TSTP Solution File: SEU046+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU046+1 : TPTP v8.2.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 03:52:50 EDT 2024
% Result : Theorem 3.00s 0.80s
% Output : Refutation 3.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 522
% Syntax : Number of formulae : 1731 ( 95 unt; 0 def)
% Number of atoms : 7414 ( 294 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 9909 (4226 ~;5032 |; 128 &)
% ( 484 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 481 ( 479 usr; 471 prp; 0-3 aty)
% Number of functors : 22 ( 22 usr; 11 con; 0-3 aty)
% Number of variables : 2712 (2670 !; 42 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7114,plain,
$false,
inference(avatar_sat_refutation,[],[f189,f194,f199,f204,f209,f214,f219,f224,f229,f234,f239,f244,f249,f254,f259,f264,f269,f274,f278,f282,f286,f295,f299,f303,f307,f321,f325,f329,f333,f337,f342,f346,f350,f354,f374,f378,f382,f386,f390,f394,f398,f403,f408,f412,f416,f438,f443,f447,f451,f455,f470,f474,f478,f491,f501,f505,f509,f510,f515,f519,f532,f543,f549,f555,f564,f570,f576,f581,f587,f592,f597,f601,f614,f619,f623,f629,f633,f637,f641,f645,f652,f673,f677,f681,f685,f713,f723,f727,f737,f741,f745,f749,f753,f758,f808,f812,f824,f831,f835,f848,f856,f863,f867,f875,f879,f891,f908,f916,f920,f924,f928,f942,f946,f950,f955,f981,f1000,f1019,f1024,f1045,f1053,f1057,f1073,f1092,f1102,f1117,f1125,f1130,f1135,f1144,f1194,f1199,f1203,f1217,f1222,f1234,f1238,f1242,f1246,f1250,f1254,f1339,f1343,f1365,f1369,f1388,f1394,f1398,f1402,f1406,f1407,f1411,f1415,f1517,f1518,f1523,f1527,f1531,f1535,f1539,f1562,f1566,f1570,f1574,f1578,f1582,f1588,f1589,f1590,f1591,f1592,f1639,f1999,f2010,f2014,f2018,f2022,f2042,f2051,f2055,f2059,f2063,f2079,f2084,f2088,f2092,f2102,f2110,f2114,f2118,f2135,f2139,f2143,f2165,f2171,f2175,f2179,f2190,f2194,f2198,f2203,f2207,f2227,f2235,f2239,f2243,f2272,f2276,f2280,f2284,f2326,f2330,f2334,f2338,f2375,f2379,f2405,f2421,f2447,f2461,f2465,f2469,f2517,f2521,f2525,f2529,f2533,f2566,f2626,f2652,f2659,f2663,f2686,f2701,f2727,f2731,f2735,f2739,f2804,f2808,f2812,f2816,f2820,f2824,f2828,f2996,f3000,f3080,f3084,f3088,f3172,f3176,f3180,f3184,f3349,f3353,f3403,f3407,f3473,f3477,f3488,f3498,f3502,f3506,f3510,f3525,f3529,f3533,f3545,f3554,f3558,f3562,f3569,f3577,f3591,f3595,f3634,f3638,f3694,f3715,f3744,f3748,f3768,f3799,f3810,f3820,f3824,f3828,f3832,f3849,f3853,f3857,f3861,f3865,f3870,f3923,f3931,f3938,f3975,f3979,f3983,f3987,f3991,f3995,f3999,f4003,f4007,f4029,f4235,f4287,f4291,f4295,f4299,f4303,f4390,f4421,f4426,f4430,f4439,f4443,f4447,f4448,f4463,f4467,f4471,f4475,f4479,f4483,f4487,f4491,f4496,f4500,f4504,f4508,f4512,f4516,f4520,f4524,f4559,f4769,f4773,f4782,f4786,f4886,f4890,f4901,f4905,f4909,f4913,f4924,f4933,f4937,f4941,f4945,f4949,f4953,f4957,f4975,f5071,f5075,f5124,f5128,f5132,f5136,f5209,f5213,f5224,f5228,f5232,f5236,f5240,f5244,f5248,f5294,f5336,f5340,f5349,f5353,f5358,f5362,f5366,f5370,f5374,f5378,f5427,f5431,f5435,f5439,f5443,f5447,f5451,f5455,f5471,f5536,f5540,f5544,f5548,f5763,f5770,f5774,f5778,f5782,f5787,f5837,f5841,f5845,f5849,f5888,f5892,f5897,f5901,f5905,f5909,f5914,f5918,f6004,f6008,f6013,f6017,f6021,f6025,f6029,f6039,f6175,f6179,f6233,f6237,f6241,f6246,f6250,f6254,f6258,f6262,f6266,f6270,f6274,f6278,f6282,f6286,f6290,f6294,f6298,f6302,f6306,f6346,f6450,f6508,f6512,f6516,f6520,f6524,f6528,f6532,f6661,f6726,f6735,f6739,f6743,f6747,f6919,f6924,f6928,f6932,f6936,f6940,f7054,f7061,f7065,f7069,f7073,f7077,f7081,f7113]) ).
fof(f7113,plain,
( ~ spl17_151
| ~ spl17_1
| ~ spl17_2
| ~ spl17_150
| spl17_22
| ~ spl17_457 ),
inference(avatar_split_clause,[],[f6911,f6745,f288,f1381,f191,f186,f1385]) ).
fof(f1385,plain,
( spl17_151
<=> function(relation_rng_restriction(sK1,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_151])]) ).
fof(f186,plain,
( spl17_1
<=> relation(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1])]) ).
fof(f191,plain,
( spl17_2
<=> function(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_2])]) ).
fof(f1381,plain,
( spl17_150
<=> relation(relation_rng_restriction(sK1,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_150])]) ).
fof(f288,plain,
( spl17_22
<=> subset(relation_dom(relation_rng_restriction(sK1,sK2)),relation_dom(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_22])]) ).
fof(f6745,plain,
( spl17_457
<=> ! [X0,X1] :
( ~ function(relation_rng_restriction(X0,X1))
| ~ relation(relation_rng_restriction(X0,X1))
| ~ function(X1)
| ~ relation(X1)
| subset(relation_dom(relation_rng_restriction(X0,X1)),relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_457])]) ).
fof(f6911,plain,
( ~ relation(relation_rng_restriction(sK1,sK2))
| ~ function(sK2)
| ~ relation(sK2)
| ~ function(relation_rng_restriction(sK1,sK2))
| spl17_22
| ~ spl17_457 ),
inference(resolution,[],[f6746,f290]) ).
fof(f290,plain,
( ~ subset(relation_dom(relation_rng_restriction(sK1,sK2)),relation_dom(sK2))
| spl17_22 ),
inference(avatar_component_clause,[],[f288]) ).
fof(f6746,plain,
( ! [X0,X1] :
( subset(relation_dom(relation_rng_restriction(X0,X1)),relation_dom(X1))
| ~ relation(relation_rng_restriction(X0,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(relation_rng_restriction(X0,X1)) )
| ~ spl17_457 ),
inference(avatar_component_clause,[],[f6745]) ).
fof(f7081,plain,
( spl17_470
| ~ spl17_82
| ~ spl17_224 ),
inference(avatar_split_clause,[],[f2622,f2531,f650,f7079]) ).
fof(f7079,plain,
( spl17_470
<=> ! [X2,X0,X1] :
( ~ function(relation_rng_restriction(sK10,X0))
| ~ relation(relation_rng_restriction(sK10,X0))
| ~ function(X0)
| ~ relation(X0)
| sP0(X1,relation_rng_restriction(sK10,X0),X2)
| ~ empty(relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_470])]) ).
fof(f650,plain,
( spl17_82
<=> ! [X1] : ~ in(X1,sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_82])]) ).
fof(f2531,plain,
( spl17_224
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(apply(X0,sK6(X2,relation_rng_restriction(X1,X0),X3)),X1)
| sP0(X2,relation_rng_restriction(X1,X0),X3)
| ~ empty(relation_dom(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_224])]) ).
fof(f2622,plain,
( ! [X2,X0,X1] :
( ~ function(relation_rng_restriction(sK10,X0))
| ~ relation(relation_rng_restriction(sK10,X0))
| ~ function(X0)
| ~ relation(X0)
| sP0(X1,relation_rng_restriction(sK10,X0),X2)
| ~ empty(relation_dom(X2)) )
| ~ spl17_82
| ~ spl17_224 ),
inference(resolution,[],[f2532,f651]) ).
fof(f651,plain,
( ! [X1] : ~ in(X1,sK10)
| ~ spl17_82 ),
inference(avatar_component_clause,[],[f650]) ).
fof(f2532,plain,
( ! [X2,X3,X0,X1] :
( in(apply(X0,sK6(X2,relation_rng_restriction(X1,X0),X3)),X1)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| ~ relation(X0)
| sP0(X2,relation_rng_restriction(X1,X0),X3)
| ~ empty(relation_dom(X3)) )
| ~ spl17_224 ),
inference(avatar_component_clause,[],[f2531]) ).
fof(f7077,plain,
( spl17_469
| ~ spl17_82
| ~ spl17_223 ),
inference(avatar_split_clause,[],[f2599,f2527,f650,f7075]) ).
fof(f7075,plain,
( spl17_469
<=> ! [X2,X0,X1] :
( ~ function(relation_rng_restriction(sK10,X0))
| ~ relation(relation_rng_restriction(sK10,X0))
| ~ function(X0)
| ~ relation(X0)
| sP0(X1,X2,relation_rng_restriction(sK10,X0))
| ~ empty(relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_469])]) ).
fof(f2527,plain,
( spl17_223
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(apply(X0,sK6(X2,X3,relation_rng_restriction(X1,X0))),X1)
| sP0(X2,X3,relation_rng_restriction(X1,X0))
| ~ empty(relation_dom(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_223])]) ).
fof(f2599,plain,
( ! [X2,X0,X1] :
( ~ function(relation_rng_restriction(sK10,X0))
| ~ relation(relation_rng_restriction(sK10,X0))
| ~ function(X0)
| ~ relation(X0)
| sP0(X1,X2,relation_rng_restriction(sK10,X0))
| ~ empty(relation_dom(X2)) )
| ~ spl17_82
| ~ spl17_223 ),
inference(resolution,[],[f2528,f651]) ).
fof(f2528,plain,
( ! [X2,X3,X0,X1] :
( in(apply(X0,sK6(X2,X3,relation_rng_restriction(X1,X0))),X1)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| ~ relation(X0)
| sP0(X2,X3,relation_rng_restriction(X1,X0))
| ~ empty(relation_dom(X3)) )
| ~ spl17_223 ),
inference(avatar_component_clause,[],[f2527]) ).
fof(f7073,plain,
( spl17_468
| ~ spl17_35
| ~ spl17_214 ),
inference(avatar_split_clause,[],[f2410,f2403,f352,f7071]) ).
fof(f7071,plain,
( spl17_468
<=> ! [X2,X0,X1] :
( ~ function(relation_rng_restriction(X0,X1))
| ~ relation(relation_rng_restriction(X0,X1))
| ~ function(X1)
| ~ relation(X1)
| subset(relation_dom(relation_rng_restriction(X0,X1)),X2)
| ~ empty(relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_468])]) ).
fof(f352,plain,
( spl17_35
<=> ! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_35])]) ).
fof(f2403,plain,
( spl17_214
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(sK8(relation_dom(relation_rng_restriction(X1,X0)),X2),relation_dom(X0))
| subset(relation_dom(relation_rng_restriction(X1,X0)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_214])]) ).
fof(f2410,plain,
( ! [X2,X0,X1] :
( ~ function(relation_rng_restriction(X0,X1))
| ~ relation(relation_rng_restriction(X0,X1))
| ~ function(X1)
| ~ relation(X1)
| subset(relation_dom(relation_rng_restriction(X0,X1)),X2)
| ~ empty(relation_dom(X1)) )
| ~ spl17_35
| ~ spl17_214 ),
inference(resolution,[],[f2404,f353]) ).
fof(f353,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) )
| ~ spl17_35 ),
inference(avatar_component_clause,[],[f352]) ).
fof(f2404,plain,
( ! [X2,X0,X1] :
( in(sK8(relation_dom(relation_rng_restriction(X1,X0)),X2),relation_dom(X0))
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| ~ relation(X0)
| subset(relation_dom(relation_rng_restriction(X1,X0)),X2) )
| ~ spl17_214 ),
inference(avatar_component_clause,[],[f2403]) ).
fof(f7069,plain,
( spl17_467
| ~ spl17_165
| ~ spl17_205 ),
inference(avatar_split_clause,[],[f2300,f2274,f1564,f7067]) ).
fof(f7067,plain,
( spl17_467
<=> ! [X4,X0,X3,X2,X1] :
( ~ empty(relation_dom(X0))
| sP0(relation_rng(relation_rng_restriction(X1,relation_rng_restriction(X2,X3))),X4,X0)
| ~ relation(relation_rng_restriction(X2,X3))
| ~ empty(relation_rng(X3))
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_467])]) ).
fof(f1564,plain,
( spl17_165
<=> ! [X2,X0,X1] :
( ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ empty(relation_rng(X2))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_165])]) ).
fof(f2274,plain,
( spl17_205
<=> ! [X0,X3,X2,X1] :
( sP0(relation_rng(relation_rng_restriction(X0,X1)),X2,X3)
| ~ empty(relation_dom(X3))
| in(apply(X2,sK6(relation_rng(relation_rng_restriction(X0,X1)),X2,X3)),relation_rng(X1))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_205])]) ).
fof(f2300,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ empty(relation_dom(X0))
| sP0(relation_rng(relation_rng_restriction(X1,relation_rng_restriction(X2,X3))),X4,X0)
| ~ relation(relation_rng_restriction(X2,X3))
| ~ empty(relation_rng(X3))
| ~ relation(X3) )
| ~ spl17_165
| ~ spl17_205 ),
inference(resolution,[],[f2275,f1565]) ).
fof(f1565,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ empty(relation_rng(X2))
| ~ relation(X2) )
| ~ spl17_165 ),
inference(avatar_component_clause,[],[f1564]) ).
fof(f2275,plain,
( ! [X2,X3,X0,X1] :
( in(apply(X2,sK6(relation_rng(relation_rng_restriction(X0,X1)),X2,X3)),relation_rng(X1))
| ~ empty(relation_dom(X3))
| sP0(relation_rng(relation_rng_restriction(X0,X1)),X2,X3)
| ~ relation(X1) )
| ~ spl17_205 ),
inference(avatar_component_clause,[],[f2274]) ).
fof(f7065,plain,
( spl17_466
| ~ spl17_132
| ~ spl17_203 ),
inference(avatar_split_clause,[],[f2268,f2241,f1132,f7063]) ).
fof(f7063,plain,
( spl17_466
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,sK10),sK10)
| in(sK6(X0,X1,sK10),relation_dom(X2))
| sP0(X0,X1,sK10)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_466])]) ).
fof(f1132,plain,
( spl17_132
<=> sK10 = relation_dom(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_132])]) ).
fof(f2241,plain,
( spl17_203
<=> ! [X0,X3,X2,X1] :
( sP0(X0,X1,X2)
| in(sK6(X0,X1,X2),relation_dom(X3))
| in(sK6(X0,X1,X2),relation_dom(X2))
| ~ sP0(X0,X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_203])]) ).
fof(f2268,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,sK10),sK10)
| in(sK6(X0,X1,sK10),relation_dom(X2))
| sP0(X0,X1,sK10)
| ~ sP0(X0,X1,X2) )
| ~ spl17_132
| ~ spl17_203 ),
inference(superposition,[],[f2242,f1134]) ).
fof(f1134,plain,
( sK10 = relation_dom(sK10)
| ~ spl17_132 ),
inference(avatar_component_clause,[],[f1132]) ).
fof(f2242,plain,
( ! [X2,X3,X0,X1] :
( in(sK6(X0,X1,X2),relation_dom(X3))
| in(sK6(X0,X1,X2),relation_dom(X2))
| sP0(X0,X1,X2)
| ~ sP0(X0,X1,X3) )
| ~ spl17_203 ),
inference(avatar_component_clause,[],[f2241]) ).
fof(f7061,plain,
( spl17_465
| ~ spl17_132
| ~ spl17_203 ),
inference(avatar_split_clause,[],[f2267,f2241,f1132,f7059]) ).
fof(f7059,plain,
( spl17_465
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),sK10)
| in(sK6(X0,X1,X2),relation_dom(X2))
| sP0(X0,X1,X2)
| ~ sP0(X0,X1,sK10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_465])]) ).
fof(f2267,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),sK10)
| in(sK6(X0,X1,X2),relation_dom(X2))
| sP0(X0,X1,X2)
| ~ sP0(X0,X1,sK10) )
| ~ spl17_132
| ~ spl17_203 ),
inference(superposition,[],[f2242,f1134]) ).
fof(f7054,plain,
( spl17_464
| ~ spl17_44
| ~ spl17_196 ),
inference(avatar_split_clause,[],[f2215,f2192,f406,f7052]) ).
fof(f7052,plain,
( spl17_464
<=> ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(sK4(powerset(powerset(X1))),X2,X0)
| subset(apply(X2,sK6(sK4(powerset(powerset(X1))),X2,X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_464])]) ).
fof(f406,plain,
( spl17_44
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_44])]) ).
fof(f2192,plain,
( spl17_196
<=> ! [X2,X0,X1] :
( sP0(sK4(powerset(X0)),X1,X2)
| ~ empty(relation_dom(X2))
| element(apply(X1,sK6(sK4(powerset(X0)),X1,X2)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_196])]) ).
fof(f2215,plain,
( ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(sK4(powerset(powerset(X1))),X2,X0)
| subset(apply(X2,sK6(sK4(powerset(powerset(X1))),X2,X0)),X1) )
| ~ spl17_44
| ~ spl17_196 ),
inference(resolution,[],[f2193,f407]) ).
fof(f407,plain,
( ! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) )
| ~ spl17_44 ),
inference(avatar_component_clause,[],[f406]) ).
fof(f2193,plain,
( ! [X2,X0,X1] :
( element(apply(X1,sK6(sK4(powerset(X0)),X1,X2)),X0)
| ~ empty(relation_dom(X2))
| sP0(sK4(powerset(X0)),X1,X2) )
| ~ spl17_196 ),
inference(avatar_component_clause,[],[f2192]) ).
fof(f6940,plain,
( spl17_463
| ~ spl17_82
| ~ spl17_226 ),
inference(avatar_split_clause,[],[f2648,f2624,f650,f6938]) ).
fof(f6938,plain,
( spl17_463
<=> ! [X0,X1] :
( ~ function(relation_rng_restriction(sK10,X0))
| ~ relation(relation_rng_restriction(sK10,X0))
| ~ function(X0)
| ~ relation(X0)
| sP0(X1,relation_rng_restriction(sK10,X0),relation_rng_restriction(sK10,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_463])]) ).
fof(f2624,plain,
( spl17_226
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(apply(X0,sK6(X2,relation_rng_restriction(X1,X0),relation_rng_restriction(X1,X0))),X1)
| sP0(X2,relation_rng_restriction(X1,X0),relation_rng_restriction(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_226])]) ).
fof(f2648,plain,
( ! [X0,X1] :
( ~ function(relation_rng_restriction(sK10,X0))
| ~ relation(relation_rng_restriction(sK10,X0))
| ~ function(X0)
| ~ relation(X0)
| sP0(X1,relation_rng_restriction(sK10,X0),relation_rng_restriction(sK10,X0)) )
| ~ spl17_82
| ~ spl17_226 ),
inference(resolution,[],[f2625,f651]) ).
fof(f2625,plain,
( ! [X2,X0,X1] :
( in(apply(X0,sK6(X2,relation_rng_restriction(X1,X0),relation_rng_restriction(X1,X0))),X1)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| ~ relation(X0)
| sP0(X2,relation_rng_restriction(X1,X0),relation_rng_restriction(X1,X0)) )
| ~ spl17_226 ),
inference(avatar_component_clause,[],[f2624]) ).
fof(f6936,plain,
( spl17_462
| ~ spl17_82
| ~ spl17_219 ),
inference(avatar_split_clause,[],[f2512,f2467,f650,f6934]) ).
fof(f6934,plain,
( spl17_462
<=> ! [X2,X0,X1] :
( ~ function(relation_rng_restriction(sK10,X0))
| ~ relation(relation_rng_restriction(sK10,X0))
| ~ function(X0)
| ~ relation(X0)
| sP0(X1,X2,relation_rng_restriction(sK10,X0))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_462])]) ).
fof(f2467,plain,
( spl17_219
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(apply(X0,sK6(X2,X3,relation_rng_restriction(X1,X0))),X1)
| sP0(X2,X3,relation_rng_restriction(X1,X0))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_219])]) ).
fof(f2512,plain,
( ! [X2,X0,X1] :
( ~ function(relation_rng_restriction(sK10,X0))
| ~ relation(relation_rng_restriction(sK10,X0))
| ~ function(X0)
| ~ relation(X0)
| sP0(X1,X2,relation_rng_restriction(sK10,X0))
| ~ empty(X1) )
| ~ spl17_82
| ~ spl17_219 ),
inference(resolution,[],[f2468,f651]) ).
fof(f2468,plain,
( ! [X2,X3,X0,X1] :
( in(apply(X0,sK6(X2,X3,relation_rng_restriction(X1,X0))),X1)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| ~ relation(X0)
| sP0(X2,X3,relation_rng_restriction(X1,X0))
| ~ empty(X2) )
| ~ spl17_219 ),
inference(avatar_component_clause,[],[f2467]) ).
fof(f6932,plain,
( spl17_461
| ~ spl17_35
| ~ spl17_215 ),
inference(avatar_split_clause,[],[f2422,f2419,f352,f6930]) ).
fof(f6930,plain,
( spl17_461
<=> ! [X2,X0,X1] :
( ~ function(relation_rng_restriction(X0,X1))
| ~ relation(relation_rng_restriction(X0,X1))
| ~ function(X1)
| ~ relation(X1)
| subset(relation_dom(relation_rng_restriction(X0,X1)),X2)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_461])]) ).
fof(f2419,plain,
( spl17_215
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(apply(X0,sK8(relation_dom(relation_rng_restriction(X1,X0)),X2)),X1)
| subset(relation_dom(relation_rng_restriction(X1,X0)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_215])]) ).
fof(f2422,plain,
( ! [X2,X0,X1] :
( ~ function(relation_rng_restriction(X0,X1))
| ~ relation(relation_rng_restriction(X0,X1))
| ~ function(X1)
| ~ relation(X1)
| subset(relation_dom(relation_rng_restriction(X0,X1)),X2)
| ~ empty(X0) )
| ~ spl17_35
| ~ spl17_215 ),
inference(resolution,[],[f2420,f353]) ).
fof(f2420,plain,
( ! [X2,X0,X1] :
( in(apply(X0,sK8(relation_dom(relation_rng_restriction(X1,X0)),X2)),X1)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| ~ relation(X0)
| subset(relation_dom(relation_rng_restriction(X1,X0)),X2) )
| ~ spl17_215 ),
inference(avatar_component_clause,[],[f2419]) ).
fof(f6928,plain,
( spl17_460
| ~ spl17_35
| ~ spl17_211 ),
inference(avatar_split_clause,[],[f2365,f2336,f352,f6926]) ).
fof(f6926,plain,
( spl17_460
<=> ! [X0,X1] :
( ~ function(relation_rng_restriction(X0,X1))
| ~ relation(relation_rng_restriction(X0,X1))
| ~ function(X1)
| ~ relation(X1)
| empty(relation_dom(relation_rng_restriction(X0,X1)))
| ~ empty(relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_460])]) ).
fof(f2336,plain,
( spl17_211
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(sK4(relation_dom(relation_rng_restriction(X1,X0))),relation_dom(X0))
| empty(relation_dom(relation_rng_restriction(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_211])]) ).
fof(f2365,plain,
( ! [X0,X1] :
( ~ function(relation_rng_restriction(X0,X1))
| ~ relation(relation_rng_restriction(X0,X1))
| ~ function(X1)
| ~ relation(X1)
| empty(relation_dom(relation_rng_restriction(X0,X1)))
| ~ empty(relation_dom(X1)) )
| ~ spl17_35
| ~ spl17_211 ),
inference(resolution,[],[f2337,f353]) ).
fof(f2337,plain,
( ! [X0,X1] :
( in(sK4(relation_dom(relation_rng_restriction(X1,X0))),relation_dom(X0))
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| ~ relation(X0)
| empty(relation_dom(relation_rng_restriction(X1,X0))) )
| ~ spl17_211 ),
inference(avatar_component_clause,[],[f2336]) ).
fof(f6924,plain,
( spl17_459
| ~ spl17_51
| ~ spl17_444 ),
inference(avatar_split_clause,[],[f6731,f6448,f453,f6921]) ).
fof(f6921,plain,
( spl17_459
<=> subset(sK4(powerset(relation_rng(relation_rng_restriction(sK1,sK2)))),relation_rng(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_459])]) ).
fof(f453,plain,
( spl17_51
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ in(sK8(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_51])]) ).
fof(f6448,plain,
( spl17_444
<=> ! [X0] :
( subset(sK4(powerset(relation_rng(relation_rng_restriction(sK1,sK2)))),X0)
| in(sK8(sK4(powerset(relation_rng(relation_rng_restriction(sK1,sK2)))),X0),relation_rng(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_444])]) ).
fof(f6731,plain,
( subset(sK4(powerset(relation_rng(relation_rng_restriction(sK1,sK2)))),relation_rng(sK2))
| ~ spl17_51
| ~ spl17_444 ),
inference(duplicate_literal_removal,[],[f6727]) ).
fof(f6727,plain,
( subset(sK4(powerset(relation_rng(relation_rng_restriction(sK1,sK2)))),relation_rng(sK2))
| subset(sK4(powerset(relation_rng(relation_rng_restriction(sK1,sK2)))),relation_rng(sK2))
| ~ spl17_51
| ~ spl17_444 ),
inference(resolution,[],[f6449,f454]) ).
fof(f454,plain,
( ! [X0,X1] :
( ~ in(sK8(X0,X1),X1)
| subset(X0,X1) )
| ~ spl17_51 ),
inference(avatar_component_clause,[],[f453]) ).
fof(f6449,plain,
( ! [X0] :
( in(sK8(sK4(powerset(relation_rng(relation_rng_restriction(sK1,sK2)))),X0),relation_rng(sK2))
| subset(sK4(powerset(relation_rng(relation_rng_restriction(sK1,sK2)))),X0) )
| ~ spl17_444 ),
inference(avatar_component_clause,[],[f6448]) ).
fof(f6919,plain,
( spl17_458
| ~ spl17_55
| ~ spl17_186 ),
inference(avatar_split_clause,[],[f2129,f2112,f489,f6917]) ).
fof(f6917,plain,
( spl17_458
<=> ! [X0,X3,X2,X1] :
( ~ empty(relation_dom(X0))
| sP0(powerset(X1),X2,X0)
| element(X3,X1)
| ~ in(X3,apply(X2,sK6(powerset(X1),X2,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_458])]) ).
fof(f489,plain,
( spl17_55
<=> ! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_55])]) ).
fof(f2112,plain,
( spl17_186
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(relation_dom(X2))
| element(apply(X1,sK6(X0,X1,X2)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_186])]) ).
fof(f2129,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(powerset(X1),X2,X0)
| element(X3,X1)
| ~ in(X3,apply(X2,sK6(powerset(X1),X2,X0))) )
| ~ spl17_55
| ~ spl17_186 ),
inference(resolution,[],[f2113,f490]) ).
fof(f490,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| element(X0,X2)
| ~ in(X0,X1) )
| ~ spl17_55 ),
inference(avatar_component_clause,[],[f489]) ).
fof(f2113,plain,
( ! [X2,X0,X1] :
( element(apply(X1,sK6(X0,X1,X2)),X0)
| ~ empty(relation_dom(X2))
| sP0(X0,X1,X2) )
| ~ spl17_186 ),
inference(avatar_component_clause,[],[f2112]) ).
fof(f6747,plain,
( spl17_457
| ~ spl17_51
| ~ spl17_214 ),
inference(avatar_split_clause,[],[f2414,f2403,f453,f6745]) ).
fof(f2414,plain,
( ! [X0,X1] :
( ~ function(relation_rng_restriction(X0,X1))
| ~ relation(relation_rng_restriction(X0,X1))
| ~ function(X1)
| ~ relation(X1)
| subset(relation_dom(relation_rng_restriction(X0,X1)),relation_dom(X1)) )
| ~ spl17_51
| ~ spl17_214 ),
inference(duplicate_literal_removal,[],[f2409]) ).
fof(f2409,plain,
( ! [X0,X1] :
( ~ function(relation_rng_restriction(X0,X1))
| ~ relation(relation_rng_restriction(X0,X1))
| ~ function(X1)
| ~ relation(X1)
| subset(relation_dom(relation_rng_restriction(X0,X1)),relation_dom(X1))
| subset(relation_dom(relation_rng_restriction(X0,X1)),relation_dom(X1)) )
| ~ spl17_51
| ~ spl17_214 ),
inference(resolution,[],[f2404,f454]) ).
fof(f6743,plain,
( spl17_456
| ~ spl17_35
| ~ spl17_212 ),
inference(avatar_split_clause,[],[f2380,f2373,f352,f6741]) ).
fof(f6741,plain,
( spl17_456
<=> ! [X0,X1] :
( ~ function(relation_rng_restriction(X0,X1))
| ~ relation(relation_rng_restriction(X0,X1))
| ~ function(X1)
| ~ relation(X1)
| empty(relation_dom(relation_rng_restriction(X0,X1)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_456])]) ).
fof(f2373,plain,
( spl17_212
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(apply(X0,sK4(relation_dom(relation_rng_restriction(X1,X0)))),X1)
| empty(relation_dom(relation_rng_restriction(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_212])]) ).
fof(f2380,plain,
( ! [X0,X1] :
( ~ function(relation_rng_restriction(X0,X1))
| ~ relation(relation_rng_restriction(X0,X1))
| ~ function(X1)
| ~ relation(X1)
| empty(relation_dom(relation_rng_restriction(X0,X1)))
| ~ empty(X0) )
| ~ spl17_35
| ~ spl17_212 ),
inference(resolution,[],[f2374,f353]) ).
fof(f2374,plain,
( ! [X0,X1] :
( in(apply(X0,sK4(relation_dom(relation_rng_restriction(X1,X0)))),X1)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| ~ relation(X0)
| empty(relation_dom(relation_rng_restriction(X1,X0))) )
| ~ spl17_212 ),
inference(avatar_component_clause,[],[f2373]) ).
fof(f6739,plain,
( spl17_455
| ~ spl17_54
| ~ spl17_186 ),
inference(avatar_split_clause,[],[f2128,f2112,f476,f6737]) ).
fof(f6737,plain,
( spl17_455
<=> ! [X2,X0,X1,X3] :
( ~ empty(relation_dom(X0))
| sP0(powerset(X1),X2,X0)
| ~ empty(X1)
| ~ in(X3,apply(X2,sK6(powerset(X1),X2,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_455])]) ).
fof(f476,plain,
( spl17_54
<=> ! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_54])]) ).
fof(f2128,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(powerset(X1),X2,X0)
| ~ empty(X1)
| ~ in(X3,apply(X2,sK6(powerset(X1),X2,X0))) )
| ~ spl17_54
| ~ spl17_186 ),
inference(resolution,[],[f2113,f477]) ).
fof(f477,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X0,X1) )
| ~ spl17_54 ),
inference(avatar_component_clause,[],[f476]) ).
fof(f6735,plain,
( spl17_454
| ~ spl17_107
| ~ spl17_152 ),
inference(avatar_split_clause,[],[f1417,f1392,f889,f6733]) ).
fof(f6733,plain,
( spl17_454
<=> ! [X2,X0,X1] :
( empty(X0)
| in(apply(X1,sK6(sK3(X0),X1,X2)),X0)
| sP0(sK3(X0),X1,X2)
| ~ empty(relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_454])]) ).
fof(f889,plain,
( spl17_107
<=> ! [X2,X0,X1] :
( in(apply(X1,sK6(X0,X1,X2)),X0)
| sP0(X0,X1,X2)
| ~ empty(relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_107])]) ).
fof(f1392,plain,
( spl17_152
<=> ! [X0,X1] :
( empty(X0)
| ~ in(X1,sK3(X0))
| in(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_152])]) ).
fof(f1417,plain,
( ! [X2,X0,X1] :
( empty(X0)
| in(apply(X1,sK6(sK3(X0),X1,X2)),X0)
| sP0(sK3(X0),X1,X2)
| ~ empty(relation_dom(X2)) )
| ~ spl17_107
| ~ spl17_152 ),
inference(resolution,[],[f1393,f890]) ).
fof(f890,plain,
( ! [X2,X0,X1] :
( in(apply(X1,sK6(X0,X1,X2)),X0)
| sP0(X0,X1,X2)
| ~ empty(relation_dom(X2)) )
| ~ spl17_107 ),
inference(avatar_component_clause,[],[f889]) ).
fof(f1393,plain,
( ! [X0,X1] :
( ~ in(X1,sK3(X0))
| empty(X0)
| in(X1,X0) )
| ~ spl17_152 ),
inference(avatar_component_clause,[],[f1392]) ).
fof(f6726,plain,
( spl17_453
| ~ spl17_107
| ~ spl17_148 ),
inference(avatar_split_clause,[],[f1371,f1367,f889,f6724]) ).
fof(f6724,plain,
( spl17_453
<=> ! [X2,X0,X1] :
( in(apply(X0,sK6(sK4(powerset(X1)),X0,X2)),X1)
| sP0(sK4(powerset(X1)),X0,X2)
| ~ empty(relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_453])]) ).
fof(f1367,plain,
( spl17_148
<=> ! [X0,X1] :
( ~ in(X0,sK4(powerset(X1)))
| in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_148])]) ).
fof(f1371,plain,
( ! [X2,X0,X1] :
( in(apply(X0,sK6(sK4(powerset(X1)),X0,X2)),X1)
| sP0(sK4(powerset(X1)),X0,X2)
| ~ empty(relation_dom(X2)) )
| ~ spl17_107
| ~ spl17_148 ),
inference(resolution,[],[f1368,f890]) ).
fof(f1368,plain,
( ! [X0,X1] :
( ~ in(X0,sK4(powerset(X1)))
| in(X0,X1) )
| ~ spl17_148 ),
inference(avatar_component_clause,[],[f1367]) ).
fof(f6661,plain,
( spl17_452
| ~ spl17_58
| ~ spl17_184 ),
inference(avatar_split_clause,[],[f2106,f2100,f507,f6659]) ).
fof(f6659,plain,
( spl17_452
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X2,relation_rng_restriction(X1,X0))) = apply(relation_rng_restriction(X1,X0),sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X2,relation_rng_restriction(X1,X0)))
| sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X2,relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X2,relation_rng_restriction(X1,X0)),relation_dom(X3))
| ~ in(sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X2,relation_rng_restriction(X1,X0)),relation_dom(X2))
| ~ sP0(relation_rng(sK2),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_452])]) ).
fof(f507,plain,
( spl17_58
<=> ! [X4,X0,X2,X1] :
( in(X4,relation_dom(X2))
| ~ in(apply(X1,X4),X0)
| ~ in(X4,relation_dom(X1))
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_58])]) ).
fof(f2100,plain,
( spl17_184
<=> ! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X2,relation_rng_restriction(X1,X0))) = apply(relation_rng_restriction(X1,X0),sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X2,relation_rng_restriction(X1,X0)))
| sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X2,relation_rng_restriction(X1,X0))
| in(apply(X2,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X2,relation_rng_restriction(X1,X0))),relation_rng(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_184])]) ).
fof(f2106,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X2,relation_rng_restriction(X1,X0))) = apply(relation_rng_restriction(X1,X0),sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X2,relation_rng_restriction(X1,X0)))
| sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X2,relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X2,relation_rng_restriction(X1,X0)),relation_dom(X3))
| ~ in(sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X2,relation_rng_restriction(X1,X0)),relation_dom(X2))
| ~ sP0(relation_rng(sK2),X2,X3) )
| ~ spl17_58
| ~ spl17_184 ),
inference(resolution,[],[f2101,f508]) ).
fof(f508,plain,
( ! [X2,X0,X1,X4] :
( ~ in(apply(X1,X4),X0)
| in(X4,relation_dom(X2))
| ~ in(X4,relation_dom(X1))
| ~ sP0(X0,X1,X2) )
| ~ spl17_58 ),
inference(avatar_component_clause,[],[f507]) ).
fof(f2101,plain,
( ! [X2,X0,X1] :
( in(apply(X2,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X2,relation_rng_restriction(X1,X0))),relation_rng(sK2))
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X2,relation_rng_restriction(X1,X0))) = apply(relation_rng_restriction(X1,X0),sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X2,relation_rng_restriction(X1,X0)))
| sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X2,relation_rng_restriction(X1,X0))
| ~ function(X0) )
| ~ spl17_184 ),
inference(avatar_component_clause,[],[f2100]) ).
fof(f6532,plain,
( spl17_451
| ~ spl17_82
| ~ spl17_215 ),
inference(avatar_split_clause,[],[f2443,f2419,f650,f6530]) ).
fof(f6530,plain,
( spl17_451
<=> ! [X0,X1] :
( ~ function(relation_rng_restriction(sK10,X0))
| ~ relation(relation_rng_restriction(sK10,X0))
| ~ function(X0)
| ~ relation(X0)
| subset(relation_dom(relation_rng_restriction(sK10,X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_451])]) ).
fof(f2443,plain,
( ! [X0,X1] :
( ~ function(relation_rng_restriction(sK10,X0))
| ~ relation(relation_rng_restriction(sK10,X0))
| ~ function(X0)
| ~ relation(X0)
| subset(relation_dom(relation_rng_restriction(sK10,X0)),X1) )
| ~ spl17_82
| ~ spl17_215 ),
inference(resolution,[],[f2420,f651]) ).
fof(f6528,plain,
( spl17_450
| ~ spl17_35
| ~ spl17_203 ),
inference(avatar_split_clause,[],[f2263,f2241,f352,f6526]) ).
fof(f6526,plain,
( spl17_450
<=> ! [X0,X3,X2,X1] :
( in(sK6(X0,X1,X2),relation_dom(X3))
| sP0(X0,X1,X2)
| ~ sP0(X0,X1,X3)
| ~ empty(relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_450])]) ).
fof(f2263,plain,
( ! [X2,X3,X0,X1] :
( in(sK6(X0,X1,X2),relation_dom(X3))
| sP0(X0,X1,X2)
| ~ sP0(X0,X1,X3)
| ~ empty(relation_dom(X2)) )
| ~ spl17_35
| ~ spl17_203 ),
inference(resolution,[],[f2242,f353]) ).
fof(f6524,plain,
( spl17_449
| ~ spl17_35
| ~ spl17_203 ),
inference(avatar_split_clause,[],[f2257,f2241,f352,f6522]) ).
fof(f6522,plain,
( spl17_449
<=> ! [X0,X3,X2,X1] :
( in(sK6(X0,X1,X2),relation_dom(X2))
| sP0(X0,X1,X2)
| ~ sP0(X0,X1,X3)
| ~ empty(relation_dom(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_449])]) ).
fof(f2257,plain,
( ! [X2,X3,X0,X1] :
( in(sK6(X0,X1,X2),relation_dom(X2))
| sP0(X0,X1,X2)
| ~ sP0(X0,X1,X3)
| ~ empty(relation_dom(X3)) )
| ~ spl17_35
| ~ spl17_203 ),
inference(resolution,[],[f2242,f353]) ).
fof(f6520,plain,
( spl17_448
| ~ spl17_132
| ~ spl17_198 ),
inference(avatar_split_clause,[],[f2223,f2201,f1132,f6518]) ).
fof(f6518,plain,
( spl17_448
<=> ! [X0,X1] :
( ~ in(sK10,sK6(X0,X1,sK10))
| sP0(X0,X1,sK10)
| element(apply(X1,sK6(X0,X1,sK10)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_448])]) ).
fof(f2201,plain,
( spl17_198
<=> ! [X2,X0,X1] :
( element(apply(X1,sK6(X0,X1,X2)),X0)
| sP0(X0,X1,X2)
| ~ in(relation_dom(X2),sK6(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_198])]) ).
fof(f2223,plain,
( ! [X0,X1] :
( ~ in(sK10,sK6(X0,X1,sK10))
| sP0(X0,X1,sK10)
| element(apply(X1,sK6(X0,X1,sK10)),X0) )
| ~ spl17_132
| ~ spl17_198 ),
inference(superposition,[],[f2202,f1134]) ).
fof(f2202,plain,
( ! [X2,X0,X1] :
( ~ in(relation_dom(X2),sK6(X0,X1,X2))
| sP0(X0,X1,X2)
| element(apply(X1,sK6(X0,X1,X2)),X0) )
| ~ spl17_198 ),
inference(avatar_component_clause,[],[f2201]) ).
fof(f6516,plain,
( spl17_447
| ~ spl17_50
| ~ spl17_176 ),
inference(avatar_split_clause,[],[f2069,f2049,f449,f6514]) ).
fof(f6514,plain,
( spl17_447
<=> ! [X2,X0,X1] :
( element(sK8(sK8(powerset(X0),X1),X2),X0)
| subset(powerset(X0),X1)
| subset(sK8(powerset(X0),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_447])]) ).
fof(f449,plain,
( spl17_50
<=> ! [X0,X1] :
( subset(X0,X1)
| in(sK8(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_50])]) ).
fof(f2049,plain,
( spl17_176
<=> ! [X2,X0,X1] :
( subset(powerset(X0),X1)
| element(X2,X0)
| ~ in(X2,sK8(powerset(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_176])]) ).
fof(f2069,plain,
( ! [X2,X0,X1] :
( element(sK8(sK8(powerset(X0),X1),X2),X0)
| subset(powerset(X0),X1)
| subset(sK8(powerset(X0),X1),X2) )
| ~ spl17_50
| ~ spl17_176 ),
inference(resolution,[],[f2050,f450]) ).
fof(f450,plain,
( ! [X0,X1] :
( in(sK8(X0,X1),X0)
| subset(X0,X1) )
| ~ spl17_50 ),
inference(avatar_component_clause,[],[f449]) ).
fof(f2050,plain,
( ! [X2,X0,X1] :
( ~ in(X2,sK8(powerset(X0),X1))
| element(X2,X0)
| subset(powerset(X0),X1) )
| ~ spl17_176 ),
inference(avatar_component_clause,[],[f2049]) ).
fof(f6512,plain,
( spl17_446
| ~ spl17_55
| ~ spl17_174 ),
inference(avatar_split_clause,[],[f2044,f2020,f489,f6510]) ).
fof(f6510,plain,
( spl17_446
<=> ! [X2,X0,X1] :
( empty(powerset(X0))
| subset(sK3(powerset(X0)),X1)
| element(X2,X0)
| ~ in(X2,sK8(sK3(powerset(X0)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_446])]) ).
fof(f2020,plain,
( spl17_174
<=> ! [X0,X1] :
( element(sK8(sK3(X0),X1),X0)
| empty(X0)
| subset(sK3(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_174])]) ).
fof(f2044,plain,
( ! [X2,X0,X1] :
( empty(powerset(X0))
| subset(sK3(powerset(X0)),X1)
| element(X2,X0)
| ~ in(X2,sK8(sK3(powerset(X0)),X1)) )
| ~ spl17_55
| ~ spl17_174 ),
inference(resolution,[],[f2021,f490]) ).
fof(f2021,plain,
( ! [X0,X1] :
( element(sK8(sK3(X0),X1),X0)
| empty(X0)
| subset(sK3(X0),X1) )
| ~ spl17_174 ),
inference(avatar_component_clause,[],[f2020]) ).
fof(f6508,plain,
( spl17_445
| ~ spl17_117
| ~ spl17_132 ),
inference(avatar_split_clause,[],[f1187,f1132,f953,f6506]) ).
fof(f6506,plain,
( spl17_445
<=> ! [X0,X1] :
( ~ in(sK10,sK6(X0,X1,sK10))
| sP0(X0,X1,sK10)
| in(apply(X1,sK6(X0,X1,sK10)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_445])]) ).
fof(f953,plain,
( spl17_117
<=> ! [X2,X0,X1] :
( in(apply(X1,sK6(X0,X1,X2)),X0)
| sP0(X0,X1,X2)
| ~ in(relation_dom(X2),sK6(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_117])]) ).
fof(f1187,plain,
( ! [X0,X1] :
( ~ in(sK10,sK6(X0,X1,sK10))
| sP0(X0,X1,sK10)
| in(apply(X1,sK6(X0,X1,sK10)),X0) )
| ~ spl17_117
| ~ spl17_132 ),
inference(superposition,[],[f954,f1134]) ).
fof(f954,plain,
( ! [X2,X0,X1] :
( ~ in(relation_dom(X2),sK6(X0,X1,X2))
| sP0(X0,X1,X2)
| in(apply(X1,sK6(X0,X1,X2)),X0) )
| ~ spl17_117 ),
inference(avatar_component_clause,[],[f953]) ).
fof(f6450,plain,
( spl17_444
| ~ spl17_66
| ~ spl17_364 ),
inference(avatar_split_clause,[],[f5268,f5222,f568,f6448]) ).
fof(f568,plain,
( spl17_66
<=> ! [X0] :
( ~ in(X0,relation_rng(relation_rng_restriction(sK1,sK2)))
| in(X0,relation_rng(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_66])]) ).
fof(f5222,plain,
( spl17_364
<=> ! [X0,X1] :
( in(sK8(sK4(powerset(X0)),X1),X0)
| subset(sK4(powerset(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_364])]) ).
fof(f5268,plain,
( ! [X0] :
( subset(sK4(powerset(relation_rng(relation_rng_restriction(sK1,sK2)))),X0)
| in(sK8(sK4(powerset(relation_rng(relation_rng_restriction(sK1,sK2)))),X0),relation_rng(sK2)) )
| ~ spl17_66
| ~ spl17_364 ),
inference(resolution,[],[f5223,f569]) ).
fof(f569,plain,
( ! [X0] :
( ~ in(X0,relation_rng(relation_rng_restriction(sK1,sK2)))
| in(X0,relation_rng(sK2)) )
| ~ spl17_66 ),
inference(avatar_component_clause,[],[f568]) ).
fof(f5223,plain,
( ! [X0,X1] :
( in(sK8(sK4(powerset(X0)),X1),X0)
| subset(sK4(powerset(X0)),X1) )
| ~ spl17_364 ),
inference(avatar_component_clause,[],[f5222]) ).
fof(f6346,plain,
( spl17_443
| ~ spl17_127
| ~ spl17_364 ),
inference(avatar_split_clause,[],[f5267,f5222,f1100,f6344]) ).
fof(f6344,plain,
( spl17_443
<=> ! [X0] :
( subset(sK4(powerset(relation_rng(relation_rng_restriction(sK1,sK2)))),X0)
| element(sK8(sK4(powerset(relation_rng(relation_rng_restriction(sK1,sK2)))),X0),relation_rng(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_443])]) ).
fof(f1100,plain,
( spl17_127
<=> ! [X0] :
( ~ in(X0,relation_rng(relation_rng_restriction(sK1,sK2)))
| element(X0,relation_rng(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_127])]) ).
fof(f5267,plain,
( ! [X0] :
( subset(sK4(powerset(relation_rng(relation_rng_restriction(sK1,sK2)))),X0)
| element(sK8(sK4(powerset(relation_rng(relation_rng_restriction(sK1,sK2)))),X0),relation_rng(sK2)) )
| ~ spl17_127
| ~ spl17_364 ),
inference(resolution,[],[f5223,f1101]) ).
fof(f1101,plain,
( ! [X0] :
( ~ in(X0,relation_rng(relation_rng_restriction(sK1,sK2)))
| element(X0,relation_rng(sK2)) )
| ~ spl17_127 ),
inference(avatar_component_clause,[],[f1100]) ).
fof(f6306,plain,
( spl17_442
| ~ spl17_82
| ~ spl17_212 ),
inference(avatar_split_clause,[],[f2401,f2373,f650,f6304]) ).
fof(f6304,plain,
( spl17_442
<=> ! [X0] :
( ~ function(relation_rng_restriction(sK10,X0))
| ~ relation(relation_rng_restriction(sK10,X0))
| ~ function(X0)
| ~ relation(X0)
| empty(relation_dom(relation_rng_restriction(sK10,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_442])]) ).
fof(f2401,plain,
( ! [X0] :
( ~ function(relation_rng_restriction(sK10,X0))
| ~ relation(relation_rng_restriction(sK10,X0))
| ~ function(X0)
| ~ relation(X0)
| empty(relation_dom(relation_rng_restriction(sK10,X0))) )
| ~ spl17_82
| ~ spl17_212 ),
inference(resolution,[],[f2374,f651]) ).
fof(f6302,plain,
( spl17_441
| ~ spl17_132
| ~ spl17_194 ),
inference(avatar_split_clause,[],[f2186,f2177,f1132,f6300]) ).
fof(f6300,plain,
( spl17_441
<=> ! [X0,X1] :
( ~ in(sK10,sK6(X0,X1,sK10))
| sP0(X0,X1,sK10)
| element(sK6(X0,X1,sK10),relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_441])]) ).
fof(f2177,plain,
( spl17_194
<=> ! [X2,X0,X1] :
( element(sK6(X0,X1,X2),relation_dom(X1))
| sP0(X0,X1,X2)
| ~ in(relation_dom(X2),sK6(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_194])]) ).
fof(f2186,plain,
( ! [X0,X1] :
( ~ in(sK10,sK6(X0,X1,sK10))
| sP0(X0,X1,sK10)
| element(sK6(X0,X1,sK10),relation_dom(X1)) )
| ~ spl17_132
| ~ spl17_194 ),
inference(superposition,[],[f2178,f1134]) ).
fof(f2178,plain,
( ! [X2,X0,X1] :
( ~ in(relation_dom(X2),sK6(X0,X1,X2))
| sP0(X0,X1,X2)
| element(sK6(X0,X1,X2),relation_dom(X1)) )
| ~ spl17_194 ),
inference(avatar_component_clause,[],[f2177]) ).
fof(f6298,plain,
( spl17_440
| ~ spl17_132
| ~ spl17_193 ),
inference(avatar_split_clause,[],[f2185,f2173,f1132,f6296]) ).
fof(f6296,plain,
( spl17_440
<=> ! [X0,X1] :
( ~ in(sK10,sK6(X0,sK10,X1))
| sP0(X0,sK10,X1)
| element(sK6(X0,sK10,X1),relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_440])]) ).
fof(f2173,plain,
( spl17_193
<=> ! [X2,X0,X1] :
( element(sK6(X0,X1,X2),relation_dom(X2))
| sP0(X0,X1,X2)
| ~ in(relation_dom(X1),sK6(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_193])]) ).
fof(f2185,plain,
( ! [X0,X1] :
( ~ in(sK10,sK6(X0,sK10,X1))
| sP0(X0,sK10,X1)
| element(sK6(X0,sK10,X1),relation_dom(X1)) )
| ~ spl17_132
| ~ spl17_193 ),
inference(superposition,[],[f2174,f1134]) ).
fof(f2174,plain,
( ! [X2,X0,X1] :
( ~ in(relation_dom(X1),sK6(X0,X1,X2))
| sP0(X0,X1,X2)
| element(sK6(X0,X1,X2),relation_dom(X2)) )
| ~ spl17_193 ),
inference(avatar_component_clause,[],[f2173]) ).
fof(f6294,plain,
( spl17_439
| ~ spl17_132
| ~ spl17_192 ),
inference(avatar_split_clause,[],[f2184,f2169,f1132,f6292]) ).
fof(f6292,plain,
( spl17_439
<=> ! [X0,X1] :
( element(sK6(X0,sK10,X1),sK10)
| element(sK6(X0,sK10,X1),relation_dom(X1))
| sP0(X0,sK10,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_439])]) ).
fof(f2169,plain,
( spl17_192
<=> ! [X2,X0,X1] :
( element(sK6(X0,X1,X2),relation_dom(X2))
| sP0(X0,X1,X2)
| element(sK6(X0,X1,X2),relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_192])]) ).
fof(f2184,plain,
( ! [X0,X1] :
( element(sK6(X0,sK10,X1),sK10)
| element(sK6(X0,sK10,X1),relation_dom(X1))
| sP0(X0,sK10,X1) )
| ~ spl17_132
| ~ spl17_192 ),
inference(superposition,[],[f2170,f1134]) ).
fof(f2170,plain,
( ! [X2,X0,X1] :
( element(sK6(X0,X1,X2),relation_dom(X2))
| element(sK6(X0,X1,X2),relation_dom(X1))
| sP0(X0,X1,X2) )
| ~ spl17_192 ),
inference(avatar_component_clause,[],[f2169]) ).
fof(f6290,plain,
( spl17_438
| ~ spl17_132
| ~ spl17_192 ),
inference(avatar_split_clause,[],[f2183,f2169,f1132,f6288]) ).
fof(f6288,plain,
( spl17_438
<=> ! [X0,X1] :
( element(sK6(X0,X1,sK10),sK10)
| element(sK6(X0,X1,sK10),relation_dom(X1))
| sP0(X0,X1,sK10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_438])]) ).
fof(f2183,plain,
( ! [X0,X1] :
( element(sK6(X0,X1,sK10),sK10)
| element(sK6(X0,X1,sK10),relation_dom(X1))
| sP0(X0,X1,sK10) )
| ~ spl17_132
| ~ spl17_192 ),
inference(superposition,[],[f2170,f1134]) ).
fof(f6286,plain,
( spl17_437
| ~ spl17_38
| ~ spl17_189 ),
inference(avatar_split_clause,[],[f2159,f2137,f380,f6284]) ).
fof(f6284,plain,
( spl17_437
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| subset(relation_rng(relation_rng_restriction(X1,X0)),X2)
| ~ in(relation_rng(X0),sK8(relation_rng(relation_rng_restriction(X1,X0)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_437])]) ).
fof(f380,plain,
( spl17_38
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_38])]) ).
fof(f2137,plain,
( spl17_189
<=> ! [X2,X0,X1] :
( in(sK8(relation_rng(relation_rng_restriction(X0,X1)),X2),relation_rng(X1))
| ~ relation(X1)
| subset(relation_rng(relation_rng_restriction(X0,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_189])]) ).
fof(f2159,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| subset(relation_rng(relation_rng_restriction(X1,X0)),X2)
| ~ in(relation_rng(X0),sK8(relation_rng(relation_rng_restriction(X1,X0)),X2)) )
| ~ spl17_38
| ~ spl17_189 ),
inference(resolution,[],[f2138,f381]) ).
fof(f381,plain,
( ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) )
| ~ spl17_38 ),
inference(avatar_component_clause,[],[f380]) ).
fof(f2138,plain,
( ! [X2,X0,X1] :
( in(sK8(relation_rng(relation_rng_restriction(X0,X1)),X2),relation_rng(X1))
| ~ relation(X1)
| subset(relation_rng(relation_rng_restriction(X0,X1)),X2) )
| ~ spl17_189 ),
inference(avatar_component_clause,[],[f2137]) ).
fof(f6282,plain,
( spl17_436
| ~ spl17_165
| ~ spl17_189 ),
inference(avatar_split_clause,[],[f2154,f2137,f1564,f6280]) ).
fof(f6280,plain,
( spl17_436
<=> ! [X0,X3,X2,X1] :
( ~ relation(relation_rng_restriction(X0,X1))
| subset(relation_rng(relation_rng_restriction(X2,relation_rng_restriction(X0,X1))),X3)
| ~ empty(relation_rng(X1))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_436])]) ).
fof(f2154,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(relation_rng_restriction(X0,X1))
| subset(relation_rng(relation_rng_restriction(X2,relation_rng_restriction(X0,X1))),X3)
| ~ empty(relation_rng(X1))
| ~ relation(X1) )
| ~ spl17_165
| ~ spl17_189 ),
inference(resolution,[],[f2138,f1565]) ).
fof(f6278,plain,
( spl17_435
| ~ spl17_38
| ~ spl17_188 ),
inference(avatar_split_clause,[],[f2149,f2133,f380,f6276]) ).
fof(f6276,plain,
( spl17_435
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(sK4(powerset(X0)),X1,X2)
| ~ in(relation_dom(X2),sK6(sK4(powerset(X0)),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_435])]) ).
fof(f2133,plain,
( spl17_188
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| in(sK6(sK4(powerset(X0)),X1,X2),relation_dom(X2))
| sP0(sK4(powerset(X0)),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_188])]) ).
fof(f2149,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(sK4(powerset(X0)),X1,X2)
| ~ in(relation_dom(X2),sK6(sK4(powerset(X0)),X1,X2)) )
| ~ spl17_38
| ~ spl17_188 ),
inference(resolution,[],[f2134,f381]) ).
fof(f2134,plain,
( ! [X2,X0,X1] :
( in(sK6(sK4(powerset(X0)),X1,X2),relation_dom(X2))
| ~ empty(X0)
| sP0(sK4(powerset(X0)),X1,X2) )
| ~ spl17_188 ),
inference(avatar_component_clause,[],[f2133]) ).
fof(f6274,plain,
( spl17_434
| ~ spl17_44
| ~ spl17_186 ),
inference(avatar_split_clause,[],[f2130,f2112,f406,f6272]) ).
fof(f6272,plain,
( spl17_434
<=> ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(powerset(X1),X2,X0)
| subset(apply(X2,sK6(powerset(X1),X2,X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_434])]) ).
fof(f2130,plain,
( ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(powerset(X1),X2,X0)
| subset(apply(X2,sK6(powerset(X1),X2,X0)),X1) )
| ~ spl17_44
| ~ spl17_186 ),
inference(resolution,[],[f2113,f407]) ).
fof(f6270,plain,
( spl17_433
| ~ spl17_54
| ~ spl17_174 ),
inference(avatar_split_clause,[],[f2043,f2020,f476,f6268]) ).
fof(f6268,plain,
( spl17_433
<=> ! [X2,X0,X1] :
( empty(powerset(X0))
| subset(sK3(powerset(X0)),X1)
| ~ empty(X0)
| ~ in(X2,sK8(sK3(powerset(X0)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_433])]) ).
fof(f2043,plain,
( ! [X2,X0,X1] :
( empty(powerset(X0))
| subset(sK3(powerset(X0)),X1)
| ~ empty(X0)
| ~ in(X2,sK8(sK3(powerset(X0)),X1)) )
| ~ spl17_54
| ~ spl17_174 ),
inference(resolution,[],[f2021,f477]) ).
fof(f6266,plain,
( spl17_432
| ~ spl17_50
| ~ spl17_173 ),
inference(avatar_split_clause,[],[f2038,f2016,f449,f6264]) ).
fof(f6264,plain,
( spl17_432
<=> ! [X2,X0,X1] :
( element(sK8(relation_rng(relation_rng_restriction(X0,X1)),X2),relation_rng(X1))
| ~ relation(X1)
| subset(relation_rng(relation_rng_restriction(X0,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_432])]) ).
fof(f2016,plain,
( spl17_173
<=> ! [X2,X0,X1] :
( ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| element(X0,relation_rng(X2))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_173])]) ).
fof(f2038,plain,
( ! [X2,X0,X1] :
( element(sK8(relation_rng(relation_rng_restriction(X0,X1)),X2),relation_rng(X1))
| ~ relation(X1)
| subset(relation_rng(relation_rng_restriction(X0,X1)),X2) )
| ~ spl17_50
| ~ spl17_173 ),
inference(resolution,[],[f2017,f450]) ).
fof(f2017,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| element(X0,relation_rng(X2))
| ~ relation(X2) )
| ~ spl17_173 ),
inference(avatar_component_clause,[],[f2016]) ).
fof(f6262,plain,
( spl17_431
| ~ spl17_55
| ~ spl17_172 ),
inference(avatar_split_clause,[],[f2030,f2012,f489,f6260]) ).
fof(f6260,plain,
( spl17_431
<=> ! [X2,X0,X1] :
( subset(sK4(powerset(powerset(X0))),X1)
| element(X2,X0)
| ~ in(X2,sK8(sK4(powerset(powerset(X0))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_431])]) ).
fof(f2012,plain,
( spl17_172
<=> ! [X0,X1] :
( element(sK8(sK4(powerset(X0)),X1),X0)
| subset(sK4(powerset(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_172])]) ).
fof(f2030,plain,
( ! [X2,X0,X1] :
( subset(sK4(powerset(powerset(X0))),X1)
| element(X2,X0)
| ~ in(X2,sK8(sK4(powerset(powerset(X0))),X1)) )
| ~ spl17_55
| ~ spl17_172 ),
inference(resolution,[],[f2013,f490]) ).
fof(f2013,plain,
( ! [X0,X1] :
( element(sK8(sK4(powerset(X0)),X1),X0)
| subset(sK4(powerset(X0)),X1) )
| ~ spl17_172 ),
inference(avatar_component_clause,[],[f2012]) ).
fof(f6258,plain,
( spl17_430
| ~ spl17_113
| ~ spl17_132 ),
inference(avatar_split_clause,[],[f1184,f1132,f926,f6256]) ).
fof(f6256,plain,
( spl17_430
<=> ! [X0,X1] :
( ~ in(sK10,sK6(X0,sK10,X1))
| sP0(X0,sK10,X1)
| in(sK6(X0,sK10,X1),relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_430])]) ).
fof(f926,plain,
( spl17_113
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),relation_dom(X2))
| sP0(X0,X1,X2)
| ~ in(relation_dom(X1),sK6(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_113])]) ).
fof(f1184,plain,
( ! [X0,X1] :
( ~ in(sK10,sK6(X0,sK10,X1))
| sP0(X0,sK10,X1)
| in(sK6(X0,sK10,X1),relation_dom(X1)) )
| ~ spl17_113
| ~ spl17_132 ),
inference(superposition,[],[f927,f1134]) ).
fof(f927,plain,
( ! [X2,X0,X1] :
( ~ in(relation_dom(X1),sK6(X0,X1,X2))
| sP0(X0,X1,X2)
| in(sK6(X0,X1,X2),relation_dom(X2)) )
| ~ spl17_113 ),
inference(avatar_component_clause,[],[f926]) ).
fof(f6254,plain,
( spl17_429
| ~ spl17_112
| ~ spl17_132 ),
inference(avatar_split_clause,[],[f1182,f1132,f922,f6252]) ).
fof(f6252,plain,
( spl17_429
<=> ! [X0,X1] :
( in(sK6(X0,X1,sK10),sK10)
| element(sK6(X0,X1,sK10),relation_dom(X1))
| sP0(X0,X1,sK10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_429])]) ).
fof(f922,plain,
( spl17_112
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),relation_dom(X2))
| sP0(X0,X1,X2)
| element(sK6(X0,X1,X2),relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_112])]) ).
fof(f1182,plain,
( ! [X0,X1] :
( in(sK6(X0,X1,sK10),sK10)
| element(sK6(X0,X1,sK10),relation_dom(X1))
| sP0(X0,X1,sK10) )
| ~ spl17_112
| ~ spl17_132 ),
inference(superposition,[],[f923,f1134]) ).
fof(f923,plain,
( ! [X2,X0,X1] :
( element(sK6(X0,X1,X2),relation_dom(X1))
| in(sK6(X0,X1,X2),relation_dom(X2))
| sP0(X0,X1,X2) )
| ~ spl17_112 ),
inference(avatar_component_clause,[],[f922]) ).
fof(f6250,plain,
( spl17_428
| ~ spl17_111
| ~ spl17_132 ),
inference(avatar_split_clause,[],[f1181,f1132,f918,f6248]) ).
fof(f6248,plain,
( spl17_428
<=> ! [X0,X1] :
( ~ in(sK10,sK6(X0,X1,sK10))
| sP0(X0,X1,sK10)
| in(sK6(X0,X1,sK10),relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_428])]) ).
fof(f918,plain,
( spl17_111
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),relation_dom(X1))
| sP0(X0,X1,X2)
| ~ in(relation_dom(X2),sK6(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_111])]) ).
fof(f1181,plain,
( ! [X0,X1] :
( ~ in(sK10,sK6(X0,X1,sK10))
| sP0(X0,X1,sK10)
| in(sK6(X0,X1,sK10),relation_dom(X1)) )
| ~ spl17_111
| ~ spl17_132 ),
inference(superposition,[],[f919,f1134]) ).
fof(f919,plain,
( ! [X2,X0,X1] :
( ~ in(relation_dom(X2),sK6(X0,X1,X2))
| sP0(X0,X1,X2)
| in(sK6(X0,X1,X2),relation_dom(X1)) )
| ~ spl17_111 ),
inference(avatar_component_clause,[],[f918]) ).
fof(f6246,plain,
( ~ spl17_427
| ~ spl17_38
| ~ spl17_391 ),
inference(avatar_split_clause,[],[f6116,f5468,f380,f6243]) ).
fof(f6243,plain,
( spl17_427
<=> in(relation_rng(sK2),sK4(sK4(powerset(relation_rng(relation_rng_restriction(sK1,sK2)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_427])]) ).
fof(f5468,plain,
( spl17_391
<=> in(sK4(sK4(powerset(relation_rng(relation_rng_restriction(sK1,sK2))))),relation_rng(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_391])]) ).
fof(f6116,plain,
( ~ in(relation_rng(sK2),sK4(sK4(powerset(relation_rng(relation_rng_restriction(sK1,sK2))))))
| ~ spl17_38
| ~ spl17_391 ),
inference(resolution,[],[f5470,f381]) ).
fof(f5470,plain,
( in(sK4(sK4(powerset(relation_rng(relation_rng_restriction(sK1,sK2))))),relation_rng(sK2))
| ~ spl17_391 ),
inference(avatar_component_clause,[],[f5468]) ).
fof(f6241,plain,
( spl17_426
| ~ spl17_108
| ~ spl17_132 ),
inference(avatar_split_clause,[],[f1179,f1132,f906,f6239]) ).
fof(f6239,plain,
( spl17_426
<=> ! [X0,X1] :
( in(sK6(X0,sK10,X1),sK10)
| element(sK6(X0,sK10,X1),relation_dom(X1))
| sP0(X0,sK10,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_426])]) ).
fof(f906,plain,
( spl17_108
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),relation_dom(X1))
| sP0(X0,X1,X2)
| element(sK6(X0,X1,X2),relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_108])]) ).
fof(f1179,plain,
( ! [X0,X1] :
( in(sK6(X0,sK10,X1),sK10)
| element(sK6(X0,sK10,X1),relation_dom(X1))
| sP0(X0,sK10,X1) )
| ~ spl17_108
| ~ spl17_132 ),
inference(superposition,[],[f907,f1134]) ).
fof(f907,plain,
( ! [X2,X0,X1] :
( element(sK6(X0,X1,X2),relation_dom(X2))
| in(sK6(X0,X1,X2),relation_dom(X1))
| sP0(X0,X1,X2) )
| ~ spl17_108 ),
inference(avatar_component_clause,[],[f906]) ).
fof(f6237,plain,
( spl17_425
| ~ spl17_59
| ~ spl17_132 ),
inference(avatar_split_clause,[],[f1172,f1132,f513,f6235]) ).
fof(f6235,plain,
( spl17_425
<=> ! [X0,X1] :
( in(sK6(X0,X1,sK10),sK10)
| in(sK6(X0,X1,sK10),relation_dom(X1))
| sP0(X0,X1,sK10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_425])]) ).
fof(f513,plain,
( spl17_59
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(sK6(X0,X1,X2),relation_dom(X1))
| in(sK6(X0,X1,X2),relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_59])]) ).
fof(f1172,plain,
( ! [X0,X1] :
( in(sK6(X0,X1,sK10),sK10)
| in(sK6(X0,X1,sK10),relation_dom(X1))
| sP0(X0,X1,sK10) )
| ~ spl17_59
| ~ spl17_132 ),
inference(superposition,[],[f514,f1134]) ).
fof(f514,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),relation_dom(X2))
| in(sK6(X0,X1,X2),relation_dom(X1))
| sP0(X0,X1,X2) )
| ~ spl17_59 ),
inference(avatar_component_clause,[],[f513]) ).
fof(f6233,plain,
( spl17_424
| ~ spl17_59
| ~ spl17_132 ),
inference(avatar_split_clause,[],[f1171,f1132,f513,f6231]) ).
fof(f6231,plain,
( spl17_424
<=> ! [X0,X1] :
( in(sK6(X0,sK10,X1),sK10)
| in(sK6(X0,sK10,X1),relation_dom(X1))
| sP0(X0,sK10,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_424])]) ).
fof(f1171,plain,
( ! [X0,X1] :
( in(sK6(X0,sK10,X1),sK10)
| in(sK6(X0,sK10,X1),relation_dom(X1))
| sP0(X0,sK10,X1) )
| ~ spl17_59
| ~ spl17_132 ),
inference(superposition,[],[f514,f1134]) ).
fof(f6179,plain,
( spl17_423
| ~ spl17_145
| ~ spl17_251 ),
inference(avatar_split_clause,[],[f3325,f3182,f1337,f6177]) ).
fof(f6177,plain,
( spl17_423
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK8(relation_dom(relation_rng_restriction(X1,X0)),X2)) = apply(relation_rng_restriction(X1,X0),sK8(relation_dom(relation_rng_restriction(X1,X0)),X2))
| ~ function(X0)
| in(sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X3,relation_rng_restriction(X1,X0)),X2)
| in(apply(X3,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X3,relation_rng_restriction(X1,X0))),relation_rng(sK2))
| sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X3,relation_rng_restriction(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_423])]) ).
fof(f1337,plain,
( spl17_145
<=> ! [X0,X1] :
( in(apply(X0,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1)),relation_rng(sK2))
| in(sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1),relation_dom(X1))
| sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_145])]) ).
fof(f3182,plain,
( spl17_251
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK8(relation_dom(relation_rng_restriction(X1,X0)),X2)) = apply(relation_rng_restriction(X1,X0),sK8(relation_dom(relation_rng_restriction(X1,X0)),X2))
| ~ in(X3,relation_dom(relation_rng_restriction(X1,X0)))
| in(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_251])]) ).
fof(f3325,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK8(relation_dom(relation_rng_restriction(X1,X0)),X2)) = apply(relation_rng_restriction(X1,X0),sK8(relation_dom(relation_rng_restriction(X1,X0)),X2))
| ~ function(X0)
| in(sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X3,relation_rng_restriction(X1,X0)),X2)
| in(apply(X3,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X3,relation_rng_restriction(X1,X0))),relation_rng(sK2))
| sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X3,relation_rng_restriction(X1,X0)) )
| ~ spl17_145
| ~ spl17_251 ),
inference(resolution,[],[f3183,f1338]) ).
fof(f1338,plain,
( ! [X0,X1] :
( in(apply(X0,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1)),relation_rng(sK2))
| in(sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1),relation_dom(X1))
| sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1) )
| ~ spl17_145 ),
inference(avatar_component_clause,[],[f1337]) ).
fof(f3183,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X3,relation_dom(relation_rng_restriction(X1,X0)))
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK8(relation_dom(relation_rng_restriction(X1,X0)),X2)) = apply(relation_rng_restriction(X1,X0),sK8(relation_dom(relation_rng_restriction(X1,X0)),X2))
| ~ function(X0)
| in(X3,X2) )
| ~ spl17_251 ),
inference(avatar_component_clause,[],[f3182]) ).
fof(f6175,plain,
( spl17_422
| ~ spl17_145
| ~ spl17_250 ),
inference(avatar_split_clause,[],[f3251,f3178,f1337,f6173]) ).
fof(f6173,plain,
( spl17_422
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK8(relation_dom(relation_rng_restriction(X1,X0)),X2)) = apply(relation_rng_restriction(X1,X0),sK8(relation_dom(relation_rng_restriction(X1,X0)),X2))
| ~ function(X0)
| element(sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X3,relation_rng_restriction(X1,X0)),X2)
| in(apply(X3,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X3,relation_rng_restriction(X1,X0))),relation_rng(sK2))
| sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X3,relation_rng_restriction(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_422])]) ).
fof(f3178,plain,
( spl17_250
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK8(relation_dom(relation_rng_restriction(X1,X0)),X2)) = apply(relation_rng_restriction(X1,X0),sK8(relation_dom(relation_rng_restriction(X1,X0)),X2))
| ~ in(X3,relation_dom(relation_rng_restriction(X1,X0)))
| element(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_250])]) ).
fof(f3251,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK8(relation_dom(relation_rng_restriction(X1,X0)),X2)) = apply(relation_rng_restriction(X1,X0),sK8(relation_dom(relation_rng_restriction(X1,X0)),X2))
| ~ function(X0)
| element(sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X3,relation_rng_restriction(X1,X0)),X2)
| in(apply(X3,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X3,relation_rng_restriction(X1,X0))),relation_rng(sK2))
| sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X3,relation_rng_restriction(X1,X0)) )
| ~ spl17_145
| ~ spl17_250 ),
inference(resolution,[],[f3179,f1338]) ).
fof(f3179,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X3,relation_dom(relation_rng_restriction(X1,X0)))
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK8(relation_dom(relation_rng_restriction(X1,X0)),X2)) = apply(relation_rng_restriction(X1,X0),sK8(relation_dom(relation_rng_restriction(X1,X0)),X2))
| ~ function(X0)
| element(X3,X2) )
| ~ spl17_250 ),
inference(avatar_component_clause,[],[f3178]) ).
fof(f6039,plain,
( spl17_421
| ~ spl17_132
| ~ spl17_190 ),
inference(avatar_split_clause,[],[f2167,f2141,f1132,f6037]) ).
fof(f6037,plain,
( spl17_421
<=> ! [X0,X1] :
( element(sK6(sK4(powerset(X0)),X1,sK10),sK10)
| sP0(sK4(powerset(X0)),X1,sK10)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_421])]) ).
fof(f2141,plain,
( spl17_190
<=> ! [X2,X0,X1] :
( element(sK6(sK4(powerset(X1)),X0,X2),relation_dom(X2))
| sP0(sK4(powerset(X1)),X0,X2)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_190])]) ).
fof(f2167,plain,
( ! [X0,X1] :
( element(sK6(sK4(powerset(X0)),X1,sK10),sK10)
| sP0(sK4(powerset(X0)),X1,sK10)
| ~ empty(X0) )
| ~ spl17_132
| ~ spl17_190 ),
inference(superposition,[],[f2142,f1134]) ).
fof(f2142,plain,
( ! [X2,X0,X1] :
( element(sK6(sK4(powerset(X1)),X0,X2),relation_dom(X2))
| sP0(sK4(powerset(X1)),X0,X2)
| ~ empty(X1) )
| ~ spl17_190 ),
inference(avatar_component_clause,[],[f2141]) ).
fof(f6029,plain,
( ~ spl17_48
| spl17_420
| ~ spl17_131
| ~ spl17_189 ),
inference(avatar_split_clause,[],[f2160,f2137,f1127,f6027,f440]) ).
fof(f440,plain,
( spl17_48
<=> relation(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_48])]) ).
fof(f6027,plain,
( spl17_420
<=> ! [X0,X1] :
( in(sK8(relation_rng(relation_rng_restriction(X0,sK10)),X1),sK10)
| subset(relation_rng(relation_rng_restriction(X0,sK10)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_420])]) ).
fof(f1127,plain,
( spl17_131
<=> sK10 = relation_rng(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_131])]) ).
fof(f2160,plain,
( ! [X0,X1] :
( in(sK8(relation_rng(relation_rng_restriction(X0,sK10)),X1),sK10)
| ~ relation(sK10)
| subset(relation_rng(relation_rng_restriction(X0,sK10)),X1) )
| ~ spl17_131
| ~ spl17_189 ),
inference(superposition,[],[f2138,f1129]) ).
fof(f1129,plain,
( sK10 = relation_rng(sK10)
| ~ spl17_131 ),
inference(avatar_component_clause,[],[f1127]) ).
fof(f6025,plain,
( spl17_419
| ~ spl17_132
| ~ spl17_188 ),
inference(avatar_split_clause,[],[f2150,f2133,f1132,f6023]) ).
fof(f6023,plain,
( spl17_419
<=> ! [X0,X1] :
( in(sK6(sK4(powerset(X0)),X1,sK10),sK10)
| ~ empty(X0)
| sP0(sK4(powerset(X0)),X1,sK10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_419])]) ).
fof(f2150,plain,
( ! [X0,X1] :
( in(sK6(sK4(powerset(X0)),X1,sK10),sK10)
| ~ empty(X0)
| sP0(sK4(powerset(X0)),X1,sK10) )
| ~ spl17_132
| ~ spl17_188 ),
inference(superposition,[],[f2134,f1134]) ).
fof(f6021,plain,
( spl17_418
| ~ spl17_165
| ~ spl17_185 ),
inference(avatar_split_clause,[],[f2122,f2108,f1564,f6019]) ).
fof(f6019,plain,
( spl17_418
<=> ! [X2,X0,X1] :
( ~ relation(relation_rng_restriction(X0,X1))
| empty(relation_rng(relation_rng_restriction(X2,relation_rng_restriction(X0,X1))))
| ~ empty(relation_rng(X1))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_418])]) ).
fof(f2108,plain,
( spl17_185
<=> ! [X0,X1] :
( in(sK4(relation_rng(relation_rng_restriction(X0,X1))),relation_rng(X1))
| ~ relation(X1)
| empty(relation_rng(relation_rng_restriction(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_185])]) ).
fof(f2122,plain,
( ! [X2,X0,X1] :
( ~ relation(relation_rng_restriction(X0,X1))
| empty(relation_rng(relation_rng_restriction(X2,relation_rng_restriction(X0,X1))))
| ~ empty(relation_rng(X1))
| ~ relation(X1) )
| ~ spl17_165
| ~ spl17_185 ),
inference(resolution,[],[f2109,f1565]) ).
fof(f2109,plain,
( ! [X0,X1] :
( in(sK4(relation_rng(relation_rng_restriction(X0,X1))),relation_rng(X1))
| ~ relation(X1)
| empty(relation_rng(relation_rng_restriction(X0,X1))) )
| ~ spl17_185 ),
inference(avatar_component_clause,[],[f2108]) ).
fof(f6017,plain,
( spl17_417
| ~ spl17_86
| ~ spl17_176 ),
inference(avatar_split_clause,[],[f2068,f2049,f683,f6015]) ).
fof(f6015,plain,
( spl17_417
<=> ! [X0,X1] :
( element(sK4(sK8(powerset(X0),X1)),X0)
| subset(powerset(X0),X1)
| empty(sK8(powerset(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_417])]) ).
fof(f683,plain,
( spl17_86
<=> ! [X0] :
( empty(X0)
| in(sK4(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_86])]) ).
fof(f2068,plain,
( ! [X0,X1] :
( element(sK4(sK8(powerset(X0),X1)),X0)
| subset(powerset(X0),X1)
| empty(sK8(powerset(X0),X1)) )
| ~ spl17_86
| ~ spl17_176 ),
inference(resolution,[],[f2050,f684]) ).
fof(f684,plain,
( ! [X0] :
( in(sK4(X0),X0)
| empty(X0) )
| ~ spl17_86 ),
inference(avatar_component_clause,[],[f683]) ).
fof(f6013,plain,
( spl17_416
| ~ spl17_54
| ~ spl17_172 ),
inference(avatar_split_clause,[],[f2029,f2012,f476,f6011]) ).
fof(f6011,plain,
( spl17_416
<=> ! [X2,X0,X1] :
( subset(sK4(powerset(powerset(X0))),X1)
| ~ empty(X0)
| ~ in(X2,sK8(sK4(powerset(powerset(X0))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_416])]) ).
fof(f2029,plain,
( ! [X2,X0,X1] :
( subset(sK4(powerset(powerset(X0))),X1)
| ~ empty(X0)
| ~ in(X2,sK8(sK4(powerset(powerset(X0))),X1)) )
| ~ spl17_54
| ~ spl17_172 ),
inference(resolution,[],[f2013,f477]) ).
fof(f6008,plain,
( spl17_415
| ~ spl17_107
| ~ spl17_171 ),
inference(avatar_split_clause,[],[f2023,f2008,f889,f6006]) ).
fof(f6006,plain,
( spl17_415
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| subset(powerset(X0),X1)
| sP0(sK8(powerset(X0),X1),X2,X3)
| ~ empty(relation_dom(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_415])]) ).
fof(f2008,plain,
( spl17_171
<=> ! [X2,X0,X1] :
( subset(powerset(X0),X1)
| ~ empty(X0)
| ~ in(X2,sK8(powerset(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_171])]) ).
fof(f2023,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| subset(powerset(X0),X1)
| sP0(sK8(powerset(X0),X1),X2,X3)
| ~ empty(relation_dom(X3)) )
| ~ spl17_107
| ~ spl17_171 ),
inference(resolution,[],[f2009,f890]) ).
fof(f2009,plain,
( ! [X2,X0,X1] :
( ~ in(X2,sK8(powerset(X0),X1))
| ~ empty(X0)
| subset(powerset(X0),X1) )
| ~ spl17_171 ),
inference(avatar_component_clause,[],[f2008]) ).
fof(f6004,plain,
( spl17_414
| ~ spl17_55
| ~ spl17_160 ),
inference(avatar_split_clause,[],[f1547,f1525,f489,f6002]) ).
fof(f6002,plain,
( spl17_414
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK3(powerset(X0)))
| element(X1,X0)
| ~ in(X1,sK4(sK3(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_414])]) ).
fof(f1525,plain,
( spl17_160
<=> ! [X0] :
( element(sK4(sK3(X0)),X0)
| empty(X0)
| empty(sK3(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_160])]) ).
fof(f1547,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK3(powerset(X0)))
| element(X1,X0)
| ~ in(X1,sK4(sK3(powerset(X0)))) )
| ~ spl17_55
| ~ spl17_160 ),
inference(resolution,[],[f1526,f490]) ).
fof(f1526,plain,
( ! [X0] :
( element(sK4(sK3(X0)),X0)
| empty(X0)
| empty(sK3(X0)) )
| ~ spl17_160 ),
inference(avatar_component_clause,[],[f1525]) ).
fof(f5918,plain,
( spl17_413
| ~ spl17_38
| ~ spl17_185 ),
inference(avatar_split_clause,[],[f2126,f2108,f380,f5916]) ).
fof(f5916,plain,
( spl17_413
<=> ! [X0,X1] :
( ~ relation(X0)
| empty(relation_rng(relation_rng_restriction(X1,X0)))
| ~ in(relation_rng(X0),sK4(relation_rng(relation_rng_restriction(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_413])]) ).
fof(f2126,plain,
( ! [X0,X1] :
( ~ relation(X0)
| empty(relation_rng(relation_rng_restriction(X1,X0)))
| ~ in(relation_rng(X0),sK4(relation_rng(relation_rng_restriction(X1,X0)))) )
| ~ spl17_38
| ~ spl17_185 ),
inference(resolution,[],[f2109,f381]) ).
fof(f5914,plain,
( spl17_412
| ~ spl17_44
| ~ spl17_174 ),
inference(avatar_split_clause,[],[f2045,f2020,f406,f5912]) ).
fof(f5912,plain,
( spl17_412
<=> ! [X0,X1] :
( empty(powerset(X0))
| subset(sK3(powerset(X0)),X1)
| subset(sK8(sK3(powerset(X0)),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_412])]) ).
fof(f2045,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| subset(sK3(powerset(X0)),X1)
| subset(sK8(sK3(powerset(X0)),X1),X0) )
| ~ spl17_44
| ~ spl17_174 ),
inference(resolution,[],[f2021,f407]) ).
fof(f5909,plain,
( spl17_411
| ~ spl17_86
| ~ spl17_173 ),
inference(avatar_split_clause,[],[f2037,f2016,f683,f5907]) ).
fof(f5907,plain,
( spl17_411
<=> ! [X0,X1] :
( element(sK4(relation_rng(relation_rng_restriction(X0,X1))),relation_rng(X1))
| ~ relation(X1)
| empty(relation_rng(relation_rng_restriction(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_411])]) ).
fof(f2037,plain,
( ! [X0,X1] :
( element(sK4(relation_rng(relation_rng_restriction(X0,X1))),relation_rng(X1))
| ~ relation(X1)
| empty(relation_rng(relation_rng_restriction(X0,X1))) )
| ~ spl17_86
| ~ spl17_173 ),
inference(resolution,[],[f2017,f684]) ).
fof(f5905,plain,
( spl17_410
| ~ spl17_107
| ~ spl17_165 ),
inference(avatar_split_clause,[],[f1988,f1564,f889,f5903]) ).
fof(f5903,plain,
( spl17_410
<=> ! [X0,X3,X2,X1] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| sP0(relation_rng(relation_rng_restriction(X1,X0)),X2,X3)
| ~ empty(relation_dom(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_410])]) ).
fof(f1988,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| sP0(relation_rng(relation_rng_restriction(X1,X0)),X2,X3)
| ~ empty(relation_dom(X3)) )
| ~ spl17_107
| ~ spl17_165 ),
inference(resolution,[],[f1565,f890]) ).
fof(f5901,plain,
( spl17_409
| ~ spl17_54
| ~ spl17_160 ),
inference(avatar_split_clause,[],[f1548,f1525,f476,f5899]) ).
fof(f5899,plain,
( spl17_409
<=> ! [X0,X1] :
( empty(powerset(X0))
| empty(sK3(powerset(X0)))
| ~ empty(X0)
| ~ in(X1,sK4(sK3(powerset(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_409])]) ).
fof(f1548,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| empty(sK3(powerset(X0)))
| ~ empty(X0)
| ~ in(X1,sK4(sK3(powerset(X0)))) )
| ~ spl17_54
| ~ spl17_160 ),
inference(resolution,[],[f1526,f477]) ).
fof(f5897,plain,
( spl17_408
| ~ spl17_55
| ~ spl17_159 ),
inference(avatar_split_clause,[],[f1543,f1521,f489,f5895]) ).
fof(f5895,plain,
( spl17_408
<=> ! [X0,X1] :
( empty(sK4(powerset(powerset(X0))))
| element(X1,X0)
| ~ in(X1,sK4(sK4(powerset(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_408])]) ).
fof(f1521,plain,
( spl17_159
<=> ! [X0] :
( element(sK4(sK4(powerset(X0))),X0)
| empty(sK4(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_159])]) ).
fof(f1543,plain,
( ! [X0,X1] :
( empty(sK4(powerset(powerset(X0))))
| element(X1,X0)
| ~ in(X1,sK4(sK4(powerset(powerset(X0))))) )
| ~ spl17_55
| ~ spl17_159 ),
inference(resolution,[],[f1522,f490]) ).
fof(f1522,plain,
( ! [X0] :
( element(sK4(sK4(powerset(X0))),X0)
| empty(sK4(powerset(X0))) )
| ~ spl17_159 ),
inference(avatar_component_clause,[],[f1521]) ).
fof(f5892,plain,
( spl17_407
| ~ spl17_38
| ~ spl17_184 ),
inference(avatar_split_clause,[],[f2105,f2100,f380,f5890]) ).
fof(f5890,plain,
( spl17_407
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X2,relation_rng_restriction(X1,X0))) = apply(relation_rng_restriction(X1,X0),sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X2,relation_rng_restriction(X1,X0)))
| sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X2,relation_rng_restriction(X1,X0))
| ~ function(X0)
| ~ in(relation_rng(sK2),apply(X2,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X2,relation_rng_restriction(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_407])]) ).
fof(f2105,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X2,relation_rng_restriction(X1,X0))) = apply(relation_rng_restriction(X1,X0),sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X2,relation_rng_restriction(X1,X0)))
| sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X2,relation_rng_restriction(X1,X0))
| ~ function(X0)
| ~ in(relation_rng(sK2),apply(X2,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X2,relation_rng_restriction(X1,X0)))) )
| ~ spl17_38
| ~ spl17_184 ),
inference(resolution,[],[f2101,f381]) ).
fof(f5888,plain,
( spl17_406
| ~ spl17_125
| ~ spl17_127 ),
inference(avatar_split_clause,[],[f1106,f1100,f1071,f5886]) ).
fof(f5886,plain,
( spl17_406
<=> ! [X2,X0,X1] :
( element(apply(X0,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,relation_rng_restriction(X1,X2))),relation_rng(sK2))
| ~ function(X2)
| ~ relation(X2)
| ~ function(relation_rng_restriction(X1,X2))
| ~ relation(relation_rng_restriction(X1,X2))
| apply(X2,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,relation_rng_restriction(X1,X2))) = apply(relation_rng_restriction(X1,X2),sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,relation_rng_restriction(X1,X2)))
| sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X0,relation_rng_restriction(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_406])]) ).
fof(f1071,plain,
( spl17_125
<=> ! [X0,X3,X2,X1] :
( apply(X0,sK6(X1,X2,relation_rng_restriction(X3,X0))) = apply(relation_rng_restriction(X3,X0),sK6(X1,X2,relation_rng_restriction(X3,X0)))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X3,X0))
| ~ relation(relation_rng_restriction(X3,X0))
| in(apply(X2,sK6(X1,X2,relation_rng_restriction(X3,X0))),X1)
| sP0(X1,X2,relation_rng_restriction(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_125])]) ).
fof(f1106,plain,
( ! [X2,X0,X1] :
( element(apply(X0,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,relation_rng_restriction(X1,X2))),relation_rng(sK2))
| ~ function(X2)
| ~ relation(X2)
| ~ function(relation_rng_restriction(X1,X2))
| ~ relation(relation_rng_restriction(X1,X2))
| apply(X2,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,relation_rng_restriction(X1,X2))) = apply(relation_rng_restriction(X1,X2),sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,relation_rng_restriction(X1,X2)))
| sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X0,relation_rng_restriction(X1,X2)) )
| ~ spl17_125
| ~ spl17_127 ),
inference(resolution,[],[f1101,f1072]) ).
fof(f1072,plain,
( ! [X2,X3,X0,X1] :
( in(apply(X2,sK6(X1,X2,relation_rng_restriction(X3,X0))),X1)
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X3,X0))
| ~ relation(relation_rng_restriction(X3,X0))
| apply(X0,sK6(X1,X2,relation_rng_restriction(X3,X0))) = apply(relation_rng_restriction(X3,X0),sK6(X1,X2,relation_rng_restriction(X3,X0)))
| sP0(X1,X2,relation_rng_restriction(X3,X0)) )
| ~ spl17_125 ),
inference(avatar_component_clause,[],[f1071]) ).
fof(f5849,plain,
( spl17_405
| ~ spl17_66
| ~ spl17_255 ),
inference(avatar_split_clause,[],[f3446,f3405,f568,f5847]) ).
fof(f5847,plain,
( spl17_405
<=> ! [X2,X0,X1] :
( in(sK6(relation_dom(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)),X1,X2),relation_dom(X2))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(X0)
| sP0(relation_dom(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)),X1,X2)
| in(apply(X0,apply(X1,sK6(relation_dom(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)),X1,X2))),relation_rng(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_405])]) ).
fof(f3405,plain,
( spl17_255
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(apply(X0,apply(X2,sK6(relation_dom(relation_rng_restriction(X1,X0)),X2,X3))),X1)
| in(sK6(relation_dom(relation_rng_restriction(X1,X0)),X2,X3),relation_dom(X3))
| sP0(relation_dom(relation_rng_restriction(X1,X0)),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_255])]) ).
fof(f3446,plain,
( ! [X2,X0,X1] :
( in(sK6(relation_dom(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)),X1,X2),relation_dom(X2))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(X0)
| sP0(relation_dom(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)),X1,X2)
| in(apply(X0,apply(X1,sK6(relation_dom(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)),X1,X2))),relation_rng(sK2)) )
| ~ spl17_66
| ~ spl17_255 ),
inference(resolution,[],[f3406,f569]) ).
fof(f3406,plain,
( ! [X2,X3,X0,X1] :
( in(apply(X0,apply(X2,sK6(relation_dom(relation_rng_restriction(X1,X0)),X2,X3))),X1)
| in(sK6(relation_dom(relation_rng_restriction(X1,X0)),X2,X3),relation_dom(X3))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(X0)
| sP0(relation_dom(relation_rng_restriction(X1,X0)),X2,X3) )
| ~ spl17_255 ),
inference(avatar_component_clause,[],[f3405]) ).
fof(f5845,plain,
( spl17_404
| ~ spl17_127
| ~ spl17_255 ),
inference(avatar_split_clause,[],[f3445,f3405,f1100,f5843]) ).
fof(f5843,plain,
( spl17_404
<=> ! [X2,X0,X1] :
( in(sK6(relation_dom(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)),X1,X2),relation_dom(X2))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(X0)
| sP0(relation_dom(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)),X1,X2)
| element(apply(X0,apply(X1,sK6(relation_dom(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)),X1,X2))),relation_rng(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_404])]) ).
fof(f3445,plain,
( ! [X2,X0,X1] :
( in(sK6(relation_dom(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)),X1,X2),relation_dom(X2))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(X0)
| sP0(relation_dom(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)),X1,X2)
| element(apply(X0,apply(X1,sK6(relation_dom(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)),X1,X2))),relation_rng(sK2)) )
| ~ spl17_127
| ~ spl17_255 ),
inference(resolution,[],[f3406,f1101]) ).
fof(f5841,plain,
( spl17_403
| ~ spl17_66
| ~ spl17_254 ),
inference(avatar_split_clause,[],[f3419,f3401,f568,f5839]) ).
fof(f5839,plain,
( spl17_403
<=> ! [X2,X0,X1] :
( element(sK6(relation_dom(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)),X1,X2),relation_dom(X2))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(X0)
| sP0(relation_dom(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)),X1,X2)
| in(apply(X0,apply(X1,sK6(relation_dom(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)),X1,X2))),relation_rng(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_403])]) ).
fof(f3401,plain,
( spl17_254
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(apply(X0,apply(X2,sK6(relation_dom(relation_rng_restriction(X1,X0)),X2,X3))),X1)
| element(sK6(relation_dom(relation_rng_restriction(X1,X0)),X2,X3),relation_dom(X3))
| sP0(relation_dom(relation_rng_restriction(X1,X0)),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_254])]) ).
fof(f3419,plain,
( ! [X2,X0,X1] :
( element(sK6(relation_dom(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)),X1,X2),relation_dom(X2))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(X0)
| sP0(relation_dom(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)),X1,X2)
| in(apply(X0,apply(X1,sK6(relation_dom(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)),X1,X2))),relation_rng(sK2)) )
| ~ spl17_66
| ~ spl17_254 ),
inference(resolution,[],[f3402,f569]) ).
fof(f3402,plain,
( ! [X2,X3,X0,X1] :
( in(apply(X0,apply(X2,sK6(relation_dom(relation_rng_restriction(X1,X0)),X2,X3))),X1)
| element(sK6(relation_dom(relation_rng_restriction(X1,X0)),X2,X3),relation_dom(X3))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(X0)
| sP0(relation_dom(relation_rng_restriction(X1,X0)),X2,X3) )
| ~ spl17_254 ),
inference(avatar_component_clause,[],[f3401]) ).
fof(f5837,plain,
( spl17_402
| ~ spl17_127
| ~ spl17_254 ),
inference(avatar_split_clause,[],[f3418,f3401,f1100,f5835]) ).
fof(f5835,plain,
( spl17_402
<=> ! [X2,X0,X1] :
( element(sK6(relation_dom(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)),X1,X2),relation_dom(X2))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(X0)
| sP0(relation_dom(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)),X1,X2)
| element(apply(X0,apply(X1,sK6(relation_dom(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)),X1,X2))),relation_rng(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_402])]) ).
fof(f3418,plain,
( ! [X2,X0,X1] :
( element(sK6(relation_dom(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)),X1,X2),relation_dom(X2))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(X0)
| sP0(relation_dom(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)),X1,X2)
| element(apply(X0,apply(X1,sK6(relation_dom(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)),X1,X2))),relation_rng(sK2)) )
| ~ spl17_127
| ~ spl17_254 ),
inference(resolution,[],[f3402,f1101]) ).
fof(f5787,plain,
( spl17_401
| ~ spl17_24
| ~ spl17_372 ),
inference(avatar_split_clause,[],[f5549,f5291,f297,f5784]) ).
fof(f5784,plain,
( spl17_401
<=> function(sK4(powerset(relation_rng(relation_rng_restriction(sK1,sK2))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_401])]) ).
fof(f297,plain,
( spl17_24
<=> ! [X0] :
( function(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_24])]) ).
fof(f5291,plain,
( spl17_372
<=> empty(sK4(powerset(relation_rng(relation_rng_restriction(sK1,sK2))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_372])]) ).
fof(f5549,plain,
( function(sK4(powerset(relation_rng(relation_rng_restriction(sK1,sK2)))))
| ~ spl17_24
| ~ spl17_372 ),
inference(resolution,[],[f5293,f298]) ).
fof(f298,plain,
( ! [X0] :
( ~ empty(X0)
| function(X0) )
| ~ spl17_24 ),
inference(avatar_component_clause,[],[f297]) ).
fof(f5293,plain,
( empty(sK4(powerset(relation_rng(relation_rng_restriction(sK1,sK2)))))
| ~ spl17_372 ),
inference(avatar_component_clause,[],[f5291]) ).
fof(f5782,plain,
( ~ spl17_48
| spl17_400
| ~ spl17_131
| ~ spl17_185 ),
inference(avatar_split_clause,[],[f2127,f2108,f1127,f5780,f440]) ).
fof(f5780,plain,
( spl17_400
<=> ! [X0] :
( in(sK4(relation_rng(relation_rng_restriction(X0,sK10))),sK10)
| empty(relation_rng(relation_rng_restriction(X0,sK10))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_400])]) ).
fof(f2127,plain,
( ! [X0] :
( in(sK4(relation_rng(relation_rng_restriction(X0,sK10))),sK10)
| ~ relation(sK10)
| empty(relation_rng(relation_rng_restriction(X0,sK10))) )
| ~ spl17_131
| ~ spl17_185 ),
inference(superposition,[],[f2109,f1129]) ).
fof(f5778,plain,
( spl17_399
| ~ spl17_44
| ~ spl17_172 ),
inference(avatar_split_clause,[],[f2031,f2012,f406,f5776]) ).
fof(f5776,plain,
( spl17_399
<=> ! [X0,X1] :
( subset(sK4(powerset(powerset(X0))),X1)
| subset(sK8(sK4(powerset(powerset(X0))),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_399])]) ).
fof(f2031,plain,
( ! [X0,X1] :
( subset(sK4(powerset(powerset(X0))),X1)
| subset(sK8(sK4(powerset(powerset(X0))),X1),X0) )
| ~ spl17_44
| ~ spl17_172 ),
inference(resolution,[],[f2013,f407]) ).
fof(f5774,plain,
( spl17_398
| ~ spl17_99
| ~ spl17_161 ),
inference(avatar_split_clause,[],[f1553,f1529,f829,f5772]) ).
fof(f5772,plain,
( spl17_398
<=> ! [X0,X1] :
( ~ subset(powerset(X0),X1)
| empty(powerset(X1))
| empty(powerset(X0))
| ~ subset(powerset(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_398])]) ).
fof(f829,plain,
( spl17_99
<=> ! [X0,X1] :
( empty(powerset(X0))
| in(X1,powerset(X0))
| ~ subset(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_99])]) ).
fof(f1529,plain,
( spl17_161
<=> ! [X0,X1] :
( empty(powerset(X0))
| ~ subset(X1,X0)
| ~ in(powerset(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_161])]) ).
fof(f1553,plain,
( ! [X0,X1] :
( ~ subset(powerset(X0),X1)
| empty(powerset(X1))
| empty(powerset(X0))
| ~ subset(powerset(X1),X0) )
| ~ spl17_99
| ~ spl17_161 ),
inference(resolution,[],[f1530,f830]) ).
fof(f830,plain,
( ! [X0,X1] :
( in(X1,powerset(X0))
| empty(powerset(X0))
| ~ subset(X1,X0) )
| ~ spl17_99 ),
inference(avatar_component_clause,[],[f829]) ).
fof(f1530,plain,
( ! [X0,X1] :
( ~ in(powerset(X0),X1)
| ~ subset(X1,X0)
| empty(powerset(X0)) )
| ~ spl17_161 ),
inference(avatar_component_clause,[],[f1529]) ).
fof(f5770,plain,
( spl17_397
| ~ spl17_54
| ~ spl17_159 ),
inference(avatar_split_clause,[],[f1544,f1521,f476,f5768]) ).
fof(f5768,plain,
( spl17_397
<=> ! [X0,X1] :
( empty(sK4(powerset(powerset(X0))))
| ~ empty(X0)
| ~ in(X1,sK4(sK4(powerset(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_397])]) ).
fof(f1544,plain,
( ! [X0,X1] :
( empty(sK4(powerset(powerset(X0))))
| ~ empty(X0)
| ~ in(X1,sK4(sK4(powerset(powerset(X0))))) )
| ~ spl17_54
| ~ spl17_159 ),
inference(resolution,[],[f1522,f477]) ).
fof(f5763,plain,
( spl17_396
| ~ spl17_145
| ~ spl17_247 ),
inference(avatar_split_clause,[],[f3148,f3086,f1337,f5761]) ).
fof(f5761,plain,
( spl17_396
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK8(relation_dom(relation_rng_restriction(X1,X0)),X2)) = apply(relation_rng_restriction(X1,X0),sK8(relation_dom(relation_rng_restriction(X1,X0)),X2))
| ~ function(X0)
| ~ empty(X2)
| in(apply(X3,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X3,relation_rng_restriction(X1,X0))),relation_rng(sK2))
| sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X3,relation_rng_restriction(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_396])]) ).
fof(f3086,plain,
( spl17_247
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK8(relation_dom(relation_rng_restriction(X1,X0)),X2)) = apply(relation_rng_restriction(X1,X0),sK8(relation_dom(relation_rng_restriction(X1,X0)),X2))
| ~ in(X3,relation_dom(relation_rng_restriction(X1,X0)))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_247])]) ).
fof(f3148,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK8(relation_dom(relation_rng_restriction(X1,X0)),X2)) = apply(relation_rng_restriction(X1,X0),sK8(relation_dom(relation_rng_restriction(X1,X0)),X2))
| ~ function(X0)
| ~ empty(X2)
| in(apply(X3,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X3,relation_rng_restriction(X1,X0))),relation_rng(sK2))
| sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X3,relation_rng_restriction(X1,X0)) )
| ~ spl17_145
| ~ spl17_247 ),
inference(resolution,[],[f3087,f1338]) ).
fof(f3087,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X3,relation_dom(relation_rng_restriction(X1,X0)))
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK8(relation_dom(relation_rng_restriction(X1,X0)),X2)) = apply(relation_rng_restriction(X1,X0),sK8(relation_dom(relation_rng_restriction(X1,X0)),X2))
| ~ function(X0)
| ~ empty(X2) )
| ~ spl17_247 ),
inference(avatar_component_clause,[],[f3086]) ).
fof(f5548,plain,
( spl17_395
| ~ spl17_66
| ~ spl17_244 ),
inference(avatar_split_clause,[],[f3061,f2998,f568,f5546]) ).
fof(f5546,plain,
( spl17_395
<=> ! [X2,X0,X1] :
( in(apply(X2,sK6(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))),X1)
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(X0)
| sP0(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| in(apply(X0,sK6(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))),relation_rng(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_395])]) ).
fof(f2998,plain,
( spl17_244
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(apply(X0,sK6(X2,X3,relation_rng_restriction(X1,X0))),X1)
| in(apply(X3,sK6(X2,X3,relation_rng_restriction(X1,X0))),X2)
| sP0(X2,X3,relation_rng_restriction(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_244])]) ).
fof(f3061,plain,
( ! [X2,X0,X1] :
( in(apply(X2,sK6(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))),X1)
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(X0)
| sP0(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| in(apply(X0,sK6(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))),relation_rng(sK2)) )
| ~ spl17_66
| ~ spl17_244 ),
inference(resolution,[],[f2999,f569]) ).
fof(f2999,plain,
( ! [X2,X3,X0,X1] :
( in(apply(X3,sK6(X2,X3,relation_rng_restriction(X1,X0))),X2)
| in(apply(X0,sK6(X2,X3,relation_rng_restriction(X1,X0))),X1)
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(X0)
| sP0(X2,X3,relation_rng_restriction(X1,X0)) )
| ~ spl17_244 ),
inference(avatar_component_clause,[],[f2998]) ).
fof(f5544,plain,
( spl17_394
| ~ spl17_127
| ~ spl17_244 ),
inference(avatar_split_clause,[],[f3060,f2998,f1100,f5542]) ).
fof(f5542,plain,
( spl17_394
<=> ! [X2,X0,X1] :
( in(apply(X2,sK6(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))),X1)
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(X0)
| sP0(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| element(apply(X0,sK6(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))),relation_rng(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_394])]) ).
fof(f3060,plain,
( ! [X2,X0,X1] :
( in(apply(X2,sK6(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))),X1)
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(X0)
| sP0(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| element(apply(X0,sK6(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))),relation_rng(sK2)) )
| ~ spl17_127
| ~ spl17_244 ),
inference(resolution,[],[f2999,f1101]) ).
fof(f5540,plain,
( spl17_393
| ~ spl17_66
| ~ spl17_243 ),
inference(avatar_split_clause,[],[f3014,f2994,f568,f5538]) ).
fof(f5538,plain,
( spl17_393
<=> ! [X2,X0,X1] :
( element(apply(X2,sK6(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))),X1)
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(X0)
| sP0(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| in(apply(X0,sK6(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))),relation_rng(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_393])]) ).
fof(f2994,plain,
( spl17_243
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(apply(X0,sK6(X2,X3,relation_rng_restriction(X1,X0))),X1)
| element(apply(X3,sK6(X2,X3,relation_rng_restriction(X1,X0))),X2)
| sP0(X2,X3,relation_rng_restriction(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_243])]) ).
fof(f3014,plain,
( ! [X2,X0,X1] :
( element(apply(X2,sK6(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))),X1)
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(X0)
| sP0(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| in(apply(X0,sK6(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))),relation_rng(sK2)) )
| ~ spl17_66
| ~ spl17_243 ),
inference(resolution,[],[f2995,f569]) ).
fof(f2995,plain,
( ! [X2,X3,X0,X1] :
( element(apply(X3,sK6(X2,X3,relation_rng_restriction(X1,X0))),X2)
| in(apply(X0,sK6(X2,X3,relation_rng_restriction(X1,X0))),X1)
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(X0)
| sP0(X2,X3,relation_rng_restriction(X1,X0)) )
| ~ spl17_243 ),
inference(avatar_component_clause,[],[f2994]) ).
fof(f5536,plain,
( spl17_392
| ~ spl17_127
| ~ spl17_243 ),
inference(avatar_split_clause,[],[f3013,f2994,f1100,f5534]) ).
fof(f5534,plain,
( spl17_392
<=> ! [X2,X0,X1] :
( element(apply(X2,sK6(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))),X1)
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(X0)
| sP0(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| element(apply(X0,sK6(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))),relation_rng(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_392])]) ).
fof(f3013,plain,
( ! [X2,X0,X1] :
( element(apply(X2,sK6(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))),X1)
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(X0)
| sP0(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| element(apply(X0,sK6(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))),relation_rng(sK2)) )
| ~ spl17_127
| ~ spl17_243 ),
inference(resolution,[],[f2995,f1101]) ).
fof(f5471,plain,
( spl17_391
| spl17_109
| ~ spl17_47
| ~ spl17_371 ),
inference(avatar_split_clause,[],[f5423,f5287,f436,f910,f5468]) ).
fof(f910,plain,
( spl17_109
<=> empty(relation_rng(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_109])]) ).
fof(f436,plain,
( spl17_47
<=> ! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_47])]) ).
fof(f5287,plain,
( spl17_371
<=> element(sK4(sK4(powerset(relation_rng(relation_rng_restriction(sK1,sK2))))),relation_rng(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_371])]) ).
fof(f5423,plain,
( empty(relation_rng(sK2))
| in(sK4(sK4(powerset(relation_rng(relation_rng_restriction(sK1,sK2))))),relation_rng(sK2))
| ~ spl17_47
| ~ spl17_371 ),
inference(resolution,[],[f5289,f437]) ).
fof(f437,plain,
( ! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) )
| ~ spl17_47 ),
inference(avatar_component_clause,[],[f436]) ).
fof(f5289,plain,
( element(sK4(sK4(powerset(relation_rng(relation_rng_restriction(sK1,sK2))))),relation_rng(sK2))
| ~ spl17_371 ),
inference(avatar_component_clause,[],[f5287]) ).
fof(f5455,plain,
( spl17_390
| ~ spl17_66
| ~ spl17_241 ),
inference(avatar_split_clause,[],[f2966,f2822,f568,f5453]) ).
fof(f5453,plain,
( spl17_390
<=> ! [X2,X0,X1] :
( in(sK6(X1,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0),X2),relation_dom(X2))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(X0)
| sP0(X1,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0),X2)
| in(apply(X0,sK6(X1,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0),X2)),relation_rng(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_390])]) ).
fof(f2822,plain,
( spl17_241
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(apply(X0,sK6(X2,relation_rng_restriction(X1,X0),X3)),X1)
| in(sK6(X2,relation_rng_restriction(X1,X0),X3),relation_dom(X3))
| sP0(X2,relation_rng_restriction(X1,X0),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_241])]) ).
fof(f2966,plain,
( ! [X2,X0,X1] :
( in(sK6(X1,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0),X2),relation_dom(X2))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(X0)
| sP0(X1,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0),X2)
| in(apply(X0,sK6(X1,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0),X2)),relation_rng(sK2)) )
| ~ spl17_66
| ~ spl17_241 ),
inference(resolution,[],[f2823,f569]) ).
fof(f2823,plain,
( ! [X2,X3,X0,X1] :
( in(apply(X0,sK6(X2,relation_rng_restriction(X1,X0),X3)),X1)
| in(sK6(X2,relation_rng_restriction(X1,X0),X3),relation_dom(X3))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(X0)
| sP0(X2,relation_rng_restriction(X1,X0),X3) )
| ~ spl17_241 ),
inference(avatar_component_clause,[],[f2822]) ).
fof(f5451,plain,
( spl17_389
| ~ spl17_127
| ~ spl17_241 ),
inference(avatar_split_clause,[],[f2965,f2822,f1100,f5449]) ).
fof(f5449,plain,
( spl17_389
<=> ! [X2,X0,X1] :
( in(sK6(X1,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0),X2),relation_dom(X2))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(X0)
| sP0(X1,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0),X2)
| element(apply(X0,sK6(X1,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0),X2)),relation_rng(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_389])]) ).
fof(f2965,plain,
( ! [X2,X0,X1] :
( in(sK6(X1,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0),X2),relation_dom(X2))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(X0)
| sP0(X1,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0),X2)
| element(apply(X0,sK6(X1,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0),X2)),relation_rng(sK2)) )
| ~ spl17_127
| ~ spl17_241 ),
inference(resolution,[],[f2823,f1101]) ).
fof(f5447,plain,
( spl17_388
| ~ spl17_66
| ~ spl17_240 ),
inference(avatar_split_clause,[],[f2942,f2818,f568,f5445]) ).
fof(f5445,plain,
( spl17_388
<=> ! [X2,X0,X1] :
( element(sK6(X1,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0),X2),relation_dom(X2))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(X0)
| sP0(X1,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0),X2)
| in(apply(X0,sK6(X1,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0),X2)),relation_rng(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_388])]) ).
fof(f2818,plain,
( spl17_240
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(apply(X0,sK6(X2,relation_rng_restriction(X1,X0),X3)),X1)
| element(sK6(X2,relation_rng_restriction(X1,X0),X3),relation_dom(X3))
| sP0(X2,relation_rng_restriction(X1,X0),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_240])]) ).
fof(f2942,plain,
( ! [X2,X0,X1] :
( element(sK6(X1,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0),X2),relation_dom(X2))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(X0)
| sP0(X1,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0),X2)
| in(apply(X0,sK6(X1,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0),X2)),relation_rng(sK2)) )
| ~ spl17_66
| ~ spl17_240 ),
inference(resolution,[],[f2819,f569]) ).
fof(f2819,plain,
( ! [X2,X3,X0,X1] :
( in(apply(X0,sK6(X2,relation_rng_restriction(X1,X0),X3)),X1)
| element(sK6(X2,relation_rng_restriction(X1,X0),X3),relation_dom(X3))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(X0)
| sP0(X2,relation_rng_restriction(X1,X0),X3) )
| ~ spl17_240 ),
inference(avatar_component_clause,[],[f2818]) ).
fof(f5443,plain,
( spl17_387
| ~ spl17_127
| ~ spl17_240 ),
inference(avatar_split_clause,[],[f2941,f2818,f1100,f5441]) ).
fof(f5441,plain,
( spl17_387
<=> ! [X2,X0,X1] :
( element(sK6(X1,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0),X2),relation_dom(X2))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(X0)
| sP0(X1,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0),X2)
| element(apply(X0,sK6(X1,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0),X2)),relation_rng(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_387])]) ).
fof(f2941,plain,
( ! [X2,X0,X1] :
( element(sK6(X1,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0),X2),relation_dom(X2))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(X0)
| sP0(X1,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0),X2)
| element(apply(X0,sK6(X1,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0),X2)),relation_rng(sK2)) )
| ~ spl17_127
| ~ spl17_240 ),
inference(resolution,[],[f2819,f1101]) ).
fof(f5439,plain,
( spl17_386
| ~ spl17_66
| ~ spl17_239 ),
inference(avatar_split_clause,[],[f2912,f2814,f568,f5437]) ).
fof(f5437,plain,
( spl17_386
<=> ! [X2,X0,X1] :
( in(sK6(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)),relation_dom(X2))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(X0)
| sP0(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| in(apply(X0,sK6(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))),relation_rng(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_386])]) ).
fof(f2814,plain,
( spl17_239
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(apply(X0,sK6(X2,X3,relation_rng_restriction(X1,X0))),X1)
| in(sK6(X2,X3,relation_rng_restriction(X1,X0)),relation_dom(X3))
| sP0(X2,X3,relation_rng_restriction(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_239])]) ).
fof(f2912,plain,
( ! [X2,X0,X1] :
( in(sK6(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)),relation_dom(X2))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(X0)
| sP0(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| in(apply(X0,sK6(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))),relation_rng(sK2)) )
| ~ spl17_66
| ~ spl17_239 ),
inference(resolution,[],[f2815,f569]) ).
fof(f2815,plain,
( ! [X2,X3,X0,X1] :
( in(apply(X0,sK6(X2,X3,relation_rng_restriction(X1,X0))),X1)
| in(sK6(X2,X3,relation_rng_restriction(X1,X0)),relation_dom(X3))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(X0)
| sP0(X2,X3,relation_rng_restriction(X1,X0)) )
| ~ spl17_239 ),
inference(avatar_component_clause,[],[f2814]) ).
fof(f5435,plain,
( spl17_385
| ~ spl17_127
| ~ spl17_239 ),
inference(avatar_split_clause,[],[f2911,f2814,f1100,f5433]) ).
fof(f5433,plain,
( spl17_385
<=> ! [X2,X0,X1] :
( in(sK6(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)),relation_dom(X2))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(X0)
| sP0(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| element(apply(X0,sK6(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))),relation_rng(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_385])]) ).
fof(f2911,plain,
( ! [X2,X0,X1] :
( in(sK6(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)),relation_dom(X2))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(X0)
| sP0(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| element(apply(X0,sK6(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))),relation_rng(sK2)) )
| ~ spl17_127
| ~ spl17_239 ),
inference(resolution,[],[f2815,f1101]) ).
fof(f5431,plain,
( spl17_384
| ~ spl17_66
| ~ spl17_238 ),
inference(avatar_split_clause,[],[f2886,f2810,f568,f5429]) ).
fof(f5429,plain,
( spl17_384
<=> ! [X2,X0,X1] :
( element(sK6(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)),relation_dom(X2))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(X0)
| sP0(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| in(apply(X0,sK6(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))),relation_rng(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_384])]) ).
fof(f2810,plain,
( spl17_238
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(apply(X0,sK6(X2,X3,relation_rng_restriction(X1,X0))),X1)
| element(sK6(X2,X3,relation_rng_restriction(X1,X0)),relation_dom(X3))
| sP0(X2,X3,relation_rng_restriction(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_238])]) ).
fof(f2886,plain,
( ! [X2,X0,X1] :
( element(sK6(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)),relation_dom(X2))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(X0)
| sP0(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| in(apply(X0,sK6(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))),relation_rng(sK2)) )
| ~ spl17_66
| ~ spl17_238 ),
inference(resolution,[],[f2811,f569]) ).
fof(f2811,plain,
( ! [X2,X3,X0,X1] :
( in(apply(X0,sK6(X2,X3,relation_rng_restriction(X1,X0))),X1)
| element(sK6(X2,X3,relation_rng_restriction(X1,X0)),relation_dom(X3))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(X0)
| sP0(X2,X3,relation_rng_restriction(X1,X0)) )
| ~ spl17_238 ),
inference(avatar_component_clause,[],[f2810]) ).
fof(f5427,plain,
( spl17_383
| ~ spl17_127
| ~ spl17_238 ),
inference(avatar_split_clause,[],[f2885,f2810,f1100,f5425]) ).
fof(f5425,plain,
( spl17_383
<=> ! [X2,X0,X1] :
( element(sK6(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)),relation_dom(X2))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(X0)
| sP0(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| element(apply(X0,sK6(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))),relation_rng(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_383])]) ).
fof(f2885,plain,
( ! [X2,X0,X1] :
( element(sK6(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)),relation_dom(X2))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(X0)
| sP0(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| element(apply(X0,sK6(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))),relation_rng(sK2)) )
| ~ spl17_127
| ~ spl17_238 ),
inference(resolution,[],[f2811,f1101]) ).
fof(f5378,plain,
( spl17_382
| ~ spl17_132
| ~ spl17_183 ),
inference(avatar_split_clause,[],[f2098,f2090,f1132,f5376]) ).
fof(f5376,plain,
( spl17_382
<=> ! [X0,X1] :
( ~ in(sK10,sK6(X0,X1,sK10))
| ~ empty(relation_dom(X1))
| sP0(X0,X1,sK10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_382])]) ).
fof(f2090,plain,
( spl17_183
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(relation_dom(X1))
| ~ in(relation_dom(X2),sK6(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_183])]) ).
fof(f2098,plain,
( ! [X0,X1] :
( ~ in(sK10,sK6(X0,X1,sK10))
| ~ empty(relation_dom(X1))
| sP0(X0,X1,sK10) )
| ~ spl17_132
| ~ spl17_183 ),
inference(superposition,[],[f2091,f1134]) ).
fof(f2091,plain,
( ! [X2,X0,X1] :
( ~ in(relation_dom(X2),sK6(X0,X1,X2))
| ~ empty(relation_dom(X1))
| sP0(X0,X1,X2) )
| ~ spl17_183 ),
inference(avatar_component_clause,[],[f2090]) ).
fof(f5374,plain,
( spl17_381
| ~ spl17_132
| ~ spl17_182 ),
inference(avatar_split_clause,[],[f2097,f2086,f1132,f5372]) ).
fof(f5372,plain,
( spl17_381
<=> ! [X0,X1] :
( element(sK6(X0,X1,sK10),sK10)
| ~ empty(relation_dom(X1))
| sP0(X0,X1,sK10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_381])]) ).
fof(f2086,plain,
( spl17_182
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(relation_dom(X1))
| element(sK6(X0,X1,X2),relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_182])]) ).
fof(f2097,plain,
( ! [X0,X1] :
( element(sK6(X0,X1,sK10),sK10)
| ~ empty(relation_dom(X1))
| sP0(X0,X1,sK10) )
| ~ spl17_132
| ~ spl17_182 ),
inference(superposition,[],[f2087,f1134]) ).
fof(f2087,plain,
( ! [X2,X0,X1] :
( element(sK6(X0,X1,X2),relation_dom(X2))
| ~ empty(relation_dom(X1))
| sP0(X0,X1,X2) )
| ~ spl17_182 ),
inference(avatar_component_clause,[],[f2086]) ).
fof(f5370,plain,
( spl17_380
| ~ spl17_132
| ~ spl17_181 ),
inference(avatar_split_clause,[],[f2095,f2082,f1132,f5368]) ).
fof(f5368,plain,
( spl17_380
<=> ! [X0,X1] :
( ~ in(sK10,sK6(X0,sK10,X1))
| ~ empty(relation_dom(X1))
| sP0(X0,sK10,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_380])]) ).
fof(f2082,plain,
( spl17_181
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(relation_dom(X2))
| ~ in(relation_dom(X1),sK6(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_181])]) ).
fof(f2095,plain,
( ! [X0,X1] :
( ~ in(sK10,sK6(X0,sK10,X1))
| ~ empty(relation_dom(X1))
| sP0(X0,sK10,X1) )
| ~ spl17_132
| ~ spl17_181 ),
inference(superposition,[],[f2083,f1134]) ).
fof(f2083,plain,
( ! [X2,X0,X1] :
( ~ in(relation_dom(X1),sK6(X0,X1,X2))
| ~ empty(relation_dom(X2))
| sP0(X0,X1,X2) )
| ~ spl17_181 ),
inference(avatar_component_clause,[],[f2082]) ).
fof(f5366,plain,
( spl17_379
| ~ spl17_132
| ~ spl17_180 ),
inference(avatar_split_clause,[],[f2094,f2077,f1132,f5364]) ).
fof(f5364,plain,
( spl17_379
<=> ! [X0,X1] :
( element(sK6(X0,sK10,X1),sK10)
| ~ empty(relation_dom(X1))
| sP0(X0,sK10,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_379])]) ).
fof(f2077,plain,
( spl17_180
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(relation_dom(X2))
| element(sK6(X0,X1,X2),relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_180])]) ).
fof(f2094,plain,
( ! [X0,X1] :
( element(sK6(X0,sK10,X1),sK10)
| ~ empty(relation_dom(X1))
| sP0(X0,sK10,X1) )
| ~ spl17_132
| ~ spl17_180 ),
inference(superposition,[],[f2078,f1134]) ).
fof(f2078,plain,
( ! [X2,X0,X1] :
( element(sK6(X0,X1,X2),relation_dom(X1))
| ~ empty(relation_dom(X2))
| sP0(X0,X1,X2) )
| ~ spl17_180 ),
inference(avatar_component_clause,[],[f2077]) ).
fof(f5362,plain,
( spl17_378
| ~ spl17_44
| ~ spl17_160 ),
inference(avatar_split_clause,[],[f1549,f1525,f406,f5360]) ).
fof(f5360,plain,
( spl17_378
<=> ! [X0] :
( empty(powerset(X0))
| empty(sK3(powerset(X0)))
| subset(sK4(sK3(powerset(X0))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_378])]) ).
fof(f1549,plain,
( ! [X0] :
( empty(powerset(X0))
| empty(sK3(powerset(X0)))
| subset(sK4(sK3(powerset(X0))),X0) )
| ~ spl17_44
| ~ spl17_160 ),
inference(resolution,[],[f1526,f407]) ).
fof(f5358,plain,
( spl17_377
| ~ spl17_53
| ~ spl17_158 ),
inference(avatar_split_clause,[],[f1542,f1515,f472,f5356]) ).
fof(f5356,plain,
( spl17_377
<=> ! [X2,X0,X1] :
( subset(powerset(X0),X1)
| ~ in(X2,sK8(powerset(X0),X1))
| in(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_377])]) ).
fof(f472,plain,
( spl17_53
<=> ! [X0,X1,X3] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_53])]) ).
fof(f1515,plain,
( spl17_158
<=> ! [X0,X1] :
( subset(powerset(X0),X1)
| subset(sK8(powerset(X0),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_158])]) ).
fof(f1542,plain,
( ! [X2,X0,X1] :
( subset(powerset(X0),X1)
| ~ in(X2,sK8(powerset(X0),X1))
| in(X2,X0) )
| ~ spl17_53
| ~ spl17_158 ),
inference(resolution,[],[f1516,f473]) ).
fof(f473,plain,
( ! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) )
| ~ spl17_53 ),
inference(avatar_component_clause,[],[f472]) ).
fof(f1516,plain,
( ! [X0,X1] :
( subset(sK8(powerset(X0),X1),X0)
| subset(powerset(X0),X1) )
| ~ spl17_158 ),
inference(avatar_component_clause,[],[f1515]) ).
fof(f5353,plain,
( spl17_376
| ~ spl17_106
| ~ spl17_132 ),
inference(avatar_split_clause,[],[f1178,f1132,f877,f5351]) ).
fof(f5351,plain,
( spl17_376
<=> ! [X0,X1] :
( in(sK6(X0,X1,sK10),sK10)
| sP0(X0,X1,sK10)
| ~ empty(relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_376])]) ).
fof(f877,plain,
( spl17_106
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),relation_dom(X2))
| sP0(X0,X1,X2)
| ~ empty(relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_106])]) ).
fof(f1178,plain,
( ! [X0,X1] :
( in(sK6(X0,X1,sK10),sK10)
| sP0(X0,X1,sK10)
| ~ empty(relation_dom(X1)) )
| ~ spl17_106
| ~ spl17_132 ),
inference(superposition,[],[f878,f1134]) ).
fof(f878,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),relation_dom(X2))
| sP0(X0,X1,X2)
| ~ empty(relation_dom(X1)) )
| ~ spl17_106 ),
inference(avatar_component_clause,[],[f877]) ).
fof(f5349,plain,
( spl17_375
| ~ spl17_105
| ~ spl17_132 ),
inference(avatar_split_clause,[],[f1177,f1132,f873,f5347]) ).
fof(f5347,plain,
( spl17_375
<=> ! [X0,X1] :
( in(sK6(X0,sK10,X1),sK10)
| sP0(X0,sK10,X1)
| ~ empty(relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_375])]) ).
fof(f873,plain,
( spl17_105
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),relation_dom(X1))
| sP0(X0,X1,X2)
| ~ empty(relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_105])]) ).
fof(f1177,plain,
( ! [X0,X1] :
( in(sK6(X0,sK10,X1),sK10)
| sP0(X0,sK10,X1)
| ~ empty(relation_dom(X1)) )
| ~ spl17_105
| ~ spl17_132 ),
inference(superposition,[],[f874,f1134]) ).
fof(f874,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),relation_dom(X1))
| sP0(X0,X1,X2)
| ~ empty(relation_dom(X2)) )
| ~ spl17_105 ),
inference(avatar_component_clause,[],[f873]) ).
fof(f5340,plain,
( spl17_374
| ~ spl17_66
| ~ spl17_226 ),
inference(avatar_split_clause,[],[f2635,f2624,f568,f5338]) ).
fof(f5338,plain,
( spl17_374
<=> ! [X0,X1] :
( ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ relation(X0)
| sP0(X1,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0),relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| in(apply(X0,sK6(X1,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0),relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))),relation_rng(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_374])]) ).
fof(f2635,plain,
( ! [X0,X1] :
( ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ relation(X0)
| sP0(X1,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0),relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| in(apply(X0,sK6(X1,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0),relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))),relation_rng(sK2)) )
| ~ spl17_66
| ~ spl17_226 ),
inference(resolution,[],[f2625,f569]) ).
fof(f5336,plain,
( spl17_373
| ~ spl17_127
| ~ spl17_226 ),
inference(avatar_split_clause,[],[f2634,f2624,f1100,f5334]) ).
fof(f5334,plain,
( spl17_373
<=> ! [X0,X1] :
( ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ relation(X0)
| sP0(X1,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0),relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| element(apply(X0,sK6(X1,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0),relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))),relation_rng(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_373])]) ).
fof(f2634,plain,
( ! [X0,X1] :
( ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ relation(X0)
| sP0(X1,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0),relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| element(apply(X0,sK6(X1,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0),relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))),relation_rng(sK2)) )
| ~ spl17_127
| ~ spl17_226 ),
inference(resolution,[],[f2625,f1101]) ).
fof(f5294,plain,
( spl17_371
| spl17_372
| ~ spl17_127
| ~ spl17_320 ),
inference(avatar_split_clause,[],[f4569,f4461,f1100,f5291,f5287]) ).
fof(f4461,plain,
( spl17_320
<=> ! [X0] :
( in(sK4(sK4(powerset(X0))),X0)
| empty(sK4(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_320])]) ).
fof(f4569,plain,
( empty(sK4(powerset(relation_rng(relation_rng_restriction(sK1,sK2)))))
| element(sK4(sK4(powerset(relation_rng(relation_rng_restriction(sK1,sK2))))),relation_rng(sK2))
| ~ spl17_127
| ~ spl17_320 ),
inference(resolution,[],[f4462,f1101]) ).
fof(f4462,plain,
( ! [X0] :
( in(sK4(sK4(powerset(X0))),X0)
| empty(sK4(powerset(X0))) )
| ~ spl17_320 ),
inference(avatar_component_clause,[],[f4461]) ).
fof(f5248,plain,
( spl17_370
| ~ spl17_132
| ~ spl17_179 ),
inference(avatar_split_clause,[],[f2075,f2061,f1132,f5246]) ).
fof(f5246,plain,
( spl17_370
<=> ! [X0,X1] :
( ~ in(sK10,sK6(X0,X1,sK10))
| ~ empty(X0)
| sP0(X0,X1,sK10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_370])]) ).
fof(f2061,plain,
( spl17_179
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(X0)
| ~ in(relation_dom(X2),sK6(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_179])]) ).
fof(f2075,plain,
( ! [X0,X1] :
( ~ in(sK10,sK6(X0,X1,sK10))
| ~ empty(X0)
| sP0(X0,X1,sK10) )
| ~ spl17_132
| ~ spl17_179 ),
inference(superposition,[],[f2062,f1134]) ).
fof(f2062,plain,
( ! [X2,X0,X1] :
( ~ in(relation_dom(X2),sK6(X0,X1,X2))
| ~ empty(X0)
| sP0(X0,X1,X2) )
| ~ spl17_179 ),
inference(avatar_component_clause,[],[f2061]) ).
fof(f5244,plain,
( spl17_369
| ~ spl17_132
| ~ spl17_178 ),
inference(avatar_split_clause,[],[f2074,f2057,f1132,f5242]) ).
fof(f5242,plain,
( spl17_369
<=> ! [X0,X1] :
( element(sK6(X0,X1,sK10),sK10)
| ~ empty(X0)
| sP0(X0,X1,sK10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_369])]) ).
fof(f2057,plain,
( spl17_178
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(X0)
| element(sK6(X0,X1,X2),relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_178])]) ).
fof(f2074,plain,
( ! [X0,X1] :
( element(sK6(X0,X1,sK10),sK10)
| ~ empty(X0)
| sP0(X0,X1,sK10) )
| ~ spl17_132
| ~ spl17_178 ),
inference(superposition,[],[f2058,f1134]) ).
fof(f2058,plain,
( ! [X2,X0,X1] :
( element(sK6(X0,X1,X2),relation_dom(X2))
| ~ empty(X0)
| sP0(X0,X1,X2) )
| ~ spl17_178 ),
inference(avatar_component_clause,[],[f2057]) ).
fof(f5240,plain,
( spl17_368
| ~ spl17_80
| ~ spl17_177 ),
inference(avatar_split_clause,[],[f2071,f2053,f643,f5238]) ).
fof(f5238,plain,
( spl17_368
<=> ! [X0,X1] :
( empty(powerset(X0))
| subset(X1,powerset(X0))
| ~ empty(sK8(X1,powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_368])]) ).
fof(f643,plain,
( spl17_80
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_80])]) ).
fof(f2053,plain,
( spl17_177
<=> ! [X0,X1] :
( empty(powerset(X0))
| ~ subset(sK8(X1,powerset(X0)),X0)
| subset(X1,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_177])]) ).
fof(f2071,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| subset(X1,powerset(X0))
| ~ empty(sK8(X1,powerset(X0))) )
| ~ spl17_80
| ~ spl17_177 ),
inference(resolution,[],[f2054,f644]) ).
fof(f644,plain,
( ! [X0,X1] :
( subset(X0,X1)
| ~ empty(X0) )
| ~ spl17_80 ),
inference(avatar_component_clause,[],[f643]) ).
fof(f2054,plain,
( ! [X0,X1] :
( ~ subset(sK8(X1,powerset(X0)),X0)
| empty(powerset(X0))
| subset(X1,powerset(X0)) )
| ~ spl17_177 ),
inference(avatar_component_clause,[],[f2053]) ).
fof(f5236,plain,
( spl17_367
| ~ spl17_50
| ~ spl17_171 ),
inference(avatar_split_clause,[],[f2028,f2008,f449,f5234]) ).
fof(f5234,plain,
( spl17_367
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| subset(powerset(X0),X1)
| subset(sK8(powerset(X0),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_367])]) ).
fof(f2028,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| subset(powerset(X0),X1)
| subset(sK8(powerset(X0),X1),X2) )
| ~ spl17_50
| ~ spl17_171 ),
inference(resolution,[],[f2009,f450]) ).
fof(f5232,plain,
( spl17_366
| ~ spl17_44
| ~ spl17_159 ),
inference(avatar_split_clause,[],[f1545,f1521,f406,f5230]) ).
fof(f5230,plain,
( spl17_366
<=> ! [X0] :
( empty(sK4(powerset(powerset(X0))))
| subset(sK4(sK4(powerset(powerset(X0)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_366])]) ).
fof(f1545,plain,
( ! [X0] :
( empty(sK4(powerset(powerset(X0))))
| subset(sK4(sK4(powerset(powerset(X0)))),X0) )
| ~ spl17_44
| ~ spl17_159 ),
inference(resolution,[],[f1522,f407]) ).
fof(f5228,plain,
( spl17_365
| ~ spl17_50
| ~ spl17_152 ),
inference(avatar_split_clause,[],[f1421,f1392,f449,f5226]) ).
fof(f5226,plain,
( spl17_365
<=> ! [X0,X1] :
( empty(X0)
| in(sK8(sK3(X0),X1),X0)
| subset(sK3(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_365])]) ).
fof(f1421,plain,
( ! [X0,X1] :
( empty(X0)
| in(sK8(sK3(X0),X1),X0)
| subset(sK3(X0),X1) )
| ~ spl17_50
| ~ spl17_152 ),
inference(resolution,[],[f1393,f450]) ).
fof(f5224,plain,
( spl17_364
| ~ spl17_50
| ~ spl17_148 ),
inference(avatar_split_clause,[],[f1375,f1367,f449,f5222]) ).
fof(f1375,plain,
( ! [X0,X1] :
( in(sK8(sK4(powerset(X0)),X1),X0)
| subset(sK4(powerset(X0)),X1) )
| ~ spl17_50
| ~ spl17_148 ),
inference(resolution,[],[f1368,f450]) ).
fof(f5213,plain,
( spl17_363
| ~ spl17_104
| ~ spl17_143 ),
inference(avatar_split_clause,[],[f1330,f1248,f865,f5211]) ).
fof(f5211,plain,
( spl17_363
<=> ! [X0,X1] :
( ~ empty(relation_dom(X0))
| relation_rng_restriction(X1,X0) = X0
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_363])]) ).
fof(f865,plain,
( spl17_104
<=> ! [X0,X1] :
( relation_rng_restriction(X0,X1) = X1
| ~ sP0(X0,X1,X1)
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_104])]) ).
fof(f1248,plain,
( spl17_143
<=> ! [X0,X1] :
( sP0(X0,X1,X1)
| ~ empty(relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_143])]) ).
fof(f1330,plain,
( ! [X0,X1] :
( ~ empty(relation_dom(X0))
| relation_rng_restriction(X1,X0) = X0
| ~ function(X0)
| ~ relation(X0) )
| ~ spl17_104
| ~ spl17_143 ),
inference(resolution,[],[f1249,f866]) ).
fof(f866,plain,
( ! [X0,X1] :
( ~ sP0(X0,X1,X1)
| relation_rng_restriction(X0,X1) = X1
| ~ function(X1)
| ~ relation(X1) )
| ~ spl17_104 ),
inference(avatar_component_clause,[],[f865]) ).
fof(f1249,plain,
( ! [X0,X1] :
( sP0(X0,X1,X1)
| ~ empty(relation_dom(X1)) )
| ~ spl17_143 ),
inference(avatar_component_clause,[],[f1248]) ).
fof(f5209,plain,
( spl17_362
| ~ spl17_103
| ~ spl17_132 ),
inference(avatar_split_clause,[],[f1176,f1132,f861,f5207]) ).
fof(f5207,plain,
( spl17_362
<=> ! [X0,X1] :
( in(sK6(X0,X1,sK10),sK10)
| sP0(X0,X1,sK10)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_362])]) ).
fof(f861,plain,
( spl17_103
<=> ! [X2,X0,X1] :
( in(sK6(X1,X0,X2),relation_dom(X2))
| sP0(X1,X0,X2)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_103])]) ).
fof(f1176,plain,
( ! [X0,X1] :
( in(sK6(X0,X1,sK10),sK10)
| sP0(X0,X1,sK10)
| ~ empty(X0) )
| ~ spl17_103
| ~ spl17_132 ),
inference(superposition,[],[f862,f1134]) ).
fof(f862,plain,
( ! [X2,X0,X1] :
( in(sK6(X1,X0,X2),relation_dom(X2))
| sP0(X1,X0,X2)
| ~ empty(X1) )
| ~ spl17_103 ),
inference(avatar_component_clause,[],[f861]) ).
fof(f5136,plain,
( spl17_361
| ~ spl17_127
| ~ spl17_244 ),
inference(avatar_split_clause,[],[f3037,f2998,f1100,f5134]) ).
fof(f5134,plain,
( spl17_361
<=> ! [X2,X0,X1] :
( in(apply(X2,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,relation_rng_restriction(X1,X2))),X1)
| ~ relation(relation_rng_restriction(X1,X2))
| ~ function(X2)
| ~ function(relation_rng_restriction(X1,X2))
| ~ relation(X2)
| sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X0,relation_rng_restriction(X1,X2))
| element(apply(X0,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,relation_rng_restriction(X1,X2))),relation_rng(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_361])]) ).
fof(f3037,plain,
( ! [X2,X0,X1] :
( in(apply(X2,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,relation_rng_restriction(X1,X2))),X1)
| ~ relation(relation_rng_restriction(X1,X2))
| ~ function(X2)
| ~ function(relation_rng_restriction(X1,X2))
| ~ relation(X2)
| sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X0,relation_rng_restriction(X1,X2))
| element(apply(X0,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,relation_rng_restriction(X1,X2))),relation_rng(sK2)) )
| ~ spl17_127
| ~ spl17_244 ),
inference(resolution,[],[f2999,f1101]) ).
fof(f5132,plain,
( spl17_360
| ~ spl17_66
| ~ spl17_231 ),
inference(avatar_split_clause,[],[f2710,f2699,f568,f5130]) ).
fof(f5130,plain,
( spl17_360
<=> ! [X2,X0,X1] :
( ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ relation(X0)
| sP0(relation_dom(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)),X1,X2)
| ~ empty(relation_dom(X2))
| in(apply(X0,apply(X1,sK6(relation_dom(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)),X1,X2))),relation_rng(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_360])]) ).
fof(f2699,plain,
( spl17_231
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(apply(X0,apply(X2,sK6(relation_dom(relation_rng_restriction(X1,X0)),X2,X3))),X1)
| sP0(relation_dom(relation_rng_restriction(X1,X0)),X2,X3)
| ~ empty(relation_dom(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_231])]) ).
fof(f2710,plain,
( ! [X2,X0,X1] :
( ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ relation(X0)
| sP0(relation_dom(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)),X1,X2)
| ~ empty(relation_dom(X2))
| in(apply(X0,apply(X1,sK6(relation_dom(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)),X1,X2))),relation_rng(sK2)) )
| ~ spl17_66
| ~ spl17_231 ),
inference(resolution,[],[f2700,f569]) ).
fof(f2700,plain,
( ! [X2,X3,X0,X1] :
( in(apply(X0,apply(X2,sK6(relation_dom(relation_rng_restriction(X1,X0)),X2,X3))),X1)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| ~ relation(X0)
| sP0(relation_dom(relation_rng_restriction(X1,X0)),X2,X3)
| ~ empty(relation_dom(X3)) )
| ~ spl17_231 ),
inference(avatar_component_clause,[],[f2699]) ).
fof(f5128,plain,
( spl17_359
| ~ spl17_127
| ~ spl17_231 ),
inference(avatar_split_clause,[],[f2709,f2699,f1100,f5126]) ).
fof(f5126,plain,
( spl17_359
<=> ! [X2,X0,X1] :
( ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ relation(X0)
| sP0(relation_dom(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)),X1,X2)
| ~ empty(relation_dom(X2))
| element(apply(X0,apply(X1,sK6(relation_dom(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)),X1,X2))),relation_rng(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_359])]) ).
fof(f2709,plain,
( ! [X2,X0,X1] :
( ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ relation(X0)
| sP0(relation_dom(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)),X1,X2)
| ~ empty(relation_dom(X2))
| element(apply(X0,apply(X1,sK6(relation_dom(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)),X1,X2))),relation_rng(sK2)) )
| ~ spl17_127
| ~ spl17_231 ),
inference(resolution,[],[f2700,f1101]) ).
fof(f5124,plain,
( spl17_358
| ~ spl17_119
| ~ spl17_145 ),
inference(avatar_split_clause,[],[f1348,f1337,f998,f5122]) ).
fof(f5122,plain,
( spl17_358
<=> ! [X2,X0,X1] :
( in(apply(X0,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,relation_rng_restriction(X1,X2))),relation_rng(sK2))
| sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X0,relation_rng_restriction(X1,X2))
| ~ relation(X2)
| ~ function(relation_rng_restriction(X1,X2))
| ~ relation(relation_rng_restriction(X1,X2))
| ~ function(X2)
| in(apply(X2,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,relation_rng_restriction(X1,X2))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_358])]) ).
fof(f998,plain,
( spl17_119
<=> ! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ in(X2,relation_dom(relation_rng_restriction(X1,X0)))
| in(apply(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_119])]) ).
fof(f1348,plain,
( ! [X2,X0,X1] :
( in(apply(X0,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,relation_rng_restriction(X1,X2))),relation_rng(sK2))
| sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X0,relation_rng_restriction(X1,X2))
| ~ relation(X2)
| ~ function(relation_rng_restriction(X1,X2))
| ~ relation(relation_rng_restriction(X1,X2))
| ~ function(X2)
| in(apply(X2,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,relation_rng_restriction(X1,X2))),X1) )
| ~ spl17_119
| ~ spl17_145 ),
inference(resolution,[],[f1338,f999]) ).
fof(f999,plain,
( ! [X2,X0,X1] :
( ~ in(X2,relation_dom(relation_rng_restriction(X1,X0)))
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(apply(X0,X2),X1) )
| ~ spl17_119 ),
inference(avatar_component_clause,[],[f998]) ).
fof(f5075,plain,
( spl17_357
| ~ spl17_127
| ~ spl17_237 ),
inference(avatar_split_clause,[],[f2851,f2806,f1100,f5073]) ).
fof(f5073,plain,
( spl17_357
<=> ! [X2,X0,X1] :
( in(sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,relation_rng_restriction(X1,X2)),relation_dom(X2))
| ~ relation(relation_rng_restriction(X1,X2))
| ~ function(X2)
| ~ function(relation_rng_restriction(X1,X2))
| ~ relation(X2)
| sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X0,relation_rng_restriction(X1,X2))
| element(apply(X0,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,relation_rng_restriction(X1,X2))),relation_rng(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_357])]) ).
fof(f2806,plain,
( spl17_237
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(sK6(X2,X3,relation_rng_restriction(X1,X0)),relation_dom(X0))
| in(apply(X3,sK6(X2,X3,relation_rng_restriction(X1,X0))),X2)
| sP0(X2,X3,relation_rng_restriction(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_237])]) ).
fof(f2851,plain,
( ! [X2,X0,X1] :
( in(sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,relation_rng_restriction(X1,X2)),relation_dom(X2))
| ~ relation(relation_rng_restriction(X1,X2))
| ~ function(X2)
| ~ function(relation_rng_restriction(X1,X2))
| ~ relation(X2)
| sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X0,relation_rng_restriction(X1,X2))
| element(apply(X0,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,relation_rng_restriction(X1,X2))),relation_rng(sK2)) )
| ~ spl17_127
| ~ spl17_237 ),
inference(resolution,[],[f2807,f1101]) ).
fof(f2807,plain,
( ! [X2,X3,X0,X1] :
( in(apply(X3,sK6(X2,X3,relation_rng_restriction(X1,X0))),X2)
| in(sK6(X2,X3,relation_rng_restriction(X1,X0)),relation_dom(X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(X0)
| sP0(X2,X3,relation_rng_restriction(X1,X0)) )
| ~ spl17_237 ),
inference(avatar_component_clause,[],[f2806]) ).
fof(f5071,plain,
( spl17_356
| ~ spl17_118
| ~ spl17_145 ),
inference(avatar_split_clause,[],[f1349,f1337,f979,f5069]) ).
fof(f5069,plain,
( spl17_356
<=> ! [X2,X0,X1] :
( in(apply(X0,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,relation_rng_restriction(X1,X2))),relation_rng(sK2))
| sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X0,relation_rng_restriction(X1,X2))
| ~ relation(X2)
| ~ function(relation_rng_restriction(X1,X2))
| ~ relation(relation_rng_restriction(X1,X2))
| ~ function(X2)
| in(sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,relation_rng_restriction(X1,X2)),relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_356])]) ).
fof(f979,plain,
( spl17_118
<=> ! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ in(X2,relation_dom(relation_rng_restriction(X1,X0)))
| in(X2,relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_118])]) ).
fof(f1349,plain,
( ! [X2,X0,X1] :
( in(apply(X0,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,relation_rng_restriction(X1,X2))),relation_rng(sK2))
| sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X0,relation_rng_restriction(X1,X2))
| ~ relation(X2)
| ~ function(relation_rng_restriction(X1,X2))
| ~ relation(relation_rng_restriction(X1,X2))
| ~ function(X2)
| in(sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,relation_rng_restriction(X1,X2)),relation_dom(X2)) )
| ~ spl17_118
| ~ spl17_145 ),
inference(resolution,[],[f1338,f980]) ).
fof(f980,plain,
( ! [X2,X0,X1] :
( ~ in(X2,relation_dom(relation_rng_restriction(X1,X0)))
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(X2,relation_dom(X0)) )
| ~ spl17_118 ),
inference(avatar_component_clause,[],[f979]) ).
fof(f4975,plain,
( spl17_355
| ~ spl17_82
| ~ spl17_331 ),
inference(avatar_split_clause,[],[f4718,f4506,f650,f4973]) ).
fof(f4973,plain,
( spl17_355
<=> ! [X0] : sP0(sK10,X0,sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_355])]) ).
fof(f4506,plain,
( spl17_331
<=> ! [X0] :
( in(sK6(sK10,X0,sK10),sK10)
| sP0(sK10,X0,sK10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_331])]) ).
fof(f4718,plain,
( ! [X0] : sP0(sK10,X0,sK10)
| ~ spl17_82
| ~ spl17_331 ),
inference(resolution,[],[f4507,f651]) ).
fof(f4507,plain,
( ! [X0] :
( in(sK6(sK10,X0,sK10),sK10)
| sP0(sK10,X0,sK10) )
| ~ spl17_331 ),
inference(avatar_component_clause,[],[f4506]) ).
fof(f4957,plain,
( spl17_354
| ~ spl17_86
| ~ spl17_171 ),
inference(avatar_split_clause,[],[f2027,f2008,f683,f4955]) ).
fof(f4955,plain,
( spl17_354
<=> ! [X0,X1] :
( ~ empty(X0)
| subset(powerset(X0),X1)
| empty(sK8(powerset(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_354])]) ).
fof(f2027,plain,
( ! [X0,X1] :
( ~ empty(X0)
| subset(powerset(X0),X1)
| empty(sK8(powerset(X0),X1)) )
| ~ spl17_86
| ~ spl17_171 ),
inference(resolution,[],[f2009,f684]) ).
fof(f4953,plain,
( spl17_353
| ~ spl17_50
| ~ spl17_165 ),
inference(avatar_split_clause,[],[f1993,f1564,f449,f4951]) ).
fof(f4951,plain,
( spl17_353
<=> ! [X2,X0,X1] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| subset(relation_rng(relation_rng_restriction(X1,X0)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_353])]) ).
fof(f1993,plain,
( ! [X2,X0,X1] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| subset(relation_rng(relation_rng_restriction(X1,X0)),X2) )
| ~ spl17_50
| ~ spl17_165 ),
inference(resolution,[],[f1565,f450]) ).
fof(f4949,plain,
( spl17_352
| ~ spl17_38
| ~ spl17_164 ),
inference(avatar_split_clause,[],[f1986,f1560,f380,f4947]) ).
fof(f4947,plain,
( spl17_352
<=> ! [X0,X1] :
( sP0(sK10,X0,X1)
| ~ in(relation_dom(X1),sK6(sK10,X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_352])]) ).
fof(f1560,plain,
( spl17_164
<=> ! [X0,X1] :
( in(sK6(sK10,X0,X1),relation_dom(X1))
| sP0(sK10,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_164])]) ).
fof(f1986,plain,
( ! [X0,X1] :
( sP0(sK10,X0,X1)
| ~ in(relation_dom(X1),sK6(sK10,X0,X1)) )
| ~ spl17_38
| ~ spl17_164 ),
inference(resolution,[],[f1561,f381]) ).
fof(f1561,plain,
( ! [X0,X1] :
( in(sK6(sK10,X0,X1),relation_dom(X1))
| sP0(sK10,X0,X1) )
| ~ spl17_164 ),
inference(avatar_component_clause,[],[f1560]) ).
fof(f4945,plain,
( spl17_351
| ~ spl17_136
| ~ spl17_156 ),
inference(avatar_split_clause,[],[f1491,f1409,f1201,f4943]) ).
fof(f4943,plain,
( spl17_351
<=> ! [X0,X1] :
( relation_rng(relation_rng(sK4(powerset(X0)))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_351])]) ).
fof(f1201,plain,
( spl17_136
<=> ! [X0] :
( ~ empty(X0)
| empty(sK4(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_136])]) ).
fof(f1409,plain,
( spl17_156
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_rng(relation_rng(X1)) = X0
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_156])]) ).
fof(f1491,plain,
( ! [X0,X1] :
( relation_rng(relation_rng(sK4(powerset(X0)))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl17_136
| ~ spl17_156 ),
inference(resolution,[],[f1410,f1202]) ).
fof(f1202,plain,
( ! [X0] :
( empty(sK4(powerset(X0)))
| ~ empty(X0) )
| ~ spl17_136 ),
inference(avatar_component_clause,[],[f1201]) ).
fof(f1410,plain,
( ! [X0,X1] :
( ~ empty(X1)
| relation_rng(relation_rng(X1)) = X0
| ~ empty(X0) )
| ~ spl17_156 ),
inference(avatar_component_clause,[],[f1409]) ).
fof(f4941,plain,
( spl17_350
| ~ spl17_136
| ~ spl17_155 ),
inference(avatar_split_clause,[],[f1469,f1404,f1201,f4939]) ).
fof(f4939,plain,
( spl17_350
<=> ! [X0,X1] :
( relation_rng(relation_dom(sK4(powerset(X0)))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_350])]) ).
fof(f1404,plain,
( spl17_155
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_rng(relation_dom(X1)) = X0
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_155])]) ).
fof(f1469,plain,
( ! [X0,X1] :
( relation_rng(relation_dom(sK4(powerset(X0)))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl17_136
| ~ spl17_155 ),
inference(resolution,[],[f1405,f1202]) ).
fof(f1405,plain,
( ! [X0,X1] :
( ~ empty(X1)
| relation_rng(relation_dom(X1)) = X0
| ~ empty(X0) )
| ~ spl17_155 ),
inference(avatar_component_clause,[],[f1404]) ).
fof(f4937,plain,
( spl17_349
| ~ spl17_136
| ~ spl17_154 ),
inference(avatar_split_clause,[],[f1447,f1400,f1201,f4935]) ).
fof(f4935,plain,
( spl17_349
<=> ! [X0,X1] :
( relation_dom(relation_rng(sK4(powerset(X0)))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_349])]) ).
fof(f1400,plain,
( spl17_154
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_dom(relation_rng(X1)) = X0
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_154])]) ).
fof(f1447,plain,
( ! [X0,X1] :
( relation_dom(relation_rng(sK4(powerset(X0)))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl17_136
| ~ spl17_154 ),
inference(resolution,[],[f1401,f1202]) ).
fof(f1401,plain,
( ! [X0,X1] :
( ~ empty(X1)
| relation_dom(relation_rng(X1)) = X0
| ~ empty(X0) )
| ~ spl17_154 ),
inference(avatar_component_clause,[],[f1400]) ).
fof(f4933,plain,
( spl17_348
| ~ spl17_136
| ~ spl17_153 ),
inference(avatar_split_clause,[],[f1425,f1396,f1201,f4931]) ).
fof(f4931,plain,
( spl17_348
<=> ! [X0,X1] :
( relation_dom(relation_dom(sK4(powerset(X0)))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_348])]) ).
fof(f1396,plain,
( spl17_153
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_dom(relation_dom(X1)) = X0
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_153])]) ).
fof(f1425,plain,
( ! [X0,X1] :
( relation_dom(relation_dom(sK4(powerset(X0)))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl17_136
| ~ spl17_153 ),
inference(resolution,[],[f1397,f1202]) ).
fof(f1397,plain,
( ! [X0,X1] :
( ~ empty(X1)
| relation_dom(relation_dom(X1)) = X0
| ~ empty(X0) )
| ~ spl17_153 ),
inference(avatar_component_clause,[],[f1396]) ).
fof(f4924,plain,
( spl17_347
| ~ spl17_82
| ~ spl17_317 ),
inference(avatar_split_clause,[],[f4525,f4437,f650,f4922]) ).
fof(f4922,plain,
( spl17_347
<=> ! [X0] : sP0(X0,sK10,sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_347])]) ).
fof(f4437,plain,
( spl17_317
<=> ! [X0] :
( in(sK6(X0,sK10,sK10),sK10)
| sP0(X0,sK10,sK10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_317])]) ).
fof(f4525,plain,
( ! [X0] : sP0(X0,sK10,sK10)
| ~ spl17_82
| ~ spl17_317 ),
inference(resolution,[],[f4438,f651]) ).
fof(f4438,plain,
( ! [X0] :
( in(sK6(X0,sK10,sK10),sK10)
| sP0(X0,sK10,sK10) )
| ~ spl17_317 ),
inference(avatar_component_clause,[],[f4437]) ).
fof(f4913,plain,
( spl17_346
| ~ spl17_66
| ~ spl17_224 ),
inference(avatar_split_clause,[],[f2609,f2531,f568,f4911]) ).
fof(f4911,plain,
( spl17_346
<=> ! [X2,X0,X1] :
( ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ relation(X0)
| sP0(X1,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0),X2)
| ~ empty(relation_dom(X2))
| in(apply(X0,sK6(X1,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0),X2)),relation_rng(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_346])]) ).
fof(f2609,plain,
( ! [X2,X0,X1] :
( ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ relation(X0)
| sP0(X1,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0),X2)
| ~ empty(relation_dom(X2))
| in(apply(X0,sK6(X1,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0),X2)),relation_rng(sK2)) )
| ~ spl17_66
| ~ spl17_224 ),
inference(resolution,[],[f2532,f569]) ).
fof(f4909,plain,
( spl17_345
| ~ spl17_127
| ~ spl17_224 ),
inference(avatar_split_clause,[],[f2608,f2531,f1100,f4907]) ).
fof(f4907,plain,
( spl17_345
<=> ! [X2,X0,X1] :
( ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ relation(X0)
| sP0(X1,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0),X2)
| ~ empty(relation_dom(X2))
| element(apply(X0,sK6(X1,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0),X2)),relation_rng(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_345])]) ).
fof(f2608,plain,
( ! [X2,X0,X1] :
( ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ relation(X0)
| sP0(X1,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0),X2)
| ~ empty(relation_dom(X2))
| element(apply(X0,sK6(X1,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0),X2)),relation_rng(sK2)) )
| ~ spl17_127
| ~ spl17_224 ),
inference(resolution,[],[f2532,f1101]) ).
fof(f4905,plain,
( spl17_344
| ~ spl17_66
| ~ spl17_223 ),
inference(avatar_split_clause,[],[f2586,f2527,f568,f4903]) ).
fof(f4903,plain,
( spl17_344
<=> ! [X2,X0,X1] :
( ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ relation(X0)
| sP0(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ empty(relation_dom(X2))
| in(apply(X0,sK6(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))),relation_rng(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_344])]) ).
fof(f2586,plain,
( ! [X2,X0,X1] :
( ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ relation(X0)
| sP0(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ empty(relation_dom(X2))
| in(apply(X0,sK6(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))),relation_rng(sK2)) )
| ~ spl17_66
| ~ spl17_223 ),
inference(resolution,[],[f2528,f569]) ).
fof(f4901,plain,
( spl17_343
| ~ spl17_127
| ~ spl17_223 ),
inference(avatar_split_clause,[],[f2585,f2527,f1100,f4899]) ).
fof(f4899,plain,
( spl17_343
<=> ! [X2,X0,X1] :
( ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ relation(X0)
| sP0(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ empty(relation_dom(X2))
| element(apply(X0,sK6(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))),relation_rng(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_343])]) ).
fof(f2585,plain,
( ! [X2,X0,X1] :
( ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ relation(X0)
| sP0(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ empty(relation_dom(X2))
| element(apply(X0,sK6(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))),relation_rng(sK2)) )
| ~ spl17_127
| ~ spl17_223 ),
inference(resolution,[],[f2528,f1101]) ).
fof(f4890,plain,
( spl17_342
| ~ spl17_66
| ~ spl17_219 ),
inference(avatar_split_clause,[],[f2499,f2467,f568,f4888]) ).
fof(f4888,plain,
( spl17_342
<=> ! [X2,X0,X1] :
( ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ relation(X0)
| sP0(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ empty(X1)
| in(apply(X0,sK6(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))),relation_rng(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_342])]) ).
fof(f2499,plain,
( ! [X2,X0,X1] :
( ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ relation(X0)
| sP0(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ empty(X1)
| in(apply(X0,sK6(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))),relation_rng(sK2)) )
| ~ spl17_66
| ~ spl17_219 ),
inference(resolution,[],[f2468,f569]) ).
fof(f4886,plain,
( spl17_341
| ~ spl17_127
| ~ spl17_219 ),
inference(avatar_split_clause,[],[f2498,f2467,f1100,f4884]) ).
fof(f4884,plain,
( spl17_341
<=> ! [X2,X0,X1] :
( ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ relation(X0)
| sP0(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ empty(X1)
| element(apply(X0,sK6(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))),relation_rng(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_341])]) ).
fof(f2498,plain,
( ! [X2,X0,X1] :
( ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ relation(X0)
| sP0(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ empty(X1)
| element(apply(X0,sK6(X1,X2,relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))),relation_rng(sK2)) )
| ~ spl17_127
| ~ spl17_219 ),
inference(resolution,[],[f2468,f1101]) ).
fof(f4786,plain,
( spl17_340
| ~ spl17_58
| ~ spl17_146 ),
inference(avatar_split_clause,[],[f1358,f1341,f507,f4784]) ).
fof(f4784,plain,
( spl17_340
<=> ! [X2,X0,X1] :
( element(sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1),relation_dom(X1))
| sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1)
| in(sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1),relation_dom(X2))
| ~ in(sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1),relation_dom(X0))
| ~ sP0(relation_rng(sK2),X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_340])]) ).
fof(f1341,plain,
( spl17_146
<=> ! [X0,X1] :
( element(sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1),relation_dom(X1))
| sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1)
| in(apply(X0,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1)),relation_rng(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_146])]) ).
fof(f1358,plain,
( ! [X2,X0,X1] :
( element(sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1),relation_dom(X1))
| sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1)
| in(sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1),relation_dom(X2))
| ~ in(sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1),relation_dom(X0))
| ~ sP0(relation_rng(sK2),X0,X2) )
| ~ spl17_58
| ~ spl17_146 ),
inference(resolution,[],[f1342,f508]) ).
fof(f1342,plain,
( ! [X0,X1] :
( in(apply(X0,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1)),relation_rng(sK2))
| element(sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1),relation_dom(X1))
| sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1) )
| ~ spl17_146 ),
inference(avatar_component_clause,[],[f1341]) ).
fof(f4782,plain,
( spl17_339
| ~ spl17_58
| ~ spl17_145 ),
inference(avatar_split_clause,[],[f1347,f1337,f507,f4780]) ).
fof(f4780,plain,
( spl17_339
<=> ! [X2,X0,X1] :
( in(sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1),relation_dom(X1))
| sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1)
| in(sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1),relation_dom(X2))
| ~ in(sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1),relation_dom(X0))
| ~ sP0(relation_rng(sK2),X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_339])]) ).
fof(f1347,plain,
( ! [X2,X0,X1] :
( in(sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1),relation_dom(X1))
| sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1)
| in(sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1),relation_dom(X2))
| ~ in(sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1),relation_dom(X0))
| ~ sP0(relation_rng(sK2),X0,X2) )
| ~ spl17_58
| ~ spl17_145 ),
inference(resolution,[],[f1338,f508]) ).
fof(f4773,plain,
( spl17_338
| ~ spl17_66
| ~ spl17_215 ),
inference(avatar_split_clause,[],[f2430,f2419,f568,f4771]) ).
fof(f4771,plain,
( spl17_338
<=> ! [X0,X1] :
( ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ relation(X0)
| subset(relation_dom(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)),X1)
| in(apply(X0,sK8(relation_dom(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)),X1)),relation_rng(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_338])]) ).
fof(f2430,plain,
( ! [X0,X1] :
( ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ relation(X0)
| subset(relation_dom(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)),X1)
| in(apply(X0,sK8(relation_dom(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)),X1)),relation_rng(sK2)) )
| ~ spl17_66
| ~ spl17_215 ),
inference(resolution,[],[f2420,f569]) ).
fof(f4769,plain,
( spl17_337
| ~ spl17_127
| ~ spl17_215 ),
inference(avatar_split_clause,[],[f2429,f2419,f1100,f4767]) ).
fof(f4767,plain,
( spl17_337
<=> ! [X0,X1] :
( ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ relation(X0)
| subset(relation_dom(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)),X1)
| element(apply(X0,sK8(relation_dom(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)),X1)),relation_rng(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_337])]) ).
fof(f2429,plain,
( ! [X0,X1] :
( ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ relation(X0)
| subset(relation_dom(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)),X1)
| element(apply(X0,sK8(relation_dom(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)),X1)),relation_rng(sK2)) )
| ~ spl17_127
| ~ spl17_215 ),
inference(resolution,[],[f2420,f1101]) ).
fof(f4559,plain,
( ~ spl17_336
| ~ spl17_38
| ~ spl17_313 ),
inference(avatar_split_clause,[],[f4457,f4415,f380,f4556]) ).
fof(f4556,plain,
( spl17_336
<=> in(relation_dom(relation_rng_restriction(sK1,sK2)),sK8(relation_dom(relation_rng_restriction(sK1,sK2)),relation_dom(sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_336])]) ).
fof(f4415,plain,
( spl17_313
<=> in(sK8(relation_dom(relation_rng_restriction(sK1,sK2)),relation_dom(sK2)),relation_dom(relation_rng_restriction(sK1,sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_313])]) ).
fof(f4457,plain,
( ~ in(relation_dom(relation_rng_restriction(sK1,sK2)),sK8(relation_dom(relation_rng_restriction(sK1,sK2)),relation_dom(sK2)))
| ~ spl17_38
| ~ spl17_313 ),
inference(resolution,[],[f4416,f381]) ).
fof(f4416,plain,
( in(sK8(relation_dom(relation_rng_restriction(sK1,sK2)),relation_dom(sK2)),relation_dom(relation_rng_restriction(sK1,sK2)))
| ~ spl17_313 ),
inference(avatar_component_clause,[],[f4415]) ).
fof(f4524,plain,
( spl17_335
| ~ spl17_132
| ~ spl17_169 ),
inference(avatar_split_clause,[],[f2006,f1580,f1132,f4522]) ).
fof(f4522,plain,
( spl17_335
<=> ! [X0] :
( element(sK6(sK10,X0,sK10),sK10)
| sP0(sK10,X0,sK10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_335])]) ).
fof(f1580,plain,
( spl17_169
<=> ! [X0,X1] :
( element(sK6(sK10,X0,X1),relation_dom(X1))
| sP0(sK10,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_169])]) ).
fof(f2006,plain,
( ! [X0] :
( element(sK6(sK10,X0,sK10),sK10)
| sP0(sK10,X0,sK10) )
| ~ spl17_132
| ~ spl17_169 ),
inference(superposition,[],[f1581,f1134]) ).
fof(f1581,plain,
( ! [X0,X1] :
( element(sK6(sK10,X0,X1),relation_dom(X1))
| sP0(sK10,X0,X1) )
| ~ spl17_169 ),
inference(avatar_component_clause,[],[f1580]) ).
fof(f4520,plain,
( spl17_334
| ~ spl17_132
| ~ spl17_167 ),
inference(avatar_split_clause,[],[f2000,f1572,f1132,f4518]) ).
fof(f4518,plain,
( spl17_334
<=> ! [X0] :
( ~ in(sK10,sK6(X0,sK10,sK10))
| sP0(X0,sK10,sK10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_334])]) ).
fof(f1572,plain,
( spl17_167
<=> ! [X0,X1] :
( sP0(X0,X1,X1)
| ~ in(relation_dom(X1),sK6(X0,X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_167])]) ).
fof(f2000,plain,
( ! [X0] :
( ~ in(sK10,sK6(X0,sK10,sK10))
| sP0(X0,sK10,sK10) )
| ~ spl17_132
| ~ spl17_167 ),
inference(superposition,[],[f1573,f1134]) ).
fof(f1573,plain,
( ! [X0,X1] :
( ~ in(relation_dom(X1),sK6(X0,X1,X1))
| sP0(X0,X1,X1) )
| ~ spl17_167 ),
inference(avatar_component_clause,[],[f1572]) ).
fof(f4516,plain,
( spl17_333
| ~ spl17_132
| ~ spl17_166 ),
inference(avatar_split_clause,[],[f1995,f1568,f1132,f4514]) ).
fof(f4514,plain,
( spl17_333
<=> ! [X0] :
( element(sK6(X0,sK10,sK10),sK10)
| sP0(X0,sK10,sK10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_333])]) ).
fof(f1568,plain,
( spl17_166
<=> ! [X0,X1] :
( sP0(X0,X1,X1)
| element(sK6(X0,X1,X1),relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_166])]) ).
fof(f1995,plain,
( ! [X0] :
( element(sK6(X0,sK10,sK10),sK10)
| sP0(X0,sK10,sK10) )
| ~ spl17_132
| ~ spl17_166 ),
inference(superposition,[],[f1569,f1134]) ).
fof(f1569,plain,
( ! [X0,X1] :
( element(sK6(X0,X1,X1),relation_dom(X1))
| sP0(X0,X1,X1) )
| ~ spl17_166 ),
inference(avatar_component_clause,[],[f1568]) ).
fof(f4512,plain,
( spl17_332
| ~ spl17_86
| ~ spl17_165 ),
inference(avatar_split_clause,[],[f1992,f1564,f683,f4510]) ).
fof(f4510,plain,
( spl17_332
<=> ! [X0,X1] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(relation_rng(relation_rng_restriction(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_332])]) ).
fof(f1992,plain,
( ! [X0,X1] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(relation_rng(relation_rng_restriction(X1,X0))) )
| ~ spl17_86
| ~ spl17_165 ),
inference(resolution,[],[f1565,f684]) ).
fof(f4508,plain,
( spl17_331
| ~ spl17_132
| ~ spl17_164 ),
inference(avatar_split_clause,[],[f1987,f1560,f1132,f4506]) ).
fof(f1987,plain,
( ! [X0] :
( in(sK6(sK10,X0,sK10),sK10)
| sP0(sK10,X0,sK10) )
| ~ spl17_132
| ~ spl17_164 ),
inference(superposition,[],[f1561,f1134]) ).
fof(f4504,plain,
( spl17_330
| ~ spl17_29
| ~ spl17_156 ),
inference(avatar_split_clause,[],[f1490,f1409,f327,f4502]) ).
fof(f4502,plain,
( spl17_330
<=> ! [X0,X1] :
( relation_rng(relation_rng(relation_rng(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_330])]) ).
fof(f327,plain,
( spl17_29
<=> ! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_29])]) ).
fof(f1490,plain,
( ! [X0,X1] :
( relation_rng(relation_rng(relation_rng(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl17_29
| ~ spl17_156 ),
inference(resolution,[],[f1410,f328]) ).
fof(f328,plain,
( ! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) )
| ~ spl17_29 ),
inference(avatar_component_clause,[],[f327]) ).
fof(f4500,plain,
( spl17_329
| ~ spl17_31
| ~ spl17_156 ),
inference(avatar_split_clause,[],[f1489,f1409,f335,f4498]) ).
fof(f4498,plain,
( spl17_329
<=> ! [X0,X1] :
( relation_rng(relation_rng(relation_dom(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_329])]) ).
fof(f335,plain,
( spl17_31
<=> ! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_31])]) ).
fof(f1489,plain,
( ! [X0,X1] :
( relation_rng(relation_rng(relation_dom(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl17_31
| ~ spl17_156 ),
inference(resolution,[],[f1410,f336]) ).
fof(f336,plain,
( ! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) )
| ~ spl17_31 ),
inference(avatar_component_clause,[],[f335]) ).
fof(f4496,plain,
( spl17_328
| ~ spl17_39
| ~ spl17_313 ),
inference(avatar_split_clause,[],[f4456,f4415,f384,f4493]) ).
fof(f4493,plain,
( spl17_328
<=> element(sK8(relation_dom(relation_rng_restriction(sK1,sK2)),relation_dom(sK2)),relation_dom(relation_rng_restriction(sK1,sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_328])]) ).
fof(f384,plain,
( spl17_39
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_39])]) ).
fof(f4456,plain,
( element(sK8(relation_dom(relation_rng_restriction(sK1,sK2)),relation_dom(sK2)),relation_dom(relation_rng_restriction(sK1,sK2)))
| ~ spl17_39
| ~ spl17_313 ),
inference(resolution,[],[f4416,f385]) ).
fof(f385,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) )
| ~ spl17_39 ),
inference(avatar_component_clause,[],[f384]) ).
fof(f4491,plain,
( spl17_327
| ~ spl17_29
| ~ spl17_155 ),
inference(avatar_split_clause,[],[f1468,f1404,f327,f4489]) ).
fof(f4489,plain,
( spl17_327
<=> ! [X0,X1] :
( relation_rng(relation_dom(relation_rng(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_327])]) ).
fof(f1468,plain,
( ! [X0,X1] :
( relation_rng(relation_dom(relation_rng(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl17_29
| ~ spl17_155 ),
inference(resolution,[],[f1405,f328]) ).
fof(f4487,plain,
( spl17_326
| ~ spl17_31
| ~ spl17_155 ),
inference(avatar_split_clause,[],[f1467,f1404,f335,f4485]) ).
fof(f4485,plain,
( spl17_326
<=> ! [X0,X1] :
( relation_rng(relation_dom(relation_dom(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_326])]) ).
fof(f1467,plain,
( ! [X0,X1] :
( relation_rng(relation_dom(relation_dom(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl17_31
| ~ spl17_155 ),
inference(resolution,[],[f1405,f336]) ).
fof(f4483,plain,
( spl17_325
| ~ spl17_29
| ~ spl17_154 ),
inference(avatar_split_clause,[],[f1446,f1400,f327,f4481]) ).
fof(f4481,plain,
( spl17_325
<=> ! [X0,X1] :
( relation_dom(relation_rng(relation_rng(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_325])]) ).
fof(f1446,plain,
( ! [X0,X1] :
( relation_dom(relation_rng(relation_rng(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl17_29
| ~ spl17_154 ),
inference(resolution,[],[f1401,f328]) ).
fof(f4479,plain,
( spl17_324
| ~ spl17_31
| ~ spl17_154 ),
inference(avatar_split_clause,[],[f1445,f1400,f335,f4477]) ).
fof(f4477,plain,
( spl17_324
<=> ! [X0,X1] :
( relation_dom(relation_rng(relation_dom(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_324])]) ).
fof(f1445,plain,
( ! [X0,X1] :
( relation_dom(relation_rng(relation_dom(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl17_31
| ~ spl17_154 ),
inference(resolution,[],[f1401,f336]) ).
fof(f4475,plain,
( spl17_323
| ~ spl17_29
| ~ spl17_153 ),
inference(avatar_split_clause,[],[f1424,f1396,f327,f4473]) ).
fof(f4473,plain,
( spl17_323
<=> ! [X0,X1] :
( relation_dom(relation_dom(relation_rng(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_323])]) ).
fof(f1424,plain,
( ! [X0,X1] :
( relation_dom(relation_dom(relation_rng(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl17_29
| ~ spl17_153 ),
inference(resolution,[],[f1397,f328]) ).
fof(f4471,plain,
( spl17_322
| ~ spl17_31
| ~ spl17_153 ),
inference(avatar_split_clause,[],[f1423,f1396,f335,f4469]) ).
fof(f4469,plain,
( spl17_322
<=> ! [X0,X1] :
( relation_dom(relation_dom(relation_dom(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_322])]) ).
fof(f1423,plain,
( ! [X0,X1] :
( relation_dom(relation_dom(relation_dom(X0))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl17_31
| ~ spl17_153 ),
inference(resolution,[],[f1397,f336]) ).
fof(f4467,plain,
( spl17_321
| ~ spl17_86
| ~ spl17_152 ),
inference(avatar_split_clause,[],[f1420,f1392,f683,f4465]) ).
fof(f4465,plain,
( spl17_321
<=> ! [X0] :
( empty(X0)
| in(sK4(sK3(X0)),X0)
| empty(sK3(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_321])]) ).
fof(f1420,plain,
( ! [X0] :
( empty(X0)
| in(sK4(sK3(X0)),X0)
| empty(sK3(X0)) )
| ~ spl17_86
| ~ spl17_152 ),
inference(resolution,[],[f1393,f684]) ).
fof(f4463,plain,
( spl17_320
| ~ spl17_86
| ~ spl17_148 ),
inference(avatar_split_clause,[],[f1374,f1367,f683,f4461]) ).
fof(f1374,plain,
( ! [X0] :
( in(sK4(sK4(powerset(X0))),X0)
| empty(sK4(powerset(X0))) )
| ~ spl17_86
| ~ spl17_148 ),
inference(resolution,[],[f1368,f684]) ).
fof(f4448,plain,
( spl17_22
| ~ spl17_50
| spl17_313 ),
inference(avatar_split_clause,[],[f4422,f4415,f449,f288]) ).
fof(f4422,plain,
( subset(relation_dom(relation_rng_restriction(sK1,sK2)),relation_dom(sK2))
| ~ spl17_50
| spl17_313 ),
inference(resolution,[],[f4417,f450]) ).
fof(f4417,plain,
( ~ in(sK8(relation_dom(relation_rng_restriction(sK1,sK2)),relation_dom(sK2)),relation_dom(relation_rng_restriction(sK1,sK2)))
| spl17_313 ),
inference(avatar_component_clause,[],[f4415]) ).
fof(f4447,plain,
( spl17_319
| ~ spl17_91
| ~ spl17_136 ),
inference(avatar_split_clause,[],[f1212,f1201,f739,f4445]) ).
fof(f4445,plain,
( spl17_319
<=> ! [X0,X1] :
( ~ empty(X0)
| ~ empty(X1)
| relation_rng(sK4(powerset(X0))) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_319])]) ).
fof(f739,plain,
( spl17_91
<=> ! [X0,X1] :
( relation_rng(X1) = X0
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_91])]) ).
fof(f1212,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ empty(X1)
| relation_rng(sK4(powerset(X0))) = X1 )
| ~ spl17_91
| ~ spl17_136 ),
inference(resolution,[],[f1202,f740]) ).
fof(f740,plain,
( ! [X0,X1] :
( ~ empty(X1)
| ~ empty(X0)
| relation_rng(X1) = X0 )
| ~ spl17_91 ),
inference(avatar_component_clause,[],[f739]) ).
fof(f4443,plain,
( spl17_318
| ~ spl17_90
| ~ spl17_136 ),
inference(avatar_split_clause,[],[f1211,f1201,f735,f4441]) ).
fof(f4441,plain,
( spl17_318
<=> ! [X0,X1] :
( ~ empty(X0)
| ~ empty(X1)
| relation_dom(sK4(powerset(X0))) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_318])]) ).
fof(f735,plain,
( spl17_90
<=> ! [X0,X1] :
( relation_dom(X1) = X0
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_90])]) ).
fof(f1211,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ empty(X1)
| relation_dom(sK4(powerset(X0))) = X1 )
| ~ spl17_90
| ~ spl17_136 ),
inference(resolution,[],[f1202,f736]) ).
fof(f736,plain,
( ! [X0,X1] :
( ~ empty(X1)
| ~ empty(X0)
| relation_dom(X1) = X0 )
| ~ spl17_90 ),
inference(avatar_component_clause,[],[f735]) ).
fof(f4439,plain,
( spl17_317
| ~ spl17_101
| ~ spl17_132 ),
inference(avatar_split_clause,[],[f1175,f1132,f846,f4437]) ).
fof(f846,plain,
( spl17_101
<=> ! [X0,X1] :
( in(sK6(X0,X1,X1),relation_dom(X1))
| sP0(X0,X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_101])]) ).
fof(f1175,plain,
( ! [X0] :
( in(sK6(X0,sK10,sK10),sK10)
| sP0(X0,sK10,sK10) )
| ~ spl17_101
| ~ spl17_132 ),
inference(superposition,[],[f847,f1134]) ).
fof(f847,plain,
( ! [X0,X1] :
( in(sK6(X0,X1,X1),relation_dom(X1))
| sP0(X0,X1,X1) )
| ~ spl17_101 ),
inference(avatar_component_clause,[],[f846]) ).
fof(f4430,plain,
( spl17_316
| ~ spl17_66
| ~ spl17_212 ),
inference(avatar_split_clause,[],[f2388,f2373,f568,f4428]) ).
fof(f4428,plain,
( spl17_316
<=> ! [X0] :
( ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ relation(X0)
| empty(relation_dom(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)))
| in(apply(X0,sK4(relation_dom(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)))),relation_rng(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_316])]) ).
fof(f2388,plain,
( ! [X0] :
( ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ relation(X0)
| empty(relation_dom(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)))
| in(apply(X0,sK4(relation_dom(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)))),relation_rng(sK2)) )
| ~ spl17_66
| ~ spl17_212 ),
inference(resolution,[],[f2374,f569]) ).
fof(f4426,plain,
( spl17_315
| ~ spl17_127
| ~ spl17_212 ),
inference(avatar_split_clause,[],[f2387,f2373,f1100,f4424]) ).
fof(f4424,plain,
( spl17_315
<=> ! [X0] :
( ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ relation(X0)
| empty(relation_dom(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)))
| element(apply(X0,sK4(relation_dom(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)))),relation_rng(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_315])]) ).
fof(f2387,plain,
( ! [X0] :
( ~ function(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ relation(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0))
| ~ function(X0)
| ~ relation(X0)
| empty(relation_dom(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)))
| element(apply(X0,sK4(relation_dom(relation_rng_restriction(relation_rng(relation_rng_restriction(sK1,sK2)),X0)))),relation_rng(sK2)) )
| ~ spl17_127
| ~ spl17_212 ),
inference(resolution,[],[f2374,f1101]) ).
fof(f4421,plain,
( ~ spl17_313
| spl17_314
| ~ spl17_58
| ~ spl17_149 ),
inference(avatar_split_clause,[],[f1519,f1377,f507,f4419,f4415]) ).
fof(f4419,plain,
( spl17_314
<=> ! [X0,X1] :
( ~ in(apply(sK2,sK8(relation_dom(relation_rng_restriction(sK1,sK2)),relation_dom(sK2))),X0)
| ~ sP0(X0,relation_rng_restriction(sK1,sK2),X1)
| in(sK8(relation_dom(relation_rng_restriction(sK1,sK2)),relation_dom(sK2)),relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_314])]) ).
fof(f1377,plain,
( spl17_149
<=> apply(sK2,sK8(relation_dom(relation_rng_restriction(sK1,sK2)),relation_dom(sK2))) = apply(relation_rng_restriction(sK1,sK2),sK8(relation_dom(relation_rng_restriction(sK1,sK2)),relation_dom(sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_149])]) ).
fof(f1519,plain,
( ! [X0,X1] :
( ~ in(apply(sK2,sK8(relation_dom(relation_rng_restriction(sK1,sK2)),relation_dom(sK2))),X0)
| in(sK8(relation_dom(relation_rng_restriction(sK1,sK2)),relation_dom(sK2)),relation_dom(X1))
| ~ in(sK8(relation_dom(relation_rng_restriction(sK1,sK2)),relation_dom(sK2)),relation_dom(relation_rng_restriction(sK1,sK2)))
| ~ sP0(X0,relation_rng_restriction(sK1,sK2),X1) )
| ~ spl17_58
| ~ spl17_149 ),
inference(superposition,[],[f508,f1379]) ).
fof(f1379,plain,
( apply(sK2,sK8(relation_dom(relation_rng_restriction(sK1,sK2)),relation_dom(sK2))) = apply(relation_rng_restriction(sK1,sK2),sK8(relation_dom(relation_rng_restriction(sK1,sK2)),relation_dom(sK2)))
| ~ spl17_149 ),
inference(avatar_component_clause,[],[f1377]) ).
fof(f4390,plain,
( spl17_312
| ~ spl17_3
| ~ spl17_69
| ~ spl17_286 ),
inference(avatar_split_clause,[],[f3842,f3830,f584,f196,f4387]) ).
fof(f4387,plain,
( spl17_312
<=> sK10 = sK4(powerset(sK10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_312])]) ).
fof(f196,plain,
( spl17_3
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_3])]) ).
fof(f584,plain,
( spl17_69
<=> empty_set = sK10 ),
introduced(avatar_definition,[new_symbols(naming,[spl17_69])]) ).
fof(f3830,plain,
( spl17_286
<=> ! [X0] :
( sK10 = sK4(powerset(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_286])]) ).
fof(f3842,plain,
( sK10 = sK4(powerset(sK10))
| ~ spl17_3
| ~ spl17_69
| ~ spl17_286 ),
inference(forward_demodulation,[],[f3833,f586]) ).
fof(f586,plain,
( empty_set = sK10
| ~ spl17_69 ),
inference(avatar_component_clause,[],[f584]) ).
fof(f3833,plain,
( sK10 = sK4(powerset(empty_set))
| ~ spl17_3
| ~ spl17_286 ),
inference(resolution,[],[f3831,f198]) ).
fof(f198,plain,
( empty(empty_set)
| ~ spl17_3 ),
inference(avatar_component_clause,[],[f196]) ).
fof(f3831,plain,
( ! [X0] :
( ~ empty(X0)
| sK10 = sK4(powerset(X0)) )
| ~ spl17_286 ),
inference(avatar_component_clause,[],[f3830]) ).
fof(f4303,plain,
( spl17_311
| ~ spl17_136
| ~ spl17_141 ),
inference(avatar_split_clause,[],[f1310,f1240,f1201,f4301]) ).
fof(f4301,plain,
( spl17_311
<=> ! [X0] :
( sK10 = relation_dom(relation_rng(sK4(powerset(X0))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_311])]) ).
fof(f1240,plain,
( spl17_141
<=> ! [X0] :
( sK10 = relation_dom(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_141])]) ).
fof(f1310,plain,
( ! [X0] :
( sK10 = relation_dom(relation_rng(sK4(powerset(X0))))
| ~ empty(X0) )
| ~ spl17_136
| ~ spl17_141 ),
inference(resolution,[],[f1241,f1202]) ).
fof(f1241,plain,
( ! [X0] :
( ~ empty(X0)
| sK10 = relation_dom(relation_rng(X0)) )
| ~ spl17_141 ),
inference(avatar_component_clause,[],[f1240]) ).
fof(f4299,plain,
( spl17_310
| ~ spl17_136
| ~ spl17_140 ),
inference(avatar_split_clause,[],[f1293,f1236,f1201,f4297]) ).
fof(f4297,plain,
( spl17_310
<=> ! [X0] :
( sK10 = relation_dom(relation_dom(sK4(powerset(X0))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_310])]) ).
fof(f1236,plain,
( spl17_140
<=> ! [X0] :
( sK10 = relation_dom(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_140])]) ).
fof(f1293,plain,
( ! [X0] :
( sK10 = relation_dom(relation_dom(sK4(powerset(X0))))
| ~ empty(X0) )
| ~ spl17_136
| ~ spl17_140 ),
inference(resolution,[],[f1237,f1202]) ).
fof(f1237,plain,
( ! [X0] :
( ~ empty(X0)
| sK10 = relation_dom(relation_dom(X0)) )
| ~ spl17_140 ),
inference(avatar_component_clause,[],[f1236]) ).
fof(f4295,plain,
( spl17_309
| ~ spl17_136
| ~ spl17_139 ),
inference(avatar_split_clause,[],[f1276,f1232,f1201,f4293]) ).
fof(f4293,plain,
( spl17_309
<=> ! [X0] :
( sK10 = relation_rng(relation_rng(sK4(powerset(X0))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_309])]) ).
fof(f1232,plain,
( spl17_139
<=> ! [X0] :
( sK10 = relation_rng(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_139])]) ).
fof(f1276,plain,
( ! [X0] :
( sK10 = relation_rng(relation_rng(sK4(powerset(X0))))
| ~ empty(X0) )
| ~ spl17_136
| ~ spl17_139 ),
inference(resolution,[],[f1233,f1202]) ).
fof(f1233,plain,
( ! [X0] :
( ~ empty(X0)
| sK10 = relation_rng(relation_rng(X0)) )
| ~ spl17_139 ),
inference(avatar_component_clause,[],[f1232]) ).
fof(f4291,plain,
( spl17_308
| ~ spl17_136
| ~ spl17_137 ),
inference(avatar_split_clause,[],[f1258,f1215,f1201,f4289]) ).
fof(f4289,plain,
( spl17_308
<=> ! [X0] :
( sK10 = relation_rng(relation_dom(sK4(powerset(X0))))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_308])]) ).
fof(f1215,plain,
( spl17_137
<=> ! [X0] :
( sK10 = relation_rng(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_137])]) ).
fof(f1258,plain,
( ! [X0] :
( sK10 = relation_rng(relation_dom(sK4(powerset(X0))))
| ~ empty(X0) )
| ~ spl17_136
| ~ spl17_137 ),
inference(resolution,[],[f1216,f1202]) ).
fof(f1216,plain,
( ! [X0] :
( ~ empty(X0)
| sK10 = relation_rng(relation_dom(X0)) )
| ~ spl17_137 ),
inference(avatar_component_clause,[],[f1215]) ).
fof(f4287,plain,
( spl17_307
| ~ spl17_46
| ~ spl17_136 ),
inference(avatar_split_clause,[],[f1207,f1201,f414,f4285]) ).
fof(f4285,plain,
( spl17_307
<=> ! [X0,X1] :
( ~ empty(X0)
| sK4(powerset(X0)) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_307])]) ).
fof(f414,plain,
( spl17_46
<=> ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_46])]) ).
fof(f1207,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK4(powerset(X0)) = X1
| ~ empty(X1) )
| ~ spl17_46
| ~ spl17_136 ),
inference(resolution,[],[f1202,f415]) ).
fof(f415,plain,
( ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) )
| ~ spl17_46 ),
inference(avatar_component_clause,[],[f414]) ).
fof(f4235,plain,
( spl17_306
| ~ spl17_58
| ~ spl17_134 ),
inference(avatar_split_clause,[],[f1230,f1192,f507,f4233]) ).
fof(f4233,plain,
( spl17_306
<=> ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X1,X0)
| in(sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X1,X0),relation_dom(X2))
| ~ in(sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X1,X0),relation_dom(X1))
| ~ sP0(relation_rng(sK2),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_306])]) ).
fof(f1192,plain,
( spl17_134
<=> ! [X0,X1] :
( sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1)
| ~ empty(relation_dom(X1))
| in(apply(X0,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1)),relation_rng(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_134])]) ).
fof(f1230,plain,
( ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X1,X0)
| in(sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X1,X0),relation_dom(X2))
| ~ in(sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X1,X0),relation_dom(X1))
| ~ sP0(relation_rng(sK2),X1,X2) )
| ~ spl17_58
| ~ spl17_134 ),
inference(resolution,[],[f1193,f508]) ).
fof(f1193,plain,
( ! [X0,X1] :
( in(apply(X0,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1)),relation_rng(sK2))
| ~ empty(relation_dom(X1))
| sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1) )
| ~ spl17_134 ),
inference(avatar_component_clause,[],[f1192]) ).
fof(f4029,plain,
( spl17_305
| ~ spl17_38
| ~ spl17_257 ),
inference(avatar_split_clause,[],[f3519,f3475,f380,f4027]) ).
fof(f4027,plain,
( spl17_305
<=> ! [X0,X1] :
( subset(relation_rng(relation_rng_restriction(X0,relation_rng_restriction(sK1,sK2))),X1)
| ~ in(relation_rng(sK2),sK8(relation_rng(relation_rng_restriction(X0,relation_rng_restriction(sK1,sK2))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_305])]) ).
fof(f3475,plain,
( spl17_257
<=> ! [X0,X1] :
( subset(relation_rng(relation_rng_restriction(X0,relation_rng_restriction(sK1,sK2))),X1)
| in(sK8(relation_rng(relation_rng_restriction(X0,relation_rng_restriction(sK1,sK2))),X1),relation_rng(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_257])]) ).
fof(f3519,plain,
( ! [X0,X1] :
( subset(relation_rng(relation_rng_restriction(X0,relation_rng_restriction(sK1,sK2))),X1)
| ~ in(relation_rng(sK2),sK8(relation_rng(relation_rng_restriction(X0,relation_rng_restriction(sK1,sK2))),X1)) )
| ~ spl17_38
| ~ spl17_257 ),
inference(resolution,[],[f3476,f381]) ).
fof(f3476,plain,
( ! [X0,X1] :
( in(sK8(relation_rng(relation_rng_restriction(X0,relation_rng_restriction(sK1,sK2))),X1),relation_rng(sK2))
| subset(relation_rng(relation_rng_restriction(X0,relation_rng_restriction(sK1,sK2))),X1) )
| ~ spl17_257 ),
inference(avatar_component_clause,[],[f3475]) ).
fof(f4007,plain,
( spl17_304
| ~ spl17_29
| ~ spl17_141 ),
inference(avatar_split_clause,[],[f1309,f1240,f327,f4005]) ).
fof(f4005,plain,
( spl17_304
<=> ! [X0] :
( sK10 = relation_dom(relation_rng(relation_rng(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_304])]) ).
fof(f1309,plain,
( ! [X0] :
( sK10 = relation_dom(relation_rng(relation_rng(X0)))
| ~ empty(X0) )
| ~ spl17_29
| ~ spl17_141 ),
inference(resolution,[],[f1241,f328]) ).
fof(f4003,plain,
( spl17_303
| ~ spl17_31
| ~ spl17_141 ),
inference(avatar_split_clause,[],[f1308,f1240,f335,f4001]) ).
fof(f4001,plain,
( spl17_303
<=> ! [X0] :
( sK10 = relation_dom(relation_rng(relation_dom(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_303])]) ).
fof(f1308,plain,
( ! [X0] :
( sK10 = relation_dom(relation_rng(relation_dom(X0)))
| ~ empty(X0) )
| ~ spl17_31
| ~ spl17_141 ),
inference(resolution,[],[f1241,f336]) ).
fof(f3999,plain,
( spl17_302
| ~ spl17_29
| ~ spl17_140 ),
inference(avatar_split_clause,[],[f1292,f1236,f327,f3997]) ).
fof(f3997,plain,
( spl17_302
<=> ! [X0] :
( sK10 = relation_dom(relation_dom(relation_rng(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_302])]) ).
fof(f1292,plain,
( ! [X0] :
( sK10 = relation_dom(relation_dom(relation_rng(X0)))
| ~ empty(X0) )
| ~ spl17_29
| ~ spl17_140 ),
inference(resolution,[],[f1237,f328]) ).
fof(f3995,plain,
( spl17_301
| ~ spl17_31
| ~ spl17_140 ),
inference(avatar_split_clause,[],[f1291,f1236,f335,f3993]) ).
fof(f3993,plain,
( spl17_301
<=> ! [X0] :
( sK10 = relation_dom(relation_dom(relation_dom(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_301])]) ).
fof(f1291,plain,
( ! [X0] :
( sK10 = relation_dom(relation_dom(relation_dom(X0)))
| ~ empty(X0) )
| ~ spl17_31
| ~ spl17_140 ),
inference(resolution,[],[f1237,f336]) ).
fof(f3991,plain,
( spl17_300
| ~ spl17_29
| ~ spl17_139 ),
inference(avatar_split_clause,[],[f1275,f1232,f327,f3989]) ).
fof(f3989,plain,
( spl17_300
<=> ! [X0] :
( sK10 = relation_rng(relation_rng(relation_rng(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_300])]) ).
fof(f1275,plain,
( ! [X0] :
( sK10 = relation_rng(relation_rng(relation_rng(X0)))
| ~ empty(X0) )
| ~ spl17_29
| ~ spl17_139 ),
inference(resolution,[],[f1233,f328]) ).
fof(f3987,plain,
( spl17_299
| ~ spl17_31
| ~ spl17_139 ),
inference(avatar_split_clause,[],[f1274,f1232,f335,f3985]) ).
fof(f3985,plain,
( spl17_299
<=> ! [X0] :
( sK10 = relation_rng(relation_rng(relation_dom(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_299])]) ).
fof(f1274,plain,
( ! [X0] :
( sK10 = relation_rng(relation_rng(relation_dom(X0)))
| ~ empty(X0) )
| ~ spl17_31
| ~ spl17_139 ),
inference(resolution,[],[f1233,f336]) ).
fof(f3983,plain,
( spl17_298
| ~ spl17_29
| ~ spl17_137 ),
inference(avatar_split_clause,[],[f1257,f1215,f327,f3981]) ).
fof(f3981,plain,
( spl17_298
<=> ! [X0] :
( sK10 = relation_rng(relation_dom(relation_rng(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_298])]) ).
fof(f1257,plain,
( ! [X0] :
( sK10 = relation_rng(relation_dom(relation_rng(X0)))
| ~ empty(X0) )
| ~ spl17_29
| ~ spl17_137 ),
inference(resolution,[],[f1216,f328]) ).
fof(f3979,plain,
( spl17_297
| ~ spl17_31
| ~ spl17_137 ),
inference(avatar_split_clause,[],[f1256,f1215,f335,f3977]) ).
fof(f3977,plain,
( spl17_297
<=> ! [X0] :
( sK10 = relation_rng(relation_dom(relation_dom(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_297])]) ).
fof(f1256,plain,
( ! [X0] :
( sK10 = relation_rng(relation_dom(relation_dom(X0)))
| ~ empty(X0) )
| ~ spl17_31
| ~ spl17_137 ),
inference(resolution,[],[f1216,f336]) ).
fof(f3975,plain,
( spl17_296
| ~ spl17_84
| ~ spl17_136 ),
inference(avatar_split_clause,[],[f1210,f1201,f675,f3973]) ).
fof(f3973,plain,
( spl17_296
<=> ! [X0] :
( ~ empty(X0)
| sK10 = relation_dom(sK4(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_296])]) ).
fof(f675,plain,
( spl17_84
<=> ! [X0] :
( relation_dom(X0) = sK10
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_84])]) ).
fof(f1210,plain,
( ! [X0] :
( ~ empty(X0)
| sK10 = relation_dom(sK4(powerset(X0))) )
| ~ spl17_84
| ~ spl17_136 ),
inference(resolution,[],[f1202,f676]) ).
fof(f676,plain,
( ! [X0] :
( ~ empty(X0)
| relation_dom(X0) = sK10 )
| ~ spl17_84 ),
inference(avatar_component_clause,[],[f675]) ).
fof(f3938,plain,
( spl17_295
| ~ spl17_83
| ~ spl17_136 ),
inference(avatar_split_clause,[],[f1209,f1201,f671,f3936]) ).
fof(f3936,plain,
( spl17_295
<=> ! [X0] :
( ~ empty(X0)
| sK10 = relation_rng(sK4(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_295])]) ).
fof(f671,plain,
( spl17_83
<=> ! [X0] :
( relation_rng(X0) = sK10
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_83])]) ).
fof(f1209,plain,
( ! [X0] :
( ~ empty(X0)
| sK10 = relation_rng(sK4(powerset(X0))) )
| ~ spl17_83
| ~ spl17_136 ),
inference(resolution,[],[f1202,f672]) ).
fof(f672,plain,
( ! [X0] :
( ~ empty(X0)
| relation_rng(X0) = sK10 )
| ~ spl17_83 ),
inference(avatar_component_clause,[],[f671]) ).
fof(f3931,plain,
( ~ spl17_48
| spl17_294
| ~ spl17_52
| ~ spl17_131 ),
inference(avatar_split_clause,[],[f1164,f1127,f468,f3929,f440]) ).
fof(f3929,plain,
( spl17_294
<=> ! [X0] : subset(relation_rng(relation_rng_restriction(X0,sK10)),sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_294])]) ).
fof(f468,plain,
( spl17_52
<=> ! [X0,X1] :
( subset(relation_rng(relation_rng_restriction(X0,X1)),relation_rng(X1))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_52])]) ).
fof(f1164,plain,
( ! [X0] :
( subset(relation_rng(relation_rng_restriction(X0,sK10)),sK10)
| ~ relation(sK10) )
| ~ spl17_52
| ~ spl17_131 ),
inference(superposition,[],[f469,f1129]) ).
fof(f469,plain,
( ! [X0,X1] :
( subset(relation_rng(relation_rng_restriction(X0,X1)),relation_rng(X1))
| ~ relation(X1) )
| ~ spl17_52 ),
inference(avatar_component_clause,[],[f468]) ).
fof(f3923,plain,
( ~ spl17_150
| spl17_293
| ~ spl17_66
| ~ spl17_205 ),
inference(avatar_split_clause,[],[f2298,f2274,f568,f3921,f1381]) ).
fof(f3921,plain,
( spl17_293
<=> ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| in(apply(X2,sK6(relation_rng(relation_rng_restriction(X1,relation_rng_restriction(sK1,sK2))),X2,X0)),relation_rng(sK2))
| sP0(relation_rng(relation_rng_restriction(X1,relation_rng_restriction(sK1,sK2))),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_293])]) ).
fof(f2298,plain,
( ! [X2,X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(relation_rng(relation_rng_restriction(X1,relation_rng_restriction(sK1,sK2))),X2,X0)
| ~ relation(relation_rng_restriction(sK1,sK2))
| in(apply(X2,sK6(relation_rng(relation_rng_restriction(X1,relation_rng_restriction(sK1,sK2))),X2,X0)),relation_rng(sK2)) )
| ~ spl17_66
| ~ spl17_205 ),
inference(resolution,[],[f2275,f569]) ).
fof(f3870,plain,
( ~ spl17_150
| ~ spl17_151
| ~ spl17_1
| ~ spl17_2
| spl17_292
| spl17_87
| ~ spl17_228 ),
inference(avatar_split_clause,[],[f2664,f2657,f710,f3867,f191,f186,f1385,f1381]) ).
fof(f3867,plain,
( spl17_292
<=> apply(sK2,sK4(relation_dom(relation_rng_restriction(sK1,sK2)))) = apply(relation_rng_restriction(sK1,sK2),sK4(relation_dom(relation_rng_restriction(sK1,sK2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_292])]) ).
fof(f710,plain,
( spl17_87
<=> empty(relation_dom(relation_rng_restriction(sK1,sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_87])]) ).
fof(f2657,plain,
( spl17_228
<=> ! [X0,X1] :
( empty(relation_dom(relation_rng_restriction(X0,X1)))
| apply(X1,sK4(relation_dom(relation_rng_restriction(X0,X1)))) = apply(relation_rng_restriction(X0,X1),sK4(relation_dom(relation_rng_restriction(X0,X1))))
| ~ function(X1)
| ~ relation(X1)
| ~ function(relation_rng_restriction(X0,X1))
| ~ relation(relation_rng_restriction(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_228])]) ).
fof(f2664,plain,
( apply(sK2,sK4(relation_dom(relation_rng_restriction(sK1,sK2)))) = apply(relation_rng_restriction(sK1,sK2),sK4(relation_dom(relation_rng_restriction(sK1,sK2))))
| ~ function(sK2)
| ~ relation(sK2)
| ~ function(relation_rng_restriction(sK1,sK2))
| ~ relation(relation_rng_restriction(sK1,sK2))
| spl17_87
| ~ spl17_228 ),
inference(resolution,[],[f2658,f712]) ).
fof(f712,plain,
( ~ empty(relation_dom(relation_rng_restriction(sK1,sK2)))
| spl17_87 ),
inference(avatar_component_clause,[],[f710]) ).
fof(f2658,plain,
( ! [X0,X1] :
( empty(relation_dom(relation_rng_restriction(X0,X1)))
| apply(X1,sK4(relation_dom(relation_rng_restriction(X0,X1)))) = apply(relation_rng_restriction(X0,X1),sK4(relation_dom(relation_rng_restriction(X0,X1))))
| ~ function(X1)
| ~ relation(X1)
| ~ function(relation_rng_restriction(X0,X1))
| ~ relation(relation_rng_restriction(X0,X1)) )
| ~ spl17_228 ),
inference(avatar_component_clause,[],[f2657]) ).
fof(f3865,plain,
( spl17_291
| ~ spl17_38
| ~ spl17_146 ),
inference(avatar_split_clause,[],[f1356,f1341,f380,f3863]) ).
fof(f3863,plain,
( spl17_291
<=> ! [X0,X1] :
( element(sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1),relation_dom(X1))
| sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1)
| ~ in(relation_rng(sK2),apply(X0,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_291])]) ).
fof(f1356,plain,
( ! [X0,X1] :
( element(sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1),relation_dom(X1))
| sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1)
| ~ in(relation_rng(sK2),apply(X0,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1))) )
| ~ spl17_38
| ~ spl17_146 ),
inference(resolution,[],[f1342,f381]) ).
fof(f3861,plain,
( spl17_290
| ~ spl17_38
| ~ spl17_145 ),
inference(avatar_split_clause,[],[f1352,f1337,f380,f3859]) ).
fof(f3859,plain,
( spl17_290
<=> ! [X0,X1] :
( in(apply(X0,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1)),relation_rng(sK2))
| sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1)
| ~ in(relation_dom(X1),sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_290])]) ).
fof(f1352,plain,
( ! [X0,X1] :
( in(apply(X0,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1)),relation_rng(sK2))
| sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1)
| ~ in(relation_dom(X1),sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1)) )
| ~ spl17_38
| ~ spl17_145 ),
inference(resolution,[],[f1338,f381]) ).
fof(f3857,plain,
( spl17_289
| ~ spl17_38
| ~ spl17_145 ),
inference(avatar_split_clause,[],[f1345,f1337,f380,f3855]) ).
fof(f3855,plain,
( spl17_289
<=> ! [X0,X1] :
( in(sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1),relation_dom(X1))
| sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1)
| ~ in(relation_rng(sK2),apply(X0,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_289])]) ).
fof(f1345,plain,
( ! [X0,X1] :
( in(sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1),relation_dom(X1))
| sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1)
| ~ in(relation_rng(sK2),apply(X0,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1))) )
| ~ spl17_38
| ~ spl17_145 ),
inference(resolution,[],[f1338,f381]) ).
fof(f3853,plain,
( spl17_288
| ~ spl17_61
| ~ spl17_127 ),
inference(avatar_split_clause,[],[f1105,f1100,f530,f3851]) ).
fof(f3851,plain,
( spl17_288
<=> ! [X0,X1] :
( element(apply(X0,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1)),relation_rng(sK2))
| in(sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1),relation_dom(X1))
| sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_288])]) ).
fof(f530,plain,
( spl17_61
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(apply(X1,sK6(X0,X1,X2)),X0)
| in(sK6(X0,X1,X2),relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_61])]) ).
fof(f1105,plain,
( ! [X0,X1] :
( element(apply(X0,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1)),relation_rng(sK2))
| in(sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1),relation_dom(X1))
| sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1) )
| ~ spl17_61
| ~ spl17_127 ),
inference(resolution,[],[f1101,f531]) ).
fof(f531,plain,
( ! [X2,X0,X1] :
( in(apply(X1,sK6(X0,X1,X2)),X0)
| in(sK6(X0,X1,X2),relation_dom(X2))
| sP0(X0,X1,X2) )
| ~ spl17_61 ),
inference(avatar_component_clause,[],[f530]) ).
fof(f3849,plain,
( spl17_287
| ~ spl17_116
| ~ spl17_127 ),
inference(avatar_split_clause,[],[f1103,f1100,f948,f3847]) ).
fof(f3847,plain,
( spl17_287
<=> ! [X0,X1] :
( element(apply(X0,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1)),relation_rng(sK2))
| element(sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1),relation_dom(X1))
| sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_287])]) ).
fof(f948,plain,
( spl17_116
<=> ! [X2,X0,X1] :
( in(apply(X1,sK6(X0,X1,X2)),X0)
| sP0(X0,X1,X2)
| element(sK6(X0,X1,X2),relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_116])]) ).
fof(f1103,plain,
( ! [X0,X1] :
( element(apply(X0,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1)),relation_rng(sK2))
| element(sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1),relation_dom(X1))
| sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1) )
| ~ spl17_116
| ~ spl17_127 ),
inference(resolution,[],[f1101,f949]) ).
fof(f949,plain,
( ! [X2,X0,X1] :
( in(apply(X1,sK6(X0,X1,X2)),X0)
| element(sK6(X0,X1,X2),relation_dom(X2))
| sP0(X0,X1,X2) )
| ~ spl17_116 ),
inference(avatar_component_clause,[],[f948]) ).
fof(f3832,plain,
( spl17_286
| ~ spl17_28
| ~ spl17_69
| ~ spl17_136 ),
inference(avatar_split_clause,[],[f1213,f1201,f584,f323,f3830]) ).
fof(f323,plain,
( spl17_28
<=> ! [X0] :
( empty_set = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_28])]) ).
fof(f1213,plain,
( ! [X0] :
( sK10 = sK4(powerset(X0))
| ~ empty(X0) )
| ~ spl17_28
| ~ spl17_69
| ~ spl17_136 ),
inference(forward_demodulation,[],[f1206,f586]) ).
fof(f1206,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = sK4(powerset(X0)) )
| ~ spl17_28
| ~ spl17_136 ),
inference(resolution,[],[f1202,f324]) ).
fof(f324,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = X0 )
| ~ spl17_28 ),
inference(avatar_component_clause,[],[f323]) ).
fof(f3828,plain,
( spl17_285
| ~ spl17_53
| ~ spl17_268 ),
inference(avatar_split_clause,[],[f3614,f3556,f472,f3826]) ).
fof(f3826,plain,
( spl17_285
<=> ! [X0,X1] :
( ~ in(X0,relation_rng(relation_rng_restriction(X1,relation_rng_restriction(sK1,sK2))))
| in(X0,relation_rng(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_285])]) ).
fof(f3556,plain,
( spl17_268
<=> ! [X0] : subset(relation_rng(relation_rng_restriction(X0,relation_rng_restriction(sK1,sK2))),relation_rng(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_268])]) ).
fof(f3614,plain,
( ! [X0,X1] :
( ~ in(X0,relation_rng(relation_rng_restriction(X1,relation_rng_restriction(sK1,sK2))))
| in(X0,relation_rng(sK2)) )
| ~ spl17_53
| ~ spl17_268 ),
inference(resolution,[],[f3557,f473]) ).
fof(f3557,plain,
( ! [X0] : subset(relation_rng(relation_rng_restriction(X0,relation_rng_restriction(sK1,sK2))),relation_rng(sK2))
| ~ spl17_268 ),
inference(avatar_component_clause,[],[f3556]) ).
fof(f3824,plain,
( spl17_284
| ~ spl17_25
| ~ spl17_136 ),
inference(avatar_split_clause,[],[f1205,f1201,f301,f3822]) ).
fof(f3822,plain,
( spl17_284
<=> ! [X0] :
( ~ empty(X0)
| relation(sK4(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_284])]) ).
fof(f301,plain,
( spl17_25
<=> ! [X0] :
( relation(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_25])]) ).
fof(f1205,plain,
( ! [X0] :
( ~ empty(X0)
| relation(sK4(powerset(X0))) )
| ~ spl17_25
| ~ spl17_136 ),
inference(resolution,[],[f1202,f302]) ).
fof(f302,plain,
( ! [X0] :
( ~ empty(X0)
| relation(X0) )
| ~ spl17_25 ),
inference(avatar_component_clause,[],[f301]) ).
fof(f3820,plain,
( spl17_283
| ~ spl17_24
| ~ spl17_136 ),
inference(avatar_split_clause,[],[f1204,f1201,f297,f3818]) ).
fof(f3818,plain,
( spl17_283
<=> ! [X0] :
( ~ empty(X0)
| function(sK4(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_283])]) ).
fof(f1204,plain,
( ! [X0] :
( ~ empty(X0)
| function(sK4(powerset(X0))) )
| ~ spl17_24
| ~ spl17_136 ),
inference(resolution,[],[f1202,f298]) ).
fof(f3810,plain,
( spl17_282
| ~ spl17_64
| ~ spl17_125 ),
inference(avatar_split_clause,[],[f1081,f1071,f553,f3808]) ).
fof(f3808,plain,
( spl17_282
<=> ! [X2,X4,X0,X3,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK6(relation_dom(relation_rng_restriction(X2,X3)),X4,relation_rng_restriction(X1,X0))) = apply(relation_rng_restriction(X1,X0),sK6(relation_dom(relation_rng_restriction(X2,X3)),X4,relation_rng_restriction(X1,X0)))
| sP0(relation_dom(relation_rng_restriction(X2,X3)),X4,relation_rng_restriction(X1,X0))
| apply(X3,apply(X4,sK6(relation_dom(relation_rng_restriction(X2,X3)),X4,relation_rng_restriction(X1,X0)))) = apply(relation_rng_restriction(X2,X3),apply(X4,sK6(relation_dom(relation_rng_restriction(X2,X3)),X4,relation_rng_restriction(X1,X0))))
| ~ function(X3)
| ~ relation(X3)
| ~ function(relation_rng_restriction(X2,X3))
| ~ relation(relation_rng_restriction(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_282])]) ).
fof(f553,plain,
( spl17_64
<=> ! [X4,X0,X2] :
( apply(X2,X4) = apply(relation_rng_restriction(X0,X2),X4)
| ~ in(X4,relation_dom(relation_rng_restriction(X0,X2)))
| ~ function(X2)
| ~ relation(X2)
| ~ function(relation_rng_restriction(X0,X2))
| ~ relation(relation_rng_restriction(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_64])]) ).
fof(f1081,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK6(relation_dom(relation_rng_restriction(X2,X3)),X4,relation_rng_restriction(X1,X0))) = apply(relation_rng_restriction(X1,X0),sK6(relation_dom(relation_rng_restriction(X2,X3)),X4,relation_rng_restriction(X1,X0)))
| sP0(relation_dom(relation_rng_restriction(X2,X3)),X4,relation_rng_restriction(X1,X0))
| apply(X3,apply(X4,sK6(relation_dom(relation_rng_restriction(X2,X3)),X4,relation_rng_restriction(X1,X0)))) = apply(relation_rng_restriction(X2,X3),apply(X4,sK6(relation_dom(relation_rng_restriction(X2,X3)),X4,relation_rng_restriction(X1,X0))))
| ~ function(X3)
| ~ relation(X3)
| ~ function(relation_rng_restriction(X2,X3))
| ~ relation(relation_rng_restriction(X2,X3)) )
| ~ spl17_64
| ~ spl17_125 ),
inference(resolution,[],[f1072,f554]) ).
fof(f554,plain,
( ! [X2,X0,X4] :
( ~ in(X4,relation_dom(relation_rng_restriction(X0,X2)))
| apply(X2,X4) = apply(relation_rng_restriction(X0,X2),X4)
| ~ function(X2)
| ~ relation(X2)
| ~ function(relation_rng_restriction(X0,X2))
| ~ relation(relation_rng_restriction(X0,X2)) )
| ~ spl17_64 ),
inference(avatar_component_clause,[],[f553]) ).
fof(f3799,plain,
( spl17_281
| ~ spl17_64
| ~ spl17_123 ),
inference(avatar_split_clause,[],[f1060,f1051,f553,f3797]) ).
fof(f3797,plain,
( spl17_281
<=> ! [X2,X4,X0,X3,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK6(X2,relation_rng_restriction(X3,X4),relation_rng_restriction(X1,X0))) = apply(relation_rng_restriction(X1,X0),sK6(X2,relation_rng_restriction(X3,X4),relation_rng_restriction(X1,X0)))
| sP0(X2,relation_rng_restriction(X3,X4),relation_rng_restriction(X1,X0))
| apply(X4,sK6(X2,relation_rng_restriction(X3,X4),relation_rng_restriction(X1,X0))) = apply(relation_rng_restriction(X3,X4),sK6(X2,relation_rng_restriction(X3,X4),relation_rng_restriction(X1,X0)))
| ~ function(X4)
| ~ relation(X4)
| ~ function(relation_rng_restriction(X3,X4))
| ~ relation(relation_rng_restriction(X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_281])]) ).
fof(f1051,plain,
( spl17_123
<=> ! [X0,X3,X2,X1] :
( apply(X0,sK6(X1,X2,relation_rng_restriction(X3,X0))) = apply(relation_rng_restriction(X3,X0),sK6(X1,X2,relation_rng_restriction(X3,X0)))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X3,X0))
| ~ relation(relation_rng_restriction(X3,X0))
| in(sK6(X1,X2,relation_rng_restriction(X3,X0)),relation_dom(X2))
| sP0(X1,X2,relation_rng_restriction(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_123])]) ).
fof(f1060,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK6(X2,relation_rng_restriction(X3,X4),relation_rng_restriction(X1,X0))) = apply(relation_rng_restriction(X1,X0),sK6(X2,relation_rng_restriction(X3,X4),relation_rng_restriction(X1,X0)))
| sP0(X2,relation_rng_restriction(X3,X4),relation_rng_restriction(X1,X0))
| apply(X4,sK6(X2,relation_rng_restriction(X3,X4),relation_rng_restriction(X1,X0))) = apply(relation_rng_restriction(X3,X4),sK6(X2,relation_rng_restriction(X3,X4),relation_rng_restriction(X1,X0)))
| ~ function(X4)
| ~ relation(X4)
| ~ function(relation_rng_restriction(X3,X4))
| ~ relation(relation_rng_restriction(X3,X4)) )
| ~ spl17_64
| ~ spl17_123 ),
inference(resolution,[],[f1052,f554]) ).
fof(f1052,plain,
( ! [X2,X3,X0,X1] :
( in(sK6(X1,X2,relation_rng_restriction(X3,X0)),relation_dom(X2))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X3,X0))
| ~ relation(relation_rng_restriction(X3,X0))
| apply(X0,sK6(X1,X2,relation_rng_restriction(X3,X0))) = apply(relation_rng_restriction(X3,X0),sK6(X1,X2,relation_rng_restriction(X3,X0)))
| sP0(X1,X2,relation_rng_restriction(X3,X0)) )
| ~ spl17_123 ),
inference(avatar_component_clause,[],[f1051]) ).
fof(f3768,plain,
( spl17_280
| ~ spl17_119
| ~ spl17_126 ),
inference(avatar_split_clause,[],[f1093,f1090,f998,f3766]) ).
fof(f3766,plain,
( spl17_280
<=> ! [X2,X4,X0,X3,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,apply(X2,sK6(relation_dom(relation_rng_restriction(X1,X0)),X2,relation_rng_restriction(X3,X4)))) = apply(relation_rng_restriction(X1,X0),apply(X2,sK6(relation_dom(relation_rng_restriction(X1,X0)),X2,relation_rng_restriction(X3,X4))))
| sP0(relation_dom(relation_rng_restriction(X1,X0)),X2,relation_rng_restriction(X3,X4))
| ~ relation(X4)
| ~ function(relation_rng_restriction(X3,X4))
| ~ relation(relation_rng_restriction(X3,X4))
| ~ function(X4)
| in(apply(X4,sK6(relation_dom(relation_rng_restriction(X1,X0)),X2,relation_rng_restriction(X3,X4))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_280])]) ).
fof(f1090,plain,
( spl17_126
<=> ! [X0,X3,X2,X1] :
( apply(X0,apply(X1,sK6(relation_dom(relation_rng_restriction(X2,X0)),X1,X3))) = apply(relation_rng_restriction(X2,X0),apply(X1,sK6(relation_dom(relation_rng_restriction(X2,X0)),X1,X3)))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X2,X0))
| ~ relation(relation_rng_restriction(X2,X0))
| in(sK6(relation_dom(relation_rng_restriction(X2,X0)),X1,X3),relation_dom(X3))
| sP0(relation_dom(relation_rng_restriction(X2,X0)),X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_126])]) ).
fof(f1093,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,apply(X2,sK6(relation_dom(relation_rng_restriction(X1,X0)),X2,relation_rng_restriction(X3,X4)))) = apply(relation_rng_restriction(X1,X0),apply(X2,sK6(relation_dom(relation_rng_restriction(X1,X0)),X2,relation_rng_restriction(X3,X4))))
| sP0(relation_dom(relation_rng_restriction(X1,X0)),X2,relation_rng_restriction(X3,X4))
| ~ relation(X4)
| ~ function(relation_rng_restriction(X3,X4))
| ~ relation(relation_rng_restriction(X3,X4))
| ~ function(X4)
| in(apply(X4,sK6(relation_dom(relation_rng_restriction(X1,X0)),X2,relation_rng_restriction(X3,X4))),X3) )
| ~ spl17_119
| ~ spl17_126 ),
inference(resolution,[],[f1091,f999]) ).
fof(f1091,plain,
( ! [X2,X3,X0,X1] :
( in(sK6(relation_dom(relation_rng_restriction(X2,X0)),X1,X3),relation_dom(X3))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X2,X0))
| ~ relation(relation_rng_restriction(X2,X0))
| apply(X0,apply(X1,sK6(relation_dom(relation_rng_restriction(X2,X0)),X1,X3))) = apply(relation_rng_restriction(X2,X0),apply(X1,sK6(relation_dom(relation_rng_restriction(X2,X0)),X1,X3)))
| sP0(relation_dom(relation_rng_restriction(X2,X0)),X1,X3) )
| ~ spl17_126 ),
inference(avatar_component_clause,[],[f1090]) ).
fof(f3748,plain,
( spl17_279
| ~ spl17_96
| ~ spl17_268 ),
inference(avatar_split_clause,[],[f3613,f3556,f806,f3746]) ).
fof(f3746,plain,
( spl17_279
<=> ! [X0,X1] :
( ~ in(X0,relation_rng(relation_rng_restriction(X1,relation_rng_restriction(sK1,sK2))))
| element(X0,relation_rng(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_279])]) ).
fof(f806,plain,
( spl17_96
<=> ! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_96])]) ).
fof(f3613,plain,
( ! [X0,X1] :
( ~ in(X0,relation_rng(relation_rng_restriction(X1,relation_rng_restriction(sK1,sK2))))
| element(X0,relation_rng(sK2)) )
| ~ spl17_96
| ~ spl17_268 ),
inference(resolution,[],[f3557,f807]) ).
fof(f807,plain,
( ! [X2,X0,X1] :
( ~ subset(X2,X1)
| ~ in(X0,X2)
| element(X0,X1) )
| ~ spl17_96 ),
inference(avatar_component_clause,[],[f806]) ).
fof(f3744,plain,
( spl17_278
| ~ spl17_118
| ~ spl17_126 ),
inference(avatar_split_clause,[],[f1094,f1090,f979,f3742]) ).
fof(f3742,plain,
( spl17_278
<=> ! [X2,X4,X0,X3,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,apply(X2,sK6(relation_dom(relation_rng_restriction(X1,X0)),X2,relation_rng_restriction(X3,X4)))) = apply(relation_rng_restriction(X1,X0),apply(X2,sK6(relation_dom(relation_rng_restriction(X1,X0)),X2,relation_rng_restriction(X3,X4))))
| sP0(relation_dom(relation_rng_restriction(X1,X0)),X2,relation_rng_restriction(X3,X4))
| ~ relation(X4)
| ~ function(relation_rng_restriction(X3,X4))
| ~ relation(relation_rng_restriction(X3,X4))
| ~ function(X4)
| in(sK6(relation_dom(relation_rng_restriction(X1,X0)),X2,relation_rng_restriction(X3,X4)),relation_dom(X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_278])]) ).
fof(f1094,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,apply(X2,sK6(relation_dom(relation_rng_restriction(X1,X0)),X2,relation_rng_restriction(X3,X4)))) = apply(relation_rng_restriction(X1,X0),apply(X2,sK6(relation_dom(relation_rng_restriction(X1,X0)),X2,relation_rng_restriction(X3,X4))))
| sP0(relation_dom(relation_rng_restriction(X1,X0)),X2,relation_rng_restriction(X3,X4))
| ~ relation(X4)
| ~ function(relation_rng_restriction(X3,X4))
| ~ relation(relation_rng_restriction(X3,X4))
| ~ function(X4)
| in(sK6(relation_dom(relation_rng_restriction(X1,X0)),X2,relation_rng_restriction(X3,X4)),relation_dom(X4)) )
| ~ spl17_118
| ~ spl17_126 ),
inference(resolution,[],[f1091,f980]) ).
fof(f3715,plain,
( spl17_277
| ~ spl17_119
| ~ spl17_125 ),
inference(avatar_split_clause,[],[f1079,f1071,f998,f3713]) ).
fof(f3713,plain,
( spl17_277
<=> ! [X2,X4,X0,X3,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK6(relation_dom(relation_rng_restriction(X2,X3)),X4,relation_rng_restriction(X1,X0))) = apply(relation_rng_restriction(X1,X0),sK6(relation_dom(relation_rng_restriction(X2,X3)),X4,relation_rng_restriction(X1,X0)))
| sP0(relation_dom(relation_rng_restriction(X2,X3)),X4,relation_rng_restriction(X1,X0))
| ~ relation(X3)
| ~ function(relation_rng_restriction(X2,X3))
| ~ relation(relation_rng_restriction(X2,X3))
| ~ function(X3)
| in(apply(X3,apply(X4,sK6(relation_dom(relation_rng_restriction(X2,X3)),X4,relation_rng_restriction(X1,X0)))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_277])]) ).
fof(f1079,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK6(relation_dom(relation_rng_restriction(X2,X3)),X4,relation_rng_restriction(X1,X0))) = apply(relation_rng_restriction(X1,X0),sK6(relation_dom(relation_rng_restriction(X2,X3)),X4,relation_rng_restriction(X1,X0)))
| sP0(relation_dom(relation_rng_restriction(X2,X3)),X4,relation_rng_restriction(X1,X0))
| ~ relation(X3)
| ~ function(relation_rng_restriction(X2,X3))
| ~ relation(relation_rng_restriction(X2,X3))
| ~ function(X3)
| in(apply(X3,apply(X4,sK6(relation_dom(relation_rng_restriction(X2,X3)),X4,relation_rng_restriction(X1,X0)))),X2) )
| ~ spl17_119
| ~ spl17_125 ),
inference(resolution,[],[f1072,f999]) ).
fof(f3694,plain,
( spl17_276
| ~ spl17_118
| ~ spl17_125 ),
inference(avatar_split_clause,[],[f1080,f1071,f979,f3692]) ).
fof(f3692,plain,
( spl17_276
<=> ! [X2,X4,X0,X3,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK6(relation_dom(relation_rng_restriction(X2,X3)),X4,relation_rng_restriction(X1,X0))) = apply(relation_rng_restriction(X1,X0),sK6(relation_dom(relation_rng_restriction(X2,X3)),X4,relation_rng_restriction(X1,X0)))
| sP0(relation_dom(relation_rng_restriction(X2,X3)),X4,relation_rng_restriction(X1,X0))
| ~ relation(X3)
| ~ function(relation_rng_restriction(X2,X3))
| ~ relation(relation_rng_restriction(X2,X3))
| ~ function(X3)
| in(apply(X4,sK6(relation_dom(relation_rng_restriction(X2,X3)),X4,relation_rng_restriction(X1,X0))),relation_dom(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_276])]) ).
fof(f1080,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK6(relation_dom(relation_rng_restriction(X2,X3)),X4,relation_rng_restriction(X1,X0))) = apply(relation_rng_restriction(X1,X0),sK6(relation_dom(relation_rng_restriction(X2,X3)),X4,relation_rng_restriction(X1,X0)))
| sP0(relation_dom(relation_rng_restriction(X2,X3)),X4,relation_rng_restriction(X1,X0))
| ~ relation(X3)
| ~ function(relation_rng_restriction(X2,X3))
| ~ relation(relation_rng_restriction(X2,X3))
| ~ function(X3)
| in(apply(X4,sK6(relation_dom(relation_rng_restriction(X2,X3)),X4,relation_rng_restriction(X1,X0))),relation_dom(X3)) )
| ~ spl17_118
| ~ spl17_125 ),
inference(resolution,[],[f1072,f980]) ).
fof(f3638,plain,
( spl17_275
| ~ spl17_119
| ~ spl17_124 ),
inference(avatar_split_clause,[],[f1064,f1055,f998,f3636]) ).
fof(f3636,plain,
( spl17_275
<=> ! [X2,X4,X0,X3,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK6(X2,relation_rng_restriction(X1,X0),relation_rng_restriction(X3,X4))) = apply(relation_rng_restriction(X1,X0),sK6(X2,relation_rng_restriction(X1,X0),relation_rng_restriction(X3,X4)))
| sP0(X2,relation_rng_restriction(X1,X0),relation_rng_restriction(X3,X4))
| ~ relation(X4)
| ~ function(relation_rng_restriction(X3,X4))
| ~ relation(relation_rng_restriction(X3,X4))
| ~ function(X4)
| in(apply(X4,sK6(X2,relation_rng_restriction(X1,X0),relation_rng_restriction(X3,X4))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_275])]) ).
fof(f1055,plain,
( spl17_124
<=> ! [X0,X3,X2,X1] :
( apply(X0,sK6(X1,relation_rng_restriction(X2,X0),X3)) = apply(relation_rng_restriction(X2,X0),sK6(X1,relation_rng_restriction(X2,X0),X3))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X2,X0))
| ~ relation(relation_rng_restriction(X2,X0))
| in(sK6(X1,relation_rng_restriction(X2,X0),X3),relation_dom(X3))
| sP0(X1,relation_rng_restriction(X2,X0),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_124])]) ).
fof(f1064,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK6(X2,relation_rng_restriction(X1,X0),relation_rng_restriction(X3,X4))) = apply(relation_rng_restriction(X1,X0),sK6(X2,relation_rng_restriction(X1,X0),relation_rng_restriction(X3,X4)))
| sP0(X2,relation_rng_restriction(X1,X0),relation_rng_restriction(X3,X4))
| ~ relation(X4)
| ~ function(relation_rng_restriction(X3,X4))
| ~ relation(relation_rng_restriction(X3,X4))
| ~ function(X4)
| in(apply(X4,sK6(X2,relation_rng_restriction(X1,X0),relation_rng_restriction(X3,X4))),X3) )
| ~ spl17_119
| ~ spl17_124 ),
inference(resolution,[],[f1056,f999]) ).
fof(f1056,plain,
( ! [X2,X3,X0,X1] :
( in(sK6(X1,relation_rng_restriction(X2,X0),X3),relation_dom(X3))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X2,X0))
| ~ relation(relation_rng_restriction(X2,X0))
| apply(X0,sK6(X1,relation_rng_restriction(X2,X0),X3)) = apply(relation_rng_restriction(X2,X0),sK6(X1,relation_rng_restriction(X2,X0),X3))
| sP0(X1,relation_rng_restriction(X2,X0),X3) )
| ~ spl17_124 ),
inference(avatar_component_clause,[],[f1055]) ).
fof(f3634,plain,
( spl17_274
| ~ spl17_119
| ~ spl17_123 ),
inference(avatar_split_clause,[],[f1058,f1051,f998,f3632]) ).
fof(f3632,plain,
( spl17_274
<=> ! [X2,X4,X0,X3,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK6(X2,relation_rng_restriction(X3,X4),relation_rng_restriction(X1,X0))) = apply(relation_rng_restriction(X1,X0),sK6(X2,relation_rng_restriction(X3,X4),relation_rng_restriction(X1,X0)))
| sP0(X2,relation_rng_restriction(X3,X4),relation_rng_restriction(X1,X0))
| ~ relation(X4)
| ~ function(relation_rng_restriction(X3,X4))
| ~ relation(relation_rng_restriction(X3,X4))
| ~ function(X4)
| in(apply(X4,sK6(X2,relation_rng_restriction(X3,X4),relation_rng_restriction(X1,X0))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_274])]) ).
fof(f1058,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK6(X2,relation_rng_restriction(X3,X4),relation_rng_restriction(X1,X0))) = apply(relation_rng_restriction(X1,X0),sK6(X2,relation_rng_restriction(X3,X4),relation_rng_restriction(X1,X0)))
| sP0(X2,relation_rng_restriction(X3,X4),relation_rng_restriction(X1,X0))
| ~ relation(X4)
| ~ function(relation_rng_restriction(X3,X4))
| ~ relation(relation_rng_restriction(X3,X4))
| ~ function(X4)
| in(apply(X4,sK6(X2,relation_rng_restriction(X3,X4),relation_rng_restriction(X1,X0))),X3) )
| ~ spl17_119
| ~ spl17_123 ),
inference(resolution,[],[f1052,f999]) ).
fof(f3595,plain,
( spl17_273
| ~ spl17_118
| ~ spl17_124 ),
inference(avatar_split_clause,[],[f1065,f1055,f979,f3593]) ).
fof(f3593,plain,
( spl17_273
<=> ! [X2,X4,X0,X3,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK6(X2,relation_rng_restriction(X1,X0),relation_rng_restriction(X3,X4))) = apply(relation_rng_restriction(X1,X0),sK6(X2,relation_rng_restriction(X1,X0),relation_rng_restriction(X3,X4)))
| sP0(X2,relation_rng_restriction(X1,X0),relation_rng_restriction(X3,X4))
| ~ relation(X4)
| ~ function(relation_rng_restriction(X3,X4))
| ~ relation(relation_rng_restriction(X3,X4))
| ~ function(X4)
| in(sK6(X2,relation_rng_restriction(X1,X0),relation_rng_restriction(X3,X4)),relation_dom(X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_273])]) ).
fof(f1065,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK6(X2,relation_rng_restriction(X1,X0),relation_rng_restriction(X3,X4))) = apply(relation_rng_restriction(X1,X0),sK6(X2,relation_rng_restriction(X1,X0),relation_rng_restriction(X3,X4)))
| sP0(X2,relation_rng_restriction(X1,X0),relation_rng_restriction(X3,X4))
| ~ relation(X4)
| ~ function(relation_rng_restriction(X3,X4))
| ~ relation(relation_rng_restriction(X3,X4))
| ~ function(X4)
| in(sK6(X2,relation_rng_restriction(X1,X0),relation_rng_restriction(X3,X4)),relation_dom(X4)) )
| ~ spl17_118
| ~ spl17_124 ),
inference(resolution,[],[f1056,f980]) ).
fof(f3591,plain,
( spl17_272
| ~ spl17_118
| ~ spl17_123 ),
inference(avatar_split_clause,[],[f1059,f1051,f979,f3589]) ).
fof(f3589,plain,
( spl17_272
<=> ! [X2,X4,X0,X3,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK6(X2,relation_rng_restriction(X3,X4),relation_rng_restriction(X1,X0))) = apply(relation_rng_restriction(X1,X0),sK6(X2,relation_rng_restriction(X3,X4),relation_rng_restriction(X1,X0)))
| sP0(X2,relation_rng_restriction(X3,X4),relation_rng_restriction(X1,X0))
| ~ relation(X4)
| ~ function(relation_rng_restriction(X3,X4))
| ~ relation(relation_rng_restriction(X3,X4))
| ~ function(X4)
| in(sK6(X2,relation_rng_restriction(X3,X4),relation_rng_restriction(X1,X0)),relation_dom(X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_272])]) ).
fof(f1059,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK6(X2,relation_rng_restriction(X3,X4),relation_rng_restriction(X1,X0))) = apply(relation_rng_restriction(X1,X0),sK6(X2,relation_rng_restriction(X3,X4),relation_rng_restriction(X1,X0)))
| sP0(X2,relation_rng_restriction(X3,X4),relation_rng_restriction(X1,X0))
| ~ relation(X4)
| ~ function(relation_rng_restriction(X3,X4))
| ~ relation(relation_rng_restriction(X3,X4))
| ~ function(X4)
| in(sK6(X2,relation_rng_restriction(X3,X4),relation_rng_restriction(X1,X0)),relation_dom(X4)) )
| ~ spl17_118
| ~ spl17_123 ),
inference(resolution,[],[f1052,f980]) ).
fof(f3577,plain,
( spl17_271
| ~ spl17_102
| ~ spl17_125 ),
inference(avatar_split_clause,[],[f1083,f1071,f854,f3575]) ).
fof(f3575,plain,
( spl17_271
<=> ! [X2,X4,X0,X3,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK6(relation_rng(relation_rng_restriction(X2,X3)),X4,relation_rng_restriction(X1,X0))) = apply(relation_rng_restriction(X1,X0),sK6(relation_rng(relation_rng_restriction(X2,X3)),X4,relation_rng_restriction(X1,X0)))
| sP0(relation_rng(relation_rng_restriction(X2,X3)),X4,relation_rng_restriction(X1,X0))
| in(apply(X4,sK6(relation_rng(relation_rng_restriction(X2,X3)),X4,relation_rng_restriction(X1,X0))),relation_rng(X3))
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_271])]) ).
fof(f854,plain,
( spl17_102
<=> ! [X2,X0,X1] :
( ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| in(X0,relation_rng(X2))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_102])]) ).
fof(f1083,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK6(relation_rng(relation_rng_restriction(X2,X3)),X4,relation_rng_restriction(X1,X0))) = apply(relation_rng_restriction(X1,X0),sK6(relation_rng(relation_rng_restriction(X2,X3)),X4,relation_rng_restriction(X1,X0)))
| sP0(relation_rng(relation_rng_restriction(X2,X3)),X4,relation_rng_restriction(X1,X0))
| in(apply(X4,sK6(relation_rng(relation_rng_restriction(X2,X3)),X4,relation_rng_restriction(X1,X0))),relation_rng(X3))
| ~ relation(X3) )
| ~ spl17_102
| ~ spl17_125 ),
inference(resolution,[],[f1072,f855]) ).
fof(f855,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| in(X0,relation_rng(X2))
| ~ relation(X2) )
| ~ spl17_102 ),
inference(avatar_component_clause,[],[f854]) ).
fof(f3569,plain,
( spl17_270
| ~ spl17_95
| ~ spl17_125 ),
inference(avatar_split_clause,[],[f1085,f1071,f756,f3567]) ).
fof(f3567,plain,
( spl17_270
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK6(sK4(powerset(X2)),X3,relation_rng_restriction(X1,X0))) = apply(relation_rng_restriction(X1,X0),sK6(sK4(powerset(X2)),X3,relation_rng_restriction(X1,X0)))
| sP0(sK4(powerset(X2)),X3,relation_rng_restriction(X1,X0))
| element(apply(X3,sK6(sK4(powerset(X2)),X3,relation_rng_restriction(X1,X0))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_270])]) ).
fof(f756,plain,
( spl17_95
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK4(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_95])]) ).
fof(f1085,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK6(sK4(powerset(X2)),X3,relation_rng_restriction(X1,X0))) = apply(relation_rng_restriction(X1,X0),sK6(sK4(powerset(X2)),X3,relation_rng_restriction(X1,X0)))
| sP0(sK4(powerset(X2)),X3,relation_rng_restriction(X1,X0))
| element(apply(X3,sK6(sK4(powerset(X2)),X3,relation_rng_restriction(X1,X0))),X2) )
| ~ spl17_95
| ~ spl17_125 ),
inference(resolution,[],[f1072,f757]) ).
fof(f757,plain,
( ! [X0,X1] :
( ~ in(X0,sK4(powerset(X1)))
| element(X0,X1) )
| ~ spl17_95 ),
inference(avatar_component_clause,[],[f756]) ).
fof(f3562,plain,
( spl17_269
| ~ spl17_38
| ~ spl17_126 ),
inference(avatar_split_clause,[],[f1097,f1090,f380,f3560]) ).
fof(f3560,plain,
( spl17_269
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,apply(X2,sK6(relation_dom(relation_rng_restriction(X1,X0)),X2,X3))) = apply(relation_rng_restriction(X1,X0),apply(X2,sK6(relation_dom(relation_rng_restriction(X1,X0)),X2,X3)))
| sP0(relation_dom(relation_rng_restriction(X1,X0)),X2,X3)
| ~ in(relation_dom(X3),sK6(relation_dom(relation_rng_restriction(X1,X0)),X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_269])]) ).
fof(f1097,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,apply(X2,sK6(relation_dom(relation_rng_restriction(X1,X0)),X2,X3))) = apply(relation_rng_restriction(X1,X0),apply(X2,sK6(relation_dom(relation_rng_restriction(X1,X0)),X2,X3)))
| sP0(relation_dom(relation_rng_restriction(X1,X0)),X2,X3)
| ~ in(relation_dom(X3),sK6(relation_dom(relation_rng_restriction(X1,X0)),X2,X3)) )
| ~ spl17_38
| ~ spl17_126 ),
inference(resolution,[],[f1091,f381]) ).
fof(f3558,plain,
( spl17_268
| ~ spl17_51
| ~ spl17_257 ),
inference(avatar_split_clause,[],[f3520,f3475,f453,f3556]) ).
fof(f3520,plain,
( ! [X0] : subset(relation_rng(relation_rng_restriction(X0,relation_rng_restriction(sK1,sK2))),relation_rng(sK2))
| ~ spl17_51
| ~ spl17_257 ),
inference(duplicate_literal_removal,[],[f3516]) ).
fof(f3516,plain,
( ! [X0] :
( subset(relation_rng(relation_rng_restriction(X0,relation_rng_restriction(sK1,sK2))),relation_rng(sK2))
| subset(relation_rng(relation_rng_restriction(X0,relation_rng_restriction(sK1,sK2))),relation_rng(sK2)) )
| ~ spl17_51
| ~ spl17_257 ),
inference(resolution,[],[f3476,f454]) ).
fof(f3554,plain,
( spl17_267
| ~ spl17_64
| ~ spl17_116 ),
inference(avatar_split_clause,[],[f969,f948,f553,f3552]) ).
fof(f3552,plain,
( spl17_267
<=> ! [X0,X3,X2,X1] :
( element(sK6(relation_dom(relation_rng_restriction(X1,X2)),X0,X3),relation_dom(X3))
| sP0(relation_dom(relation_rng_restriction(X1,X2)),X0,X3)
| apply(X2,apply(X0,sK6(relation_dom(relation_rng_restriction(X1,X2)),X0,X3))) = apply(relation_rng_restriction(X1,X2),apply(X0,sK6(relation_dom(relation_rng_restriction(X1,X2)),X0,X3)))
| ~ function(X2)
| ~ relation(X2)
| ~ function(relation_rng_restriction(X1,X2))
| ~ relation(relation_rng_restriction(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_267])]) ).
fof(f969,plain,
( ! [X2,X3,X0,X1] :
( element(sK6(relation_dom(relation_rng_restriction(X1,X2)),X0,X3),relation_dom(X3))
| sP0(relation_dom(relation_rng_restriction(X1,X2)),X0,X3)
| apply(X2,apply(X0,sK6(relation_dom(relation_rng_restriction(X1,X2)),X0,X3))) = apply(relation_rng_restriction(X1,X2),apply(X0,sK6(relation_dom(relation_rng_restriction(X1,X2)),X0,X3)))
| ~ function(X2)
| ~ relation(X2)
| ~ function(relation_rng_restriction(X1,X2))
| ~ relation(relation_rng_restriction(X1,X2)) )
| ~ spl17_64
| ~ spl17_116 ),
inference(resolution,[],[f949,f554]) ).
fof(f3545,plain,
( spl17_266
| ~ spl17_97
| ~ spl17_125 ),
inference(avatar_split_clause,[],[f1084,f1071,f810,f3543]) ).
fof(f3543,plain,
( spl17_266
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK6(sK3(X2),X3,relation_rng_restriction(X1,X0))) = apply(relation_rng_restriction(X1,X0),sK6(sK3(X2),X3,relation_rng_restriction(X1,X0)))
| sP0(sK3(X2),X3,relation_rng_restriction(X1,X0))
| element(apply(X3,sK6(sK3(X2),X3,relation_rng_restriction(X1,X0))),X2)
| empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_266])]) ).
fof(f810,plain,
( spl17_97
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK3(X1))
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_97])]) ).
fof(f1084,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK6(sK3(X2),X3,relation_rng_restriction(X1,X0))) = apply(relation_rng_restriction(X1,X0),sK6(sK3(X2),X3,relation_rng_restriction(X1,X0)))
| sP0(sK3(X2),X3,relation_rng_restriction(X1,X0))
| element(apply(X3,sK6(sK3(X2),X3,relation_rng_restriction(X1,X0))),X2)
| empty(X2) )
| ~ spl17_97
| ~ spl17_125 ),
inference(resolution,[],[f1072,f811]) ).
fof(f811,plain,
( ! [X0,X1] :
( ~ in(X0,sK3(X1))
| element(X0,X1)
| empty(X1) )
| ~ spl17_97 ),
inference(avatar_component_clause,[],[f810]) ).
fof(f3533,plain,
( spl17_265
| ~ spl17_38
| ~ spl17_125 ),
inference(avatar_split_clause,[],[f1076,f1071,f380,f3531]) ).
fof(f3531,plain,
( spl17_265
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK6(X2,X3,relation_rng_restriction(X1,X0))) = apply(relation_rng_restriction(X1,X0),sK6(X2,X3,relation_rng_restriction(X1,X0)))
| sP0(X2,X3,relation_rng_restriction(X1,X0))
| ~ in(X2,apply(X3,sK6(X2,X3,relation_rng_restriction(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_265])]) ).
fof(f1076,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK6(X2,X3,relation_rng_restriction(X1,X0))) = apply(relation_rng_restriction(X1,X0),sK6(X2,X3,relation_rng_restriction(X1,X0)))
| sP0(X2,X3,relation_rng_restriction(X1,X0))
| ~ in(X2,apply(X3,sK6(X2,X3,relation_rng_restriction(X1,X0)))) )
| ~ spl17_38
| ~ spl17_125 ),
inference(resolution,[],[f1072,f381]) ).
fof(f3529,plain,
( spl17_264
| ~ spl17_64
| ~ spl17_114 ),
inference(avatar_split_clause,[],[f960,f940,f553,f3527]) ).
fof(f3527,plain,
( spl17_264
<=> ! [X0,X3,X2,X1] :
( element(apply(X1,sK6(X0,X1,relation_rng_restriction(X2,X3))),X0)
| sP0(X0,X1,relation_rng_restriction(X2,X3))
| apply(X3,sK6(X0,X1,relation_rng_restriction(X2,X3))) = apply(relation_rng_restriction(X2,X3),sK6(X0,X1,relation_rng_restriction(X2,X3)))
| ~ function(X3)
| ~ relation(X3)
| ~ function(relation_rng_restriction(X2,X3))
| ~ relation(relation_rng_restriction(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_264])]) ).
fof(f940,plain,
( spl17_114
<=> ! [X2,X0,X1] :
( in(sK6(X1,X0,X2),relation_dom(X2))
| sP0(X1,X0,X2)
| element(apply(X0,sK6(X1,X0,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_114])]) ).
fof(f960,plain,
( ! [X2,X3,X0,X1] :
( element(apply(X1,sK6(X0,X1,relation_rng_restriction(X2,X3))),X0)
| sP0(X0,X1,relation_rng_restriction(X2,X3))
| apply(X3,sK6(X0,X1,relation_rng_restriction(X2,X3))) = apply(relation_rng_restriction(X2,X3),sK6(X0,X1,relation_rng_restriction(X2,X3)))
| ~ function(X3)
| ~ relation(X3)
| ~ function(relation_rng_restriction(X2,X3))
| ~ relation(relation_rng_restriction(X2,X3)) )
| ~ spl17_64
| ~ spl17_114 ),
inference(resolution,[],[f941,f554]) ).
fof(f941,plain,
( ! [X2,X0,X1] :
( element(apply(X0,sK6(X1,X0,X2)),X1)
| in(sK6(X1,X0,X2),relation_dom(X2))
| sP0(X1,X0,X2) )
| ~ spl17_114 ),
inference(avatar_component_clause,[],[f940]) ).
fof(f3525,plain,
( spl17_263
| ~ spl17_64
| ~ spl17_107 ),
inference(avatar_split_clause,[],[f897,f889,f553,f3523]) ).
fof(f3523,plain,
( spl17_263
<=> ! [X0,X3,X2,X1] :
( sP0(relation_dom(relation_rng_restriction(X0,X1)),X2,X3)
| ~ empty(relation_dom(X3))
| apply(X1,apply(X2,sK6(relation_dom(relation_rng_restriction(X0,X1)),X2,X3))) = apply(relation_rng_restriction(X0,X1),apply(X2,sK6(relation_dom(relation_rng_restriction(X0,X1)),X2,X3)))
| ~ function(X1)
| ~ relation(X1)
| ~ function(relation_rng_restriction(X0,X1))
| ~ relation(relation_rng_restriction(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_263])]) ).
fof(f897,plain,
( ! [X2,X3,X0,X1] :
( sP0(relation_dom(relation_rng_restriction(X0,X1)),X2,X3)
| ~ empty(relation_dom(X3))
| apply(X1,apply(X2,sK6(relation_dom(relation_rng_restriction(X0,X1)),X2,X3))) = apply(relation_rng_restriction(X0,X1),apply(X2,sK6(relation_dom(relation_rng_restriction(X0,X1)),X2,X3)))
| ~ function(X1)
| ~ relation(X1)
| ~ function(relation_rng_restriction(X0,X1))
| ~ relation(relation_rng_restriction(X0,X1)) )
| ~ spl17_64
| ~ spl17_107 ),
inference(resolution,[],[f890,f554]) ).
fof(f3510,plain,
( spl17_262
| ~ spl17_38
| ~ spl17_124 ),
inference(avatar_split_clause,[],[f1068,f1055,f380,f3508]) ).
fof(f3508,plain,
( spl17_262
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK6(X2,relation_rng_restriction(X1,X0),X3)) = apply(relation_rng_restriction(X1,X0),sK6(X2,relation_rng_restriction(X1,X0),X3))
| sP0(X2,relation_rng_restriction(X1,X0),X3)
| ~ in(relation_dom(X3),sK6(X2,relation_rng_restriction(X1,X0),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_262])]) ).
fof(f1068,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK6(X2,relation_rng_restriction(X1,X0),X3)) = apply(relation_rng_restriction(X1,X0),sK6(X2,relation_rng_restriction(X1,X0),X3))
| sP0(X2,relation_rng_restriction(X1,X0),X3)
| ~ in(relation_dom(X3),sK6(X2,relation_rng_restriction(X1,X0),X3)) )
| ~ spl17_38
| ~ spl17_124 ),
inference(resolution,[],[f1056,f381]) ).
fof(f3506,plain,
( spl17_261
| ~ spl17_38
| ~ spl17_123 ),
inference(avatar_split_clause,[],[f1062,f1051,f380,f3504]) ).
fof(f3504,plain,
( spl17_261
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK6(X2,X3,relation_rng_restriction(X1,X0))) = apply(relation_rng_restriction(X1,X0),sK6(X2,X3,relation_rng_restriction(X1,X0)))
| sP0(X2,X3,relation_rng_restriction(X1,X0))
| ~ in(relation_dom(X3),sK6(X2,X3,relation_rng_restriction(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_261])]) ).
fof(f1062,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK6(X2,X3,relation_rng_restriction(X1,X0))) = apply(relation_rng_restriction(X1,X0),sK6(X2,X3,relation_rng_restriction(X1,X0)))
| sP0(X2,X3,relation_rng_restriction(X1,X0))
| ~ in(relation_dom(X3),sK6(X2,X3,relation_rng_restriction(X1,X0))) )
| ~ spl17_38
| ~ spl17_123 ),
inference(resolution,[],[f1052,f381]) ).
fof(f3502,plain,
( spl17_260
| ~ spl17_64
| ~ spl17_112 ),
inference(avatar_split_clause,[],[f935,f922,f553,f3500]) ).
fof(f3500,plain,
( spl17_260
<=> ! [X0,X3,X2,X1] :
( element(sK6(X0,X1,relation_rng_restriction(X2,X3)),relation_dom(X1))
| sP0(X0,X1,relation_rng_restriction(X2,X3))
| apply(X3,sK6(X0,X1,relation_rng_restriction(X2,X3))) = apply(relation_rng_restriction(X2,X3),sK6(X0,X1,relation_rng_restriction(X2,X3)))
| ~ function(X3)
| ~ relation(X3)
| ~ function(relation_rng_restriction(X2,X3))
| ~ relation(relation_rng_restriction(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_260])]) ).
fof(f935,plain,
( ! [X2,X3,X0,X1] :
( element(sK6(X0,X1,relation_rng_restriction(X2,X3)),relation_dom(X1))
| sP0(X0,X1,relation_rng_restriction(X2,X3))
| apply(X3,sK6(X0,X1,relation_rng_restriction(X2,X3))) = apply(relation_rng_restriction(X2,X3),sK6(X0,X1,relation_rng_restriction(X2,X3)))
| ~ function(X3)
| ~ relation(X3)
| ~ function(relation_rng_restriction(X2,X3))
| ~ relation(relation_rng_restriction(X2,X3)) )
| ~ spl17_64
| ~ spl17_112 ),
inference(resolution,[],[f923,f554]) ).
fof(f3498,plain,
( spl17_259
| ~ spl17_64
| ~ spl17_108 ),
inference(avatar_split_clause,[],[f930,f906,f553,f3496]) ).
fof(f3496,plain,
( spl17_259
<=> ! [X0,X3,X2,X1] :
( element(sK6(X0,relation_rng_restriction(X1,X2),X3),relation_dom(X3))
| sP0(X0,relation_rng_restriction(X1,X2),X3)
| apply(X2,sK6(X0,relation_rng_restriction(X1,X2),X3)) = apply(relation_rng_restriction(X1,X2),sK6(X0,relation_rng_restriction(X1,X2),X3))
| ~ function(X2)
| ~ relation(X2)
| ~ function(relation_rng_restriction(X1,X2))
| ~ relation(relation_rng_restriction(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_259])]) ).
fof(f930,plain,
( ! [X2,X3,X0,X1] :
( element(sK6(X0,relation_rng_restriction(X1,X2),X3),relation_dom(X3))
| sP0(X0,relation_rng_restriction(X1,X2),X3)
| apply(X2,sK6(X0,relation_rng_restriction(X1,X2),X3)) = apply(relation_rng_restriction(X1,X2),sK6(X0,relation_rng_restriction(X1,X2),X3))
| ~ function(X2)
| ~ relation(X2)
| ~ function(relation_rng_restriction(X1,X2))
| ~ relation(relation_rng_restriction(X1,X2)) )
| ~ spl17_64
| ~ spl17_108 ),
inference(resolution,[],[f907,f554]) ).
fof(f3488,plain,
( spl17_258
| ~ spl17_89
| ~ spl17_125 ),
inference(avatar_split_clause,[],[f1086,f1071,f725,f3486]) ).
fof(f3486,plain,
( spl17_258
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK6(sK4(powerset(X2)),X3,relation_rng_restriction(X1,X0))) = apply(relation_rng_restriction(X1,X0),sK6(sK4(powerset(X2)),X3,relation_rng_restriction(X1,X0)))
| sP0(sK4(powerset(X2)),X3,relation_rng_restriction(X1,X0))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_258])]) ).
fof(f725,plain,
( spl17_89
<=> ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK4(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_89])]) ).
fof(f1086,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK6(sK4(powerset(X2)),X3,relation_rng_restriction(X1,X0))) = apply(relation_rng_restriction(X1,X0),sK6(sK4(powerset(X2)),X3,relation_rng_restriction(X1,X0)))
| sP0(sK4(powerset(X2)),X3,relation_rng_restriction(X1,X0))
| ~ empty(X2) )
| ~ spl17_89
| ~ spl17_125 ),
inference(resolution,[],[f1072,f726]) ).
fof(f726,plain,
( ! [X0,X1] :
( ~ in(X1,sK4(powerset(X0)))
| ~ empty(X0) )
| ~ spl17_89 ),
inference(avatar_component_clause,[],[f725]) ).
fof(f3477,plain,
( spl17_109
| spl17_257
| ~ spl17_47
| ~ spl17_246 ),
inference(avatar_split_clause,[],[f3272,f3082,f436,f3475,f910]) ).
fof(f3082,plain,
( spl17_246
<=> ! [X0,X1] :
( subset(relation_rng(relation_rng_restriction(X0,relation_rng_restriction(sK1,sK2))),X1)
| element(sK8(relation_rng(relation_rng_restriction(X0,relation_rng_restriction(sK1,sK2))),X1),relation_rng(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_246])]) ).
fof(f3272,plain,
( ! [X0,X1] :
( subset(relation_rng(relation_rng_restriction(X0,relation_rng_restriction(sK1,sK2))),X1)
| empty(relation_rng(sK2))
| in(sK8(relation_rng(relation_rng_restriction(X0,relation_rng_restriction(sK1,sK2))),X1),relation_rng(sK2)) )
| ~ spl17_47
| ~ spl17_246 ),
inference(resolution,[],[f3083,f437]) ).
fof(f3083,plain,
( ! [X0,X1] :
( element(sK8(relation_rng(relation_rng_restriction(X0,relation_rng_restriction(sK1,sK2))),X1),relation_rng(sK2))
| subset(relation_rng(relation_rng_restriction(X0,relation_rng_restriction(sK1,sK2))),X1) )
| ~ spl17_246 ),
inference(avatar_component_clause,[],[f3082]) ).
fof(f3473,plain,
( spl17_256
| ~ spl17_64
| ~ spl17_101 ),
inference(avatar_split_clause,[],[f849,f846,f553,f3471]) ).
fof(f3471,plain,
( spl17_256
<=> ! [X2,X0,X1] :
( sP0(X0,relation_rng_restriction(X1,X2),relation_rng_restriction(X1,X2))
| apply(X2,sK6(X0,relation_rng_restriction(X1,X2),relation_rng_restriction(X1,X2))) = apply(relation_rng_restriction(X1,X2),sK6(X0,relation_rng_restriction(X1,X2),relation_rng_restriction(X1,X2)))
| ~ function(X2)
| ~ relation(X2)
| ~ function(relation_rng_restriction(X1,X2))
| ~ relation(relation_rng_restriction(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_256])]) ).
fof(f849,plain,
( ! [X2,X0,X1] :
( sP0(X0,relation_rng_restriction(X1,X2),relation_rng_restriction(X1,X2))
| apply(X2,sK6(X0,relation_rng_restriction(X1,X2),relation_rng_restriction(X1,X2))) = apply(relation_rng_restriction(X1,X2),sK6(X0,relation_rng_restriction(X1,X2),relation_rng_restriction(X1,X2)))
| ~ function(X2)
| ~ relation(X2)
| ~ function(relation_rng_restriction(X1,X2))
| ~ relation(relation_rng_restriction(X1,X2)) )
| ~ spl17_64
| ~ spl17_101 ),
inference(resolution,[],[f847,f554]) ).
fof(f3407,plain,
( spl17_255
| ~ spl17_61
| ~ spl17_119 ),
inference(avatar_split_clause,[],[f1003,f998,f530,f3405]) ).
fof(f1003,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(apply(X0,apply(X2,sK6(relation_dom(relation_rng_restriction(X1,X0)),X2,X3))),X1)
| in(sK6(relation_dom(relation_rng_restriction(X1,X0)),X2,X3),relation_dom(X3))
| sP0(relation_dom(relation_rng_restriction(X1,X0)),X2,X3) )
| ~ spl17_61
| ~ spl17_119 ),
inference(resolution,[],[f999,f531]) ).
fof(f3403,plain,
( spl17_254
| ~ spl17_116
| ~ spl17_119 ),
inference(avatar_split_clause,[],[f1001,f998,f948,f3401]) ).
fof(f1001,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(apply(X0,apply(X2,sK6(relation_dom(relation_rng_restriction(X1,X0)),X2,X3))),X1)
| element(sK6(relation_dom(relation_rng_restriction(X1,X0)),X2,X3),relation_dom(X3))
| sP0(relation_dom(relation_rng_restriction(X1,X0)),X2,X3) )
| ~ spl17_116
| ~ spl17_119 ),
inference(resolution,[],[f999,f949]) ).
fof(f3353,plain,
( spl17_253
| ~ spl17_61
| ~ spl17_118 ),
inference(avatar_split_clause,[],[f984,f979,f530,f3351]) ).
fof(f3351,plain,
( spl17_253
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(apply(X2,sK6(relation_dom(relation_rng_restriction(X1,X0)),X2,X3)),relation_dom(X0))
| in(sK6(relation_dom(relation_rng_restriction(X1,X0)),X2,X3),relation_dom(X3))
| sP0(relation_dom(relation_rng_restriction(X1,X0)),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_253])]) ).
fof(f984,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(apply(X2,sK6(relation_dom(relation_rng_restriction(X1,X0)),X2,X3)),relation_dom(X0))
| in(sK6(relation_dom(relation_rng_restriction(X1,X0)),X2,X3),relation_dom(X3))
| sP0(relation_dom(relation_rng_restriction(X1,X0)),X2,X3) )
| ~ spl17_61
| ~ spl17_118 ),
inference(resolution,[],[f980,f531]) ).
fof(f3349,plain,
( spl17_252
| ~ spl17_116
| ~ spl17_118 ),
inference(avatar_split_clause,[],[f982,f979,f948,f3347]) ).
fof(f3347,plain,
( spl17_252
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(apply(X2,sK6(relation_dom(relation_rng_restriction(X1,X0)),X2,X3)),relation_dom(X0))
| element(sK6(relation_dom(relation_rng_restriction(X1,X0)),X2,X3),relation_dom(X3))
| sP0(relation_dom(relation_rng_restriction(X1,X0)),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_252])]) ).
fof(f982,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(apply(X2,sK6(relation_dom(relation_rng_restriction(X1,X0)),X2,X3)),relation_dom(X0))
| element(sK6(relation_dom(relation_rng_restriction(X1,X0)),X2,X3),relation_dom(X3))
| sP0(relation_dom(relation_rng_restriction(X1,X0)),X2,X3) )
| ~ spl17_116
| ~ spl17_118 ),
inference(resolution,[],[f980,f949]) ).
fof(f3184,plain,
( spl17_251
| ~ spl17_53
| ~ spl17_122 ),
inference(avatar_split_clause,[],[f1049,f1043,f472,f3182]) ).
fof(f1043,plain,
( spl17_122
<=> ! [X2,X0,X1] :
( apply(X0,sK8(relation_dom(relation_rng_restriction(X1,X0)),X2)) = apply(relation_rng_restriction(X1,X0),sK8(relation_dom(relation_rng_restriction(X1,X0)),X2))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| subset(relation_dom(relation_rng_restriction(X1,X0)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_122])]) ).
fof(f1049,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK8(relation_dom(relation_rng_restriction(X1,X0)),X2)) = apply(relation_rng_restriction(X1,X0),sK8(relation_dom(relation_rng_restriction(X1,X0)),X2))
| ~ in(X3,relation_dom(relation_rng_restriction(X1,X0)))
| in(X3,X2) )
| ~ spl17_53
| ~ spl17_122 ),
inference(resolution,[],[f1044,f473]) ).
fof(f1044,plain,
( ! [X2,X0,X1] :
( subset(relation_dom(relation_rng_restriction(X1,X0)),X2)
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK8(relation_dom(relation_rng_restriction(X1,X0)),X2)) = apply(relation_rng_restriction(X1,X0),sK8(relation_dom(relation_rng_restriction(X1,X0)),X2)) )
| ~ spl17_122 ),
inference(avatar_component_clause,[],[f1043]) ).
fof(f3180,plain,
( spl17_250
| ~ spl17_96
| ~ spl17_122 ),
inference(avatar_split_clause,[],[f1047,f1043,f806,f3178]) ).
fof(f1047,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK8(relation_dom(relation_rng_restriction(X1,X0)),X2)) = apply(relation_rng_restriction(X1,X0),sK8(relation_dom(relation_rng_restriction(X1,X0)),X2))
| ~ in(X3,relation_dom(relation_rng_restriction(X1,X0)))
| element(X3,X2) )
| ~ spl17_96
| ~ spl17_122 ),
inference(resolution,[],[f1044,f807]) ).
fof(f3176,plain,
( spl17_249
| ~ spl17_64
| ~ spl17_106 ),
inference(avatar_split_clause,[],[f884,f877,f553,f3174]) ).
fof(f3174,plain,
( spl17_249
<=> ! [X0,X3,X2,X1] :
( sP0(X0,X1,relation_rng_restriction(X2,X3))
| ~ empty(relation_dom(X1))
| apply(X3,sK6(X0,X1,relation_rng_restriction(X2,X3))) = apply(relation_rng_restriction(X2,X3),sK6(X0,X1,relation_rng_restriction(X2,X3)))
| ~ function(X3)
| ~ relation(X3)
| ~ function(relation_rng_restriction(X2,X3))
| ~ relation(relation_rng_restriction(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_249])]) ).
fof(f884,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,X1,relation_rng_restriction(X2,X3))
| ~ empty(relation_dom(X1))
| apply(X3,sK6(X0,X1,relation_rng_restriction(X2,X3))) = apply(relation_rng_restriction(X2,X3),sK6(X0,X1,relation_rng_restriction(X2,X3)))
| ~ function(X3)
| ~ relation(X3)
| ~ function(relation_rng_restriction(X2,X3))
| ~ relation(relation_rng_restriction(X2,X3)) )
| ~ spl17_64
| ~ spl17_106 ),
inference(resolution,[],[f878,f554]) ).
fof(f3172,plain,
( spl17_248
| ~ spl17_64
| ~ spl17_105 ),
inference(avatar_split_clause,[],[f880,f873,f553,f3170]) ).
fof(f3170,plain,
( spl17_248
<=> ! [X0,X3,X2,X1] :
( sP0(X0,relation_rng_restriction(X1,X2),X3)
| ~ empty(relation_dom(X3))
| apply(X2,sK6(X0,relation_rng_restriction(X1,X2),X3)) = apply(relation_rng_restriction(X1,X2),sK6(X0,relation_rng_restriction(X1,X2),X3))
| ~ function(X2)
| ~ relation(X2)
| ~ function(relation_rng_restriction(X1,X2))
| ~ relation(relation_rng_restriction(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_248])]) ).
fof(f880,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,relation_rng_restriction(X1,X2),X3)
| ~ empty(relation_dom(X3))
| apply(X2,sK6(X0,relation_rng_restriction(X1,X2),X3)) = apply(relation_rng_restriction(X1,X2),sK6(X0,relation_rng_restriction(X1,X2),X3))
| ~ function(X2)
| ~ relation(X2)
| ~ function(relation_rng_restriction(X1,X2))
| ~ relation(relation_rng_restriction(X1,X2)) )
| ~ spl17_64
| ~ spl17_105 ),
inference(resolution,[],[f874,f554]) ).
fof(f3088,plain,
( spl17_247
| ~ spl17_94
| ~ spl17_122 ),
inference(avatar_split_clause,[],[f1048,f1043,f751,f3086]) ).
fof(f751,plain,
( spl17_94
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,X2)
| ~ subset(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_94])]) ).
fof(f1048,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK8(relation_dom(relation_rng_restriction(X1,X0)),X2)) = apply(relation_rng_restriction(X1,X0),sK8(relation_dom(relation_rng_restriction(X1,X0)),X2))
| ~ in(X3,relation_dom(relation_rng_restriction(X1,X0)))
| ~ empty(X2) )
| ~ spl17_94
| ~ spl17_122 ),
inference(resolution,[],[f1044,f752]) ).
fof(f752,plain,
( ! [X2,X0,X1] :
( ~ subset(X2,X0)
| ~ in(X1,X2)
| ~ empty(X0) )
| ~ spl17_94 ),
inference(avatar_component_clause,[],[f751]) ).
fof(f3084,plain,
( spl17_246
| ~ spl17_150
| ~ spl17_127
| ~ spl17_189 ),
inference(avatar_split_clause,[],[f2151,f2137,f1100,f1381,f3082]) ).
fof(f2151,plain,
( ! [X0,X1] :
( ~ relation(relation_rng_restriction(sK1,sK2))
| subset(relation_rng(relation_rng_restriction(X0,relation_rng_restriction(sK1,sK2))),X1)
| element(sK8(relation_rng(relation_rng_restriction(X0,relation_rng_restriction(sK1,sK2))),X1),relation_rng(sK2)) )
| ~ spl17_127
| ~ spl17_189 ),
inference(resolution,[],[f2138,f1101]) ).
fof(f3080,plain,
( spl17_245
| ~ spl17_64
| ~ spl17_103 ),
inference(avatar_split_clause,[],[f868,f861,f553,f3078]) ).
fof(f3078,plain,
( spl17_245
<=> ! [X0,X3,X2,X1] :
( sP0(X0,X1,relation_rng_restriction(X2,X3))
| ~ empty(X0)
| apply(X3,sK6(X0,X1,relation_rng_restriction(X2,X3))) = apply(relation_rng_restriction(X2,X3),sK6(X0,X1,relation_rng_restriction(X2,X3)))
| ~ function(X3)
| ~ relation(X3)
| ~ function(relation_rng_restriction(X2,X3))
| ~ relation(relation_rng_restriction(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_245])]) ).
fof(f868,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,X1,relation_rng_restriction(X2,X3))
| ~ empty(X0)
| apply(X3,sK6(X0,X1,relation_rng_restriction(X2,X3))) = apply(relation_rng_restriction(X2,X3),sK6(X0,X1,relation_rng_restriction(X2,X3)))
| ~ function(X3)
| ~ relation(X3)
| ~ function(relation_rng_restriction(X2,X3))
| ~ relation(relation_rng_restriction(X2,X3)) )
| ~ spl17_64
| ~ spl17_103 ),
inference(resolution,[],[f862,f554]) ).
fof(f3000,plain,
( spl17_244
| ~ spl17_61
| ~ spl17_119 ),
inference(avatar_split_clause,[],[f1009,f998,f530,f2998]) ).
fof(f1009,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(apply(X0,sK6(X2,X3,relation_rng_restriction(X1,X0))),X1)
| in(apply(X3,sK6(X2,X3,relation_rng_restriction(X1,X0))),X2)
| sP0(X2,X3,relation_rng_restriction(X1,X0)) )
| ~ spl17_61
| ~ spl17_119 ),
inference(resolution,[],[f999,f531]) ).
fof(f2996,plain,
( spl17_243
| ~ spl17_114
| ~ spl17_119 ),
inference(avatar_split_clause,[],[f1005,f998,f940,f2994]) ).
fof(f1005,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(apply(X0,sK6(X2,X3,relation_rng_restriction(X1,X0))),X1)
| element(apply(X3,sK6(X2,X3,relation_rng_restriction(X1,X0))),X2)
| sP0(X2,X3,relation_rng_restriction(X1,X0)) )
| ~ spl17_114
| ~ spl17_119 ),
inference(resolution,[],[f999,f941]) ).
fof(f2828,plain,
( spl17_242
| ~ spl17_82
| ~ spl17_125 ),
inference(avatar_split_clause,[],[f1087,f1071,f650,f2826]) ).
fof(f2826,plain,
( spl17_242
<=> ! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK6(sK10,X2,relation_rng_restriction(X1,X0))) = apply(relation_rng_restriction(X1,X0),sK6(sK10,X2,relation_rng_restriction(X1,X0)))
| sP0(sK10,X2,relation_rng_restriction(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_242])]) ).
fof(f1087,plain,
( ! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK6(sK10,X2,relation_rng_restriction(X1,X0))) = apply(relation_rng_restriction(X1,X0),sK6(sK10,X2,relation_rng_restriction(X1,X0)))
| sP0(sK10,X2,relation_rng_restriction(X1,X0)) )
| ~ spl17_82
| ~ spl17_125 ),
inference(resolution,[],[f1072,f651]) ).
fof(f2824,plain,
( spl17_241
| ~ spl17_59
| ~ spl17_119 ),
inference(avatar_split_clause,[],[f1013,f998,f513,f2822]) ).
fof(f1013,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(apply(X0,sK6(X2,relation_rng_restriction(X1,X0),X3)),X1)
| in(sK6(X2,relation_rng_restriction(X1,X0),X3),relation_dom(X3))
| sP0(X2,relation_rng_restriction(X1,X0),X3) )
| ~ spl17_59
| ~ spl17_119 ),
inference(resolution,[],[f999,f514]) ).
fof(f2820,plain,
( spl17_240
| ~ spl17_108
| ~ spl17_119 ),
inference(avatar_split_clause,[],[f1011,f998,f906,f2818]) ).
fof(f1011,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(apply(X0,sK6(X2,relation_rng_restriction(X1,X0),X3)),X1)
| element(sK6(X2,relation_rng_restriction(X1,X0),X3),relation_dom(X3))
| sP0(X2,relation_rng_restriction(X1,X0),X3) )
| ~ spl17_108
| ~ spl17_119 ),
inference(resolution,[],[f999,f907]) ).
fof(f2816,plain,
( spl17_239
| ~ spl17_59
| ~ spl17_119 ),
inference(avatar_split_clause,[],[f1010,f998,f513,f2814]) ).
fof(f1010,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(apply(X0,sK6(X2,X3,relation_rng_restriction(X1,X0))),X1)
| in(sK6(X2,X3,relation_rng_restriction(X1,X0)),relation_dom(X3))
| sP0(X2,X3,relation_rng_restriction(X1,X0)) )
| ~ spl17_59
| ~ spl17_119 ),
inference(resolution,[],[f999,f514]) ).
fof(f2812,plain,
( spl17_238
| ~ spl17_112
| ~ spl17_119 ),
inference(avatar_split_clause,[],[f1006,f998,f922,f2810]) ).
fof(f1006,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(apply(X0,sK6(X2,X3,relation_rng_restriction(X1,X0))),X1)
| element(sK6(X2,X3,relation_rng_restriction(X1,X0)),relation_dom(X3))
| sP0(X2,X3,relation_rng_restriction(X1,X0)) )
| ~ spl17_112
| ~ spl17_119 ),
inference(resolution,[],[f999,f923]) ).
fof(f2808,plain,
( spl17_237
| ~ spl17_61
| ~ spl17_118 ),
inference(avatar_split_clause,[],[f990,f979,f530,f2806]) ).
fof(f990,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(sK6(X2,X3,relation_rng_restriction(X1,X0)),relation_dom(X0))
| in(apply(X3,sK6(X2,X3,relation_rng_restriction(X1,X0))),X2)
| sP0(X2,X3,relation_rng_restriction(X1,X0)) )
| ~ spl17_61
| ~ spl17_118 ),
inference(resolution,[],[f980,f531]) ).
fof(f2804,plain,
( spl17_236
| ~ spl17_114
| ~ spl17_118 ),
inference(avatar_split_clause,[],[f986,f979,f940,f2802]) ).
fof(f2802,plain,
( spl17_236
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(sK6(X2,X3,relation_rng_restriction(X1,X0)),relation_dom(X0))
| element(apply(X3,sK6(X2,X3,relation_rng_restriction(X1,X0))),X2)
| sP0(X2,X3,relation_rng_restriction(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_236])]) ).
fof(f986,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(sK6(X2,X3,relation_rng_restriction(X1,X0)),relation_dom(X0))
| element(apply(X3,sK6(X2,X3,relation_rng_restriction(X1,X0))),X2)
| sP0(X2,X3,relation_rng_restriction(X1,X0)) )
| ~ spl17_114
| ~ spl17_118 ),
inference(resolution,[],[f980,f941]) ).
fof(f2739,plain,
( spl17_235
| ~ spl17_59
| ~ spl17_118 ),
inference(avatar_split_clause,[],[f994,f979,f513,f2737]) ).
fof(f2737,plain,
( spl17_235
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(sK6(X2,relation_rng_restriction(X1,X0),X3),relation_dom(X0))
| in(sK6(X2,relation_rng_restriction(X1,X0),X3),relation_dom(X3))
| sP0(X2,relation_rng_restriction(X1,X0),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_235])]) ).
fof(f994,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(sK6(X2,relation_rng_restriction(X1,X0),X3),relation_dom(X0))
| in(sK6(X2,relation_rng_restriction(X1,X0),X3),relation_dom(X3))
| sP0(X2,relation_rng_restriction(X1,X0),X3) )
| ~ spl17_59
| ~ spl17_118 ),
inference(resolution,[],[f980,f514]) ).
fof(f2735,plain,
( spl17_234
| ~ spl17_108
| ~ spl17_118 ),
inference(avatar_split_clause,[],[f992,f979,f906,f2733]) ).
fof(f2733,plain,
( spl17_234
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(sK6(X2,relation_rng_restriction(X1,X0),X3),relation_dom(X0))
| element(sK6(X2,relation_rng_restriction(X1,X0),X3),relation_dom(X3))
| sP0(X2,relation_rng_restriction(X1,X0),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_234])]) ).
fof(f992,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(sK6(X2,relation_rng_restriction(X1,X0),X3),relation_dom(X0))
| element(sK6(X2,relation_rng_restriction(X1,X0),X3),relation_dom(X3))
| sP0(X2,relation_rng_restriction(X1,X0),X3) )
| ~ spl17_108
| ~ spl17_118 ),
inference(resolution,[],[f980,f907]) ).
fof(f2731,plain,
( spl17_233
| ~ spl17_59
| ~ spl17_118 ),
inference(avatar_split_clause,[],[f991,f979,f513,f2729]) ).
fof(f2729,plain,
( spl17_233
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(sK6(X2,X3,relation_rng_restriction(X1,X0)),relation_dom(X0))
| in(sK6(X2,X3,relation_rng_restriction(X1,X0)),relation_dom(X3))
| sP0(X2,X3,relation_rng_restriction(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_233])]) ).
fof(f991,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(sK6(X2,X3,relation_rng_restriction(X1,X0)),relation_dom(X0))
| in(sK6(X2,X3,relation_rng_restriction(X1,X0)),relation_dom(X3))
| sP0(X2,X3,relation_rng_restriction(X1,X0)) )
| ~ spl17_59
| ~ spl17_118 ),
inference(resolution,[],[f980,f514]) ).
fof(f2727,plain,
( spl17_232
| ~ spl17_112
| ~ spl17_118 ),
inference(avatar_split_clause,[],[f987,f979,f922,f2725]) ).
fof(f2725,plain,
( spl17_232
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(sK6(X2,X3,relation_rng_restriction(X1,X0)),relation_dom(X0))
| element(sK6(X2,X3,relation_rng_restriction(X1,X0)),relation_dom(X3))
| sP0(X2,X3,relation_rng_restriction(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_232])]) ).
fof(f987,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(sK6(X2,X3,relation_rng_restriction(X1,X0)),relation_dom(X0))
| element(sK6(X2,X3,relation_rng_restriction(X1,X0)),relation_dom(X3))
| sP0(X2,X3,relation_rng_restriction(X1,X0)) )
| ~ spl17_112
| ~ spl17_118 ),
inference(resolution,[],[f980,f923]) ).
fof(f2701,plain,
( spl17_231
| ~ spl17_107
| ~ spl17_119 ),
inference(avatar_split_clause,[],[f1002,f998,f889,f2699]) ).
fof(f1002,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(apply(X0,apply(X2,sK6(relation_dom(relation_rng_restriction(X1,X0)),X2,X3))),X1)
| sP0(relation_dom(relation_rng_restriction(X1,X0)),X2,X3)
| ~ empty(relation_dom(X3)) )
| ~ spl17_107
| ~ spl17_119 ),
inference(resolution,[],[f999,f890]) ).
fof(f2686,plain,
( spl17_230
| ~ spl17_38
| ~ spl17_134 ),
inference(avatar_split_clause,[],[f1228,f1192,f380,f2684]) ).
fof(f2684,plain,
( spl17_230
<=> ! [X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X1,X0)
| ~ in(relation_rng(sK2),apply(X1,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_230])]) ).
fof(f1228,plain,
( ! [X0,X1] :
( ~ empty(relation_dom(X0))
| sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X1,X0)
| ~ in(relation_rng(sK2),apply(X1,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X1,X0))) )
| ~ spl17_38
| ~ spl17_134 ),
inference(resolution,[],[f1193,f381]) ).
fof(f2663,plain,
( spl17_229
| ~ spl17_107
| ~ spl17_118 ),
inference(avatar_split_clause,[],[f983,f979,f889,f2661]) ).
fof(f2661,plain,
( spl17_229
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(apply(X2,sK6(relation_dom(relation_rng_restriction(X1,X0)),X2,X3)),relation_dom(X0))
| sP0(relation_dom(relation_rng_restriction(X1,X0)),X2,X3)
| ~ empty(relation_dom(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_229])]) ).
fof(f983,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(apply(X2,sK6(relation_dom(relation_rng_restriction(X1,X0)),X2,X3)),relation_dom(X0))
| sP0(relation_dom(relation_rng_restriction(X1,X0)),X2,X3)
| ~ empty(relation_dom(X3)) )
| ~ spl17_107
| ~ spl17_118 ),
inference(resolution,[],[f980,f890]) ).
fof(f2659,plain,
( spl17_228
| ~ spl17_64
| ~ spl17_86 ),
inference(avatar_split_clause,[],[f717,f683,f553,f2657]) ).
fof(f717,plain,
( ! [X0,X1] :
( empty(relation_dom(relation_rng_restriction(X0,X1)))
| apply(X1,sK4(relation_dom(relation_rng_restriction(X0,X1)))) = apply(relation_rng_restriction(X0,X1),sK4(relation_dom(relation_rng_restriction(X0,X1))))
| ~ function(X1)
| ~ relation(X1)
| ~ function(relation_rng_restriction(X0,X1))
| ~ relation(relation_rng_restriction(X0,X1)) )
| ~ spl17_64
| ~ spl17_86 ),
inference(resolution,[],[f684,f554]) ).
fof(f2652,plain,
( spl17_227
| ~ spl17_63
| ~ spl17_99 ),
inference(avatar_split_clause,[],[f840,f829,f547,f2650]) ).
fof(f2650,plain,
( spl17_227
<=> ! [X2,X0,X1] :
( empty(powerset(X0))
| ~ subset(apply(X1,sK6(powerset(X0),X1,X2)),X0)
| sP0(powerset(X0),X1,X2)
| ~ in(sK6(powerset(X0),X1,X2),relation_dom(X1))
| ~ in(sK6(powerset(X0),X1,X2),relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_227])]) ).
fof(f547,plain,
( spl17_63
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ in(apply(X1,sK6(X0,X1,X2)),X0)
| ~ in(sK6(X0,X1,X2),relation_dom(X1))
| ~ in(sK6(X0,X1,X2),relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_63])]) ).
fof(f840,plain,
( ! [X2,X0,X1] :
( empty(powerset(X0))
| ~ subset(apply(X1,sK6(powerset(X0),X1,X2)),X0)
| sP0(powerset(X0),X1,X2)
| ~ in(sK6(powerset(X0),X1,X2),relation_dom(X1))
| ~ in(sK6(powerset(X0),X1,X2),relation_dom(X2)) )
| ~ spl17_63
| ~ spl17_99 ),
inference(resolution,[],[f830,f548]) ).
fof(f548,plain,
( ! [X2,X0,X1] :
( ~ in(apply(X1,sK6(X0,X1,X2)),X0)
| sP0(X0,X1,X2)
| ~ in(sK6(X0,X1,X2),relation_dom(X1))
| ~ in(sK6(X0,X1,X2),relation_dom(X2)) )
| ~ spl17_63 ),
inference(avatar_component_clause,[],[f547]) ).
fof(f2626,plain,
( spl17_226
| ~ spl17_101
| ~ spl17_119 ),
inference(avatar_split_clause,[],[f1014,f998,f846,f2624]) ).
fof(f1014,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(apply(X0,sK6(X2,relation_rng_restriction(X1,X0),relation_rng_restriction(X1,X0))),X1)
| sP0(X2,relation_rng_restriction(X1,X0),relation_rng_restriction(X1,X0)) )
| ~ spl17_101
| ~ spl17_119 ),
inference(resolution,[],[f999,f847]) ).
fof(f2566,plain,
( spl17_225
| ~ spl17_107
| ~ spl17_127 ),
inference(avatar_split_clause,[],[f1104,f1100,f889,f2564]) ).
fof(f2564,plain,
( spl17_225
<=> ! [X0,X1] :
( element(apply(X0,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1)),relation_rng(sK2))
| sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1)
| ~ empty(relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_225])]) ).
fof(f1104,plain,
( ! [X0,X1] :
( element(apply(X0,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1)),relation_rng(sK2))
| sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1)
| ~ empty(relation_dom(X1)) )
| ~ spl17_107
| ~ spl17_127 ),
inference(resolution,[],[f1101,f890]) ).
fof(f2533,plain,
( spl17_224
| ~ spl17_105
| ~ spl17_119 ),
inference(avatar_split_clause,[],[f1012,f998,f873,f2531]) ).
fof(f1012,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(apply(X0,sK6(X2,relation_rng_restriction(X1,X0),X3)),X1)
| sP0(X2,relation_rng_restriction(X1,X0),X3)
| ~ empty(relation_dom(X3)) )
| ~ spl17_105
| ~ spl17_119 ),
inference(resolution,[],[f999,f874]) ).
fof(f2529,plain,
( spl17_223
| ~ spl17_106
| ~ spl17_119 ),
inference(avatar_split_clause,[],[f1007,f998,f877,f2527]) ).
fof(f1007,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(apply(X0,sK6(X2,X3,relation_rng_restriction(X1,X0))),X1)
| sP0(X2,X3,relation_rng_restriction(X1,X0))
| ~ empty(relation_dom(X3)) )
| ~ spl17_106
| ~ spl17_119 ),
inference(resolution,[],[f999,f878]) ).
fof(f2525,plain,
( spl17_222
| ~ spl17_101
| ~ spl17_118 ),
inference(avatar_split_clause,[],[f995,f979,f846,f2523]) ).
fof(f2523,plain,
( spl17_222
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(sK6(X2,relation_rng_restriction(X1,X0),relation_rng_restriction(X1,X0)),relation_dom(X0))
| sP0(X2,relation_rng_restriction(X1,X0),relation_rng_restriction(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_222])]) ).
fof(f995,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(sK6(X2,relation_rng_restriction(X1,X0),relation_rng_restriction(X1,X0)),relation_dom(X0))
| sP0(X2,relation_rng_restriction(X1,X0),relation_rng_restriction(X1,X0)) )
| ~ spl17_101
| ~ spl17_118 ),
inference(resolution,[],[f980,f847]) ).
fof(f2521,plain,
( spl17_221
| ~ spl17_102
| ~ spl17_116 ),
inference(avatar_split_clause,[],[f971,f948,f854,f2519]) ).
fof(f2519,plain,
( spl17_221
<=> ! [X0,X3,X2,X1] :
( element(sK6(relation_rng(relation_rng_restriction(X1,X2)),X0,X3),relation_dom(X3))
| sP0(relation_rng(relation_rng_restriction(X1,X2)),X0,X3)
| in(apply(X0,sK6(relation_rng(relation_rng_restriction(X1,X2)),X0,X3)),relation_rng(X2))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_221])]) ).
fof(f971,plain,
( ! [X2,X3,X0,X1] :
( element(sK6(relation_rng(relation_rng_restriction(X1,X2)),X0,X3),relation_dom(X3))
| sP0(relation_rng(relation_rng_restriction(X1,X2)),X0,X3)
| in(apply(X0,sK6(relation_rng(relation_rng_restriction(X1,X2)),X0,X3)),relation_rng(X2))
| ~ relation(X2) )
| ~ spl17_102
| ~ spl17_116 ),
inference(resolution,[],[f949,f855]) ).
fof(f2517,plain,
( spl17_220
| ~ spl17_61
| ~ spl17_102 ),
inference(avatar_split_clause,[],[f857,f854,f530,f2515]) ).
fof(f2515,plain,
( spl17_220
<=> ! [X0,X3,X2,X1] :
( in(apply(X0,sK6(relation_rng(relation_rng_restriction(X1,X2)),X0,X3)),relation_rng(X2))
| ~ relation(X2)
| in(sK6(relation_rng(relation_rng_restriction(X1,X2)),X0,X3),relation_dom(X3))
| sP0(relation_rng(relation_rng_restriction(X1,X2)),X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_220])]) ).
fof(f857,plain,
( ! [X2,X3,X0,X1] :
( in(apply(X0,sK6(relation_rng(relation_rng_restriction(X1,X2)),X0,X3)),relation_rng(X2))
| ~ relation(X2)
| in(sK6(relation_rng(relation_rng_restriction(X1,X2)),X0,X3),relation_dom(X3))
| sP0(relation_rng(relation_rng_restriction(X1,X2)),X0,X3) )
| ~ spl17_61
| ~ spl17_102 ),
inference(resolution,[],[f855,f531]) ).
fof(f2469,plain,
( spl17_219
| ~ spl17_103
| ~ spl17_119 ),
inference(avatar_split_clause,[],[f1008,f998,f861,f2467]) ).
fof(f1008,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(apply(X0,sK6(X2,X3,relation_rng_restriction(X1,X0))),X1)
| sP0(X2,X3,relation_rng_restriction(X1,X0))
| ~ empty(X2) )
| ~ spl17_103
| ~ spl17_119 ),
inference(resolution,[],[f999,f862]) ).
fof(f2465,plain,
( spl17_218
| ~ spl17_105
| ~ spl17_118 ),
inference(avatar_split_clause,[],[f993,f979,f873,f2463]) ).
fof(f2463,plain,
( spl17_218
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(sK6(X2,relation_rng_restriction(X1,X0),X3),relation_dom(X0))
| sP0(X2,relation_rng_restriction(X1,X0),X3)
| ~ empty(relation_dom(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_218])]) ).
fof(f993,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(sK6(X2,relation_rng_restriction(X1,X0),X3),relation_dom(X0))
| sP0(X2,relation_rng_restriction(X1,X0),X3)
| ~ empty(relation_dom(X3)) )
| ~ spl17_105
| ~ spl17_118 ),
inference(resolution,[],[f980,f874]) ).
fof(f2461,plain,
( spl17_217
| ~ spl17_106
| ~ spl17_118 ),
inference(avatar_split_clause,[],[f988,f979,f877,f2459]) ).
fof(f2459,plain,
( spl17_217
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(sK6(X2,X3,relation_rng_restriction(X1,X0)),relation_dom(X0))
| sP0(X2,X3,relation_rng_restriction(X1,X0))
| ~ empty(relation_dom(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_217])]) ).
fof(f988,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(sK6(X2,X3,relation_rng_restriction(X1,X0)),relation_dom(X0))
| sP0(X2,X3,relation_rng_restriction(X1,X0))
| ~ empty(relation_dom(X3)) )
| ~ spl17_106
| ~ spl17_118 ),
inference(resolution,[],[f980,f878]) ).
fof(f2447,plain,
( spl17_216
| ~ spl17_103
| ~ spl17_118 ),
inference(avatar_split_clause,[],[f989,f979,f861,f2445]) ).
fof(f2445,plain,
( spl17_216
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(sK6(X2,X3,relation_rng_restriction(X1,X0)),relation_dom(X0))
| sP0(X2,X3,relation_rng_restriction(X1,X0))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_216])]) ).
fof(f989,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(sK6(X2,X3,relation_rng_restriction(X1,X0)),relation_dom(X0))
| sP0(X2,X3,relation_rng_restriction(X1,X0))
| ~ empty(X2) )
| ~ spl17_103
| ~ spl17_118 ),
inference(resolution,[],[f980,f862]) ).
fof(f2421,plain,
( spl17_215
| ~ spl17_50
| ~ spl17_119 ),
inference(avatar_split_clause,[],[f1015,f998,f449,f2419]) ).
fof(f1015,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(apply(X0,sK8(relation_dom(relation_rng_restriction(X1,X0)),X2)),X1)
| subset(relation_dom(relation_rng_restriction(X1,X0)),X2) )
| ~ spl17_50
| ~ spl17_119 ),
inference(resolution,[],[f999,f450]) ).
fof(f2405,plain,
( spl17_214
| ~ spl17_50
| ~ spl17_118 ),
inference(avatar_split_clause,[],[f996,f979,f449,f2403]) ).
fof(f996,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(sK8(relation_dom(relation_rng_restriction(X1,X0)),X2),relation_dom(X0))
| subset(relation_dom(relation_rng_restriction(X1,X0)),X2) )
| ~ spl17_50
| ~ spl17_118 ),
inference(resolution,[],[f980,f450]) ).
fof(f2379,plain,
( spl17_213
| ~ spl17_38
| ~ spl17_202 ),
inference(avatar_split_clause,[],[f2315,f2237,f380,f2377]) ).
fof(f2377,plain,
( spl17_213
<=> ! [X0] :
( empty(relation_rng(relation_rng_restriction(X0,relation_rng_restriction(sK1,sK2))))
| ~ in(relation_rng(sK2),sK4(relation_rng(relation_rng_restriction(X0,relation_rng_restriction(sK1,sK2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_213])]) ).
fof(f2237,plain,
( spl17_202
<=> ! [X0] :
( empty(relation_rng(relation_rng_restriction(X0,relation_rng_restriction(sK1,sK2))))
| in(sK4(relation_rng(relation_rng_restriction(X0,relation_rng_restriction(sK1,sK2)))),relation_rng(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_202])]) ).
fof(f2315,plain,
( ! [X0] :
( empty(relation_rng(relation_rng_restriction(X0,relation_rng_restriction(sK1,sK2))))
| ~ in(relation_rng(sK2),sK4(relation_rng(relation_rng_restriction(X0,relation_rng_restriction(sK1,sK2))))) )
| ~ spl17_38
| ~ spl17_202 ),
inference(resolution,[],[f2238,f381]) ).
fof(f2238,plain,
( ! [X0] :
( in(sK4(relation_rng(relation_rng_restriction(X0,relation_rng_restriction(sK1,sK2)))),relation_rng(sK2))
| empty(relation_rng(relation_rng_restriction(X0,relation_rng_restriction(sK1,sK2)))) )
| ~ spl17_202 ),
inference(avatar_component_clause,[],[f2237]) ).
fof(f2375,plain,
( spl17_212
| ~ spl17_86
| ~ spl17_119 ),
inference(avatar_split_clause,[],[f1004,f998,f683,f2373]) ).
fof(f1004,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(apply(X0,sK4(relation_dom(relation_rng_restriction(X1,X0)))),X1)
| empty(relation_dom(relation_rng_restriction(X1,X0))) )
| ~ spl17_86
| ~ spl17_119 ),
inference(resolution,[],[f999,f684]) ).
fof(f2338,plain,
( spl17_211
| ~ spl17_86
| ~ spl17_118 ),
inference(avatar_split_clause,[],[f985,f979,f683,f2336]) ).
fof(f985,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(sK4(relation_dom(relation_rng_restriction(X1,X0))),relation_dom(X0))
| empty(relation_dom(relation_rng_restriction(X1,X0))) )
| ~ spl17_86
| ~ spl17_118 ),
inference(resolution,[],[f980,f684]) ).
fof(f2334,plain,
( spl17_210
| ~ spl17_95
| ~ spl17_116 ),
inference(avatar_split_clause,[],[f973,f948,f756,f2332]) ).
fof(f2332,plain,
( spl17_210
<=> ! [X2,X0,X1] :
( element(sK6(sK4(powerset(X1)),X0,X2),relation_dom(X2))
| sP0(sK4(powerset(X1)),X0,X2)
| element(apply(X0,sK6(sK4(powerset(X1)),X0,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_210])]) ).
fof(f973,plain,
( ! [X2,X0,X1] :
( element(sK6(sK4(powerset(X1)),X0,X2),relation_dom(X2))
| sP0(sK4(powerset(X1)),X0,X2)
| element(apply(X0,sK6(sK4(powerset(X1)),X0,X2)),X1) )
| ~ spl17_95
| ~ spl17_116 ),
inference(resolution,[],[f949,f757]) ).
fof(f2330,plain,
( spl17_209
| ~ spl17_55
| ~ spl17_114 ),
inference(avatar_split_clause,[],[f956,f940,f489,f2328]) ).
fof(f2328,plain,
( spl17_209
<=> ! [X0,X3,X2,X1] :
( in(sK6(powerset(X1),X0,X2),relation_dom(X2))
| sP0(powerset(X1),X0,X2)
| element(X3,X1)
| ~ in(X3,apply(X0,sK6(powerset(X1),X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_209])]) ).
fof(f956,plain,
( ! [X2,X3,X0,X1] :
( in(sK6(powerset(X1),X0,X2),relation_dom(X2))
| sP0(powerset(X1),X0,X2)
| element(X3,X1)
| ~ in(X3,apply(X0,sK6(powerset(X1),X0,X2))) )
| ~ spl17_55
| ~ spl17_114 ),
inference(resolution,[],[f941,f490]) ).
fof(f2326,plain,
( spl17_208
| ~ spl17_61
| ~ spl17_95 ),
inference(avatar_split_clause,[],[f802,f756,f530,f2324]) ).
fof(f2324,plain,
( spl17_208
<=> ! [X2,X0,X1] :
( element(apply(X0,sK6(sK4(powerset(X1)),X0,X2)),X1)
| in(sK6(sK4(powerset(X1)),X0,X2),relation_dom(X2))
| sP0(sK4(powerset(X1)),X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_208])]) ).
fof(f802,plain,
( ! [X2,X0,X1] :
( element(apply(X0,sK6(sK4(powerset(X1)),X0,X2)),X1)
| in(sK6(sK4(powerset(X1)),X0,X2),relation_dom(X2))
| sP0(sK4(powerset(X1)),X0,X2) )
| ~ spl17_61
| ~ spl17_95 ),
inference(resolution,[],[f757,f531]) ).
fof(f2284,plain,
( spl17_207
| ~ spl17_97
| ~ spl17_116 ),
inference(avatar_split_clause,[],[f972,f948,f810,f2282]) ).
fof(f2282,plain,
( spl17_207
<=> ! [X2,X0,X1] :
( element(sK6(sK3(X1),X0,X2),relation_dom(X2))
| sP0(sK3(X1),X0,X2)
| element(apply(X0,sK6(sK3(X1),X0,X2)),X1)
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_207])]) ).
fof(f972,plain,
( ! [X2,X0,X1] :
( element(sK6(sK3(X1),X0,X2),relation_dom(X2))
| sP0(sK3(X1),X0,X2)
| element(apply(X0,sK6(sK3(X1),X0,X2)),X1)
| empty(X1) )
| ~ spl17_97
| ~ spl17_116 ),
inference(resolution,[],[f949,f811]) ).
fof(f2280,plain,
( spl17_206
| ~ spl17_54
| ~ spl17_114 ),
inference(avatar_split_clause,[],[f957,f940,f476,f2278]) ).
fof(f2278,plain,
( spl17_206
<=> ! [X2,X0,X1,X3] :
( in(sK6(powerset(X1),X0,X2),relation_dom(X2))
| sP0(powerset(X1),X0,X2)
| ~ empty(X1)
| ~ in(X3,apply(X0,sK6(powerset(X1),X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_206])]) ).
fof(f957,plain,
( ! [X2,X3,X0,X1] :
( in(sK6(powerset(X1),X0,X2),relation_dom(X2))
| sP0(powerset(X1),X0,X2)
| ~ empty(X1)
| ~ in(X3,apply(X0,sK6(powerset(X1),X0,X2))) )
| ~ spl17_54
| ~ spl17_114 ),
inference(resolution,[],[f941,f477]) ).
fof(f2276,plain,
( spl17_205
| ~ spl17_102
| ~ spl17_107 ),
inference(avatar_split_clause,[],[f899,f889,f854,f2274]) ).
fof(f899,plain,
( ! [X2,X3,X0,X1] :
( sP0(relation_rng(relation_rng_restriction(X0,X1)),X2,X3)
| ~ empty(relation_dom(X3))
| in(apply(X2,sK6(relation_rng(relation_rng_restriction(X0,X1)),X2,X3)),relation_rng(X1))
| ~ relation(X1) )
| ~ spl17_102
| ~ spl17_107 ),
inference(resolution,[],[f890,f855]) ).
fof(f2272,plain,
( spl17_204
| ~ spl17_61
| ~ spl17_97 ),
inference(avatar_split_clause,[],[f825,f810,f530,f2270]) ).
fof(f2270,plain,
( spl17_204
<=> ! [X2,X0,X1] :
( element(apply(X0,sK6(sK3(X1),X0,X2)),X1)
| empty(X1)
| in(sK6(sK3(X1),X0,X2),relation_dom(X2))
| sP0(sK3(X1),X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_204])]) ).
fof(f825,plain,
( ! [X2,X0,X1] :
( element(apply(X0,sK6(sK3(X1),X0,X2)),X1)
| empty(X1)
| in(sK6(sK3(X1),X0,X2),relation_dom(X2))
| sP0(sK3(X1),X0,X2) )
| ~ spl17_61
| ~ spl17_97 ),
inference(resolution,[],[f811,f531]) ).
fof(f2243,plain,
( spl17_203
| ~ spl17_59
| ~ spl17_120 ),
inference(avatar_split_clause,[],[f1036,f1017,f513,f2241]) ).
fof(f1017,plain,
( spl17_120
<=> ! [X0,X3,X2,X1] :
( in(sK6(X1,X0,X2),relation_dom(X2))
| sP0(X1,X0,X2)
| in(sK6(X1,X0,X2),relation_dom(X3))
| ~ in(sK6(X1,X0,X2),relation_dom(X0))
| ~ sP0(X1,X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_120])]) ).
fof(f1036,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,X1,X2)
| in(sK6(X0,X1,X2),relation_dom(X3))
| in(sK6(X0,X1,X2),relation_dom(X2))
| ~ sP0(X0,X1,X3) )
| ~ spl17_59
| ~ spl17_120 ),
inference(duplicate_literal_removal,[],[f1033]) ).
fof(f1033,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,X1,X2)
| in(sK6(X0,X1,X2),relation_dom(X3))
| in(sK6(X0,X1,X2),relation_dom(X2))
| ~ sP0(X0,X1,X3)
| in(sK6(X0,X1,X2),relation_dom(X2))
| sP0(X0,X1,X2) )
| ~ spl17_59
| ~ spl17_120 ),
inference(resolution,[],[f1018,f514]) ).
fof(f1018,plain,
( ! [X2,X3,X0,X1] :
( ~ in(sK6(X1,X0,X2),relation_dom(X0))
| sP0(X1,X0,X2)
| in(sK6(X1,X0,X2),relation_dom(X3))
| in(sK6(X1,X0,X2),relation_dom(X2))
| ~ sP0(X1,X0,X3) )
| ~ spl17_120 ),
inference(avatar_component_clause,[],[f1017]) ).
fof(f2239,plain,
( spl17_109
| spl17_202
| ~ spl17_47
| ~ spl17_191 ),
inference(avatar_split_clause,[],[f2199,f2163,f436,f2237,f910]) ).
fof(f2163,plain,
( spl17_191
<=> ! [X0] :
( empty(relation_rng(relation_rng_restriction(X0,relation_rng_restriction(sK1,sK2))))
| element(sK4(relation_rng(relation_rng_restriction(X0,relation_rng_restriction(sK1,sK2)))),relation_rng(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_191])]) ).
fof(f2199,plain,
( ! [X0] :
( empty(relation_rng(relation_rng_restriction(X0,relation_rng_restriction(sK1,sK2))))
| empty(relation_rng(sK2))
| in(sK4(relation_rng(relation_rng_restriction(X0,relation_rng_restriction(sK1,sK2)))),relation_rng(sK2)) )
| ~ spl17_47
| ~ spl17_191 ),
inference(resolution,[],[f2164,f437]) ).
fof(f2164,plain,
( ! [X0] :
( element(sK4(relation_rng(relation_rng_restriction(X0,relation_rng_restriction(sK1,sK2)))),relation_rng(sK2))
| empty(relation_rng(relation_rng_restriction(X0,relation_rng_restriction(sK1,sK2)))) )
| ~ spl17_191 ),
inference(avatar_component_clause,[],[f2163]) ).
fof(f2235,plain,
( spl17_201
| ~ spl17_44
| ~ spl17_114 ),
inference(avatar_split_clause,[],[f958,f940,f406,f2233]) ).
fof(f2233,plain,
( spl17_201
<=> ! [X2,X0,X1] :
( in(sK6(powerset(X1),X0,X2),relation_dom(X2))
| sP0(powerset(X1),X0,X2)
| subset(apply(X0,sK6(powerset(X1),X0,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_201])]) ).
fof(f958,plain,
( ! [X2,X0,X1] :
( in(sK6(powerset(X1),X0,X2),relation_dom(X2))
| sP0(powerset(X1),X0,X2)
| subset(apply(X0,sK6(powerset(X1),X0,X2)),X1) )
| ~ spl17_44
| ~ spl17_114 ),
inference(resolution,[],[f941,f407]) ).
fof(f2227,plain,
( spl17_200
| ~ spl17_58
| ~ spl17_99 ),
inference(avatar_split_clause,[],[f841,f829,f507,f2225]) ).
fof(f2225,plain,
( spl17_200
<=> ! [X0,X3,X2,X1] :
( empty(powerset(X0))
| ~ subset(apply(X1,X2),X0)
| in(X2,relation_dom(X3))
| ~ in(X2,relation_dom(X1))
| ~ sP0(powerset(X0),X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_200])]) ).
fof(f841,plain,
( ! [X2,X3,X0,X1] :
( empty(powerset(X0))
| ~ subset(apply(X1,X2),X0)
| in(X2,relation_dom(X3))
| ~ in(X2,relation_dom(X1))
| ~ sP0(powerset(X0),X1,X3) )
| ~ spl17_58
| ~ spl17_99 ),
inference(resolution,[],[f830,f508]) ).
fof(f2207,plain,
( spl17_199
| ~ spl17_38
| ~ spl17_116 ),
inference(avatar_split_clause,[],[f966,f948,f380,f2205]) ).
fof(f2205,plain,
( spl17_199
<=> ! [X2,X0,X1] :
( element(sK6(X1,X0,X2),relation_dom(X2))
| sP0(X1,X0,X2)
| ~ in(X1,apply(X0,sK6(X1,X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_199])]) ).
fof(f966,plain,
( ! [X2,X0,X1] :
( element(sK6(X1,X0,X2),relation_dom(X2))
| sP0(X1,X0,X2)
| ~ in(X1,apply(X0,sK6(X1,X0,X2))) )
| ~ spl17_38
| ~ spl17_116 ),
inference(resolution,[],[f949,f381]) ).
fof(f2203,plain,
( spl17_198
| ~ spl17_38
| ~ spl17_114 ),
inference(avatar_split_clause,[],[f962,f940,f380,f2201]) ).
fof(f962,plain,
( ! [X2,X0,X1] :
( element(apply(X1,sK6(X0,X1,X2)),X0)
| sP0(X0,X1,X2)
| ~ in(relation_dom(X2),sK6(X0,X1,X2)) )
| ~ spl17_38
| ~ spl17_114 ),
inference(resolution,[],[f941,f381]) ).
fof(f2198,plain,
( spl17_197
| ~ spl17_39
| ~ spl17_114 ),
inference(avatar_split_clause,[],[f961,f940,f384,f2196]) ).
fof(f2196,plain,
( spl17_197
<=> ! [X2,X0,X1] :
( element(apply(X1,sK6(X0,X1,X2)),X0)
| sP0(X0,X1,X2)
| element(sK6(X0,X1,X2),relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_197])]) ).
fof(f961,plain,
( ! [X2,X0,X1] :
( element(apply(X1,sK6(X0,X1,X2)),X0)
| sP0(X0,X1,X2)
| element(sK6(X0,X1,X2),relation_dom(X2)) )
| ~ spl17_39
| ~ spl17_114 ),
inference(resolution,[],[f941,f385]) ).
fof(f2194,plain,
( spl17_196
| ~ spl17_95
| ~ spl17_107 ),
inference(avatar_split_clause,[],[f901,f889,f756,f2192]) ).
fof(f901,plain,
( ! [X2,X0,X1] :
( sP0(sK4(powerset(X0)),X1,X2)
| ~ empty(relation_dom(X2))
| element(apply(X1,sK6(sK4(powerset(X0)),X1,X2)),X0) )
| ~ spl17_95
| ~ spl17_107 ),
inference(resolution,[],[f890,f757]) ).
fof(f2190,plain,
( spl17_195
| ~ spl17_97
| ~ spl17_107 ),
inference(avatar_split_clause,[],[f900,f889,f810,f2188]) ).
fof(f2188,plain,
( spl17_195
<=> ! [X2,X0,X1] :
( sP0(sK3(X0),X1,X2)
| ~ empty(relation_dom(X2))
| element(apply(X1,sK6(sK3(X0),X1,X2)),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_195])]) ).
fof(f900,plain,
( ! [X2,X0,X1] :
( sP0(sK3(X0),X1,X2)
| ~ empty(relation_dom(X2))
| element(apply(X1,sK6(sK3(X0),X1,X2)),X0)
| empty(X0) )
| ~ spl17_97
| ~ spl17_107 ),
inference(resolution,[],[f890,f811]) ).
fof(f2179,plain,
( spl17_194
| ~ spl17_38
| ~ spl17_112 ),
inference(avatar_split_clause,[],[f937,f922,f380,f2177]) ).
fof(f937,plain,
( ! [X2,X0,X1] :
( element(sK6(X0,X1,X2),relation_dom(X1))
| sP0(X0,X1,X2)
| ~ in(relation_dom(X2),sK6(X0,X1,X2)) )
| ~ spl17_38
| ~ spl17_112 ),
inference(resolution,[],[f923,f381]) ).
fof(f2175,plain,
( spl17_193
| ~ spl17_38
| ~ spl17_108 ),
inference(avatar_split_clause,[],[f932,f906,f380,f2173]) ).
fof(f932,plain,
( ! [X2,X0,X1] :
( element(sK6(X0,X1,X2),relation_dom(X2))
| sP0(X0,X1,X2)
| ~ in(relation_dom(X1),sK6(X0,X1,X2)) )
| ~ spl17_38
| ~ spl17_108 ),
inference(resolution,[],[f907,f381]) ).
fof(f2171,plain,
( spl17_192
| ~ spl17_39
| ~ spl17_108 ),
inference(avatar_split_clause,[],[f931,f906,f384,f2169]) ).
fof(f931,plain,
( ! [X2,X0,X1] :
( element(sK6(X0,X1,X2),relation_dom(X2))
| sP0(X0,X1,X2)
| element(sK6(X0,X1,X2),relation_dom(X1)) )
| ~ spl17_39
| ~ spl17_108 ),
inference(resolution,[],[f907,f385]) ).
fof(f2165,plain,
( spl17_191
| ~ spl17_150
| ~ spl17_127
| ~ spl17_185 ),
inference(avatar_split_clause,[],[f2119,f2108,f1100,f1381,f2163]) ).
fof(f2119,plain,
( ! [X0] :
( ~ relation(relation_rng_restriction(sK1,sK2))
| empty(relation_rng(relation_rng_restriction(X0,relation_rng_restriction(sK1,sK2))))
| element(sK4(relation_rng(relation_rng_restriction(X0,relation_rng_restriction(sK1,sK2)))),relation_rng(sK2)) )
| ~ spl17_127
| ~ spl17_185 ),
inference(resolution,[],[f2109,f1101]) ).
fof(f2143,plain,
( spl17_190
| ~ spl17_89
| ~ spl17_116 ),
inference(avatar_split_clause,[],[f974,f948,f725,f2141]) ).
fof(f974,plain,
( ! [X2,X0,X1] :
( element(sK6(sK4(powerset(X1)),X0,X2),relation_dom(X2))
| sP0(sK4(powerset(X1)),X0,X2)
| ~ empty(X1) )
| ~ spl17_89
| ~ spl17_116 ),
inference(resolution,[],[f949,f726]) ).
fof(f2139,plain,
( spl17_189
| ~ spl17_50
| ~ spl17_102 ),
inference(avatar_split_clause,[],[f859,f854,f449,f2137]) ).
fof(f859,plain,
( ! [X2,X0,X1] :
( in(sK8(relation_rng(relation_rng_restriction(X0,X1)),X2),relation_rng(X1))
| ~ relation(X1)
| subset(relation_rng(relation_rng_restriction(X0,X1)),X2) )
| ~ spl17_50
| ~ spl17_102 ),
inference(resolution,[],[f855,f450]) ).
fof(f2135,plain,
( spl17_188
| ~ spl17_61
| ~ spl17_89 ),
inference(avatar_split_clause,[],[f731,f725,f530,f2133]) ).
fof(f731,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| in(sK6(sK4(powerset(X0)),X1,X2),relation_dom(X2))
| sP0(sK4(powerset(X0)),X1,X2) )
| ~ spl17_61
| ~ spl17_89 ),
inference(resolution,[],[f726,f531]) ).
fof(f2118,plain,
( spl17_187
| ~ spl17_38
| ~ spl17_107 ),
inference(avatar_split_clause,[],[f894,f889,f380,f2116]) ).
fof(f2116,plain,
( spl17_187
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(relation_dom(X2))
| ~ in(X0,apply(X1,sK6(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_187])]) ).
fof(f894,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(relation_dom(X2))
| ~ in(X0,apply(X1,sK6(X0,X1,X2))) )
| ~ spl17_38
| ~ spl17_107 ),
inference(resolution,[],[f890,f381]) ).
fof(f2114,plain,
( spl17_186
| ~ spl17_39
| ~ spl17_107 ),
inference(avatar_split_clause,[],[f893,f889,f384,f2112]) ).
fof(f893,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(relation_dom(X2))
| element(apply(X1,sK6(X0,X1,X2)),X0) )
| ~ spl17_39
| ~ spl17_107 ),
inference(resolution,[],[f890,f385]) ).
fof(f2110,plain,
( spl17_185
| ~ spl17_86
| ~ spl17_102 ),
inference(avatar_split_clause,[],[f858,f854,f683,f2108]) ).
fof(f858,plain,
( ! [X0,X1] :
( in(sK4(relation_rng(relation_rng_restriction(X0,X1))),relation_rng(X1))
| ~ relation(X1)
| empty(relation_rng(relation_rng_restriction(X0,X1))) )
| ~ spl17_86
| ~ spl17_102 ),
inference(resolution,[],[f855,f684]) ).
fof(f2102,plain,
( spl17_184
| ~ spl17_66
| ~ spl17_125 ),
inference(avatar_split_clause,[],[f1082,f1071,f568,f2100]) ).
fof(f1082,plain,
( ! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| apply(X0,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X2,relation_rng_restriction(X1,X0))) = apply(relation_rng_restriction(X1,X0),sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X2,relation_rng_restriction(X1,X0)))
| sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X2,relation_rng_restriction(X1,X0))
| in(apply(X2,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X2,relation_rng_restriction(X1,X0))),relation_rng(sK2)) )
| ~ spl17_66
| ~ spl17_125 ),
inference(resolution,[],[f1072,f569]) ).
fof(f2092,plain,
( spl17_183
| ~ spl17_38
| ~ spl17_106 ),
inference(avatar_split_clause,[],[f886,f877,f380,f2090]) ).
fof(f886,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(relation_dom(X1))
| ~ in(relation_dom(X2),sK6(X0,X1,X2)) )
| ~ spl17_38
| ~ spl17_106 ),
inference(resolution,[],[f878,f381]) ).
fof(f2088,plain,
( spl17_182
| ~ spl17_39
| ~ spl17_106 ),
inference(avatar_split_clause,[],[f885,f877,f384,f2086]) ).
fof(f885,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(relation_dom(X1))
| element(sK6(X0,X1,X2),relation_dom(X2)) )
| ~ spl17_39
| ~ spl17_106 ),
inference(resolution,[],[f878,f385]) ).
fof(f2084,plain,
( spl17_181
| ~ spl17_38
| ~ spl17_105 ),
inference(avatar_split_clause,[],[f882,f873,f380,f2082]) ).
fof(f882,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(relation_dom(X2))
| ~ in(relation_dom(X1),sK6(X0,X1,X2)) )
| ~ spl17_38
| ~ spl17_105 ),
inference(resolution,[],[f874,f381]) ).
fof(f2079,plain,
( spl17_180
| ~ spl17_39
| ~ spl17_105 ),
inference(avatar_split_clause,[],[f881,f873,f384,f2077]) ).
fof(f881,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(relation_dom(X2))
| element(sK6(X0,X1,X2),relation_dom(X1)) )
| ~ spl17_39
| ~ spl17_105 ),
inference(resolution,[],[f874,f385]) ).
fof(f2063,plain,
( spl17_179
| ~ spl17_38
| ~ spl17_103 ),
inference(avatar_split_clause,[],[f870,f861,f380,f2061]) ).
fof(f870,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(X0)
| ~ in(relation_dom(X2),sK6(X0,X1,X2)) )
| ~ spl17_38
| ~ spl17_103 ),
inference(resolution,[],[f862,f381]) ).
fof(f2059,plain,
( spl17_178
| ~ spl17_39
| ~ spl17_103 ),
inference(avatar_split_clause,[],[f869,f861,f384,f2057]) ).
fof(f869,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(X0)
| element(sK6(X0,X1,X2),relation_dom(X2)) )
| ~ spl17_39
| ~ spl17_103 ),
inference(resolution,[],[f862,f385]) ).
fof(f2055,plain,
( spl17_177
| ~ spl17_51
| ~ spl17_99 ),
inference(avatar_split_clause,[],[f839,f829,f453,f2053]) ).
fof(f839,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| ~ subset(sK8(X1,powerset(X0)),X0)
| subset(X1,powerset(X0)) )
| ~ spl17_51
| ~ spl17_99 ),
inference(resolution,[],[f830,f454]) ).
fof(f2051,plain,
( spl17_176
| ~ spl17_55
| ~ spl17_92 ),
inference(avatar_split_clause,[],[f791,f743,f489,f2049]) ).
fof(f743,plain,
( spl17_92
<=> ! [X0,X1] :
( subset(X0,X1)
| element(sK8(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_92])]) ).
fof(f791,plain,
( ! [X2,X0,X1] :
( subset(powerset(X0),X1)
| element(X2,X0)
| ~ in(X2,sK8(powerset(X0),X1)) )
| ~ spl17_55
| ~ spl17_92 ),
inference(resolution,[],[f744,f490]) ).
fof(f744,plain,
( ! [X0,X1] :
( element(sK8(X0,X1),X0)
| subset(X0,X1) )
| ~ spl17_92 ),
inference(avatar_component_clause,[],[f743]) ).
fof(f2042,plain,
( spl17_175
| ~ spl17_38
| ~ spl17_75 ),
inference(avatar_split_clause,[],[f657,f621,f380,f2040]) ).
fof(f2040,plain,
( spl17_175
<=> ! [X0] :
( subset(relation_rng(relation_rng_restriction(sK1,sK2)),X0)
| ~ in(relation_rng(sK2),sK8(relation_rng(relation_rng_restriction(sK1,sK2)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_175])]) ).
fof(f621,plain,
( spl17_75
<=> ! [X0] :
( in(sK8(relation_rng(relation_rng_restriction(sK1,sK2)),X0),relation_rng(sK2))
| subset(relation_rng(relation_rng_restriction(sK1,sK2)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_75])]) ).
fof(f657,plain,
( ! [X0] :
( subset(relation_rng(relation_rng_restriction(sK1,sK2)),X0)
| ~ in(relation_rng(sK2),sK8(relation_rng(relation_rng_restriction(sK1,sK2)),X0)) )
| ~ spl17_38
| ~ spl17_75 ),
inference(resolution,[],[f622,f381]) ).
fof(f622,plain,
( ! [X0] :
( in(sK8(relation_rng(relation_rng_restriction(sK1,sK2)),X0),relation_rng(sK2))
| subset(relation_rng(relation_rng_restriction(sK1,sK2)),X0) )
| ~ spl17_75 ),
inference(avatar_component_clause,[],[f621]) ).
fof(f2022,plain,
( spl17_174
| ~ spl17_50
| ~ spl17_97 ),
inference(avatar_split_clause,[],[f827,f810,f449,f2020]) ).
fof(f827,plain,
( ! [X0,X1] :
( element(sK8(sK3(X0),X1),X0)
| empty(X0)
| subset(sK3(X0),X1) )
| ~ spl17_50
| ~ spl17_97 ),
inference(resolution,[],[f811,f450]) ).
fof(f2018,plain,
( spl17_173
| ~ spl17_52
| ~ spl17_96 ),
inference(avatar_split_clause,[],[f815,f806,f468,f2016]) ).
fof(f815,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| element(X0,relation_rng(X2))
| ~ relation(X2) )
| ~ spl17_52
| ~ spl17_96 ),
inference(resolution,[],[f807,f469]) ).
fof(f2014,plain,
( spl17_172
| ~ spl17_50
| ~ spl17_95 ),
inference(avatar_split_clause,[],[f804,f756,f449,f2012]) ).
fof(f804,plain,
( ! [X0,X1] :
( element(sK8(sK4(powerset(X0)),X1),X0)
| subset(sK4(powerset(X0)),X1) )
| ~ spl17_50
| ~ spl17_95 ),
inference(resolution,[],[f757,f450]) ).
fof(f2010,plain,
( spl17_171
| ~ spl17_54
| ~ spl17_92 ),
inference(avatar_split_clause,[],[f792,f743,f476,f2008]) ).
fof(f792,plain,
( ! [X2,X0,X1] :
( subset(powerset(X0),X1)
| ~ empty(X0)
| ~ in(X2,sK8(powerset(X0),X1)) )
| ~ spl17_54
| ~ spl17_92 ),
inference(resolution,[],[f744,f477]) ).
fof(f1999,plain,
( spl17_170
| ~ spl17_39
| ~ spl17_75 ),
inference(avatar_split_clause,[],[f656,f621,f384,f1997]) ).
fof(f1997,plain,
( spl17_170
<=> ! [X0] :
( subset(relation_rng(relation_rng_restriction(sK1,sK2)),X0)
| element(sK8(relation_rng(relation_rng_restriction(sK1,sK2)),X0),relation_rng(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_170])]) ).
fof(f656,plain,
( ! [X0] :
( subset(relation_rng(relation_rng_restriction(sK1,sK2)),X0)
| element(sK8(relation_rng(relation_rng_restriction(sK1,sK2)),X0),relation_rng(sK2)) )
| ~ spl17_39
| ~ spl17_75 ),
inference(resolution,[],[f622,f385]) ).
fof(f1639,plain,
( spl17_79
| ~ spl17_28
| ~ spl17_69 ),
inference(avatar_split_clause,[],[f1593,f584,f323,f639]) ).
fof(f639,plain,
( spl17_79
<=> ! [X0] :
( sK10 = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_79])]) ).
fof(f1593,plain,
( ! [X0] :
( sK10 = X0
| ~ empty(X0) )
| ~ spl17_28
| ~ spl17_69 ),
inference(forward_demodulation,[],[f324,f586]) ).
fof(f1592,plain,
( ~ spl17_3
| ~ spl17_81 ),
inference(avatar_contradiction_clause,[],[f1583]) ).
fof(f1583,plain,
( $false
| ~ spl17_3
| ~ spl17_81 ),
inference(resolution,[],[f648,f198]) ).
fof(f648,plain,
( ! [X0] : ~ empty(X0)
| ~ spl17_81 ),
inference(avatar_component_clause,[],[f647]) ).
fof(f647,plain,
( spl17_81
<=> ! [X0] : ~ empty(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_81])]) ).
fof(f1591,plain,
( ~ spl17_20
| ~ spl17_81 ),
inference(avatar_contradiction_clause,[],[f1584]) ).
fof(f1584,plain,
( $false
| ~ spl17_20
| ~ spl17_81 ),
inference(resolution,[],[f648,f281]) ).
fof(f281,plain,
( ! [X0] : empty(sK5(X0))
| ~ spl17_20 ),
inference(avatar_component_clause,[],[f280]) ).
fof(f280,plain,
( spl17_20
<=> ! [X0] : empty(sK5(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_20])]) ).
fof(f1590,plain,
( ~ spl17_6
| ~ spl17_81 ),
inference(avatar_contradiction_clause,[],[f1585]) ).
fof(f1585,plain,
( $false
| ~ spl17_6
| ~ spl17_81 ),
inference(resolution,[],[f648,f213]) ).
fof(f213,plain,
( empty(sK10)
| ~ spl17_6 ),
inference(avatar_component_clause,[],[f211]) ).
fof(f211,plain,
( spl17_6
<=> empty(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_6])]) ).
fof(f1589,plain,
( ~ spl17_9
| ~ spl17_81 ),
inference(avatar_contradiction_clause,[],[f1586]) ).
fof(f1586,plain,
( $false
| ~ spl17_9
| ~ spl17_81 ),
inference(resolution,[],[f648,f228]) ).
fof(f228,plain,
( empty(sK12)
| ~ spl17_9 ),
inference(avatar_component_clause,[],[f226]) ).
fof(f226,plain,
( spl17_9
<=> empty(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_9])]) ).
fof(f1588,plain,
( ~ spl17_17
| ~ spl17_81 ),
inference(avatar_contradiction_clause,[],[f1587]) ).
fof(f1587,plain,
( $false
| ~ spl17_17
| ~ spl17_81 ),
inference(resolution,[],[f648,f268]) ).
fof(f268,plain,
( empty(sK16)
| ~ spl17_17 ),
inference(avatar_component_clause,[],[f266]) ).
fof(f266,plain,
( spl17_17
<=> empty(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_17])]) ).
fof(f1582,plain,
( spl17_169
| ~ spl17_82
| ~ spl17_116 ),
inference(avatar_split_clause,[],[f975,f948,f650,f1580]) ).
fof(f975,plain,
( ! [X0,X1] :
( element(sK6(sK10,X0,X1),relation_dom(X1))
| sP0(sK10,X0,X1) )
| ~ spl17_82
| ~ spl17_116 ),
inference(resolution,[],[f949,f651]) ).
fof(f1578,plain,
( spl17_168
| ~ spl17_89
| ~ spl17_107 ),
inference(avatar_split_clause,[],[f902,f889,f725,f1576]) ).
fof(f1576,plain,
( spl17_168
<=> ! [X2,X0,X1] :
( sP0(sK4(powerset(X0)),X1,X2)
| ~ empty(relation_dom(X2))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_168])]) ).
fof(f902,plain,
( ! [X2,X0,X1] :
( sP0(sK4(powerset(X0)),X1,X2)
| ~ empty(relation_dom(X2))
| ~ empty(X0) )
| ~ spl17_89
| ~ spl17_107 ),
inference(resolution,[],[f890,f726]) ).
fof(f1574,plain,
( spl17_167
| ~ spl17_38
| ~ spl17_101 ),
inference(avatar_split_clause,[],[f851,f846,f380,f1572]) ).
fof(f851,plain,
( ! [X0,X1] :
( sP0(X0,X1,X1)
| ~ in(relation_dom(X1),sK6(X0,X1,X1)) )
| ~ spl17_38
| ~ spl17_101 ),
inference(resolution,[],[f847,f381]) ).
fof(f1570,plain,
( spl17_166
| ~ spl17_39
| ~ spl17_101 ),
inference(avatar_split_clause,[],[f850,f846,f384,f1568]) ).
fof(f850,plain,
( ! [X0,X1] :
( sP0(X0,X1,X1)
| element(sK6(X0,X1,X1),relation_dom(X1)) )
| ~ spl17_39
| ~ spl17_101 ),
inference(resolution,[],[f847,f385]) ).
fof(f1566,plain,
( spl17_165
| ~ spl17_52
| ~ spl17_94 ),
inference(avatar_split_clause,[],[f797,f751,f468,f1564]) ).
fof(f797,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ empty(relation_rng(X2))
| ~ relation(X2) )
| ~ spl17_52
| ~ spl17_94 ),
inference(resolution,[],[f752,f469]) ).
fof(f1562,plain,
( spl17_164
| ~ spl17_61
| ~ spl17_82 ),
inference(avatar_split_clause,[],[f654,f650,f530,f1560]) ).
fof(f654,plain,
( ! [X0,X1] :
( in(sK6(sK10,X0,X1),relation_dom(X1))
| sP0(sK10,X0,X1) )
| ~ spl17_61
| ~ spl17_82 ),
inference(resolution,[],[f651,f531]) ).
fof(f1539,plain,
( spl17_163
| ~ spl17_35
| ~ spl17_105 ),
inference(avatar_split_clause,[],[f883,f873,f352,f1537]) ).
fof(f1537,plain,
( spl17_163
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(relation_dom(X2))
| ~ empty(relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_163])]) ).
fof(f883,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(relation_dom(X2))
| ~ empty(relation_dom(X1)) )
| ~ spl17_35
| ~ spl17_105 ),
inference(resolution,[],[f874,f353]) ).
fof(f1535,plain,
( spl17_162
| ~ spl17_38
| ~ spl17_100 ),
inference(avatar_split_clause,[],[f843,f833,f380,f1533]) ).
fof(f1533,plain,
( spl17_162
<=> ! [X0] :
( empty(powerset(X0))
| empty(X0)
| ~ in(powerset(X0),sK3(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_162])]) ).
fof(f833,plain,
( spl17_100
<=> ! [X0] :
( empty(powerset(X0))
| in(sK3(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_100])]) ).
fof(f843,plain,
( ! [X0] :
( empty(powerset(X0))
| empty(X0)
| ~ in(powerset(X0),sK3(X0)) )
| ~ spl17_38
| ~ spl17_100 ),
inference(resolution,[],[f834,f381]) ).
fof(f834,plain,
( ! [X0] :
( in(sK3(X0),powerset(X0))
| empty(powerset(X0))
| empty(X0) )
| ~ spl17_100 ),
inference(avatar_component_clause,[],[f833]) ).
fof(f1531,plain,
( spl17_161
| ~ spl17_38
| ~ spl17_99 ),
inference(avatar_split_clause,[],[f837,f829,f380,f1529]) ).
fof(f837,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| ~ subset(X1,X0)
| ~ in(powerset(X0),X1) )
| ~ spl17_38
| ~ spl17_99 ),
inference(resolution,[],[f830,f381]) ).
fof(f1527,plain,
( spl17_160
| ~ spl17_86
| ~ spl17_97 ),
inference(avatar_split_clause,[],[f826,f810,f683,f1525]) ).
fof(f826,plain,
( ! [X0] :
( element(sK4(sK3(X0)),X0)
| empty(X0)
| empty(sK3(X0)) )
| ~ spl17_86
| ~ spl17_97 ),
inference(resolution,[],[f811,f684]) ).
fof(f1523,plain,
( spl17_159
| ~ spl17_86
| ~ spl17_95 ),
inference(avatar_split_clause,[],[f803,f756,f683,f1521]) ).
fof(f803,plain,
( ! [X0] :
( element(sK4(sK4(powerset(X0))),X0)
| empty(sK4(powerset(X0))) )
| ~ spl17_86
| ~ spl17_95 ),
inference(resolution,[],[f757,f684]) ).
fof(f1518,plain,
( ~ spl17_1
| ~ spl17_2
| ~ spl17_49
| spl17_151 ),
inference(avatar_split_clause,[],[f1390,f1385,f445,f191,f186]) ).
fof(f445,plain,
( spl17_49
<=> ! [X0,X1] :
( function(relation_rng_restriction(X0,X1))
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_49])]) ).
fof(f1390,plain,
( ~ function(sK2)
| ~ relation(sK2)
| ~ spl17_49
| spl17_151 ),
inference(resolution,[],[f1387,f446]) ).
fof(f446,plain,
( ! [X0,X1] :
( function(relation_rng_restriction(X0,X1))
| ~ function(X1)
| ~ relation(X1) )
| ~ spl17_49 ),
inference(avatar_component_clause,[],[f445]) ).
fof(f1387,plain,
( ~ function(relation_rng_restriction(sK1,sK2))
| spl17_151 ),
inference(avatar_component_clause,[],[f1385]) ).
fof(f1517,plain,
( spl17_158
| ~ spl17_44
| ~ spl17_92 ),
inference(avatar_split_clause,[],[f793,f743,f406,f1515]) ).
fof(f793,plain,
( ! [X0,X1] :
( subset(powerset(X0),X1)
| subset(sK8(powerset(X0),X1),X0) )
| ~ spl17_44
| ~ spl17_92 ),
inference(resolution,[],[f744,f407]) ).
fof(f1415,plain,
( spl17_157
| ~ spl17_35
| ~ spl17_103 ),
inference(avatar_split_clause,[],[f871,f861,f352,f1413]) ).
fof(f1413,plain,
( spl17_157
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(X0)
| ~ empty(relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_157])]) ).
fof(f871,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(X0)
| ~ empty(relation_dom(X2)) )
| ~ spl17_35
| ~ spl17_103 ),
inference(resolution,[],[f862,f353]) ).
fof(f1411,plain,
( spl17_156
| ~ spl17_29
| ~ spl17_91 ),
inference(avatar_split_clause,[],[f777,f739,f327,f1409]) ).
fof(f777,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_rng(relation_rng(X1)) = X0
| ~ empty(X1) )
| ~ spl17_29
| ~ spl17_91 ),
inference(resolution,[],[f740,f328]) ).
fof(f1407,plain,
( ~ spl17_1
| ~ spl17_37
| spl17_150 ),
inference(avatar_split_clause,[],[f1389,f1381,f376,f186]) ).
fof(f376,plain,
( spl17_37
<=> ! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_37])]) ).
fof(f1389,plain,
( ~ relation(sK2)
| ~ spl17_37
| spl17_150 ),
inference(resolution,[],[f1383,f377]) ).
fof(f377,plain,
( ! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) )
| ~ spl17_37 ),
inference(avatar_component_clause,[],[f376]) ).
fof(f1383,plain,
( ~ relation(relation_rng_restriction(sK1,sK2))
| spl17_150 ),
inference(avatar_component_clause,[],[f1381]) ).
fof(f1406,plain,
( spl17_155
| ~ spl17_31
| ~ spl17_91 ),
inference(avatar_split_clause,[],[f776,f739,f335,f1404]) ).
fof(f776,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_rng(relation_dom(X1)) = X0
| ~ empty(X1) )
| ~ spl17_31
| ~ spl17_91 ),
inference(resolution,[],[f740,f336]) ).
fof(f1402,plain,
( spl17_154
| ~ spl17_29
| ~ spl17_90 ),
inference(avatar_split_clause,[],[f761,f735,f327,f1400]) ).
fof(f761,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_dom(relation_rng(X1)) = X0
| ~ empty(X1) )
| ~ spl17_29
| ~ spl17_90 ),
inference(resolution,[],[f736,f328]) ).
fof(f1398,plain,
( spl17_153
| ~ spl17_31
| ~ spl17_90 ),
inference(avatar_split_clause,[],[f760,f735,f335,f1396]) ).
fof(f760,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_dom(relation_dom(X1)) = X0
| ~ empty(X1) )
| ~ spl17_31
| ~ spl17_90 ),
inference(resolution,[],[f736,f336]) ).
fof(f1394,plain,
( spl17_152
| ~ spl17_53
| ~ spl17_85 ),
inference(avatar_split_clause,[],[f708,f679,f472,f1392]) ).
fof(f679,plain,
( spl17_85
<=> ! [X0] :
( subset(sK3(X0),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_85])]) ).
fof(f708,plain,
( ! [X0,X1] :
( empty(X0)
| ~ in(X1,sK3(X0))
| in(X1,X0) )
| ~ spl17_53
| ~ spl17_85 ),
inference(resolution,[],[f680,f473]) ).
fof(f680,plain,
( ! [X0] :
( subset(sK3(X0),X0)
| empty(X0) )
| ~ spl17_85 ),
inference(avatar_component_clause,[],[f679]) ).
fof(f1388,plain,
( spl17_149
| ~ spl17_150
| ~ spl17_151
| ~ spl17_1
| ~ spl17_2
| spl17_22
| ~ spl17_122 ),
inference(avatar_split_clause,[],[f1046,f1043,f288,f191,f186,f1385,f1381,f1377]) ).
fof(f1046,plain,
( ~ function(sK2)
| ~ relation(sK2)
| ~ function(relation_rng_restriction(sK1,sK2))
| ~ relation(relation_rng_restriction(sK1,sK2))
| apply(sK2,sK8(relation_dom(relation_rng_restriction(sK1,sK2)),relation_dom(sK2))) = apply(relation_rng_restriction(sK1,sK2),sK8(relation_dom(relation_rng_restriction(sK1,sK2)),relation_dom(sK2)))
| spl17_22
| ~ spl17_122 ),
inference(resolution,[],[f1044,f290]) ).
fof(f1369,plain,
( spl17_148
| ~ spl17_53
| ~ spl17_78 ),
inference(avatar_split_clause,[],[f660,f635,f472,f1367]) ).
fof(f635,plain,
( spl17_78
<=> ! [X0] : subset(sK4(powerset(X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_78])]) ).
fof(f660,plain,
( ! [X0,X1] :
( ~ in(X0,sK4(powerset(X1)))
| in(X0,X1) )
| ~ spl17_53
| ~ spl17_78 ),
inference(resolution,[],[f636,f473]) ).
fof(f636,plain,
( ! [X0] : subset(sK4(powerset(X0)),X0)
| ~ spl17_78 ),
inference(avatar_component_clause,[],[f635]) ).
fof(f1365,plain,
( ~ spl17_147
| ~ spl17_38
| ~ spl17_128 ),
inference(avatar_split_clause,[],[f1120,f1110,f380,f1362]) ).
fof(f1362,plain,
( spl17_147
<=> in(relation_rng(sK2),sK4(relation_rng(relation_rng_restriction(sK1,sK2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_147])]) ).
fof(f1110,plain,
( spl17_128
<=> in(sK4(relation_rng(relation_rng_restriction(sK1,sK2))),relation_rng(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_128])]) ).
fof(f1120,plain,
( ~ in(relation_rng(sK2),sK4(relation_rng(relation_rng_restriction(sK1,sK2))))
| ~ spl17_38
| ~ spl17_128 ),
inference(resolution,[],[f1112,f381]) ).
fof(f1112,plain,
( in(sK4(relation_rng(relation_rng_restriction(sK1,sK2))),relation_rng(sK2))
| ~ spl17_128 ),
inference(avatar_component_clause,[],[f1110]) ).
fof(f1343,plain,
( spl17_146
| ~ spl17_66
| ~ spl17_116 ),
inference(avatar_split_clause,[],[f970,f948,f568,f1341]) ).
fof(f970,plain,
( ! [X0,X1] :
( element(sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1),relation_dom(X1))
| sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1)
| in(apply(X0,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1)),relation_rng(sK2)) )
| ~ spl17_66
| ~ spl17_116 ),
inference(resolution,[],[f949,f569]) ).
fof(f1339,plain,
( spl17_145
| ~ spl17_61
| ~ spl17_66 ),
inference(avatar_split_clause,[],[f572,f568,f530,f1337]) ).
fof(f572,plain,
( ! [X0,X1] :
( in(apply(X0,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1)),relation_rng(sK2))
| in(sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1),relation_dom(X1))
| sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1) )
| ~ spl17_61
| ~ spl17_66 ),
inference(resolution,[],[f569,f531]) ).
fof(f1254,plain,
( spl17_144
| ~ spl17_82
| ~ spl17_107 ),
inference(avatar_split_clause,[],[f903,f889,f650,f1252]) ).
fof(f1252,plain,
( spl17_144
<=> ! [X0,X1] :
( sP0(sK10,X0,X1)
| ~ empty(relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_144])]) ).
fof(f903,plain,
( ! [X0,X1] :
( sP0(sK10,X0,X1)
| ~ empty(relation_dom(X1)) )
| ~ spl17_82
| ~ spl17_107 ),
inference(resolution,[],[f890,f651]) ).
fof(f1250,plain,
( spl17_143
| ~ spl17_35
| ~ spl17_101 ),
inference(avatar_split_clause,[],[f852,f846,f352,f1248]) ).
fof(f852,plain,
( ! [X0,X1] :
( sP0(X0,X1,X1)
| ~ empty(relation_dom(X1)) )
| ~ spl17_35
| ~ spl17_101 ),
inference(resolution,[],[f847,f353]) ).
fof(f1246,plain,
( spl17_142
| ~ spl17_50
| ~ spl17_89 ),
inference(avatar_split_clause,[],[f733,f725,f449,f1244]) ).
fof(f1244,plain,
( spl17_142
<=> ! [X0,X1] :
( ~ empty(X0)
| subset(sK4(powerset(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_142])]) ).
fof(f733,plain,
( ! [X0,X1] :
( ~ empty(X0)
| subset(sK4(powerset(X0)),X1) )
| ~ spl17_50
| ~ spl17_89 ),
inference(resolution,[],[f726,f450]) ).
fof(f1242,plain,
( spl17_141
| ~ spl17_29
| ~ spl17_84 ),
inference(avatar_split_clause,[],[f699,f675,f327,f1240]) ).
fof(f699,plain,
( ! [X0] :
( sK10 = relation_dom(relation_rng(X0))
| ~ empty(X0) )
| ~ spl17_29
| ~ spl17_84 ),
inference(resolution,[],[f676,f328]) ).
fof(f1238,plain,
( spl17_140
| ~ spl17_31
| ~ spl17_84 ),
inference(avatar_split_clause,[],[f698,f675,f335,f1236]) ).
fof(f698,plain,
( ! [X0] :
( sK10 = relation_dom(relation_dom(X0))
| ~ empty(X0) )
| ~ spl17_31
| ~ spl17_84 ),
inference(resolution,[],[f676,f336]) ).
fof(f1234,plain,
( spl17_139
| ~ spl17_29
| ~ spl17_83 ),
inference(avatar_split_clause,[],[f688,f671,f327,f1232]) ).
fof(f688,plain,
( ! [X0] :
( sK10 = relation_rng(relation_rng(X0))
| ~ empty(X0) )
| ~ spl17_29
| ~ spl17_83 ),
inference(resolution,[],[f672,f328]) ).
fof(f1222,plain,
( spl17_138
| ~ spl17_24
| ~ spl17_129 ),
inference(avatar_split_clause,[],[f1146,f1114,f297,f1219]) ).
fof(f1219,plain,
( spl17_138
<=> function(relation_rng(relation_rng_restriction(sK1,sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_138])]) ).
fof(f1114,plain,
( spl17_129
<=> empty(relation_rng(relation_rng_restriction(sK1,sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_129])]) ).
fof(f1146,plain,
( function(relation_rng(relation_rng_restriction(sK1,sK2)))
| ~ spl17_24
| ~ spl17_129 ),
inference(resolution,[],[f1116,f298]) ).
fof(f1116,plain,
( empty(relation_rng(relation_rng_restriction(sK1,sK2)))
| ~ spl17_129 ),
inference(avatar_component_clause,[],[f1114]) ).
fof(f1217,plain,
( spl17_137
| ~ spl17_31
| ~ spl17_83 ),
inference(avatar_split_clause,[],[f687,f671,f335,f1215]) ).
fof(f687,plain,
( ! [X0] :
( sK10 = relation_rng(relation_dom(X0))
| ~ empty(X0) )
| ~ spl17_31
| ~ spl17_83 ),
inference(resolution,[],[f672,f336]) ).
fof(f1203,plain,
( spl17_136
| ~ spl17_86
| ~ spl17_89 ),
inference(avatar_split_clause,[],[f732,f725,f683,f1201]) ).
fof(f732,plain,
( ! [X0] :
( ~ empty(X0)
| empty(sK4(powerset(X0))) )
| ~ spl17_86
| ~ spl17_89 ),
inference(resolution,[],[f726,f684]) ).
fof(f1199,plain,
( spl17_135
| ~ spl17_38
| ~ spl17_86 ),
inference(avatar_split_clause,[],[f715,f683,f380,f1197]) ).
fof(f1197,plain,
( spl17_135
<=> ! [X0] :
( empty(X0)
| ~ in(X0,sK4(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_135])]) ).
fof(f715,plain,
( ! [X0] :
( empty(X0)
| ~ in(X0,sK4(X0)) )
| ~ spl17_38
| ~ spl17_86 ),
inference(resolution,[],[f684,f381]) ).
fof(f1194,plain,
( spl17_134
| ~ spl17_66
| ~ spl17_107 ),
inference(avatar_split_clause,[],[f898,f889,f568,f1192]) ).
fof(f898,plain,
( ! [X0,X1] :
( sP0(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1)
| ~ empty(relation_dom(X1))
| in(apply(X0,sK6(relation_rng(relation_rng_restriction(sK1,sK2)),X0,X1)),relation_rng(sK2)) )
| ~ spl17_66
| ~ spl17_107 ),
inference(resolution,[],[f890,f569]) ).
fof(f1144,plain,
( spl17_133
| ~ spl17_39
| ~ spl17_128 ),
inference(avatar_split_clause,[],[f1119,f1110,f384,f1141]) ).
fof(f1141,plain,
( spl17_133
<=> element(sK4(relation_rng(relation_rng_restriction(sK1,sK2))),relation_rng(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_133])]) ).
fof(f1119,plain,
( element(sK4(relation_rng(relation_rng_restriction(sK1,sK2))),relation_rng(sK2))
| ~ spl17_39
| ~ spl17_128 ),
inference(resolution,[],[f1112,f385]) ).
fof(f1135,plain,
( spl17_132
| ~ spl17_3
| ~ spl17_69
| ~ spl17_84 ),
inference(avatar_split_clause,[],[f704,f675,f584,f196,f1132]) ).
fof(f704,plain,
( sK10 = relation_dom(sK10)
| ~ spl17_3
| ~ spl17_69
| ~ spl17_84 ),
inference(forward_demodulation,[],[f697,f586]) ).
fof(f697,plain,
( sK10 = relation_dom(empty_set)
| ~ spl17_3
| ~ spl17_84 ),
inference(resolution,[],[f676,f198]) ).
fof(f1130,plain,
( spl17_131
| ~ spl17_3
| ~ spl17_69
| ~ spl17_83 ),
inference(avatar_split_clause,[],[f693,f671,f584,f196,f1127]) ).
fof(f693,plain,
( sK10 = relation_rng(sK10)
| ~ spl17_3
| ~ spl17_69
| ~ spl17_83 ),
inference(forward_demodulation,[],[f686,f586]) ).
fof(f686,plain,
( sK10 = relation_rng(empty_set)
| ~ spl17_3
| ~ spl17_83 ),
inference(resolution,[],[f672,f198]) ).
fof(f1125,plain,
( spl17_130
| ~ spl17_34
| ~ spl17_74 ),
inference(avatar_split_clause,[],[f624,f617,f348,f1123]) ).
fof(f1123,plain,
( spl17_130
<=> ! [X0] : element(sK10,powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_130])]) ).
fof(f348,plain,
( spl17_34
<=> ! [X0] : element(sK5(X0),powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_34])]) ).
fof(f617,plain,
( spl17_74
<=> ! [X0] : sK5(X0) = sK10 ),
introduced(avatar_definition,[new_symbols(naming,[spl17_74])]) ).
fof(f624,plain,
( ! [X0] : element(sK10,powerset(X0))
| ~ spl17_34
| ~ spl17_74 ),
inference(superposition,[],[f349,f618]) ).
fof(f618,plain,
( ! [X0] : sK5(X0) = sK10
| ~ spl17_74 ),
inference(avatar_component_clause,[],[f617]) ).
fof(f349,plain,
( ! [X0] : element(sK5(X0),powerset(X0))
| ~ spl17_34 ),
inference(avatar_component_clause,[],[f348]) ).
fof(f1117,plain,
( spl17_128
| spl17_129
| ~ spl17_66
| ~ spl17_86 ),
inference(avatar_split_clause,[],[f718,f683,f568,f1114,f1110]) ).
fof(f718,plain,
( empty(relation_rng(relation_rng_restriction(sK1,sK2)))
| in(sK4(relation_rng(relation_rng_restriction(sK1,sK2))),relation_rng(sK2))
| ~ spl17_66
| ~ spl17_86 ),
inference(resolution,[],[f684,f569]) ).
fof(f1102,plain,
( spl17_127
| ~ spl17_23
| ~ spl17_96 ),
inference(avatar_split_clause,[],[f816,f806,f292,f1100]) ).
fof(f292,plain,
( spl17_23
<=> subset(relation_rng(relation_rng_restriction(sK1,sK2)),relation_rng(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_23])]) ).
fof(f816,plain,
( ! [X0] :
( ~ in(X0,relation_rng(relation_rng_restriction(sK1,sK2)))
| element(X0,relation_rng(sK2)) )
| ~ spl17_23
| ~ spl17_96 ),
inference(resolution,[],[f807,f293]) ).
fof(f293,plain,
( subset(relation_rng(relation_rng_restriction(sK1,sK2)),relation_rng(sK2))
| ~ spl17_23 ),
inference(avatar_component_clause,[],[f292]) ).
fof(f1092,plain,
( spl17_126
| ~ spl17_61
| ~ spl17_64 ),
inference(avatar_split_clause,[],[f560,f553,f530,f1090]) ).
fof(f560,plain,
( ! [X2,X3,X0,X1] :
( apply(X0,apply(X1,sK6(relation_dom(relation_rng_restriction(X2,X0)),X1,X3))) = apply(relation_rng_restriction(X2,X0),apply(X1,sK6(relation_dom(relation_rng_restriction(X2,X0)),X1,X3)))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X2,X0))
| ~ relation(relation_rng_restriction(X2,X0))
| in(sK6(relation_dom(relation_rng_restriction(X2,X0)),X1,X3),relation_dom(X3))
| sP0(relation_dom(relation_rng_restriction(X2,X0)),X1,X3) )
| ~ spl17_61
| ~ spl17_64 ),
inference(resolution,[],[f554,f531]) ).
fof(f1073,plain,
( spl17_125
| ~ spl17_61
| ~ spl17_64 ),
inference(avatar_split_clause,[],[f557,f553,f530,f1071]) ).
fof(f557,plain,
( ! [X2,X3,X0,X1] :
( apply(X0,sK6(X1,X2,relation_rng_restriction(X3,X0))) = apply(relation_rng_restriction(X3,X0),sK6(X1,X2,relation_rng_restriction(X3,X0)))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X3,X0))
| ~ relation(relation_rng_restriction(X3,X0))
| in(apply(X2,sK6(X1,X2,relation_rng_restriction(X3,X0))),X1)
| sP0(X1,X2,relation_rng_restriction(X3,X0)) )
| ~ spl17_61
| ~ spl17_64 ),
inference(resolution,[],[f554,f531]) ).
fof(f1057,plain,
( spl17_124
| ~ spl17_59
| ~ spl17_64 ),
inference(avatar_split_clause,[],[f559,f553,f513,f1055]) ).
fof(f559,plain,
( ! [X2,X3,X0,X1] :
( apply(X0,sK6(X1,relation_rng_restriction(X2,X0),X3)) = apply(relation_rng_restriction(X2,X0),sK6(X1,relation_rng_restriction(X2,X0),X3))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X2,X0))
| ~ relation(relation_rng_restriction(X2,X0))
| in(sK6(X1,relation_rng_restriction(X2,X0),X3),relation_dom(X3))
| sP0(X1,relation_rng_restriction(X2,X0),X3) )
| ~ spl17_59
| ~ spl17_64 ),
inference(resolution,[],[f554,f514]) ).
fof(f1053,plain,
( spl17_123
| ~ spl17_59
| ~ spl17_64 ),
inference(avatar_split_clause,[],[f558,f553,f513,f1051]) ).
fof(f558,plain,
( ! [X2,X3,X0,X1] :
( apply(X0,sK6(X1,X2,relation_rng_restriction(X3,X0))) = apply(relation_rng_restriction(X3,X0),sK6(X1,X2,relation_rng_restriction(X3,X0)))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X3,X0))
| ~ relation(relation_rng_restriction(X3,X0))
| in(sK6(X1,X2,relation_rng_restriction(X3,X0)),relation_dom(X2))
| sP0(X1,X2,relation_rng_restriction(X3,X0)) )
| ~ spl17_59
| ~ spl17_64 ),
inference(resolution,[],[f554,f514]) ).
fof(f1045,plain,
( spl17_122
| ~ spl17_50
| ~ spl17_64 ),
inference(avatar_split_clause,[],[f556,f553,f449,f1043]) ).
fof(f556,plain,
( ! [X2,X0,X1] :
( apply(X0,sK8(relation_dom(relation_rng_restriction(X1,X0)),X2)) = apply(relation_rng_restriction(X1,X0),sK8(relation_dom(relation_rng_restriction(X1,X0)),X2))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| subset(relation_dom(relation_rng_restriction(X1,X0)),X2) )
| ~ spl17_50
| ~ spl17_64 ),
inference(resolution,[],[f554,f450]) ).
fof(f1024,plain,
( ~ spl17_121
| ~ spl17_29
| spl17_109 ),
inference(avatar_split_clause,[],[f951,f910,f327,f1021]) ).
fof(f1021,plain,
( spl17_121
<=> empty(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_121])]) ).
fof(f951,plain,
( ~ empty(sK2)
| ~ spl17_29
| spl17_109 ),
inference(resolution,[],[f912,f328]) ).
fof(f912,plain,
( ~ empty(relation_rng(sK2))
| spl17_109 ),
inference(avatar_component_clause,[],[f910]) ).
fof(f1019,plain,
( spl17_120
| ~ spl17_58
| ~ spl17_61 ),
inference(avatar_split_clause,[],[f536,f530,f507,f1017]) ).
fof(f536,plain,
( ! [X2,X3,X0,X1] :
( in(sK6(X1,X0,X2),relation_dom(X2))
| sP0(X1,X0,X2)
| in(sK6(X1,X0,X2),relation_dom(X3))
| ~ in(sK6(X1,X0,X2),relation_dom(X0))
| ~ sP0(X1,X0,X3) )
| ~ spl17_58
| ~ spl17_61 ),
inference(resolution,[],[f531,f508]) ).
fof(f1000,plain,
( spl17_119
| ~ spl17_57
| ~ spl17_60 ),
inference(avatar_split_clause,[],[f527,f517,f503,f998]) ).
fof(f503,plain,
( spl17_57
<=> ! [X2,X4,X0,X1] :
( in(apply(X1,X4),X0)
| ~ in(X4,relation_dom(X2))
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_57])]) ).
fof(f517,plain,
( spl17_60
<=> ! [X2,X0] :
( sP0(X0,X2,relation_rng_restriction(X0,X2))
| ~ function(X2)
| ~ relation(X2)
| ~ function(relation_rng_restriction(X0,X2))
| ~ relation(relation_rng_restriction(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_60])]) ).
fof(f527,plain,
( ! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ in(X2,relation_dom(relation_rng_restriction(X1,X0)))
| in(apply(X0,X2),X1) )
| ~ spl17_57
| ~ spl17_60 ),
inference(resolution,[],[f518,f504]) ).
fof(f504,plain,
( ! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| ~ in(X4,relation_dom(X2))
| in(apply(X1,X4),X0) )
| ~ spl17_57 ),
inference(avatar_component_clause,[],[f503]) ).
fof(f518,plain,
( ! [X2,X0] :
( sP0(X0,X2,relation_rng_restriction(X0,X2))
| ~ function(X2)
| ~ relation(X2)
| ~ function(relation_rng_restriction(X0,X2))
| ~ relation(relation_rng_restriction(X0,X2)) )
| ~ spl17_60 ),
inference(avatar_component_clause,[],[f517]) ).
fof(f981,plain,
( spl17_118
| ~ spl17_56
| ~ spl17_60 ),
inference(avatar_split_clause,[],[f528,f517,f499,f979]) ).
fof(f499,plain,
( spl17_56
<=> ! [X4,X0,X1,X2] :
( in(X4,relation_dom(X1))
| ~ in(X4,relation_dom(X2))
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_56])]) ).
fof(f528,plain,
( ! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ in(X2,relation_dom(relation_rng_restriction(X1,X0)))
| in(X2,relation_dom(X0)) )
| ~ spl17_56
| ~ spl17_60 ),
inference(resolution,[],[f518,f500]) ).
fof(f500,plain,
( ! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| ~ in(X4,relation_dom(X2))
| in(X4,relation_dom(X1)) )
| ~ spl17_56 ),
inference(avatar_component_clause,[],[f499]) ).
fof(f955,plain,
( spl17_117
| ~ spl17_38
| ~ spl17_61 ),
inference(avatar_split_clause,[],[f538,f530,f380,f953]) ).
fof(f538,plain,
( ! [X2,X0,X1] :
( in(apply(X1,sK6(X0,X1,X2)),X0)
| sP0(X0,X1,X2)
| ~ in(relation_dom(X2),sK6(X0,X1,X2)) )
| ~ spl17_38
| ~ spl17_61 ),
inference(resolution,[],[f531,f381]) ).
fof(f950,plain,
( spl17_116
| ~ spl17_39
| ~ spl17_61 ),
inference(avatar_split_clause,[],[f537,f530,f384,f948]) ).
fof(f537,plain,
( ! [X2,X0,X1] :
( in(apply(X1,sK6(X0,X1,X2)),X0)
| sP0(X0,X1,X2)
| element(sK6(X0,X1,X2),relation_dom(X2)) )
| ~ spl17_39
| ~ spl17_61 ),
inference(resolution,[],[f531,f385]) ).
fof(f946,plain,
( spl17_115
| ~ spl17_38
| ~ spl17_61 ),
inference(avatar_split_clause,[],[f534,f530,f380,f944]) ).
fof(f944,plain,
( spl17_115
<=> ! [X2,X0,X1] :
( in(sK6(X1,X0,X2),relation_dom(X2))
| sP0(X1,X0,X2)
| ~ in(X1,apply(X0,sK6(X1,X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_115])]) ).
fof(f534,plain,
( ! [X2,X0,X1] :
( in(sK6(X1,X0,X2),relation_dom(X2))
| sP0(X1,X0,X2)
| ~ in(X1,apply(X0,sK6(X1,X0,X2))) )
| ~ spl17_38
| ~ spl17_61 ),
inference(resolution,[],[f531,f381]) ).
fof(f942,plain,
( spl17_114
| ~ spl17_39
| ~ spl17_61 ),
inference(avatar_split_clause,[],[f533,f530,f384,f940]) ).
fof(f533,plain,
( ! [X2,X0,X1] :
( in(sK6(X1,X0,X2),relation_dom(X2))
| sP0(X1,X0,X2)
| element(apply(X0,sK6(X1,X0,X2)),X1) )
| ~ spl17_39
| ~ spl17_61 ),
inference(resolution,[],[f531,f385]) ).
fof(f928,plain,
( spl17_113
| ~ spl17_38
| ~ spl17_59 ),
inference(avatar_split_clause,[],[f524,f513,f380,f926]) ).
fof(f524,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),relation_dom(X2))
| sP0(X0,X1,X2)
| ~ in(relation_dom(X1),sK6(X0,X1,X2)) )
| ~ spl17_38
| ~ spl17_59 ),
inference(resolution,[],[f514,f381]) ).
fof(f924,plain,
( spl17_112
| ~ spl17_39
| ~ spl17_59 ),
inference(avatar_split_clause,[],[f523,f513,f384,f922]) ).
fof(f523,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),relation_dom(X2))
| sP0(X0,X1,X2)
| element(sK6(X0,X1,X2),relation_dom(X1)) )
| ~ spl17_39
| ~ spl17_59 ),
inference(resolution,[],[f514,f385]) ).
fof(f920,plain,
( spl17_111
| ~ spl17_38
| ~ spl17_59 ),
inference(avatar_split_clause,[],[f521,f513,f380,f918]) ).
fof(f521,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),relation_dom(X1))
| sP0(X0,X1,X2)
| ~ in(relation_dom(X2),sK6(X0,X1,X2)) )
| ~ spl17_38
| ~ spl17_59 ),
inference(resolution,[],[f514,f381]) ).
fof(f916,plain,
( ~ spl17_109
| spl17_110
| ~ spl17_23
| ~ spl17_94 ),
inference(avatar_split_clause,[],[f798,f751,f292,f914,f910]) ).
fof(f914,plain,
( spl17_110
<=> ! [X0] : ~ in(X0,relation_rng(relation_rng_restriction(sK1,sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_110])]) ).
fof(f798,plain,
( ! [X0] :
( ~ in(X0,relation_rng(relation_rng_restriction(sK1,sK2)))
| ~ empty(relation_rng(sK2)) )
| ~ spl17_23
| ~ spl17_94 ),
inference(resolution,[],[f752,f293]) ).
fof(f908,plain,
( spl17_108
| ~ spl17_39
| ~ spl17_59 ),
inference(avatar_split_clause,[],[f520,f513,f384,f906]) ).
fof(f520,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),relation_dom(X1))
| sP0(X0,X1,X2)
| element(sK6(X0,X1,X2),relation_dom(X2)) )
| ~ spl17_39
| ~ spl17_59 ),
inference(resolution,[],[f514,f385]) ).
fof(f891,plain,
( spl17_107
| ~ spl17_35
| ~ spl17_61 ),
inference(avatar_split_clause,[],[f539,f530,f352,f889]) ).
fof(f539,plain,
( ! [X2,X0,X1] :
( in(apply(X1,sK6(X0,X1,X2)),X0)
| sP0(X0,X1,X2)
| ~ empty(relation_dom(X2)) )
| ~ spl17_35
| ~ spl17_61 ),
inference(resolution,[],[f531,f353]) ).
fof(f879,plain,
( spl17_106
| ~ spl17_35
| ~ spl17_59 ),
inference(avatar_split_clause,[],[f525,f513,f352,f877]) ).
fof(f525,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),relation_dom(X2))
| sP0(X0,X1,X2)
| ~ empty(relation_dom(X1)) )
| ~ spl17_35
| ~ spl17_59 ),
inference(resolution,[],[f514,f353]) ).
fof(f875,plain,
( spl17_105
| ~ spl17_35
| ~ spl17_59 ),
inference(avatar_split_clause,[],[f522,f513,f352,f873]) ).
fof(f522,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),relation_dom(X1))
| sP0(X0,X1,X2)
| ~ empty(relation_dom(X2)) )
| ~ spl17_35
| ~ spl17_59 ),
inference(resolution,[],[f514,f353]) ).
fof(f867,plain,
( spl17_104
| ~ spl17_65 ),
inference(avatar_split_clause,[],[f566,f562,f865]) ).
fof(f562,plain,
( spl17_65
<=> ! [X2,X0,X1] :
( relation_rng_restriction(X0,X2) = X1
| apply(X2,sK7(X1,X2)) != apply(X1,sK7(X1,X2))
| ~ sP0(X0,X2,X1)
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_65])]) ).
fof(f566,plain,
( ! [X0,X1] :
( relation_rng_restriction(X0,X1) = X1
| ~ sP0(X0,X1,X1)
| ~ function(X1)
| ~ relation(X1) )
| ~ spl17_65 ),
inference(duplicate_literal_removal,[],[f565]) ).
fof(f565,plain,
( ! [X0,X1] :
( relation_rng_restriction(X0,X1) = X1
| ~ sP0(X0,X1,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X1) )
| ~ spl17_65 ),
inference(equality_resolution,[],[f563]) ).
fof(f563,plain,
( ! [X2,X0,X1] :
( apply(X2,sK7(X1,X2)) != apply(X1,sK7(X1,X2))
| relation_rng_restriction(X0,X2) = X1
| ~ sP0(X0,X2,X1)
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) )
| ~ spl17_65 ),
inference(avatar_component_clause,[],[f562]) ).
fof(f863,plain,
( spl17_103
| ~ spl17_35
| ~ spl17_61 ),
inference(avatar_split_clause,[],[f535,f530,f352,f861]) ).
fof(f535,plain,
( ! [X2,X0,X1] :
( in(sK6(X1,X0,X2),relation_dom(X2))
| sP0(X1,X0,X2)
| ~ empty(X1) )
| ~ spl17_35
| ~ spl17_61 ),
inference(resolution,[],[f531,f353]) ).
fof(f856,plain,
( spl17_102
| ~ spl17_52
| ~ spl17_53 ),
inference(avatar_split_clause,[],[f481,f472,f468,f854]) ).
fof(f481,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| in(X0,relation_rng(X2))
| ~ relation(X2) )
| ~ spl17_52
| ~ spl17_53 ),
inference(resolution,[],[f473,f469]) ).
fof(f848,plain,
( spl17_101
| ~ spl17_59 ),
inference(avatar_split_clause,[],[f526,f513,f846]) ).
fof(f526,plain,
( ! [X0,X1] :
( in(sK6(X0,X1,X1),relation_dom(X1))
| sP0(X0,X1,X1) )
| ~ spl17_59 ),
inference(factoring,[],[f514]) ).
fof(f835,plain,
( spl17_100
| ~ spl17_40
| ~ spl17_47 ),
inference(avatar_split_clause,[],[f457,f436,f388,f833]) ).
fof(f388,plain,
( spl17_40
<=> ! [X0] :
( element(sK3(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_40])]) ).
fof(f457,plain,
( ! [X0] :
( empty(powerset(X0))
| in(sK3(X0),powerset(X0))
| empty(X0) )
| ~ spl17_40
| ~ spl17_47 ),
inference(resolution,[],[f437,f389]) ).
fof(f389,plain,
( ! [X0] :
( element(sK3(X0),powerset(X0))
| empty(X0) )
| ~ spl17_40 ),
inference(avatar_component_clause,[],[f388]) ).
fof(f831,plain,
( spl17_99
| ~ spl17_45
| ~ spl17_47 ),
inference(avatar_split_clause,[],[f456,f436,f410,f829]) ).
fof(f410,plain,
( spl17_45
<=> ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_45])]) ).
fof(f456,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| in(X1,powerset(X0))
| ~ subset(X1,X0) )
| ~ spl17_45
| ~ spl17_47 ),
inference(resolution,[],[f437,f411]) ).
fof(f411,plain,
( ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) )
| ~ spl17_45 ),
inference(avatar_component_clause,[],[f410]) ).
fof(f824,plain,
( ~ spl17_98
| ~ spl17_31
| spl17_87 ),
inference(avatar_split_clause,[],[f754,f710,f335,f821]) ).
fof(f821,plain,
( spl17_98
<=> empty(relation_rng_restriction(sK1,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_98])]) ).
fof(f754,plain,
( ~ empty(relation_rng_restriction(sK1,sK2))
| ~ spl17_31
| spl17_87 ),
inference(resolution,[],[f712,f336]) ).
fof(f812,plain,
( spl17_97
| ~ spl17_40
| ~ spl17_55 ),
inference(avatar_split_clause,[],[f493,f489,f388,f810]) ).
fof(f493,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK3(X1))
| empty(X1) )
| ~ spl17_40
| ~ spl17_55 ),
inference(resolution,[],[f490,f389]) ).
fof(f808,plain,
( spl17_96
| ~ spl17_45
| ~ spl17_55 ),
inference(avatar_split_clause,[],[f492,f489,f410,f806]) ).
fof(f492,plain,
( ! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,X1) )
| ~ spl17_45
| ~ spl17_55 ),
inference(resolution,[],[f490,f411]) ).
fof(f758,plain,
( spl17_95
| ~ spl17_26
| ~ spl17_55 ),
inference(avatar_split_clause,[],[f494,f489,f305,f756]) ).
fof(f305,plain,
( spl17_26
<=> ! [X0] : element(sK4(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_26])]) ).
fof(f494,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK4(powerset(X1))) )
| ~ spl17_26
| ~ spl17_55 ),
inference(resolution,[],[f490,f306]) ).
fof(f306,plain,
( ! [X0] : element(sK4(X0),X0)
| ~ spl17_26 ),
inference(avatar_component_clause,[],[f305]) ).
fof(f753,plain,
( spl17_94
| ~ spl17_45
| ~ spl17_54 ),
inference(avatar_split_clause,[],[f482,f476,f410,f751]) ).
fof(f482,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,X2)
| ~ subset(X2,X0) )
| ~ spl17_45
| ~ spl17_54 ),
inference(resolution,[],[f477,f411]) ).
fof(f749,plain,
( spl17_93
| ~ spl17_38
| ~ spl17_50 ),
inference(avatar_split_clause,[],[f463,f449,f380,f747]) ).
fof(f747,plain,
( spl17_93
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ in(X0,sK8(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_93])]) ).
fof(f463,plain,
( ! [X0,X1] :
( subset(X0,X1)
| ~ in(X0,sK8(X0,X1)) )
| ~ spl17_38
| ~ spl17_50 ),
inference(resolution,[],[f450,f381]) ).
fof(f745,plain,
( spl17_92
| ~ spl17_39
| ~ spl17_50 ),
inference(avatar_split_clause,[],[f462,f449,f384,f743]) ).
fof(f462,plain,
( ! [X0,X1] :
( subset(X0,X1)
| element(sK8(X0,X1),X0) )
| ~ spl17_39
| ~ spl17_50 ),
inference(resolution,[],[f450,f385]) ).
fof(f741,plain,
( spl17_91
| ~ spl17_29
| ~ spl17_46 ),
inference(avatar_split_clause,[],[f427,f414,f327,f739]) ).
fof(f427,plain,
( ! [X0,X1] :
( relation_rng(X1) = X0
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl17_29
| ~ spl17_46 ),
inference(resolution,[],[f415,f328]) ).
fof(f737,plain,
( spl17_90
| ~ spl17_31
| ~ spl17_46 ),
inference(avatar_split_clause,[],[f426,f414,f335,f735]) ).
fof(f426,plain,
( ! [X0,X1] :
( relation_dom(X1) = X0
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl17_31
| ~ spl17_46 ),
inference(resolution,[],[f415,f336]) ).
fof(f727,plain,
( spl17_89
| ~ spl17_26
| ~ spl17_54 ),
inference(avatar_split_clause,[],[f484,f476,f305,f725]) ).
fof(f484,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK4(powerset(X0))) )
| ~ spl17_26
| ~ spl17_54 ),
inference(resolution,[],[f477,f306]) ).
fof(f723,plain,
( spl17_88
| ~ spl17_6
| ~ spl17_20
| ~ spl17_28
| ~ spl17_34
| ~ spl17_47 ),
inference(avatar_split_clause,[],[f461,f436,f348,f323,f280,f211,f721]) ).
fof(f721,plain,
( spl17_88
<=> ! [X0] :
( in(sK10,powerset(X0))
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_88])]) ).
fof(f461,plain,
( ! [X0] :
( in(sK10,powerset(X0))
| empty(powerset(X0)) )
| ~ spl17_6
| ~ spl17_20
| ~ spl17_28
| ~ spl17_34
| ~ spl17_47 ),
inference(forward_demodulation,[],[f460,f357]) ).
fof(f357,plain,
( empty_set = sK10
| ~ spl17_6
| ~ spl17_28 ),
inference(resolution,[],[f324,f213]) ).
fof(f460,plain,
( ! [X0] :
( in(empty_set,powerset(X0))
| empty(powerset(X0)) )
| ~ spl17_20
| ~ spl17_28
| ~ spl17_34
| ~ spl17_47 ),
inference(forward_demodulation,[],[f459,f356]) ).
fof(f356,plain,
( ! [X0] : empty_set = sK5(X0)
| ~ spl17_20
| ~ spl17_28 ),
inference(resolution,[],[f324,f281]) ).
fof(f459,plain,
( ! [X0] :
( empty(powerset(X0))
| in(sK5(X0),powerset(X0)) )
| ~ spl17_34
| ~ spl17_47 ),
inference(resolution,[],[f437,f349]) ).
fof(f713,plain,
( ~ spl17_87
| spl17_22
| ~ spl17_80 ),
inference(avatar_split_clause,[],[f668,f643,f288,f710]) ).
fof(f668,plain,
( ~ empty(relation_dom(relation_rng_restriction(sK1,sK2)))
| spl17_22
| ~ spl17_80 ),
inference(resolution,[],[f644,f290]) ).
fof(f685,plain,
( spl17_86
| ~ spl17_26
| ~ spl17_47 ),
inference(avatar_split_clause,[],[f458,f436,f305,f683]) ).
fof(f458,plain,
( ! [X0] :
( empty(X0)
| in(sK4(X0),X0) )
| ~ spl17_26
| ~ spl17_47 ),
inference(resolution,[],[f437,f306]) ).
fof(f681,plain,
( spl17_85
| ~ spl17_40
| ~ spl17_44 ),
inference(avatar_split_clause,[],[f421,f406,f388,f679]) ).
fof(f421,plain,
( ! [X0] :
( subset(sK3(X0),X0)
| empty(X0) )
| ~ spl17_40
| ~ spl17_44 ),
inference(resolution,[],[f407,f389]) ).
fof(f677,plain,
( spl17_84
| ~ spl17_6
| ~ spl17_28
| ~ spl17_31 ),
inference(avatar_split_clause,[],[f369,f335,f323,f211,f675]) ).
fof(f369,plain,
( ! [X0] :
( relation_dom(X0) = sK10
| ~ empty(X0) )
| ~ spl17_6
| ~ spl17_28
| ~ spl17_31 ),
inference(forward_demodulation,[],[f366,f357]) ).
fof(f366,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = relation_dom(X0) )
| ~ spl17_28
| ~ spl17_31 ),
inference(resolution,[],[f336,f324]) ).
fof(f673,plain,
( spl17_83
| ~ spl17_6
| ~ spl17_28
| ~ spl17_29 ),
inference(avatar_split_clause,[],[f365,f327,f323,f211,f671]) ).
fof(f365,plain,
( ! [X0] :
( relation_rng(X0) = sK10
| ~ empty(X0) )
| ~ spl17_6
| ~ spl17_28
| ~ spl17_29 ),
inference(forward_demodulation,[],[f362,f357]) ).
fof(f362,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = relation_rng(X0) )
| ~ spl17_28
| ~ spl17_29 ),
inference(resolution,[],[f328,f324]) ).
fof(f652,plain,
( spl17_81
| spl17_82
| ~ spl17_6
| ~ spl17_20
| ~ spl17_28
| ~ spl17_34
| ~ spl17_54 ),
inference(avatar_split_clause,[],[f487,f476,f348,f323,f280,f211,f650,f647]) ).
fof(f487,plain,
( ! [X0,X1] :
( ~ in(X1,sK10)
| ~ empty(X0) )
| ~ spl17_6
| ~ spl17_20
| ~ spl17_28
| ~ spl17_34
| ~ spl17_54 ),
inference(forward_demodulation,[],[f486,f357]) ).
fof(f486,plain,
( ! [X0,X1] :
( ~ in(X1,empty_set)
| ~ empty(X0) )
| ~ spl17_20
| ~ spl17_28
| ~ spl17_34
| ~ spl17_54 ),
inference(forward_demodulation,[],[f485,f356]) ).
fof(f485,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK5(X0)) )
| ~ spl17_34
| ~ spl17_54 ),
inference(resolution,[],[f477,f349]) ).
fof(f645,plain,
( spl17_80
| ~ spl17_35
| ~ spl17_50 ),
inference(avatar_split_clause,[],[f464,f449,f352,f643]) ).
fof(f464,plain,
( ! [X0,X1] :
( subset(X0,X1)
| ~ empty(X0) )
| ~ spl17_35
| ~ spl17_50 ),
inference(resolution,[],[f450,f353]) ).
fof(f641,plain,
( spl17_79
| ~ spl17_6
| ~ spl17_46 ),
inference(avatar_split_clause,[],[f429,f414,f211,f639]) ).
fof(f429,plain,
( ! [X0] :
( sK10 = X0
| ~ empty(X0) )
| ~ spl17_6
| ~ spl17_46 ),
inference(resolution,[],[f415,f213]) ).
fof(f637,plain,
( spl17_78
| ~ spl17_26
| ~ spl17_44 ),
inference(avatar_split_clause,[],[f419,f406,f305,f635]) ).
fof(f419,plain,
( ! [X0] : subset(sK4(powerset(X0)),X0)
| ~ spl17_26
| ~ spl17_44 ),
inference(resolution,[],[f407,f306]) ).
fof(f633,plain,
( spl17_77
| ~ spl17_24
| ~ spl17_31 ),
inference(avatar_split_clause,[],[f368,f335,f297,f631]) ).
fof(f631,plain,
( spl17_77
<=> ! [X0] :
( ~ empty(X0)
| function(relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_77])]) ).
fof(f368,plain,
( ! [X0] :
( ~ empty(X0)
| function(relation_dom(X0)) )
| ~ spl17_24
| ~ spl17_31 ),
inference(resolution,[],[f336,f298]) ).
fof(f629,plain,
( spl17_76
| ~ spl17_24
| ~ spl17_29 ),
inference(avatar_split_clause,[],[f364,f327,f297,f627]) ).
fof(f627,plain,
( spl17_76
<=> ! [X0] :
( ~ empty(X0)
| function(relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_76])]) ).
fof(f364,plain,
( ! [X0] :
( ~ empty(X0)
| function(relation_rng(X0)) )
| ~ spl17_24
| ~ spl17_29 ),
inference(resolution,[],[f328,f298]) ).
fof(f623,plain,
( spl17_75
| ~ spl17_50
| ~ spl17_66 ),
inference(avatar_split_clause,[],[f571,f568,f449,f621]) ).
fof(f571,plain,
( ! [X0] :
( in(sK8(relation_rng(relation_rng_restriction(sK1,sK2)),X0),relation_rng(sK2))
| subset(relation_rng(relation_rng_restriction(sK1,sK2)),X0) )
| ~ spl17_50
| ~ spl17_66 ),
inference(resolution,[],[f569,f450]) ).
fof(f619,plain,
( spl17_74
| ~ spl17_69
| ~ spl17_73 ),
inference(avatar_split_clause,[],[f615,f612,f584,f617]) ).
fof(f612,plain,
( spl17_73
<=> ! [X0] : empty_set = sK5(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_73])]) ).
fof(f615,plain,
( ! [X0] : sK5(X0) = sK10
| ~ spl17_69
| ~ spl17_73 ),
inference(forward_demodulation,[],[f613,f586]) ).
fof(f613,plain,
( ! [X0] : empty_set = sK5(X0)
| ~ spl17_73 ),
inference(avatar_component_clause,[],[f612]) ).
fof(f614,plain,
( spl17_73
| ~ spl17_20
| ~ spl17_28 ),
inference(avatar_split_clause,[],[f356,f323,f280,f612]) ).
fof(f601,plain,
( spl17_72
| ~ spl17_6
| ~ spl17_20
| ~ spl17_28
| ~ spl17_34
| ~ spl17_44 ),
inference(avatar_split_clause,[],[f423,f406,f348,f323,f280,f211,f599]) ).
fof(f599,plain,
( spl17_72
<=> ! [X0] : subset(sK10,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_72])]) ).
fof(f423,plain,
( ! [X0] : subset(sK10,X0)
| ~ spl17_6
| ~ spl17_20
| ~ spl17_28
| ~ spl17_34
| ~ spl17_44 ),
inference(forward_demodulation,[],[f422,f357]) ).
fof(f422,plain,
( ! [X0] : subset(empty_set,X0)
| ~ spl17_20
| ~ spl17_28
| ~ spl17_34
| ~ spl17_44 ),
inference(forward_demodulation,[],[f420,f356]) ).
fof(f420,plain,
( ! [X0] : subset(sK5(X0),X0)
| ~ spl17_34
| ~ spl17_44 ),
inference(resolution,[],[f407,f349]) ).
fof(f597,plain,
( spl17_71
| ~ spl17_6
| ~ spl17_17
| ~ spl17_28 ),
inference(avatar_split_clause,[],[f361,f323,f266,f211,f594]) ).
fof(f594,plain,
( spl17_71
<=> sK10 = sK16 ),
introduced(avatar_definition,[new_symbols(naming,[spl17_71])]) ).
fof(f361,plain,
( sK10 = sK16
| ~ spl17_6
| ~ spl17_17
| ~ spl17_28 ),
inference(forward_demodulation,[],[f359,f357]) ).
fof(f359,plain,
( empty_set = sK16
| ~ spl17_17
| ~ spl17_28 ),
inference(resolution,[],[f324,f268]) ).
fof(f592,plain,
( spl17_70
| ~ spl17_6
| ~ spl17_9
| ~ spl17_28 ),
inference(avatar_split_clause,[],[f360,f323,f226,f211,f589]) ).
fof(f589,plain,
( spl17_70
<=> sK10 = sK12 ),
introduced(avatar_definition,[new_symbols(naming,[spl17_70])]) ).
fof(f360,plain,
( sK10 = sK12
| ~ spl17_6
| ~ spl17_9
| ~ spl17_28 ),
inference(forward_demodulation,[],[f358,f357]) ).
fof(f358,plain,
( empty_set = sK12
| ~ spl17_9
| ~ spl17_28 ),
inference(resolution,[],[f324,f228]) ).
fof(f587,plain,
( spl17_69
| ~ spl17_6
| ~ spl17_28 ),
inference(avatar_split_clause,[],[f357,f323,f211,f584]) ).
fof(f581,plain,
( spl17_68
| ~ spl17_20
| ~ spl17_25 ),
inference(avatar_split_clause,[],[f314,f301,f280,f579]) ).
fof(f579,plain,
( spl17_68
<=> ! [X0] : relation(sK5(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_68])]) ).
fof(f314,plain,
( ! [X0] : relation(sK5(X0))
| ~ spl17_20
| ~ spl17_25 ),
inference(resolution,[],[f302,f281]) ).
fof(f576,plain,
( spl17_67
| ~ spl17_20
| ~ spl17_24 ),
inference(avatar_split_clause,[],[f309,f297,f280,f574]) ).
fof(f574,plain,
( spl17_67
<=> ! [X0] : function(sK5(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_67])]) ).
fof(f309,plain,
( ! [X0] : function(sK5(X0))
| ~ spl17_20
| ~ spl17_24 ),
inference(resolution,[],[f298,f281]) ).
fof(f570,plain,
( spl17_66
| ~ spl17_23
| ~ spl17_53 ),
inference(avatar_split_clause,[],[f511,f472,f292,f568]) ).
fof(f511,plain,
( ! [X0] :
( ~ in(X0,relation_rng(relation_rng_restriction(sK1,sK2)))
| in(X0,relation_rng(sK2)) )
| ~ spl17_23
| ~ spl17_53 ),
inference(resolution,[],[f293,f473]) ).
fof(f564,plain,
spl17_65,
inference(avatar_split_clause,[],[f159,f562]) ).
fof(f159,plain,
! [X2,X0,X1] :
( relation_rng_restriction(X0,X2) = X1
| apply(X2,sK7(X1,X2)) != apply(X1,sK7(X1,X2))
| ~ sP0(X0,X2,X1)
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f95]) ).
fof(f95,plain,
! [X0,X1] :
( ! [X2] :
( ( ( relation_rng_restriction(X0,X2) = X1
| ( apply(X2,sK7(X1,X2)) != apply(X1,sK7(X1,X2))
& in(sK7(X1,X2),relation_dom(X1)) )
| ~ sP0(X0,X2,X1) )
& ( ( ! [X4] :
( apply(X2,X4) = apply(X1,X4)
| ~ in(X4,relation_dom(X1)) )
& sP0(X0,X2,X1) )
| relation_rng_restriction(X0,X2) != X1 ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f93,f94]) ).
fof(f94,plain,
! [X1,X2] :
( ? [X3] :
( apply(X2,X3) != apply(X1,X3)
& in(X3,relation_dom(X1)) )
=> ( apply(X2,sK7(X1,X2)) != apply(X1,sK7(X1,X2))
& in(sK7(X1,X2),relation_dom(X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f93,plain,
! [X0,X1] :
( ! [X2] :
( ( ( relation_rng_restriction(X0,X2) = X1
| ? [X3] :
( apply(X2,X3) != apply(X1,X3)
& in(X3,relation_dom(X1)) )
| ~ sP0(X0,X2,X1) )
& ( ( ! [X4] :
( apply(X2,X4) = apply(X1,X4)
| ~ in(X4,relation_dom(X1)) )
& sP0(X0,X2,X1) )
| relation_rng_restriction(X0,X2) != X1 ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(rectify,[],[f92]) ).
fof(f92,plain,
! [X0,X1] :
( ! [X2] :
( ( ( relation_rng_restriction(X0,X2) = X1
| ? [X3] :
( apply(X2,X3) != apply(X1,X3)
& in(X3,relation_dom(X1)) )
| ~ sP0(X0,X2,X1) )
& ( ( ! [X3] :
( apply(X2,X3) = apply(X1,X3)
| ~ in(X3,relation_dom(X1)) )
& sP0(X0,X2,X1) )
| relation_rng_restriction(X0,X2) != X1 ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f91]) ).
fof(f91,plain,
! [X0,X1] :
( ! [X2] :
( ( ( relation_rng_restriction(X0,X2) = X1
| ? [X3] :
( apply(X2,X3) != apply(X1,X3)
& in(X3,relation_dom(X1)) )
| ~ sP0(X0,X2,X1) )
& ( ( ! [X3] :
( apply(X2,X3) = apply(X1,X3)
| ~ in(X3,relation_dom(X1)) )
& sP0(X0,X2,X1) )
| relation_rng_restriction(X0,X2) != X1 ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(nnf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0,X1] :
( ! [X2] :
( ( relation_rng_restriction(X0,X2) = X1
<=> ( ! [X3] :
( apply(X2,X3) = apply(X1,X3)
| ~ in(X3,relation_dom(X1)) )
& sP0(X0,X2,X1) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(definition_folding,[],[f69,f76]) ).
fof(f76,plain,
! [X0,X2,X1] :
( sP0(X0,X2,X1)
<=> ! [X4] :
( in(X4,relation_dom(X1))
<=> ( in(apply(X2,X4),X0)
& in(X4,relation_dom(X2)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f69,plain,
! [X0,X1] :
( ! [X2] :
( ( relation_rng_restriction(X0,X2) = X1
<=> ( ! [X3] :
( apply(X2,X3) = apply(X1,X3)
| ~ in(X3,relation_dom(X1)) )
& ! [X4] :
( in(X4,relation_dom(X1))
<=> ( in(apply(X2,X4),X0)
& in(X4,relation_dom(X2)) ) ) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f68]) ).
fof(f68,plain,
! [X0,X1] :
( ! [X2] :
( ( relation_rng_restriction(X0,X2) = X1
<=> ( ! [X3] :
( apply(X2,X3) = apply(X1,X3)
| ~ in(X3,relation_dom(X1)) )
& ! [X4] :
( in(X4,relation_dom(X1))
<=> ( in(apply(X2,X4),X0)
& in(X4,relation_dom(X2)) ) ) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( relation_rng_restriction(X0,X2) = X1
<=> ( ! [X3] :
( in(X3,relation_dom(X1))
=> apply(X2,X3) = apply(X1,X3) )
& ! [X4] :
( in(X4,relation_dom(X1))
<=> ( in(apply(X2,X4),X0)
& in(X4,relation_dom(X2)) ) ) ) ) ) ),
inference(rectify,[],[f36]) ).
fof(f36,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( relation_rng_restriction(X0,X2) = X1
<=> ( ! [X3] :
( in(X3,relation_dom(X1))
=> apply(X2,X3) = apply(X1,X3) )
& ! [X3] :
( in(X3,relation_dom(X1))
<=> ( in(apply(X2,X3),X0)
& in(X3,relation_dom(X2)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_funct_1) ).
fof(f555,plain,
spl17_64,
inference(avatar_split_clause,[],[f183,f553]) ).
fof(f183,plain,
! [X2,X0,X4] :
( apply(X2,X4) = apply(relation_rng_restriction(X0,X2),X4)
| ~ in(X4,relation_dom(relation_rng_restriction(X0,X2)))
| ~ function(X2)
| ~ relation(X2)
| ~ function(relation_rng_restriction(X0,X2))
| ~ relation(relation_rng_restriction(X0,X2)) ),
inference(equality_resolution,[],[f157]) ).
fof(f157,plain,
! [X2,X0,X1,X4] :
( apply(X2,X4) = apply(X1,X4)
| ~ in(X4,relation_dom(X1))
| relation_rng_restriction(X0,X2) != X1
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f95]) ).
fof(f549,plain,
spl17_63,
inference(avatar_split_clause,[],[f155,f547]) ).
fof(f155,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ in(apply(X1,sK6(X0,X1,X2)),X0)
| ~ in(sK6(X0,X1,X2),relation_dom(X1))
| ~ in(sK6(X0,X1,X2),relation_dom(X2)) ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ( ( ~ in(apply(X1,sK6(X0,X1,X2)),X0)
| ~ in(sK6(X0,X1,X2),relation_dom(X1))
| ~ in(sK6(X0,X1,X2),relation_dom(X2)) )
& ( ( in(apply(X1,sK6(X0,X1,X2)),X0)
& in(sK6(X0,X1,X2),relation_dom(X1)) )
| in(sK6(X0,X1,X2),relation_dom(X2)) ) ) )
& ( ! [X4] :
( ( in(X4,relation_dom(X2))
| ~ in(apply(X1,X4),X0)
| ~ in(X4,relation_dom(X1)) )
& ( ( in(apply(X1,X4),X0)
& in(X4,relation_dom(X1)) )
| ~ in(X4,relation_dom(X2)) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f88,f89]) ).
fof(f89,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(apply(X1,X3),X0)
| ~ in(X3,relation_dom(X1))
| ~ in(X3,relation_dom(X2)) )
& ( ( in(apply(X1,X3),X0)
& in(X3,relation_dom(X1)) )
| in(X3,relation_dom(X2)) ) )
=> ( ( ~ in(apply(X1,sK6(X0,X1,X2)),X0)
| ~ in(sK6(X0,X1,X2),relation_dom(X1))
| ~ in(sK6(X0,X1,X2),relation_dom(X2)) )
& ( ( in(apply(X1,sK6(X0,X1,X2)),X0)
& in(sK6(X0,X1,X2),relation_dom(X1)) )
| in(sK6(X0,X1,X2),relation_dom(X2)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f88,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ? [X3] :
( ( ~ in(apply(X1,X3),X0)
| ~ in(X3,relation_dom(X1))
| ~ in(X3,relation_dom(X2)) )
& ( ( in(apply(X1,X3),X0)
& in(X3,relation_dom(X1)) )
| in(X3,relation_dom(X2)) ) ) )
& ( ! [X4] :
( ( in(X4,relation_dom(X2))
| ~ in(apply(X1,X4),X0)
| ~ in(X4,relation_dom(X1)) )
& ( ( in(apply(X1,X4),X0)
& in(X4,relation_dom(X1)) )
| ~ in(X4,relation_dom(X2)) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f87]) ).
fof(f87,plain,
! [X0,X2,X1] :
( ( sP0(X0,X2,X1)
| ? [X4] :
( ( ~ in(apply(X2,X4),X0)
| ~ in(X4,relation_dom(X2))
| ~ in(X4,relation_dom(X1)) )
& ( ( in(apply(X2,X4),X0)
& in(X4,relation_dom(X2)) )
| in(X4,relation_dom(X1)) ) ) )
& ( ! [X4] :
( ( in(X4,relation_dom(X1))
| ~ in(apply(X2,X4),X0)
| ~ in(X4,relation_dom(X2)) )
& ( ( in(apply(X2,X4),X0)
& in(X4,relation_dom(X2)) )
| ~ in(X4,relation_dom(X1)) ) )
| ~ sP0(X0,X2,X1) ) ),
inference(flattening,[],[f86]) ).
fof(f86,plain,
! [X0,X2,X1] :
( ( sP0(X0,X2,X1)
| ? [X4] :
( ( ~ in(apply(X2,X4),X0)
| ~ in(X4,relation_dom(X2))
| ~ in(X4,relation_dom(X1)) )
& ( ( in(apply(X2,X4),X0)
& in(X4,relation_dom(X2)) )
| in(X4,relation_dom(X1)) ) ) )
& ( ! [X4] :
( ( in(X4,relation_dom(X1))
| ~ in(apply(X2,X4),X0)
| ~ in(X4,relation_dom(X2)) )
& ( ( in(apply(X2,X4),X0)
& in(X4,relation_dom(X2)) )
| ~ in(X4,relation_dom(X1)) ) )
| ~ sP0(X0,X2,X1) ) ),
inference(nnf_transformation,[],[f76]) ).
fof(f543,plain,
spl17_62,
inference(avatar_split_clause,[],[f158,f541]) ).
fof(f541,plain,
( spl17_62
<=> ! [X2,X0,X1] :
( relation_rng_restriction(X0,X2) = X1
| in(sK7(X1,X2),relation_dom(X1))
| ~ sP0(X0,X2,X1)
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_62])]) ).
fof(f158,plain,
! [X2,X0,X1] :
( relation_rng_restriction(X0,X2) = X1
| in(sK7(X1,X2),relation_dom(X1))
| ~ sP0(X0,X2,X1)
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f95]) ).
fof(f532,plain,
spl17_61,
inference(avatar_split_clause,[],[f154,f530]) ).
fof(f154,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(apply(X1,sK6(X0,X1,X2)),X0)
| in(sK6(X0,X1,X2),relation_dom(X2)) ),
inference(cnf_transformation,[],[f90]) ).
fof(f519,plain,
spl17_60,
inference(avatar_split_clause,[],[f184,f517]) ).
fof(f184,plain,
! [X2,X0] :
( sP0(X0,X2,relation_rng_restriction(X0,X2))
| ~ function(X2)
| ~ relation(X2)
| ~ function(relation_rng_restriction(X0,X2))
| ~ relation(relation_rng_restriction(X0,X2)) ),
inference(equality_resolution,[],[f156]) ).
fof(f156,plain,
! [X2,X0,X1] :
( sP0(X0,X2,X1)
| relation_rng_restriction(X0,X2) != X1
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f95]) ).
fof(f515,plain,
spl17_59,
inference(avatar_split_clause,[],[f153,f513]) ).
fof(f153,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(sK6(X0,X1,X2),relation_dom(X1))
| in(sK6(X0,X1,X2),relation_dom(X2)) ),
inference(cnf_transformation,[],[f90]) ).
fof(f510,plain,
( ~ spl17_1
| spl17_23
| ~ spl17_52 ),
inference(avatar_split_clause,[],[f479,f468,f292,f186]) ).
fof(f479,plain,
( ~ relation(sK2)
| spl17_23
| ~ spl17_52 ),
inference(resolution,[],[f469,f294]) ).
fof(f294,plain,
( ~ subset(relation_rng(relation_rng_restriction(sK1,sK2)),relation_rng(sK2))
| spl17_23 ),
inference(avatar_component_clause,[],[f292]) ).
fof(f509,plain,
spl17_58,
inference(avatar_split_clause,[],[f152,f507]) ).
fof(f152,plain,
! [X2,X0,X1,X4] :
( in(X4,relation_dom(X2))
| ~ in(apply(X1,X4),X0)
| ~ in(X4,relation_dom(X1))
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f90]) ).
fof(f505,plain,
spl17_57,
inference(avatar_split_clause,[],[f151,f503]) ).
fof(f151,plain,
! [X2,X0,X1,X4] :
( in(apply(X1,X4),X0)
| ~ in(X4,relation_dom(X2))
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f90]) ).
fof(f501,plain,
spl17_56,
inference(avatar_split_clause,[],[f150,f499]) ).
fof(f150,plain,
! [X2,X0,X1,X4] :
( in(X4,relation_dom(X1))
| ~ in(X4,relation_dom(X2))
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f90]) ).
fof(f491,plain,
spl17_55,
inference(avatar_split_clause,[],[f167,f489]) ).
fof(f167,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,[],[f32]) ).
fof(f32,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f478,plain,
spl17_54,
inference(avatar_split_clause,[],[f168,f476]) ).
fof(f168,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,[],[f33]) ).
fof(f33,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f474,plain,
spl17_53,
inference(avatar_split_clause,[],[f160,f472]) ).
fof(f160,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f99]) ).
fof(f99,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK8(X0,X1),X1)
& in(sK8(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f97,f98]) ).
fof(f98,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK8(X0,X1),X1)
& in(sK8(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f97,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f96]) ).
fof(f96,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f470,plain,
spl17_52,
inference(avatar_split_clause,[],[f144,f468]) ).
fof(f144,plain,
! [X0,X1] :
( subset(relation_rng(relation_rng_restriction(X0,X1)),relation_rng(X1))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0,X1] :
( subset(relation_rng(relation_rng_restriction(X0,X1)),relation_rng(X1))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_rng(relation_rng_restriction(X0,X1)),relation_rng(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_relat_1) ).
fof(f455,plain,
spl17_51,
inference(avatar_split_clause,[],[f162,f453]) ).
fof(f162,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK8(X0,X1),X1) ),
inference(cnf_transformation,[],[f99]) ).
fof(f451,plain,
spl17_50,
inference(avatar_split_clause,[],[f161,f449]) ).
fof(f161,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK8(X0,X1),X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f447,plain,
spl17_49,
inference(avatar_split_clause,[],[f149,f445]) ).
fof(f149,plain,
! [X0,X1] :
( function(relation_rng_restriction(X0,X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0,X1] :
( ( function(relation_rng_restriction(X0,X1))
& relation(relation_rng_restriction(X0,X1)) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f66]) ).
fof(f66,plain,
! [X0,X1] :
( ( function(relation_rng_restriction(X0,X1))
& relation(relation_rng_restriction(X0,X1)) )
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( function(relation_rng_restriction(X0,X1))
& relation(relation_rng_restriction(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_funct_1) ).
fof(f443,plain,
( spl17_48
| ~ spl17_6
| ~ spl17_25 ),
inference(avatar_split_clause,[],[f315,f301,f211,f440]) ).
fof(f315,plain,
( relation(sK10)
| ~ spl17_6
| ~ spl17_25 ),
inference(resolution,[],[f302,f213]) ).
fof(f438,plain,
spl17_47,
inference(avatar_split_clause,[],[f147,f436]) ).
fof(f147,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f64]) ).
fof(f64,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f416,plain,
spl17_46,
inference(avatar_split_clause,[],[f165,f414]) ).
fof(f165,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,[],[f39]) ).
fof(f39,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(f412,plain,
spl17_45,
inference(avatar_split_clause,[],[f164,f410]) ).
fof(f164,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f100]) ).
fof(f100,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f408,plain,
spl17_44,
inference(avatar_split_clause,[],[f163,f406]) ).
fof(f163,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f100]) ).
fof(f403,plain,
( spl17_43
| ~ spl17_9
| ~ spl17_24 ),
inference(avatar_split_clause,[],[f311,f297,f226,f400]) ).
fof(f400,plain,
( spl17_43
<=> function(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_43])]) ).
fof(f311,plain,
( function(sK12)
| ~ spl17_9
| ~ spl17_24 ),
inference(resolution,[],[f298,f228]) ).
fof(f398,plain,
spl17_42,
inference(avatar_split_clause,[],[f136,f396]) ).
fof(f396,plain,
( spl17_42
<=> ! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_42])]) ).
fof(f136,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(flattening,[],[f56]) ).
fof(f56,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/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(f394,plain,
spl17_41,
inference(avatar_split_clause,[],[f135,f392]) ).
fof(f392,plain,
( spl17_41
<=> ! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_41])]) ).
fof(f135,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(flattening,[],[f54]) ).
fof(f54,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/sandbox2/benchmark/theBenchmark.p',fc6_relat_1) ).
fof(f390,plain,
spl17_40,
inference(avatar_split_clause,[],[f126,f388]) ).
fof(f126,plain,
! [X0] :
( element(sK3(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0] :
( ( ~ empty(sK3(X0))
& element(sK3(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f48,f80]) ).
fof(f80,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( ~ empty(sK3(X0))
& element(sK3(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f48,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/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f386,plain,
spl17_39,
inference(avatar_split_clause,[],[f146,f384]) ).
fof(f146,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f382,plain,
spl17_38,
inference(avatar_split_clause,[],[f145,f380]) ).
fof(f145,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f378,plain,
spl17_37,
inference(avatar_split_clause,[],[f143,f376]) ).
fof(f143,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] :
( relation(X1)
=> relation(relation_rng_restriction(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_relat_1) ).
fof(f374,plain,
( spl17_36
| ~ spl17_6
| ~ spl17_24 ),
inference(avatar_split_clause,[],[f310,f297,f211,f371]) ).
fof(f371,plain,
( spl17_36
<=> function(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_36])]) ).
fof(f310,plain,
( function(sK10)
| ~ spl17_6
| ~ spl17_24 ),
inference(resolution,[],[f298,f213]) ).
fof(f354,plain,
spl17_35,
inference(avatar_split_clause,[],[f166,f352]) ).
fof(f166,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,[],[f35]) ).
fof(f35,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f350,plain,
spl17_34,
inference(avatar_split_clause,[],[f140,f348]) ).
fof(f140,plain,
! [X0] : element(sK5(X0),powerset(X0)),
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
! [X0] :
( empty(sK5(X0))
& element(sK5(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f23,f84]) ).
fof(f84,plain,
! [X0] :
( ? [X1] :
( empty(X1)
& element(X1,powerset(X0)) )
=> ( empty(sK5(X0))
& element(sK5(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f23,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f346,plain,
spl17_33,
inference(avatar_split_clause,[],[f134,f344]) ).
fof(f344,plain,
( spl17_33
<=> ! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_33])]) ).
fof(f134,plain,
! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f53,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/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(f342,plain,
( spl17_32
| ~ spl17_3
| ~ spl17_24 ),
inference(avatar_split_clause,[],[f308,f297,f196,f339]) ).
fof(f339,plain,
( spl17_32
<=> function(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_32])]) ).
fof(f308,plain,
( function(empty_set)
| ~ spl17_3
| ~ spl17_24 ),
inference(resolution,[],[f298,f198]) ).
fof(f337,plain,
spl17_31,
inference(avatar_split_clause,[],[f133,f335]) ).
fof(f133,plain,
! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f333,plain,
spl17_30,
inference(avatar_split_clause,[],[f132,f331]) ).
fof(f331,plain,
( spl17_30
<=> ! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_30])]) ).
fof(f132,plain,
! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,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/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).
fof(f329,plain,
spl17_29,
inference(avatar_split_clause,[],[f131,f327]) ).
fof(f131,plain,
! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f325,plain,
spl17_28,
inference(avatar_split_clause,[],[f130,f323]) ).
fof(f130,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f321,plain,
spl17_27,
inference(avatar_split_clause,[],[f127,f319]) ).
fof(f319,plain,
( spl17_27
<=> ! [X0] :
( ~ empty(sK3(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_27])]) ).
fof(f127,plain,
! [X0] :
( ~ empty(sK3(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f307,plain,
spl17_26,
inference(avatar_split_clause,[],[f139,f305]) ).
fof(f139,plain,
! [X0] : element(sK4(X0),X0),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
! [X0] : element(sK4(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f7,f82]) ).
fof(f82,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK4(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f7,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f303,plain,
spl17_25,
inference(avatar_split_clause,[],[f129,f301]) ).
fof(f129,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( empty(X0)
=> relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(f299,plain,
spl17_24,
inference(avatar_split_clause,[],[f128,f297]) ).
fof(f128,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( empty(X0)
=> function(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
fof(f295,plain,
( ~ spl17_22
| ~ spl17_23 ),
inference(avatar_split_clause,[],[f119,f292,f288]) ).
fof(f119,plain,
( ~ subset(relation_rng(relation_rng_restriction(sK1,sK2)),relation_rng(sK2))
| ~ subset(relation_dom(relation_rng_restriction(sK1,sK2)),relation_dom(sK2)) ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
( ( ~ subset(relation_rng(relation_rng_restriction(sK1,sK2)),relation_rng(sK2))
| ~ subset(relation_dom(relation_rng_restriction(sK1,sK2)),relation_dom(sK2)) )
& function(sK2)
& relation(sK2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f47,f78]) ).
fof(f78,plain,
( ? [X0,X1] :
( ( ~ subset(relation_rng(relation_rng_restriction(X0,X1)),relation_rng(X1))
| ~ subset(relation_dom(relation_rng_restriction(X0,X1)),relation_dom(X1)) )
& function(X1)
& relation(X1) )
=> ( ( ~ subset(relation_rng(relation_rng_restriction(sK1,sK2)),relation_rng(sK2))
| ~ subset(relation_dom(relation_rng_restriction(sK1,sK2)),relation_dom(sK2)) )
& function(sK2)
& relation(sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f47,plain,
? [X0,X1] :
( ( ~ subset(relation_rng(relation_rng_restriction(X0,X1)),relation_rng(X1))
| ~ subset(relation_dom(relation_rng_restriction(X0,X1)),relation_dom(X1)) )
& function(X1)
& relation(X1) ),
inference(flattening,[],[f46]) ).
fof(f46,plain,
? [X0,X1] :
( ( ~ subset(relation_rng(relation_rng_restriction(X0,X1)),relation_rng(X1))
| ~ subset(relation_dom(relation_rng_restriction(X0,X1)),relation_dom(X1)) )
& function(X1)
& relation(X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,negated_conjecture,
~ ! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( subset(relation_rng(relation_rng_restriction(X0,X1)),relation_rng(X1))
& subset(relation_dom(relation_rng_restriction(X0,X1)),relation_dom(X1)) ) ),
inference(negated_conjecture,[],[f37]) ).
fof(f37,conjecture,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( subset(relation_rng(relation_rng_restriction(X0,X1)),relation_rng(X1))
& subset(relation_dom(relation_rng_restriction(X0,X1)),relation_dom(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t89_funct_1) ).
fof(f286,plain,
spl17_21,
inference(avatar_split_clause,[],[f142,f284]) ).
fof(f284,plain,
( spl17_21
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_21])]) ).
fof(f142,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f40]) ).
fof(f40,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f27]) ).
fof(f27,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f282,plain,
spl17_20,
inference(avatar_split_clause,[],[f141,f280]) ).
fof(f141,plain,
! [X0] : empty(sK5(X0)),
inference(cnf_transformation,[],[f85]) ).
fof(f278,plain,
spl17_19,
inference(avatar_split_clause,[],[f125,f276]) ).
fof(f276,plain,
( spl17_19
<=> ! [X0] : ~ empty(powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_19])]) ).
fof(f125,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f274,plain,
spl17_18,
inference(avatar_split_clause,[],[f182,f271]) ).
fof(f271,plain,
( spl17_18
<=> function(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_18])]) ).
fof(f182,plain,
function(sK16),
inference(cnf_transformation,[],[f116]) ).
fof(f116,plain,
( function(sK16)
& empty(sK16)
& relation(sK16) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f21,f115]) ).
fof(f115,plain,
( ? [X0] :
( function(X0)
& empty(X0)
& relation(X0) )
=> ( function(sK16)
& empty(sK16)
& relation(sK16) ) ),
introduced(choice_axiom,[]) ).
fof(f21,axiom,
? [X0] :
( function(X0)
& empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(f269,plain,
spl17_17,
inference(avatar_split_clause,[],[f181,f266]) ).
fof(f181,plain,
empty(sK16),
inference(cnf_transformation,[],[f116]) ).
fof(f264,plain,
spl17_16,
inference(avatar_split_clause,[],[f180,f261]) ).
fof(f261,plain,
( spl17_16
<=> relation(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_16])]) ).
fof(f180,plain,
relation(sK16),
inference(cnf_transformation,[],[f116]) ).
fof(f259,plain,
spl17_15,
inference(avatar_split_clause,[],[f179,f256]) ).
fof(f256,plain,
( spl17_15
<=> function(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_15])]) ).
fof(f179,plain,
function(sK15),
inference(cnf_transformation,[],[f114]) ).
fof(f114,plain,
( function(sK15)
& relation(sK15) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f45,f113]) ).
fof(f113,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK15)
& relation(sK15) ) ),
introduced(choice_axiom,[]) ).
fof(f45,plain,
? [X0] :
( function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f25]) ).
fof(f25,axiom,
? [X0] :
( one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
fof(f254,plain,
spl17_14,
inference(avatar_split_clause,[],[f178,f251]) ).
fof(f251,plain,
( spl17_14
<=> relation(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_14])]) ).
fof(f178,plain,
relation(sK15),
inference(cnf_transformation,[],[f114]) ).
fof(f249,plain,
spl17_13,
inference(avatar_split_clause,[],[f177,f246]) ).
fof(f246,plain,
( spl17_13
<=> function(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_13])]) ).
fof(f177,plain,
function(sK14),
inference(cnf_transformation,[],[f112]) ).
fof(f112,plain,
( function(sK14)
& relation(sK14) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f17,f111]) ).
fof(f111,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK14)
& relation(sK14) ) ),
introduced(choice_axiom,[]) ).
fof(f17,axiom,
? [X0] :
( function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
fof(f244,plain,
spl17_12,
inference(avatar_split_clause,[],[f176,f241]) ).
fof(f241,plain,
( spl17_12
<=> relation(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_12])]) ).
fof(f176,plain,
relation(sK14),
inference(cnf_transformation,[],[f112]) ).
fof(f239,plain,
spl17_11,
inference(avatar_split_clause,[],[f175,f236]) ).
fof(f236,plain,
( spl17_11
<=> relation(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_11])]) ).
fof(f175,plain,
relation(sK13),
inference(cnf_transformation,[],[f110]) ).
fof(f110,plain,
relation(sK13),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f43,f109]) ).
fof(f109,plain,
( ? [X0] : relation(X0)
=> relation(sK13) ),
introduced(choice_axiom,[]) ).
fof(f43,plain,
? [X0] : relation(X0),
inference(pure_predicate_removal,[],[f26]) ).
fof(f26,axiom,
? [X0] :
( relation_empty_yielding(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
fof(f234,plain,
spl17_10,
inference(avatar_split_clause,[],[f174,f231]) ).
fof(f231,plain,
( spl17_10
<=> relation(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_10])]) ).
fof(f174,plain,
relation(sK12),
inference(cnf_transformation,[],[f108]) ).
fof(f108,plain,
( relation(sK12)
& empty(sK12) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f18,f107]) ).
fof(f107,plain,
( ? [X0] :
( relation(X0)
& empty(X0) )
=> ( relation(sK12)
& empty(sK12) ) ),
introduced(choice_axiom,[]) ).
fof(f18,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f229,plain,
spl17_9,
inference(avatar_split_clause,[],[f173,f226]) ).
fof(f173,plain,
empty(sK12),
inference(cnf_transformation,[],[f108]) ).
fof(f224,plain,
spl17_8,
inference(avatar_split_clause,[],[f172,f221]) ).
fof(f221,plain,
( spl17_8
<=> relation(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_8])]) ).
fof(f172,plain,
relation(sK11),
inference(cnf_transformation,[],[f106]) ).
fof(f106,plain,
( relation(sK11)
& ~ empty(sK11) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f22,f105]) ).
fof(f105,plain,
( ? [X0] :
( relation(X0)
& ~ empty(X0) )
=> ( relation(sK11)
& ~ empty(sK11) ) ),
introduced(choice_axiom,[]) ).
fof(f22,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f219,plain,
~ spl17_7,
inference(avatar_split_clause,[],[f171,f216]) ).
fof(f216,plain,
( spl17_7
<=> empty(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_7])]) ).
fof(f171,plain,
~ empty(sK11),
inference(cnf_transformation,[],[f106]) ).
fof(f214,plain,
spl17_6,
inference(avatar_split_clause,[],[f170,f211]) ).
fof(f170,plain,
empty(sK10),
inference(cnf_transformation,[],[f104]) ).
fof(f104,plain,
empty(sK10),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f20,f103]) ).
fof(f103,plain,
( ? [X0] : empty(X0)
=> empty(sK10) ),
introduced(choice_axiom,[]) ).
fof(f20,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f209,plain,
~ spl17_5,
inference(avatar_split_clause,[],[f169,f206]) ).
fof(f206,plain,
( spl17_5
<=> empty(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_5])]) ).
fof(f169,plain,
~ empty(sK9),
inference(cnf_transformation,[],[f102]) ).
fof(f102,plain,
~ empty(sK9),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f24,f101]) ).
fof(f101,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK9) ),
introduced(choice_axiom,[]) ).
fof(f24,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f204,plain,
spl17_4,
inference(avatar_split_clause,[],[f122,f201]) ).
fof(f201,plain,
( spl17_4
<=> relation(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_4])]) ).
fof(f122,plain,
relation(empty_set),
inference(cnf_transformation,[],[f11]) ).
fof(f11,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f199,plain,
spl17_3,
inference(avatar_split_clause,[],[f120,f196]) ).
fof(f120,plain,
empty(empty_set),
inference(cnf_transformation,[],[f10]) ).
fof(f10,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f194,plain,
spl17_2,
inference(avatar_split_clause,[],[f118,f191]) ).
fof(f118,plain,
function(sK2),
inference(cnf_transformation,[],[f79]) ).
fof(f189,plain,
spl17_1,
inference(avatar_split_clause,[],[f117,f186]) ).
fof(f117,plain,
relation(sK2),
inference(cnf_transformation,[],[f79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU046+1 : TPTP v8.2.0. Released v3.2.0.
% 0.11/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun May 19 16:32:23 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (8835)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37 % (8838)WARNING: value z3 for option sas not known
% 0.14/0.37 % (8839)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.37 % (8836)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.37 % (8838)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)
% 0.14/0.37 % (8840)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.37 % (8837)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.37 % (8842)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.37 TRYING [1]
% 0.14/0.37 % (8841)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.37 TRYING [2]
% 0.14/0.38 TRYING [3]
% 0.14/0.39 TRYING [1]
% 0.14/0.40 TRYING [2]
% 0.14/0.41 TRYING [4]
% 0.20/0.46 TRYING [3]
% 0.20/0.46 TRYING [5]
% 0.20/0.48 TRYING [1]
% 0.20/0.48 TRYING [2]
% 0.20/0.49 TRYING [3]
% 0.20/0.50 TRYING [4]
% 0.20/0.53 TRYING [5]
% 0.20/0.54 TRYING [6]
% 0.20/0.54 TRYING [4]
% 1.75/0.62 TRYING [6]
% 2.57/0.71 TRYING [7]
% 2.57/0.71 TRYING [5]
% 3.00/0.78 % (8840)First to succeed.
% 3.00/0.80 % (8840)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-8835"
% 3.00/0.80 % (8840)Refutation found. Thanks to Tanya!
% 3.00/0.80 % SZS status Theorem for theBenchmark
% 3.00/0.80 % SZS output start Proof for theBenchmark
% See solution above
% 3.00/0.81 % (8840)------------------------------
% 3.00/0.81 % (8840)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 3.00/0.81 % (8840)Termination reason: Refutation
% 3.00/0.81
% 3.00/0.81 % (8840)Memory used [KB]: 5901
% 3.00/0.81 % (8840)Time elapsed: 0.436 s
% 3.00/0.81 % (8840)Instructions burned: 1103 (million)
% 3.00/0.81 % (8835)Success in time 0.45 s
%------------------------------------------------------------------------------