) ).
fof(f333,plain,
( ! [X0] : element(sK11(X0),X0)
| ~ spl21_28 ),
inference(avatar_component_clause,[],[f332]) ).
fof(f4878,plain,
( spl21_407
| ~ spl21_47
| ~ spl21_220 ),
inference(avatar_split_clause,[],[f2076,f2056,f437,f4876]) ).
fof(f4876,plain,
( spl21_407
<=> ! [X0,X1] :
( ~ empty(relation_dom(X0))
| sP2(X0,relation_dom(X1))
| ~ empty(relation_rng(X1))
| ~ sP3(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_407])]) ).
fof(f2056,plain,
( spl21_220
<=> ! [X2,X0,X1] :
( sP2(X0,relation_dom(X1))
| ~ empty(relation_dom(X0))
| ~ sP2(X1,X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_220])]) ).
fof(f2076,plain,
( ! [X0,X1] :
( ~ empty(relation_dom(X0))
| sP2(X0,relation_dom(X1))
| ~ empty(relation_rng(X1))
| ~ sP3(X1) )
| ~ spl21_47
| ~ spl21_220 ),
inference(resolution,[],[f2057,f438]) ).
fof(f2057,plain,
( ! [X2,X0,X1] :
( ~ sP2(X1,X2)
| ~ empty(relation_dom(X0))
| sP2(X0,relation_dom(X1))
| ~ empty(X2) )
| ~ spl21_220 ),
inference(avatar_component_clause,[],[f2056]) ).
fof(f4874,plain,
( spl21_406
| ~ spl21_36
| ~ spl21_209 ),
inference(avatar_split_clause,[],[f1956,f1933,f375,f4872]) ).
fof(f4872,plain,
( spl21_406
<=> ! [X0,X1] :
( sK14 = relation_inverse_image(relation_dom(X0),singleton(X1))
| ~ empty(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_406])]) ).
fof(f375,plain,
( spl21_36
<=> ! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_36])]) ).
fof(f1933,plain,
( spl21_209
<=> ! [X0,X1] :
( ~ relation(X0)
| sK14 = relation_inverse_image(X0,singleton(X1))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_209])]) ).
fof(f1956,plain,
( ! [X0,X1] :
( sK14 = relation_inverse_image(relation_dom(X0),singleton(X1))
| ~ empty(relation_dom(X0))
| ~ empty(X0) )
| ~ spl21_36
| ~ spl21_209 ),
inference(resolution,[],[f1934,f376]) ).
fof(f376,plain,
( ! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) )
| ~ spl21_36 ),
inference(avatar_component_clause,[],[f375]) ).
fof(f1934,plain,
( ! [X0,X1] :
( ~ relation(X0)
| sK14 = relation_inverse_image(X0,singleton(X1))
| ~ empty(X0) )
| ~ spl21_209 ),
inference(avatar_component_clause,[],[f1933]) ).
fof(f4870,plain,
( spl21_405
| ~ spl21_34
| ~ spl21_209 ),
inference(avatar_split_clause,[],[f1955,f1933,f367,f4868]) ).
fof(f4868,plain,
( spl21_405
<=> ! [X0,X1] :
( sK14 = relation_inverse_image(relation_rng(X0),singleton(X1))
| ~ empty(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_405])]) ).
fof(f367,plain,
( spl21_34
<=> ! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_34])]) ).
fof(f1955,plain,
( ! [X0,X1] :
( sK14 = relation_inverse_image(relation_rng(X0),singleton(X1))
| ~ empty(relation_rng(X0))
| ~ empty(X0) )
| ~ spl21_34
| ~ spl21_209 ),
inference(resolution,[],[f1934,f368]) ).
fof(f368,plain,
( ! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) )
| ~ spl21_34 ),
inference(avatar_component_clause,[],[f367]) ).
fof(f4866,plain,
( spl21_404
| ~ spl21_60
| ~ spl21_205 ),
inference(avatar_split_clause,[],[f1947,f1917,f549,f4864]) ).
fof(f4864,plain,
( spl21_404
<=> ! [X0] :
( empty(sK11(powerset(X0)))
| empty(X0)
| in(sK11(sK11(powerset(X0))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_404])]) ).
fof(f549,plain,
( spl21_60
<=> ! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_60])]) ).
fof(f1947,plain,
( ! [X0] :
( empty(sK11(powerset(X0)))
| empty(X0)
| in(sK11(sK11(powerset(X0))),X0) )
| ~ spl21_60
| ~ spl21_205 ),
inference(resolution,[],[f1918,f550]) ).
fof(f550,plain,
( ! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) )
| ~ spl21_60 ),
inference(avatar_component_clause,[],[f549]) ).
fof(f4862,plain,
( spl21_403
| ~ spl21_55
| ~ spl21_205 ),
inference(avatar_split_clause,[],[f1946,f1917,f502,f4860]) ).
fof(f4860,plain,
( spl21_403
<=> ! [X0] :
( empty(sK11(powerset(powerset(X0))))
| subset(sK11(sK11(powerset(powerset(X0)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_403])]) ).
fof(f1946,plain,
( ! [X0] :
( empty(sK11(powerset(powerset(X0))))
| subset(sK11(sK11(powerset(powerset(X0)))),X0) )
| ~ spl21_55
| ~ spl21_205 ),
inference(resolution,[],[f1918,f503]) ).
fof(f4858,plain,
( spl21_402
| ~ spl21_144
| ~ spl21_203 ),
inference(avatar_split_clause,[],[f1911,f1811,f1216,f4856]) ).
fof(f4856,plain,
( spl21_402
<=> ! [X0,X1] :
( ~ sP3(X0)
| ~ empty(relation_dom(X0))
| sP2(X1,relation_rng(X0))
| ~ empty(relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_402])]) ).
fof(f1216,plain,
( spl21_144
<=> ! [X0,X1] :
( in(sK8(X0,X1),X1)
| sP2(X0,X1)
| ~ empty(relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_144])]) ).
fof(f1911,plain,
( ! [X0,X1] :
( ~ sP3(X0)
| ~ empty(relation_dom(X0))
| sP2(X1,relation_rng(X0))
| ~ empty(relation_dom(X1)) )
| ~ spl21_144
| ~ spl21_203 ),
inference(resolution,[],[f1812,f1217]) ).
fof(f1217,plain,
( ! [X0,X1] :
( in(sK8(X0,X1),X1)
| sP2(X0,X1)
| ~ empty(relation_dom(X0)) )
| ~ spl21_144 ),
inference(avatar_component_clause,[],[f1216]) ).
fof(f4722,plain,
( spl21_401
| ~ spl21_23
| ~ spl21_229 ),
inference(avatar_split_clause,[],[f2170,f2143,f312,f4720]) ).
fof(f4720,plain,
( spl21_401
<=> ! [X0] :
( singleton(X0) = sK5(singleton(X0))
| sK14 = sK5(singleton(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_401])]) ).
fof(f312,plain,
( spl21_23
<=> ! [X0] : ~ empty(singleton(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_23])]) ).
fof(f2143,plain,
( spl21_229
<=> ! [X0] :
( empty(singleton(X0))
| singleton(X0) = sK5(singleton(X0))
| sK14 = sK5(singleton(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_229])]) ).
fof(f2170,plain,
( ! [X0] :
( singleton(X0) = sK5(singleton(X0))
| sK14 = sK5(singleton(X0)) )
| ~ spl21_23
| ~ spl21_229 ),
inference(resolution,[],[f2144,f313]) ).
fof(f313,plain,
( ! [X0] : ~ empty(singleton(X0))
| ~ spl21_23 ),
inference(avatar_component_clause,[],[f312]) ).
fof(f2144,plain,
( ! [X0] :
( empty(singleton(X0))
| singleton(X0) = sK5(singleton(X0))
| sK14 = sK5(singleton(X0)) )
| ~ spl21_229 ),
inference(avatar_component_clause,[],[f2143]) ).
fof(f4718,plain,
( spl21_400
| ~ spl21_186
| ~ spl21_202 ),
inference(avatar_split_clause,[],[f1888,f1807,f1626,f4716]) ).
fof(f4716,plain,
( spl21_400
<=> ! [X0,X1] :
( relation_dom(relation_dom(sK11(powerset(X0)))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_400])]) ).
fof(f1626,plain,
( spl21_186
<=> ! [X0] :
( ~ empty(X0)
| empty(sK11(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_186])]) ).
fof(f1807,plain,
( spl21_202
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_dom(relation_dom(X1)) = X0
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_202])]) ).
fof(f1888,plain,
( ! [X0,X1] :
( relation_dom(relation_dom(sK11(powerset(X0)))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl21_186
| ~ spl21_202 ),
inference(resolution,[],[f1808,f1627]) ).
fof(f1627,plain,
( ! [X0] :
( empty(sK11(powerset(X0)))
| ~ empty(X0) )
| ~ spl21_186 ),
inference(avatar_component_clause,[],[f1626]) ).
fof(f1808,plain,
( ! [X0,X1] :
( ~ empty(X1)
| relation_dom(relation_dom(X1)) = X0
| ~ empty(X0) )
| ~ spl21_202 ),
inference(avatar_component_clause,[],[f1807]) ).
fof(f4714,plain,
( spl21_399
| ~ spl21_186
| ~ spl21_201 ),
inference(avatar_split_clause,[],[f1866,f1803,f1626,f4712]) ).
fof(f4712,plain,
( spl21_399
<=> ! [X0,X1] :
( relation_dom(relation_rng(sK11(powerset(X0)))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_399])]) ).
fof(f1803,plain,
( spl21_201
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_dom(relation_rng(X1)) = X0
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_201])]) ).
fof(f1866,plain,
( ! [X0,X1] :
( relation_dom(relation_rng(sK11(powerset(X0)))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl21_186
| ~ spl21_201 ),
inference(resolution,[],[f1804,f1627]) ).
fof(f1804,plain,
( ! [X0,X1] :
( ~ empty(X1)
| relation_dom(relation_rng(X1)) = X0
| ~ empty(X0) )
| ~ spl21_201 ),
inference(avatar_component_clause,[],[f1803]) ).
fof(f4693,plain,
( spl21_398
| ~ spl21_186
| ~ spl21_200 ),
inference(avatar_split_clause,[],[f1839,f1799,f1626,f4691]) ).
fof(f4691,plain,
( spl21_398
<=> ! [X0,X1] :
( relation_rng(relation_dom(sK11(powerset(X0)))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_398])]) ).
fof(f1799,plain,
( spl21_200
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_rng(relation_dom(X1)) = X0
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_200])]) ).
fof(f1839,plain,
( ! [X0,X1] :
( relation_rng(relation_dom(sK11(powerset(X0)))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl21_186
| ~ spl21_200 ),
inference(resolution,[],[f1800,f1627]) ).
fof(f1800,plain,
( ! [X0,X1] :
( ~ empty(X1)
| relation_rng(relation_dom(X1)) = X0
| ~ empty(X0) )
| ~ spl21_200 ),
inference(avatar_component_clause,[],[f1799]) ).
fof(f4689,plain,
( spl21_397
| ~ spl21_186
| ~ spl21_199 ),
inference(avatar_split_clause,[],[f1817,f1795,f1626,f4687]) ).
fof(f4687,plain,
( spl21_397
<=> ! [X0,X1] :
( relation_rng(relation_rng(sK11(powerset(X0)))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_397])]) ).
fof(f1795,plain,
( spl21_199
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_rng(relation_rng(X1)) = X0
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_199])]) ).
fof(f1817,plain,
( ! [X0,X1] :
( relation_rng(relation_rng(sK11(powerset(X0)))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl21_186
| ~ spl21_199 ),
inference(resolution,[],[f1796,f1627]) ).
fof(f1796,plain,
( ! [X0,X1] :
( ~ empty(X1)
| relation_rng(relation_rng(X1)) = X0
| ~ empty(X0) )
| ~ spl21_199 ),
inference(avatar_component_clause,[],[f1795]) ).
fof(f4685,plain,
( spl21_396
| ~ spl21_72
| ~ spl21_188 ),
inference(avatar_split_clause,[],[f1684,f1647,f644,f4683]) ).
fof(f4683,plain,
( spl21_396
<=> ! [X2,X0,X1] :
( ~ sP2(X0,sK14)
| ~ in(X1,relation_dom(X2))
| ~ sP2(X2,relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_396])]) ).
fof(f1684,plain,
( ! [X2,X0,X1] :
( ~ sP2(X0,sK14)
| ~ in(X1,relation_dom(X2))
| ~ sP2(X2,relation_dom(X0)) )
| ~ spl21_72
| ~ spl21_188 ),
inference(resolution,[],[f1648,f645]) ).
fof(f4681,plain,
( spl21_395
| ~ spl21_76
| ~ spl21_188 ),
inference(avatar_split_clause,[],[f1674,f1647,f668,f4679]) ).
fof(f4679,plain,
( spl21_395
<=> ! [X0,X1] :
( ~ sP2(X0,sK14)
| in(sK8(X0,X1),X1)
| sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_395])]) ).
fof(f1674,plain,
( ! [X0,X1] :
( ~ sP2(X0,sK14)
| in(sK8(X0,X1),X1)
| sP2(X0,X1) )
| ~ spl21_76
| ~ spl21_188 ),
inference(resolution,[],[f1648,f669]) ).
fof(f4677,plain,
( spl21_394
| ~ spl21_156
| ~ spl21_188 ),
inference(avatar_split_clause,[],[f1672,f1647,f1310,f4675]) ).
fof(f4675,plain,
( spl21_394
<=> ! [X0,X1] :
( ~ sP2(X0,sK14)
| element(sK8(X0,X1),X1)
| sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_394])]) ).
fof(f1672,plain,
( ! [X0,X1] :
( ~ sP2(X0,sK14)
| element(sK8(X0,X1),X1)
| sP2(X0,X1) )
| ~ spl21_156
| ~ spl21_188 ),
inference(resolution,[],[f1648,f1311]) ).
fof(f4664,plain,
( spl21_393
| ~ spl21_164
| ~ spl21_169 ),
inference(avatar_split_clause,[],[f1469,f1465,f1413,f4662]) ).
fof(f4662,plain,
( spl21_393
<=> ! [X0,X1] :
( element(sK8(X0,relation_inverse_image(sK4,relation_image(sK4,X1))),X1)
| ~ function(X0)
| ~ relation(X0)
| relation_image(X0,singleton(sK9(X0,relation_inverse_image(sK4,relation_image(sK4,X1))))) = singleton(apply(X0,sK9(X0,relation_inverse_image(sK4,relation_image(sK4,X1)))))
| sP2(X0,relation_inverse_image(sK4,relation_image(sK4,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_393])]) ).
fof(f1413,plain,
( spl21_164
<=> ! [X0,X1] :
( relation_image(X0,singleton(sK9(X0,X1))) = singleton(apply(X0,sK9(X0,X1)))
| ~ function(X0)
| ~ relation(X0)
| in(sK8(X0,X1),X1)
| sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_164])]) ).
fof(f1465,plain,
( spl21_169
<=> ! [X0,X1] :
( ~ in(X0,relation_inverse_image(sK4,relation_image(sK4,X1)))
| element(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_169])]) ).
fof(f1469,plain,
( ! [X0,X1] :
( element(sK8(X0,relation_inverse_image(sK4,relation_image(sK4,X1))),X1)
| ~ function(X0)
| ~ relation(X0)
| relation_image(X0,singleton(sK9(X0,relation_inverse_image(sK4,relation_image(sK4,X1))))) = singleton(apply(X0,sK9(X0,relation_inverse_image(sK4,relation_image(sK4,X1)))))
| sP2(X0,relation_inverse_image(sK4,relation_image(sK4,X1))) )
| ~ spl21_164
| ~ spl21_169 ),
inference(resolution,[],[f1466,f1414]) ).
fof(f1414,plain,
( ! [X0,X1] :
( in(sK8(X0,X1),X1)
| ~ function(X0)
| ~ relation(X0)
| relation_image(X0,singleton(sK9(X0,X1))) = singleton(apply(X0,sK9(X0,X1)))
| sP2(X0,X1) )
| ~ spl21_164 ),
inference(avatar_component_clause,[],[f1413]) ).
fof(f1466,plain,
( ! [X0,X1] :
( ~ in(X0,relation_inverse_image(sK4,relation_image(sK4,X1)))
| element(X0,X1) )
| ~ spl21_169 ),
inference(avatar_component_clause,[],[f1465]) ).
fof(f4608,plain,
( ~ spl21_58
| ~ spl21_47
| spl21_386 ),
inference(avatar_split_clause,[],[f4434,f4341,f437,f540]) ).
fof(f540,plain,
( spl21_58
<=> sP3(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_58])]) ).
fof(f4341,plain,
( spl21_386
<=> sP2(sK4,relation_rng(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_386])]) ).
fof(f4434,plain,
( ~ sP3(sK4)
| ~ spl21_47
| spl21_386 ),
inference(resolution,[],[f4343,f438]) ).
fof(f4343,plain,
( ~ sP2(sK4,relation_rng(sK4))
| spl21_386 ),
inference(avatar_component_clause,[],[f4341]) ).
fof(f4368,plain,
( spl21_392
| ~ spl21_188
| ~ spl21_236 ),
inference(avatar_split_clause,[],[f2235,f2203,f1647,f4366]) ).
fof(f4366,plain,
( spl21_392
<=> ! [X0,X1] :
( ~ empty(X0)
| sP2(X1,sK11(powerset(X0)))
| ~ sP2(X1,sK14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_392])]) ).
fof(f2235,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sP2(X1,sK11(powerset(X0)))
| ~ sP2(X1,sK14) )
| ~ spl21_188
| ~ spl21_236 ),
inference(resolution,[],[f2204,f1648]) ).
fof(f4364,plain,
( spl21_391
| ~ spl21_120
| ~ spl21_218 ),
inference(avatar_split_clause,[],[f2023,f2008,f999,f4362]) ).
fof(f4362,plain,
( spl21_391
<=> ! [X0,X1] :
( ~ sP3(X0)
| ~ sP2(X0,X1)
| ~ empty(X1)
| empty(relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_391])]) ).
fof(f999,plain,
( spl21_120
<=> ! [X0] :
( empty(X0)
| in(sK11(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_120])]) ).
fof(f2008,plain,
( spl21_218
<=> ! [X2,X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ sP3(X1)
| ~ sP2(X1,X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_218])]) ).
fof(f2023,plain,
( ! [X0,X1] :
( ~ sP3(X0)
| ~ sP2(X0,X1)
| ~ empty(X1)
| empty(relation_rng(X0)) )
| ~ spl21_120
| ~ spl21_218 ),
inference(resolution,[],[f2009,f1000]) ).
fof(f1000,plain,
( ! [X0] :
( in(sK11(X0),X0)
| empty(X0) )
| ~ spl21_120 ),
inference(avatar_component_clause,[],[f999]) ).
fof(f2009,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ sP3(X1)
| ~ sP2(X1,X2)
| ~ empty(X2) )
| ~ spl21_218 ),
inference(avatar_component_clause,[],[f2008]) ).
fof(f4360,plain,
( spl21_390
| ~ spl21_47
| ~ spl21_211 ),
inference(avatar_split_clause,[],[f1979,f1941,f437,f4358]) ).
fof(f4358,plain,
( spl21_390
<=> ! [X0,X1] :
( ~ empty(X0)
| sP2(X1,X0)
| ~ empty(relation_rng(X1))
| ~ sP3(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_390])]) ).
fof(f1941,plain,
( spl21_211
<=> ! [X2,X0,X1] :
( sP2(X0,X1)
| ~ empty(X1)
| ~ sP2(X0,X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_211])]) ).
fof(f1979,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sP2(X1,X0)
| ~ empty(relation_rng(X1))
| ~ sP3(X1) )
| ~ spl21_47
| ~ spl21_211 ),
inference(resolution,[],[f1942,f438]) ).
fof(f1942,plain,
( ! [X2,X0,X1] :
( ~ sP2(X0,X2)
| ~ empty(X1)
| sP2(X0,X1)
| ~ empty(X2) )
| ~ spl21_211 ),
inference(avatar_component_clause,[],[f1941]) ).
fof(f4356,plain,
( spl21_389
| ~ spl21_60
| ~ spl21_206 ),
inference(avatar_split_clause,[],[f1952,f1921,f549,f4354]) ).
fof(f4354,plain,
( spl21_389
<=> ! [X0] :
( empty(X0)
| empty(sK5(X0))
| in(sK11(sK5(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_389])]) ).
fof(f1952,plain,
( ! [X0] :
( empty(X0)
| empty(sK5(X0))
| in(sK11(sK5(X0)),X0) )
| ~ spl21_60
| ~ spl21_206 ),
inference(duplicate_literal_removal,[],[f1951]) ).
fof(f1951,plain,
( ! [X0] :
( empty(X0)
| empty(sK5(X0))
| empty(X0)
| in(sK11(sK5(X0)),X0) )
| ~ spl21_60
| ~ spl21_206 ),
inference(resolution,[],[f1922,f550]) ).
fof(f4352,plain,
( spl21_388
| ~ spl21_35
| ~ spl21_202 ),
inference(avatar_split_clause,[],[f1886,f1807,f371,f4350]) ).
fof(f4350,plain,
( spl21_388
<=> ! [X0,X1] :
( relation_dom(relation_dom(relation_dom(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_388])]) ).
fof(f371,plain,
( spl21_35
<=> ! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_35])]) ).
fof(f1886,plain,
( ! [X0,X1] :
( relation_dom(relation_dom(relation_dom(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl21_35
| ~ spl21_202 ),
inference(resolution,[],[f1808,f372]) ).
fof(f372,plain,
( ! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) )
| ~ spl21_35 ),
inference(avatar_component_clause,[],[f371]) ).
fof(f4348,plain,
( spl21_387
| ~ spl21_33
| ~ spl21_202 ),
inference(avatar_split_clause,[],[f1885,f1807,f363,f4346]) ).
fof(f4346,plain,
( spl21_387
<=> ! [X0,X1] :
( relation_dom(relation_dom(relation_rng(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_387])]) ).
fof(f363,plain,
( spl21_33
<=> ! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_33])]) ).
fof(f1885,plain,
( ! [X0,X1] :
( relation_dom(relation_dom(relation_rng(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl21_33
| ~ spl21_202 ),
inference(resolution,[],[f1808,f364]) ).
fof(f364,plain,
( ! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) )
| ~ spl21_33 ),
inference(avatar_component_clause,[],[f363]) ).
fof(f4344,plain,
( ~ spl21_386
| ~ spl21_116
| spl21_371 ),
inference(avatar_split_clause,[],[f4276,f4151,f981,f4341]) ).
fof(f981,plain,
( spl21_116
<=> ! [X0] :
( in(apply(sK4,sK6(sK4)),X0)
| ~ sP2(sK4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_116])]) ).
fof(f4151,plain,
( spl21_371
<=> in(apply(sK4,sK6(sK4)),relation_rng(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_371])]) ).
fof(f4276,plain,
( ~ sP2(sK4,relation_rng(sK4))
| ~ spl21_116
| spl21_371 ),
inference(resolution,[],[f4153,f982]) ).
fof(f982,plain,
( ! [X0] :
( in(apply(sK4,sK6(sK4)),X0)
| ~ sP2(sK4,X0) )
| ~ spl21_116 ),
inference(avatar_component_clause,[],[f981]) ).
fof(f4153,plain,
( ~ in(apply(sK4,sK6(sK4)),relation_rng(sK4))
| spl21_371 ),
inference(avatar_component_clause,[],[f4151]) ).
fof(f4339,plain,
( spl21_385
| ~ spl21_35
| ~ spl21_201 ),
inference(avatar_split_clause,[],[f1864,f1803,f371,f4337]) ).
fof(f4337,plain,
( spl21_385
<=> ! [X0,X1] :
( relation_dom(relation_rng(relation_dom(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_385])]) ).
fof(f1864,plain,
( ! [X0,X1] :
( relation_dom(relation_rng(relation_dom(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl21_35
| ~ spl21_201 ),
inference(resolution,[],[f1804,f372]) ).
fof(f4335,plain,
( spl21_384
| ~ spl21_33
| ~ spl21_201 ),
inference(avatar_split_clause,[],[f1863,f1803,f363,f4333]) ).
fof(f4333,plain,
( spl21_384
<=> ! [X0,X1] :
( relation_dom(relation_rng(relation_rng(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_384])]) ).
fof(f1863,plain,
( ! [X0,X1] :
( relation_dom(relation_rng(relation_rng(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl21_33
| ~ spl21_201 ),
inference(resolution,[],[f1804,f364]) ).
fof(f4331,plain,
( spl21_383
| ~ spl21_35
| ~ spl21_200 ),
inference(avatar_split_clause,[],[f1837,f1799,f371,f4329]) ).
fof(f4329,plain,
( spl21_383
<=> ! [X0,X1] :
( relation_rng(relation_dom(relation_dom(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_383])]) ).
fof(f1837,plain,
( ! [X0,X1] :
( relation_rng(relation_dom(relation_dom(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl21_35
| ~ spl21_200 ),
inference(resolution,[],[f1800,f372]) ).
fof(f4327,plain,
( spl21_382
| ~ spl21_33
| ~ spl21_200 ),
inference(avatar_split_clause,[],[f1836,f1799,f363,f4325]) ).
fof(f4325,plain,
( spl21_382
<=> ! [X0,X1] :
( relation_rng(relation_dom(relation_rng(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_382])]) ).
fof(f1836,plain,
( ! [X0,X1] :
( relation_rng(relation_dom(relation_rng(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl21_33
| ~ spl21_200 ),
inference(resolution,[],[f1800,f364]) ).
fof(f4323,plain,
( spl21_381
| ~ spl21_35
| ~ spl21_199 ),
inference(avatar_split_clause,[],[f1815,f1795,f371,f4321]) ).
fof(f4321,plain,
( spl21_381
<=> ! [X0,X1] :
( relation_rng(relation_rng(relation_dom(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_381])]) ).
fof(f1815,plain,
( ! [X0,X1] :
( relation_rng(relation_rng(relation_dom(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl21_35
| ~ spl21_199 ),
inference(resolution,[],[f1796,f372]) ).
fof(f4319,plain,
( spl21_380
| ~ spl21_33
| ~ spl21_199 ),
inference(avatar_split_clause,[],[f1814,f1795,f363,f4317]) ).
fof(f4317,plain,
( spl21_380
<=> ! [X0,X1] :
( relation_rng(relation_rng(relation_rng(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_380])]) ).
fof(f1814,plain,
( ! [X0,X1] :
( relation_rng(relation_rng(relation_rng(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl21_33
| ~ spl21_199 ),
inference(resolution,[],[f1796,f364]) ).
fof(f4315,plain,
( spl21_379
| ~ spl21_144
| ~ spl21_188 ),
inference(avatar_split_clause,[],[f1681,f1647,f1216,f4313]) ).
fof(f4313,plain,
( spl21_379
<=> ! [X0,X1] :
( ~ sP2(X0,sK14)
| sP2(X1,relation_dom(X0))
| ~ empty(relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_379])]) ).
fof(f1681,plain,
( ! [X0,X1] :
( ~ sP2(X0,sK14)
| sP2(X1,relation_dom(X0))
| ~ empty(relation_dom(X1)) )
| ~ spl21_144
| ~ spl21_188 ),
inference(resolution,[],[f1648,f1217]) ).
fof(f4311,plain,
( spl21_378
| ~ spl21_132
| ~ spl21_186 ),
inference(avatar_split_clause,[],[f1642,f1626,f1086,f4309]) ).
fof(f4309,plain,
( spl21_378
<=> ! [X0,X1] :
( ~ empty(X0)
| ~ empty(X1)
| relation_dom(sK11(powerset(X0))) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_378])]) ).
fof(f1086,plain,
( spl21_132
<=> ! [X0,X1] :
( relation_dom(X1) = X0
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_132])]) ).
fof(f1642,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ empty(X1)
| relation_dom(sK11(powerset(X0))) = X1 )
| ~ spl21_132
| ~ spl21_186 ),
inference(resolution,[],[f1627,f1087]) ).
fof(f1087,plain,
( ! [X0,X1] :
( ~ empty(X1)
| ~ empty(X0)
| relation_dom(X1) = X0 )
| ~ spl21_132 ),
inference(avatar_component_clause,[],[f1086]) ).
fof(f4307,plain,
( spl21_377
| ~ spl21_131
| ~ spl21_186 ),
inference(avatar_split_clause,[],[f1641,f1626,f1082,f4305]) ).
fof(f4305,plain,
( spl21_377
<=> ! [X0,X1] :
( ~ empty(X0)
| ~ empty(X1)
| relation_rng(sK11(powerset(X0))) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_377])]) ).
fof(f1082,plain,
( spl21_131
<=> ! [X0,X1] :
( relation_rng(X1) = X0
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_131])]) ).
fof(f1641,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ empty(X1)
| relation_rng(sK11(powerset(X0))) = X1 )
| ~ spl21_131
| ~ spl21_186 ),
inference(resolution,[],[f1627,f1083]) ).
fof(f1083,plain,
( ! [X0,X1] :
( ~ empty(X1)
| ~ empty(X0)
| relation_rng(X1) = X0 )
| ~ spl21_131 ),
inference(avatar_component_clause,[],[f1082]) ).
fof(f4174,plain,
( spl21_376
| ~ spl21_186
| ~ spl21_192 ),
inference(avatar_split_clause,[],[f1745,f1663,f1626,f4172]) ).
fof(f4172,plain,
( spl21_376
<=> ! [X0] :
( sK14 = relation_dom(relation_dom(sK11(powerset(X0))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_376])]) ).
fof(f1663,plain,
( spl21_192
<=> ! [X0] :
( sK14 = relation_dom(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_192])]) ).
fof(f1745,plain,
( ! [X0] :
( sK14 = relation_dom(relation_dom(sK11(powerset(X0))))
| ~ empty(X0) )
| ~ spl21_186
| ~ spl21_192 ),
inference(resolution,[],[f1664,f1627]) ).
fof(f1664,plain,
( ! [X0] :
( ~ empty(X0)
| sK14 = relation_dom(relation_dom(X0)) )
| ~ spl21_192 ),
inference(avatar_component_clause,[],[f1663]) ).
fof(f4170,plain,
( spl21_375
| ~ spl21_186
| ~ spl21_191 ),
inference(avatar_split_clause,[],[f1728,f1659,f1626,f4168]) ).
fof(f4168,plain,
( spl21_375
<=> ! [X0] :
( sK14 = relation_dom(relation_rng(sK11(powerset(X0))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_375])]) ).
fof(f1659,plain,
( spl21_191
<=> ! [X0] :
( sK14 = relation_dom(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_191])]) ).
fof(f1728,plain,
( ! [X0] :
( sK14 = relation_dom(relation_rng(sK11(powerset(X0))))
| ~ empty(X0) )
| ~ spl21_186
| ~ spl21_191 ),
inference(resolution,[],[f1660,f1627]) ).
fof(f1660,plain,
( ! [X0] :
( ~ empty(X0)
| sK14 = relation_dom(relation_rng(X0)) )
| ~ spl21_191 ),
inference(avatar_component_clause,[],[f1659]) ).
fof(f4166,plain,
( spl21_374
| ~ spl21_186
| ~ spl21_190 ),
inference(avatar_split_clause,[],[f1711,f1655,f1626,f4164]) ).
fof(f4164,plain,
( spl21_374
<=> ! [X0] :
( sK14 = relation_rng(relation_dom(sK11(powerset(X0))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_374])]) ).
fof(f1655,plain,
( spl21_190
<=> ! [X0] :
( sK14 = relation_rng(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_190])]) ).
fof(f1711,plain,
( ! [X0] :
( sK14 = relation_rng(relation_dom(sK11(powerset(X0))))
| ~ empty(X0) )
| ~ spl21_186
| ~ spl21_190 ),
inference(resolution,[],[f1656,f1627]) ).
fof(f1656,plain,
( ! [X0] :
( ~ empty(X0)
| sK14 = relation_rng(relation_dom(X0)) )
| ~ spl21_190 ),
inference(avatar_component_clause,[],[f1655]) ).
fof(f4162,plain,
( spl21_373
| ~ spl21_186
| ~ spl21_189 ),
inference(avatar_split_clause,[],[f1694,f1651,f1626,f4160]) ).
fof(f4160,plain,
( spl21_373
<=> ! [X0] :
( sK14 = relation_rng(relation_rng(sK11(powerset(X0))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_373])]) ).
fof(f1651,plain,
( spl21_189
<=> ! [X0] :
( sK14 = relation_rng(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_189])]) ).
fof(f1694,plain,
( ! [X0] :
( sK14 = relation_rng(relation_rng(sK11(powerset(X0))))
| ~ empty(X0) )
| ~ spl21_186
| ~ spl21_189 ),
inference(resolution,[],[f1652,f1627]) ).
fof(f1652,plain,
( ! [X0] :
( ~ empty(X0)
| sK14 = relation_rng(relation_rng(X0)) )
| ~ spl21_189 ),
inference(avatar_component_clause,[],[f1651]) ).
fof(f4158,plain,
( spl21_372
| ~ spl21_146
| ~ spl21_188 ),
inference(avatar_split_clause,[],[f1676,f1647,f1243,f4156]) ).
fof(f4156,plain,
( spl21_372
<=> ! [X0,X1] :
( ~ sP2(X0,sK14)
| ~ in(X1,relation_rng(X0))
| ~ sP3(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_372])]) ).
fof(f1243,plain,
( spl21_146
<=> ! [X0,X1] :
( ~ in(X0,relation_rng(X1))
| in(sK10(X1,X0),relation_dom(X1))
| ~ sP3(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_146])]) ).
fof(f1676,plain,
( ! [X0,X1] :
( ~ sP2(X0,sK14)
| ~ in(X1,relation_rng(X0))
| ~ sP3(X0) )
| ~ spl21_146
| ~ spl21_188 ),
inference(resolution,[],[f1648,f1244]) ).
fof(f1244,plain,
( ! [X0,X1] :
( in(sK10(X1,X0),relation_dom(X1))
| ~ in(X0,relation_rng(X1))
| ~ sP3(X1) )
| ~ spl21_146 ),
inference(avatar_component_clause,[],[f1243]) ).
fof(f4154,plain,
( ~ spl21_1
| ~ spl21_371
| ~ spl21_316
| ~ spl21_321 ),
inference(avatar_split_clause,[],[f3365,f3338,f3289,f4151,f204]) ).
fof(f204,plain,
( spl21_1
<=> relation(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_1])]) ).
fof(f3289,plain,
( spl21_316
<=> ! [X0] :
( sK14 != relation_inverse_image(X0,relation_image(sK4,singleton(sK6(sK4))))
| ~ in(apply(sK4,sK6(sK4)),relation_rng(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_316])]) ).
fof(f3338,plain,
( spl21_321
<=> sK14 = relation_inverse_image(sK4,relation_image(sK4,singleton(sK6(sK4)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_321])]) ).
fof(f3365,plain,
( ~ in(apply(sK4,sK6(sK4)),relation_rng(sK4))
| ~ relation(sK4)
| ~ spl21_316
| ~ spl21_321 ),
inference(trivial_inequality_removal,[],[f3364]) ).
fof(f3364,plain,
( sK14 != sK14
| ~ in(apply(sK4,sK6(sK4)),relation_rng(sK4))
| ~ relation(sK4)
| ~ spl21_316
| ~ spl21_321 ),
inference(superposition,[],[f3290,f3340]) ).
fof(f3340,plain,
( sK14 = relation_inverse_image(sK4,relation_image(sK4,singleton(sK6(sK4))))
| ~ spl21_321 ),
inference(avatar_component_clause,[],[f3338]) ).
fof(f3290,plain,
( ! [X0] :
( sK14 != relation_inverse_image(X0,relation_image(sK4,singleton(sK6(sK4))))
| ~ in(apply(sK4,sK6(sK4)),relation_rng(X0))
| ~ relation(X0) )
| ~ spl21_316 ),
inference(avatar_component_clause,[],[f3289]) ).
fof(f4149,plain,
( spl21_370
| ~ spl21_57
| ~ spl21_186 ),
inference(avatar_split_clause,[],[f1637,f1626,f512,f4147]) ).
fof(f4147,plain,
( spl21_370
<=> ! [X0,X1] :
( ~ empty(X0)
| sK11(powerset(X0)) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_370])]) ).
fof(f512,plain,
( spl21_57
<=> ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_57])]) ).
fof(f1637,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK11(powerset(X0)) = X1
| ~ empty(X1) )
| ~ spl21_57
| ~ spl21_186 ),
inference(resolution,[],[f1627,f513]) ).
fof(f513,plain,
( ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) )
| ~ spl21_57 ),
inference(avatar_component_clause,[],[f512]) ).
fof(f4125,plain,
( spl21_369
| ~ spl21_58
| ~ spl21_296 ),
inference(avatar_split_clause,[],[f2999,f2991,f540,f4123]) ).
fof(f4123,plain,
( spl21_369
<=> ! [X0] :
( ~ relation(X0)
| sK8(sK4,relation_dom(X0)) = apply(sK4,sK9(sK4,relation_dom(X0)))
| relation_image(X0,singleton(sK8(sK4,relation_dom(X0)))) = singleton(apply(X0,sK8(sK4,relation_dom(X0))))
| relation_dom(X0) = relation_rng(sK4)
| ~ function(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_369])]) ).
fof(f2991,plain,
( spl21_296
<=> ! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| sK8(X1,relation_dom(X0)) = apply(X1,sK9(X1,relation_dom(X0)))
| relation_image(X0,singleton(sK8(X1,relation_dom(X0)))) = singleton(apply(X0,sK8(X1,relation_dom(X0))))
| relation_dom(X0) = relation_rng(X1)
| ~ sP3(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_296])]) ).
fof(f2999,plain,
( ! [X0] :
( ~ relation(X0)
| sK8(sK4,relation_dom(X0)) = apply(sK4,sK9(sK4,relation_dom(X0)))
| relation_image(X0,singleton(sK8(sK4,relation_dom(X0)))) = singleton(apply(X0,sK8(sK4,relation_dom(X0))))
| relation_dom(X0) = relation_rng(sK4)
| ~ function(X0) )
| ~ spl21_58
| ~ spl21_296 ),
inference(resolution,[],[f2992,f542]) ).
fof(f542,plain,
( sP3(sK4)
| ~ spl21_58 ),
inference(avatar_component_clause,[],[f540]) ).
fof(f2992,plain,
( ! [X0,X1] :
( ~ sP3(X1)
| ~ relation(X0)
| sK8(X1,relation_dom(X0)) = apply(X1,sK9(X1,relation_dom(X0)))
| relation_image(X0,singleton(sK8(X1,relation_dom(X0)))) = singleton(apply(X0,sK8(X1,relation_dom(X0))))
| relation_dom(X0) = relation_rng(X1)
| ~ function(X0) )
| ~ spl21_296 ),
inference(avatar_component_clause,[],[f2991]) ).
fof(f4098,plain,
( spl21_368
| ~ spl21_164
| ~ spl21_168 ),
inference(avatar_split_clause,[],[f1456,f1452,f1413,f4096]) ).
fof(f4096,plain,
( spl21_368
<=> ! [X0,X1] :
( ~ empty(X0)
| ~ function(X1)
| ~ relation(X1)
| relation_image(X1,singleton(sK9(X1,relation_inverse_image(sK4,relation_image(sK4,X0))))) = singleton(apply(X1,sK9(X1,relation_inverse_image(sK4,relation_image(sK4,X0)))))
| sP2(X1,relation_inverse_image(sK4,relation_image(sK4,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_368])]) ).
fof(f1452,plain,
( spl21_168
<=> ! [X0,X1] :
( ~ in(X0,relation_inverse_image(sK4,relation_image(sK4,X1)))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_168])]) ).
fof(f1456,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ function(X1)
| ~ relation(X1)
| relation_image(X1,singleton(sK9(X1,relation_inverse_image(sK4,relation_image(sK4,X0))))) = singleton(apply(X1,sK9(X1,relation_inverse_image(sK4,relation_image(sK4,X0)))))
| sP2(X1,relation_inverse_image(sK4,relation_image(sK4,X0))) )
| ~ spl21_164
| ~ spl21_168 ),
inference(resolution,[],[f1453,f1414]) ).
fof(f1453,plain,
( ! [X0,X1] :
( ~ in(X0,relation_inverse_image(sK4,relation_image(sK4,X1)))
| ~ empty(X1) )
| ~ spl21_168 ),
inference(avatar_component_clause,[],[f1452]) ).
fof(f4085,plain,
( spl21_367
| ~ spl21_77
| ~ spl21_169 ),
inference(avatar_split_clause,[],[f1472,f1465,f679,f4083]) ).
fof(f4083,plain,
( spl21_367
<=> ! [X0,X1] :
( element(sK8(X0,relation_inverse_image(sK4,relation_image(sK4,X1))),X1)
| apply(X0,sK9(X0,relation_inverse_image(sK4,relation_image(sK4,X1)))) = sK8(X0,relation_inverse_image(sK4,relation_image(sK4,X1)))
| sP2(X0,relation_inverse_image(sK4,relation_image(sK4,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_367])]) ).
fof(f679,plain,
( spl21_77
<=> ! [X0,X1] :
( sP2(X0,X1)
| sK8(X0,X1) = apply(X0,sK9(X0,X1))
| in(sK8(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_77])]) ).
fof(f1472,plain,
( ! [X0,X1] :
( element(sK8(X0,relation_inverse_image(sK4,relation_image(sK4,X1))),X1)
| apply(X0,sK9(X0,relation_inverse_image(sK4,relation_image(sK4,X1)))) = sK8(X0,relation_inverse_image(sK4,relation_image(sK4,X1)))
| sP2(X0,relation_inverse_image(sK4,relation_image(sK4,X1))) )
| ~ spl21_77
| ~ spl21_169 ),
inference(resolution,[],[f1466,f680]) ).
fof(f680,plain,
( ! [X0,X1] :
( in(sK8(X0,X1),X1)
| sK8(X0,X1) = apply(X0,sK9(X0,X1))
| sP2(X0,X1) )
| ~ spl21_77 ),
inference(avatar_component_clause,[],[f679]) ).
fof(f4062,plain,
( spl21_204
| ~ spl21_8
| ~ spl21_31
| ~ spl21_342 ),
inference(avatar_split_clause,[],[f3568,f3560,f355,f238,f1859]) ).
fof(f1859,plain,
( spl21_204
<=> empty(relation_image(sK4,singleton(sK6(sK4)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_204])]) ).
fof(f238,plain,
( spl21_8
<=> empty(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_8])]) ).
fof(f355,plain,
( spl21_31
<=> ! [X0] :
( ~ empty(sK5(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_31])]) ).
fof(f3560,plain,
( spl21_342
<=> sK14 = sK5(relation_image(sK4,singleton(sK6(sK4)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_342])]) ).
fof(f3568,plain,
( ~ empty(sK14)
| empty(relation_image(sK4,singleton(sK6(sK4))))
| ~ spl21_31
| ~ spl21_342 ),
inference(superposition,[],[f356,f3562]) ).
fof(f3562,plain,
( sK14 = sK5(relation_image(sK4,singleton(sK6(sK4))))
| ~ spl21_342 ),
inference(avatar_component_clause,[],[f3560]) ).
fof(f356,plain,
( ! [X0] :
( ~ empty(sK5(X0))
| empty(X0) )
| ~ spl21_31 ),
inference(avatar_component_clause,[],[f355]) ).
fof(f3805,plain,
( spl21_366
| ~ spl21_8
| ~ spl21_6
| ~ spl21_85
| ~ spl21_209 ),
inference(avatar_split_clause,[],[f1967,f1933,f729,f228,f238,f3803]) ).
fof(f3803,plain,
( spl21_366
<=> ! [X0] : sK14 = relation_inverse_image(sK14,singleton(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_366])]) ).
fof(f228,plain,
( spl21_6
<=> relation(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_6])]) ).
fof(f729,plain,
( spl21_85
<=> empty_set = sK14 ),
introduced(avatar_definition,[new_symbols(naming,[spl21_85])]) ).
fof(f1967,plain,
( ! [X0] :
( ~ empty(sK14)
| sK14 = relation_inverse_image(sK14,singleton(X0)) )
| ~ spl21_6
| ~ spl21_85
| ~ spl21_209 ),
inference(forward_demodulation,[],[f1966,f731]) ).
fof(f731,plain,
( empty_set = sK14
| ~ spl21_85 ),
inference(avatar_component_clause,[],[f729]) ).
fof(f1966,plain,
( ! [X0] :
( sK14 = relation_inverse_image(sK14,singleton(X0))
| ~ empty(empty_set) )
| ~ spl21_6
| ~ spl21_85
| ~ spl21_209 ),
inference(forward_demodulation,[],[f1957,f731]) ).
fof(f1957,plain,
( ! [X0] :
( sK14 = relation_inverse_image(empty_set,singleton(X0))
| ~ empty(empty_set) )
| ~ spl21_6
| ~ spl21_209 ),
inference(resolution,[],[f1934,f230]) ).
fof(f230,plain,
( relation(empty_set)
| ~ spl21_6 ),
inference(avatar_component_clause,[],[f228]) ).
fof(f3801,plain,
( ~ spl21_364
| spl21_365
| ~ spl21_14
| ~ spl21_209 ),
inference(avatar_split_clause,[],[f1963,f1933,f268,f3799,f3795]) ).
fof(f3795,plain,
( spl21_364
<=> empty(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_364])]) ).
fof(f3799,plain,
( spl21_365
<=> ! [X0] : sK14 = relation_inverse_image(sK18,singleton(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_365])]) ).
fof(f268,plain,
( spl21_14
<=> relation(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_14])]) ).
fof(f1963,plain,
( ! [X0] :
( sK14 = relation_inverse_image(sK18,singleton(X0))
| ~ empty(sK18) )
| ~ spl21_14
| ~ spl21_209 ),
inference(resolution,[],[f1934,f270]) ).
fof(f270,plain,
( relation(sK18)
| ~ spl21_14 ),
inference(avatar_component_clause,[],[f268]) ).
fof(f3793,plain,
( ~ spl21_362
| spl21_363
| ~ spl21_11
| ~ spl21_209 ),
inference(avatar_split_clause,[],[f1961,f1933,f253,f3791,f3787]) ).
fof(f3787,plain,
( spl21_362
<=> empty(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_362])]) ).
fof(f3791,plain,
( spl21_363
<=> ! [X0] : sK14 = relation_inverse_image(sK16,singleton(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_363])]) ).
fof(f253,plain,
( spl21_11
<=> relation(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_11])]) ).
fof(f1961,plain,
( ! [X0] :
( sK14 = relation_inverse_image(sK16,singleton(X0))
| ~ empty(sK16) )
| ~ spl21_11
| ~ spl21_209 ),
inference(resolution,[],[f1934,f255]) ).
fof(f255,plain,
( relation(sK16)
| ~ spl21_11 ),
inference(avatar_component_clause,[],[f253]) ).
fof(f3785,plain,
( spl21_361
| ~ spl21_120
| ~ spl21_203 ),
inference(avatar_split_clause,[],[f1908,f1811,f999,f3783]) ).
fof(f3783,plain,
( spl21_361
<=> ! [X0] :
( ~ sP3(X0)
| ~ empty(relation_dom(X0))
| empty(relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_361])]) ).
fof(f1908,plain,
( ! [X0] :
( ~ sP3(X0)
| ~ empty(relation_dom(X0))
| empty(relation_rng(X0)) )
| ~ spl21_120
| ~ spl21_203 ),
inference(resolution,[],[f1812,f1000]) ).
fof(f3781,plain,
( spl21_360
| ~ spl21_47
| ~ spl21_195 ),
inference(avatar_split_clause,[],[f1779,f1764,f437,f3779]) ).
fof(f3779,plain,
( spl21_360
<=> ! [X0] :
( ~ empty(relation_rng(X0))
| empty(relation_dom(X0))
| ~ sP3(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_360])]) ).
fof(f1779,plain,
( ! [X0] :
( ~ empty(relation_rng(X0))
| empty(relation_dom(X0))
| ~ sP3(X0) )
| ~ spl21_47
| ~ spl21_195 ),
inference(resolution,[],[f1765,f438]) ).
fof(f3777,plain,
( ~ spl21_1
| ~ spl21_359
| ~ spl21_73
| ~ spl21_320 ),
inference(avatar_split_clause,[],[f3515,f3307,f649,f3774,f204]) ).
fof(f3774,plain,
( spl21_359
<=> in(relation_rng(sK4),relation_rng(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_359])]) ).
fof(f649,plain,
( spl21_73
<=> ! [X0,X1] :
( relation_inverse_image(X1,singleton(X0)) != sK14
| ~ in(X0,relation_rng(X1))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_73])]) ).
fof(f3307,plain,
( spl21_320
<=> sK14 = relation_inverse_image(sK4,singleton(relation_rng(sK4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_320])]) ).
fof(f3515,plain,
( ~ in(relation_rng(sK4),relation_rng(sK4))
| ~ relation(sK4)
| ~ spl21_73
| ~ spl21_320 ),
inference(trivial_inequality_removal,[],[f3514]) ).
fof(f3514,plain,
( sK14 != sK14
| ~ in(relation_rng(sK4),relation_rng(sK4))
| ~ relation(sK4)
| ~ spl21_73
| ~ spl21_320 ),
inference(superposition,[],[f650,f3309]) ).
fof(f3309,plain,
( sK14 = relation_inverse_image(sK4,singleton(relation_rng(sK4)))
| ~ spl21_320 ),
inference(avatar_component_clause,[],[f3307]) ).
fof(f650,plain,
( ! [X0,X1] :
( relation_inverse_image(X1,singleton(X0)) != sK14
| ~ in(X0,relation_rng(X1))
| ~ relation(X1) )
| ~ spl21_73 ),
inference(avatar_component_clause,[],[f649]) ).
fof(f3772,plain,
( spl21_358
| ~ spl21_35
| ~ spl21_192 ),
inference(avatar_split_clause,[],[f1743,f1663,f371,f3770]) ).
fof(f3770,plain,
( spl21_358
<=> ! [X0] :
( sK14 = relation_dom(relation_dom(relation_dom(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_358])]) ).
fof(f1743,plain,
( ! [X0] :
( sK14 = relation_dom(relation_dom(relation_dom(X0)))
| ~ empty(X0) )
| ~ spl21_35
| ~ spl21_192 ),
inference(resolution,[],[f1664,f372]) ).
fof(f3768,plain,
( spl21_357
| ~ spl21_33
| ~ spl21_192 ),
inference(avatar_split_clause,[],[f1742,f1663,f363,f3766]) ).
fof(f3766,plain,
( spl21_357
<=> ! [X0] :
( sK14 = relation_dom(relation_dom(relation_rng(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_357])]) ).
fof(f1742,plain,
( ! [X0] :
( sK14 = relation_dom(relation_dom(relation_rng(X0)))
| ~ empty(X0) )
| ~ spl21_33
| ~ spl21_192 ),
inference(resolution,[],[f1664,f364]) ).
fof(f3764,plain,
( spl21_356
| ~ spl21_35
| ~ spl21_191 ),
inference(avatar_split_clause,[],[f1726,f1659,f371,f3762]) ).
fof(f3762,plain,
( spl21_356
<=> ! [X0] :
( sK14 = relation_dom(relation_rng(relation_dom(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_356])]) ).
fof(f1726,plain,
( ! [X0] :
( sK14 = relation_dom(relation_rng(relation_dom(X0)))
| ~ empty(X0) )
| ~ spl21_35
| ~ spl21_191 ),
inference(resolution,[],[f1660,f372]) ).
fof(f3760,plain,
( spl21_355
| ~ spl21_33
| ~ spl21_191 ),
inference(avatar_split_clause,[],[f1725,f1659,f363,f3758]) ).
fof(f3758,plain,
( spl21_355
<=> ! [X0] :
( sK14 = relation_dom(relation_rng(relation_rng(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_355])]) ).
fof(f1725,plain,
( ! [X0] :
( sK14 = relation_dom(relation_rng(relation_rng(X0)))
| ~ empty(X0) )
| ~ spl21_33
| ~ spl21_191 ),
inference(resolution,[],[f1660,f364]) ).
fof(f3756,plain,
( spl21_354
| ~ spl21_35
| ~ spl21_190 ),
inference(avatar_split_clause,[],[f1709,f1655,f371,f3754]) ).
fof(f3754,plain,
( spl21_354
<=> ! [X0] :
( sK14 = relation_rng(relation_dom(relation_dom(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_354])]) ).
fof(f1709,plain,
( ! [X0] :
( sK14 = relation_rng(relation_dom(relation_dom(X0)))
| ~ empty(X0) )
| ~ spl21_35
| ~ spl21_190 ),
inference(resolution,[],[f1656,f372]) ).
fof(f3752,plain,
( spl21_353
| ~ spl21_33
| ~ spl21_190 ),
inference(avatar_split_clause,[],[f1708,f1655,f363,f3750]) ).
fof(f3750,plain,
( spl21_353
<=> ! [X0] :
( sK14 = relation_rng(relation_dom(relation_rng(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_353])]) ).
fof(f1708,plain,
( ! [X0] :
( sK14 = relation_rng(relation_dom(relation_rng(X0)))
| ~ empty(X0) )
| ~ spl21_33
| ~ spl21_190 ),
inference(resolution,[],[f1656,f364]) ).
fof(f3748,plain,
( spl21_352
| ~ spl21_35
| ~ spl21_189 ),
inference(avatar_split_clause,[],[f1692,f1651,f371,f3746]) ).
fof(f3746,plain,
( spl21_352
<=> ! [X0] :
( sK14 = relation_rng(relation_rng(relation_dom(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_352])]) ).
fof(f1692,plain,
( ! [X0] :
( sK14 = relation_rng(relation_rng(relation_dom(X0)))
| ~ empty(X0) )
| ~ spl21_35
| ~ spl21_189 ),
inference(resolution,[],[f1652,f372]) ).
fof(f3744,plain,
( spl21_351
| ~ spl21_33
| ~ spl21_189 ),
inference(avatar_split_clause,[],[f1691,f1651,f363,f3742]) ).
fof(f3742,plain,
( spl21_351
<=> ! [X0] :
( sK14 = relation_rng(relation_rng(relation_rng(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_351])]) ).
fof(f1691,plain,
( ! [X0] :
( sK14 = relation_rng(relation_rng(relation_rng(X0)))
| ~ empty(X0) )
| ~ spl21_33
| ~ spl21_189 ),
inference(resolution,[],[f1652,f364]) ).
fof(f3740,plain,
( spl21_350
| ~ spl21_145
| ~ spl21_188 ),
inference(avatar_split_clause,[],[f1673,f1647,f1220,f3738]) ).
fof(f3738,plain,
( spl21_350
<=> ! [X0,X1] :
( ~ sP2(X0,sK14)
| sP2(X0,X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_350])]) ).
fof(f1220,plain,
( spl21_145
<=> ! [X0,X1] :
( in(sK9(X0,X1),relation_dom(X0))
| sP2(X0,X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_145])]) ).
fof(f1673,plain,
( ! [X0,X1] :
( ~ sP2(X0,sK14)
| sP2(X0,X1)
| ~ empty(X1) )
| ~ spl21_145
| ~ spl21_188 ),
inference(resolution,[],[f1648,f1221]) ).
fof(f1221,plain,
( ! [X0,X1] :
( in(sK9(X0,X1),relation_dom(X0))
| sP2(X0,X1)
| ~ empty(X1) )
| ~ spl21_145 ),
inference(avatar_component_clause,[],[f1220]) ).
fof(f3736,plain,
( spl21_349
| ~ spl21_113
| ~ spl21_186 ),
inference(avatar_split_clause,[],[f1640,f1626,f969,f3734]) ).
fof(f3734,plain,
( spl21_349
<=> ! [X0] :
( ~ empty(X0)
| sK14 = relation_dom(sK11(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_349])]) ).
fof(f969,plain,
( spl21_113
<=> ! [X0] :
( relation_dom(X0) = sK14
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_113])]) ).
fof(f1640,plain,
( ! [X0] :
( ~ empty(X0)
| sK14 = relation_dom(sK11(powerset(X0))) )
| ~ spl21_113
| ~ spl21_186 ),
inference(resolution,[],[f1627,f970]) ).
fof(f970,plain,
( ! [X0] :
( ~ empty(X0)
| relation_dom(X0) = sK14 )
| ~ spl21_113 ),
inference(avatar_component_clause,[],[f969]) ).
fof(f3732,plain,
( spl21_348
| ~ spl21_112
| ~ spl21_186 ),
inference(avatar_split_clause,[],[f1639,f1626,f965,f3730]) ).
fof(f3730,plain,
( spl21_348
<=> ! [X0] :
( ~ empty(X0)
| sK14 = relation_rng(sK11(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_348])]) ).
fof(f965,plain,
( spl21_112
<=> ! [X0] :
( relation_rng(X0) = sK14
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_112])]) ).
fof(f1639,plain,
( ! [X0] :
( ~ empty(X0)
| sK14 = relation_rng(sK11(powerset(X0))) )
| ~ spl21_112
| ~ spl21_186 ),
inference(resolution,[],[f1627,f966]) ).
fof(f966,plain,
( ! [X0] :
( ~ empty(X0)
| relation_rng(X0) = sK14 )
| ~ spl21_112 ),
inference(avatar_component_clause,[],[f965]) ).
fof(f3663,plain,
( spl21_347
| ~ spl21_35
| ~ spl21_198 ),
inference(avatar_split_clause,[],[f1792,f1776,f371,f3661]) ).
fof(f3661,plain,
( spl21_347
<=> ! [X0,X1] :
( sP2(X0,X1)
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_347])]) ).
fof(f1776,plain,
( spl21_198
<=> ! [X0,X1] :
( sP2(X0,X1)
| ~ empty(relation_dom(X0))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_198])]) ).
fof(f1792,plain,
( ! [X0,X1] :
( sP2(X0,X1)
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl21_35
| ~ spl21_198 ),
inference(resolution,[],[f1777,f372]) ).
fof(f1777,plain,
( ! [X0,X1] :
( ~ empty(relation_dom(X0))
| sP2(X0,X1)
| ~ empty(X1) )
| ~ spl21_198 ),
inference(avatar_component_clause,[],[f1776]) ).
fof(f3659,plain,
( spl21_346
| ~ spl21_47
| ~ spl21_193 ),
inference(avatar_split_clause,[],[f1759,f1667,f437,f3657]) ).
fof(f3657,plain,
( spl21_346
<=> ! [X0] :
( ~ empty(relation_rng(X0))
| sP0(X0)
| ~ sP3(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_346])]) ).
fof(f1759,plain,
( ! [X0] :
( ~ empty(relation_rng(X0))
| sP0(X0)
| ~ sP3(X0) )
| ~ spl21_47
| ~ spl21_193 ),
inference(resolution,[],[f1668,f438]) ).
fof(f3655,plain,
( spl21_345
| ~ spl21_109
| ~ spl21_186 ),
inference(avatar_split_clause,[],[f1638,f1626,f863,f3653]) ).
fof(f3653,plain,
( spl21_345
<=> ! [X0] :
( ~ empty(X0)
| sK14 = sK11(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_345])]) ).
fof(f863,plain,
( spl21_109
<=> ! [X0] :
( sK14 = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_109])]) ).
fof(f1638,plain,
( ! [X0] :
( ~ empty(X0)
| sK14 = sK11(powerset(X0)) )
| ~ spl21_109
| ~ spl21_186 ),
inference(resolution,[],[f1627,f864]) ).
fof(f864,plain,
( ! [X0] :
( ~ empty(X0)
| sK14 = X0 )
| ~ spl21_109 ),
inference(avatar_component_clause,[],[f863]) ).
fof(f3587,plain,
( ~ spl21_344
| ~ spl21_331
| spl21_332 ),
inference(avatar_split_clause,[],[f3483,f3456,f3452,f3584]) ).
fof(f3584,plain,
( spl21_344
<=> sK14 = relation_image(sK4,singleton(sK6(sK4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_344])]) ).
fof(f3452,plain,
( spl21_331
<=> sK14 = sK11(powerset(relation_image(sK4,singleton(sK6(sK4))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_331])]) ).
fof(f3456,plain,
( spl21_332
<=> relation_image(sK4,singleton(sK6(sK4))) = sK11(powerset(relation_image(sK4,singleton(sK6(sK4))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_332])]) ).
fof(f3483,plain,
( sK14 != relation_image(sK4,singleton(sK6(sK4)))
| ~ spl21_331
| spl21_332 ),
inference(superposition,[],[f3457,f3454]) ).
fof(f3454,plain,
( sK14 = sK11(powerset(relation_image(sK4,singleton(sK6(sK4)))))
| ~ spl21_331 ),
inference(avatar_component_clause,[],[f3452]) ).
fof(f3457,plain,
( relation_image(sK4,singleton(sK6(sK4))) != sK11(powerset(relation_image(sK4,singleton(sK6(sK4)))))
| spl21_332 ),
inference(avatar_component_clause,[],[f3456]) ).
fof(f3567,plain,
( spl21_342
| spl21_343
| spl21_204
| ~ spl21_170
| ~ spl21_229 ),
inference(avatar_split_clause,[],[f2188,f2143,f1478,f1859,f3564,f3560]) ).
fof(f3564,plain,
( spl21_343
<=> relation_image(sK4,singleton(sK6(sK4))) = sK5(relation_image(sK4,singleton(sK6(sK4)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_343])]) ).
fof(f1478,plain,
( spl21_170
<=> singleton(apply(sK4,sK6(sK4))) = relation_image(sK4,singleton(sK6(sK4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_170])]) ).
fof(f2188,plain,
( empty(relation_image(sK4,singleton(sK6(sK4))))
| relation_image(sK4,singleton(sK6(sK4))) = sK5(relation_image(sK4,singleton(sK6(sK4))))
| sK14 = sK5(relation_image(sK4,singleton(sK6(sK4))))
| ~ spl21_170
| ~ spl21_229 ),
inference(superposition,[],[f2144,f1480]) ).
fof(f1480,plain,
( singleton(apply(sK4,sK6(sK4))) = relation_image(sK4,singleton(sK6(sK4)))
| ~ spl21_170 ),
inference(avatar_component_clause,[],[f1478]) ).
fof(f3543,plain,
( spl21_340
| spl21_341
| ~ spl21_102
| ~ spl21_170 ),
inference(avatar_split_clause,[],[f1488,f1478,f832,f3540,f3536]) ).
fof(f3536,plain,
( spl21_340
<=> sK14 = relation_inverse_image(sK4,relation_image(sK4,relation_image(sK4,singleton(sK6(sK4))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_340])]) ).
fof(f3540,plain,
( spl21_341
<=> relation_image(sK4,singleton(sK6(sK4))) = relation_inverse_image(sK4,relation_image(sK4,relation_image(sK4,singleton(sK6(sK4))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_341])]) ).
fof(f832,plain,
( spl21_102
<=> ! [X0] :
( singleton(X0) = relation_inverse_image(sK4,relation_image(sK4,singleton(X0)))
| sK14 = relation_inverse_image(sK4,relation_image(sK4,singleton(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_102])]) ).
fof(f1488,plain,
( relation_image(sK4,singleton(sK6(sK4))) = relation_inverse_image(sK4,relation_image(sK4,relation_image(sK4,singleton(sK6(sK4)))))
| sK14 = relation_inverse_image(sK4,relation_image(sK4,relation_image(sK4,singleton(sK6(sK4)))))
| ~ spl21_102
| ~ spl21_170 ),
inference(superposition,[],[f833,f1480]) ).
fof(f833,plain,
( ! [X0] :
( singleton(X0) = relation_inverse_image(sK4,relation_image(sK4,singleton(X0)))
| sK14 = relation_inverse_image(sK4,relation_image(sK4,singleton(X0))) )
| ~ spl21_102 ),
inference(avatar_component_clause,[],[f832]) ).
fof(f3534,plain,
( spl21_339
| ~ spl21_76
| ~ spl21_169 ),
inference(avatar_split_clause,[],[f1473,f1465,f668,f3532]) ).
fof(f3532,plain,
( spl21_339
<=> ! [X0,X1] :
( element(sK8(X0,relation_inverse_image(sK4,relation_image(sK4,X1))),X1)
| in(sK9(X0,relation_inverse_image(sK4,relation_image(sK4,X1))),relation_dom(X0))
| sP2(X0,relation_inverse_image(sK4,relation_image(sK4,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_339])]) ).
fof(f1473,plain,
( ! [X0,X1] :
( element(sK8(X0,relation_inverse_image(sK4,relation_image(sK4,X1))),X1)
| in(sK9(X0,relation_inverse_image(sK4,relation_image(sK4,X1))),relation_dom(X0))
| sP2(X0,relation_inverse_image(sK4,relation_image(sK4,X1))) )
| ~ spl21_76
| ~ spl21_169 ),
inference(resolution,[],[f1466,f669]) ).
fof(f3530,plain,
( spl21_338
| ~ spl21_154
| ~ spl21_169 ),
inference(avatar_split_clause,[],[f1470,f1465,f1302,f3528]) ).
fof(f3528,plain,
( spl21_338
<=> ! [X0,X1] :
( element(sK8(X0,relation_inverse_image(sK4,relation_image(sK4,X1))),X1)
| element(sK9(X0,relation_inverse_image(sK4,relation_image(sK4,X1))),relation_dom(X0))
| sP2(X0,relation_inverse_image(sK4,relation_image(sK4,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_338])]) ).
fof(f1470,plain,
( ! [X0,X1] :
( element(sK8(X0,relation_inverse_image(sK4,relation_image(sK4,X1))),X1)
| element(sK9(X0,relation_inverse_image(sK4,relation_image(sK4,X1))),relation_dom(X0))
| sP2(X0,relation_inverse_image(sK4,relation_image(sK4,X1))) )
| ~ spl21_154
| ~ spl21_169 ),
inference(resolution,[],[f1466,f1303]) ).
fof(f3526,plain,
( spl21_337
| ~ spl21_77
| ~ spl21_168 ),
inference(avatar_split_clause,[],[f1459,f1452,f679,f3524]) ).
fof(f3524,plain,
( spl21_337
<=> ! [X0,X1] :
( ~ empty(X0)
| apply(X1,sK9(X1,relation_inverse_image(sK4,relation_image(sK4,X0)))) = sK8(X1,relation_inverse_image(sK4,relation_image(sK4,X0)))
| sP2(X1,relation_inverse_image(sK4,relation_image(sK4,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_337])]) ).
fof(f1459,plain,
( ! [X0,X1] :
( ~ empty(X0)
| apply(X1,sK9(X1,relation_inverse_image(sK4,relation_image(sK4,X0)))) = sK8(X1,relation_inverse_image(sK4,relation_image(sK4,X0)))
| sP2(X1,relation_inverse_image(sK4,relation_image(sK4,X0))) )
| ~ spl21_77
| ~ spl21_168 ),
inference(resolution,[],[f1453,f680]) ).
fof(f3499,plain,
( spl21_336
| ~ spl21_120
| ~ spl21_188 ),
inference(avatar_split_clause,[],[f1678,f1647,f999,f3497]) ).
fof(f3497,plain,
( spl21_336
<=> ! [X0] :
( ~ sP2(X0,sK14)
| empty(relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_336])]) ).
fof(f1678,plain,
( ! [X0] :
( ~ sP2(X0,sK14)
| empty(relation_dom(X0)) )
| ~ spl21_120
| ~ spl21_188 ),
inference(resolution,[],[f1648,f1000]) ).
fof(f3495,plain,
( spl21_335
| ~ spl21_177
| ~ spl21_186 ),
inference(avatar_split_clause,[],[f1643,f1626,f1530,f3493]) ).
fof(f3493,plain,
( spl21_335
<=> ! [X0] :
( ~ empty(X0)
| sP0(sK11(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_335])]) ).
fof(f1530,plain,
( spl21_177
<=> ! [X0] :
( sP0(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_177])]) ).
fof(f1643,plain,
( ! [X0] :
( ~ empty(X0)
| sP0(sK11(powerset(X0))) )
| ~ spl21_177
| ~ spl21_186 ),
inference(resolution,[],[f1627,f1531]) ).
fof(f1531,plain,
( ! [X0] :
( ~ empty(X0)
| sP0(X0) )
| ~ spl21_177 ),
inference(avatar_component_clause,[],[f1530]) ).
fof(f3491,plain,
( spl21_334
| ~ spl21_27
| ~ spl21_186 ),
inference(avatar_split_clause,[],[f1636,f1626,f328,f3489]) ).
fof(f3489,plain,
( spl21_334
<=> ! [X0] :
( ~ empty(X0)
| relation(sK11(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_334])]) ).
fof(f328,plain,
( spl21_27
<=> ! [X0] :
( relation(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_27])]) ).
fof(f1636,plain,
( ! [X0] :
( ~ empty(X0)
| relation(sK11(powerset(X0))) )
| ~ spl21_27
| ~ spl21_186 ),
inference(resolution,[],[f1627,f329]) ).
fof(f329,plain,
( ! [X0] :
( ~ empty(X0)
| relation(X0) )
| ~ spl21_27 ),
inference(avatar_component_clause,[],[f328]) ).
fof(f3487,plain,
( spl21_333
| ~ spl21_26
| ~ spl21_186 ),
inference(avatar_split_clause,[],[f1635,f1626,f324,f3485]) ).
fof(f3485,plain,
( spl21_333
<=> ! [X0] :
( ~ empty(X0)
| function(sK11(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_333])]) ).
fof(f324,plain,
( spl21_26
<=> ! [X0] :
( function(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_26])]) ).
fof(f1635,plain,
( ! [X0] :
( ~ empty(X0)
| function(sK11(powerset(X0))) )
| ~ spl21_26
| ~ spl21_186 ),
inference(resolution,[],[f1627,f325]) ).
fof(f325,plain,
( ! [X0] :
( ~ empty(X0)
| function(X0) )
| ~ spl21_26 ),
inference(avatar_component_clause,[],[f324]) ).
fof(f3459,plain,
( spl21_331
| spl21_332
| ~ spl21_170
| ~ spl21_223 ),
inference(avatar_split_clause,[],[f2110,f2087,f1478,f3456,f3452]) ).
fof(f2110,plain,
( relation_image(sK4,singleton(sK6(sK4))) = sK11(powerset(relation_image(sK4,singleton(sK6(sK4)))))
| sK14 = sK11(powerset(relation_image(sK4,singleton(sK6(sK4)))))
| ~ spl21_170
| ~ spl21_223 ),
inference(superposition,[],[f2088,f1480]) ).
fof(f3424,plain,
( spl21_330
| ~ spl21_35
| ~ spl21_197 ),
inference(avatar_split_clause,[],[f1791,f1772,f371,f3422]) ).
fof(f3422,plain,
( spl21_330
<=> ! [X0] :
( one_to_one(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_330])]) ).
fof(f1772,plain,
( spl21_197
<=> ! [X0] :
( ~ empty(relation_dom(X0))
| one_to_one(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_197])]) ).
fof(f1791,plain,
( ! [X0] :
( one_to_one(relation_dom(X0))
| ~ empty(X0) )
| ~ spl21_35
| ~ spl21_197 ),
inference(duplicate_literal_removal,[],[f1788]) ).
fof(f1788,plain,
( ! [X0] :
( one_to_one(relation_dom(X0))
| ~ empty(X0)
| ~ empty(X0) )
| ~ spl21_35
| ~ spl21_197 ),
inference(resolution,[],[f1773,f372]) ).
fof(f1773,plain,
( ! [X0] :
( ~ empty(relation_dom(X0))
| one_to_one(relation_dom(X0))
| ~ empty(X0) )
| ~ spl21_197 ),
inference(avatar_component_clause,[],[f1772]) ).
fof(f3420,plain,
( spl21_329
| ~ spl21_33
| ~ spl21_196 ),
inference(avatar_split_clause,[],[f1787,f1768,f363,f3418]) ).
fof(f3418,plain,
( spl21_329
<=> ! [X0] :
( one_to_one(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_329])]) ).
fof(f1768,plain,
( spl21_196
<=> ! [X0] :
( ~ empty(relation_rng(X0))
| one_to_one(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_196])]) ).
fof(f1787,plain,
( ! [X0] :
( one_to_one(relation_rng(X0))
| ~ empty(X0) )
| ~ spl21_33
| ~ spl21_196 ),
inference(duplicate_literal_removal,[],[f1784]) ).
fof(f1784,plain,
( ! [X0] :
( one_to_one(relation_rng(X0))
| ~ empty(X0)
| ~ empty(X0) )
| ~ spl21_33
| ~ spl21_196 ),
inference(resolution,[],[f1769,f364]) ).
fof(f1769,plain,
( ! [X0] :
( ~ empty(relation_rng(X0))
| one_to_one(relation_rng(X0))
| ~ empty(X0) )
| ~ spl21_196 ),
inference(avatar_component_clause,[],[f1768]) ).
fof(f3416,plain,
( spl21_328
| ~ spl21_52
| ~ spl21_188 ),
inference(avatar_split_clause,[],[f1670,f1647,f490,f3414]) ).
fof(f3414,plain,
( spl21_328
<=> ! [X0] :
( ~ sP2(X0,sK14)
| sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_328])]) ).
fof(f490,plain,
( spl21_52
<=> ! [X0] :
( sP0(X0)
| in(sK6(X0),relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_52])]) ).
fof(f1670,plain,
( ! [X0] :
( ~ sP2(X0,sK14)
| sP0(X0) )
| ~ spl21_52
| ~ spl21_188 ),
inference(resolution,[],[f1648,f491]) ).
fof(f491,plain,
( ! [X0] :
( in(sK6(X0),relation_dom(X0))
| sP0(X0) )
| ~ spl21_52 ),
inference(avatar_component_clause,[],[f490]) ).
fof(f3412,plain,
( spl21_327
| ~ spl21_35
| ~ spl21_187 ),
inference(avatar_split_clause,[],[f1644,f1630,f371,f3410]) ).
fof(f3410,plain,
( spl21_327
<=> ! [X0] :
( sP2(X0,sK14)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_327])]) ).
fof(f1630,plain,
( spl21_187
<=> ! [X0] :
( sP2(X0,sK14)
| ~ empty(relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_187])]) ).
fof(f1644,plain,
( ! [X0] :
( sP2(X0,sK14)
| ~ empty(X0) )
| ~ spl21_35
| ~ spl21_187 ),
inference(resolution,[],[f1631,f372]) ).
fof(f1631,plain,
( ! [X0] :
( ~ empty(relation_dom(X0))
| sP2(X0,sK14) )
| ~ spl21_187 ),
inference(avatar_component_clause,[],[f1630]) ).
fof(f3408,plain,
( ~ spl21_326
| ~ spl21_321
| spl21_322 ),
inference(avatar_split_clause,[],[f3366,f3342,f3338,f3405]) ).
fof(f3405,plain,
( spl21_326
<=> sK14 = singleton(sK7(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_326])]) ).
fof(f3366,plain,
( sK14 != singleton(sK7(sK4))
| ~ spl21_321
| spl21_322 ),
inference(superposition,[],[f3343,f3340]) ).
fof(f3343,plain,
( singleton(sK7(sK4)) != relation_inverse_image(sK4,relation_image(sK4,singleton(sK6(sK4))))
| spl21_322 ),
inference(avatar_component_clause,[],[f3342]) ).
fof(f3380,plain,
( ~ spl21_100
| spl21_325
| ~ spl21_47
| ~ spl21_178 ),
inference(avatar_split_clause,[],[f1560,f1534,f437,f3377,f821]) ).
fof(f821,plain,
( spl21_100
<=> sP3(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_100])]) ).
fof(f3377,plain,
( spl21_325
<=> sP2(sK14,sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_325])]) ).
fof(f1534,plain,
( spl21_178
<=> sK14 = relation_rng(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_178])]) ).
fof(f1560,plain,
( sP2(sK14,sK14)
| ~ sP3(sK14)
| ~ spl21_47
| ~ spl21_178 ),
inference(superposition,[],[f438,f1536]) ).
fof(f1536,plain,
( sK14 = relation_rng(sK14)
| ~ spl21_178 ),
inference(avatar_component_clause,[],[f1534]) ).
fof(f3375,plain,
( spl21_324
| ~ spl21_35
| ~ spl21_177 ),
inference(avatar_split_clause,[],[f1548,f1530,f371,f3373]) ).
fof(f3373,plain,
( spl21_324
<=> ! [X0] :
( sP0(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_324])]) ).
fof(f1548,plain,
( ! [X0] :
( sP0(relation_dom(X0))
| ~ empty(X0) )
| ~ spl21_35
| ~ spl21_177 ),
inference(resolution,[],[f1531,f372]) ).
fof(f3371,plain,
( spl21_323
| ~ spl21_33
| ~ spl21_177 ),
inference(avatar_split_clause,[],[f1547,f1530,f363,f3369]) ).
fof(f3369,plain,
( spl21_323
<=> ! [X0] :
( sP0(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_323])]) ).
fof(f1547,plain,
( ! [X0] :
( sP0(relation_rng(X0))
| ~ empty(X0) )
| ~ spl21_33
| ~ spl21_177 ),
inference(resolution,[],[f1531,f364]) ).
fof(f3345,plain,
( spl21_321
| spl21_322
| ~ spl21_102
| ~ spl21_172 ),
inference(avatar_split_clause,[],[f1501,f1497,f832,f3342,f3338]) ).
fof(f1497,plain,
( spl21_172
<=> relation_image(sK4,singleton(sK7(sK4))) = relation_image(sK4,singleton(sK6(sK4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_172])]) ).
fof(f1501,plain,
( singleton(sK7(sK4)) = relation_inverse_image(sK4,relation_image(sK4,singleton(sK6(sK4))))
| sK14 = relation_inverse_image(sK4,relation_image(sK4,singleton(sK6(sK4))))
| ~ spl21_102
| ~ spl21_172 ),
inference(superposition,[],[f833,f1499]) ).
fof(f1499,plain,
( relation_image(sK4,singleton(sK7(sK4))) = relation_image(sK4,singleton(sK6(sK4)))
| ~ spl21_172 ),
inference(avatar_component_clause,[],[f1497]) ).
fof(f3310,plain,
( spl21_320
| ~ spl21_1
| ~ spl21_314 ),
inference(avatar_split_clause,[],[f3265,f3244,f204,f3307]) ).
fof(f3244,plain,
( spl21_314
<=> ! [X0] :
( sK14 = relation_inverse_image(X0,singleton(relation_rng(sK4)))
| sK14 = relation_inverse_image(sK4,singleton(relation_rng(X0)))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_314])]) ).
fof(f3265,plain,
( sK14 = relation_inverse_image(sK4,singleton(relation_rng(sK4)))
| ~ spl21_1
| ~ spl21_314 ),
inference(duplicate_literal_removal,[],[f3257]) ).
fof(f3257,plain,
( sK14 = relation_inverse_image(sK4,singleton(relation_rng(sK4)))
| sK14 = relation_inverse_image(sK4,singleton(relation_rng(sK4)))
| ~ spl21_1
| ~ spl21_314 ),
inference(resolution,[],[f3245,f206]) ).
fof(f206,plain,
( relation(sK4)
| ~ spl21_1 ),
inference(avatar_component_clause,[],[f204]) ).
fof(f3245,plain,
( ! [X0] :
( ~ relation(X0)
| sK14 = relation_inverse_image(sK4,singleton(relation_rng(X0)))
| sK14 = relation_inverse_image(X0,singleton(relation_rng(sK4))) )
| ~ spl21_314 ),
inference(avatar_component_clause,[],[f3244]) ).
fof(f3305,plain,
( spl21_319
| ~ spl21_144
| ~ spl21_169 ),
inference(avatar_split_clause,[],[f1471,f1465,f1216,f3303]) ).
fof(f3303,plain,
( spl21_319
<=> ! [X0,X1] :
( element(sK8(X0,relation_inverse_image(sK4,relation_image(sK4,X1))),X1)
| sP2(X0,relation_inverse_image(sK4,relation_image(sK4,X1)))
| ~ empty(relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_319])]) ).
fof(f1471,plain,
( ! [X0,X1] :
( element(sK8(X0,relation_inverse_image(sK4,relation_image(sK4,X1))),X1)
| sP2(X0,relation_inverse_image(sK4,relation_image(sK4,X1)))
| ~ empty(relation_dom(X0)) )
| ~ spl21_144
| ~ spl21_169 ),
inference(resolution,[],[f1466,f1217]) ).
fof(f3301,plain,
( spl21_318
| ~ spl21_76
| ~ spl21_168 ),
inference(avatar_split_clause,[],[f1460,f1452,f668,f3299]) ).
fof(f3299,plain,
( spl21_318
<=> ! [X0,X1] :
( ~ empty(X0)
| in(sK9(X1,relation_inverse_image(sK4,relation_image(sK4,X0))),relation_dom(X1))
| sP2(X1,relation_inverse_image(sK4,relation_image(sK4,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_318])]) ).
fof(f1460,plain,
( ! [X0,X1] :
( ~ empty(X0)
| in(sK9(X1,relation_inverse_image(sK4,relation_image(sK4,X0))),relation_dom(X1))
| sP2(X1,relation_inverse_image(sK4,relation_image(sK4,X0))) )
| ~ spl21_76
| ~ spl21_168 ),
inference(resolution,[],[f1453,f669]) ).
fof(f3297,plain,
( spl21_317
| ~ spl21_154
| ~ spl21_168 ),
inference(avatar_split_clause,[],[f1457,f1452,f1302,f3295]) ).
fof(f3295,plain,
( spl21_317
<=> ! [X0,X1] :
( ~ empty(X0)
| element(sK9(X1,relation_inverse_image(sK4,relation_image(sK4,X0))),relation_dom(X1))
| sP2(X1,relation_inverse_image(sK4,relation_image(sK4,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_317])]) ).
fof(f1457,plain,
( ! [X0,X1] :
( ~ empty(X0)
| element(sK9(X1,relation_inverse_image(sK4,relation_image(sK4,X0))),relation_dom(X1))
| sP2(X1,relation_inverse_image(sK4,relation_image(sK4,X0))) )
| ~ spl21_154
| ~ spl21_168 ),
inference(resolution,[],[f1453,f1303]) ).
fof(f3291,plain,
( spl21_316
| ~ spl21_73
| ~ spl21_170 ),
inference(avatar_split_clause,[],[f1487,f1478,f649,f3289]) ).
fof(f1487,plain,
( ! [X0] :
( sK14 != relation_inverse_image(X0,relation_image(sK4,singleton(sK6(sK4))))
| ~ in(apply(sK4,sK6(sK4)),relation_rng(X0))
| ~ relation(X0) )
| ~ spl21_73
| ~ spl21_170 ),
inference(superposition,[],[f650,f1480]) ).
fof(f3279,plain,
( spl21_315
| ~ spl21_67
| ~ spl21_170 ),
inference(avatar_split_clause,[],[f1486,f1478,f618,f3277]) ).
fof(f3277,plain,
( spl21_315
<=> ! [X0] :
( ~ subset(X0,relation_image(sK4,singleton(sK6(sK4))))
| relation_image(sK4,singleton(sK6(sK4))) = X0
| sK14 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_315])]) ).
fof(f618,plain,
( spl21_67
<=> ! [X0,X1] :
( sK14 = X0
| singleton(X1) = X0
| ~ subset(X0,singleton(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_67])]) ).
fof(f1486,plain,
( ! [X0] :
( ~ subset(X0,relation_image(sK4,singleton(sK6(sK4))))
| relation_image(sK4,singleton(sK6(sK4))) = X0
| sK14 = X0 )
| ~ spl21_67
| ~ spl21_170 ),
inference(superposition,[],[f619,f1480]) ).
fof(f619,plain,
( ! [X0,X1] :
( ~ subset(X0,singleton(X1))
| singleton(X1) = X0
| sK14 = X0 )
| ~ spl21_67 ),
inference(avatar_component_clause,[],[f618]) ).
fof(f3246,plain,
( spl21_314
| ~ spl21_1
| ~ spl21_253 ),
inference(avatar_split_clause,[],[f2397,f2388,f204,f3244]) ).
fof(f2388,plain,
( spl21_253
<=> ! [X0,X1] :
( ~ relation(X0)
| sK14 = relation_inverse_image(X0,singleton(relation_rng(X1)))
| sK14 = relation_inverse_image(X1,singleton(relation_rng(X0)))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_253])]) ).
fof(f2397,plain,
( ! [X0] :
( sK14 = relation_inverse_image(X0,singleton(relation_rng(sK4)))
| sK14 = relation_inverse_image(sK4,singleton(relation_rng(X0)))
| ~ relation(X0) )
| ~ spl21_1
| ~ spl21_253 ),
inference(resolution,[],[f2389,f206]) ).
fof(f2389,plain,
( ! [X0,X1] :
( ~ relation(X1)
| sK14 = relation_inverse_image(X0,singleton(relation_rng(X1)))
| sK14 = relation_inverse_image(X1,singleton(relation_rng(X0)))
| ~ relation(X0) )
| ~ spl21_253 ),
inference(avatar_component_clause,[],[f2388]) ).
fof(f3242,plain,
( spl21_313
| ~ spl21_116
| ~ spl21_138 ),
inference(avatar_split_clause,[],[f2450,f1166,f981,f3240]) ).
fof(f3240,plain,
( spl21_313
<=> ! [X0,X1] :
( ~ sP2(sK4,relation_dom(X0))
| ~ sP2(X0,X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_313])]) ).
fof(f2450,plain,
( ! [X0,X1] :
( ~ sP2(sK4,relation_dom(X0))
| ~ sP2(X0,X1)
| ~ empty(X1) )
| ~ spl21_116
| ~ spl21_138 ),
inference(resolution,[],[f982,f1167]) ).
fof(f3238,plain,
( spl21_312
| ~ spl21_72
| ~ spl21_169 ),
inference(avatar_split_clause,[],[f1474,f1465,f644,f3236]) ).
fof(f3236,plain,
( spl21_312
<=> ! [X2,X0,X1] :
( element(apply(X0,X1),X2)
| ~ in(X1,relation_dom(X0))
| ~ sP2(X0,relation_inverse_image(sK4,relation_image(sK4,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_312])]) ).
fof(f1474,plain,
( ! [X2,X0,X1] :
( element(apply(X0,X1),X2)
| ~ in(X1,relation_dom(X0))
| ~ sP2(X0,relation_inverse_image(sK4,relation_image(sK4,X2))) )
| ~ spl21_72
| ~ spl21_169 ),
inference(resolution,[],[f1466,f645]) ).
fof(f3217,plain,
( ~ spl21_1
| spl21_311
| ~ spl21_58
| ~ spl21_249 ),
inference(avatar_split_clause,[],[f2359,f2346,f540,f3215,f204]) ).
fof(f3215,plain,
( spl21_311
<=> ! [X0] :
( apply(sK4,sK10(sK4,X0)) = X0
| sK14 = relation_inverse_image(sK4,singleton(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_311])]) ).
fof(f2346,plain,
( spl21_249
<=> ! [X0,X1] :
( apply(X0,sK10(X0,X1)) = X1
| ~ sP3(X0)
| sK14 = relation_inverse_image(X0,singleton(X1))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_249])]) ).
fof(f2359,plain,
( ! [X0] :
( apply(sK4,sK10(sK4,X0)) = X0
| sK14 = relation_inverse_image(sK4,singleton(X0))
| ~ relation(sK4) )
| ~ spl21_58
| ~ spl21_249 ),
inference(resolution,[],[f2347,f542]) ).
fof(f2347,plain,
( ! [X0,X1] :
( ~ sP3(X0)
| apply(X0,sK10(X0,X1)) = X1
| sK14 = relation_inverse_image(X0,singleton(X1))
| ~ relation(X0) )
| ~ spl21_249 ),
inference(avatar_component_clause,[],[f2346]) ).
fof(f3195,plain,
( spl21_310
| ~ spl21_169
| ~ spl21_172 ),
inference(avatar_split_clause,[],[f1502,f1497,f1465,f3193]) ).
fof(f3193,plain,
( spl21_310
<=> ! [X0] :
( ~ in(X0,relation_inverse_image(sK4,relation_image(sK4,singleton(sK6(sK4)))))
| element(X0,singleton(sK7(sK4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_310])]) ).
fof(f1502,plain,
( ! [X0] :
( ~ in(X0,relation_inverse_image(sK4,relation_image(sK4,singleton(sK6(sK4)))))
| element(X0,singleton(sK7(sK4))) )
| ~ spl21_169
| ~ spl21_172 ),
inference(superposition,[],[f1466,f1499]) ).
fof(f3191,plain,
( spl21_309
| ~ spl21_61
| ~ spl21_170 ),
inference(avatar_split_clause,[],[f1485,f1478,f553,f3189]) ).
fof(f3189,plain,
( spl21_309
<=> ! [X0] :
( ~ subset(singleton(X0),relation_image(sK4,singleton(sK6(sK4))))
| apply(sK4,sK6(sK4)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_309])]) ).
fof(f1485,plain,
( ! [X0] :
( ~ subset(singleton(X0),relation_image(sK4,singleton(sK6(sK4))))
| apply(sK4,sK6(sK4)) = X0 )
| ~ spl21_61
| ~ spl21_170 ),
inference(superposition,[],[f554,f1480]) ).
fof(f3187,plain,
( spl21_308
| ~ spl21_61
| ~ spl21_170 ),
inference(avatar_split_clause,[],[f1484,f1478,f553,f3185]) ).
fof(f3185,plain,
( spl21_308
<=> ! [X0] :
( ~ subset(relation_image(sK4,singleton(sK6(sK4))),singleton(X0))
| apply(sK4,sK6(sK4)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_308])]) ).
fof(f1484,plain,
( ! [X0] :
( ~ subset(relation_image(sK4,singleton(sK6(sK4))),singleton(X0))
| apply(sK4,sK6(sK4)) = X0 )
| ~ spl21_61
| ~ spl21_170 ),
inference(superposition,[],[f554,f1480]) ).
fof(f3183,plain,
( spl21_307
| ~ spl21_116
| ~ spl21_203 ),
inference(avatar_split_clause,[],[f2447,f1811,f981,f3181]) ).
fof(f3181,plain,
( spl21_307
<=> ! [X0] :
( ~ sP2(sK4,relation_rng(X0))
| ~ sP3(X0)
| ~ empty(relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_307])]) ).
fof(f2447,plain,
( ! [X0] :
( ~ sP2(sK4,relation_rng(X0))
| ~ sP3(X0)
| ~ empty(relation_dom(X0)) )
| ~ spl21_116
| ~ spl21_203 ),
inference(resolution,[],[f982,f1812]) ).
fof(f3179,plain,
( spl21_306
| ~ spl21_120
| ~ spl21_169 ),
inference(avatar_split_clause,[],[f1468,f1465,f999,f3177]) ).
fof(f3177,plain,
( spl21_306
<=> ! [X0] :
( element(sK11(relation_inverse_image(sK4,relation_image(sK4,X0))),X0)
| empty(relation_inverse_image(sK4,relation_image(sK4,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_306])]) ).
fof(f1468,plain,
( ! [X0] :
( element(sK11(relation_inverse_image(sK4,relation_image(sK4,X0))),X0)
| empty(relation_inverse_image(sK4,relation_image(sK4,X0))) )
| ~ spl21_120
| ~ spl21_169 ),
inference(resolution,[],[f1466,f1000]) ).
fof(f3168,plain,
( spl21_305
| ~ spl21_72
| ~ spl21_168 ),
inference(avatar_split_clause,[],[f1461,f1452,f644,f3166]) ).
fof(f3166,plain,
( spl21_305
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,relation_dom(X2))
| ~ sP2(X2,relation_inverse_image(sK4,relation_image(sK4,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_305])]) ).
fof(f1461,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,relation_dom(X2))
| ~ sP2(X2,relation_inverse_image(sK4,relation_image(sK4,X0))) )
| ~ spl21_72
| ~ spl21_168 ),
inference(resolution,[],[f1453,f645]) ).
fof(f3146,plain,
( spl21_304
| ~ spl21_144
| ~ spl21_168 ),
inference(avatar_split_clause,[],[f1458,f1452,f1216,f3144]) ).
fof(f3144,plain,
( spl21_304
<=> ! [X0,X1] :
( ~ empty(X0)
| sP2(X1,relation_inverse_image(sK4,relation_image(sK4,X0)))
| ~ empty(relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_304])]) ).
fof(f1458,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sP2(X1,relation_inverse_image(sK4,relation_image(sK4,X0)))
| ~ empty(relation_dom(X1)) )
| ~ spl21_144
| ~ spl21_168 ),
inference(resolution,[],[f1453,f1217]) ).
fof(f3138,plain,
( spl21_303
| ~ spl21_4
| ~ spl21_172 ),
inference(avatar_split_clause,[],[f1504,f1497,f219,f3135]) ).
fof(f3135,plain,
( spl21_303
<=> subset(relation_inverse_image(sK4,relation_image(sK4,singleton(sK6(sK4)))),singleton(sK7(sK4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_303])]) ).
fof(f1504,plain,
( subset(relation_inverse_image(sK4,relation_image(sK4,singleton(sK6(sK4)))),singleton(sK7(sK4)))
| ~ spl21_4
| ~ spl21_172 ),
inference(superposition,[],[f220,f1499]) ).
fof(f3109,plain,
( spl21_302
| ~ spl21_165
| ~ spl21_167 ),
inference(avatar_split_clause,[],[f1450,f1443,f1417,f3107]) ).
fof(f3107,plain,
( spl21_302
<=> ! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| sK8(X1,relation_dom(X0)) = apply(X1,sK9(X1,relation_dom(X0)))
| relation_image(X0,singleton(sK8(X1,relation_dom(X0)))) = singleton(apply(X0,sK8(X1,relation_dom(X0))))
| ~ in(X2,relation_dom(X1))
| relation_image(X0,singleton(apply(X1,X2))) = singleton(apply(X0,apply(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_302])]) ).
fof(f1417,plain,
( spl21_165
<=> ! [X2,X0,X1] :
( relation_image(X0,singleton(apply(X1,X2))) = singleton(apply(X0,apply(X1,X2)))
| ~ function(X0)
| ~ relation(X0)
| ~ in(X2,relation_dom(X1))
| ~ sP2(X1,relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_165])]) ).
fof(f1443,plain,
( spl21_167
<=> ! [X0,X1] :
( relation_image(X0,singleton(sK8(X1,relation_dom(X0)))) = singleton(apply(X0,sK8(X1,relation_dom(X0))))
| ~ function(X0)
| ~ relation(X0)
| sK8(X1,relation_dom(X0)) = apply(X1,sK9(X1,relation_dom(X0)))
| sP2(X1,relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_167])]) ).
fof(f1450,plain,
( ! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| sK8(X1,relation_dom(X0)) = apply(X1,sK9(X1,relation_dom(X0)))
| relation_image(X0,singleton(sK8(X1,relation_dom(X0)))) = singleton(apply(X0,sK8(X1,relation_dom(X0))))
| ~ in(X2,relation_dom(X1))
| relation_image(X0,singleton(apply(X1,X2))) = singleton(apply(X0,apply(X1,X2))) )
| ~ spl21_165
| ~ spl21_167 ),
inference(duplicate_literal_removal,[],[f1446]) ).
fof(f1446,plain,
( ! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| sK8(X1,relation_dom(X0)) = apply(X1,sK9(X1,relation_dom(X0)))
| relation_image(X0,singleton(sK8(X1,relation_dom(X0)))) = singleton(apply(X0,sK8(X1,relation_dom(X0))))
| ~ function(X0)
| ~ relation(X0)
| ~ in(X2,relation_dom(X1))
| relation_image(X0,singleton(apply(X1,X2))) = singleton(apply(X0,apply(X1,X2))) )
| ~ spl21_165
| ~ spl21_167 ),
inference(resolution,[],[f1444,f1418]) ).
fof(f1418,plain,
( ! [X2,X0,X1] :
( ~ sP2(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0)
| ~ in(X2,relation_dom(X1))
| relation_image(X0,singleton(apply(X1,X2))) = singleton(apply(X0,apply(X1,X2))) )
| ~ spl21_165 ),
inference(avatar_component_clause,[],[f1417]) ).
fof(f1444,plain,
( ! [X0,X1] :
( sP2(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0)
| sK8(X1,relation_dom(X0)) = apply(X1,sK9(X1,relation_dom(X0)))
| relation_image(X0,singleton(sK8(X1,relation_dom(X0)))) = singleton(apply(X0,sK8(X1,relation_dom(X0)))) )
| ~ spl21_167 ),
inference(avatar_component_clause,[],[f1443]) ).
fof(f3085,plain,
( spl21_301
| ~ spl21_45
| ~ spl21_116 ),
inference(avatar_split_clause,[],[f2445,f981,f429,f3083]) ).
fof(f3083,plain,
( spl21_301
<=> ! [X0] :
( ~ sP2(sK4,X0)
| ~ in(X0,apply(sK4,sK6(sK4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_301])]) ).
fof(f429,plain,
( spl21_45
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_45])]) ).
fof(f2445,plain,
( ! [X0] :
( ~ sP2(sK4,X0)
| ~ in(X0,apply(sK4,sK6(sK4))) )
| ~ spl21_45
| ~ spl21_116 ),
inference(resolution,[],[f982,f430]) ).
fof(f430,plain,
( ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) )
| ~ spl21_45 ),
inference(avatar_component_clause,[],[f429]) ).
fof(f3081,plain,
( spl21_300
| ~ spl21_78
| ~ spl21_164 ),
inference(avatar_split_clause,[],[f1426,f1413,f683,f3079]) ).
fof(f3079,plain,
( spl21_300
<=> ! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,singleton(sK9(X0,relation_dom(X1)))) = singleton(apply(X0,sK9(X0,relation_dom(X1))))
| sP2(X0,relation_dom(X1))
| relation_image(X1,singleton(sK8(X0,relation_dom(X1)))) = singleton(apply(X1,sK8(X0,relation_dom(X1))))
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_300])]) ).
fof(f683,plain,
( spl21_78
<=> ! [X0,X1] :
( relation_image(X1,singleton(X0)) = singleton(apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_78])]) ).
fof(f1426,plain,
( ! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,singleton(sK9(X0,relation_dom(X1)))) = singleton(apply(X0,sK9(X0,relation_dom(X1))))
| sP2(X0,relation_dom(X1))
| relation_image(X1,singleton(sK8(X0,relation_dom(X1)))) = singleton(apply(X1,sK8(X0,relation_dom(X1))))
| ~ function(X1)
| ~ relation(X1) )
| ~ spl21_78
| ~ spl21_164 ),
inference(resolution,[],[f1414,f684]) ).
fof(f684,plain,
( ! [X0,X1] :
( ~ in(X0,relation_dom(X1))
| relation_image(X1,singleton(X0)) = singleton(apply(X1,X0))
| ~ function(X1)
| ~ relation(X1) )
| ~ spl21_78 ),
inference(avatar_component_clause,[],[f683]) ).
fof(f3055,plain,
( spl21_299
| ~ spl21_75
| ~ spl21_167 ),
inference(avatar_split_clause,[],[f1447,f1443,f663,f3053]) ).
fof(f3053,plain,
( spl21_299
<=> ! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| sK8(X1,relation_dom(X0)) = apply(X1,sK9(X1,relation_dom(X0)))
| relation_image(X0,singleton(sK8(X1,relation_dom(X0)))) = singleton(apply(X0,sK8(X1,relation_dom(X0))))
| ~ in(X2,relation_dom(X0))
| apply(X1,sK10(X1,X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_299])]) ).
fof(f663,plain,
( spl21_75
<=> ! [X5,X0,X1] :
( apply(X0,sK10(X0,X5)) = X5
| ~ in(X5,X1)
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_75])]) ).
fof(f1447,plain,
( ! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| sK8(X1,relation_dom(X0)) = apply(X1,sK9(X1,relation_dom(X0)))
| relation_image(X0,singleton(sK8(X1,relation_dom(X0)))) = singleton(apply(X0,sK8(X1,relation_dom(X0))))
| ~ in(X2,relation_dom(X0))
| apply(X1,sK10(X1,X2)) = X2 )
| ~ spl21_75
| ~ spl21_167 ),
inference(resolution,[],[f1444,f664]) ).
fof(f664,plain,
( ! [X0,X1,X5] :
( ~ sP2(X0,X1)
| ~ in(X5,X1)
| apply(X0,sK10(X0,X5)) = X5 )
| ~ spl21_75 ),
inference(avatar_component_clause,[],[f663]) ).
fof(f3029,plain,
( spl21_298
| ~ spl21_68
| ~ spl21_167 ),
inference(avatar_split_clause,[],[f1448,f1443,f625,f3027]) ).
fof(f3027,plain,
( spl21_298
<=> ! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| sK8(X1,relation_dom(X0)) = apply(X1,sK9(X1,relation_dom(X0)))
| relation_image(X0,singleton(sK8(X1,relation_dom(X0)))) = singleton(apply(X0,sK8(X1,relation_dom(X0))))
| ~ in(X2,relation_dom(X0))
| in(sK10(X1,X2),relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_298])]) ).
fof(f625,plain,
( spl21_68
<=> ! [X5,X0,X1] :
( in(sK10(X0,X5),relation_dom(X0))
| ~ in(X5,X1)
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_68])]) ).
fof(f1448,plain,
( ! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| sK8(X1,relation_dom(X0)) = apply(X1,sK9(X1,relation_dom(X0)))
| relation_image(X0,singleton(sK8(X1,relation_dom(X0)))) = singleton(apply(X0,sK8(X1,relation_dom(X0))))
| ~ in(X2,relation_dom(X0))
| in(sK10(X1,X2),relation_dom(X1)) )
| ~ spl21_68
| ~ spl21_167 ),
inference(resolution,[],[f1444,f626]) ).
fof(f626,plain,
( ! [X0,X1,X5] :
( ~ sP2(X0,X1)
| ~ in(X5,X1)
| in(sK10(X0,X5),relation_dom(X0)) )
| ~ spl21_68 ),
inference(avatar_component_clause,[],[f625]) ).
fof(f3007,plain,
( spl21_297
| ~ spl21_152
| ~ spl21_164 ),
inference(avatar_split_clause,[],[f1424,f1413,f1287,f3005]) ).
fof(f3005,plain,
( spl21_297
<=> ! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,singleton(sK9(X0,relation_rng(X1)))) = singleton(apply(X0,sK9(X0,relation_rng(X1))))
| sP2(X0,relation_rng(X1))
| sK8(X0,relation_rng(X1)) = apply(X1,sK10(X1,sK8(X0,relation_rng(X1))))
| ~ sP3(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_297])]) ).
fof(f1287,plain,
( spl21_152
<=> ! [X0,X1] :
( ~ in(X0,relation_rng(X1))
| apply(X1,sK10(X1,X0)) = X0
| ~ sP3(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_152])]) ).
fof(f1424,plain,
( ! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,singleton(sK9(X0,relation_rng(X1)))) = singleton(apply(X0,sK9(X0,relation_rng(X1))))
| sP2(X0,relation_rng(X1))
| sK8(X0,relation_rng(X1)) = apply(X1,sK10(X1,sK8(X0,relation_rng(X1))))
| ~ sP3(X1) )
| ~ spl21_152
| ~ spl21_164 ),
inference(resolution,[],[f1414,f1288]) ).
fof(f1288,plain,
( ! [X0,X1] :
( ~ in(X0,relation_rng(X1))
| apply(X1,sK10(X1,X0)) = X0
| ~ sP3(X1) )
| ~ spl21_152 ),
inference(avatar_component_clause,[],[f1287]) ).
fof(f2993,plain,
( spl21_296
| ~ spl21_62
| ~ spl21_167 ),
inference(avatar_split_clause,[],[f1449,f1443,f583,f2991]) ).
fof(f1449,plain,
( ! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| sK8(X1,relation_dom(X0)) = apply(X1,sK9(X1,relation_dom(X0)))
| relation_image(X0,singleton(sK8(X1,relation_dom(X0)))) = singleton(apply(X0,sK8(X1,relation_dom(X0))))
| relation_dom(X0) = relation_rng(X1)
| ~ sP3(X1) )
| ~ spl21_62
| ~ spl21_167 ),
inference(resolution,[],[f1444,f584]) ).
fof(f2989,plain,
( spl21_295
| ~ spl21_46
| ~ spl21_116 ),
inference(avatar_split_clause,[],[f2444,f981,f433,f2987]) ).
fof(f2987,plain,
( spl21_295
<=> ! [X0] :
( ~ sP2(sK4,X0)
| element(apply(sK4,sK6(sK4)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_295])]) ).
fof(f433,plain,
( spl21_46
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_46])]) ).
fof(f2444,plain,
( ! [X0] :
( ~ sP2(sK4,X0)
| element(apply(sK4,sK6(sK4)),X0) )
| ~ spl21_46
| ~ spl21_116 ),
inference(resolution,[],[f982,f434]) ).
fof(f434,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) )
| ~ spl21_46 ),
inference(avatar_component_clause,[],[f433]) ).
fof(f2985,plain,
( spl21_294
| ~ spl21_149
| ~ spl21_164 ),
inference(avatar_split_clause,[],[f1427,f1413,f1256,f2983]) ).
fof(f2983,plain,
( spl21_294
<=> ! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,singleton(sK9(X0,apply(X1,X2)))) = singleton(apply(X0,sK9(X0,apply(X1,X2))))
| sP2(X0,apply(X1,X2))
| ~ sP2(X1,sK8(X0,apply(X1,X2)))
| ~ in(X2,relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_294])]) ).
fof(f1256,plain,
( spl21_149
<=> ! [X2,X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ sP2(X1,X2)
| ~ in(X2,apply(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_149])]) ).
fof(f1427,plain,
( ! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,singleton(sK9(X0,apply(X1,X2)))) = singleton(apply(X0,sK9(X0,apply(X1,X2))))
| sP2(X0,apply(X1,X2))
| ~ sP2(X1,sK8(X0,apply(X1,X2)))
| ~ in(X2,relation_dom(X1)) )
| ~ spl21_149
| ~ spl21_164 ),
inference(resolution,[],[f1414,f1257]) ).
fof(f1257,plain,
( ! [X2,X0,X1] :
( ~ in(X2,apply(X1,X0))
| ~ sP2(X1,X2)
| ~ in(X0,relation_dom(X1)) )
| ~ spl21_149 ),
inference(avatar_component_clause,[],[f1256]) ).
fof(f2959,plain,
( spl21_293
| ~ spl21_158
| ~ spl21_165 ),
inference(avatar_split_clause,[],[f1432,f1417,f1318,f2957]) ).
fof(f2957,plain,
( spl21_293
<=> ! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X2))
| relation_image(X0,singleton(apply(X2,X1))) = singleton(apply(X0,apply(X2,X1)))
| sK8(X2,relation_dom(X0)) = apply(X2,sK9(X2,relation_dom(X0)))
| ~ empty(relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_293])]) ).
fof(f1432,plain,
( ! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X2))
| relation_image(X0,singleton(apply(X2,X1))) = singleton(apply(X0,apply(X2,X1)))
| sK8(X2,relation_dom(X0)) = apply(X2,sK9(X2,relation_dom(X0)))
| ~ empty(relation_dom(X0)) )
| ~ spl21_158
| ~ spl21_165 ),
inference(resolution,[],[f1418,f1319]) ).
fof(f2950,plain,
( spl21_292
| ~ spl21_134
| ~ spl21_164 ),
inference(avatar_split_clause,[],[f1429,f1413,f1094,f2948]) ).
fof(f2948,plain,
( spl21_292
<=> ! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,singleton(sK9(X0,sK11(powerset(X1))))) = singleton(apply(X0,sK9(X0,sK11(powerset(X1)))))
| sP2(X0,sK11(powerset(X1)))
| element(sK8(X0,sK11(powerset(X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_292])]) ).
fof(f1094,plain,
( spl21_134
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK11(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_134])]) ).
fof(f1429,plain,
( ! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,singleton(sK9(X0,sK11(powerset(X1))))) = singleton(apply(X0,sK9(X0,sK11(powerset(X1)))))
| sP2(X0,sK11(powerset(X1)))
| element(sK8(X0,sK11(powerset(X1))),X1) )
| ~ spl21_134
| ~ spl21_164 ),
inference(resolution,[],[f1414,f1095]) ).
fof(f1095,plain,
( ! [X0,X1] :
( ~ in(X0,sK11(powerset(X1)))
| element(X0,X1) )
| ~ spl21_134 ),
inference(avatar_component_clause,[],[f1094]) ).
fof(f2941,plain,
( spl21_291
| ~ spl21_136
| ~ spl21_164 ),
inference(avatar_split_clause,[],[f1428,f1413,f1157,f2939]) ).
fof(f2939,plain,
( spl21_291
<=> ! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,singleton(sK9(X0,sK5(X1)))) = singleton(apply(X0,sK9(X0,sK5(X1))))
| sP2(X0,sK5(X1))
| element(sK8(X0,sK5(X1)),X1)
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_291])]) ).
fof(f1157,plain,
( spl21_136
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK5(X1))
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_136])]) ).
fof(f1428,plain,
( ! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,singleton(sK9(X0,sK5(X1)))) = singleton(apply(X0,sK9(X0,sK5(X1))))
| sP2(X0,sK5(X1))
| element(sK8(X0,sK5(X1)),X1)
| empty(X1) )
| ~ spl21_136
| ~ spl21_164 ),
inference(resolution,[],[f1414,f1158]) ).
fof(f1158,plain,
( ! [X0,X1] :
( ~ in(X0,sK5(X1))
| element(X0,X1)
| empty(X1) )
| ~ spl21_136 ),
inference(avatar_component_clause,[],[f1157]) ).
fof(f2899,plain,
( spl21_290
| ~ spl21_45
| ~ spl21_166 ),
inference(avatar_split_clause,[],[f1441,f1434,f429,f2897]) ).
fof(f2897,plain,
( spl21_290
<=> ! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,singleton(sK8(X1,relation_dom(X0)))) = singleton(apply(X0,sK8(X1,relation_dom(X0))))
| sP2(X1,relation_dom(X0))
| ~ in(relation_dom(X1),sK9(X1,relation_dom(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_290])]) ).
fof(f1434,plain,
( spl21_166
<=> ! [X0,X1] :
( relation_image(X0,singleton(sK8(X1,relation_dom(X0)))) = singleton(apply(X0,sK8(X1,relation_dom(X0))))
| ~ function(X0)
| ~ relation(X0)
| in(sK9(X1,relation_dom(X0)),relation_dom(X1))
| sP2(X1,relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_166])]) ).
fof(f1441,plain,
( ! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,singleton(sK8(X1,relation_dom(X0)))) = singleton(apply(X0,sK8(X1,relation_dom(X0))))
| sP2(X1,relation_dom(X0))
| ~ in(relation_dom(X1),sK9(X1,relation_dom(X0))) )
| ~ spl21_45
| ~ spl21_166 ),
inference(resolution,[],[f1435,f430]) ).
fof(f1435,plain,
( ! [X0,X1] :
( in(sK9(X1,relation_dom(X0)),relation_dom(X1))
| ~ function(X0)
| ~ relation(X0)
| relation_image(X0,singleton(sK8(X1,relation_dom(X0)))) = singleton(apply(X0,sK8(X1,relation_dom(X0))))
| sP2(X1,relation_dom(X0)) )
| ~ spl21_166 ),
inference(avatar_component_clause,[],[f1434]) ).
fof(f2895,plain,
( spl21_289
| ~ spl21_78
| ~ spl21_154 ),
inference(avatar_split_clause,[],[f1327,f1302,f683,f2893]) ).
fof(f2893,plain,
( spl21_289
<=> ! [X0,X1] :
( element(sK9(X0,relation_dom(X1)),relation_dom(X0))
| sP2(X0,relation_dom(X1))
| relation_image(X1,singleton(sK8(X0,relation_dom(X1)))) = singleton(apply(X1,sK8(X0,relation_dom(X1))))
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_289])]) ).
fof(f1327,plain,
( ! [X0,X1] :
( element(sK9(X0,relation_dom(X1)),relation_dom(X0))
| sP2(X0,relation_dom(X1))
| relation_image(X1,singleton(sK8(X0,relation_dom(X1)))) = singleton(apply(X1,sK8(X0,relation_dom(X1))))
| ~ function(X1)
| ~ relation(X1) )
| ~ spl21_78
| ~ spl21_154 ),
inference(resolution,[],[f1303,f684]) ).
fof(f2891,plain,
( spl21_288
| ~ spl21_77
| ~ spl21_152 ),
inference(avatar_split_clause,[],[f1293,f1287,f679,f2889]) ).
fof(f2889,plain,
( spl21_288
<=> ! [X0,X1] :
( sK8(X1,relation_rng(X0)) = apply(X0,sK10(X0,sK8(X1,relation_rng(X0))))
| ~ sP3(X0)
| sK8(X1,relation_rng(X0)) = apply(X1,sK9(X1,relation_rng(X0)))
| sP2(X1,relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_288])]) ).
fof(f1293,plain,
( ! [X0,X1] :
( sK8(X1,relation_rng(X0)) = apply(X0,sK10(X0,sK8(X1,relation_rng(X0))))
| ~ sP3(X0)
| sK8(X1,relation_rng(X0)) = apply(X1,sK9(X1,relation_rng(X0)))
| sP2(X1,relation_rng(X0)) )
| ~ spl21_77
| ~ spl21_152 ),
inference(resolution,[],[f1288,f680]) ).
fof(f2884,plain,
( spl21_287
| ~ spl21_77
| ~ spl21_149 ),
inference(avatar_split_clause,[],[f1279,f1256,f679,f2882]) ).
fof(f2882,plain,
( spl21_287
<=> ! [X2,X0,X1] :
( ~ sP2(X0,sK8(X1,apply(X0,X2)))
| ~ in(X2,relation_dom(X0))
| sK8(X1,apply(X0,X2)) = apply(X1,sK9(X1,apply(X0,X2)))
| sP2(X1,apply(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_287])]) ).
fof(f1279,plain,
( ! [X2,X0,X1] :
( ~ sP2(X0,sK8(X1,apply(X0,X2)))
| ~ in(X2,relation_dom(X0))
| sK8(X1,apply(X0,X2)) = apply(X1,sK9(X1,apply(X0,X2)))
| sP2(X1,apply(X0,X2)) )
| ~ spl21_77
| ~ spl21_149 ),
inference(resolution,[],[f1257,f680]) ).
fof(f2835,plain,
( spl21_286
| ~ spl21_138
| ~ spl21_166 ),
inference(avatar_split_clause,[],[f1437,f1434,f1166,f2833]) ).
fof(f2833,plain,
( spl21_286
<=> ! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,singleton(sK8(X1,relation_dom(X0)))) = singleton(apply(X0,sK8(X1,relation_dom(X0))))
| sP2(X1,relation_dom(X0))
| ~ sP2(X1,X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_286])]) ).
fof(f1437,plain,
( ! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,singleton(sK8(X1,relation_dom(X0)))) = singleton(apply(X0,sK8(X1,relation_dom(X0))))
| sP2(X1,relation_dom(X0))
| ~ sP2(X1,X2)
| ~ empty(X2) )
| ~ spl21_138
| ~ spl21_166 ),
inference(resolution,[],[f1435,f1167]) ).
fof(f2831,plain,
( spl21_285
| ~ spl21_126
| ~ spl21_164 ),
inference(avatar_split_clause,[],[f1430,f1413,f1052,f2829]) ).
fof(f2829,plain,
( spl21_285
<=> ! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,singleton(sK9(X0,sK11(powerset(X1))))) = singleton(apply(X0,sK9(X0,sK11(powerset(X1)))))
| sP2(X0,sK11(powerset(X1)))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_285])]) ).
fof(f1052,plain,
( spl21_126
<=> ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK11(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_126])]) ).
fof(f1430,plain,
( ! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,singleton(sK9(X0,sK11(powerset(X1))))) = singleton(apply(X0,sK9(X0,sK11(powerset(X1)))))
| sP2(X0,sK11(powerset(X1)))
| ~ empty(X1) )
| ~ spl21_126
| ~ spl21_164 ),
inference(resolution,[],[f1414,f1053]) ).
fof(f1053,plain,
( ! [X0,X1] :
( ~ in(X1,sK11(powerset(X0)))
| ~ empty(X0) )
| ~ spl21_126 ),
inference(avatar_component_clause,[],[f1052]) ).
fof(f2827,plain,
( spl21_284
| ~ spl21_109
| ~ spl21_215 ),
inference(avatar_split_clause,[],[f2038,f1996,f863,f2825]) ).
fof(f2825,plain,
( spl21_284
<=> ! [X0] :
( ~ empty(X0)
| sK14 = relation_inverse_image(sK4,relation_image(sK4,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_284])]) ).
fof(f1996,plain,
( spl21_215
<=> ! [X0] :
( ~ empty(X0)
| empty(relation_inverse_image(sK4,relation_image(sK4,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_215])]) ).
fof(f2038,plain,
( ! [X0] :
( ~ empty(X0)
| sK14 = relation_inverse_image(sK4,relation_image(sK4,X0)) )
| ~ spl21_109
| ~ spl21_215 ),
inference(resolution,[],[f1997,f864]) ).
fof(f1997,plain,
( ! [X0] :
( empty(relation_inverse_image(sK4,relation_image(sK4,X0)))
| ~ empty(X0) )
| ~ spl21_215 ),
inference(avatar_component_clause,[],[f1996]) ).
fof(f2823,plain,
( spl21_283
| ~ spl21_138
| ~ spl21_164 ),
inference(avatar_split_clause,[],[f1425,f1413,f1166,f2821]) ).
fof(f2821,plain,
( spl21_283
<=> ! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,singleton(sK9(X0,relation_dom(X1)))) = singleton(apply(X0,sK9(X0,relation_dom(X1))))
| sP2(X0,relation_dom(X1))
| ~ sP2(X1,X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_283])]) ).
fof(f1425,plain,
( ! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,singleton(sK9(X0,relation_dom(X1)))) = singleton(apply(X0,sK9(X0,relation_dom(X1))))
| sP2(X0,relation_dom(X1))
| ~ sP2(X1,X2)
| ~ empty(X2) )
| ~ spl21_138
| ~ spl21_164 ),
inference(resolution,[],[f1414,f1167]) ).
fof(f2790,plain,
( spl21_282
| ~ spl21_152
| ~ spl21_154 ),
inference(avatar_split_clause,[],[f1325,f1302,f1287,f2788]) ).
fof(f2788,plain,
( spl21_282
<=> ! [X0,X1] :
( element(sK9(X0,relation_rng(X1)),relation_dom(X0))
| sP2(X0,relation_rng(X1))
| sK8(X0,relation_rng(X1)) = apply(X1,sK10(X1,sK8(X0,relation_rng(X1))))
| ~ sP3(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_282])]) ).
fof(f1325,plain,
( ! [X0,X1] :
( element(sK9(X0,relation_rng(X1)),relation_dom(X0))
| sP2(X0,relation_rng(X1))
| sK8(X0,relation_rng(X1)) = apply(X1,sK10(X1,sK8(X0,relation_rng(X1))))
| ~ sP3(X1) )
| ~ spl21_152
| ~ spl21_154 ),
inference(resolution,[],[f1303,f1288]) ).
fof(f2786,plain,
( spl21_281
| ~ spl21_76
| ~ spl21_152 ),
inference(avatar_split_clause,[],[f1294,f1287,f668,f2784]) ).
fof(f2784,plain,
( spl21_281
<=> ! [X0,X1] :
( sK8(X1,relation_rng(X0)) = apply(X0,sK10(X0,sK8(X1,relation_rng(X0))))
| ~ sP3(X0)
| in(sK9(X1,relation_rng(X0)),relation_dom(X1))
| sP2(X1,relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_281])]) ).
fof(f1294,plain,
( ! [X0,X1] :
( sK8(X1,relation_rng(X0)) = apply(X0,sK10(X0,sK8(X1,relation_rng(X0))))
| ~ sP3(X0)
| in(sK9(X1,relation_rng(X0)),relation_dom(X1))
| sP2(X1,relation_rng(X0)) )
| ~ spl21_76
| ~ spl21_152 ),
inference(resolution,[],[f1288,f669]) ).
fof(f2782,plain,
( spl21_280
| ~ spl21_78
| ~ spl21_144 ),
inference(avatar_split_clause,[],[f1232,f1216,f683,f2780]) ).
fof(f2780,plain,
( spl21_280
<=> ! [X0,X1] :
( sP2(X0,relation_dom(X1))
| ~ empty(relation_dom(X0))
| relation_image(X1,singleton(sK8(X0,relation_dom(X1)))) = singleton(apply(X1,sK8(X0,relation_dom(X1))))
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_280])]) ).
fof(f1232,plain,
( ! [X0,X1] :
( sP2(X0,relation_dom(X1))
| ~ empty(relation_dom(X0))
| relation_image(X1,singleton(sK8(X0,relation_dom(X1)))) = singleton(apply(X1,sK8(X0,relation_dom(X1))))
| ~ function(X1)
| ~ relation(X1) )
| ~ spl21_78
| ~ spl21_144 ),
inference(resolution,[],[f1217,f684]) ).
fof(f2760,plain,
( spl21_279
| ~ spl21_45
| ~ spl21_164 ),
inference(avatar_split_clause,[],[f1423,f1413,f429,f2758]) ).
fof(f2758,plain,
( spl21_279
<=> ! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,singleton(sK9(X0,X1))) = singleton(apply(X0,sK9(X0,X1)))
| sP2(X0,X1)
| ~ in(X1,sK8(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_279])]) ).
fof(f1423,plain,
( ! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,singleton(sK9(X0,X1))) = singleton(apply(X0,sK9(X0,X1)))
| sP2(X0,X1)
| ~ in(X1,sK8(X0,X1)) )
| ~ spl21_45
| ~ spl21_164 ),
inference(resolution,[],[f1414,f430]) ).
fof(f2756,plain,
( spl21_278
| ~ spl21_78
| ~ spl21_156 ),
inference(avatar_split_clause,[],[f1334,f1310,f683,f2754]) ).
fof(f2754,plain,
( spl21_278
<=> ! [X0,X1] :
( element(sK8(X0,X1),X1)
| sP2(X0,X1)
| relation_image(X0,singleton(sK9(X0,X1))) = singleton(apply(X0,sK9(X0,X1)))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_278])]) ).
fof(f1334,plain,
( ! [X0,X1] :
( element(sK8(X0,X1),X1)
| sP2(X0,X1)
| relation_image(X0,singleton(sK9(X0,X1))) = singleton(apply(X0,sK9(X0,X1)))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl21_78
| ~ spl21_156 ),
inference(resolution,[],[f1311,f684]) ).
fof(f2752,plain,
( spl21_277
| ~ spl21_77
| ~ spl21_134 ),
inference(avatar_split_clause,[],[f1149,f1094,f679,f2750]) ).
fof(f2750,plain,
( spl21_277
<=> ! [X0,X1] :
( element(sK8(X0,sK11(powerset(X1))),X1)
| sK8(X0,sK11(powerset(X1))) = apply(X0,sK9(X0,sK11(powerset(X1))))
| sP2(X0,sK11(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_277])]) ).
fof(f1149,plain,
( ! [X0,X1] :
( element(sK8(X0,sK11(powerset(X1))),X1)
| sK8(X0,sK11(powerset(X1))) = apply(X0,sK9(X0,sK11(powerset(X1))))
| sP2(X0,sK11(powerset(X1))) )
| ~ spl21_77
| ~ spl21_134 ),
inference(resolution,[],[f1095,f680]) ).
fof(f2734,plain,
( spl21_276
| ~ spl21_64
| ~ spl21_160 ),
inference(avatar_split_clause,[],[f1367,f1351,f599,f2732]) ).
fof(f2732,plain,
( spl21_276
<=> ! [X2,X0,X1] :
( sP2(X0,powerset(X1))
| sK8(X0,powerset(X1)) = apply(X0,sK9(X0,powerset(X1)))
| element(X2,X1)
| ~ in(X2,sK8(X0,powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_276])]) ).
fof(f599,plain,
( spl21_64
<=> ! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_64])]) ).
fof(f1351,plain,
( spl21_160
<=> ! [X0,X1] :
( sK8(X0,X1) = apply(X0,sK9(X0,X1))
| sP2(X0,X1)
| element(sK8(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_160])]) ).
fof(f1367,plain,
( ! [X2,X0,X1] :
( sP2(X0,powerset(X1))
| sK8(X0,powerset(X1)) = apply(X0,sK9(X0,powerset(X1)))
| element(X2,X1)
| ~ in(X2,sK8(X0,powerset(X1))) )
| ~ spl21_64
| ~ spl21_160 ),
inference(resolution,[],[f1352,f600]) ).
fof(f600,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| element(X0,X2)
| ~ in(X0,X1) )
| ~ spl21_64 ),
inference(avatar_component_clause,[],[f599]) ).
fof(f1352,plain,
( ! [X0,X1] :
( element(sK8(X0,X1),X1)
| sP2(X0,X1)
| sK8(X0,X1) = apply(X0,sK9(X0,X1)) )
| ~ spl21_160 ),
inference(avatar_component_clause,[],[f1351]) ).
fof(f2730,plain,
( spl21_275
| ~ spl21_149
| ~ spl21_154 ),
inference(avatar_split_clause,[],[f1328,f1302,f1256,f2728]) ).
fof(f2728,plain,
( spl21_275
<=> ! [X2,X0,X1] :
( element(sK9(X0,apply(X1,X2)),relation_dom(X0))
| sP2(X0,apply(X1,X2))
| ~ sP2(X1,sK8(X0,apply(X1,X2)))
| ~ in(X2,relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_275])]) ).
fof(f1328,plain,
( ! [X2,X0,X1] :
( element(sK9(X0,apply(X1,X2)),relation_dom(X0))
| sP2(X0,apply(X1,X2))
| ~ sP2(X1,sK8(X0,apply(X1,X2)))
| ~ in(X2,relation_dom(X1)) )
| ~ spl21_149
| ~ spl21_154 ),
inference(resolution,[],[f1303,f1257]) ).
fof(f2726,plain,
( spl21_274
| ~ spl21_76
| ~ spl21_149 ),
inference(avatar_split_clause,[],[f1280,f1256,f668,f2724]) ).
fof(f2724,plain,
( spl21_274
<=> ! [X2,X0,X1] :
( ~ sP2(X0,sK8(X1,apply(X0,X2)))
| ~ in(X2,relation_dom(X0))
| in(sK9(X1,apply(X0,X2)),relation_dom(X1))
| sP2(X1,apply(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_274])]) ).
fof(f1280,plain,
( ! [X2,X0,X1] :
( ~ sP2(X0,sK8(X1,apply(X0,X2)))
| ~ in(X2,relation_dom(X0))
| in(sK9(X1,apply(X0,X2)),relation_dom(X1))
| sP2(X1,apply(X0,X2)) )
| ~ spl21_76
| ~ spl21_149 ),
inference(resolution,[],[f1257,f669]) ).
fof(f2694,plain,
( spl21_273
| ~ spl21_63
| ~ spl21_160 ),
inference(avatar_split_clause,[],[f1366,f1351,f587,f2692]) ).
fof(f2692,plain,
( spl21_273
<=> ! [X2,X0,X1] :
( sP2(X0,powerset(X1))
| sK8(X0,powerset(X1)) = apply(X0,sK9(X0,powerset(X1)))
| ~ empty(X1)
| ~ in(X2,sK8(X0,powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_273])]) ).
fof(f1366,plain,
( ! [X2,X0,X1] :
( sP2(X0,powerset(X1))
| sK8(X0,powerset(X1)) = apply(X0,sK9(X0,powerset(X1)))
| ~ empty(X1)
| ~ in(X2,sK8(X0,powerset(X1))) )
| ~ spl21_63
| ~ spl21_160 ),
inference(resolution,[],[f1352,f588]) ).
fof(f2690,plain,
( spl21_272
| ~ spl21_78
| ~ spl21_146 ),
inference(avatar_split_clause,[],[f1268,f1243,f683,f2688]) ).
fof(f2688,plain,
( spl21_272
<=> ! [X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ sP3(X1)
| relation_image(X1,singleton(sK10(X1,X0))) = singleton(apply(X1,sK10(X1,X0)))
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_272])]) ).
fof(f1268,plain,
( ! [X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ sP3(X1)
| relation_image(X1,singleton(sK10(X1,X0))) = singleton(apply(X1,sK10(X1,X0)))
| ~ function(X1)
| ~ relation(X1) )
| ~ spl21_78
| ~ spl21_146 ),
inference(resolution,[],[f1244,f684]) ).
fof(f2686,plain,
( spl21_271
| ~ spl21_77
| ~ spl21_136 ),
inference(avatar_split_clause,[],[f1177,f1157,f679,f2684]) ).
fof(f2684,plain,
( spl21_271
<=> ! [X0,X1] :
( element(sK8(X0,sK5(X1)),X1)
| empty(X1)
| sK8(X0,sK5(X1)) = apply(X0,sK9(X0,sK5(X1)))
| sP2(X0,sK5(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_271])]) ).
fof(f1177,plain,
( ! [X0,X1] :
( element(sK8(X0,sK5(X1)),X1)
| empty(X1)
| sK8(X0,sK5(X1)) = apply(X0,sK9(X0,sK5(X1)))
| sP2(X0,sK5(X1)) )
| ~ spl21_77
| ~ spl21_136 ),
inference(resolution,[],[f1158,f680]) ).
fof(f2634,plain,
( spl21_270
| ~ spl21_144
| ~ spl21_152 ),
inference(avatar_split_clause,[],[f1292,f1287,f1216,f2632]) ).
fof(f2632,plain,
( spl21_270
<=> ! [X0,X1] :
( sK8(X1,relation_rng(X0)) = apply(X0,sK10(X0,sK8(X1,relation_rng(X0))))
| ~ sP3(X0)
| sP2(X1,relation_rng(X0))
| ~ empty(relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_270])]) ).
fof(f1292,plain,
( ! [X0,X1] :
( sK8(X1,relation_rng(X0)) = apply(X0,sK10(X0,sK8(X1,relation_rng(X0))))
| ~ sP3(X0)
| sP2(X1,relation_rng(X0))
| ~ empty(relation_dom(X1)) )
| ~ spl21_144
| ~ spl21_152 ),
inference(resolution,[],[f1288,f1217]) ).
fof(f2630,plain,
( spl21_269
| ~ spl21_78
| ~ spl21_145 ),
inference(avatar_split_clause,[],[f1238,f1220,f683,f2628]) ).
fof(f2628,plain,
( spl21_269
<=> ! [X0,X1] :
( sP2(X0,X1)
| ~ empty(X1)
| relation_image(X0,singleton(sK9(X0,X1))) = singleton(apply(X0,sK9(X0,X1)))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_269])]) ).
fof(f1238,plain,
( ! [X0,X1] :
( sP2(X0,X1)
| ~ empty(X1)
| relation_image(X0,singleton(sK9(X0,X1))) = singleton(apply(X0,sK9(X0,X1)))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl21_78
| ~ spl21_145 ),
inference(resolution,[],[f1221,f684]) ).
fof(f2623,plain,
( spl21_268
| ~ spl21_116
| ~ spl21_126 ),
inference(avatar_split_clause,[],[f2463,f1052,f981,f2621]) ).
fof(f2621,plain,
( spl21_268
<=> ! [X0] :
( ~ sP2(sK4,sK11(powerset(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_268])]) ).
fof(f2463,plain,
( ! [X0] :
( ~ sP2(sK4,sK11(powerset(X0)))
| ~ empty(X0) )
| ~ spl21_116
| ~ spl21_126 ),
inference(resolution,[],[f982,f1053]) ).
fof(f2615,plain,
( spl21_267
| ~ spl21_55
| ~ spl21_160 ),
inference(avatar_split_clause,[],[f1368,f1351,f502,f2613]) ).
fof(f2613,plain,
( spl21_267
<=> ! [X0,X1] :
( sP2(X0,powerset(X1))
| sK8(X0,powerset(X1)) = apply(X0,sK9(X0,powerset(X1)))
| subset(sK8(X0,powerset(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_267])]) ).
fof(f1368,plain,
( ! [X0,X1] :
( sP2(X0,powerset(X1))
| sK8(X0,powerset(X1)) = apply(X0,sK9(X0,powerset(X1)))
| subset(sK8(X0,powerset(X1)),X1) )
| ~ spl21_55
| ~ spl21_160 ),
inference(resolution,[],[f1352,f503]) ).
fof(f2611,plain,
( spl21_266
| ~ spl21_72
| ~ spl21_152 ),
inference(avatar_split_clause,[],[f1295,f1287,f644,f2609]) ).
fof(f2609,plain,
( spl21_266
<=> ! [X2,X0,X1] :
( apply(X1,X2) = apply(X0,sK10(X0,apply(X1,X2)))
| ~ sP3(X0)
| ~ in(X2,relation_dom(X1))
| ~ sP2(X1,relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_266])]) ).
fof(f1295,plain,
( ! [X2,X0,X1] :
( apply(X1,X2) = apply(X0,sK10(X0,apply(X1,X2)))
| ~ sP3(X0)
| ~ in(X2,relation_dom(X1))
| ~ sP2(X1,relation_rng(X0)) )
| ~ spl21_72
| ~ spl21_152 ),
inference(resolution,[],[f1288,f645]) ).
fof(f2515,plain,
( spl21_265
| ~ spl21_116
| ~ spl21_188 ),
inference(avatar_split_clause,[],[f2449,f1647,f981,f2513]) ).
fof(f2513,plain,
( spl21_265
<=> ! [X0] :
( ~ sP2(sK4,relation_dom(X0))
| ~ sP2(X0,sK14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_265])]) ).
fof(f2449,plain,
( ! [X0] :
( ~ sP2(sK4,relation_dom(X0))
| ~ sP2(X0,sK14) )
| ~ spl21_116
| ~ spl21_188 ),
inference(resolution,[],[f982,f1648]) ).
fof(f2511,plain,
( spl21_264
| ~ spl21_111
| ~ spl21_164 ),
inference(avatar_split_clause,[],[f1431,f1413,f870,f2509]) ).
fof(f2509,plain,
( spl21_264
<=> ! [X0] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,singleton(sK9(X0,sK14))) = singleton(apply(X0,sK9(X0,sK14)))
| sP2(X0,sK14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_264])]) ).
fof(f870,plain,
( spl21_111
<=> ! [X1] : ~ in(X1,sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_111])]) ).
fof(f1431,plain,
( ! [X0] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,singleton(sK9(X0,sK14))) = singleton(apply(X0,sK9(X0,sK14)))
| sP2(X0,sK14) )
| ~ spl21_111
| ~ spl21_164 ),
inference(resolution,[],[f1414,f871]) ).
fof(f871,plain,
( ! [X1] : ~ in(X1,sK14)
| ~ spl21_111 ),
inference(avatar_component_clause,[],[f870]) ).
fof(f2507,plain,
( spl21_263
| ~ spl21_64
| ~ spl21_156 ),
inference(avatar_split_clause,[],[f1339,f1310,f599,f2505]) ).
fof(f2505,plain,
( spl21_263
<=> ! [X2,X0,X1] :
( in(sK9(X0,powerset(X1)),relation_dom(X0))
| sP2(X0,powerset(X1))
| element(X2,X1)
| ~ in(X2,sK8(X0,powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_263])]) ).
fof(f1339,plain,
( ! [X2,X0,X1] :
( in(sK9(X0,powerset(X1)),relation_dom(X0))
| sP2(X0,powerset(X1))
| element(X2,X1)
| ~ in(X2,sK8(X0,powerset(X1))) )
| ~ spl21_64
| ~ spl21_156 ),
inference(resolution,[],[f1311,f600]) ).
fof(f2503,plain,
( spl21_262
| ~ spl21_134
| ~ spl21_154 ),
inference(avatar_split_clause,[],[f1330,f1302,f1094,f2501]) ).
fof(f2501,plain,
( spl21_262
<=> ! [X0,X1] :
( element(sK9(X0,sK11(powerset(X1))),relation_dom(X0))
| sP2(X0,sK11(powerset(X1)))
| element(sK8(X0,sK11(powerset(X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_262])]) ).
fof(f1330,plain,
( ! [X0,X1] :
( element(sK9(X0,sK11(powerset(X1))),relation_dom(X0))
| sP2(X0,sK11(powerset(X1)))
| element(sK8(X0,sK11(powerset(X1))),X1) )
| ~ spl21_134
| ~ spl21_154 ),
inference(resolution,[],[f1303,f1095]) ).
fof(f2499,plain,
( spl21_261
| ~ spl21_77
| ~ spl21_138 ),
inference(avatar_split_clause,[],[f1185,f1166,f679,f2497]) ).
fof(f2497,plain,
( spl21_261
<=> ! [X2,X0,X1] :
( ~ sP2(X0,X1)
| ~ empty(X1)
| sK8(X2,relation_dom(X0)) = apply(X2,sK9(X2,relation_dom(X0)))
| sP2(X2,relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_261])]) ).
fof(f1185,plain,
( ! [X2,X0,X1] :
( ~ sP2(X0,X1)
| ~ empty(X1)
| sK8(X2,relation_dom(X0)) = apply(X2,sK9(X2,relation_dom(X0)))
| sP2(X2,relation_dom(X0)) )
| ~ spl21_77
| ~ spl21_138 ),
inference(resolution,[],[f1167,f680]) ).
fof(f2495,plain,
( spl21_260
| ~ spl21_76
| ~ spl21_134 ),
inference(avatar_split_clause,[],[f1150,f1094,f668,f2493]) ).
fof(f2493,plain,
( spl21_260
<=> ! [X0,X1] :
( element(sK8(X0,sK11(powerset(X1))),X1)
| in(sK9(X0,sK11(powerset(X1))),relation_dom(X0))
| sP2(X0,sK11(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_260])]) ).
fof(f1150,plain,
( ! [X0,X1] :
( element(sK8(X0,sK11(powerset(X1))),X1)
| in(sK9(X0,sK11(powerset(X1))),relation_dom(X0))
| sP2(X0,sK11(powerset(X1))) )
| ~ spl21_76
| ~ spl21_134 ),
inference(resolution,[],[f1095,f669]) ).
fof(f2491,plain,
( spl21_259
| ~ spl21_77
| ~ spl21_126 ),
inference(avatar_split_clause,[],[f1062,f1052,f679,f2489]) ).
fof(f2489,plain,
( spl21_259
<=> ! [X0,X1] :
( ~ empty(X0)
| sK8(X1,sK11(powerset(X0))) = apply(X1,sK9(X1,sK11(powerset(X0))))
| sP2(X1,sK11(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_259])]) ).
fof(f1062,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK8(X1,sK11(powerset(X0))) = apply(X1,sK9(X1,sK11(powerset(X0))))
| sP2(X1,sK11(powerset(X0))) )
| ~ spl21_77
| ~ spl21_126 ),
inference(resolution,[],[f1053,f680]) ).
fof(f2487,plain,
( spl21_258
| ~ spl21_78
| ~ spl21_120 ),
inference(avatar_split_clause,[],[f1028,f999,f683,f2485]) ).
fof(f2485,plain,
( spl21_258
<=> ! [X0] :
( empty(relation_dom(X0))
| relation_image(X0,singleton(sK11(relation_dom(X0)))) = singleton(apply(X0,sK11(relation_dom(X0))))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_258])]) ).
fof(f1028,plain,
( ! [X0] :
( empty(relation_dom(X0))
| relation_image(X0,singleton(sK11(relation_dom(X0)))) = singleton(apply(X0,sK11(relation_dom(X0))))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl21_78
| ~ spl21_120 ),
inference(resolution,[],[f1000,f684]) ).
fof(f2430,plain,
( spl21_257
| ~ spl21_63
| ~ spl21_156 ),
inference(avatar_split_clause,[],[f1338,f1310,f587,f2428]) ).
fof(f2428,plain,
( spl21_257
<=> ! [X2,X0,X1] :
( in(sK9(X0,powerset(X1)),relation_dom(X0))
| sP2(X0,powerset(X1))
| ~ empty(X1)
| ~ in(X2,sK8(X0,powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_257])]) ).
fof(f1338,plain,
( ! [X2,X0,X1] :
( in(sK9(X0,powerset(X1)),relation_dom(X0))
| sP2(X0,powerset(X1))
| ~ empty(X1)
| ~ in(X2,sK8(X0,powerset(X1))) )
| ~ spl21_63
| ~ spl21_156 ),
inference(resolution,[],[f1311,f588]) ).
fof(f2426,plain,
( spl21_256
| ~ spl21_136
| ~ spl21_154 ),
inference(avatar_split_clause,[],[f1329,f1302,f1157,f2424]) ).
fof(f2424,plain,
( spl21_256
<=> ! [X0,X1] :
( element(sK9(X0,sK5(X1)),relation_dom(X0))
| sP2(X0,sK5(X1))
| element(sK8(X0,sK5(X1)),X1)
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_256])]) ).
fof(f1329,plain,
( ! [X0,X1] :
( element(sK9(X0,sK5(X1)),relation_dom(X0))
| sP2(X0,sK5(X1))
| element(sK8(X0,sK5(X1)),X1)
| empty(X1) )
| ~ spl21_136
| ~ spl21_154 ),
inference(resolution,[],[f1303,f1158]) ).
fof(f2422,plain,
( spl21_255
| ~ spl21_144
| ~ spl21_149 ),
inference(avatar_split_clause,[],[f1278,f1256,f1216,f2420]) ).
fof(f2420,plain,
( spl21_255
<=> ! [X2,X0,X1] :
( ~ sP2(X0,sK8(X1,apply(X0,X2)))
| ~ in(X2,relation_dom(X0))
| sP2(X1,apply(X0,X2))
| ~ empty(relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_255])]) ).
fof(f1278,plain,
( ! [X2,X0,X1] :
( ~ sP2(X0,sK8(X1,apply(X0,X2)))
| ~ in(X2,relation_dom(X0))
| sP2(X1,apply(X0,X2))
| ~ empty(relation_dom(X1)) )
| ~ spl21_144
| ~ spl21_149 ),
inference(resolution,[],[f1257,f1217]) ).
fof(f2418,plain,
( spl21_254
| ~ spl21_76
| ~ spl21_136 ),
inference(avatar_split_clause,[],[f1178,f1157,f668,f2416]) ).
fof(f2416,plain,
( spl21_254
<=> ! [X0,X1] :
( element(sK8(X0,sK5(X1)),X1)
| empty(X1)
| in(sK9(X0,sK5(X1)),relation_dom(X0))
| sP2(X0,sK5(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_254])]) ).
fof(f1178,plain,
( ! [X0,X1] :
( element(sK8(X0,sK5(X1)),X1)
| empty(X1)
| in(sK9(X0,sK5(X1)),relation_dom(X0))
| sP2(X0,sK5(X1)) )
| ~ spl21_76
| ~ spl21_136 ),
inference(resolution,[],[f1158,f669]) ).
fof(f2390,plain,
( spl21_253
| ~ spl21_74
| ~ spl21_151 ),
inference(avatar_split_clause,[],[f1284,f1264,f653,f2388]) ).
fof(f1264,plain,
( spl21_151
<=> ! [X0,X1] :
( sK14 = relation_inverse_image(X0,singleton(X1))
| ~ relation(X0)
| ~ in(relation_rng(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_151])]) ).
fof(f1284,plain,
( ! [X0,X1] :
( ~ relation(X0)
| sK14 = relation_inverse_image(X0,singleton(relation_rng(X1)))
| sK14 = relation_inverse_image(X1,singleton(relation_rng(X0)))
| ~ relation(X1) )
| ~ spl21_74
| ~ spl21_151 ),
inference(resolution,[],[f1265,f654]) ).
fof(f1265,plain,
( ! [X0,X1] :
( ~ in(relation_rng(X0),X1)
| ~ relation(X0)
| sK14 = relation_inverse_image(X0,singleton(X1)) )
| ~ spl21_151 ),
inference(avatar_component_clause,[],[f1264]) ).
fof(f2386,plain,
( spl21_252
| ~ spl21_72
| ~ spl21_149 ),
inference(avatar_split_clause,[],[f1281,f1256,f644,f2384]) ).
fof(f2384,plain,
( spl21_252
<=> ! [X0,X3,X2,X1] :
( ~ sP2(X0,apply(X1,X2))
| ~ in(X3,relation_dom(X0))
| ~ in(X2,relation_dom(X1))
| ~ sP2(X1,apply(X0,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_252])]) ).
fof(f1281,plain,
( ! [X2,X3,X0,X1] :
( ~ sP2(X0,apply(X1,X2))
| ~ in(X3,relation_dom(X0))
| ~ in(X2,relation_dom(X1))
| ~ sP2(X1,apply(X0,X3)) )
| ~ spl21_72
| ~ spl21_149 ),
inference(resolution,[],[f1257,f645]) ).
fof(f2356,plain,
( spl21_251
| ~ spl21_62
| ~ spl21_158 ),
inference(avatar_split_clause,[],[f1345,f1318,f583,f2354]) ).
fof(f2354,plain,
( spl21_251
<=> ! [X0,X1] :
( sK8(X0,X1) = apply(X0,sK9(X0,X1))
| ~ empty(X1)
| relation_rng(X0) = X1
| ~ sP3(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_251])]) ).
fof(f1345,plain,
( ! [X0,X1] :
( sK8(X0,X1) = apply(X0,sK9(X0,X1))
| ~ empty(X1)
| relation_rng(X0) = X1
| ~ sP3(X0) )
| ~ spl21_62
| ~ spl21_158 ),
inference(resolution,[],[f1319,f584]) ).
fof(f2352,plain,
( spl21_250
| ~ spl21_55
| ~ spl21_156 ),
inference(avatar_split_clause,[],[f1340,f1310,f502,f2350]) ).
fof(f1340,plain,
( ! [X0,X1] :
( in(sK9(X0,powerset(X1)),relation_dom(X0))
| sP2(X0,powerset(X1))
| subset(sK8(X0,powerset(X1)),X1) )
| ~ spl21_55
| ~ spl21_156 ),
inference(resolution,[],[f1311,f503]) ).
fof(f2348,plain,
( spl21_249
| ~ spl21_74
| ~ spl21_152 ),
inference(avatar_split_clause,[],[f1290,f1287,f653,f2346]) ).
fof(f1290,plain,
( ! [X0,X1] :
( apply(X0,sK10(X0,X1)) = X1
| ~ sP3(X0)
| sK14 = relation_inverse_image(X0,singleton(X1))
| ~ relation(X0) )
| ~ spl21_74
| ~ spl21_152 ),
inference(resolution,[],[f1288,f654]) ).
fof(f2292,plain,
( spl21_248
| ~ spl21_138
| ~ spl21_154 ),
inference(avatar_split_clause,[],[f1326,f1302,f1166,f2290]) ).
fof(f2290,plain,
( spl21_248
<=> ! [X2,X0,X1] :
( element(sK9(X0,relation_dom(X1)),relation_dom(X0))
| sP2(X0,relation_dom(X1))
| ~ sP2(X1,X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_248])]) ).
fof(f1326,plain,
( ! [X2,X0,X1] :
( element(sK9(X0,relation_dom(X1)),relation_dom(X0))
| sP2(X0,relation_dom(X1))
| ~ sP2(X1,X2)
| ~ empty(X2) )
| ~ spl21_138
| ~ spl21_154 ),
inference(resolution,[],[f1303,f1167]) ).
fof(f2288,plain,
( spl21_247
| ~ spl21_120
| ~ spl21_152 ),
inference(avatar_split_clause,[],[f1291,f1287,f999,f2286]) ).
fof(f2286,plain,
( spl21_247
<=> ! [X0] :
( sK11(relation_rng(X0)) = apply(X0,sK10(X0,sK11(relation_rng(X0))))
| ~ sP3(X0)
| empty(relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_247])]) ).
fof(f1291,plain,
( ! [X0] :
( sK11(relation_rng(X0)) = apply(X0,sK10(X0,sK11(relation_rng(X0))))
| ~ sP3(X0)
| empty(relation_rng(X0)) )
| ~ spl21_120
| ~ spl21_152 ),
inference(resolution,[],[f1288,f1000]) ).
fof(f2284,plain,
( spl21_246
| ~ spl21_139
| ~ spl21_151 ),
inference(avatar_split_clause,[],[f1285,f1264,f1189,f2282]) ).
fof(f2282,plain,
( spl21_246
<=> ! [X0,X1] :
( ~ relation(X0)
| sK14 = relation_inverse_image(X0,singleton(powerset(X1)))
| empty(powerset(X1))
| ~ subset(relation_rng(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_246])]) ).
fof(f1285,plain,
( ! [X0,X1] :
( ~ relation(X0)
| sK14 = relation_inverse_image(X0,singleton(powerset(X1)))
| empty(powerset(X1))
| ~ subset(relation_rng(X0),X1) )
| ~ spl21_139
| ~ spl21_151 ),
inference(resolution,[],[f1265,f1190]) ).
fof(f2280,plain,
( spl21_245
| ~ spl21_64
| ~ spl21_147 ),
inference(avatar_split_clause,[],[f1273,f1247,f599,f2278]) ).
fof(f2278,plain,
( spl21_245
<=> ! [X0,X3,X2,X1] :
( ~ sP2(X0,powerset(X1))
| ~ in(X2,relation_dom(X0))
| element(X3,X1)
| ~ in(X3,apply(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_245])]) ).
fof(f1247,plain,
( spl21_147
<=> ! [X2,X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ sP2(X1,X2)
| element(apply(X1,X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_147])]) ).
fof(f1273,plain,
( ! [X2,X3,X0,X1] :
( ~ sP2(X0,powerset(X1))
| ~ in(X2,relation_dom(X0))
| element(X3,X1)
| ~ in(X3,apply(X0,X2)) )
| ~ spl21_64
| ~ spl21_147 ),
inference(resolution,[],[f1248,f600]) ).
fof(f1248,plain,
( ! [X2,X0,X1] :
( element(apply(X1,X0),X2)
| ~ sP2(X1,X2)
| ~ in(X0,relation_dom(X1)) )
| ~ spl21_147 ),
inference(avatar_component_clause,[],[f1247]) ).
fof(f2276,plain,
( spl21_244
| ~ spl21_76
| ~ spl21_138 ),
inference(avatar_split_clause,[],[f1186,f1166,f668,f2274]) ).
fof(f2274,plain,
( spl21_244
<=> ! [X2,X0,X1] :
( ~ sP2(X0,X1)
| ~ empty(X1)
| in(sK9(X2,relation_dom(X0)),relation_dom(X2))
| sP2(X2,relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_244])]) ).
fof(f1186,plain,
( ! [X2,X0,X1] :
( ~ sP2(X0,X1)
| ~ empty(X1)
| in(sK9(X2,relation_dom(X0)),relation_dom(X2))
| sP2(X2,relation_dom(X0)) )
| ~ spl21_76
| ~ spl21_138 ),
inference(resolution,[],[f1167,f669]) ).
fof(f2234,plain,
( spl21_173
| spl21_243
| ~ spl21_13
| ~ spl21_12
| ~ spl21_162 ),
inference(avatar_split_clause,[],[f1378,f1359,f258,f263,f2231,f1506]) ).
fof(f1506,plain,
( spl21_173
<=> sP0(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_173])]) ).
fof(f2231,plain,
( spl21_243
<=> relation_image(sK17,singleton(sK6(sK17))) = singleton(apply(sK17,sK6(sK17))) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_243])]) ).
fof(f263,plain,
( spl21_13
<=> function(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_13])]) ).
fof(f258,plain,
( spl21_12
<=> relation(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_12])]) ).
fof(f1359,plain,
( spl21_162
<=> ! [X0] :
( relation_image(X0,singleton(sK6(X0))) = singleton(apply(X0,sK6(X0)))
| ~ function(X0)
| ~ relation(X0)
| sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_162])]) ).
fof(f1378,plain,
( ~ function(sK17)
| relation_image(sK17,singleton(sK6(sK17))) = singleton(apply(sK17,sK6(sK17)))
| sP0(sK17)
| ~ spl21_12
| ~ spl21_162 ),
inference(resolution,[],[f1360,f260]) ).
fof(f260,plain,
( relation(sK17)
| ~ spl21_12 ),
inference(avatar_component_clause,[],[f258]) ).
fof(f1360,plain,
( ! [X0] :
( ~ relation(X0)
| ~ function(X0)
| relation_image(X0,singleton(sK6(X0))) = singleton(apply(X0,sK6(X0)))
| sP0(X0) )
| ~ spl21_162 ),
inference(avatar_component_clause,[],[f1359]) ).
fof(f2229,plain,
( spl21_242
| ~ spl21_126
| ~ spl21_154 ),
inference(avatar_split_clause,[],[f1331,f1302,f1052,f2227]) ).
fof(f2227,plain,
( spl21_242
<=> ! [X0,X1] :
( element(sK9(X0,sK11(powerset(X1))),relation_dom(X0))
| sP2(X0,sK11(powerset(X1)))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_242])]) ).
fof(f1331,plain,
( ! [X0,X1] :
( element(sK9(X0,sK11(powerset(X1))),relation_dom(X0))
| sP2(X0,sK11(powerset(X1)))
| ~ empty(X1) )
| ~ spl21_126
| ~ spl21_154 ),
inference(resolution,[],[f1303,f1053]) ).
fof(f2225,plain,
( spl21_241
| ~ spl21_63
| ~ spl21_147 ),
inference(avatar_split_clause,[],[f1272,f1247,f587,f2223]) ).
fof(f2223,plain,
( spl21_241
<=> ! [X2,X0,X1,X3] :
( ~ sP2(X0,powerset(X1))
| ~ in(X2,relation_dom(X0))
| ~ empty(X1)
| ~ in(X3,apply(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_241])]) ).
fof(f1272,plain,
( ! [X2,X3,X0,X1] :
( ~ sP2(X0,powerset(X1))
| ~ in(X2,relation_dom(X0))
| ~ empty(X1)
| ~ in(X3,apply(X0,X2)) )
| ~ spl21_63
| ~ spl21_147 ),
inference(resolution,[],[f1248,f588]) ).
fof(f2221,plain,
( spl21_240
| ~ spl21_134
| ~ spl21_144 ),
inference(avatar_split_clause,[],[f1234,f1216,f1094,f2219]) ).
fof(f2219,plain,
( spl21_240
<=> ! [X0,X1] :
( sP2(X0,sK11(powerset(X1)))
| ~ empty(relation_dom(X0))
| element(sK8(X0,sK11(powerset(X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_240])]) ).
fof(f1234,plain,
( ! [X0,X1] :
( sP2(X0,sK11(powerset(X1)))
| ~ empty(relation_dom(X0))
| element(sK8(X0,sK11(powerset(X1))),X1) )
| ~ spl21_134
| ~ spl21_144 ),
inference(resolution,[],[f1217,f1095]) ).
fof(f2217,plain,
( spl21_239
| ~ spl21_136
| ~ spl21_144 ),
inference(avatar_split_clause,[],[f1233,f1216,f1157,f2215]) ).
fof(f2215,plain,
( spl21_239
<=> ! [X0,X1] :
( sP2(X0,sK5(X1))
| ~ empty(relation_dom(X0))
| element(sK8(X0,sK5(X1)),X1)
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_239])]) ).
fof(f1233,plain,
( ! [X0,X1] :
( sP2(X0,sK5(X1))
| ~ empty(relation_dom(X0))
| element(sK8(X0,sK5(X1)),X1)
| empty(X1) )
| ~ spl21_136
| ~ spl21_144 ),
inference(resolution,[],[f1217,f1158]) ).
fof(f2213,plain,
( spl21_238
| ~ spl21_72
| ~ spl21_136 ),
inference(avatar_split_clause,[],[f1179,f1157,f644,f2211]) ).
fof(f2211,plain,
( spl21_238
<=> ! [X2,X0,X1] :
( element(apply(X0,X1),X2)
| empty(X2)
| ~ in(X1,relation_dom(X0))
| ~ sP2(X0,sK5(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_238])]) ).
fof(f1179,plain,
( ! [X2,X0,X1] :
( element(apply(X0,X1),X2)
| empty(X2)
| ~ in(X1,relation_dom(X0))
| ~ sP2(X0,sK5(X2)) )
| ~ spl21_72
| ~ spl21_136 ),
inference(resolution,[],[f1158,f645]) ).
fof(f2209,plain,
( spl21_237
| ~ spl21_177
| ~ spl21_215 ),
inference(avatar_split_clause,[],[f2043,f1996,f1530,f2207]) ).
fof(f2207,plain,
( spl21_237
<=> ! [X0] :
( ~ empty(X0)
| sP0(relation_inverse_image(sK4,relation_image(sK4,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_237])]) ).
fof(f2043,plain,
( ! [X0] :
( ~ empty(X0)
| sP0(relation_inverse_image(sK4,relation_image(sK4,X0))) )
| ~ spl21_177
| ~ spl21_215 ),
inference(resolution,[],[f1997,f1531]) ).
fof(f2205,plain,
( spl21_236
| ~ spl21_76
| ~ spl21_126 ),
inference(avatar_split_clause,[],[f1063,f1052,f668,f2203]) ).
fof(f1063,plain,
( ! [X0,X1] :
( ~ empty(X0)
| in(sK9(X1,sK11(powerset(X0))),relation_dom(X1))
| sP2(X1,sK11(powerset(X0))) )
| ~ spl21_76
| ~ spl21_126 ),
inference(resolution,[],[f1053,f669]) ).
fof(f2169,plain,
( spl21_235
| ~ spl21_45
| ~ spl21_156 ),
inference(avatar_split_clause,[],[f1337,f1310,f429,f2167]) ).
fof(f1337,plain,
( ! [X0,X1] :
( element(sK8(X0,X1),X1)
| sP2(X0,X1)
| ~ in(relation_dom(X0),sK9(X0,X1)) )
| ~ spl21_45
| ~ spl21_156 ),
inference(resolution,[],[f1311,f430]) ).
fof(f2165,plain,
( spl21_234
| ~ spl21_45
| ~ spl21_154 ),
inference(avatar_split_clause,[],[f1324,f1302,f429,f2163]) ).
fof(f2163,plain,
( spl21_234
<=> ! [X0,X1] :
( element(sK9(X0,X1),relation_dom(X0))
| sP2(X0,X1)
| ~ in(X1,sK8(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_234])]) ).
fof(f1324,plain,
( ! [X0,X1] :
( element(sK9(X0,X1),relation_dom(X0))
| sP2(X0,X1)
| ~ in(X1,sK8(X0,X1)) )
| ~ spl21_45
| ~ spl21_154 ),
inference(resolution,[],[f1303,f430]) ).
fof(f2161,plain,
( spl21_233
| ~ spl21_46
| ~ spl21_154 ),
inference(avatar_split_clause,[],[f1323,f1302,f433,f2159]) ).
fof(f1323,plain,
( ! [X0,X1] :
( element(sK9(X0,X1),relation_dom(X0))
| sP2(X0,X1)
| element(sK8(X0,X1),X1) )
| ~ spl21_46
| ~ spl21_154 ),
inference(resolution,[],[f1303,f434]) ).
fof(f2157,plain,
( spl21_232
| ~ spl21_27
| ~ spl21_215 ),
inference(avatar_split_clause,[],[f2036,f1996,f328,f2155]) ).
fof(f2155,plain,
( spl21_232
<=> ! [X0] :
( ~ empty(X0)
| relation(relation_inverse_image(sK4,relation_image(sK4,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_232])]) ).
fof(f2036,plain,
( ! [X0] :
( ~ empty(X0)
| relation(relation_inverse_image(sK4,relation_image(sK4,X0))) )
| ~ spl21_27
| ~ spl21_215 ),
inference(resolution,[],[f1997,f329]) ).
fof(f2153,plain,
( spl21_231
| ~ spl21_120
| ~ spl21_149 ),
inference(avatar_split_clause,[],[f1277,f1256,f999,f2151]) ).
fof(f2151,plain,
( spl21_231
<=> ! [X0,X1] :
( ~ sP2(X0,sK11(apply(X0,X1)))
| ~ in(X1,relation_dom(X0))
| empty(apply(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_231])]) ).
fof(f1277,plain,
( ! [X0,X1] :
( ~ sP2(X0,sK11(apply(X0,X1)))
| ~ in(X1,relation_dom(X0))
| empty(apply(X0,X1)) )
| ~ spl21_120
| ~ spl21_149 ),
inference(resolution,[],[f1257,f1000]) ).
fof(f2149,plain,
( spl21_230
| ~ spl21_72
| ~ spl21_134 ),
inference(avatar_split_clause,[],[f1151,f1094,f644,f2147]) ).
fof(f2147,plain,
( spl21_230
<=> ! [X2,X0,X1] :
( element(apply(X0,X1),X2)
| ~ in(X1,relation_dom(X0))
| ~ sP2(X0,sK11(powerset(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_230])]) ).
fof(f1151,plain,
( ! [X2,X0,X1] :
( element(apply(X0,X1),X2)
| ~ in(X1,relation_dom(X0))
| ~ sP2(X0,sK11(powerset(X2))) )
| ~ spl21_72
| ~ spl21_134 ),
inference(resolution,[],[f1095,f645]) ).
fof(f2145,plain,
( spl21_229
| ~ spl21_67
| ~ spl21_114 ),
inference(avatar_split_clause,[],[f1024,f973,f618,f2143]) ).
fof(f973,plain,
( spl21_114
<=> ! [X0] :
( subset(sK5(X0),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_114])]) ).
fof(f1024,plain,
( ! [X0] :
( empty(singleton(X0))
| singleton(X0) = sK5(singleton(X0))
| sK14 = sK5(singleton(X0)) )
| ~ spl21_67
| ~ spl21_114 ),
inference(resolution,[],[f974,f619]) ).
fof(f974,plain,
( ! [X0] :
( subset(sK5(X0),X0)
| empty(X0) )
| ~ spl21_114 ),
inference(avatar_component_clause,[],[f973]) ).
fof(f2109,plain,
( spl21_228
| ~ spl21_138
| ~ spl21_156 ),
inference(avatar_split_clause,[],[f1333,f1310,f1166,f2107]) ).
fof(f1333,plain,
( ! [X2,X0,X1] :
( element(sK8(X0,X1),X1)
| sP2(X0,X1)
| ~ sP2(X0,X2)
| ~ empty(X2) )
| ~ spl21_138
| ~ spl21_156 ),
inference(resolution,[],[f1311,f1167]) ).
fof(f2105,plain,
( spl21_227
| ~ spl21_55
| ~ spl21_147 ),
inference(avatar_split_clause,[],[f1274,f1247,f502,f2103]) ).
fof(f2103,plain,
( spl21_227
<=> ! [X2,X0,X1] :
( ~ sP2(X0,powerset(X1))
| ~ in(X2,relation_dom(X0))
| subset(apply(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_227])]) ).
fof(f1274,plain,
( ! [X2,X0,X1] :
( ~ sP2(X0,powerset(X1))
| ~ in(X2,relation_dom(X0))
| subset(apply(X0,X2),X1) )
| ~ spl21_55
| ~ spl21_147 ),
inference(resolution,[],[f1248,f503]) ).
fof(f2101,plain,
( spl21_226
| ~ spl21_26
| ~ spl21_215 ),
inference(avatar_split_clause,[],[f2035,f1996,f324,f2099]) ).
fof(f2099,plain,
( spl21_226
<=> ! [X0] :
( ~ empty(X0)
| function(relation_inverse_image(sK4,relation_image(sK4,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_226])]) ).
fof(f2035,plain,
( ! [X0] :
( ~ empty(X0)
| function(relation_inverse_image(sK4,relation_image(sK4,X0))) )
| ~ spl21_26
| ~ spl21_215 ),
inference(resolution,[],[f1997,f325]) ).
fof(f2097,plain,
( spl21_225
| ~ spl21_72
| ~ spl21_138 ),
inference(avatar_split_clause,[],[f1187,f1166,f644,f2095]) ).
fof(f2095,plain,
( spl21_225
<=> ! [X0,X3,X2,X1] :
( ~ sP2(X0,X1)
| ~ empty(X1)
| ~ in(X2,relation_dom(X3))
| ~ sP2(X3,relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_225])]) ).
fof(f1187,plain,
( ! [X2,X3,X0,X1] :
( ~ sP2(X0,X1)
| ~ empty(X1)
| ~ in(X2,relation_dom(X3))
| ~ sP2(X3,relation_dom(X0)) )
| ~ spl21_72
| ~ spl21_138 ),
inference(resolution,[],[f1167,f645]) ).
fof(f2093,plain,
( spl21_224
| ~ spl21_76
| ~ spl21_138 ),
inference(avatar_split_clause,[],[f1182,f1166,f668,f2091]) ).
fof(f1182,plain,
( ! [X2,X0,X1] :
( ~ sP2(X0,X1)
| ~ empty(X1)
| in(sK8(X0,X2),X2)
| sP2(X0,X2) )
| ~ spl21_76
| ~ spl21_138 ),
inference(resolution,[],[f1167,f669]) ).
fof(f2089,plain,
( spl21_223
| ~ spl21_67
| ~ spl21_106 ),
inference(avatar_split_clause,[],[f956,f851,f618,f2087]) ).
fof(f851,plain,
( spl21_106
<=> ! [X0] : subset(sK11(powerset(X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_106])]) ).
fof(f956,plain,
( ! [X0] :
( singleton(X0) = sK11(powerset(singleton(X0)))
| sK14 = sK11(powerset(singleton(X0))) )
| ~ spl21_67
| ~ spl21_106 ),
inference(resolution,[],[f852,f619]) ).
fof(f852,plain,
( ! [X0] : subset(sK11(powerset(X0)),X0)
| ~ spl21_106 ),
inference(avatar_component_clause,[],[f851]) ).
fof(f2066,plain,
( spl21_222
| ~ spl21_45
| ~ spl21_146 ),
inference(avatar_split_clause,[],[f1271,f1243,f429,f2064]) ).
fof(f2064,plain,
( spl21_222
<=> ! [X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ sP3(X1)
| ~ in(relation_dom(X1),sK10(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_222])]) ).
fof(f1271,plain,
( ! [X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ sP3(X1)
| ~ in(relation_dom(X1),sK10(X1,X0)) )
| ~ spl21_45
| ~ spl21_146 ),
inference(resolution,[],[f1244,f430]) ).
fof(f2062,plain,
( spl21_221
| ~ spl21_46
| ~ spl21_146 ),
inference(avatar_split_clause,[],[f1270,f1243,f433,f2060]) ).
fof(f2060,plain,
( spl21_221
<=> ! [X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ sP3(X1)
| element(sK10(X1,X0),relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_221])]) ).
fof(f1270,plain,
( ! [X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ sP3(X1)
| element(sK10(X1,X0),relation_dom(X1)) )
| ~ spl21_46
| ~ spl21_146 ),
inference(resolution,[],[f1244,f434]) ).
fof(f2058,plain,
( spl21_220
| ~ spl21_138
| ~ spl21_144 ),
inference(avatar_split_clause,[],[f1231,f1216,f1166,f2056]) ).
fof(f1231,plain,
( ! [X2,X0,X1] :
( sP2(X0,relation_dom(X1))
| ~ empty(relation_dom(X0))
| ~ sP2(X1,X2)
| ~ empty(X2) )
| ~ spl21_138
| ~ spl21_144 ),
inference(resolution,[],[f1217,f1167]) ).
fof(f2034,plain,
( spl21_219
| ~ spl21_77
| ~ spl21_111 ),
inference(avatar_split_clause,[],[f952,f870,f679,f2032]) ).
fof(f2032,plain,
( spl21_219
<=> ! [X0] :
( sK8(X0,sK14) = apply(X0,sK9(X0,sK14))
| sP2(X0,sK14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_219])]) ).
fof(f952,plain,
( ! [X0] :
( sK8(X0,sK14) = apply(X0,sK9(X0,sK14))
| sP2(X0,sK14) )
| ~ spl21_77
| ~ spl21_111 ),
inference(resolution,[],[f871,f680]) ).
fof(f2010,plain,
( spl21_218
| ~ spl21_138
| ~ spl21_146 ),
inference(avatar_split_clause,[],[f1267,f1243,f1166,f2008]) ).
fof(f1267,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ sP3(X1)
| ~ sP2(X1,X2)
| ~ empty(X2) )
| ~ spl21_138
| ~ spl21_146 ),
inference(resolution,[],[f1244,f1167]) ).
fof(f2006,plain,
( spl21_217
| ~ spl21_45
| ~ spl21_145 ),
inference(avatar_split_clause,[],[f1241,f1220,f429,f2004]) ).
fof(f2004,plain,
( spl21_217
<=> ! [X0,X1] :
( sP2(X0,X1)
| ~ empty(X1)
| ~ in(relation_dom(X0),sK9(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_217])]) ).
fof(f1241,plain,
( ! [X0,X1] :
( sP2(X0,X1)
| ~ empty(X1)
| ~ in(relation_dom(X0),sK9(X0,X1)) )
| ~ spl21_45
| ~ spl21_145 ),
inference(resolution,[],[f1221,f430]) ).
fof(f2002,plain,
( spl21_216
| ~ spl21_46
| ~ spl21_145 ),
inference(avatar_split_clause,[],[f1240,f1220,f433,f2000]) ).
fof(f2000,plain,
( spl21_216
<=> ! [X0,X1] :
( sP2(X0,X1)
| ~ empty(X1)
| element(sK9(X0,X1),relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_216])]) ).
fof(f1240,plain,
( ! [X0,X1] :
( sP2(X0,X1)
| ~ empty(X1)
| element(sK9(X0,X1),relation_dom(X0)) )
| ~ spl21_46
| ~ spl21_145 ),
inference(resolution,[],[f1221,f434]) ).
fof(f1998,plain,
( spl21_215
| ~ spl21_120
| ~ spl21_168 ),
inference(avatar_split_clause,[],[f1455,f1452,f999,f1996]) ).
fof(f1455,plain,
( ! [X0] :
( ~ empty(X0)
| empty(relation_inverse_image(sK4,relation_image(sK4,X0))) )
| ~ spl21_120
| ~ spl21_168 ),
inference(resolution,[],[f1453,f1000]) ).
fof(f1994,plain,
( spl21_214
| ~ spl21_45
| ~ spl21_144 ),
inference(avatar_split_clause,[],[f1230,f1216,f429,f1992]) ).
fof(f1992,plain,
( spl21_214
<=> ! [X0,X1] :
( sP2(X0,X1)
| ~ empty(relation_dom(X0))
| ~ in(X1,sK8(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_214])]) ).
fof(f1230,plain,
( ! [X0,X1] :
( sP2(X0,X1)
| ~ empty(relation_dom(X0))
| ~ in(X1,sK8(X0,X1)) )
| ~ spl21_45
| ~ spl21_144 ),
inference(resolution,[],[f1217,f430]) ).
fof(f1990,plain,
( spl21_213
| ~ spl21_46
| ~ spl21_144 ),
inference(avatar_split_clause,[],[f1229,f1216,f433,f1988]) ).
fof(f1229,plain,
( ! [X0,X1] :
( sP2(X0,X1)
| ~ empty(relation_dom(X0))
| element(sK8(X0,X1),X1) )
| ~ spl21_46
| ~ spl21_144 ),
inference(resolution,[],[f1217,f434]) ).
fof(f1986,plain,
( spl21_212
| ~ spl21_72
| ~ spl21_126 ),
inference(avatar_split_clause,[],[f1064,f1052,f644,f1984]) ).
fof(f1984,plain,
( spl21_212
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,relation_dom(X2))
| ~ sP2(X2,sK11(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_212])]) ).
fof(f1064,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,relation_dom(X2))
| ~ sP2(X2,sK11(powerset(X0))) )
| ~ spl21_72
| ~ spl21_126 ),
inference(resolution,[],[f1053,f645]) ).
fof(f1943,plain,
( spl21_211
| ~ spl21_138
| ~ spl21_145 ),
inference(avatar_split_clause,[],[f1237,f1220,f1166,f1941]) ).
fof(f1237,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1)
| ~ empty(X1)
| ~ sP2(X0,X2)
| ~ empty(X2) )
| ~ spl21_138
| ~ spl21_145 ),
inference(resolution,[],[f1221,f1167]) ).
fof(f1939,plain,
( spl21_210
| ~ spl21_126
| ~ spl21_144 ),
inference(avatar_split_clause,[],[f1235,f1216,f1052,f1937]) ).
fof(f1235,plain,
( ! [X0,X1] :
( sP2(X0,sK11(powerset(X1)))
| ~ empty(relation_dom(X0))
| ~ empty(X1) )
| ~ spl21_126
| ~ spl21_144 ),
inference(resolution,[],[f1217,f1053]) ).
fof(f1935,plain,
( spl21_209
| ~ spl21_33
| ~ spl21_143 ),
inference(avatar_split_clause,[],[f1227,f1212,f363,f1933]) ).
fof(f1212,plain,
( spl21_143
<=> ! [X0,X1] :
( sK14 = relation_inverse_image(X0,singleton(X1))
| ~ relation(X0)
| ~ empty(relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_143])]) ).
fof(f1227,plain,
( ! [X0,X1] :
( ~ relation(X0)
| sK14 = relation_inverse_image(X0,singleton(X1))
| ~ empty(X0) )
| ~ spl21_33
| ~ spl21_143 ),
inference(resolution,[],[f1213,f364]) ).
fof(f1213,plain,
( ! [X0,X1] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| sK14 = relation_inverse_image(X0,singleton(X1)) )
| ~ spl21_143 ),
inference(avatar_component_clause,[],[f1212]) ).
fof(f1931,plain,
( spl21_208
| ~ spl21_45
| ~ spl21_140 ),
inference(avatar_split_clause,[],[f1201,f1193,f429,f1929]) ).
fof(f1929,plain,
( spl21_208
<=> ! [X0] :
( empty(powerset(X0))
| empty(X0)
| ~ in(powerset(X0),sK5(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_208])]) ).
fof(f1193,plain,
( spl21_140
<=> ! [X0] :
( empty(powerset(X0))
| in(sK5(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_140])]) ).
fof(f1201,plain,
( ! [X0] :
( empty(powerset(X0))
| empty(X0)
| ~ in(powerset(X0),sK5(X0)) )
| ~ spl21_45
| ~ spl21_140 ),
inference(resolution,[],[f1194,f430]) ).
fof(f1194,plain,
( ! [X0] :
( in(sK5(X0),powerset(X0))
| empty(powerset(X0))
| empty(X0) )
| ~ spl21_140 ),
inference(avatar_component_clause,[],[f1193]) ).
fof(f1927,plain,
( spl21_207
| ~ spl21_45
| ~ spl21_139 ),
inference(avatar_split_clause,[],[f1198,f1189,f429,f1925]) ).
fof(f1198,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| ~ subset(X1,X0)
| ~ in(powerset(X0),X1) )
| ~ spl21_45
| ~ spl21_139 ),
inference(resolution,[],[f1190,f430]) ).
fof(f1923,plain,
( spl21_206
| ~ spl21_120
| ~ spl21_136 ),
inference(avatar_split_clause,[],[f1176,f1157,f999,f1921]) ).
fof(f1176,plain,
( ! [X0] :
( element(sK11(sK5(X0)),X0)
| empty(X0)
| empty(sK5(X0)) )
| ~ spl21_120
| ~ spl21_136 ),
inference(resolution,[],[f1158,f1000]) ).
fof(f1919,plain,
( spl21_205
| ~ spl21_120
| ~ spl21_134 ),
inference(avatar_split_clause,[],[f1148,f1094,f999,f1917]) ).
fof(f1148,plain,
( ! [X0] :
( element(sK11(sK11(powerset(X0))),X0)
| empty(sK11(powerset(X0))) )
| ~ spl21_120
| ~ spl21_134 ),
inference(resolution,[],[f1095,f1000]) ).
fof(f1862,plain,
( ~ spl21_204
| ~ spl21_23
| ~ spl21_170 ),
inference(avatar_split_clause,[],[f1482,f1478,f312,f1859]) ).
fof(f1482,plain,
( ~ empty(relation_image(sK4,singleton(sK6(sK4))))
| ~ spl21_23
| ~ spl21_170 ),
inference(superposition,[],[f313,f1480]) ).
fof(f1813,plain,
( spl21_203
| ~ spl21_38
| ~ spl21_146 ),
inference(avatar_split_clause,[],[f1269,f1243,f383,f1811]) ).
fof(f383,plain,
( spl21_38
<=> ! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_38])]) ).
fof(f1269,plain,
( ! [X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ sP3(X1)
| ~ empty(relation_dom(X1)) )
| ~ spl21_38
| ~ spl21_146 ),
inference(resolution,[],[f1244,f384]) ).
fof(f384,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) )
| ~ spl21_38 ),
inference(avatar_component_clause,[],[f383]) ).
fof(f1809,plain,
( spl21_202
| ~ spl21_35
| ~ spl21_132 ),
inference(avatar_split_clause,[],[f1127,f1086,f371,f1807]) ).
fof(f1127,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_dom(relation_dom(X1)) = X0
| ~ empty(X1) )
| ~ spl21_35
| ~ spl21_132 ),
inference(resolution,[],[f1087,f372]) ).
fof(f1805,plain,
( spl21_201
| ~ spl21_33
| ~ spl21_132 ),
inference(avatar_split_clause,[],[f1126,f1086,f363,f1803]) ).
fof(f1126,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_dom(relation_rng(X1)) = X0
| ~ empty(X1) )
| ~ spl21_33
| ~ spl21_132 ),
inference(resolution,[],[f1087,f364]) ).
fof(f1801,plain,
( spl21_200
| ~ spl21_35
| ~ spl21_131 ),
inference(avatar_split_clause,[],[f1111,f1082,f371,f1799]) ).
fof(f1111,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_rng(relation_dom(X1)) = X0
| ~ empty(X1) )
| ~ spl21_35
| ~ spl21_131 ),
inference(resolution,[],[f1083,f372]) ).
fof(f1797,plain,
( spl21_199
| ~ spl21_33
| ~ spl21_131 ),
inference(avatar_split_clause,[],[f1110,f1082,f363,f1795]) ).
fof(f1110,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_rng(relation_rng(X1)) = X0
| ~ empty(X1) )
| ~ spl21_33
| ~ spl21_131 ),
inference(resolution,[],[f1083,f364]) ).
fof(f1778,plain,
( spl21_198
| ~ spl21_38
| ~ spl21_144 ),
inference(avatar_split_clause,[],[f1228,f1216,f383,f1776]) ).
fof(f1228,plain,
( ! [X0,X1] :
( sP2(X0,X1)
| ~ empty(relation_dom(X0))
| ~ empty(X1) )
| ~ spl21_38
| ~ spl21_144 ),
inference(resolution,[],[f1217,f384]) ).
fof(f1774,plain,
( spl21_197
| ~ spl21_104
| ~ spl21_142 ),
inference(avatar_split_clause,[],[f1226,f1207,f843,f1772]) ).
fof(f843,plain,
( spl21_104
<=> ! [X0] :
( ~ empty(X0)
| function(relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_104])]) ).
fof(f1207,plain,
( spl21_142
<=> ! [X0] :
( ~ function(relation_dom(X0))
| ~ empty(relation_dom(X0))
| one_to_one(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_142])]) ).
fof(f1226,plain,
( ! [X0] :
( ~ empty(relation_dom(X0))
| one_to_one(relation_dom(X0))
| ~ empty(X0) )
| ~ spl21_104
| ~ spl21_142 ),
inference(duplicate_literal_removal,[],[f1225]) ).
fof(f1225,plain,
( ! [X0] :
( ~ empty(relation_dom(X0))
| one_to_one(relation_dom(X0))
| ~ empty(X0)
| ~ empty(X0) )
| ~ spl21_104
| ~ spl21_142 ),
inference(resolution,[],[f1208,f844]) ).
fof(f844,plain,
( ! [X0] :
( function(relation_dom(X0))
| ~ empty(X0) )
| ~ spl21_104 ),
inference(avatar_component_clause,[],[f843]) ).
fof(f1208,plain,
( ! [X0] :
( ~ function(relation_dom(X0))
| ~ empty(relation_dom(X0))
| one_to_one(relation_dom(X0))
| ~ empty(X0) )
| ~ spl21_142 ),
inference(avatar_component_clause,[],[f1207]) ).
fof(f1770,plain,
( spl21_196
| ~ spl21_103
| ~ spl21_141 ),
inference(avatar_split_clause,[],[f1224,f1203,f839,f1768]) ).
fof(f839,plain,
( spl21_103
<=> ! [X0] :
( ~ empty(X0)
| function(relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_103])]) ).
fof(f1203,plain,
( spl21_141
<=> ! [X0] :
( ~ function(relation_rng(X0))
| ~ empty(relation_rng(X0))
| one_to_one(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_141])]) ).
fof(f1224,plain,
( ! [X0] :
( ~ empty(relation_rng(X0))
| one_to_one(relation_rng(X0))
| ~ empty(X0) )
| ~ spl21_103
| ~ spl21_141 ),
inference(duplicate_literal_removal,[],[f1223]) ).
fof(f1223,plain,
( ! [X0] :
( ~ empty(relation_rng(X0))
| one_to_one(relation_rng(X0))
| ~ empty(X0)
| ~ empty(X0) )
| ~ spl21_103
| ~ spl21_141 ),
inference(resolution,[],[f1204,f840]) ).
fof(f840,plain,
( ! [X0] :
( function(relation_rng(X0))
| ~ empty(X0) )
| ~ spl21_103 ),
inference(avatar_component_clause,[],[f839]) ).
fof(f1204,plain,
( ! [X0] :
( ~ function(relation_rng(X0))
| ~ empty(relation_rng(X0))
| one_to_one(relation_rng(X0))
| ~ empty(X0) )
| ~ spl21_141 ),
inference(avatar_component_clause,[],[f1203]) ).
fof(f1766,plain,
( spl21_195
| ~ spl21_120
| ~ spl21_138 ),
inference(avatar_split_clause,[],[f1184,f1166,f999,f1764]) ).
fof(f1184,plain,
( ! [X0,X1] :
( ~ sP2(X0,X1)
| ~ empty(X1)
| empty(relation_dom(X0)) )
| ~ spl21_120
| ~ spl21_138 ),
inference(resolution,[],[f1167,f1000]) ).
fof(f1690,plain,
( ~ spl21_194
| ~ spl21_115
| ~ spl21_188 ),
inference(avatar_split_clause,[],[f1677,f1647,f977,f1687]) ).
fof(f1687,plain,
( spl21_194
<=> sP2(sK4,sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_194])]) ).
fof(f977,plain,
( spl21_115
<=> in(sK7(sK4),relation_dom(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_115])]) ).
fof(f1677,plain,
( ~ sP2(sK4,sK14)
| ~ spl21_115
| ~ spl21_188 ),
inference(resolution,[],[f1648,f978]) ).
fof(f978,plain,
( in(sK7(sK4),relation_dom(sK4))
| ~ spl21_115 ),
inference(avatar_component_clause,[],[f977]) ).
fof(f1669,plain,
( spl21_193
| ~ spl21_52
| ~ spl21_138 ),
inference(avatar_split_clause,[],[f1180,f1166,f490,f1667]) ).
fof(f1180,plain,
( ! [X0,X1] :
( ~ sP2(X0,X1)
| ~ empty(X1)
| sP0(X0) )
| ~ spl21_52
| ~ spl21_138 ),
inference(resolution,[],[f1167,f491]) ).
fof(f1665,plain,
( spl21_192
| ~ spl21_35
| ~ spl21_113 ),
inference(avatar_split_clause,[],[f1014,f969,f371,f1663]) ).
fof(f1014,plain,
( ! [X0] :
( sK14 = relation_dom(relation_dom(X0))
| ~ empty(X0) )
| ~ spl21_35
| ~ spl21_113 ),
inference(resolution,[],[f970,f372]) ).
fof(f1661,plain,
( spl21_191
| ~ spl21_33
| ~ spl21_113 ),
inference(avatar_split_clause,[],[f1013,f969,f363,f1659]) ).
fof(f1013,plain,
( ! [X0] :
( sK14 = relation_dom(relation_rng(X0))
| ~ empty(X0) )
| ~ spl21_33
| ~ spl21_113 ),
inference(resolution,[],[f970,f364]) ).
fof(f1657,plain,
( spl21_190
| ~ spl21_35
| ~ spl21_112 ),
inference(avatar_split_clause,[],[f1003,f965,f371,f1655]) ).
fof(f1003,plain,
( ! [X0] :
( sK14 = relation_rng(relation_dom(X0))
| ~ empty(X0) )
| ~ spl21_35
| ~ spl21_112 ),
inference(resolution,[],[f966,f372]) ).
fof(f1653,plain,
( spl21_189
| ~ spl21_33
| ~ spl21_112 ),
inference(avatar_split_clause,[],[f1002,f965,f363,f1651]) ).
fof(f1002,plain,
( ! [X0] :
( sK14 = relation_rng(relation_rng(X0))
| ~ empty(X0) )
| ~ spl21_33
| ~ spl21_112 ),
inference(resolution,[],[f966,f364]) ).
fof(f1649,plain,
( spl21_188
| ~ spl21_72
| ~ spl21_111 ),
inference(avatar_split_clause,[],[f954,f870,f644,f1647]) ).
fof(f954,plain,
( ! [X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ sP2(X1,sK14) )
| ~ spl21_72
| ~ spl21_111 ),
inference(resolution,[],[f871,f645]) ).
fof(f1632,plain,
( spl21_187
| ~ spl21_111
| ~ spl21_144 ),
inference(avatar_split_clause,[],[f1236,f1216,f870,f1630]) ).
fof(f1236,plain,
( ! [X0] :
( sP2(X0,sK14)
| ~ empty(relation_dom(X0)) )
| ~ spl21_111
| ~ spl21_144 ),
inference(resolution,[],[f1217,f871]) ).
fof(f1628,plain,
( spl21_186
| ~ spl21_120
| ~ spl21_126 ),
inference(avatar_split_clause,[],[f1061,f1052,f999,f1626]) ).
fof(f1061,plain,
( ! [X0] :
( ~ empty(X0)
| empty(sK11(powerset(X0))) )
| ~ spl21_120
| ~ spl21_126 ),
inference(resolution,[],[f1053,f1000]) ).
fof(f1624,plain,
( spl21_185
| ~ spl21_45
| ~ spl21_120 ),
inference(avatar_split_clause,[],[f1027,f999,f429,f1622]) ).
fof(f1622,plain,
( spl21_185
<=> ! [X0] :
( empty(X0)
| ~ in(X0,sK11(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_185])]) ).
fof(f1027,plain,
( ! [X0] :
( empty(X0)
| ~ in(X0,sK11(X0)) )
| ~ spl21_45
| ~ spl21_120 ),
inference(resolution,[],[f1000,f430]) ).
fof(f1612,plain,
( spl21_184
| ~ spl21_104
| ~ spl21_130 ),
inference(avatar_split_clause,[],[f1109,f1078,f843,f1610]) ).
fof(f1610,plain,
( spl21_184
<=> ! [X0] :
( sP3(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_184])]) ).
fof(f1078,plain,
( spl21_130
<=> ! [X0] :
( ~ function(relation_dom(X0))
| sP3(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_130])]) ).
fof(f1109,plain,
( ! [X0] :
( sP3(relation_dom(X0))
| ~ empty(X0) )
| ~ spl21_104
| ~ spl21_130 ),
inference(duplicate_literal_removal,[],[f1108]) ).
fof(f1108,plain,
( ! [X0] :
( sP3(relation_dom(X0))
| ~ empty(X0)
| ~ empty(X0) )
| ~ spl21_104
| ~ spl21_130 ),
inference(resolution,[],[f1079,f844]) ).
fof(f1079,plain,
( ! [X0] :
( ~ function(relation_dom(X0))
| sP3(relation_dom(X0))
| ~ empty(X0) )
| ~ spl21_130 ),
inference(avatar_component_clause,[],[f1078]) ).
fof(f1608,plain,
( spl21_183
| ~ spl21_103
| ~ spl21_129 ),
inference(avatar_split_clause,[],[f1107,f1074,f839,f1606]) ).
fof(f1606,plain,
( spl21_183
<=> ! [X0] :
( sP3(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_183])]) ).
fof(f1074,plain,
( spl21_129
<=> ! [X0] :
( ~ function(relation_rng(X0))
| sP3(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_129])]) ).
fof(f1107,plain,
( ! [X0] :
( sP3(relation_rng(X0))
| ~ empty(X0) )
| ~ spl21_103
| ~ spl21_129 ),
inference(duplicate_literal_removal,[],[f1106]) ).
fof(f1106,plain,
( ! [X0] :
( sP3(relation_rng(X0))
| ~ empty(X0)
| ~ empty(X0) )
| ~ spl21_103
| ~ spl21_129 ),
inference(resolution,[],[f1075,f840]) ).
fof(f1075,plain,
( ! [X0] :
( ~ function(relation_rng(X0))
| sP3(relation_rng(X0))
| ~ empty(X0) )
| ~ spl21_129 ),
inference(avatar_component_clause,[],[f1074]) ).
fof(f1604,plain,
( spl21_182
| ~ spl21_104
| ~ spl21_128 ),
inference(avatar_split_clause,[],[f1105,f1070,f843,f1602]) ).
fof(f1602,plain,
( spl21_182
<=> ! [X0] :
( sP1(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_182])]) ).
fof(f1070,plain,
( spl21_128
<=> ! [X0] :
( ~ function(relation_dom(X0))
| sP1(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_128])]) ).
fof(f1105,plain,
( ! [X0] :
( sP1(relation_dom(X0))
| ~ empty(X0) )
| ~ spl21_104
| ~ spl21_128 ),
inference(duplicate_literal_removal,[],[f1104]) ).
fof(f1104,plain,
( ! [X0] :
( sP1(relation_dom(X0))
| ~ empty(X0)
| ~ empty(X0) )
| ~ spl21_104
| ~ spl21_128 ),
inference(resolution,[],[f1071,f844]) ).
fof(f1071,plain,
( ! [X0] :
( ~ function(relation_dom(X0))
| sP1(relation_dom(X0))
| ~ empty(X0) )
| ~ spl21_128 ),
inference(avatar_component_clause,[],[f1070]) ).
fof(f1600,plain,
( ~ spl21_58
| ~ spl21_181
| ~ spl21_47
| ~ spl21_159 ),
inference(avatar_split_clause,[],[f1521,f1347,f437,f1597,f540]) ).
fof(f1597,plain,
( spl21_181
<=> empty(relation_rng(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_181])]) ).
fof(f1347,plain,
( spl21_159
<=> ! [X0] :
( ~ sP2(sK4,X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_159])]) ).
fof(f1521,plain,
( ~ empty(relation_rng(sK4))
| ~ sP3(sK4)
| ~ spl21_47
| ~ spl21_159 ),
inference(resolution,[],[f1348,f438]) ).
fof(f1348,plain,
( ! [X0] :
( ~ sP2(sK4,X0)
| ~ empty(X0) )
| ~ spl21_159 ),
inference(avatar_component_clause,[],[f1347]) ).
fof(f1595,plain,
( spl21_180
| ~ spl21_103
| ~ spl21_127 ),
inference(avatar_split_clause,[],[f1103,f1066,f839,f1593]) ).
fof(f1593,plain,
( spl21_180
<=> ! [X0] :
( sP1(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_180])]) ).
fof(f1066,plain,
( spl21_127
<=> ! [X0] :
( ~ function(relation_rng(X0))
| sP1(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_127])]) ).
fof(f1103,plain,
( ! [X0] :
( sP1(relation_rng(X0))
| ~ empty(X0) )
| ~ spl21_103
| ~ spl21_127 ),
inference(duplicate_literal_removal,[],[f1102]) ).
fof(f1102,plain,
( ! [X0] :
( sP1(relation_rng(X0))
| ~ empty(X0)
| ~ empty(X0) )
| ~ spl21_103
| ~ spl21_127 ),
inference(resolution,[],[f1067,f840]) ).
fof(f1067,plain,
( ! [X0] :
( ~ function(relation_rng(X0))
| sP1(relation_rng(X0))
| ~ empty(X0) )
| ~ spl21_127 ),
inference(avatar_component_clause,[],[f1066]) ).
fof(f1542,plain,
( spl21_179
| ~ spl21_5
| ~ spl21_85
| ~ spl21_113 ),
inference(avatar_split_clause,[],[f1020,f969,f729,f223,f1539]) ).
fof(f223,plain,
( spl21_5
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_5])]) ).
fof(f1020,plain,
( sK14 = relation_dom(sK14)
| ~ spl21_5
| ~ spl21_85
| ~ spl21_113 ),
inference(forward_demodulation,[],[f1015,f731]) ).
fof(f1015,plain,
( sK14 = relation_dom(empty_set)
| ~ spl21_5
| ~ spl21_113 ),
inference(resolution,[],[f970,f225]) ).
fof(f225,plain,
( empty(empty_set)
| ~ spl21_5 ),
inference(avatar_component_clause,[],[f223]) ).
fof(f1537,plain,
( spl21_178
| ~ spl21_5
| ~ spl21_85
| ~ spl21_112 ),
inference(avatar_split_clause,[],[f1009,f965,f729,f223,f1534]) ).
fof(f1009,plain,
( sK14 = relation_rng(sK14)
| ~ spl21_5
| ~ spl21_85
| ~ spl21_112 ),
inference(forward_demodulation,[],[f1004,f731]) ).
fof(f1004,plain,
( sK14 = relation_rng(empty_set)
| ~ spl21_5
| ~ spl21_112 ),
inference(resolution,[],[f966,f225]) ).
fof(f1532,plain,
( spl21_177
| ~ spl21_35
| ~ spl21_105 ),
inference(avatar_split_clause,[],[f955,f847,f371,f1530]) ).
fof(f847,plain,
( spl21_105
<=> ! [X0] :
( sP0(X0)
| ~ empty(relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_105])]) ).
fof(f955,plain,
( ! [X0] :
( sP0(X0)
| ~ empty(X0) )
| ~ spl21_35
| ~ spl21_105 ),
inference(resolution,[],[f848,f372]) ).
fof(f848,plain,
( ! [X0] :
( ~ empty(relation_dom(X0))
| sP0(X0) )
| ~ spl21_105 ),
inference(avatar_component_clause,[],[f847]) ).
fof(f1528,plain,
( spl21_176
| ~ spl21_37
| ~ spl21_101 ),
inference(avatar_split_clause,[],[f829,f826,f379,f1526]) ).
fof(f1526,plain,
( spl21_176
<=> ! [X0] : element(sK14,powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_176])]) ).
fof(f379,plain,
( spl21_37
<=> ! [X0] : element(sK12(X0),powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_37])]) ).
fof(f826,plain,
( spl21_101
<=> ! [X0] : sK12(X0) = sK14 ),
introduced(avatar_definition,[new_symbols(naming,[spl21_101])]) ).
fof(f829,plain,
( ! [X0] : element(sK14,powerset(X0))
| ~ spl21_37
| ~ spl21_101 ),
inference(superposition,[],[f380,f827]) ).
fof(f827,plain,
( ! [X0] : sK12(X0) = sK14
| ~ spl21_101 ),
inference(avatar_component_clause,[],[f826]) ).
fof(f380,plain,
( ! [X0] : element(sK12(X0),powerset(X0))
| ~ spl21_37 ),
inference(avatar_component_clause,[],[f379]) ).
fof(f1520,plain,
( spl21_175
| ~ spl21_119
| ~ spl21_40
| ~ spl21_97 ),
inference(avatar_split_clause,[],[f805,f800,f407,f994,f1517]) ).
fof(f1517,plain,
( spl21_175
<=> sP0(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_175])]) ).
fof(f994,plain,
( spl21_119
<=> one_to_one(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_119])]) ).
fof(f407,plain,
( spl21_40
<=> ! [X0] :
( sP0(X0)
| ~ one_to_one(X0)
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_40])]) ).
fof(f800,plain,
( spl21_97
<=> sP1(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_97])]) ).
fof(f805,plain,
( ~ one_to_one(sK14)
| sP0(sK14)
| ~ spl21_40
| ~ spl21_97 ),
inference(resolution,[],[f802,f408]) ).
fof(f408,plain,
( ! [X0] :
( ~ sP1(X0)
| ~ one_to_one(X0)
| sP0(X0) )
| ~ spl21_40 ),
inference(avatar_component_clause,[],[f407]) ).
fof(f802,plain,
( sP1(sK14)
| ~ spl21_97 ),
inference(avatar_component_clause,[],[f800]) ).
fof(f1515,plain,
( spl21_174
| ~ spl21_16
| ~ spl21_40
| ~ spl21_96 ),
inference(avatar_split_clause,[],[f798,f793,f407,f278,f1512]) ).
fof(f1512,plain,
( spl21_174
<=> sP0(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_174])]) ).
fof(f278,plain,
( spl21_16
<=> one_to_one(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_16])]) ).
fof(f793,plain,
( spl21_96
<=> sP1(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_96])]) ).
fof(f798,plain,
( ~ one_to_one(sK18)
| sP0(sK18)
| ~ spl21_40
| ~ spl21_96 ),
inference(resolution,[],[f795,f408]) ).
fof(f795,plain,
( sP1(sK18)
| ~ spl21_96 ),
inference(avatar_component_clause,[],[f793]) ).
fof(f1509,plain,
( spl21_117
| ~ spl21_173
| ~ spl21_41
| ~ spl21_95 ),
inference(avatar_split_clause,[],[f790,f786,f411,f1506,f985]) ).
fof(f985,plain,
( spl21_117
<=> one_to_one(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_117])]) ).
fof(f411,plain,
( spl21_41
<=> ! [X0] :
( one_to_one(X0)
| ~ sP0(X0)
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_41])]) ).
fof(f786,plain,
( spl21_95
<=> sP1(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_95])]) ).
fof(f790,plain,
( ~ sP0(sK17)
| one_to_one(sK17)
| ~ spl21_41
| ~ spl21_95 ),
inference(resolution,[],[f788,f412]) ).
fof(f412,plain,
( ! [X0] :
( ~ sP1(X0)
| ~ sP0(X0)
| one_to_one(X0) )
| ~ spl21_41 ),
inference(avatar_component_clause,[],[f411]) ).
fof(f788,plain,
( sP1(sK17)
| ~ spl21_95 ),
inference(avatar_component_clause,[],[f786]) ).
fof(f1500,plain,
( spl21_172
| ~ spl21_170
| ~ spl21_171 ),
inference(avatar_split_clause,[],[f1495,f1491,f1478,f1497]) ).
fof(f1491,plain,
( spl21_171
<=> relation_image(sK4,singleton(sK7(sK4))) = singleton(apply(sK4,sK6(sK4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_171])]) ).
fof(f1495,plain,
( relation_image(sK4,singleton(sK7(sK4))) = relation_image(sK4,singleton(sK6(sK4)))
| ~ spl21_170
| ~ spl21_171 ),
inference(forward_demodulation,[],[f1493,f1480]) ).
fof(f1493,plain,
( relation_image(sK4,singleton(sK7(sK4))) = singleton(apply(sK4,sK6(sK4)))
| ~ spl21_171 ),
inference(avatar_component_clause,[],[f1491]) ).
fof(f1494,plain,
( spl21_71
| ~ spl21_2
| spl21_171
| ~ spl21_1
| ~ spl21_89
| ~ spl21_163 ),
inference(avatar_split_clause,[],[f1405,f1363,f748,f204,f1491,f209,f639]) ).
fof(f209,plain,
( spl21_2
<=> function(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_2])]) ).
fof(f748,plain,
( spl21_89
<=> apply(sK4,sK6(sK4)) = apply(sK4,sK7(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_89])]) ).
fof(f1363,plain,
( spl21_163
<=> ! [X0] :
( relation_image(X0,singleton(sK7(X0))) = singleton(apply(X0,sK7(X0)))
| ~ function(X0)
| ~ relation(X0)
| sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_163])]) ).
fof(f1405,plain,
( relation_image(sK4,singleton(sK7(sK4))) = singleton(apply(sK4,sK6(sK4)))
| ~ function(sK4)
| sP0(sK4)
| ~ spl21_1
| ~ spl21_89
| ~ spl21_163 ),
inference(forward_demodulation,[],[f1394,f750]) ).
fof(f750,plain,
( apply(sK4,sK6(sK4)) = apply(sK4,sK7(sK4))
| ~ spl21_89 ),
inference(avatar_component_clause,[],[f748]) ).
fof(f1394,plain,
( ~ function(sK4)
| relation_image(sK4,singleton(sK7(sK4))) = singleton(apply(sK4,sK7(sK4)))
| sP0(sK4)
| ~ spl21_1
| ~ spl21_163 ),
inference(resolution,[],[f1364,f206]) ).
fof(f1364,plain,
( ! [X0] :
( ~ relation(X0)
| ~ function(X0)
| relation_image(X0,singleton(sK7(X0))) = singleton(apply(X0,sK7(X0)))
| sP0(X0) )
| ~ spl21_163 ),
inference(avatar_component_clause,[],[f1363]) ).
fof(f1481,plain,
( spl21_71
| spl21_170
| ~ spl21_2
| ~ spl21_1
| ~ spl21_162 ),
inference(avatar_split_clause,[],[f1374,f1359,f204,f209,f1478,f639]) ).
fof(f1374,plain,
( ~ function(sK4)
| singleton(apply(sK4,sK6(sK4))) = relation_image(sK4,singleton(sK6(sK4)))
| sP0(sK4)
| ~ spl21_1
| ~ spl21_162 ),
inference(resolution,[],[f1360,f206]) ).
fof(f1467,plain,
( spl21_169
| ~ spl21_4
| ~ spl21_135 ),
inference(avatar_split_clause,[],[f1170,f1153,f219,f1465]) ).
fof(f1153,plain,
( spl21_135
<=> ! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_135])]) ).
fof(f1170,plain,
( ! [X0,X1] :
( ~ in(X0,relation_inverse_image(sK4,relation_image(sK4,X1)))
| element(X0,X1) )
| ~ spl21_4
| ~ spl21_135 ),
inference(resolution,[],[f1154,f220]) ).
fof(f1154,plain,
( ! [X2,X0,X1] :
( ~ subset(X2,X1)
| ~ in(X0,X2)
| element(X0,X1) )
| ~ spl21_135 ),
inference(avatar_component_clause,[],[f1153]) ).
fof(f1454,plain,
( spl21_168
| ~ spl21_4
| ~ spl21_133 ),
inference(avatar_split_clause,[],[f1143,f1090,f219,f1452]) ).
fof(f1090,plain,
( spl21_133
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,X2)
| ~ subset(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_133])]) ).
fof(f1143,plain,
( ! [X0,X1] :
( ~ in(X0,relation_inverse_image(sK4,relation_image(sK4,X1)))
| ~ empty(X1) )
| ~ spl21_4
| ~ spl21_133 ),
inference(resolution,[],[f1091,f220]) ).
fof(f1091,plain,
( ! [X2,X0,X1] :
( ~ subset(X2,X0)
| ~ in(X1,X2)
| ~ empty(X0) )
| ~ spl21_133 ),
inference(avatar_component_clause,[],[f1090]) ).
fof(f1445,plain,
( spl21_167
| ~ spl21_77
| ~ spl21_78 ),
inference(avatar_split_clause,[],[f692,f683,f679,f1443]) ).
fof(f692,plain,
( ! [X0,X1] :
( relation_image(X0,singleton(sK8(X1,relation_dom(X0)))) = singleton(apply(X0,sK8(X1,relation_dom(X0))))
| ~ function(X0)
| ~ relation(X0)
| sK8(X1,relation_dom(X0)) = apply(X1,sK9(X1,relation_dom(X0)))
| sP2(X1,relation_dom(X0)) )
| ~ spl21_77
| ~ spl21_78 ),
inference(resolution,[],[f684,f680]) ).
fof(f1436,plain,
( spl21_166
| ~ spl21_76
| ~ spl21_78 ),
inference(avatar_split_clause,[],[f693,f683,f668,f1434]) ).
fof(f693,plain,
( ! [X0,X1] :
( relation_image(X0,singleton(sK8(X1,relation_dom(X0)))) = singleton(apply(X0,sK8(X1,relation_dom(X0))))
| ~ function(X0)
| ~ relation(X0)
| in(sK9(X1,relation_dom(X0)),relation_dom(X1))
| sP2(X1,relation_dom(X0)) )
| ~ spl21_76
| ~ spl21_78 ),
inference(resolution,[],[f684,f669]) ).
fof(f1419,plain,
( spl21_165
| ~ spl21_72
| ~ spl21_78 ),
inference(avatar_split_clause,[],[f694,f683,f644,f1417]) ).
fof(f694,plain,
( ! [X2,X0,X1] :
( relation_image(X0,singleton(apply(X1,X2))) = singleton(apply(X0,apply(X1,X2)))
| ~ function(X0)
| ~ relation(X0)
| ~ in(X2,relation_dom(X1))
| ~ sP2(X1,relation_dom(X0)) )
| ~ spl21_72
| ~ spl21_78 ),
inference(resolution,[],[f684,f645]) ).
fof(f1415,plain,
( spl21_164
| ~ spl21_76
| ~ spl21_78 ),
inference(avatar_split_clause,[],[f691,f683,f668,f1413]) ).
fof(f691,plain,
( ! [X0,X1] :
( relation_image(X0,singleton(sK9(X0,X1))) = singleton(apply(X0,sK9(X0,X1)))
| ~ function(X0)
| ~ relation(X0)
| in(sK8(X0,X1),X1)
| sP2(X0,X1) )
| ~ spl21_76
| ~ spl21_78 ),
inference(resolution,[],[f684,f669]) ).
fof(f1365,plain,
( spl21_163
| ~ spl21_53
| ~ spl21_78 ),
inference(avatar_split_clause,[],[f690,f683,f494,f1363]) ).
fof(f494,plain,
( spl21_53
<=> ! [X0] :
( sP0(X0)
| in(sK7(X0),relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_53])]) ).
fof(f690,plain,
( ! [X0] :
( relation_image(X0,singleton(sK7(X0))) = singleton(apply(X0,sK7(X0)))
| ~ function(X0)
| ~ relation(X0)
| sP0(X0) )
| ~ spl21_53
| ~ spl21_78 ),
inference(resolution,[],[f684,f495]) ).
fof(f495,plain,
( ! [X0] :
( in(sK7(X0),relation_dom(X0))
| sP0(X0) )
| ~ spl21_53 ),
inference(avatar_component_clause,[],[f494]) ).
fof(f1361,plain,
( spl21_162
| ~ spl21_52
| ~ spl21_78 ),
inference(avatar_split_clause,[],[f689,f683,f490,f1359]) ).
fof(f689,plain,
( ! [X0] :
( relation_image(X0,singleton(sK6(X0))) = singleton(apply(X0,sK6(X0)))
| ~ function(X0)
| ~ relation(X0)
| sP0(X0) )
| ~ spl21_52
| ~ spl21_78 ),
inference(resolution,[],[f684,f491]) ).
fof(f1357,plain,
( spl21_161
| ~ spl21_45
| ~ spl21_77 ),
inference(avatar_split_clause,[],[f687,f679,f429,f1355]) ).
fof(f1355,plain,
( spl21_161
<=> ! [X0,X1] :
( sK8(X0,X1) = apply(X0,sK9(X0,X1))
| sP2(X0,X1)
| ~ in(X1,sK8(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_161])]) ).
fof(f687,plain,
( ! [X0,X1] :
( sK8(X0,X1) = apply(X0,sK9(X0,X1))
| sP2(X0,X1)
| ~ in(X1,sK8(X0,X1)) )
| ~ spl21_45
| ~ spl21_77 ),
inference(resolution,[],[f680,f430]) ).
fof(f1353,plain,
( spl21_160
| ~ spl21_46
| ~ spl21_77 ),
inference(avatar_split_clause,[],[f686,f679,f433,f1351]) ).
fof(f686,plain,
( ! [X0,X1] :
( sK8(X0,X1) = apply(X0,sK9(X0,X1))
| sP2(X0,X1)
| element(sK8(X0,X1),X1) )
| ~ spl21_46
| ~ spl21_77 ),
inference(resolution,[],[f680,f434]) ).
fof(f1349,plain,
( spl21_159
| ~ spl21_115
| ~ spl21_138 ),
inference(avatar_split_clause,[],[f1183,f1166,f977,f1347]) ).
fof(f1183,plain,
( ! [X0] :
( ~ sP2(sK4,X0)
| ~ empty(X0) )
| ~ spl21_115
| ~ spl21_138 ),
inference(resolution,[],[f1167,f978]) ).
fof(f1320,plain,
( spl21_158
| ~ spl21_38
| ~ spl21_77 ),
inference(avatar_split_clause,[],[f688,f679,f383,f1318]) ).
fof(f688,plain,
( ! [X0,X1] :
( sK8(X0,X1) = apply(X0,sK9(X0,X1))
| sP2(X0,X1)
| ~ empty(X1) )
| ~ spl21_38
| ~ spl21_77 ),
inference(resolution,[],[f680,f384]) ).
fof(f1316,plain,
( spl21_157
| ~ spl21_45
| ~ spl21_76 ),
inference(avatar_split_clause,[],[f676,f668,f429,f1314]) ).
fof(f1314,plain,
( spl21_157
<=> ! [X0,X1] :
( in(sK9(X0,X1),relation_dom(X0))
| sP2(X0,X1)
| ~ in(X1,sK8(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_157])]) ).
fof(f676,plain,
( ! [X0,X1] :
( in(sK9(X0,X1),relation_dom(X0))
| sP2(X0,X1)
| ~ in(X1,sK8(X0,X1)) )
| ~ spl21_45
| ~ spl21_76 ),
inference(resolution,[],[f669,f430]) ).
fof(f1312,plain,
( spl21_156
| ~ spl21_46
| ~ spl21_76 ),
inference(avatar_split_clause,[],[f675,f668,f433,f1310]) ).
fof(f675,plain,
( ! [X0,X1] :
( in(sK9(X0,X1),relation_dom(X0))
| sP2(X0,X1)
| element(sK8(X0,X1),X1) )
| ~ spl21_46
| ~ spl21_76 ),
inference(resolution,[],[f669,f434]) ).
fof(f1308,plain,
( spl21_155
| ~ spl21_45
| ~ spl21_76 ),
inference(avatar_split_clause,[],[f673,f668,f429,f1306]) ).
fof(f673,plain,
( ! [X0,X1] :
( in(sK8(X0,X1),X1)
| sP2(X0,X1)
| ~ in(relation_dom(X0),sK9(X0,X1)) )
| ~ spl21_45
| ~ spl21_76 ),
inference(resolution,[],[f669,f430]) ).
fof(f1304,plain,
( spl21_154
| ~ spl21_46
| ~ spl21_76 ),
inference(avatar_split_clause,[],[f672,f668,f433,f1302]) ).
fof(f672,plain,
( ! [X0,X1] :
( in(sK8(X0,X1),X1)
| sP2(X0,X1)
| element(sK9(X0,X1),relation_dom(X0)) )
| ~ spl21_46
| ~ spl21_76 ),
inference(resolution,[],[f669,f434]) ).
fof(f1300,plain,
( ~ spl21_153
| ~ spl21_45
| ~ spl21_115 ),
inference(avatar_split_clause,[],[f1100,f977,f429,f1297]) ).
fof(f1297,plain,
( spl21_153
<=> in(relation_dom(sK4),sK7(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_153])]) ).
fof(f1100,plain,
( ~ in(relation_dom(sK4),sK7(sK4))
| ~ spl21_45
| ~ spl21_115 ),
inference(resolution,[],[f978,f430]) ).
fof(f1289,plain,
( spl21_152
| ~ spl21_47
| ~ spl21_75 ),
inference(avatar_split_clause,[],[f666,f663,f437,f1287]) ).
fof(f666,plain,
( ! [X0,X1] :
( ~ in(X0,relation_rng(X1))
| apply(X1,sK10(X1,X0)) = X0
| ~ sP3(X1) )
| ~ spl21_47
| ~ spl21_75 ),
inference(resolution,[],[f664,f438]) ).
fof(f1266,plain,
( spl21_151
| ~ spl21_45
| ~ spl21_74 ),
inference(avatar_split_clause,[],[f660,f653,f429,f1264]) ).
fof(f660,plain,
( ! [X0,X1] :
( sK14 = relation_inverse_image(X0,singleton(X1))
| ~ relation(X0)
| ~ in(relation_rng(X0),X1) )
| ~ spl21_45
| ~ spl21_74 ),
inference(resolution,[],[f654,f430]) ).
fof(f1262,plain,
( spl21_150
| ~ spl21_46
| ~ spl21_74 ),
inference(avatar_split_clause,[],[f659,f653,f433,f1260]) ).
fof(f1260,plain,
( spl21_150
<=> ! [X0,X1] :
( sK14 = relation_inverse_image(X0,singleton(X1))
| ~ relation(X0)
| element(X1,relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_150])]) ).
fof(f659,plain,
( ! [X0,X1] :
( sK14 = relation_inverse_image(X0,singleton(X1))
| ~ relation(X0)
| element(X1,relation_rng(X0)) )
| ~ spl21_46
| ~ spl21_74 ),
inference(resolution,[],[f654,f434]) ).
fof(f1258,plain,
( spl21_149
| ~ spl21_45
| ~ spl21_72 ),
inference(avatar_split_clause,[],[f657,f644,f429,f1256]) ).
fof(f657,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ sP2(X1,X2)
| ~ in(X2,apply(X1,X0)) )
| ~ spl21_45
| ~ spl21_72 ),
inference(resolution,[],[f645,f430]) ).
fof(f1254,plain,
( spl21_148
| ~ spl21_46
| ~ spl21_115 ),
inference(avatar_split_clause,[],[f1099,f977,f433,f1251]) ).
fof(f1251,plain,
( spl21_148
<=> element(sK7(sK4),relation_dom(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_148])]) ).
fof(f1099,plain,
( element(sK7(sK4),relation_dom(sK4))
| ~ spl21_46
| ~ spl21_115 ),
inference(resolution,[],[f978,f434]) ).
fof(f1249,plain,
( spl21_147
| ~ spl21_46
| ~ spl21_72 ),
inference(avatar_split_clause,[],[f656,f644,f433,f1247]) ).
fof(f656,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ sP2(X1,X2)
| element(apply(X1,X0),X2) )
| ~ spl21_46
| ~ spl21_72 ),
inference(resolution,[],[f645,f434]) ).
fof(f1245,plain,
( spl21_146
| ~ spl21_47
| ~ spl21_68 ),
inference(avatar_split_clause,[],[f647,f625,f437,f1243]) ).
fof(f647,plain,
( ! [X0,X1] :
( ~ in(X0,relation_rng(X1))
| in(sK10(X1,X0),relation_dom(X1))
| ~ sP3(X1) )
| ~ spl21_47
| ~ spl21_68 ),
inference(resolution,[],[f626,f438]) ).
fof(f1222,plain,
( spl21_145
| ~ spl21_38
| ~ spl21_76 ),
inference(avatar_split_clause,[],[f677,f668,f383,f1220]) ).
fof(f677,plain,
( ! [X0,X1] :
( in(sK9(X0,X1),relation_dom(X0))
| sP2(X0,X1)
| ~ empty(X1) )
| ~ spl21_38
| ~ spl21_76 ),
inference(resolution,[],[f669,f384]) ).
fof(f1218,plain,
( spl21_144
| ~ spl21_38
| ~ spl21_76 ),
inference(avatar_split_clause,[],[f674,f668,f383,f1216]) ).
fof(f674,plain,
( ! [X0,X1] :
( in(sK8(X0,X1),X1)
| sP2(X0,X1)
| ~ empty(relation_dom(X0)) )
| ~ spl21_38
| ~ spl21_76 ),
inference(resolution,[],[f669,f384]) ).
fof(f1214,plain,
( spl21_143
| ~ spl21_38
| ~ spl21_74 ),
inference(avatar_split_clause,[],[f661,f653,f383,f1212]) ).
fof(f661,plain,
( ! [X0,X1] :
( sK14 = relation_inverse_image(X0,singleton(X1))
| ~ relation(X0)
| ~ empty(relation_rng(X0)) )
| ~ spl21_38
| ~ spl21_74 ),
inference(resolution,[],[f654,f384]) ).
fof(f1209,plain,
( spl21_142
| ~ spl21_36
| ~ spl21_59 ),
inference(avatar_split_clause,[],[f557,f545,f375,f1207]) ).
fof(f545,plain,
( spl21_59
<=> ! [X0] :
( one_to_one(X0)
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_59])]) ).
fof(f557,plain,
( ! [X0] :
( ~ function(relation_dom(X0))
| ~ empty(relation_dom(X0))
| one_to_one(relation_dom(X0))
| ~ empty(X0) )
| ~ spl21_36
| ~ spl21_59 ),
inference(resolution,[],[f546,f376]) ).
fof(f546,plain,
( ! [X0] :
( ~ relation(X0)
| ~ function(X0)
| ~ empty(X0)
| one_to_one(X0) )
| ~ spl21_59 ),
inference(avatar_component_clause,[],[f545]) ).
fof(f1205,plain,
( spl21_141
| ~ spl21_34
| ~ spl21_59 ),
inference(avatar_split_clause,[],[f556,f545,f367,f1203]) ).
fof(f556,plain,
( ! [X0] :
( ~ function(relation_rng(X0))
| ~ empty(relation_rng(X0))
| one_to_one(relation_rng(X0))
| ~ empty(X0) )
| ~ spl21_34
| ~ spl21_59 ),
inference(resolution,[],[f546,f368]) ).
fof(f1195,plain,
( spl21_140
| ~ spl21_49
| ~ spl21_60 ),
inference(avatar_split_clause,[],[f576,f549,f478,f1193]) ).
fof(f478,plain,
( spl21_49
<=> ! [X0] :
( element(sK5(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_49])]) ).
fof(f576,plain,
( ! [X0] :
( empty(powerset(X0))
| in(sK5(X0),powerset(X0))
| empty(X0) )
| ~ spl21_49
| ~ spl21_60 ),
inference(resolution,[],[f550,f479]) ).
fof(f479,plain,
( ! [X0] :
( element(sK5(X0),powerset(X0))
| empty(X0) )
| ~ spl21_49 ),
inference(avatar_component_clause,[],[f478]) ).
fof(f1191,plain,
( spl21_139
| ~ spl21_56
| ~ spl21_60 ),
inference(avatar_split_clause,[],[f575,f549,f506,f1189]) ).
fof(f506,plain,
( spl21_56
<=> ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_56])]) ).
fof(f575,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| in(X1,powerset(X0))
| ~ subset(X1,X0) )
| ~ spl21_56
| ~ spl21_60 ),
inference(resolution,[],[f550,f507]) ).
fof(f507,plain,
( ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) )
| ~ spl21_56 ),
inference(avatar_component_clause,[],[f506]) ).
fof(f1168,plain,
( spl21_138
| ~ spl21_38
| ~ spl21_72 ),
inference(avatar_split_clause,[],[f658,f644,f383,f1166]) ).
fof(f658,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ sP2(X1,X2)
| ~ empty(X2) )
| ~ spl21_38
| ~ spl21_72 ),
inference(resolution,[],[f645,f384]) ).
fof(f1164,plain,
( ~ spl21_137
| ~ spl21_38
| ~ spl21_115 ),
inference(avatar_split_clause,[],[f1098,f977,f383,f1161]) ).
fof(f1161,plain,
( spl21_137
<=> empty(relation_dom(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_137])]) ).
fof(f1098,plain,
( ~ empty(relation_dom(sK4))
| ~ spl21_38
| ~ spl21_115 ),
inference(resolution,[],[f978,f384]) ).
fof(f1159,plain,
( spl21_136
| ~ spl21_49
| ~ spl21_64 ),
inference(avatar_split_clause,[],[f603,f599,f478,f1157]) ).
fof(f603,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK5(X1))
| empty(X1) )
| ~ spl21_49
| ~ spl21_64 ),
inference(resolution,[],[f600,f479]) ).
fof(f1155,plain,
( spl21_135
| ~ spl21_56
| ~ spl21_64 ),
inference(avatar_split_clause,[],[f602,f599,f506,f1153]) ).
fof(f602,plain,
( ! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,X1) )
| ~ spl21_56
| ~ spl21_64 ),
inference(resolution,[],[f600,f507]) ).
fof(f1096,plain,
( spl21_134
| ~ spl21_28
| ~ spl21_64 ),
inference(avatar_split_clause,[],[f604,f599,f332,f1094]) ).
fof(f604,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK11(powerset(X1))) )
| ~ spl21_28
| ~ spl21_64 ),
inference(resolution,[],[f600,f333]) ).
fof(f1092,plain,
( spl21_133
| ~ spl21_56
| ~ spl21_63 ),
inference(avatar_split_clause,[],[f592,f587,f506,f1090]) ).
fof(f592,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,X2)
| ~ subset(X2,X0) )
| ~ spl21_56
| ~ spl21_63 ),
inference(resolution,[],[f588,f507]) ).
fof(f1088,plain,
( spl21_132
| ~ spl21_35
| ~ spl21_57 ),
inference(avatar_split_clause,[],[f530,f512,f371,f1086]) ).
fof(f530,plain,
( ! [X0,X1] :
( relation_dom(X1) = X0
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl21_35
| ~ spl21_57 ),
inference(resolution,[],[f513,f372]) ).
fof(f1084,plain,
( spl21_131
| ~ spl21_33
| ~ spl21_57 ),
inference(avatar_split_clause,[],[f529,f512,f363,f1082]) ).
fof(f529,plain,
( ! [X0,X1] :
( relation_rng(X1) = X0
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl21_33
| ~ spl21_57 ),
inference(resolution,[],[f513,f364]) ).
fof(f1080,plain,
( spl21_130
| ~ spl21_36
| ~ spl21_44 ),
inference(avatar_split_clause,[],[f457,f425,f375,f1078]) ).
fof(f425,plain,
( spl21_44
<=> ! [X0] :
( sP3(X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_44])]) ).
fof(f457,plain,
( ! [X0] :
( ~ function(relation_dom(X0))
| sP3(relation_dom(X0))
| ~ empty(X0) )
| ~ spl21_36
| ~ spl21_44 ),
inference(resolution,[],[f426,f376]) ).
fof(f426,plain,
( ! [X0] :
( ~ relation(X0)
| ~ function(X0)
| sP3(X0) )
| ~ spl21_44 ),
inference(avatar_component_clause,[],[f425]) ).
fof(f1076,plain,
( spl21_129
| ~ spl21_34
| ~ spl21_44 ),
inference(avatar_split_clause,[],[f456,f425,f367,f1074]) ).
fof(f456,plain,
( ! [X0] :
( ~ function(relation_rng(X0))
| sP3(relation_rng(X0))
| ~ empty(X0) )
| ~ spl21_34
| ~ spl21_44 ),
inference(resolution,[],[f426,f368]) ).
fof(f1072,plain,
( spl21_128
| ~ spl21_36
| ~ spl21_43 ),
inference(avatar_split_clause,[],[f441,f421,f375,f1070]) ).
fof(f421,plain,
( spl21_43
<=> ! [X0] :
( sP1(X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_43])]) ).
fof(f441,plain,
( ! [X0] :
( ~ function(relation_dom(X0))
| sP1(relation_dom(X0))
| ~ empty(X0) )
| ~ spl21_36
| ~ spl21_43 ),
inference(resolution,[],[f422,f376]) ).
fof(f422,plain,
( ! [X0] :
( ~ relation(X0)
| ~ function(X0)
| sP1(X0) )
| ~ spl21_43 ),
inference(avatar_component_clause,[],[f421]) ).
fof(f1068,plain,
( spl21_127
| ~ spl21_34
| ~ spl21_43 ),
inference(avatar_split_clause,[],[f440,f421,f367,f1066]) ).
fof(f440,plain,
( ! [X0] :
( ~ function(relation_rng(X0))
| sP1(relation_rng(X0))
| ~ empty(X0) )
| ~ spl21_34
| ~ spl21_43 ),
inference(resolution,[],[f422,f368]) ).
fof(f1057,plain,
( spl21_71
| ~ spl21_53
| spl21_115 ),
inference(avatar_split_clause,[],[f1030,f977,f494,f639]) ).
fof(f1030,plain,
( sP0(sK4)
| ~ spl21_53
| spl21_115 ),
inference(resolution,[],[f979,f495]) ).
fof(f979,plain,
( ~ in(sK7(sK4),relation_dom(sK4))
| spl21_115 ),
inference(avatar_component_clause,[],[f977]) ).
fof(f1054,plain,
( spl21_126
| ~ spl21_28
| ~ spl21_63 ),
inference(avatar_split_clause,[],[f594,f587,f332,f1052]) ).
fof(f594,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK11(powerset(X0))) )
| ~ spl21_28
| ~ spl21_63 ),
inference(resolution,[],[f588,f333]) ).
fof(f1050,plain,
( spl21_125
| ~ spl21_8
| ~ spl21_24
| ~ spl21_32
| ~ spl21_37
| ~ spl21_60 ),
inference(avatar_split_clause,[],[f580,f549,f379,f359,f316,f238,f1048]) ).
fof(f1048,plain,
( spl21_125
<=> ! [X0] :
( in(sK14,powerset(X0))
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_125])]) ).
fof(f316,plain,
( spl21_24
<=> ! [X0] : empty(sK12(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_24])]) ).
fof(f359,plain,
( spl21_32
<=> ! [X0] :
( empty_set = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_32])]) ).
fof(f580,plain,
( ! [X0] :
( in(sK14,powerset(X0))
| empty(powerset(X0)) )
| ~ spl21_8
| ~ spl21_24
| ~ spl21_32
| ~ spl21_37
| ~ spl21_60 ),
inference(forward_demodulation,[],[f579,f393]) ).
fof(f393,plain,
( empty_set = sK14
| ~ spl21_8
| ~ spl21_32 ),
inference(resolution,[],[f360,f240]) ).
fof(f240,plain,
( empty(sK14)
| ~ spl21_8 ),
inference(avatar_component_clause,[],[f238]) ).
fof(f360,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = X0 )
| ~ spl21_32 ),
inference(avatar_component_clause,[],[f359]) ).
fof(f579,plain,
( ! [X0] :
( in(empty_set,powerset(X0))
| empty(powerset(X0)) )
| ~ spl21_24
| ~ spl21_32
| ~ spl21_37
| ~ spl21_60 ),
inference(forward_demodulation,[],[f578,f392]) ).
fof(f392,plain,
( ! [X0] : empty_set = sK12(X0)
| ~ spl21_24
| ~ spl21_32 ),
inference(resolution,[],[f360,f317]) ).
fof(f317,plain,
( ! [X0] : empty(sK12(X0))
| ~ spl21_24 ),
inference(avatar_component_clause,[],[f316]) ).
fof(f578,plain,
( ! [X0] :
( empty(powerset(X0))
| in(sK12(X0),powerset(X0)) )
| ~ spl21_37
| ~ spl21_60 ),
inference(resolution,[],[f550,f380]) ).
fof(f1046,plain,
( spl21_124
| ~ spl21_45
| ~ spl21_53 ),
inference(avatar_split_clause,[],[f521,f494,f429,f1044]) ).
fof(f1044,plain,
( spl21_124
<=> ! [X0] :
( sP0(X0)
| ~ in(relation_dom(X0),sK7(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_124])]) ).
fof(f521,plain,
( ! [X0] :
( sP0(X0)
| ~ in(relation_dom(X0),sK7(X0)) )
| ~ spl21_45
| ~ spl21_53 ),
inference(resolution,[],[f495,f430]) ).
fof(f1042,plain,
( spl21_123
| ~ spl21_46
| ~ spl21_53 ),
inference(avatar_split_clause,[],[f520,f494,f433,f1040]) ).
fof(f1040,plain,
( spl21_123
<=> ! [X0] :
( sP0(X0)
| element(sK7(X0),relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_123])]) ).
fof(f520,plain,
( ! [X0] :
( sP0(X0)
| element(sK7(X0),relation_dom(X0)) )
| ~ spl21_46
| ~ spl21_53 ),
inference(resolution,[],[f495,f434]) ).
fof(f1038,plain,
( spl21_122
| ~ spl21_45
| ~ spl21_52 ),
inference(avatar_split_clause,[],[f518,f490,f429,f1036]) ).
fof(f1036,plain,
( spl21_122
<=> ! [X0] :
( sP0(X0)
| ~ in(relation_dom(X0),sK6(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_122])]) ).
fof(f518,plain,
( ! [X0] :
( sP0(X0)
| ~ in(relation_dom(X0),sK6(X0)) )
| ~ spl21_45
| ~ spl21_52 ),
inference(resolution,[],[f491,f430]) ).
fof(f1034,plain,
( spl21_121
| ~ spl21_46
| ~ spl21_52 ),
inference(avatar_split_clause,[],[f517,f490,f433,f1032]) ).
fof(f1032,plain,
( spl21_121
<=> ! [X0] :
( sP0(X0)
| element(sK6(X0),relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_121])]) ).
fof(f517,plain,
( ! [X0] :
( sP0(X0)
| element(sK6(X0),relation_dom(X0)) )
| ~ spl21_46
| ~ spl21_52 ),
inference(resolution,[],[f491,f434]) ).
fof(f1001,plain,
( spl21_120
| ~ spl21_28
| ~ spl21_60 ),
inference(avatar_split_clause,[],[f577,f549,f332,f999]) ).
fof(f577,plain,
( ! [X0] :
( empty(X0)
| in(sK11(X0),X0) )
| ~ spl21_28
| ~ spl21_60 ),
inference(resolution,[],[f550,f333]) ).
fof(f997,plain,
( ~ spl21_39
| ~ spl21_8
| spl21_119
| ~ spl21_6
| ~ spl21_8
| ~ spl21_32
| ~ spl21_59 ),
inference(avatar_split_clause,[],[f568,f545,f359,f238,f228,f994,f238,f387]) ).
fof(f387,plain,
( spl21_39
<=> function(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_39])]) ).
fof(f568,plain,
( one_to_one(sK14)
| ~ empty(sK14)
| ~ function(sK14)
| ~ spl21_6
| ~ spl21_8
| ~ spl21_32
| ~ spl21_59 ),
inference(forward_demodulation,[],[f567,f393]) ).
fof(f567,plain,
( ~ empty(sK14)
| ~ function(sK14)
| one_to_one(empty_set)
| ~ spl21_6
| ~ spl21_8
| ~ spl21_32
| ~ spl21_59 ),
inference(forward_demodulation,[],[f566,f393]) ).
fof(f566,plain,
( ~ function(sK14)
| ~ empty(empty_set)
| one_to_one(empty_set)
| ~ spl21_6
| ~ spl21_8
| ~ spl21_32
| ~ spl21_59 ),
inference(forward_demodulation,[],[f558,f393]) ).
fof(f558,plain,
( ~ function(empty_set)
| ~ empty(empty_set)
| one_to_one(empty_set)
| ~ spl21_6
| ~ spl21_59 ),
inference(resolution,[],[f546,f230]) ).
fof(f992,plain,
( spl21_117
| ~ spl21_118
| ~ spl21_13
| ~ spl21_12
| ~ spl21_59 ),
inference(avatar_split_clause,[],[f562,f545,f258,f263,f989,f985]) ).
fof(f989,plain,
( spl21_118
<=> empty(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_118])]) ).
fof(f562,plain,
( ~ function(sK17)
| ~ empty(sK17)
| one_to_one(sK17)
| ~ spl21_12
| ~ spl21_59 ),
inference(resolution,[],[f546,f260]) ).
fof(f983,plain,
( ~ spl21_115
| spl21_116
| ~ spl21_72
| ~ spl21_89 ),
inference(avatar_split_clause,[],[f819,f748,f644,f981,f977]) ).
fof(f819,plain,
( ! [X0] :
( in(apply(sK4,sK6(sK4)),X0)
| ~ in(sK7(sK4),relation_dom(sK4))
| ~ sP2(sK4,X0) )
| ~ spl21_72
| ~ spl21_89 ),
inference(superposition,[],[f645,f750]) ).
fof(f975,plain,
( spl21_114
| ~ spl21_49
| ~ spl21_55 ),
inference(avatar_split_clause,[],[f525,f502,f478,f973]) ).
fof(f525,plain,
( ! [X0] :
( subset(sK5(X0),X0)
| empty(X0) )
| ~ spl21_49
| ~ spl21_55 ),
inference(resolution,[],[f503,f479]) ).
fof(f971,plain,
( spl21_113
| ~ spl21_8
| ~ spl21_32
| ~ spl21_35 ),
inference(avatar_split_clause,[],[f405,f371,f359,f238,f969]) ).
fof(f405,plain,
( ! [X0] :
( relation_dom(X0) = sK14
| ~ empty(X0) )
| ~ spl21_8
| ~ spl21_32
| ~ spl21_35 ),
inference(forward_demodulation,[],[f402,f393]) ).
fof(f402,plain,
( ! [X0] :
( ~ empty(X0)
| relation_dom(X0) = empty_set )
| ~ spl21_32
| ~ spl21_35 ),
inference(resolution,[],[f372,f360]) ).
fof(f967,plain,
( spl21_112
| ~ spl21_8
| ~ spl21_32
| ~ spl21_33 ),
inference(avatar_split_clause,[],[f401,f363,f359,f238,f965]) ).
fof(f401,plain,
( ! [X0] :
( relation_rng(X0) = sK14
| ~ empty(X0) )
| ~ spl21_8
| ~ spl21_32
| ~ spl21_33 ),
inference(forward_demodulation,[],[f398,f393]) ).
fof(f398,plain,
( ! [X0] :
( ~ empty(X0)
| relation_rng(X0) = empty_set )
| ~ spl21_32
| ~ spl21_33 ),
inference(resolution,[],[f364,f360]) ).
fof(f912,plain,
( spl21_109
| ~ spl21_32
| ~ spl21_85 ),
inference(avatar_split_clause,[],[f883,f729,f359,f863]) ).
fof(f883,plain,
( ! [X0] :
( sK14 = X0
| ~ empty(X0) )
| ~ spl21_32
| ~ spl21_85 ),
inference(forward_demodulation,[],[f360,f731]) ).
fof(f882,plain,
( ~ spl21_5
| ~ spl21_110 ),
inference(avatar_contradiction_clause,[],[f873]) ).
fof(f873,plain,
( $false
| ~ spl21_5
| ~ spl21_110 ),
inference(resolution,[],[f868,f225]) ).
fof(f868,plain,
( ! [X0] : ~ empty(X0)
| ~ spl21_110 ),
inference(avatar_component_clause,[],[f867]) ).
fof(f867,plain,
( spl21_110
<=> ! [X0] : ~ empty(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_110])]) ).
fof(f881,plain,
( ~ spl21_24
| ~ spl21_110 ),
inference(avatar_contradiction_clause,[],[f874]) ).
fof(f874,plain,
( $false
| ~ spl21_24
| ~ spl21_110 ),
inference(resolution,[],[f868,f317]) ).
fof(f880,plain,
( ~ spl21_8
| ~ spl21_110 ),
inference(avatar_contradiction_clause,[],[f875]) ).
fof(f875,plain,
( $false
| ~ spl21_8
| ~ spl21_110 ),
inference(resolution,[],[f868,f240]) ).
fof(f879,plain,
( ~ spl21_18
| ~ spl21_110 ),
inference(avatar_contradiction_clause,[],[f876]) ).
fof(f876,plain,
( $false
| ~ spl21_18
| ~ spl21_110 ),
inference(resolution,[],[f868,f290]) ).
fof(f290,plain,
( empty(sK19)
| ~ spl21_18 ),
inference(avatar_component_clause,[],[f288]) ).
fof(f288,plain,
( spl21_18
<=> empty(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_18])]) ).
fof(f878,plain,
( ~ spl21_20
| ~ spl21_110 ),
inference(avatar_contradiction_clause,[],[f877]) ).
fof(f877,plain,
( $false
| ~ spl21_20
| ~ spl21_110 ),
inference(resolution,[],[f868,f300]) ).
fof(f300,plain,
( empty(sK20)
| ~ spl21_20 ),
inference(avatar_component_clause,[],[f298]) ).
fof(f298,plain,
( spl21_20
<=> empty(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_20])]) ).
fof(f872,plain,
( spl21_110
| spl21_111
| ~ spl21_8
| ~ spl21_24
| ~ spl21_32
| ~ spl21_37
| ~ spl21_63 ),
inference(avatar_split_clause,[],[f597,f587,f379,f359,f316,f238,f870,f867]) ).
fof(f597,plain,
( ! [X0,X1] :
( ~ in(X1,sK14)
| ~ empty(X0) )
| ~ spl21_8
| ~ spl21_24
| ~ spl21_32
| ~ spl21_37
| ~ spl21_63 ),
inference(forward_demodulation,[],[f596,f393]) ).
fof(f596,plain,
( ! [X0,X1] :
( ~ in(X1,empty_set)
| ~ empty(X0) )
| ~ spl21_24
| ~ spl21_32
| ~ spl21_37
| ~ spl21_63 ),
inference(forward_demodulation,[],[f595,f392]) ).
fof(f595,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK12(X0)) )
| ~ spl21_37
| ~ spl21_63 ),
inference(resolution,[],[f588,f380]) ).
fof(f865,plain,
( spl21_109
| ~ spl21_8
| ~ spl21_57 ),
inference(avatar_split_clause,[],[f533,f512,f238,f863]) ).
fof(f533,plain,
( ! [X0] :
( sK14 = X0
| ~ empty(X0) )
| ~ spl21_8
| ~ spl21_57 ),
inference(resolution,[],[f513,f240]) ).
fof(f861,plain,
( spl21_107
| spl21_108
| ~ spl21_102 ),
inference(avatar_split_clause,[],[f837,f832,f859,f855]) ).
fof(f855,plain,
( spl21_107
<=> sK14 = relation_inverse_image(sK4,relation_image(sK4,sK14)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_107])]) ).
fof(f859,plain,
( spl21_108
<=> ! [X0] : singleton(X0) != sK14 ),
introduced(avatar_definition,[new_symbols(naming,[spl21_108])]) ).
fof(f837,plain,
( ! [X0] :
( singleton(X0) != sK14
| sK14 = relation_inverse_image(sK4,relation_image(sK4,sK14)) )
| ~ spl21_102 ),
inference(inner_rewriting,[],[f836]) ).
fof(f836,plain,
( ! [X0] :
( singleton(X0) != sK14
| sK14 = relation_inverse_image(sK4,relation_image(sK4,singleton(X0))) )
| ~ spl21_102 ),
inference(equality_factoring,[],[f833]) ).
fof(f853,plain,
( spl21_106
| ~ spl21_28
| ~ spl21_55 ),
inference(avatar_split_clause,[],[f523,f502,f332,f851]) ).
fof(f523,plain,
( ! [X0] : subset(sK11(powerset(X0)),X0)
| ~ spl21_28
| ~ spl21_55 ),
inference(resolution,[],[f503,f333]) ).
fof(f849,plain,
( spl21_105
| ~ spl21_38
| ~ spl21_52 ),
inference(avatar_split_clause,[],[f519,f490,f383,f847]) ).
fof(f519,plain,
( ! [X0] :
( sP0(X0)
| ~ empty(relation_dom(X0)) )
| ~ spl21_38
| ~ spl21_52 ),
inference(resolution,[],[f491,f384]) ).
fof(f845,plain,
( spl21_104
| ~ spl21_26
| ~ spl21_35 ),
inference(avatar_split_clause,[],[f404,f371,f324,f843]) ).
fof(f404,plain,
( ! [X0] :
( ~ empty(X0)
| function(relation_dom(X0)) )
| ~ spl21_26
| ~ spl21_35 ),
inference(resolution,[],[f372,f325]) ).
fof(f841,plain,
( spl21_103
| ~ spl21_26
| ~ spl21_33 ),
inference(avatar_split_clause,[],[f400,f363,f324,f839]) ).
fof(f400,plain,
( ! [X0] :
( ~ empty(X0)
| function(relation_rng(X0)) )
| ~ spl21_26
| ~ spl21_33 ),
inference(resolution,[],[f364,f325]) ).
fof(f834,plain,
( spl21_102
| ~ spl21_4
| ~ spl21_67 ),
inference(avatar_split_clause,[],[f622,f618,f219,f832]) ).
fof(f622,plain,
( ! [X0] :
( singleton(X0) = relation_inverse_image(sK4,relation_image(sK4,singleton(X0)))
| sK14 = relation_inverse_image(sK4,relation_image(sK4,singleton(X0))) )
| ~ spl21_4
| ~ spl21_67 ),
inference(resolution,[],[f619,f220]) ).
fof(f828,plain,
( spl21_101
| ~ spl21_85
| ~ spl21_90 ),
inference(avatar_split_clause,[],[f766,f763,f729,f826]) ).
fof(f763,plain,
( spl21_90
<=> ! [X0] : empty_set = sK12(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_90])]) ).
fof(f766,plain,
( ! [X0] : sK12(X0) = sK14
| ~ spl21_85
| ~ spl21_90 ),
inference(forward_demodulation,[],[f764,f731]) ).
fof(f764,plain,
( ! [X0] : empty_set = sK12(X0)
| ~ spl21_90 ),
inference(avatar_component_clause,[],[f763]) ).
fof(f824,plain,
( ~ spl21_39
| spl21_100
| ~ spl21_6
| ~ spl21_8
| ~ spl21_32
| ~ spl21_44 ),
inference(avatar_split_clause,[],[f467,f425,f359,f238,f228,f821,f387]) ).
fof(f467,plain,
( sP3(sK14)
| ~ function(sK14)
| ~ spl21_6
| ~ spl21_8
| ~ spl21_32
| ~ spl21_44 ),
inference(forward_demodulation,[],[f466,f393]) ).
fof(f466,plain,
( ~ function(sK14)
| sP3(empty_set)
| ~ spl21_6
| ~ spl21_8
| ~ spl21_32
| ~ spl21_44 ),
inference(forward_demodulation,[],[f458,f393]) ).
fof(f458,plain,
( ~ function(empty_set)
| sP3(empty_set)
| ~ spl21_6
| ~ spl21_44 ),
inference(resolution,[],[f426,f230]) ).
fof(f815,plain,
( spl21_99
| ~ spl21_15
| ~ spl21_14
| ~ spl21_44 ),
inference(avatar_split_clause,[],[f463,f425,f268,f273,f812]) ).
fof(f812,plain,
( spl21_99
<=> sP3(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_99])]) ).
fof(f273,plain,
( spl21_15
<=> function(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_15])]) ).
fof(f463,plain,
( ~ function(sK18)
| sP3(sK18)
| ~ spl21_14
| ~ spl21_44 ),
inference(resolution,[],[f426,f270]) ).
fof(f810,plain,
( spl21_98
| ~ spl21_13
| ~ spl21_12
| ~ spl21_44 ),
inference(avatar_split_clause,[],[f462,f425,f258,f263,f807]) ).
fof(f807,plain,
( spl21_98
<=> sP3(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_98])]) ).
fof(f462,plain,
( ~ function(sK17)
| sP3(sK17)
| ~ spl21_12
| ~ spl21_44 ),
inference(resolution,[],[f426,f260]) ).
fof(f803,plain,
( ~ spl21_39
| spl21_97
| ~ spl21_6
| ~ spl21_8
| ~ spl21_32
| ~ spl21_43 ),
inference(avatar_split_clause,[],[f451,f421,f359,f238,f228,f800,f387]) ).
fof(f451,plain,
( sP1(sK14)
| ~ function(sK14)
| ~ spl21_6
| ~ spl21_8
| ~ spl21_32
| ~ spl21_43 ),
inference(forward_demodulation,[],[f450,f393]) ).
fof(f450,plain,
( ~ function(sK14)
| sP1(empty_set)
| ~ spl21_6
| ~ spl21_8
| ~ spl21_32
| ~ spl21_43 ),
inference(forward_demodulation,[],[f442,f393]) ).
fof(f442,plain,
( ~ function(empty_set)
| sP1(empty_set)
| ~ spl21_6
| ~ spl21_43 ),
inference(resolution,[],[f422,f230]) ).
fof(f796,plain,
( spl21_96
| ~ spl21_15
| ~ spl21_14
| ~ spl21_43 ),
inference(avatar_split_clause,[],[f447,f421,f268,f273,f793]) ).
fof(f447,plain,
( ~ function(sK18)
| sP1(sK18)
| ~ spl21_14
| ~ spl21_43 ),
inference(resolution,[],[f422,f270]) ).
fof(f789,plain,
( spl21_95
| ~ spl21_13
| ~ spl21_12
| ~ spl21_43 ),
inference(avatar_split_clause,[],[f446,f421,f258,f263,f786]) ).
fof(f446,plain,
( ~ function(sK17)
| sP1(sK17)
| ~ spl21_12
| ~ spl21_43 ),
inference(resolution,[],[f422,f260]) ).
fof(f784,plain,
( spl21_93
| ~ spl21_94
| ~ spl21_11
| ~ spl21_43 ),
inference(avatar_split_clause,[],[f445,f421,f253,f781,f777]) ).
fof(f777,plain,
( spl21_93
<=> sP1(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_93])]) ).
fof(f781,plain,
( spl21_94
<=> function(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_94])]) ).
fof(f445,plain,
( ~ function(sK16)
| sP1(sK16)
| ~ spl21_11
| ~ spl21_43 ),
inference(resolution,[],[f422,f255]) ).
fof(f775,plain,
( spl21_91
| ~ spl21_92
| ~ spl21_10
| ~ spl21_43 ),
inference(avatar_split_clause,[],[f444,f421,f248,f772,f768]) ).
fof(f768,plain,
( spl21_91
<=> sP1(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_91])]) ).
fof(f772,plain,
( spl21_92
<=> function(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_92])]) ).
fof(f248,plain,
( spl21_10
<=> relation(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_10])]) ).
fof(f444,plain,
( ~ function(sK15)
| sP1(sK15)
| ~ spl21_10
| ~ spl21_43 ),
inference(resolution,[],[f422,f250]) ).
fof(f250,plain,
( relation(sK15)
| ~ spl21_10 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f765,plain,
( spl21_90
| ~ spl21_24
| ~ spl21_32 ),
inference(avatar_split_clause,[],[f392,f359,f316,f763]) ).
fof(f751,plain,
( spl21_89
| ~ spl21_65
| spl21_71 ),
inference(avatar_split_clause,[],[f671,f639,f609,f748]) ).
fof(f609,plain,
( spl21_65
<=> ! [X0] :
( sP0(X0)
| apply(X0,sK6(X0)) = apply(X0,sK7(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_65])]) ).
fof(f671,plain,
( apply(sK4,sK6(sK4)) = apply(sK4,sK7(sK4))
| ~ spl21_65
| spl21_71 ),
inference(resolution,[],[f641,f610]) ).
fof(f610,plain,
( ! [X0] :
( sP0(X0)
| apply(X0,sK6(X0)) = apply(X0,sK7(X0)) )
| ~ spl21_65 ),
inference(avatar_component_clause,[],[f609]) ).
fof(f641,plain,
( ~ sP0(sK4)
| spl21_71 ),
inference(avatar_component_clause,[],[f639]) ).
fof(f746,plain,
( spl21_88
| ~ spl21_8
| ~ spl21_24
| ~ spl21_32
| ~ spl21_37
| ~ spl21_55 ),
inference(avatar_split_clause,[],[f527,f502,f379,f359,f316,f238,f744]) ).
fof(f744,plain,
( spl21_88
<=> ! [X0] : subset(sK14,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_88])]) ).
fof(f527,plain,
( ! [X0] : subset(sK14,X0)
| ~ spl21_8
| ~ spl21_24
| ~ spl21_32
| ~ spl21_37
| ~ spl21_55 ),
inference(forward_demodulation,[],[f526,f393]) ).
fof(f526,plain,
( ! [X0] : subset(empty_set,X0)
| ~ spl21_24
| ~ spl21_32
| ~ spl21_37
| ~ spl21_55 ),
inference(forward_demodulation,[],[f524,f392]) ).
fof(f524,plain,
( ! [X0] : subset(sK12(X0),X0)
| ~ spl21_37
| ~ spl21_55 ),
inference(resolution,[],[f503,f380]) ).
fof(f742,plain,
( spl21_87
| ~ spl21_8
| ~ spl21_20
| ~ spl21_32 ),
inference(avatar_split_clause,[],[f397,f359,f298,f238,f739]) ).
fof(f739,plain,
( spl21_87
<=> sK14 = sK20 ),
introduced(avatar_definition,[new_symbols(naming,[spl21_87])]) ).
fof(f397,plain,
( sK14 = sK20
| ~ spl21_8
| ~ spl21_20
| ~ spl21_32 ),
inference(forward_demodulation,[],[f395,f393]) ).
fof(f395,plain,
( empty_set = sK20
| ~ spl21_20
| ~ spl21_32 ),
inference(resolution,[],[f360,f300]) ).
fof(f737,plain,
( spl21_86
| ~ spl21_8
| ~ spl21_18
| ~ spl21_32 ),
inference(avatar_split_clause,[],[f396,f359,f288,f238,f734]) ).
fof(f734,plain,
( spl21_86
<=> sK14 = sK19 ),
introduced(avatar_definition,[new_symbols(naming,[spl21_86])]) ).
fof(f396,plain,
( sK14 = sK19
| ~ spl21_8
| ~ spl21_18
| ~ spl21_32 ),
inference(forward_demodulation,[],[f394,f393]) ).
fof(f394,plain,
( empty_set = sK19
| ~ spl21_18
| ~ spl21_32 ),
inference(resolution,[],[f360,f290]) ).
fof(f732,plain,
( spl21_85
| ~ spl21_8
| ~ spl21_32 ),
inference(avatar_split_clause,[],[f393,f359,f238,f729]) ).
fof(f726,plain,
( spl21_84
| ~ spl21_24
| ~ spl21_27 ),
inference(avatar_split_clause,[],[f345,f328,f316,f724]) ).
fof(f724,plain,
( spl21_84
<=> ! [X0] : relation(sK12(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_84])]) ).
fof(f345,plain,
( ! [X0] : relation(sK12(X0))
| ~ spl21_24
| ~ spl21_27 ),
inference(resolution,[],[f329,f317]) ).
fof(f721,plain,
( spl21_83
| ~ spl21_24
| ~ spl21_26 ),
inference(avatar_split_clause,[],[f340,f324,f316,f719]) ).
fof(f719,plain,
( spl21_83
<=> ! [X0] : function(sK12(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_83])]) ).
fof(f340,plain,
( ! [X0] : function(sK12(X0))
| ~ spl21_24
| ~ spl21_26 ),
inference(resolution,[],[f325,f317]) ).
fof(f714,plain,
( spl21_82
| ~ spl21_8
| ~ spl21_27 ),
inference(avatar_split_clause,[],[f346,f328,f238,f711]) ).
fof(f711,plain,
( spl21_82
<=> relation(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_82])]) ).
fof(f346,plain,
( relation(sK14)
| ~ spl21_8
| ~ spl21_27 ),
inference(resolution,[],[f329,f240]) ).
fof(f709,plain,
( spl21_3
| ~ spl21_81
| ~ spl21_2
| ~ spl21_1
| ~ spl21_59 ),
inference(avatar_split_clause,[],[f559,f545,f204,f209,f706,f214]) ).
fof(f214,plain,
( spl21_3
<=> one_to_one(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_3])]) ).
fof(f706,plain,
( spl21_81
<=> empty(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_81])]) ).
fof(f559,plain,
( ~ function(sK4)
| ~ empty(sK4)
| one_to_one(sK4)
| ~ spl21_1
| ~ spl21_59 ),
inference(resolution,[],[f546,f206]) ).
fof(f702,plain,
spl21_80,
inference(avatar_split_clause,[],[f146,f700]) ).
fof(f700,plain,
( spl21_80
<=> ! [X4,X0,X3] :
( X3 = X4
| apply(X0,X3) != apply(X0,X4)
| ~ in(X4,relation_dom(X0))
| ~ in(X3,relation_dom(X0))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_80])]) ).
fof(f146,plain,
! [X3,X0,X4] :
( X3 = X4
| apply(X0,X3) != apply(X0,X4)
| ~ in(X4,relation_dom(X0))
| ~ in(X3,relation_dom(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0] :
( ( sP0(X0)
| ( sK6(X0) != sK7(X0)
& apply(X0,sK6(X0)) = apply(X0,sK7(X0))
& in(sK7(X0),relation_dom(X0))
& in(sK6(X0),relation_dom(X0)) ) )
& ( ! [X3,X4] :
( X3 = X4
| apply(X0,X3) != apply(X0,X4)
| ~ in(X4,relation_dom(X0))
| ~ in(X3,relation_dom(X0)) )
| ~ sP0(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f88,f89]) ).
fof(f89,plain,
! [X0] :
( ? [X1,X2] :
( X1 != X2
& apply(X0,X1) = apply(X0,X2)
& in(X2,relation_dom(X0))
& in(X1,relation_dom(X0)) )
=> ( sK6(X0) != sK7(X0)
& apply(X0,sK6(X0)) = apply(X0,sK7(X0))
& in(sK7(X0),relation_dom(X0))
& in(sK6(X0),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f88,plain,
! [X0] :
( ( sP0(X0)
| ? [X1,X2] :
( X1 != X2
& apply(X0,X1) = apply(X0,X2)
& in(X2,relation_dom(X0))
& in(X1,relation_dom(X0)) ) )
& ( ! [X3,X4] :
( X3 = X4
| apply(X0,X3) != apply(X0,X4)
| ~ in(X4,relation_dom(X0))
| ~ in(X3,relation_dom(X0)) )
| ~ sP0(X0) ) ),
inference(rectify,[],[f87]) ).
fof(f87,plain,
! [X0] :
( ( sP0(X0)
| ? [X1,X2] :
( X1 != X2
& apply(X0,X1) = apply(X0,X2)
& in(X2,relation_dom(X0))
& in(X1,relation_dom(X0)) ) )
& ( ! [X1,X2] :
( X1 = X2
| apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0)) )
| ~ sP0(X0) ) ),
inference(nnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0] :
( sP0(X0)
<=> ! [X1,X2] :
( X1 = X2
| apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f698,plain,
spl21_79,
inference(avatar_split_clause,[],[f159,f696]) ).
fof(f696,plain,
( spl21_79
<=> ! [X0,X1,X3] :
( sP2(X0,X1)
| apply(X0,X3) != sK8(X0,X1)
| ~ in(X3,relation_dom(X0))
| ~ in(sK8(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_79])]) ).
fof(f159,plain,
! [X3,X0,X1] :
( sP2(X0,X1)
| apply(X0,X3) != sK8(X0,X1)
| ~ in(X3,relation_dom(X0))
| ~ in(sK8(X0,X1),X1) ),
inference(cnf_transformation,[],[f97]) ).
fof(f97,plain,
! [X0,X1] :
( ( sP2(X0,X1)
| ( ( ! [X3] :
( apply(X0,X3) != sK8(X0,X1)
| ~ in(X3,relation_dom(X0)) )
| ~ in(sK8(X0,X1),X1) )
& ( ( sK8(X0,X1) = apply(X0,sK9(X0,X1))
& in(sK9(X0,X1),relation_dom(X0)) )
| in(sK8(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0)) ) )
& ( ( apply(X0,sK10(X0,X5)) = X5
& in(sK10(X0,X5),relation_dom(X0)) )
| ~ in(X5,X1) ) )
| ~ sP2(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10])],[f93,f96,f95,f94]) ).
fof(f94,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
| ~ in(X2,X1) )
& ( ? [X4] :
( apply(X0,X4) = X2
& in(X4,relation_dom(X0)) )
| in(X2,X1) ) )
=> ( ( ! [X3] :
( apply(X0,X3) != sK8(X0,X1)
| ~ in(X3,relation_dom(X0)) )
| ~ in(sK8(X0,X1),X1) )
& ( ? [X4] :
( apply(X0,X4) = sK8(X0,X1)
& in(X4,relation_dom(X0)) )
| in(sK8(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f95,plain,
! [X0,X1] :
( ? [X4] :
( apply(X0,X4) = sK8(X0,X1)
& in(X4,relation_dom(X0)) )
=> ( sK8(X0,X1) = apply(X0,sK9(X0,X1))
& in(sK9(X0,X1),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f96,plain,
! [X0,X5] :
( ? [X7] :
( apply(X0,X7) = X5
& in(X7,relation_dom(X0)) )
=> ( apply(X0,sK10(X0,X5)) = X5
& in(sK10(X0,X5),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f93,plain,
! [X0,X1] :
( ( sP2(X0,X1)
| ? [X2] :
( ( ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
| ~ in(X2,X1) )
& ( ? [X4] :
( apply(X0,X4) = X2
& in(X4,relation_dom(X0)) )
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0)) ) )
& ( ? [X7] :
( apply(X0,X7) = X5
& in(X7,relation_dom(X0)) )
| ~ in(X5,X1) ) )
| ~ sP2(X0,X1) ) ),
inference(rectify,[],[f92]) ).
fof(f92,plain,
! [X0,X1] :
( ( sP2(X0,X1)
| ? [X2] :
( ( ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
| ~ in(X2,X1) )
& ( ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) )
& ( ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| ~ in(X2,X1) ) )
| ~ sP2(X0,X1) ) ),
inference(nnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0,X1] :
( sP2(X0,X1)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f685,plain,
spl21_78,
inference(avatar_split_clause,[],[f174,f683]) ).
fof(f174,plain,
! [X0,X1] :
( relation_image(X1,singleton(X0)) = singleton(apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0,X1] :
( relation_image(X1,singleton(X0)) = singleton(apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f69]) ).
fof(f69,plain,
! [X0,X1] :
( relation_image(X1,singleton(X0)) = singleton(apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( in(X0,relation_dom(X1))
=> relation_image(X1,singleton(X0)) = singleton(apply(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t117_funct_1) ).
fof(f681,plain,
spl21_77,
inference(avatar_split_clause,[],[f158,f679]) ).
fof(f158,plain,
! [X0,X1] :
( sP2(X0,X1)
| sK8(X0,X1) = apply(X0,sK9(X0,X1))
| in(sK8(X0,X1),X1) ),
inference(cnf_transformation,[],[f97]) ).
fof(f670,plain,
spl21_76,
inference(avatar_split_clause,[],[f157,f668]) ).
fof(f157,plain,
! [X0,X1] :
( sP2(X0,X1)
| in(sK9(X0,X1),relation_dom(X0))
| in(sK8(X0,X1),X1) ),
inference(cnf_transformation,[],[f97]) ).
fof(f665,plain,
spl21_75,
inference(avatar_split_clause,[],[f155,f663]) ).
fof(f155,plain,
! [X0,X1,X5] :
( apply(X0,sK10(X0,X5)) = X5
| ~ in(X5,X1)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f97]) ).
fof(f655,plain,
( spl21_74
| ~ spl21_8
| ~ spl21_32
| ~ spl21_70 ),
inference(avatar_split_clause,[],[f637,f634,f359,f238,f653]) ).
fof(f634,plain,
( spl21_70
<=> ! [X0,X1] :
( in(X0,relation_rng(X1))
| empty_set = relation_inverse_image(X1,singleton(X0))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_70])]) ).
fof(f637,plain,
( ! [X0,X1] :
( relation_inverse_image(X1,singleton(X0)) = sK14
| in(X0,relation_rng(X1))
| ~ relation(X1) )
| ~ spl21_8
| ~ spl21_32
| ~ spl21_70 ),
inference(forward_demodulation,[],[f635,f393]) ).
fof(f635,plain,
( ! [X0,X1] :
( in(X0,relation_rng(X1))
| empty_set = relation_inverse_image(X1,singleton(X0))
| ~ relation(X1) )
| ~ spl21_70 ),
inference(avatar_component_clause,[],[f634]) ).
fof(f651,plain,
( spl21_73
| ~ spl21_8
| ~ spl21_32
| ~ spl21_69 ),
inference(avatar_split_clause,[],[f632,f629,f359,f238,f649]) ).
fof(f629,plain,
( spl21_69
<=> ! [X0,X1] :
( empty_set != relation_inverse_image(X1,singleton(X0))
| ~ in(X0,relation_rng(X1))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_69])]) ).
fof(f632,plain,
( ! [X0,X1] :
( relation_inverse_image(X1,singleton(X0)) != sK14
| ~ in(X0,relation_rng(X1))
| ~ relation(X1) )
| ~ spl21_8
| ~ spl21_32
| ~ spl21_69 ),
inference(forward_demodulation,[],[f630,f393]) ).
fof(f630,plain,
( ! [X0,X1] :
( empty_set != relation_inverse_image(X1,singleton(X0))
| ~ in(X0,relation_rng(X1))
| ~ relation(X1) )
| ~ spl21_69 ),
inference(avatar_component_clause,[],[f629]) ).
fof(f646,plain,
spl21_72,
inference(avatar_split_clause,[],[f200,f644]) ).
fof(f200,plain,
! [X0,X1,X6] :
( in(apply(X0,X6),X1)
| ~ in(X6,relation_dom(X0))
| ~ sP2(X0,X1) ),
inference(equality_resolution,[],[f156]) ).
fof(f156,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0))
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f97]) ).
fof(f642,plain,
( spl21_3
| ~ spl21_71
| ~ spl21_41
| ~ spl21_48 ),
inference(avatar_split_clause,[],[f509,f473,f411,f639,f214]) ).
fof(f473,plain,
( spl21_48
<=> sP1(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_48])]) ).
fof(f509,plain,
( ~ sP0(sK4)
| one_to_one(sK4)
| ~ spl21_41
| ~ spl21_48 ),
inference(resolution,[],[f475,f412]) ).
fof(f475,plain,
( sP1(sK4)
| ~ spl21_48 ),
inference(avatar_component_clause,[],[f473]) ).
fof(f636,plain,
spl21_70,
inference(avatar_split_clause,[],[f169,f634]) ).
fof(f169,plain,
! [X0,X1] :
( in(X0,relation_rng(X1))
| empty_set = relation_inverse_image(X1,singleton(X0))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f102,plain,
! [X0,X1] :
( ( ( in(X0,relation_rng(X1))
| empty_set = relation_inverse_image(X1,singleton(X0)) )
& ( empty_set != relation_inverse_image(X1,singleton(X0))
| ~ in(X0,relation_rng(X1)) ) )
| ~ relation(X1) ),
inference(nnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0,X1] :
( ( in(X0,relation_rng(X1))
<=> empty_set != relation_inverse_image(X1,singleton(X0)) )
| ~ relation(X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0,X1] :
( relation(X1)
=> ( in(X0,relation_rng(X1))
<=> empty_set != relation_inverse_image(X1,singleton(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t142_funct_1) ).
fof(f631,plain,
spl21_69,
inference(avatar_split_clause,[],[f168,f629]) ).
fof(f168,plain,
! [X0,X1] :
( empty_set != relation_inverse_image(X1,singleton(X0))
| ~ in(X0,relation_rng(X1))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f627,plain,
spl21_68,
inference(avatar_split_clause,[],[f154,f625]) ).
fof(f154,plain,
! [X0,X1,X5] :
( in(sK10(X0,X5),relation_dom(X0))
| ~ in(X5,X1)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f97]) ).
fof(f620,plain,
( spl21_67
| ~ spl21_8
| ~ spl21_32
| ~ spl21_66 ),
inference(avatar_split_clause,[],[f616,f613,f359,f238,f618]) ).
fof(f613,plain,
( spl21_66
<=> ! [X0,X1] :
( singleton(X1) = X0
| empty_set = X0
| ~ subset(X0,singleton(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_66])]) ).
fof(f616,plain,
( ! [X0,X1] :
( sK14 = X0
| singleton(X1) = X0
| ~ subset(X0,singleton(X1)) )
| ~ spl21_8
| ~ spl21_32
| ~ spl21_66 ),
inference(forward_demodulation,[],[f614,f393]) ).
fof(f614,plain,
( ! [X0,X1] :
( singleton(X1) = X0
| empty_set = X0
| ~ subset(X0,singleton(X1)) )
| ~ spl21_66 ),
inference(avatar_component_clause,[],[f613]) ).
fof(f615,plain,
spl21_66,
inference(avatar_split_clause,[],[f175,f613]) ).
fof(f175,plain,
! [X0,X1] :
( singleton(X1) = X0
| empty_set = X0
| ~ subset(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f104]) ).
fof(f104,plain,
! [X0,X1] :
( ( subset(X0,singleton(X1))
| ( singleton(X1) != X0
& empty_set != X0 ) )
& ( singleton(X1) = X0
| empty_set = X0
| ~ subset(X0,singleton(X1)) ) ),
inference(flattening,[],[f103]) ).
fof(f103,plain,
! [X0,X1] :
( ( subset(X0,singleton(X1))
| ( singleton(X1) != X0
& empty_set != X0 ) )
& ( singleton(X1) = X0
| empty_set = X0
| ~ subset(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( singleton(X1) = X0
| empty_set = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_zfmisc_1) ).
fof(f611,plain,
spl21_65,
inference(avatar_split_clause,[],[f149,f609]) ).
fof(f149,plain,
! [X0] :
( sP0(X0)
| apply(X0,sK6(X0)) = apply(X0,sK7(X0)) ),
inference(cnf_transformation,[],[f90]) ).
fof(f601,plain,
spl21_64,
inference(avatar_split_clause,[],[f182,f599]) ).
fof(f182,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f73]) ).
fof(f73,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f589,plain,
spl21_63,
inference(avatar_split_clause,[],[f183,f587]) ).
fof(f183,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f585,plain,
spl21_62,
inference(avatar_split_clause,[],[f153,f583]) ).
fof(f153,plain,
! [X0,X1] :
( relation_rng(X0) = X1
| ~ sP2(X0,X1)
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f91,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ~ sP2(X0,X1) )
& ( sP2(X0,X1)
| relation_rng(X0) != X1 ) )
| ~ sP3(X0) ),
inference(nnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> sP2(X0,X1) )
| ~ sP3(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f555,plain,
spl21_61,
inference(avatar_split_clause,[],[f173,f553]) ).
fof(f173,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(singleton(X0),singleton(X1)) ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(singleton(X0),singleton(X1)) ),
inference(ennf_transformation,[],[f39]) ).
fof(f39,axiom,
! [X0,X1] :
( subset(singleton(X0),singleton(X1))
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_zfmisc_1) ).
fof(f551,plain,
spl21_60,
inference(avatar_split_clause,[],[f172,f549]) ).
fof(f172,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f66]) ).
fof(f66,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f547,plain,
spl21_59,
inference(avatar_split_clause,[],[f163,f545]) ).
fof(f163,plain,
! [X0] :
( one_to_one(X0)
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0] :
( ( one_to_one(X0)
& function(X0)
& relation(X0) )
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ),
inference(flattening,[],[f61]) ).
fof(f61,plain,
! [X0] :
( ( one_to_one(X0)
& function(X0)
& relation(X0) )
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( ( function(X0)
& empty(X0)
& relation(X0) )
=> ( one_to_one(X0)
& function(X0)
& relation(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_funct_1) ).
fof(f543,plain,
( spl21_58
| ~ spl21_2
| ~ spl21_1
| ~ spl21_44 ),
inference(avatar_split_clause,[],[f459,f425,f204,f209,f540]) ).
fof(f459,plain,
( ~ function(sK4)
| sP3(sK4)
| ~ spl21_1
| ~ spl21_44 ),
inference(resolution,[],[f426,f206]) ).
fof(f514,plain,
spl21_57,
inference(avatar_split_clause,[],[f180,f512]) ).
fof(f180,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f41,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(f508,plain,
spl21_56,
inference(avatar_split_clause,[],[f179,f506]) ).
fof(f179,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f105]) ).
fof(f105,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f504,plain,
spl21_55,
inference(avatar_split_clause,[],[f178,f502]) ).
fof(f178,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f105]) ).
fof(f500,plain,
spl21_54,
inference(avatar_split_clause,[],[f150,f498]) ).
fof(f150,plain,
! [X0] :
( sP0(X0)
| sK6(X0) != sK7(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f496,plain,
spl21_53,
inference(avatar_split_clause,[],[f148,f494]) ).
fof(f148,plain,
! [X0] :
( sP0(X0)
| in(sK7(X0),relation_dom(X0)) ),
inference(cnf_transformation,[],[f90]) ).
fof(f492,plain,
spl21_52,
inference(avatar_split_clause,[],[f147,f490]) ).
fof(f147,plain,
! [X0] :
( sP0(X0)
| in(sK6(X0),relation_dom(X0)) ),
inference(cnf_transformation,[],[f90]) ).
fof(f488,plain,
spl21_51,
inference(avatar_split_clause,[],[f143,f486]) ).
fof(f486,plain,
( spl21_51
<=> ! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_51])]) ).
fof(f143,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(flattening,[],[f55]) ).
fof(f55,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_dom(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(f484,plain,
spl21_50,
inference(avatar_split_clause,[],[f142,f482]) ).
fof(f482,plain,
( spl21_50
<=> ! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_50])]) ).
fof(f142,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(flattening,[],[f53]) ).
fof(f53,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_rng(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).
fof(f480,plain,
spl21_49,
inference(avatar_split_clause,[],[f133,f478]) ).
fof(f133,plain,
! [X0] :
( element(sK5(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
! [X0] :
( ( ~ empty(sK5(X0))
& element(sK5(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f47,f84]) ).
fof(f84,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( ~ empty(sK5(X0))
& element(sK5(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f47,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f476,plain,
( spl21_48
| ~ spl21_2
| ~ spl21_1
| ~ spl21_43 ),
inference(avatar_split_clause,[],[f443,f421,f204,f209,f473]) ).
fof(f443,plain,
( ~ function(sK4)
| sP1(sK4)
| ~ spl21_1
| ~ spl21_43 ),
inference(resolution,[],[f422,f206]) ).
fof(f439,plain,
spl21_47,
inference(avatar_split_clause,[],[f199,f437]) ).
fof(f199,plain,
! [X0] :
( sP2(X0,relation_rng(X0))
| ~ sP3(X0) ),
inference(equality_resolution,[],[f152]) ).
fof(f152,plain,
! [X0,X1] :
( sP2(X0,X1)
| relation_rng(X0) != X1
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f435,plain,
spl21_46,
inference(avatar_split_clause,[],[f171,f433]) ).
fof(f171,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(f431,plain,
spl21_45,
inference(avatar_split_clause,[],[f170,f429]) ).
fof(f170,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f427,plain,
spl21_44,
inference(avatar_split_clause,[],[f160,f425]) ).
fof(f160,plain,
! [X0] :
( sP3(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0] :
( sP3(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f60,f80,f79]) ).
fof(f60,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f59]) ).
fof(f59,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_funct_1) ).
fof(f423,plain,
spl21_43,
inference(avatar_split_clause,[],[f151,f421]) ).
fof(f151,plain,
! [X0] :
( sP1(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
! [X0] :
( sP1(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f58,f77,f76]) ).
fof(f77,plain,
! [X0] :
( ( one_to_one(X0)
<=> sP0(X0) )
| ~ sP1(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f58,plain,
! [X0] :
( ( one_to_one(X0)
<=> ! [X1,X2] :
( X1 = X2
| apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0)) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f57]) ).
fof(f57,plain,
! [X0] :
( ( one_to_one(X0)
<=> ! [X1,X2] :
( X1 = X2
| apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0)) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
<=> ! [X1,X2] :
( ( apply(X0,X1) = apply(X0,X2)
& in(X2,relation_dom(X0))
& in(X1,relation_dom(X0)) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_funct_1) ).
fof(f418,plain,
( spl21_42
| ~ spl21_20
| ~ spl21_26 ),
inference(avatar_split_clause,[],[f343,f324,f298,f415]) ).
fof(f415,plain,
( spl21_42
<=> function(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_42])]) ).
fof(f343,plain,
( function(sK20)
| ~ spl21_20
| ~ spl21_26 ),
inference(resolution,[],[f325,f300]) ).
fof(f413,plain,
spl21_41,
inference(avatar_split_clause,[],[f145,f411]) ).
fof(f145,plain,
! [X0] :
( one_to_one(X0)
| ~ sP0(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0] :
( ( ( one_to_one(X0)
| ~ sP0(X0) )
& ( sP0(X0)
| ~ one_to_one(X0) ) )
| ~ sP1(X0) ),
inference(nnf_transformation,[],[f77]) ).
fof(f409,plain,
spl21_40,
inference(avatar_split_clause,[],[f144,f407]) ).
fof(f144,plain,
! [X0] :
( sP0(X0)
| ~ one_to_one(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f390,plain,
( spl21_39
| ~ spl21_8
| ~ spl21_26 ),
inference(avatar_split_clause,[],[f341,f324,f238,f387]) ).
fof(f341,plain,
( function(sK14)
| ~ spl21_8
| ~ spl21_26 ),
inference(resolution,[],[f325,f240]) ).
fof(f385,plain,
spl21_38,
inference(avatar_split_clause,[],[f181,f383]) ).
fof(f181,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f381,plain,
spl21_37,
inference(avatar_split_clause,[],[f165,f379]) ).
fof(f165,plain,
! [X0] : element(sK12(X0),powerset(X0)),
inference(cnf_transformation,[],[f101]) ).
fof(f101,plain,
! [X0] :
( empty(sK12(X0))
& element(sK12(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f23,f100]) ).
fof(f100,plain,
! [X0] :
( ? [X1] :
( empty(X1)
& element(X1,powerset(X0)) )
=> ( empty(sK12(X0))
& element(sK12(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f23,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f377,plain,
spl21_36,
inference(avatar_split_clause,[],[f141,f375]) ).
fof(f141,plain,
! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0] :
( ( relation(relation_dom(X0))
& empty(relation_dom(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(f373,plain,
spl21_35,
inference(avatar_split_clause,[],[f140,f371]) ).
fof(f140,plain,
! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f369,plain,
spl21_34,
inference(avatar_split_clause,[],[f139,f367]) ).
fof(f139,plain,
! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0] :
( ( relation(relation_rng(X0))
& empty(relation_rng(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_rng(X0))
& empty(relation_rng(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).
fof(f365,plain,
spl21_33,
inference(avatar_split_clause,[],[f138,f363]) ).
fof(f138,plain,
! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f361,plain,
spl21_32,
inference(avatar_split_clause,[],[f137,f359]) ).
fof(f137,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f357,plain,
spl21_31,
inference(avatar_split_clause,[],[f134,f355]) ).
fof(f134,plain,
! [X0] :
( ~ empty(sK5(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f353,plain,
( spl21_30
| ~ spl21_5
| ~ spl21_26 ),
inference(avatar_split_clause,[],[f339,f324,f223,f350]) ).
fof(f350,plain,
( spl21_30
<=> function(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_30])]) ).
fof(f339,plain,
( function(empty_set)
| ~ spl21_5
| ~ spl21_26 ),
inference(resolution,[],[f325,f225]) ).
fof(f338,plain,
spl21_29,
inference(avatar_split_clause,[],[f202,f336]) ).
fof(f336,plain,
( spl21_29
<=> ! [X1] : subset(empty_set,singleton(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_29])]) ).
fof(f202,plain,
! [X1] : subset(empty_set,singleton(X1)),
inference(equality_resolution,[],[f176]) ).
fof(f176,plain,
! [X0,X1] :
( subset(X0,singleton(X1))
| empty_set != X0 ),
inference(cnf_transformation,[],[f104]) ).
fof(f334,plain,
spl21_28,
inference(avatar_split_clause,[],[f164,f332]) ).
fof(f164,plain,
! [X0] : element(sK11(X0),X0),
inference(cnf_transformation,[],[f99]) ).
fof(f99,plain,
! [X0] : element(sK11(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f7,f98]) ).
fof(f98,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK11(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f7,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f330,plain,
spl21_27,
inference(avatar_split_clause,[],[f136,f328]) ).
fof(f136,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( empty(X0)
=> relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(f326,plain,
spl21_26,
inference(avatar_split_clause,[],[f135,f324]) ).
fof(f135,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( empty(X0)
=> function(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
fof(f322,plain,
spl21_25,
inference(avatar_split_clause,[],[f167,f320]) ).
fof(f320,plain,
( spl21_25
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_25])]) ).
fof(f167,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f27]) ).
fof(f27,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f318,plain,
spl21_24,
inference(avatar_split_clause,[],[f166,f316]) ).
fof(f166,plain,
! [X0] : empty(sK12(X0)),
inference(cnf_transformation,[],[f101]) ).
fof(f314,plain,
spl21_23,
inference(avatar_split_clause,[],[f132,f312]) ).
fof(f132,plain,
! [X0] : ~ empty(singleton(X0)),
inference(cnf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] : ~ empty(singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).
fof(f310,plain,
spl21_22,
inference(avatar_split_clause,[],[f131,f308]) ).
fof(f308,plain,
( spl21_22
<=> ! [X0] : ~ empty(powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_22])]) ).
fof(f131,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f306,plain,
spl21_21,
inference(avatar_split_clause,[],[f198,f303]) ).
fof(f303,plain,
( spl21_21
<=> relation(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_21])]) ).
fof(f198,plain,
relation(sK20),
inference(cnf_transformation,[],[f121]) ).
fof(f121,plain,
( relation(sK20)
& empty(sK20) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f18,f120]) ).
fof(f120,plain,
( ? [X0] :
( relation(X0)
& empty(X0) )
=> ( relation(sK20)
& empty(sK20) ) ),
introduced(choice_axiom,[]) ).
fof(f18,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f301,plain,
spl21_20,
inference(avatar_split_clause,[],[f197,f298]) ).
fof(f197,plain,
empty(sK20),
inference(cnf_transformation,[],[f121]) ).
fof(f296,plain,
spl21_19,
inference(avatar_split_clause,[],[f196,f293]) ).
fof(f293,plain,
( spl21_19
<=> function(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_19])]) ).
fof(f196,plain,
function(sK19),
inference(cnf_transformation,[],[f119]) ).
fof(f119,plain,
( function(sK19)
& empty(sK19)
& relation(sK19) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f21,f118]) ).
fof(f118,plain,
( ? [X0] :
( function(X0)
& empty(X0)
& relation(X0) )
=> ( function(sK19)
& empty(sK19)
& relation(sK19) ) ),
introduced(choice_axiom,[]) ).
fof(f21,axiom,
? [X0] :
( function(X0)
& empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(f291,plain,
spl21_18,
inference(avatar_split_clause,[],[f195,f288]) ).
fof(f195,plain,
empty(sK19),
inference(cnf_transformation,[],[f119]) ).
fof(f286,plain,
spl21_17,
inference(avatar_split_clause,[],[f194,f283]) ).
fof(f283,plain,
( spl21_17
<=> relation(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_17])]) ).
fof(f194,plain,
relation(sK19),
inference(cnf_transformation,[],[f119]) ).
fof(f281,plain,
spl21_16,
inference(avatar_split_clause,[],[f193,f278]) ).
fof(f193,plain,
one_to_one(sK18),
inference(cnf_transformation,[],[f117]) ).
fof(f117,plain,
( one_to_one(sK18)
& function(sK18)
& relation(sK18) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f25,f116]) ).
fof(f116,plain,
( ? [X0] :
( one_to_one(X0)
& function(X0)
& relation(X0) )
=> ( one_to_one(sK18)
& function(sK18)
& relation(sK18) ) ),
introduced(choice_axiom,[]) ).
fof(f25,axiom,
? [X0] :
( one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).
fof(f276,plain,
spl21_15,
inference(avatar_split_clause,[],[f192,f273]) ).
fof(f192,plain,
function(sK18),
inference(cnf_transformation,[],[f117]) ).
fof(f271,plain,
spl21_14,
inference(avatar_split_clause,[],[f191,f268]) ).
fof(f191,plain,
relation(sK18),
inference(cnf_transformation,[],[f117]) ).
fof(f266,plain,
spl21_13,
inference(avatar_split_clause,[],[f190,f263]) ).
fof(f190,plain,
function(sK17),
inference(cnf_transformation,[],[f115]) ).
fof(f115,plain,
( function(sK17)
& relation(sK17) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f17,f114]) ).
fof(f114,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK17)
& relation(sK17) ) ),
introduced(choice_axiom,[]) ).
fof(f17,axiom,
? [X0] :
( function(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
fof(f261,plain,
spl21_12,
inference(avatar_split_clause,[],[f189,f258]) ).
fof(f189,plain,
relation(sK17),
inference(cnf_transformation,[],[f115]) ).
fof(f256,plain,
spl21_11,
inference(avatar_split_clause,[],[f188,f253]) ).
fof(f188,plain,
relation(sK16),
inference(cnf_transformation,[],[f113]) ).
fof(f113,plain,
relation(sK16),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f44,f112]) ).
fof(f112,plain,
( ? [X0] : relation(X0)
=> relation(sK16) ),
introduced(choice_axiom,[]) ).
fof(f44,plain,
? [X0] : relation(X0),
inference(pure_predicate_removal,[],[f26]) ).
fof(f26,axiom,
? [X0] :
( relation_empty_yielding(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).
fof(f251,plain,
spl21_10,
inference(avatar_split_clause,[],[f187,f248]) ).
fof(f187,plain,
relation(sK15),
inference(cnf_transformation,[],[f111]) ).
fof(f111,plain,
( relation(sK15)
& ~ empty(sK15) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f22,f110]) ).
fof(f110,plain,
( ? [X0] :
( relation(X0)
& ~ empty(X0) )
=> ( relation(sK15)
& ~ empty(sK15) ) ),
introduced(choice_axiom,[]) ).
fof(f22,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f246,plain,
~ spl21_9,
inference(avatar_split_clause,[],[f186,f243]) ).
fof(f243,plain,
( spl21_9
<=> empty(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_9])]) ).
fof(f186,plain,
~ empty(sK15),
inference(cnf_transformation,[],[f111]) ).
fof(f241,plain,
spl21_8,
inference(avatar_split_clause,[],[f185,f238]) ).
fof(f185,plain,
empty(sK14),
inference(cnf_transformation,[],[f109]) ).
fof(f109,plain,
empty(sK14),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f20,f108]) ).
fof(f108,plain,
( ? [X0] : empty(X0)
=> empty(sK14) ),
introduced(choice_axiom,[]) ).
fof(f20,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f236,plain,
~ spl21_7,
inference(avatar_split_clause,[],[f184,f233]) ).
fof(f233,plain,
( spl21_7
<=> empty(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_7])]) ).
fof(f184,plain,
~ empty(sK13),
inference(cnf_transformation,[],[f107]) ).
fof(f107,plain,
~ empty(sK13),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f24,f106]) ).
fof(f106,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK13) ),
introduced(choice_axiom,[]) ).
fof(f24,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f231,plain,
spl21_6,
inference(avatar_split_clause,[],[f128,f228]) ).
fof(f128,plain,
relation(empty_set),
inference(cnf_transformation,[],[f12]) ).
fof(f12,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f226,plain,
spl21_5,
inference(avatar_split_clause,[],[f126,f223]) ).
fof(f126,plain,
empty(empty_set),
inference(cnf_transformation,[],[f10]) ).
fof(f10,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f221,plain,
spl21_4,
inference(avatar_split_clause,[],[f124,f219]) ).
fof(f124,plain,
! [X1] : subset(relation_inverse_image(sK4,relation_image(sK4,X1)),X1),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
( ~ one_to_one(sK4)
& ! [X1] : subset(relation_inverse_image(sK4,relation_image(sK4,X1)),X1)
& function(sK4)
& relation(sK4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f46,f82]) ).
fof(f82,plain,
( ? [X0] :
( ~ one_to_one(X0)
& ! [X1] : subset(relation_inverse_image(X0,relation_image(X0,X1)),X1)
& function(X0)
& relation(X0) )
=> ( ~ one_to_one(sK4)
& ! [X1] : subset(relation_inverse_image(sK4,relation_image(sK4,X1)),X1)
& function(sK4)
& relation(sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f46,plain,
? [X0] :
( ~ one_to_one(X0)
& ! [X1] : subset(relation_inverse_image(X0,relation_image(X0,X1)),X1)
& function(X0)
& relation(X0) ),
inference(flattening,[],[f45]) ).
fof(f45,plain,
? [X0] :
( ~ one_to_one(X0)
& ! [X1] : subset(relation_inverse_image(X0,relation_image(X0,X1)),X1)
& function(X0)
& relation(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,negated_conjecture,
~ ! [X0] :
( ( function(X0)
& relation(X0) )
=> ( ! [X1] : subset(relation_inverse_image(X0,relation_image(X0,X1)),X1)
=> one_to_one(X0) ) ),
inference(negated_conjecture,[],[f30]) ).
fof(f30,conjecture,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( ! [X1] : subset(relation_inverse_image(X0,relation_image(X0,X1)),X1)
=> one_to_one(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t153_funct_1) ).
fof(f217,plain,
~ spl21_3,
inference(avatar_split_clause,[],[f125,f214]) ).
fof(f125,plain,
~ one_to_one(sK4),
inference(cnf_transformation,[],[f83]) ).
fof(f212,plain,
spl21_2,
inference(avatar_split_clause,[],[f123,f209]) ).
fof(f123,plain,
function(sK4),
inference(cnf_transformation,[],[f83]) ).
fof(f207,plain,
spl21_1,
inference(avatar_split_clause,[],[f122,f204]) ).
fof(f122,plain,
relation(sK4),
inference(cnf_transformation,[],[f83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU072+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n018.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri May 3 11:48:31 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (11600)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37 % (11603)WARNING: value z3 for option sas not known
% 0.14/0.38 % (11603)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.38 % (11602)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38 % (11601)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 % (11604)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (11605)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.38 % (11606)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.38 % (11607)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [2]
% 0.14/0.39 TRYING [3]
% 0.22/0.39 TRYING [4]
% 0.22/0.39 TRYING [1]
% 0.22/0.39 TRYING [2]
% 0.22/0.41 TRYING [5]
% 0.22/0.41 TRYING [3]
% 0.22/0.43 TRYING [6]
% 0.22/0.47 TRYING [4]
% 0.22/0.48 TRYING [7]
% 1.39/0.56 % (11605)First to succeed.
% 1.39/0.56 TRYING [5]
% 1.39/0.57 % (11605)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-11600"
% 1.39/0.58 % (11605)Refutation found. Thanks to Tanya!
% 1.39/0.58 % SZS status Theorem for theBenchmark
% 1.39/0.58 % SZS output start Proof for theBenchmark
% See solution above
% 1.39/0.58 % (11605)------------------------------
% 1.39/0.58 % (11605)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 1.39/0.58 % (11605)Termination reason: Refutation
% 1.39/0.58
% 1.39/0.58 % (11605)Memory used [KB]: 3423
% 1.39/0.58 % (11605)Time elapsed: 0.197 s
% 1.39/0.58 % (11605)Instructions burned: 348 (million)
% 1.39/0.58 % (11600)Success in time 0.22 s
%------------------------------------------------------------------------------