TSTP Solution File: SEU023+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU023+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 09:26:44 EDT 2024
% Result : Theorem 0.22s 0.52s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 394
% Syntax : Number of formulae : 1314 ( 109 unt; 0 def)
% Number of atoms : 4828 ( 595 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 6504 (2990 ~;2957 |; 167 &)
% ( 346 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 352 ( 350 usr; 340 prp; 0-4 aty)
% Number of functors : 22 ( 22 usr; 11 con; 0-2 aty)
% Number of variables : 1500 (1462 !; 38 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4678,plain,
$false,
inference(avatar_sat_refutation,[],[f208,f213,f218,f223,f228,f233,f238,f243,f248,f253,f258,f263,f268,f273,f278,f283,f288,f293,f298,f303,f308,f312,f316,f320,f329,f333,f337,f341,f356,f360,f364,f368,f372,f376,f380,f384,f388,f393,f413,f417,f423,f428,f432,f436,f440,f444,f448,f452,f469,f473,f477,f481,f485,f490,f494,f498,f502,f506,f510,f553,f557,f567,f572,f576,f580,f590,f594,f598,f603,f607,f614,f619,f626,f633,f637,f642,f646,f652,f658,f667,f671,f676,f682,f687,f692,f704,f709,f715,f740,f744,f748,f753,f760,f766,f767,f768,f769,f770,f792,f856,f860,f873,f882,f887,f891,f931,f935,f943,f947,f951,f955,f959,f968,f972,f1014,f1018,f1022,f1026,f1068,f1072,f1082,f1086,f1090,f1094,f1098,f1142,f1146,f1152,f1163,f1168,f1172,f1176,f1180,f1215,f1234,f1238,f1273,f1280,f1289,f1298,f1304,f1313,f1318,f1319,f1324,f1347,f1351,f1363,f1364,f1372,f1384,f1390,f1395,f1401,f1405,f1410,f1422,f1427,f1435,f1440,f1453,f1457,f1463,f1469,f1473,f1486,f1510,f1514,f1530,f1534,f1548,f1552,f1556,f1560,f1564,f1568,f1572,f1576,f1580,f1584,f1588,f1592,f1596,f1732,f1820,f1824,f1836,f1840,f1844,f1848,f1852,f1856,f1860,f1864,f1868,f1872,f1876,f1880,f1884,f1888,f1892,f1896,f2024,f2140,f2144,f2148,f2152,f2156,f2160,f2164,f2168,f2172,f2176,f2180,f2184,f2188,f2211,f2215,f2391,f2395,f2399,f2403,f2426,f2430,f2434,f2438,f2442,f2446,f2450,f2454,f2679,f2683,f2687,f2691,f2695,f2699,f2703,f2707,f2750,f2845,f2849,f2853,f2912,f2916,f2920,f2924,f2928,f2932,f3064,f3075,f3079,f3086,f3090,f3094,f3104,f3111,f3137,f3155,f3159,f3163,f3167,f3252,f3256,f3260,f3264,f3268,f3272,f3276,f3347,f3389,f3393,f3397,f3401,f3405,f3409,f3413,f3417,f3422,f3426,f3430,f3606,f3610,f3614,f3618,f3622,f3626,f3630,f3634,f3650,f3654,f3658,f3662,f3666,f3670,f3674,f3678,f3720,f3894,f3982,f4000,f4018,f4022,f4027,f4031,f4035,f4039,f4043,f4170,f4174,f4178,f4182,f4186,f4190,f4194,f4198,f4202,f4206,f4210,f4414,f4418,f4422,f4440,f4458,f4462,f4466,f4470,f4474,f4478,f4482,f4592,f4596,f4600,f4604,f4608,f4612,f4670,f4675,f4677]) ).
fof(f4677,plain,
( spl18_26
| ~ spl18_25
| ~ spl18_339 ),
inference(avatar_split_clause,[],[f4676,f4672,f322,f326]) ).
fof(f326,plain,
( spl18_26
<=> sK3 = apply(relation_composition(sK4,function_inverse(sK4)),sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_26])]) ).
fof(f322,plain,
( spl18_25
<=> sK3 = apply(function_inverse(sK4),apply(sK4,sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_25])]) ).
fof(f4672,plain,
( spl18_339
<=> apply(relation_composition(sK4,function_inverse(sK4)),sK3) = apply(function_inverse(sK4),apply(sK4,sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_339])]) ).
fof(f4676,plain,
( sK3 = apply(relation_composition(sK4,function_inverse(sK4)),sK3)
| ~ spl18_25
| ~ spl18_339 ),
inference(forward_demodulation,[],[f4674,f323]) ).
fof(f323,plain,
( sK3 = apply(function_inverse(sK4),apply(sK4,sK3))
| ~ spl18_25 ),
inference(avatar_component_clause,[],[f322]) ).
fof(f4674,plain,
( apply(relation_composition(sK4,function_inverse(sK4)),sK3) = apply(function_inverse(sK4),apply(sK4,sK3))
| ~ spl18_339 ),
inference(avatar_component_clause,[],[f4672]) ).
fof(f4675,plain,
( ~ spl18_138
| spl18_339
| ~ spl18_90
| ~ spl18_139 ),
inference(avatar_split_clause,[],[f1379,f1270,f713,f4672,f1266]) ).
fof(f1266,plain,
( spl18_138
<=> function(function_inverse(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_138])]) ).
fof(f713,plain,
( spl18_90
<=> ! [X0] :
( apply(X0,apply(sK4,sK3)) = apply(relation_composition(sK4,X0),sK3)
| ~ relation(X0)
| ~ function(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_90])]) ).
fof(f1270,plain,
( spl18_139
<=> relation(function_inverse(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_139])]) ).
fof(f1379,plain,
( apply(relation_composition(sK4,function_inverse(sK4)),sK3) = apply(function_inverse(sK4),apply(sK4,sK3))
| ~ function(function_inverse(sK4))
| ~ spl18_90
| ~ spl18_139 ),
inference(resolution,[],[f1271,f714]) ).
fof(f714,plain,
( ! [X0] :
( ~ relation(X0)
| apply(X0,apply(sK4,sK3)) = apply(relation_composition(sK4,X0),sK3)
| ~ function(X0) )
| ~ spl18_90 ),
inference(avatar_component_clause,[],[f713]) ).
fof(f1271,plain,
( relation(function_inverse(sK4))
| ~ spl18_139 ),
inference(avatar_component_clause,[],[f1270]) ).
fof(f4670,plain,
( spl18_338
| ~ spl18_35
| ~ spl18_188 ),
inference(avatar_split_clause,[],[f2407,f1834,f374,f4668]) ).
fof(f4668,plain,
( spl18_338
<=> ! [X0] :
( sK11 = relation_composition(relation_dom(relation_dom(X0)),sK4)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_338])]) ).
fof(f374,plain,
( spl18_35
<=> ! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_35])]) ).
fof(f1834,plain,
( spl18_188
<=> ! [X0] :
( sK11 = relation_composition(relation_dom(X0),sK4)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_188])]) ).
fof(f2407,plain,
( ! [X0] :
( sK11 = relation_composition(relation_dom(relation_dom(X0)),sK4)
| ~ empty(X0) )
| ~ spl18_35
| ~ spl18_188 ),
inference(resolution,[],[f1835,f375]) ).
fof(f375,plain,
( ! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) )
| ~ spl18_35 ),
inference(avatar_component_clause,[],[f374]) ).
fof(f1835,plain,
( ! [X0] :
( ~ empty(X0)
| sK11 = relation_composition(relation_dom(X0),sK4) )
| ~ spl18_188 ),
inference(avatar_component_clause,[],[f1834]) ).
fof(f4612,plain,
( spl18_337
| ~ spl18_143
| ~ spl18_239 ),
inference(avatar_split_clause,[],[f2839,f2705,f1301,f4610]) ).
fof(f4610,plain,
( spl18_337
<=> ! [X0] :
( ~ in(relation_dom(X0),apply(sK11,sK3))
| ~ sP1(sK11,X0)
| ~ in(apply(sK4,sK3),relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_337])]) ).
fof(f1301,plain,
( spl18_143
<=> apply(sK11,apply(sK4,sK3)) = apply(sK11,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_143])]) ).
fof(f2705,plain,
( spl18_239
<=> ! [X2,X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ sP1(X2,X1)
| ~ in(relation_dom(X1),apply(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_239])]) ).
fof(f2839,plain,
( ! [X0] :
( ~ in(relation_dom(X0),apply(sK11,sK3))
| ~ sP1(sK11,X0)
| ~ in(apply(sK4,sK3),relation_rng(X0)) )
| ~ spl18_143
| ~ spl18_239 ),
inference(superposition,[],[f2706,f1303]) ).
fof(f1303,plain,
( apply(sK11,apply(sK4,sK3)) = apply(sK11,sK3)
| ~ spl18_143 ),
inference(avatar_component_clause,[],[f1301]) ).
fof(f2706,plain,
( ! [X2,X0,X1] :
( ~ in(relation_dom(X1),apply(X2,X0))
| ~ sP1(X2,X1)
| ~ in(X0,relation_rng(X1)) )
| ~ spl18_239 ),
inference(avatar_component_clause,[],[f2705]) ).
fof(f4608,plain,
( spl18_336
| ~ spl18_143
| ~ spl18_238 ),
inference(avatar_split_clause,[],[f2831,f2701,f1301,f4606]) ).
fof(f4606,plain,
( spl18_336
<=> ! [X0] :
( element(apply(sK11,sK3),relation_dom(X0))
| ~ sP1(sK11,X0)
| ~ in(apply(sK4,sK3),relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_336])]) ).
fof(f2701,plain,
( spl18_238
<=> ! [X2,X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ sP1(X2,X1)
| element(apply(X2,X0),relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_238])]) ).
fof(f2831,plain,
( ! [X0] :
( element(apply(sK11,sK3),relation_dom(X0))
| ~ sP1(sK11,X0)
| ~ in(apply(sK4,sK3),relation_rng(X0)) )
| ~ spl18_143
| ~ spl18_238 ),
inference(superposition,[],[f2702,f1303]) ).
fof(f2702,plain,
( ! [X2,X0,X1] :
( element(apply(X2,X0),relation_dom(X1))
| ~ sP1(X2,X1)
| ~ in(X0,relation_rng(X1)) )
| ~ spl18_238 ),
inference(avatar_component_clause,[],[f2701]) ).
fof(f4604,plain,
( spl18_335
| ~ spl18_91
| ~ spl18_148 ),
inference(avatar_split_clause,[],[f1358,f1349,f738,f4602]) ).
fof(f4602,plain,
( spl18_335
<=> ! [X0] :
( apply(relation_rng(X0),apply(sK4,sK3)) = apply(relation_composition(sK4,relation_rng(X0)),sK3)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_335])]) ).
fof(f738,plain,
( spl18_91
<=> ! [X0] :
( ~ empty(X0)
| function(relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_91])]) ).
fof(f1349,plain,
( spl18_148
<=> ! [X0] :
( apply(relation_rng(X0),apply(sK4,sK3)) = apply(relation_composition(sK4,relation_rng(X0)),sK3)
| ~ function(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_148])]) ).
fof(f1358,plain,
( ! [X0] :
( apply(relation_rng(X0),apply(sK4,sK3)) = apply(relation_composition(sK4,relation_rng(X0)),sK3)
| ~ empty(X0) )
| ~ spl18_91
| ~ spl18_148 ),
inference(duplicate_literal_removal,[],[f1356]) ).
fof(f1356,plain,
( ! [X0] :
( apply(relation_rng(X0),apply(sK4,sK3)) = apply(relation_composition(sK4,relation_rng(X0)),sK3)
| ~ empty(X0)
| ~ empty(X0) )
| ~ spl18_91
| ~ spl18_148 ),
inference(resolution,[],[f1350,f739]) ).
fof(f739,plain,
( ! [X0] :
( function(relation_rng(X0))
| ~ empty(X0) )
| ~ spl18_91 ),
inference(avatar_component_clause,[],[f738]) ).
fof(f1350,plain,
( ! [X0] :
( ~ function(relation_rng(X0))
| apply(relation_rng(X0),apply(sK4,sK3)) = apply(relation_composition(sK4,relation_rng(X0)),sK3)
| ~ empty(X0) )
| ~ spl18_148 ),
inference(avatar_component_clause,[],[f1349]) ).
fof(f4600,plain,
( spl18_334
| ~ spl18_92
| ~ spl18_147 ),
inference(avatar_split_clause,[],[f1354,f1345,f742,f4598]) ).
fof(f4598,plain,
( spl18_334
<=> ! [X0] :
( apply(relation_dom(X0),apply(sK4,sK3)) = apply(relation_composition(sK4,relation_dom(X0)),sK3)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_334])]) ).
fof(f742,plain,
( spl18_92
<=> ! [X0] :
( ~ empty(X0)
| function(relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_92])]) ).
fof(f1345,plain,
( spl18_147
<=> ! [X0] :
( apply(relation_dom(X0),apply(sK4,sK3)) = apply(relation_composition(sK4,relation_dom(X0)),sK3)
| ~ function(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_147])]) ).
fof(f1354,plain,
( ! [X0] :
( apply(relation_dom(X0),apply(sK4,sK3)) = apply(relation_composition(sK4,relation_dom(X0)),sK3)
| ~ empty(X0) )
| ~ spl18_92
| ~ spl18_147 ),
inference(duplicate_literal_removal,[],[f1352]) ).
fof(f1352,plain,
( ! [X0] :
( apply(relation_dom(X0),apply(sK4,sK3)) = apply(relation_composition(sK4,relation_dom(X0)),sK3)
| ~ empty(X0)
| ~ empty(X0) )
| ~ spl18_92
| ~ spl18_147 ),
inference(resolution,[],[f1346,f743]) ).
fof(f743,plain,
( ! [X0] :
( function(relation_dom(X0))
| ~ empty(X0) )
| ~ spl18_92 ),
inference(avatar_component_clause,[],[f742]) ).
fof(f1346,plain,
( ! [X0] :
( ~ function(relation_dom(X0))
| apply(relation_dom(X0),apply(sK4,sK3)) = apply(relation_composition(sK4,relation_dom(X0)),sK3)
| ~ empty(X0) )
| ~ spl18_147 ),
inference(avatar_component_clause,[],[f1345]) ).
fof(f4596,plain,
( spl18_333
| ~ spl18_128
| ~ spl18_143 ),
inference(avatar_split_clause,[],[f1305,f1301,f1144,f4594]) ).
fof(f4594,plain,
( spl18_333
<=> ! [X0] :
( in(apply(sK11,sK3),relation_dom(X0))
| ~ in(apply(sK4,sK3),relation_rng(X0))
| ~ sP1(sK11,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_333])]) ).
fof(f1144,plain,
( spl18_128
<=> ! [X2,X0,X1] :
( ~ in(X0,relation_rng(X1))
| in(apply(X2,X0),relation_dom(X1))
| ~ sP1(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_128])]) ).
fof(f1305,plain,
( ! [X0] :
( in(apply(sK11,sK3),relation_dom(X0))
| ~ in(apply(sK4,sK3),relation_rng(X0))
| ~ sP1(sK11,X0) )
| ~ spl18_128
| ~ spl18_143 ),
inference(superposition,[],[f1145,f1303]) ).
fof(f1145,plain,
( ! [X2,X0,X1] :
( in(apply(X2,X0),relation_dom(X1))
| ~ in(X0,relation_rng(X1))
| ~ sP1(X2,X1) )
| ~ spl18_128 ),
inference(avatar_component_clause,[],[f1144]) ).
fof(f4592,plain,
( spl18_332
| ~ spl18_33
| ~ spl18_185 ),
inference(avatar_split_clause,[],[f2346,f1730,f366,f4590]) ).
fof(f4590,plain,
( spl18_332
<=> ! [X0] :
( sK11 = relation_composition(sK4,relation_rng(relation_rng(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_332])]) ).
fof(f366,plain,
( spl18_33
<=> ! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_33])]) ).
fof(f1730,plain,
( spl18_185
<=> ! [X0] :
( sK11 = relation_composition(sK4,relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_185])]) ).
fof(f2346,plain,
( ! [X0] :
( sK11 = relation_composition(sK4,relation_rng(relation_rng(X0)))
| ~ empty(X0) )
| ~ spl18_33
| ~ spl18_185 ),
inference(resolution,[],[f1731,f367]) ).
fof(f367,plain,
( ! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) )
| ~ spl18_33 ),
inference(avatar_component_clause,[],[f366]) ).
fof(f1731,plain,
( ! [X0] :
( ~ empty(X0)
| sK11 = relation_composition(sK4,relation_rng(X0)) )
| ~ spl18_185 ),
inference(avatar_component_clause,[],[f1730]) ).
fof(f4482,plain,
( spl18_331
| ~ spl18_139
| ~ spl18_249 ),
inference(avatar_split_clause,[],[f3043,f2930,f1270,f4480]) ).
fof(f4480,plain,
( spl18_331
<=> ! [X2,X0,X1] :
( relation_composition(X0,relation_composition(X1,function_inverse(sK4))) = X2
| ~ empty(X2)
| ~ empty(X0)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_331])]) ).
fof(f2930,plain,
( spl18_249
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| relation_composition(X0,relation_composition(X1,X2)) = X3
| ~ empty(X3)
| ~ relation(X2)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_249])]) ).
fof(f3043,plain,
( ! [X2,X0,X1] :
( relation_composition(X0,relation_composition(X1,function_inverse(sK4))) = X2
| ~ empty(X2)
| ~ empty(X0)
| ~ relation(X1) )
| ~ spl18_139
| ~ spl18_249 ),
inference(resolution,[],[f2931,f1271]) ).
fof(f2931,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X2)
| relation_composition(X0,relation_composition(X1,X2)) = X3
| ~ empty(X3)
| ~ empty(X0)
| ~ relation(X1) )
| ~ spl18_249 ),
inference(avatar_component_clause,[],[f2930]) ).
fof(f4478,plain,
( spl18_330
| ~ spl18_139
| ~ spl18_248 ),
inference(avatar_split_clause,[],[f3024,f2926,f1270,f4476]) ).
fof(f4476,plain,
( spl18_330
<=> ! [X2,X0,X1] :
( relation_composition(X0,relation_composition(function_inverse(sK4),X1)) = X2
| ~ empty(X2)
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_330])]) ).
fof(f2926,plain,
( spl18_248
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| relation_composition(X0,relation_composition(X1,X2)) = X3
| ~ empty(X3)
| ~ relation(X1)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_248])]) ).
fof(f3024,plain,
( ! [X2,X0,X1] :
( relation_composition(X0,relation_composition(function_inverse(sK4),X1)) = X2
| ~ empty(X2)
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl18_139
| ~ spl18_248 ),
inference(resolution,[],[f2927,f1271]) ).
fof(f2927,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X1)
| relation_composition(X0,relation_composition(X1,X2)) = X3
| ~ empty(X3)
| ~ empty(X0)
| ~ empty(X2) )
| ~ spl18_248 ),
inference(avatar_component_clause,[],[f2926]) ).
fof(f4474,plain,
( spl18_329
| ~ spl18_35
| ~ spl18_185 ),
inference(avatar_split_clause,[],[f2345,f1730,f374,f4472]) ).
fof(f4472,plain,
( spl18_329
<=> ! [X0] :
( sK11 = relation_composition(sK4,relation_rng(relation_dom(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_329])]) ).
fof(f2345,plain,
( ! [X0] :
( sK11 = relation_composition(sK4,relation_rng(relation_dom(X0)))
| ~ empty(X0) )
| ~ spl18_35
| ~ spl18_185 ),
inference(resolution,[],[f1731,f375]) ).
fof(f4470,plain,
( spl18_328
| ~ spl18_139
| ~ spl18_247 ),
inference(avatar_split_clause,[],[f3005,f2922,f1270,f4468]) ).
fof(f4468,plain,
( spl18_328
<=> ! [X2,X0,X1] :
( relation_composition(X0,relation_composition(X1,function_inverse(sK4))) = X2
| ~ empty(X2)
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_328])]) ).
fof(f2922,plain,
( spl18_247
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| relation_composition(X0,relation_composition(X1,X2)) = X3
| ~ empty(X3)
| ~ relation(X2)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_247])]) ).
fof(f3005,plain,
( ! [X2,X0,X1] :
( relation_composition(X0,relation_composition(X1,function_inverse(sK4))) = X2
| ~ empty(X2)
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl18_139
| ~ spl18_247 ),
inference(resolution,[],[f2923,f1271]) ).
fof(f2923,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X2)
| relation_composition(X0,relation_composition(X1,X2)) = X3
| ~ empty(X3)
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl18_247 ),
inference(avatar_component_clause,[],[f2922]) ).
fof(f4466,plain,
( spl18_327
| ~ spl18_139
| ~ spl18_246 ),
inference(avatar_split_clause,[],[f2986,f2918,f1270,f4464]) ).
fof(f4464,plain,
( spl18_327
<=> ! [X2,X0,X1] :
( relation_composition(relation_composition(X0,function_inverse(sK4)),X1) = X2
| ~ empty(X2)
| ~ empty(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_327])]) ).
fof(f2918,plain,
( spl18_246
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| relation_composition(relation_composition(X1,X2),X0) = X3
| ~ empty(X3)
| ~ relation(X2)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_246])]) ).
fof(f2986,plain,
( ! [X2,X0,X1] :
( relation_composition(relation_composition(X0,function_inverse(sK4)),X1) = X2
| ~ empty(X2)
| ~ empty(X1)
| ~ relation(X0) )
| ~ spl18_139
| ~ spl18_246 ),
inference(resolution,[],[f2919,f1271]) ).
fof(f2919,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X2)
| relation_composition(relation_composition(X1,X2),X0) = X3
| ~ empty(X3)
| ~ empty(X0)
| ~ relation(X1) )
| ~ spl18_246 ),
inference(avatar_component_clause,[],[f2918]) ).
fof(f4462,plain,
( spl18_326
| ~ spl18_139
| ~ spl18_245 ),
inference(avatar_split_clause,[],[f2953,f2914,f1270,f4460]) ).
fof(f4460,plain,
( spl18_326
<=> ! [X2,X0,X1] :
( relation_composition(relation_composition(function_inverse(sK4),X0),X1) = X2
| ~ empty(X2)
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_326])]) ).
fof(f2914,plain,
( spl18_245
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| relation_composition(relation_composition(X1,X2),X0) = X3
| ~ empty(X3)
| ~ relation(X1)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_245])]) ).
fof(f2953,plain,
( ! [X2,X0,X1] :
( relation_composition(relation_composition(function_inverse(sK4),X0),X1) = X2
| ~ empty(X2)
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl18_139
| ~ spl18_245 ),
inference(resolution,[],[f2915,f1271]) ).
fof(f2915,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X1)
| relation_composition(relation_composition(X1,X2),X0) = X3
| ~ empty(X3)
| ~ empty(X0)
| ~ empty(X2) )
| ~ spl18_245 ),
inference(avatar_component_clause,[],[f2914]) ).
fof(f4458,plain,
( spl18_325
| ~ spl18_139
| ~ spl18_244 ),
inference(avatar_split_clause,[],[f2934,f2910,f1270,f4456]) ).
fof(f4456,plain,
( spl18_325
<=> ! [X2,X0,X1] :
( relation_composition(relation_composition(X0,function_inverse(sK4)),X1) = X2
| ~ empty(X2)
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_325])]) ).
fof(f2910,plain,
( spl18_244
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| relation_composition(relation_composition(X1,X2),X0) = X3
| ~ empty(X3)
| ~ relation(X2)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_244])]) ).
fof(f2934,plain,
( ! [X2,X0,X1] :
( relation_composition(relation_composition(X0,function_inverse(sK4)),X1) = X2
| ~ empty(X2)
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl18_139
| ~ spl18_244 ),
inference(resolution,[],[f2911,f1271]) ).
fof(f2911,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X2)
| relation_composition(relation_composition(X1,X2),X0) = X3
| ~ empty(X3)
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl18_244 ),
inference(avatar_component_clause,[],[f2910]) ).
fof(f4440,plain,
( ~ spl18_138
| spl18_324
| ~ spl18_139
| ~ spl18_243 ),
inference(avatar_split_clause,[],[f2888,f2851,f1270,f4438,f1266]) ).
fof(f4438,plain,
( spl18_324
<=> ! [X0,X1] :
( relation_composition(X0,function_inverse(function_inverse(sK4))) = X1
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_324])]) ).
fof(f2851,plain,
( spl18_243
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| relation_composition(X0,function_inverse(X1)) = X2
| ~ empty(X2)
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_243])]) ).
fof(f2888,plain,
( ! [X0,X1] :
( relation_composition(X0,function_inverse(function_inverse(sK4))) = X1
| ~ empty(X1)
| ~ function(function_inverse(sK4))
| ~ empty(X0) )
| ~ spl18_139
| ~ spl18_243 ),
inference(resolution,[],[f2852,f1271]) ).
fof(f2852,plain,
( ! [X2,X0,X1] :
( ~ relation(X1)
| relation_composition(X0,function_inverse(X1)) = X2
| ~ empty(X2)
| ~ function(X1)
| ~ empty(X0) )
| ~ spl18_243 ),
inference(avatar_component_clause,[],[f2851]) ).
fof(f4422,plain,
( ~ spl18_138
| spl18_323
| ~ spl18_139
| ~ spl18_242 ),
inference(avatar_split_clause,[],[f2866,f2847,f1270,f4420,f1266]) ).
fof(f4420,plain,
( spl18_323
<=> ! [X0,X1] :
( relation_composition(function_inverse(function_inverse(sK4)),X0) = X1
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_323])]) ).
fof(f2847,plain,
( spl18_242
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| relation_composition(function_inverse(X1),X0) = X2
| ~ empty(X2)
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_242])]) ).
fof(f2866,plain,
( ! [X0,X1] :
( relation_composition(function_inverse(function_inverse(sK4)),X0) = X1
| ~ empty(X1)
| ~ function(function_inverse(sK4))
| ~ empty(X0) )
| ~ spl18_139
| ~ spl18_242 ),
inference(resolution,[],[f2848,f1271]) ).
fof(f2848,plain,
( ! [X2,X0,X1] :
( ~ relation(X1)
| relation_composition(function_inverse(X1),X0) = X2
| ~ empty(X2)
| ~ function(X1)
| ~ empty(X0) )
| ~ spl18_242 ),
inference(avatar_component_clause,[],[f2847]) ).
fof(f4418,plain,
( spl18_322
| ~ spl18_25
| ~ spl18_239 ),
inference(avatar_split_clause,[],[f2840,f2705,f322,f4416]) ).
fof(f4416,plain,
( spl18_322
<=> ! [X0] :
( ~ in(relation_dom(X0),sK3)
| ~ sP1(function_inverse(sK4),X0)
| ~ in(apply(sK4,sK3),relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_322])]) ).
fof(f2840,plain,
( ! [X0] :
( ~ in(relation_dom(X0),sK3)
| ~ sP1(function_inverse(sK4),X0)
| ~ in(apply(sK4,sK3),relation_rng(X0)) )
| ~ spl18_25
| ~ spl18_239 ),
inference(superposition,[],[f2706,f323]) ).
fof(f4414,plain,
( spl18_321
| ~ spl18_25
| ~ spl18_238 ),
inference(avatar_split_clause,[],[f2832,f2701,f322,f4412]) ).
fof(f4412,plain,
( spl18_321
<=> ! [X0] :
( element(sK3,relation_dom(X0))
| ~ sP1(function_inverse(sK4),X0)
| ~ in(apply(sK4,sK3),relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_321])]) ).
fof(f2832,plain,
( ! [X0] :
( element(sK3,relation_dom(X0))
| ~ sP1(function_inverse(sK4),X0)
| ~ in(apply(sK4,sK3),relation_rng(X0)) )
| ~ spl18_25
| ~ spl18_238 ),
inference(superposition,[],[f2702,f323]) ).
fof(f4210,plain,
( spl18_320
| ~ spl18_1
| ~ spl18_249 ),
inference(avatar_split_clause,[],[f3050,f2930,f205,f4208]) ).
fof(f4208,plain,
( spl18_320
<=> ! [X2,X0,X1] :
( relation_composition(X0,relation_composition(X1,sK4)) = X2
| ~ empty(X2)
| ~ empty(X0)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_320])]) ).
fof(f205,plain,
( spl18_1
<=> relation(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_1])]) ).
fof(f3050,plain,
( ! [X2,X0,X1] :
( relation_composition(X0,relation_composition(X1,sK4)) = X2
| ~ empty(X2)
| ~ empty(X0)
| ~ relation(X1) )
| ~ spl18_1
| ~ spl18_249 ),
inference(resolution,[],[f2931,f207]) ).
fof(f207,plain,
( relation(sK4)
| ~ spl18_1 ),
inference(avatar_component_clause,[],[f205]) ).
fof(f4206,plain,
( spl18_319
| ~ spl18_1
| ~ spl18_248 ),
inference(avatar_split_clause,[],[f3031,f2926,f205,f4204]) ).
fof(f4204,plain,
( spl18_319
<=> ! [X2,X0,X1] :
( relation_composition(X0,relation_composition(sK4,X1)) = X2
| ~ empty(X2)
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_319])]) ).
fof(f3031,plain,
( ! [X2,X0,X1] :
( relation_composition(X0,relation_composition(sK4,X1)) = X2
| ~ empty(X2)
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl18_1
| ~ spl18_248 ),
inference(resolution,[],[f2927,f207]) ).
fof(f4202,plain,
( spl18_318
| ~ spl18_1
| ~ spl18_247 ),
inference(avatar_split_clause,[],[f3012,f2922,f205,f4200]) ).
fof(f4200,plain,
( spl18_318
<=> ! [X2,X0,X1] :
( relation_composition(X0,relation_composition(X1,sK4)) = X2
| ~ empty(X2)
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_318])]) ).
fof(f3012,plain,
( ! [X2,X0,X1] :
( relation_composition(X0,relation_composition(X1,sK4)) = X2
| ~ empty(X2)
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl18_1
| ~ spl18_247 ),
inference(resolution,[],[f2923,f207]) ).
fof(f4198,plain,
( spl18_317
| ~ spl18_1
| ~ spl18_246 ),
inference(avatar_split_clause,[],[f2993,f2918,f205,f4196]) ).
fof(f4196,plain,
( spl18_317
<=> ! [X2,X0,X1] :
( relation_composition(relation_composition(X0,sK4),X1) = X2
| ~ empty(X2)
| ~ empty(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_317])]) ).
fof(f2993,plain,
( ! [X2,X0,X1] :
( relation_composition(relation_composition(X0,sK4),X1) = X2
| ~ empty(X2)
| ~ empty(X1)
| ~ relation(X0) )
| ~ spl18_1
| ~ spl18_246 ),
inference(resolution,[],[f2919,f207]) ).
fof(f4194,plain,
( spl18_316
| ~ spl18_1
| ~ spl18_245 ),
inference(avatar_split_clause,[],[f2960,f2914,f205,f4192]) ).
fof(f4192,plain,
( spl18_316
<=> ! [X2,X0,X1] :
( relation_composition(relation_composition(sK4,X0),X1) = X2
| ~ empty(X2)
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_316])]) ).
fof(f2960,plain,
( ! [X2,X0,X1] :
( relation_composition(relation_composition(sK4,X0),X1) = X2
| ~ empty(X2)
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl18_1
| ~ spl18_245 ),
inference(resolution,[],[f2915,f207]) ).
fof(f4190,plain,
( spl18_315
| ~ spl18_1
| ~ spl18_244 ),
inference(avatar_split_clause,[],[f2941,f2910,f205,f4188]) ).
fof(f4188,plain,
( spl18_315
<=> ! [X2,X0,X1] :
( relation_composition(relation_composition(X0,sK4),X1) = X2
| ~ empty(X2)
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_315])]) ).
fof(f2941,plain,
( ! [X2,X0,X1] :
( relation_composition(relation_composition(X0,sK4),X1) = X2
| ~ empty(X2)
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl18_1
| ~ spl18_244 ),
inference(resolution,[],[f2911,f207]) ).
fof(f4186,plain,
( spl18_314
| ~ spl18_54
| ~ spl18_137 ),
inference(avatar_split_clause,[],[f1253,f1236,f483,f4184]) ).
fof(f4184,plain,
( spl18_314
<=> ! [X2,X0,X1] :
( relation_composition(X1,X2) = relation_composition(X0,sK4)
| ~ empty(X0)
| ~ relation(X1)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_314])]) ).
fof(f483,plain,
( spl18_54
<=> ! [X0,X1] :
( empty(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_54])]) ).
fof(f1236,plain,
( spl18_137
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_composition(X0,sK4) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_137])]) ).
fof(f1253,plain,
( ! [X2,X0,X1] :
( relation_composition(X1,X2) = relation_composition(X0,sK4)
| ~ empty(X0)
| ~ relation(X1)
| ~ empty(X2) )
| ~ spl18_54
| ~ spl18_137 ),
inference(resolution,[],[f1237,f484]) ).
fof(f484,plain,
( ! [X0,X1] :
( empty(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) )
| ~ spl18_54 ),
inference(avatar_component_clause,[],[f483]) ).
fof(f1237,plain,
( ! [X0,X1] :
( ~ empty(X1)
| relation_composition(X0,sK4) = X1
| ~ empty(X0) )
| ~ spl18_137 ),
inference(avatar_component_clause,[],[f1236]) ).
fof(f4182,plain,
( spl18_313
| ~ spl18_57
| ~ spl18_137 ),
inference(avatar_split_clause,[],[f1252,f1236,f496,f4180]) ).
fof(f4180,plain,
( spl18_313
<=> ! [X2,X0,X1] :
( relation_composition(X1,X2) = relation_composition(X0,sK4)
| ~ empty(X0)
| ~ relation(X2)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_313])]) ).
fof(f496,plain,
( spl18_57
<=> ! [X0,X1] :
( empty(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_57])]) ).
fof(f1252,plain,
( ! [X2,X0,X1] :
( relation_composition(X1,X2) = relation_composition(X0,sK4)
| ~ empty(X0)
| ~ relation(X2)
| ~ empty(X1) )
| ~ spl18_57
| ~ spl18_137 ),
inference(resolution,[],[f1237,f497]) ).
fof(f497,plain,
( ! [X0,X1] :
( empty(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) )
| ~ spl18_57 ),
inference(avatar_component_clause,[],[f496]) ).
fof(f4178,plain,
( spl18_312
| ~ spl18_54
| ~ spl18_136 ),
inference(avatar_split_clause,[],[f1240,f1232,f483,f4176]) ).
fof(f4176,plain,
( spl18_312
<=> ! [X2,X0,X1] :
( relation_composition(X1,X2) = relation_composition(sK4,X0)
| ~ empty(X0)
| ~ relation(X1)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_312])]) ).
fof(f1232,plain,
( spl18_136
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_composition(sK4,X0) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_136])]) ).
fof(f1240,plain,
( ! [X2,X0,X1] :
( relation_composition(X1,X2) = relation_composition(sK4,X0)
| ~ empty(X0)
| ~ relation(X1)
| ~ empty(X2) )
| ~ spl18_54
| ~ spl18_136 ),
inference(resolution,[],[f1233,f484]) ).
fof(f1233,plain,
( ! [X0,X1] :
( ~ empty(X1)
| relation_composition(sK4,X0) = X1
| ~ empty(X0) )
| ~ spl18_136 ),
inference(avatar_component_clause,[],[f1232]) ).
fof(f4174,plain,
( spl18_311
| ~ spl18_57
| ~ spl18_136 ),
inference(avatar_split_clause,[],[f1239,f1232,f496,f4172]) ).
fof(f4172,plain,
( spl18_311
<=> ! [X2,X0,X1] :
( relation_composition(X1,X2) = relation_composition(sK4,X0)
| ~ empty(X0)
| ~ relation(X2)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_311])]) ).
fof(f1239,plain,
( ! [X2,X0,X1] :
( relation_composition(X1,X2) = relation_composition(sK4,X0)
| ~ empty(X0)
| ~ relation(X2)
| ~ empty(X1) )
| ~ spl18_57
| ~ spl18_136 ),
inference(resolution,[],[f1233,f497]) ).
fof(f4170,plain,
( spl18_310
| ~ spl18_5
| ~ spl18_85
| ~ spl18_302 ),
inference(avatar_split_clause,[],[f4011,f3998,f679,f225,f4167]) ).
fof(f4167,plain,
( spl18_310
<=> sK11 = relation_composition(sK11,function_inverse(function_inverse(sK4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_310])]) ).
fof(f225,plain,
( spl18_5
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_5])]) ).
fof(f679,plain,
( spl18_85
<=> empty_set = sK11 ),
introduced(avatar_definition,[new_symbols(naming,[spl18_85])]) ).
fof(f3998,plain,
( spl18_302
<=> ! [X0] :
( ~ empty(X0)
| sK11 = relation_composition(X0,function_inverse(function_inverse(sK4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_302])]) ).
fof(f4011,plain,
( sK11 = relation_composition(sK11,function_inverse(function_inverse(sK4)))
| ~ spl18_5
| ~ spl18_85
| ~ spl18_302 ),
inference(forward_demodulation,[],[f4003,f681]) ).
fof(f681,plain,
( empty_set = sK11
| ~ spl18_85 ),
inference(avatar_component_clause,[],[f679]) ).
fof(f4003,plain,
( sK11 = relation_composition(empty_set,function_inverse(function_inverse(sK4)))
| ~ spl18_5
| ~ spl18_302 ),
inference(resolution,[],[f3999,f227]) ).
fof(f227,plain,
( empty(empty_set)
| ~ spl18_5 ),
inference(avatar_component_clause,[],[f225]) ).
fof(f3999,plain,
( ! [X0] :
( ~ empty(X0)
| sK11 = relation_composition(X0,function_inverse(function_inverse(sK4))) )
| ~ spl18_302 ),
inference(avatar_component_clause,[],[f3998]) ).
fof(f4043,plain,
( spl18_309
| ~ spl18_139
| ~ spl18_237 ),
inference(avatar_split_clause,[],[f2809,f2697,f1270,f4041]) ).
fof(f4041,plain,
( spl18_309
<=> ! [X0,X1] :
( ~ empty(X0)
| sK11 = relation_composition(X0,relation_composition(X1,function_inverse(sK4)))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_309])]) ).
fof(f2697,plain,
( spl18_237
<=> ! [X2,X0,X1] :
( sK11 = relation_composition(X0,relation_composition(X1,X2))
| ~ empty(X0)
| ~ relation(X2)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_237])]) ).
fof(f2809,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK11 = relation_composition(X0,relation_composition(X1,function_inverse(sK4)))
| ~ relation(X1) )
| ~ spl18_139
| ~ spl18_237 ),
inference(resolution,[],[f2698,f1271]) ).
fof(f2698,plain,
( ! [X2,X0,X1] :
( ~ relation(X2)
| ~ empty(X0)
| sK11 = relation_composition(X0,relation_composition(X1,X2))
| ~ relation(X1) )
| ~ spl18_237 ),
inference(avatar_component_clause,[],[f2697]) ).
fof(f4039,plain,
( spl18_308
| ~ spl18_139
| ~ spl18_236 ),
inference(avatar_split_clause,[],[f2790,f2693,f1270,f4037]) ).
fof(f4037,plain,
( spl18_308
<=> ! [X0,X1] :
( ~ empty(X0)
| sK11 = relation_composition(X0,relation_composition(function_inverse(sK4),X1))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_308])]) ).
fof(f2693,plain,
( spl18_236
<=> ! [X2,X0,X1] :
( sK11 = relation_composition(X0,relation_composition(X1,X2))
| ~ empty(X0)
| ~ relation(X1)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_236])]) ).
fof(f2790,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK11 = relation_composition(X0,relation_composition(function_inverse(sK4),X1))
| ~ empty(X1) )
| ~ spl18_139
| ~ spl18_236 ),
inference(resolution,[],[f2694,f1271]) ).
fof(f2694,plain,
( ! [X2,X0,X1] :
( ~ relation(X1)
| ~ empty(X0)
| sK11 = relation_composition(X0,relation_composition(X1,X2))
| ~ empty(X2) )
| ~ spl18_236 ),
inference(avatar_component_clause,[],[f2693]) ).
fof(f4035,plain,
( spl18_307
| ~ spl18_139
| ~ spl18_235 ),
inference(avatar_split_clause,[],[f2771,f2689,f1270,f4033]) ).
fof(f4033,plain,
( spl18_307
<=> ! [X0,X1] :
( ~ empty(X0)
| sK11 = relation_composition(X0,relation_composition(X1,function_inverse(sK4)))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_307])]) ).
fof(f2689,plain,
( spl18_235
<=> ! [X2,X0,X1] :
( sK11 = relation_composition(X0,relation_composition(X1,X2))
| ~ empty(X0)
| ~ relation(X2)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_235])]) ).
fof(f2771,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK11 = relation_composition(X0,relation_composition(X1,function_inverse(sK4)))
| ~ empty(X1) )
| ~ spl18_139
| ~ spl18_235 ),
inference(resolution,[],[f2690,f1271]) ).
fof(f2690,plain,
( ! [X2,X0,X1] :
( ~ relation(X2)
| ~ empty(X0)
| sK11 = relation_composition(X0,relation_composition(X1,X2))
| ~ empty(X1) )
| ~ spl18_235 ),
inference(avatar_component_clause,[],[f2689]) ).
fof(f4031,plain,
( spl18_306
| ~ spl18_139
| ~ spl18_234 ),
inference(avatar_split_clause,[],[f2752,f2685,f1270,f4029]) ).
fof(f4029,plain,
( spl18_306
<=> ! [X0,X1] :
( ~ empty(X0)
| sK11 = relation_composition(relation_composition(X1,function_inverse(sK4)),X0)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_306])]) ).
fof(f2685,plain,
( spl18_234
<=> ! [X2,X0,X1] :
( sK11 = relation_composition(relation_composition(X0,X1),X2)
| ~ empty(X2)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_234])]) ).
fof(f2752,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK11 = relation_composition(relation_composition(X1,function_inverse(sK4)),X0)
| ~ relation(X1) )
| ~ spl18_139
| ~ spl18_234 ),
inference(resolution,[],[f2686,f1271]) ).
fof(f2686,plain,
( ! [X2,X0,X1] :
( ~ relation(X1)
| ~ empty(X2)
| sK11 = relation_composition(relation_composition(X0,X1),X2)
| ~ relation(X0) )
| ~ spl18_234 ),
inference(avatar_component_clause,[],[f2685]) ).
fof(f4027,plain,
( spl18_305
| ~ spl18_5
| ~ spl18_85
| ~ spl18_301 ),
inference(avatar_split_clause,[],[f3993,f3980,f679,f225,f4024]) ).
fof(f4024,plain,
( spl18_305
<=> sK11 = relation_composition(function_inverse(function_inverse(sK4)),sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_305])]) ).
fof(f3980,plain,
( spl18_301
<=> ! [X0] :
( ~ empty(X0)
| sK11 = relation_composition(function_inverse(function_inverse(sK4)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_301])]) ).
fof(f3993,plain,
( sK11 = relation_composition(function_inverse(function_inverse(sK4)),sK11)
| ~ spl18_5
| ~ spl18_85
| ~ spl18_301 ),
inference(forward_demodulation,[],[f3985,f681]) ).
fof(f3985,plain,
( sK11 = relation_composition(function_inverse(function_inverse(sK4)),empty_set)
| ~ spl18_5
| ~ spl18_301 ),
inference(resolution,[],[f3981,f227]) ).
fof(f3981,plain,
( ! [X0] :
( ~ empty(X0)
| sK11 = relation_composition(function_inverse(function_inverse(sK4)),X0) )
| ~ spl18_301 ),
inference(avatar_component_clause,[],[f3980]) ).
fof(f4022,plain,
( spl18_304
| ~ spl18_139
| ~ spl18_233 ),
inference(avatar_split_clause,[],[f2728,f2681,f1270,f4020]) ).
fof(f4020,plain,
( spl18_304
<=> ! [X0,X1] :
( ~ empty(X0)
| sK11 = relation_composition(relation_composition(function_inverse(sK4),X1),X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_304])]) ).
fof(f2681,plain,
( spl18_233
<=> ! [X2,X0,X1] :
( sK11 = relation_composition(relation_composition(X0,X1),X2)
| ~ empty(X2)
| ~ relation(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_233])]) ).
fof(f2728,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK11 = relation_composition(relation_composition(function_inverse(sK4),X1),X0)
| ~ empty(X1) )
| ~ spl18_139
| ~ spl18_233 ),
inference(resolution,[],[f2682,f1271]) ).
fof(f2682,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X2)
| sK11 = relation_composition(relation_composition(X0,X1),X2)
| ~ empty(X1) )
| ~ spl18_233 ),
inference(avatar_component_clause,[],[f2681]) ).
fof(f4018,plain,
( spl18_303
| ~ spl18_139
| ~ spl18_232 ),
inference(avatar_split_clause,[],[f2709,f2677,f1270,f4016]) ).
fof(f4016,plain,
( spl18_303
<=> ! [X0,X1] :
( ~ empty(X0)
| sK11 = relation_composition(relation_composition(X1,function_inverse(sK4)),X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_303])]) ).
fof(f2677,plain,
( spl18_232
<=> ! [X2,X0,X1] :
( sK11 = relation_composition(relation_composition(X0,X1),X2)
| ~ empty(X2)
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_232])]) ).
fof(f2709,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK11 = relation_composition(relation_composition(X1,function_inverse(sK4)),X0)
| ~ empty(X1) )
| ~ spl18_139
| ~ spl18_232 ),
inference(resolution,[],[f2678,f1271]) ).
fof(f2678,plain,
( ! [X2,X0,X1] :
( ~ relation(X1)
| ~ empty(X2)
| sK11 = relation_composition(relation_composition(X0,X1),X2)
| ~ empty(X0) )
| ~ spl18_232 ),
inference(avatar_component_clause,[],[f2677]) ).
fof(f4000,plain,
( ~ spl18_138
| spl18_302
| ~ spl18_139
| ~ spl18_225 ),
inference(avatar_split_clause,[],[f2573,f2428,f1270,f3998,f1266]) ).
fof(f2428,plain,
( spl18_225
<=> ! [X0,X1] :
( sK11 = relation_composition(X0,function_inverse(X1))
| ~ empty(X0)
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_225])]) ).
fof(f2573,plain,
( ! [X0] :
( ~ empty(X0)
| ~ function(function_inverse(sK4))
| sK11 = relation_composition(X0,function_inverse(function_inverse(sK4))) )
| ~ spl18_139
| ~ spl18_225 ),
inference(resolution,[],[f2429,f1271]) ).
fof(f2429,plain,
( ! [X0,X1] :
( ~ relation(X1)
| ~ empty(X0)
| ~ function(X1)
| sK11 = relation_composition(X0,function_inverse(X1)) )
| ~ spl18_225 ),
inference(avatar_component_clause,[],[f2428]) ).
fof(f3982,plain,
( ~ spl18_138
| spl18_301
| ~ spl18_139
| ~ spl18_224 ),
inference(avatar_split_clause,[],[f2551,f2424,f1270,f3980,f1266]) ).
fof(f2424,plain,
( spl18_224
<=> ! [X0,X1] :
( sK11 = relation_composition(function_inverse(X0),X1)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_224])]) ).
fof(f2551,plain,
( ! [X0] :
( ~ empty(X0)
| ~ function(function_inverse(sK4))
| sK11 = relation_composition(function_inverse(function_inverse(sK4)),X0) )
| ~ spl18_139
| ~ spl18_224 ),
inference(resolution,[],[f2425,f1271]) ).
fof(f2425,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| ~ function(X0)
| sK11 = relation_composition(function_inverse(X0),X1) )
| ~ spl18_224 ),
inference(avatar_component_clause,[],[f2424]) ).
fof(f3894,plain,
( spl18_300
| ~ spl18_33
| ~ spl18_182 ),
inference(avatar_split_clause,[],[f2193,f1586,f366,f3892]) ).
fof(f3892,plain,
( spl18_300
<=> ! [X0] :
( sK11 = relation_composition(sK4,relation_dom(relation_rng(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_300])]) ).
fof(f1586,plain,
( spl18_182
<=> ! [X0] :
( sK11 = relation_composition(sK4,relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_182])]) ).
fof(f2193,plain,
( ! [X0] :
( sK11 = relation_composition(sK4,relation_dom(relation_rng(X0)))
| ~ empty(X0) )
| ~ spl18_33
| ~ spl18_182 ),
inference(resolution,[],[f1587,f367]) ).
fof(f1587,plain,
( ! [X0] :
( ~ empty(X0)
| sK11 = relation_composition(sK4,relation_dom(X0)) )
| ~ spl18_182 ),
inference(avatar_component_clause,[],[f1586]) ).
fof(f3720,plain,
( spl18_299
| ~ spl18_35
| ~ spl18_182 ),
inference(avatar_split_clause,[],[f2192,f1586,f374,f3718]) ).
fof(f3718,plain,
( spl18_299
<=> ! [X0] :
( sK11 = relation_composition(sK4,relation_dom(relation_dom(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_299])]) ).
fof(f2192,plain,
( ! [X0] :
( sK11 = relation_composition(sK4,relation_dom(relation_dom(X0)))
| ~ empty(X0) )
| ~ spl18_35
| ~ spl18_182 ),
inference(resolution,[],[f1587,f375]) ).
fof(f3678,plain,
( spl18_298
| ~ spl18_1
| ~ spl18_237 ),
inference(avatar_split_clause,[],[f2816,f2697,f205,f3676]) ).
fof(f3676,plain,
( spl18_298
<=> ! [X0,X1] :
( ~ empty(X0)
| sK11 = relation_composition(X0,relation_composition(X1,sK4))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_298])]) ).
fof(f2816,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK11 = relation_composition(X0,relation_composition(X1,sK4))
| ~ relation(X1) )
| ~ spl18_1
| ~ spl18_237 ),
inference(resolution,[],[f2698,f207]) ).
fof(f3674,plain,
( spl18_297
| ~ spl18_1
| ~ spl18_236 ),
inference(avatar_split_clause,[],[f2797,f2693,f205,f3672]) ).
fof(f3672,plain,
( spl18_297
<=> ! [X0,X1] :
( ~ empty(X0)
| sK11 = relation_composition(X0,relation_composition(sK4,X1))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_297])]) ).
fof(f2797,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK11 = relation_composition(X0,relation_composition(sK4,X1))
| ~ empty(X1) )
| ~ spl18_1
| ~ spl18_236 ),
inference(resolution,[],[f2694,f207]) ).
fof(f3670,plain,
( spl18_296
| ~ spl18_1
| ~ spl18_235 ),
inference(avatar_split_clause,[],[f2778,f2689,f205,f3668]) ).
fof(f3668,plain,
( spl18_296
<=> ! [X0,X1] :
( ~ empty(X0)
| sK11 = relation_composition(X0,relation_composition(X1,sK4))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_296])]) ).
fof(f2778,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK11 = relation_composition(X0,relation_composition(X1,sK4))
| ~ empty(X1) )
| ~ spl18_1
| ~ spl18_235 ),
inference(resolution,[],[f2690,f207]) ).
fof(f3666,plain,
( spl18_295
| ~ spl18_1
| ~ spl18_234 ),
inference(avatar_split_clause,[],[f2759,f2685,f205,f3664]) ).
fof(f3664,plain,
( spl18_295
<=> ! [X0,X1] :
( ~ empty(X0)
| sK11 = relation_composition(relation_composition(X1,sK4),X0)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_295])]) ).
fof(f2759,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK11 = relation_composition(relation_composition(X1,sK4),X0)
| ~ relation(X1) )
| ~ spl18_1
| ~ spl18_234 ),
inference(resolution,[],[f2686,f207]) ).
fof(f3662,plain,
( spl18_294
| ~ spl18_1
| ~ spl18_233 ),
inference(avatar_split_clause,[],[f2735,f2681,f205,f3660]) ).
fof(f3660,plain,
( spl18_294
<=> ! [X0,X1] :
( ~ empty(X0)
| sK11 = relation_composition(relation_composition(sK4,X1),X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_294])]) ).
fof(f2735,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK11 = relation_composition(relation_composition(sK4,X1),X0)
| ~ empty(X1) )
| ~ spl18_1
| ~ spl18_233 ),
inference(resolution,[],[f2682,f207]) ).
fof(f3658,plain,
( spl18_293
| ~ spl18_1
| ~ spl18_232 ),
inference(avatar_split_clause,[],[f2716,f2677,f205,f3656]) ).
fof(f3656,plain,
( spl18_293
<=> ! [X0,X1] :
( ~ empty(X0)
| sK11 = relation_composition(relation_composition(X1,sK4),X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_293])]) ).
fof(f2716,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK11 = relation_composition(relation_composition(X1,sK4),X0)
| ~ empty(X1) )
| ~ spl18_1
| ~ spl18_232 ),
inference(resolution,[],[f2678,f207]) ).
fof(f3654,plain,
( spl18_292
| ~ spl18_139
| ~ spl18_223 ),
inference(avatar_split_clause,[],[f2532,f2401,f1270,f3652]) ).
fof(f3652,plain,
( spl18_292
<=> ! [X0,X1] :
( relation_rng(relation_composition(function_inverse(sK4),X0)) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_292])]) ).
fof(f2401,plain,
( spl18_223
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| relation_rng(relation_composition(X1,X2)) = X0
| ~ relation(X1)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_223])]) ).
fof(f2532,plain,
( ! [X0,X1] :
( relation_rng(relation_composition(function_inverse(sK4),X0)) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl18_139
| ~ spl18_223 ),
inference(resolution,[],[f2402,f1271]) ).
fof(f2402,plain,
( ! [X2,X0,X1] :
( ~ relation(X1)
| relation_rng(relation_composition(X1,X2)) = X0
| ~ empty(X0)
| ~ empty(X2) )
| ~ spl18_223 ),
inference(avatar_component_clause,[],[f2401]) ).
fof(f3650,plain,
( spl18_291
| ~ spl18_139
| ~ spl18_222 ),
inference(avatar_split_clause,[],[f2513,f2397,f1270,f3648]) ).
fof(f3648,plain,
( spl18_291
<=> ! [X0,X1] :
( relation_rng(relation_composition(X0,function_inverse(sK4))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_291])]) ).
fof(f2397,plain,
( spl18_222
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| relation_rng(relation_composition(X1,X2)) = X0
| ~ relation(X2)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_222])]) ).
fof(f2513,plain,
( ! [X0,X1] :
( relation_rng(relation_composition(X0,function_inverse(sK4))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl18_139
| ~ spl18_222 ),
inference(resolution,[],[f2398,f1271]) ).
fof(f2398,plain,
( ! [X2,X0,X1] :
( ~ relation(X2)
| relation_rng(relation_composition(X1,X2)) = X0
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl18_222 ),
inference(avatar_component_clause,[],[f2397]) ).
fof(f3634,plain,
( spl18_290
| ~ spl18_139
| ~ spl18_221 ),
inference(avatar_split_clause,[],[f2475,f2393,f1270,f3632]) ).
fof(f3632,plain,
( spl18_290
<=> ! [X0,X1] :
( relation_dom(relation_composition(function_inverse(sK4),X0)) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_290])]) ).
fof(f2393,plain,
( spl18_221
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| relation_dom(relation_composition(X1,X2)) = X0
| ~ relation(X1)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_221])]) ).
fof(f2475,plain,
( ! [X0,X1] :
( relation_dom(relation_composition(function_inverse(sK4),X0)) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl18_139
| ~ spl18_221 ),
inference(resolution,[],[f2394,f1271]) ).
fof(f2394,plain,
( ! [X2,X0,X1] :
( ~ relation(X1)
| relation_dom(relation_composition(X1,X2)) = X0
| ~ empty(X0)
| ~ empty(X2) )
| ~ spl18_221 ),
inference(avatar_component_clause,[],[f2393]) ).
fof(f3630,plain,
( spl18_289
| ~ spl18_139
| ~ spl18_220 ),
inference(avatar_split_clause,[],[f2456,f2389,f1270,f3628]) ).
fof(f3628,plain,
( spl18_289
<=> ! [X0,X1] :
( relation_dom(relation_composition(X0,function_inverse(sK4))) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_289])]) ).
fof(f2389,plain,
( spl18_220
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| relation_dom(relation_composition(X1,X2)) = X0
| ~ relation(X2)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_220])]) ).
fof(f2456,plain,
( ! [X0,X1] :
( relation_dom(relation_composition(X0,function_inverse(sK4))) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl18_139
| ~ spl18_220 ),
inference(resolution,[],[f2390,f1271]) ).
fof(f2390,plain,
( ! [X2,X0,X1] :
( ~ relation(X2)
| relation_dom(relation_composition(X1,X2)) = X0
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl18_220 ),
inference(avatar_component_clause,[],[f2389]) ).
fof(f3626,plain,
( spl18_288
| ~ spl18_137
| ~ spl18_169 ),
inference(avatar_split_clause,[],[f1526,f1512,f1236,f3624]) ).
fof(f3624,plain,
( spl18_288
<=> ! [X0,X1] :
( ~ empty(X0)
| sK8(powerset(X0)) = relation_composition(X1,sK4)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_288])]) ).
fof(f1512,plain,
( spl18_169
<=> ! [X0] :
( ~ empty(X0)
| empty(sK8(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_169])]) ).
fof(f1526,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK8(powerset(X0)) = relation_composition(X1,sK4)
| ~ empty(X1) )
| ~ spl18_137
| ~ spl18_169 ),
inference(resolution,[],[f1513,f1237]) ).
fof(f1513,plain,
( ! [X0] :
( empty(sK8(powerset(X0)))
| ~ empty(X0) )
| ~ spl18_169 ),
inference(avatar_component_clause,[],[f1512]) ).
fof(f3622,plain,
( spl18_287
| ~ spl18_136
| ~ spl18_169 ),
inference(avatar_split_clause,[],[f1525,f1512,f1232,f3620]) ).
fof(f3620,plain,
( spl18_287
<=> ! [X0,X1] :
( ~ empty(X0)
| sK8(powerset(X0)) = relation_composition(sK4,X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_287])]) ).
fof(f1525,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK8(powerset(X0)) = relation_composition(sK4,X1)
| ~ empty(X1) )
| ~ spl18_136
| ~ spl18_169 ),
inference(resolution,[],[f1513,f1233]) ).
fof(f3618,plain,
( spl18_286
| ~ spl18_54
| ~ spl18_129 ),
inference(avatar_split_clause,[],[f1219,f1150,f483,f3616]) ).
fof(f3616,plain,
( spl18_286
<=> ! [X0,X1] :
( sK11 = relation_composition(relation_composition(X0,X1),sK4)
| ~ relation(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_286])]) ).
fof(f1150,plain,
( spl18_129
<=> ! [X0] :
( sK11 = relation_composition(X0,sK4)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_129])]) ).
fof(f1219,plain,
( ! [X0,X1] :
( sK11 = relation_composition(relation_composition(X0,X1),sK4)
| ~ relation(X0)
| ~ empty(X1) )
| ~ spl18_54
| ~ spl18_129 ),
inference(resolution,[],[f1151,f484]) ).
fof(f1151,plain,
( ! [X0] :
( ~ empty(X0)
| sK11 = relation_composition(X0,sK4) )
| ~ spl18_129 ),
inference(avatar_component_clause,[],[f1150]) ).
fof(f3614,plain,
( spl18_285
| ~ spl18_57
| ~ spl18_129 ),
inference(avatar_split_clause,[],[f1218,f1150,f496,f3612]) ).
fof(f3612,plain,
( spl18_285
<=> ! [X0,X1] :
( sK11 = relation_composition(relation_composition(X0,X1),sK4)
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_285])]) ).
fof(f1218,plain,
( ! [X0,X1] :
( sK11 = relation_composition(relation_composition(X0,X1),sK4)
| ~ relation(X1)
| ~ empty(X0) )
| ~ spl18_57
| ~ spl18_129 ),
inference(resolution,[],[f1151,f497]) ).
fof(f3610,plain,
( spl18_284
| ~ spl18_54
| ~ spl18_123 ),
inference(avatar_split_clause,[],[f1198,f1084,f483,f3608]) ).
fof(f3608,plain,
( spl18_284
<=> ! [X0,X1] :
( sK11 = relation_composition(sK4,relation_composition(X0,X1))
| ~ relation(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_284])]) ).
fof(f1084,plain,
( spl18_123
<=> ! [X0] :
( sK11 = relation_composition(sK4,X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_123])]) ).
fof(f1198,plain,
( ! [X0,X1] :
( sK11 = relation_composition(sK4,relation_composition(X0,X1))
| ~ relation(X0)
| ~ empty(X1) )
| ~ spl18_54
| ~ spl18_123 ),
inference(resolution,[],[f1085,f484]) ).
fof(f1085,plain,
( ! [X0] :
( ~ empty(X0)
| sK11 = relation_composition(sK4,X0) )
| ~ spl18_123 ),
inference(avatar_component_clause,[],[f1084]) ).
fof(f3606,plain,
( spl18_283
| ~ spl18_57
| ~ spl18_123 ),
inference(avatar_split_clause,[],[f1197,f1084,f496,f3604]) ).
fof(f3604,plain,
( spl18_283
<=> ! [X0,X1] :
( sK11 = relation_composition(sK4,relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_283])]) ).
fof(f1197,plain,
( ! [X0,X1] :
( sK11 = relation_composition(sK4,relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) )
| ~ spl18_57
| ~ spl18_123 ),
inference(resolution,[],[f1085,f497]) ).
fof(f3430,plain,
( spl18_282
| ~ spl18_1
| ~ spl18_223 ),
inference(avatar_split_clause,[],[f2539,f2401,f205,f3428]) ).
fof(f3428,plain,
( spl18_282
<=> ! [X0,X1] :
( relation_rng(relation_composition(sK4,X0)) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_282])]) ).
fof(f2539,plain,
( ! [X0,X1] :
( relation_rng(relation_composition(sK4,X0)) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl18_1
| ~ spl18_223 ),
inference(resolution,[],[f2402,f207]) ).
fof(f3426,plain,
( spl18_281
| ~ spl18_1
| ~ spl18_222 ),
inference(avatar_split_clause,[],[f2520,f2397,f205,f3424]) ).
fof(f3424,plain,
( spl18_281
<=> ! [X0,X1] :
( relation_rng(relation_composition(X0,sK4)) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_281])]) ).
fof(f2520,plain,
( ! [X0,X1] :
( relation_rng(relation_composition(X0,sK4)) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl18_1
| ~ spl18_222 ),
inference(resolution,[],[f2398,f207]) ).
fof(f3422,plain,
( spl18_280
| ~ spl18_5
| ~ spl18_85
| ~ spl18_266 ),
inference(avatar_split_clause,[],[f3301,f3258,f679,f225,f3419]) ).
fof(f3419,plain,
( spl18_280
<=> sK11 = relation_composition(sK8(powerset(sK11)),sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_280])]) ).
fof(f3258,plain,
( spl18_266
<=> ! [X0] :
( ~ empty(X0)
| sK11 = relation_composition(sK8(powerset(X0)),sK4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_266])]) ).
fof(f3301,plain,
( sK11 = relation_composition(sK8(powerset(sK11)),sK4)
| ~ spl18_5
| ~ spl18_85
| ~ spl18_266 ),
inference(forward_demodulation,[],[f3293,f681]) ).
fof(f3293,plain,
( sK11 = relation_composition(sK8(powerset(empty_set)),sK4)
| ~ spl18_5
| ~ spl18_266 ),
inference(resolution,[],[f3259,f227]) ).
fof(f3259,plain,
( ! [X0] :
( ~ empty(X0)
| sK11 = relation_composition(sK8(powerset(X0)),sK4) )
| ~ spl18_266 ),
inference(avatar_component_clause,[],[f3258]) ).
fof(f3417,plain,
( spl18_279
| ~ spl18_1
| ~ spl18_221 ),
inference(avatar_split_clause,[],[f2482,f2393,f205,f3415]) ).
fof(f3415,plain,
( spl18_279
<=> ! [X0,X1] :
( relation_dom(relation_composition(sK4,X0)) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_279])]) ).
fof(f2482,plain,
( ! [X0,X1] :
( relation_dom(relation_composition(sK4,X0)) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl18_1
| ~ spl18_221 ),
inference(resolution,[],[f2394,f207]) ).
fof(f3413,plain,
( spl18_278
| ~ spl18_1
| ~ spl18_220 ),
inference(avatar_split_clause,[],[f2463,f2389,f205,f3411]) ).
fof(f3411,plain,
( spl18_278
<=> ! [X0,X1] :
( relation_dom(relation_composition(X0,sK4)) = X1
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_278])]) ).
fof(f2463,plain,
( ! [X0,X1] :
( relation_dom(relation_composition(X0,sK4)) = X1
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl18_1
| ~ spl18_220 ),
inference(resolution,[],[f2390,f207]) ).
fof(f3409,plain,
( spl18_277
| ~ spl18_125
| ~ spl18_139 ),
inference(avatar_split_clause,[],[f1375,f1270,f1092,f3407]) ).
fof(f3407,plain,
( spl18_277
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_composition(function_inverse(sK4),X0) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_277])]) ).
fof(f1092,plain,
( spl18_125
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| relation_composition(X0,X1) = X2
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_125])]) ).
fof(f1375,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_composition(function_inverse(sK4),X0) = X1
| ~ empty(X1) )
| ~ spl18_125
| ~ spl18_139 ),
inference(resolution,[],[f1271,f1093]) ).
fof(f1093,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| relation_composition(X0,X1) = X2
| ~ empty(X2) )
| ~ spl18_125 ),
inference(avatar_component_clause,[],[f1092]) ).
fof(f3405,plain,
( spl18_276
| ~ spl18_126
| ~ spl18_139 ),
inference(avatar_split_clause,[],[f1374,f1270,f1096,f3403]) ).
fof(f3403,plain,
( spl18_276
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_composition(X0,function_inverse(sK4)) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_276])]) ).
fof(f1096,plain,
( spl18_126
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| relation_composition(X1,X0) = X2
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_126])]) ).
fof(f1374,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_composition(X0,function_inverse(sK4)) = X1
| ~ empty(X1) )
| ~ spl18_126
| ~ spl18_139 ),
inference(resolution,[],[f1271,f1097]) ).
fof(f1097,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| relation_composition(X1,X0) = X2
| ~ empty(X2) )
| ~ spl18_126 ),
inference(avatar_component_clause,[],[f1096]) ).
fof(f3401,plain,
( spl18_275
| ~ spl18_33
| ~ spl18_137 ),
inference(avatar_split_clause,[],[f1256,f1236,f366,f3399]) ).
fof(f3399,plain,
( spl18_275
<=> ! [X0,X1] :
( relation_rng(X1) = relation_composition(X0,sK4)
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_275])]) ).
fof(f1256,plain,
( ! [X0,X1] :
( relation_rng(X1) = relation_composition(X0,sK4)
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl18_33
| ~ spl18_137 ),
inference(resolution,[],[f1237,f367]) ).
fof(f3397,plain,
( spl18_274
| ~ spl18_35
| ~ spl18_137 ),
inference(avatar_split_clause,[],[f1255,f1236,f374,f3395]) ).
fof(f3395,plain,
( spl18_274
<=> ! [X0,X1] :
( relation_dom(X1) = relation_composition(X0,sK4)
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_274])]) ).
fof(f1255,plain,
( ! [X0,X1] :
( relation_dom(X1) = relation_composition(X0,sK4)
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl18_35
| ~ spl18_137 ),
inference(resolution,[],[f1237,f375]) ).
fof(f3393,plain,
( spl18_273
| ~ spl18_33
| ~ spl18_136 ),
inference(avatar_split_clause,[],[f1243,f1232,f366,f3391]) ).
fof(f3391,plain,
( spl18_273
<=> ! [X0,X1] :
( relation_rng(X1) = relation_composition(sK4,X0)
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_273])]) ).
fof(f1243,plain,
( ! [X0,X1] :
( relation_rng(X1) = relation_composition(sK4,X0)
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl18_33
| ~ spl18_136 ),
inference(resolution,[],[f1233,f367]) ).
fof(f3389,plain,
( spl18_272
| ~ spl18_35
| ~ spl18_136 ),
inference(avatar_split_clause,[],[f1242,f1232,f374,f3387]) ).
fof(f3387,plain,
( spl18_272
<=> ! [X0,X1] :
( relation_dom(X1) = relation_composition(sK4,X0)
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_272])]) ).
fof(f1242,plain,
( ! [X0,X1] :
( relation_dom(X1) = relation_composition(sK4,X0)
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl18_35
| ~ spl18_136 ),
inference(resolution,[],[f1233,f375]) ).
fof(f3347,plain,
( spl18_271
| ~ spl18_5
| ~ spl18_85
| ~ spl18_265 ),
inference(avatar_split_clause,[],[f3287,f3254,f679,f225,f3344]) ).
fof(f3344,plain,
( spl18_271
<=> sK11 = relation_composition(sK4,sK8(powerset(sK11))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_271])]) ).
fof(f3254,plain,
( spl18_265
<=> ! [X0] :
( ~ empty(X0)
| sK11 = relation_composition(sK4,sK8(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_265])]) ).
fof(f3287,plain,
( sK11 = relation_composition(sK4,sK8(powerset(sK11)))
| ~ spl18_5
| ~ spl18_85
| ~ spl18_265 ),
inference(forward_demodulation,[],[f3279,f681]) ).
fof(f3279,plain,
( sK11 = relation_composition(sK4,sK8(powerset(empty_set)))
| ~ spl18_5
| ~ spl18_265 ),
inference(resolution,[],[f3255,f227]) ).
fof(f3255,plain,
( ! [X0] :
( ~ empty(X0)
| sK11 = relation_composition(sK4,sK8(powerset(X0))) )
| ~ spl18_265 ),
inference(avatar_component_clause,[],[f3254]) ).
fof(f3276,plain,
( spl18_270
| ~ spl18_139
| ~ spl18_209 ),
inference(avatar_split_clause,[],[f2274,f2154,f1270,f3274]) ).
fof(f3274,plain,
( spl18_270
<=> ! [X0] :
( sK11 = relation_dom(relation_composition(function_inverse(sK4),X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_270])]) ).
fof(f2154,plain,
( spl18_209
<=> ! [X0,X1] :
( sK11 = relation_dom(relation_composition(X0,X1))
| ~ relation(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_209])]) ).
fof(f2274,plain,
( ! [X0] :
( sK11 = relation_dom(relation_composition(function_inverse(sK4),X0))
| ~ empty(X0) )
| ~ spl18_139
| ~ spl18_209 ),
inference(resolution,[],[f2155,f1271]) ).
fof(f2155,plain,
( ! [X0,X1] :
( ~ relation(X0)
| sK11 = relation_dom(relation_composition(X0,X1))
| ~ empty(X1) )
| ~ spl18_209 ),
inference(avatar_component_clause,[],[f2154]) ).
fof(f3272,plain,
( spl18_269
| ~ spl18_139
| ~ spl18_208 ),
inference(avatar_split_clause,[],[f2255,f2150,f1270,f3270]) ).
fof(f3270,plain,
( spl18_269
<=> ! [X0] :
( sK11 = relation_dom(relation_composition(X0,function_inverse(sK4)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_269])]) ).
fof(f2150,plain,
( spl18_208
<=> ! [X0,X1] :
( sK11 = relation_dom(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_208])]) ).
fof(f2255,plain,
( ! [X0] :
( sK11 = relation_dom(relation_composition(X0,function_inverse(sK4)))
| ~ empty(X0) )
| ~ spl18_139
| ~ spl18_208 ),
inference(resolution,[],[f2151,f1271]) ).
fof(f2151,plain,
( ! [X0,X1] :
( ~ relation(X1)
| sK11 = relation_dom(relation_composition(X0,X1))
| ~ empty(X0) )
| ~ spl18_208 ),
inference(avatar_component_clause,[],[f2150]) ).
fof(f3268,plain,
( spl18_268
| ~ spl18_139
| ~ spl18_206 ),
inference(avatar_split_clause,[],[f2236,f2142,f1270,f3266]) ).
fof(f3266,plain,
( spl18_268
<=> ! [X0] :
( sK11 = relation_rng(relation_composition(function_inverse(sK4),X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_268])]) ).
fof(f2142,plain,
( spl18_206
<=> ! [X0,X1] :
( sK11 = relation_rng(relation_composition(X0,X1))
| ~ relation(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_206])]) ).
fof(f2236,plain,
( ! [X0] :
( sK11 = relation_rng(relation_composition(function_inverse(sK4),X0))
| ~ empty(X0) )
| ~ spl18_139
| ~ spl18_206 ),
inference(resolution,[],[f2143,f1271]) ).
fof(f2143,plain,
( ! [X0,X1] :
( ~ relation(X0)
| sK11 = relation_rng(relation_composition(X0,X1))
| ~ empty(X1) )
| ~ spl18_206 ),
inference(avatar_component_clause,[],[f2142]) ).
fof(f3264,plain,
( spl18_267
| ~ spl18_139
| ~ spl18_205 ),
inference(avatar_split_clause,[],[f2217,f2138,f1270,f3262]) ).
fof(f3262,plain,
( spl18_267
<=> ! [X0] :
( sK11 = relation_rng(relation_composition(X0,function_inverse(sK4)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_267])]) ).
fof(f2138,plain,
( spl18_205
<=> ! [X0,X1] :
( sK11 = relation_rng(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_205])]) ).
fof(f2217,plain,
( ! [X0] :
( sK11 = relation_rng(relation_composition(X0,function_inverse(sK4)))
| ~ empty(X0) )
| ~ spl18_139
| ~ spl18_205 ),
inference(resolution,[],[f2139,f1271]) ).
fof(f2139,plain,
( ! [X0,X1] :
( ~ relation(X1)
| sK11 = relation_rng(relation_composition(X0,X1))
| ~ empty(X0) )
| ~ spl18_205 ),
inference(avatar_component_clause,[],[f2138]) ).
fof(f3260,plain,
( spl18_266
| ~ spl18_129
| ~ spl18_169 ),
inference(avatar_split_clause,[],[f1524,f1512,f1150,f3258]) ).
fof(f1524,plain,
( ! [X0] :
( ~ empty(X0)
| sK11 = relation_composition(sK8(powerset(X0)),sK4) )
| ~ spl18_129
| ~ spl18_169 ),
inference(resolution,[],[f1513,f1151]) ).
fof(f3256,plain,
( spl18_265
| ~ spl18_123
| ~ spl18_169 ),
inference(avatar_split_clause,[],[f1523,f1512,f1084,f3254]) ).
fof(f1523,plain,
( ! [X0] :
( ~ empty(X0)
| sK11 = relation_composition(sK4,sK8(powerset(X0))) )
| ~ spl18_123
| ~ spl18_169 ),
inference(resolution,[],[f1513,f1085]) ).
fof(f3252,plain,
( spl18_263
| ~ spl18_264
| ~ spl18_138
| ~ spl18_52
| ~ spl18_139 ),
inference(avatar_split_clause,[],[f1378,f1270,f475,f1266,f3249,f3245]) ).
fof(f3245,plain,
( spl18_263
<=> one_to_one(function_inverse(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_263])]) ).
fof(f3249,plain,
( spl18_264
<=> empty(function_inverse(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_264])]) ).
fof(f475,plain,
( spl18_52
<=> ! [X0] :
( one_to_one(X0)
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_52])]) ).
fof(f1378,plain,
( ~ function(function_inverse(sK4))
| ~ empty(function_inverse(sK4))
| one_to_one(function_inverse(sK4))
| ~ spl18_52
| ~ spl18_139 ),
inference(resolution,[],[f1271,f476]) ).
fof(f476,plain,
( ! [X0] :
( ~ relation(X0)
| ~ function(X0)
| ~ empty(X0)
| one_to_one(X0) )
| ~ spl18_52 ),
inference(avatar_component_clause,[],[f475]) ).
fof(f3167,plain,
( spl18_262
| ~ spl18_1
| ~ spl18_209 ),
inference(avatar_split_clause,[],[f2281,f2154,f205,f3165]) ).
fof(f3165,plain,
( spl18_262
<=> ! [X0] :
( sK11 = relation_dom(relation_composition(sK4,X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_262])]) ).
fof(f2281,plain,
( ! [X0] :
( sK11 = relation_dom(relation_composition(sK4,X0))
| ~ empty(X0) )
| ~ spl18_1
| ~ spl18_209 ),
inference(resolution,[],[f2155,f207]) ).
fof(f3163,plain,
( spl18_261
| ~ spl18_1
| ~ spl18_208 ),
inference(avatar_split_clause,[],[f2262,f2150,f205,f3161]) ).
fof(f3161,plain,
( spl18_261
<=> ! [X0] :
( sK11 = relation_dom(relation_composition(X0,sK4))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_261])]) ).
fof(f2262,plain,
( ! [X0] :
( sK11 = relation_dom(relation_composition(X0,sK4))
| ~ empty(X0) )
| ~ spl18_1
| ~ spl18_208 ),
inference(resolution,[],[f2151,f207]) ).
fof(f3159,plain,
( spl18_260
| ~ spl18_1
| ~ spl18_206 ),
inference(avatar_split_clause,[],[f2243,f2142,f205,f3157]) ).
fof(f3157,plain,
( spl18_260
<=> ! [X0] :
( sK11 = relation_rng(relation_composition(sK4,X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_260])]) ).
fof(f2243,plain,
( ! [X0] :
( sK11 = relation_rng(relation_composition(sK4,X0))
| ~ empty(X0) )
| ~ spl18_1
| ~ spl18_206 ),
inference(resolution,[],[f2143,f207]) ).
fof(f3155,plain,
( spl18_259
| ~ spl18_1
| ~ spl18_205 ),
inference(avatar_split_clause,[],[f2224,f2138,f205,f3153]) ).
fof(f3153,plain,
( spl18_259
<=> ! [X0] :
( sK11 = relation_rng(relation_composition(X0,sK4))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_259])]) ).
fof(f2224,plain,
( ! [X0] :
( sK11 = relation_rng(relation_composition(X0,sK4))
| ~ empty(X0) )
| ~ spl18_1
| ~ spl18_205 ),
inference(resolution,[],[f2139,f207]) ).
fof(f3137,plain,
( spl18_258
| ~ spl18_76
| ~ spl18_128 ),
inference(avatar_split_clause,[],[f1153,f1144,f635,f3135]) ).
fof(f3135,plain,
( spl18_258
<=> ! [X0,X3,X2,X1] :
( ~ in(X0,relation_rng(X1))
| ~ sP1(X2,X1)
| apply(relation_composition(X1,X3),apply(X2,X0)) = apply(X3,apply(X1,apply(X2,X0)))
| ~ function(X3)
| ~ relation(X3)
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_258])]) ).
fof(f635,plain,
( spl18_76
<=> ! [X2,X0,X1] :
( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_76])]) ).
fof(f1153,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ sP1(X2,X1)
| apply(relation_composition(X1,X3),apply(X2,X0)) = apply(X3,apply(X1,apply(X2,X0)))
| ~ function(X3)
| ~ relation(X3)
| ~ function(X1)
| ~ relation(X1) )
| ~ spl18_76
| ~ spl18_128 ),
inference(resolution,[],[f1145,f636]) ).
fof(f636,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_dom(X1))
| apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) )
| ~ spl18_76 ),
inference(avatar_component_clause,[],[f635]) ).
fof(f3111,plain,
( spl18_257
| ~ spl18_76
| ~ spl18_105 ),
inference(avatar_split_clause,[],[f924,f889,f635,f3109]) ).
fof(f3109,plain,
( spl18_257
<=> ! [X0,X1] :
( empty(relation_dom(X0))
| apply(relation_composition(X0,X1),sK8(relation_dom(X0))) = apply(X1,apply(X0,sK8(relation_dom(X0))))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_257])]) ).
fof(f889,plain,
( spl18_105
<=> ! [X0] :
( empty(X0)
| in(sK8(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_105])]) ).
fof(f924,plain,
( ! [X0,X1] :
( empty(relation_dom(X0))
| apply(relation_composition(X0,X1),sK8(relation_dom(X0))) = apply(X1,apply(X0,sK8(relation_dom(X0))))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) )
| ~ spl18_76
| ~ spl18_105 ),
inference(resolution,[],[f890,f636]) ).
fof(f890,plain,
( ! [X0] :
( in(sK8(X0),X0)
| empty(X0) )
| ~ spl18_105 ),
inference(avatar_component_clause,[],[f889]) ).
fof(f3104,plain,
( spl18_256
| ~ spl18_72
| ~ spl18_128 ),
inference(avatar_split_clause,[],[f1154,f1144,f612,f3102]) ).
fof(f3102,plain,
( spl18_256
<=> ! [X0,X3,X2,X1] :
( ~ in(X0,relation_rng(X1))
| ~ sP1(X2,X1)
| apply(X2,X0) = apply(X3,apply(X1,apply(X2,X0)))
| ~ sP1(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_256])]) ).
fof(f612,plain,
( spl18_72
<=> ! [X5,X1,X0] :
( apply(X0,apply(X1,X5)) = X5
| ~ in(X5,relation_dom(X1))
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_72])]) ).
fof(f1154,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ sP1(X2,X1)
| apply(X2,X0) = apply(X3,apply(X1,apply(X2,X0)))
| ~ sP1(X3,X1) )
| ~ spl18_72
| ~ spl18_128 ),
inference(resolution,[],[f1145,f613]) ).
fof(f613,plain,
( ! [X0,X1,X5] :
( ~ in(X5,relation_dom(X1))
| apply(X0,apply(X1,X5)) = X5
| ~ sP1(X0,X1) )
| ~ spl18_72 ),
inference(avatar_component_clause,[],[f612]) ).
fof(f3094,plain,
( spl18_255
| ~ spl18_50
| ~ spl18_134 ),
inference(avatar_split_clause,[],[f1210,f1178,f467,f3092]) ).
fof(f3092,plain,
( spl18_255
<=> ! [X0] :
( ~ relation(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0)
| ~ function(function_inverse(X0))
| relation_rng(X0) = relation_dom(function_inverse(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_255])]) ).
fof(f467,plain,
( spl18_50
<=> ! [X0,X1] :
( relation_dom(X0) = relation_rng(X1)
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_50])]) ).
fof(f1178,plain,
( spl18_134
<=> ! [X0] :
( ~ function(function_inverse(X0))
| ~ relation(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0)
| sP1(function_inverse(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_134])]) ).
fof(f1210,plain,
( ! [X0] :
( ~ relation(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0)
| ~ function(function_inverse(X0))
| relation_rng(X0) = relation_dom(function_inverse(X0)) )
| ~ spl18_50
| ~ spl18_134 ),
inference(resolution,[],[f1179,f468]) ).
fof(f468,plain,
( ! [X0,X1] :
( ~ sP1(X0,X1)
| relation_dom(X0) = relation_rng(X1) )
| ~ spl18_50 ),
inference(avatar_component_clause,[],[f467]) ).
fof(f1179,plain,
( ! [X0] :
( sP1(function_inverse(X0),X0)
| ~ relation(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0)
| ~ function(function_inverse(X0)) )
| ~ spl18_134 ),
inference(avatar_component_clause,[],[f1178]) ).
fof(f3090,plain,
( spl18_254
| ~ spl18_71
| ~ spl18_128 ),
inference(avatar_split_clause,[],[f1155,f1144,f605,f3088]) ).
fof(f3088,plain,
( spl18_254
<=> ! [X2,X0,X1,X3] :
( ~ in(X0,relation_rng(X1))
| ~ sP1(X2,X1)
| in(apply(X1,apply(X2,X0)),relation_rng(X1))
| ~ sP1(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_254])]) ).
fof(f605,plain,
( spl18_71
<=> ! [X5,X1,X0] :
( in(apply(X1,X5),relation_rng(X1))
| ~ in(X5,relation_dom(X1))
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_71])]) ).
fof(f1155,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ sP1(X2,X1)
| in(apply(X1,apply(X2,X0)),relation_rng(X1))
| ~ sP1(X3,X1) )
| ~ spl18_71
| ~ spl18_128 ),
inference(resolution,[],[f1145,f606]) ).
fof(f606,plain,
( ! [X0,X1,X5] :
( ~ in(X5,relation_dom(X1))
| in(apply(X1,X5),relation_rng(X1))
| ~ sP1(X0,X1) )
| ~ spl18_71 ),
inference(avatar_component_clause,[],[f605]) ).
fof(f3086,plain,
( spl18_253
| ~ spl18_5
| ~ spl18_85
| ~ spl18_207 ),
inference(avatar_split_clause,[],[f2981,f2146,f679,f225,f3083]) ).
fof(f3083,plain,
( spl18_253
<=> sK11 = relation_composition(function_inverse(sK4),sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_253])]) ).
fof(f2146,plain,
( spl18_207
<=> ! [X0] :
( sK11 = relation_composition(function_inverse(sK4),X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_207])]) ).
fof(f2981,plain,
( sK11 = relation_composition(function_inverse(sK4),sK11)
| ~ spl18_5
| ~ spl18_85
| ~ spl18_207 ),
inference(forward_demodulation,[],[f2973,f681]) ).
fof(f2973,plain,
( sK11 = relation_composition(function_inverse(sK4),empty_set)
| ~ spl18_5
| ~ spl18_207 ),
inference(resolution,[],[f2147,f227]) ).
fof(f2147,plain,
( ! [X0] :
( ~ empty(X0)
| sK11 = relation_composition(function_inverse(sK4),X0) )
| ~ spl18_207 ),
inference(avatar_component_clause,[],[f2146]) ).
fof(f3079,plain,
( spl18_252
| ~ spl18_105
| ~ spl18_130 ),
inference(avatar_split_clause,[],[f1164,f1161,f889,f3077]) ).
fof(f3077,plain,
( spl18_252
<=> ! [X0,X1] :
( sK8(relation_rng(X0)) = apply(X0,apply(X1,sK8(relation_rng(X0))))
| ~ sP1(X1,X0)
| empty(relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_252])]) ).
fof(f1161,plain,
( spl18_130
<=> ! [X2,X0,X1] :
( ~ in(X0,relation_rng(X1))
| apply(X1,apply(X2,X0)) = X0
| ~ sP1(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_130])]) ).
fof(f1164,plain,
( ! [X0,X1] :
( sK8(relation_rng(X0)) = apply(X0,apply(X1,sK8(relation_rng(X0))))
| ~ sP1(X1,X0)
| empty(relation_rng(X0)) )
| ~ spl18_105
| ~ spl18_130 ),
inference(resolution,[],[f1162,f890]) ).
fof(f1162,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_rng(X1))
| apply(X1,apply(X2,X0)) = X0
| ~ sP1(X2,X1) )
| ~ spl18_130 ),
inference(avatar_component_clause,[],[f1161]) ).
fof(f3075,plain,
( spl18_251
| ~ spl18_72
| ~ spl18_105 ),
inference(avatar_split_clause,[],[f925,f889,f612,f3073]) ).
fof(f3073,plain,
( spl18_251
<=> ! [X0,X1] :
( empty(relation_dom(X0))
| sK8(relation_dom(X0)) = apply(X1,apply(X0,sK8(relation_dom(X0))))
| ~ sP1(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_251])]) ).
fof(f925,plain,
( ! [X0,X1] :
( empty(relation_dom(X0))
| sK8(relation_dom(X0)) = apply(X1,apply(X0,sK8(relation_dom(X0))))
| ~ sP1(X1,X0) )
| ~ spl18_72
| ~ spl18_105 ),
inference(resolution,[],[f890,f613]) ).
fof(f3064,plain,
( spl18_250
| ~ spl18_68
| ~ spl18_133 ),
inference(avatar_split_clause,[],[f1194,f1174,f592,f3062]) ).
fof(f3062,plain,
( spl18_250
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ empty(relation_composition(X0,X1))
| one_to_one(relation_composition(X0,X1))
| ~ function(X1)
| ~ function(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_250])]) ).
fof(f592,plain,
( spl18_68
<=> ! [X0,X1] :
( function(relation_composition(X0,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_68])]) ).
fof(f1174,plain,
( spl18_133
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ function(relation_composition(X1,X0))
| ~ empty(relation_composition(X1,X0))
| one_to_one(relation_composition(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_133])]) ).
fof(f1194,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ empty(relation_composition(X0,X1))
| one_to_one(relation_composition(X0,X1))
| ~ function(X1)
| ~ function(X0) )
| ~ spl18_68
| ~ spl18_133 ),
inference(duplicate_literal_removal,[],[f1193]) ).
fof(f1193,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ empty(relation_composition(X0,X1))
| one_to_one(relation_composition(X0,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) )
| ~ spl18_68
| ~ spl18_133 ),
inference(resolution,[],[f1175,f593]) ).
fof(f593,plain,
( ! [X0,X1] :
( function(relation_composition(X0,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) )
| ~ spl18_68 ),
inference(avatar_component_clause,[],[f592]) ).
fof(f1175,plain,
( ! [X0,X1] :
( ~ function(relation_composition(X1,X0))
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_composition(X1,X0))
| one_to_one(relation_composition(X1,X0)) )
| ~ spl18_133 ),
inference(avatar_component_clause,[],[f1174]) ).
fof(f2932,plain,
( spl18_249
| ~ spl18_59
| ~ spl18_126 ),
inference(avatar_split_clause,[],[f1124,f1096,f504,f2930]) ).
fof(f504,plain,
( spl18_59
<=> ! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_59])]) ).
fof(f1124,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| relation_composition(X0,relation_composition(X1,X2)) = X3
| ~ empty(X3)
| ~ relation(X2)
| ~ relation(X1) )
| ~ spl18_59
| ~ spl18_126 ),
inference(resolution,[],[f1097,f505]) ).
fof(f505,plain,
( ! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl18_59 ),
inference(avatar_component_clause,[],[f504]) ).
fof(f2928,plain,
( spl18_248
| ~ spl18_56
| ~ spl18_126 ),
inference(avatar_split_clause,[],[f1123,f1096,f492,f2926]) ).
fof(f492,plain,
( spl18_56
<=> ! [X0,X1] :
( relation(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_56])]) ).
fof(f1123,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| relation_composition(X0,relation_composition(X1,X2)) = X3
| ~ empty(X3)
| ~ relation(X1)
| ~ empty(X2) )
| ~ spl18_56
| ~ spl18_126 ),
inference(resolution,[],[f1097,f493]) ).
fof(f493,plain,
( ! [X0,X1] :
( relation(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) )
| ~ spl18_56 ),
inference(avatar_component_clause,[],[f492]) ).
fof(f2924,plain,
( spl18_247
| ~ spl18_58
| ~ spl18_126 ),
inference(avatar_split_clause,[],[f1122,f1096,f500,f2922]) ).
fof(f500,plain,
( spl18_58
<=> ! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_58])]) ).
fof(f1122,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| relation_composition(X0,relation_composition(X1,X2)) = X3
| ~ empty(X3)
| ~ relation(X2)
| ~ empty(X1) )
| ~ spl18_58
| ~ spl18_126 ),
inference(resolution,[],[f1097,f501]) ).
fof(f501,plain,
( ! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) )
| ~ spl18_58 ),
inference(avatar_component_clause,[],[f500]) ).
fof(f2920,plain,
( spl18_246
| ~ spl18_59
| ~ spl18_125 ),
inference(avatar_split_clause,[],[f1106,f1092,f504,f2918]) ).
fof(f1106,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| relation_composition(relation_composition(X1,X2),X0) = X3
| ~ empty(X3)
| ~ relation(X2)
| ~ relation(X1) )
| ~ spl18_59
| ~ spl18_125 ),
inference(resolution,[],[f1093,f505]) ).
fof(f2916,plain,
( spl18_245
| ~ spl18_56
| ~ spl18_125 ),
inference(avatar_split_clause,[],[f1105,f1092,f492,f2914]) ).
fof(f1105,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| relation_composition(relation_composition(X1,X2),X0) = X3
| ~ empty(X3)
| ~ relation(X1)
| ~ empty(X2) )
| ~ spl18_56
| ~ spl18_125 ),
inference(resolution,[],[f1093,f493]) ).
fof(f2912,plain,
( spl18_244
| ~ spl18_58
| ~ spl18_125 ),
inference(avatar_split_clause,[],[f1104,f1092,f500,f2910]) ).
fof(f1104,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| relation_composition(relation_composition(X1,X2),X0) = X3
| ~ empty(X3)
| ~ relation(X2)
| ~ empty(X1) )
| ~ spl18_58
| ~ spl18_125 ),
inference(resolution,[],[f1093,f501]) ).
fof(f2853,plain,
( spl18_243
| ~ spl18_46
| ~ spl18_126 ),
inference(avatar_split_clause,[],[f1121,f1096,f438,f2851]) ).
fof(f438,plain,
( spl18_46
<=> ! [X0] :
( relation(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_46])]) ).
fof(f1121,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| relation_composition(X0,function_inverse(X1)) = X2
| ~ empty(X2)
| ~ function(X1)
| ~ relation(X1) )
| ~ spl18_46
| ~ spl18_126 ),
inference(resolution,[],[f1097,f439]) ).
fof(f439,plain,
( ! [X0] :
( relation(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl18_46 ),
inference(avatar_component_clause,[],[f438]) ).
fof(f2849,plain,
( spl18_242
| ~ spl18_46
| ~ spl18_125 ),
inference(avatar_split_clause,[],[f1103,f1092,f438,f2847]) ).
fof(f1103,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| relation_composition(function_inverse(X1),X0) = X2
| ~ empty(X2)
| ~ function(X1)
| ~ relation(X1) )
| ~ spl18_46
| ~ spl18_125 ),
inference(resolution,[],[f1093,f439]) ).
fof(f2845,plain,
( spl18_241
| ~ spl18_71
| ~ spl18_105 ),
inference(avatar_split_clause,[],[f926,f889,f605,f2843]) ).
fof(f2843,plain,
( spl18_241
<=> ! [X0,X1] :
( empty(relation_dom(X0))
| in(apply(X0,sK8(relation_dom(X0))),relation_rng(X0))
| ~ sP1(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_241])]) ).
fof(f926,plain,
( ! [X0,X1] :
( empty(relation_dom(X0))
| in(apply(X0,sK8(relation_dom(X0))),relation_rng(X0))
| ~ sP1(X1,X0) )
| ~ spl18_71
| ~ spl18_105 ),
inference(resolution,[],[f890,f606]) ).
fof(f2750,plain,
( spl18_240
| ~ spl18_5
| ~ spl18_85
| ~ spl18_204 ),
inference(avatar_split_clause,[],[f2672,f2022,f679,f225,f2747]) ).
fof(f2747,plain,
( spl18_240
<=> sK11 = relation_composition(sK11,function_inverse(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_240])]) ).
fof(f2022,plain,
( spl18_204
<=> ! [X0] :
( sK11 = relation_composition(X0,function_inverse(sK4))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_204])]) ).
fof(f2672,plain,
( sK11 = relation_composition(sK11,function_inverse(sK4))
| ~ spl18_5
| ~ spl18_85
| ~ spl18_204 ),
inference(forward_demodulation,[],[f2664,f681]) ).
fof(f2664,plain,
( sK11 = relation_composition(empty_set,function_inverse(sK4))
| ~ spl18_5
| ~ spl18_204 ),
inference(resolution,[],[f2023,f227]) ).
fof(f2023,plain,
( ! [X0] :
( ~ empty(X0)
| sK11 = relation_composition(X0,function_inverse(sK4)) )
| ~ spl18_204 ),
inference(avatar_component_clause,[],[f2022]) ).
fof(f2707,plain,
( spl18_239
| ~ spl18_40
| ~ spl18_128 ),
inference(avatar_split_clause,[],[f1158,f1144,f411,f2705]) ).
fof(f411,plain,
( spl18_40
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_40])]) ).
fof(f1158,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ sP1(X2,X1)
| ~ in(relation_dom(X1),apply(X2,X0)) )
| ~ spl18_40
| ~ spl18_128 ),
inference(resolution,[],[f1145,f412]) ).
fof(f412,plain,
( ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) )
| ~ spl18_40 ),
inference(avatar_component_clause,[],[f411]) ).
fof(f2703,plain,
( spl18_238
| ~ spl18_41
| ~ spl18_128 ),
inference(avatar_split_clause,[],[f1157,f1144,f415,f2701]) ).
fof(f415,plain,
( spl18_41
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_41])]) ).
fof(f1157,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ sP1(X2,X1)
| element(apply(X2,X0),relation_dom(X1)) )
| ~ spl18_41
| ~ spl18_128 ),
inference(resolution,[],[f1145,f416]) ).
fof(f416,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) )
| ~ spl18_41 ),
inference(avatar_component_clause,[],[f415]) ).
fof(f2699,plain,
( spl18_237
| ~ spl18_59
| ~ spl18_117 ),
inference(avatar_split_clause,[],[f1048,f1016,f504,f2697]) ).
fof(f1016,plain,
( spl18_117
<=> ! [X0,X1] :
( relation_composition(X1,X0) = sK11
| ~ relation(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_117])]) ).
fof(f1048,plain,
( ! [X2,X0,X1] :
( sK11 = relation_composition(X0,relation_composition(X1,X2))
| ~ empty(X0)
| ~ relation(X2)
| ~ relation(X1) )
| ~ spl18_59
| ~ spl18_117 ),
inference(resolution,[],[f1017,f505]) ).
fof(f1017,plain,
( ! [X0,X1] :
( ~ relation(X0)
| relation_composition(X1,X0) = sK11
| ~ empty(X1) )
| ~ spl18_117 ),
inference(avatar_component_clause,[],[f1016]) ).
fof(f2695,plain,
( spl18_236
| ~ spl18_56
| ~ spl18_117 ),
inference(avatar_split_clause,[],[f1047,f1016,f492,f2693]) ).
fof(f1047,plain,
( ! [X2,X0,X1] :
( sK11 = relation_composition(X0,relation_composition(X1,X2))
| ~ empty(X0)
| ~ relation(X1)
| ~ empty(X2) )
| ~ spl18_56
| ~ spl18_117 ),
inference(resolution,[],[f1017,f493]) ).
fof(f2691,plain,
( spl18_235
| ~ spl18_58
| ~ spl18_117 ),
inference(avatar_split_clause,[],[f1046,f1016,f500,f2689]) ).
fof(f1046,plain,
( ! [X2,X0,X1] :
( sK11 = relation_composition(X0,relation_composition(X1,X2))
| ~ empty(X0)
| ~ relation(X2)
| ~ empty(X1) )
| ~ spl18_58
| ~ spl18_117 ),
inference(resolution,[],[f1017,f501]) ).
fof(f2687,plain,
( spl18_234
| ~ spl18_59
| ~ spl18_116 ),
inference(avatar_split_clause,[],[f1030,f1012,f504,f2685]) ).
fof(f1012,plain,
( spl18_116
<=> ! [X0,X1] :
( relation_composition(X0,X1) = sK11
| ~ relation(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_116])]) ).
fof(f1030,plain,
( ! [X2,X0,X1] :
( sK11 = relation_composition(relation_composition(X0,X1),X2)
| ~ empty(X2)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl18_59
| ~ spl18_116 ),
inference(resolution,[],[f1013,f505]) ).
fof(f1013,plain,
( ! [X0,X1] :
( ~ relation(X0)
| relation_composition(X0,X1) = sK11
| ~ empty(X1) )
| ~ spl18_116 ),
inference(avatar_component_clause,[],[f1012]) ).
fof(f2683,plain,
( spl18_233
| ~ spl18_56
| ~ spl18_116 ),
inference(avatar_split_clause,[],[f1029,f1012,f492,f2681]) ).
fof(f1029,plain,
( ! [X2,X0,X1] :
( sK11 = relation_composition(relation_composition(X0,X1),X2)
| ~ empty(X2)
| ~ relation(X0)
| ~ empty(X1) )
| ~ spl18_56
| ~ spl18_116 ),
inference(resolution,[],[f1013,f493]) ).
fof(f2679,plain,
( spl18_232
| ~ spl18_58
| ~ spl18_116 ),
inference(avatar_split_clause,[],[f1028,f1012,f500,f2677]) ).
fof(f1028,plain,
( ! [X2,X0,X1] :
( sK11 = relation_composition(relation_composition(X0,X1),X2)
| ~ empty(X2)
| ~ relation(X1)
| ~ empty(X0) )
| ~ spl18_58
| ~ spl18_116 ),
inference(resolution,[],[f1013,f501]) ).
fof(f2454,plain,
( spl18_231
| ~ spl18_111
| ~ spl18_132 ),
inference(avatar_split_clause,[],[f1190,f1170,f953,f2452]) ).
fof(f2452,plain,
( spl18_231
<=> ! [X0,X1] :
( ~ empty(X0)
| ~ relation(X1)
| ~ empty(relation_composition(X0,X1))
| one_to_one(relation_composition(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_231])]) ).
fof(f953,plain,
( spl18_111
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| function(relation_composition(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_111])]) ).
fof(f1170,plain,
( spl18_132
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| ~ function(relation_composition(X1,X0))
| ~ empty(relation_composition(X1,X0))
| one_to_one(relation_composition(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_132])]) ).
fof(f1190,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ relation(X1)
| ~ empty(relation_composition(X0,X1))
| one_to_one(relation_composition(X0,X1)) )
| ~ spl18_111
| ~ spl18_132 ),
inference(duplicate_literal_removal,[],[f1186]) ).
fof(f1186,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ relation(X1)
| ~ empty(relation_composition(X0,X1))
| one_to_one(relation_composition(X0,X1))
| ~ empty(X0)
| ~ relation(X1) )
| ~ spl18_111
| ~ spl18_132 ),
inference(resolution,[],[f1171,f954]) ).
fof(f954,plain,
( ! [X0,X1] :
( function(relation_composition(X1,X0))
| ~ empty(X1)
| ~ relation(X0) )
| ~ spl18_111 ),
inference(avatar_component_clause,[],[f953]) ).
fof(f1171,plain,
( ! [X0,X1] :
( ~ function(relation_composition(X1,X0))
| ~ empty(X1)
| ~ relation(X0)
| ~ empty(relation_composition(X1,X0))
| one_to_one(relation_composition(X1,X0)) )
| ~ spl18_132 ),
inference(avatar_component_clause,[],[f1170]) ).
fof(f2450,plain,
( spl18_230
| ~ spl18_110
| ~ spl18_131 ),
inference(avatar_split_clause,[],[f1185,f1166,f949,f2448]) ).
fof(f2448,plain,
( spl18_230
<=> ! [X0,X1] :
( ~ empty(X0)
| ~ relation(X1)
| ~ empty(relation_composition(X1,X0))
| one_to_one(relation_composition(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_230])]) ).
fof(f949,plain,
( spl18_110
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| function(relation_composition(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_110])]) ).
fof(f1166,plain,
( spl18_131
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| ~ function(relation_composition(X0,X1))
| ~ empty(relation_composition(X0,X1))
| one_to_one(relation_composition(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_131])]) ).
fof(f1185,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ relation(X1)
| ~ empty(relation_composition(X1,X0))
| one_to_one(relation_composition(X1,X0)) )
| ~ spl18_110
| ~ spl18_131 ),
inference(duplicate_literal_removal,[],[f1182]) ).
fof(f1182,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ relation(X1)
| ~ empty(relation_composition(X1,X0))
| one_to_one(relation_composition(X1,X0))
| ~ empty(X0)
| ~ relation(X1) )
| ~ spl18_110
| ~ spl18_131 ),
inference(resolution,[],[f1167,f950]) ).
fof(f950,plain,
( ! [X0,X1] :
( function(relation_composition(X0,X1))
| ~ empty(X1)
| ~ relation(X0) )
| ~ spl18_110 ),
inference(avatar_component_clause,[],[f949]) ).
fof(f1167,plain,
( ! [X0,X1] :
( ~ function(relation_composition(X0,X1))
| ~ empty(X1)
| ~ relation(X0)
| ~ empty(relation_composition(X0,X1))
| one_to_one(relation_composition(X0,X1)) )
| ~ spl18_131 ),
inference(avatar_component_clause,[],[f1166]) ).
fof(f2446,plain,
( spl18_229
| ~ spl18_34
| ~ spl18_126 ),
inference(avatar_split_clause,[],[f1127,f1096,f370,f2444]) ).
fof(f2444,plain,
( spl18_229
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| relation_composition(X0,relation_rng(X1)) = X2
| ~ empty(X2)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_229])]) ).
fof(f370,plain,
( spl18_34
<=> ! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_34])]) ).
fof(f1127,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| relation_composition(X0,relation_rng(X1)) = X2
| ~ empty(X2)
| ~ empty(X1) )
| ~ spl18_34
| ~ spl18_126 ),
inference(resolution,[],[f1097,f371]) ).
fof(f371,plain,
( ! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) )
| ~ spl18_34 ),
inference(avatar_component_clause,[],[f370]) ).
fof(f2442,plain,
( spl18_228
| ~ spl18_36
| ~ spl18_126 ),
inference(avatar_split_clause,[],[f1126,f1096,f378,f2440]) ).
fof(f2440,plain,
( spl18_228
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| relation_composition(X0,relation_dom(X1)) = X2
| ~ empty(X2)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_228])]) ).
fof(f378,plain,
( spl18_36
<=> ! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_36])]) ).
fof(f1126,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| relation_composition(X0,relation_dom(X1)) = X2
| ~ empty(X2)
| ~ empty(X1) )
| ~ spl18_36
| ~ spl18_126 ),
inference(resolution,[],[f1097,f379]) ).
fof(f379,plain,
( ! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) )
| ~ spl18_36 ),
inference(avatar_component_clause,[],[f378]) ).
fof(f2438,plain,
( spl18_227
| ~ spl18_34
| ~ spl18_125 ),
inference(avatar_split_clause,[],[f1109,f1092,f370,f2436]) ).
fof(f2436,plain,
( spl18_227
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| relation_composition(relation_rng(X1),X0) = X2
| ~ empty(X2)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_227])]) ).
fof(f1109,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| relation_composition(relation_rng(X1),X0) = X2
| ~ empty(X2)
| ~ empty(X1) )
| ~ spl18_34
| ~ spl18_125 ),
inference(resolution,[],[f1093,f371]) ).
fof(f2434,plain,
( spl18_226
| ~ spl18_36
| ~ spl18_125 ),
inference(avatar_split_clause,[],[f1108,f1092,f378,f2432]) ).
fof(f2432,plain,
( spl18_226
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| relation_composition(relation_dom(X1),X0) = X2
| ~ empty(X2)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_226])]) ).
fof(f1108,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| relation_composition(relation_dom(X1),X0) = X2
| ~ empty(X2)
| ~ empty(X1) )
| ~ spl18_36
| ~ spl18_125 ),
inference(resolution,[],[f1093,f379]) ).
fof(f2430,plain,
( spl18_225
| ~ spl18_46
| ~ spl18_117 ),
inference(avatar_split_clause,[],[f1045,f1016,f438,f2428]) ).
fof(f1045,plain,
( ! [X0,X1] :
( sK11 = relation_composition(X0,function_inverse(X1))
| ~ empty(X0)
| ~ function(X1)
| ~ relation(X1) )
| ~ spl18_46
| ~ spl18_117 ),
inference(resolution,[],[f1017,f439]) ).
fof(f2426,plain,
( spl18_224
| ~ spl18_46
| ~ spl18_116 ),
inference(avatar_split_clause,[],[f1027,f1012,f438,f2424]) ).
fof(f1027,plain,
( ! [X0,X1] :
( sK11 = relation_composition(function_inverse(X0),X1)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) )
| ~ spl18_46
| ~ spl18_116 ),
inference(resolution,[],[f1013,f439]) ).
fof(f2403,plain,
( spl18_223
| ~ spl18_54
| ~ spl18_109 ),
inference(avatar_split_clause,[],[f992,f945,f483,f2401]) ).
fof(f945,plain,
( spl18_109
<=> ! [X0,X1] :
( relation_rng(X1) = X0
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_109])]) ).
fof(f992,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| relation_rng(relation_composition(X1,X2)) = X0
| ~ relation(X1)
| ~ empty(X2) )
| ~ spl18_54
| ~ spl18_109 ),
inference(resolution,[],[f946,f484]) ).
fof(f946,plain,
( ! [X0,X1] :
( ~ empty(X1)
| ~ empty(X0)
| relation_rng(X1) = X0 )
| ~ spl18_109 ),
inference(avatar_component_clause,[],[f945]) ).
fof(f2399,plain,
( spl18_222
| ~ spl18_57
| ~ spl18_109 ),
inference(avatar_split_clause,[],[f991,f945,f496,f2397]) ).
fof(f991,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| relation_rng(relation_composition(X1,X2)) = X0
| ~ relation(X2)
| ~ empty(X1) )
| ~ spl18_57
| ~ spl18_109 ),
inference(resolution,[],[f946,f497]) ).
fof(f2395,plain,
( spl18_221
| ~ spl18_54
| ~ spl18_108 ),
inference(avatar_split_clause,[],[f974,f941,f483,f2393]) ).
fof(f941,plain,
( spl18_108
<=> ! [X0,X1] :
( relation_dom(X1) = X0
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_108])]) ).
fof(f974,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| relation_dom(relation_composition(X1,X2)) = X0
| ~ relation(X1)
| ~ empty(X2) )
| ~ spl18_54
| ~ spl18_108 ),
inference(resolution,[],[f942,f484]) ).
fof(f942,plain,
( ! [X0,X1] :
( ~ empty(X1)
| ~ empty(X0)
| relation_dom(X1) = X0 )
| ~ spl18_108 ),
inference(avatar_component_clause,[],[f941]) ).
fof(f2391,plain,
( spl18_220
| ~ spl18_57
| ~ spl18_108 ),
inference(avatar_split_clause,[],[f973,f941,f496,f2389]) ).
fof(f973,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| relation_dom(relation_composition(X1,X2)) = X0
| ~ relation(X2)
| ~ empty(X1) )
| ~ spl18_57
| ~ spl18_108 ),
inference(resolution,[],[f942,f497]) ).
fof(f2215,plain,
( spl18_219
| ~ spl18_38
| ~ spl18_128 ),
inference(avatar_split_clause,[],[f1156,f1144,f386,f2213]) ).
fof(f2213,plain,
( spl18_219
<=> ! [X2,X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ sP1(X2,X1)
| ~ empty(relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_219])]) ).
fof(f386,plain,
( spl18_38
<=> ! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_38])]) ).
fof(f1156,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ sP1(X2,X1)
| ~ empty(relation_dom(X1)) )
| ~ spl18_38
| ~ spl18_128 ),
inference(resolution,[],[f1145,f387]) ).
fof(f387,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) )
| ~ spl18_38 ),
inference(avatar_component_clause,[],[f386]) ).
fof(f2211,plain,
( spl18_218
| ~ spl18_47
| ~ spl18_127 ),
inference(avatar_split_clause,[],[f1148,f1140,f442,f2209]) ).
fof(f2209,plain,
( spl18_218
<=> ! [X0] :
( ~ empty(function_inverse(X0))
| one_to_one(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_218])]) ).
fof(f442,plain,
( spl18_47
<=> ! [X0] :
( function(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_47])]) ).
fof(f1140,plain,
( spl18_127
<=> ! [X0] :
( ~ function(function_inverse(X0))
| ~ empty(function_inverse(X0))
| one_to_one(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_127])]) ).
fof(f1148,plain,
( ! [X0] :
( ~ empty(function_inverse(X0))
| one_to_one(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl18_47
| ~ spl18_127 ),
inference(duplicate_literal_removal,[],[f1147]) ).
fof(f1147,plain,
( ! [X0] :
( ~ empty(function_inverse(X0))
| one_to_one(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0)
| ~ function(X0)
| ~ relation(X0) )
| ~ spl18_47
| ~ spl18_127 ),
inference(resolution,[],[f1141,f443]) ).
fof(f443,plain,
( ! [X0] :
( function(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl18_47 ),
inference(avatar_component_clause,[],[f442]) ).
fof(f1141,plain,
( ! [X0] :
( ~ function(function_inverse(X0))
| ~ empty(function_inverse(X0))
| one_to_one(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl18_127 ),
inference(avatar_component_clause,[],[f1140]) ).
fof(f2188,plain,
( spl18_217
| ~ spl18_40
| ~ spl18_121 ),
inference(avatar_split_clause,[],[f1078,f1070,f411,f2186]) ).
fof(f2186,plain,
( spl18_217
<=> ! [X0] :
( empty(powerset(X0))
| empty(X0)
| ~ in(powerset(X0),sK5(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_217])]) ).
fof(f1070,plain,
( spl18_121
<=> ! [X0] :
( empty(powerset(X0))
| in(sK5(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_121])]) ).
fof(f1078,plain,
( ! [X0] :
( empty(powerset(X0))
| empty(X0)
| ~ in(powerset(X0),sK5(X0)) )
| ~ spl18_40
| ~ spl18_121 ),
inference(resolution,[],[f1071,f412]) ).
fof(f1071,plain,
( ! [X0] :
( in(sK5(X0),powerset(X0))
| empty(powerset(X0))
| empty(X0) )
| ~ spl18_121 ),
inference(avatar_component_clause,[],[f1070]) ).
fof(f2184,plain,
( spl18_216
| ~ spl18_40
| ~ spl18_120 ),
inference(avatar_split_clause,[],[f1075,f1066,f411,f2182]) ).
fof(f2182,plain,
( spl18_216
<=> ! [X0,X1] :
( empty(powerset(X0))
| ~ subset(X1,X0)
| ~ in(powerset(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_216])]) ).
fof(f1066,plain,
( spl18_120
<=> ! [X0,X1] :
( empty(powerset(X0))
| in(X1,powerset(X0))
| ~ subset(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_120])]) ).
fof(f1075,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| ~ subset(X1,X0)
| ~ in(powerset(X0),X1) )
| ~ spl18_40
| ~ spl18_120 ),
inference(resolution,[],[f1067,f412]) ).
fof(f1067,plain,
( ! [X0,X1] :
( in(X1,powerset(X0))
| empty(powerset(X0))
| ~ subset(X1,X0) )
| ~ spl18_120 ),
inference(avatar_component_clause,[],[f1066]) ).
fof(f2180,plain,
( spl18_215
| ~ spl18_105
| ~ spl18_119 ),
inference(avatar_split_clause,[],[f1064,f1024,f889,f2178]) ).
fof(f2178,plain,
( spl18_215
<=> ! [X0] :
( element(sK8(sK5(X0)),X0)
| empty(X0)
| empty(sK5(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_215])]) ).
fof(f1024,plain,
( spl18_119
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK5(X1))
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_119])]) ).
fof(f1064,plain,
( ! [X0] :
( element(sK8(sK5(X0)),X0)
| empty(X0)
| empty(sK5(X0)) )
| ~ spl18_105
| ~ spl18_119 ),
inference(resolution,[],[f1025,f890]) ).
fof(f1025,plain,
( ! [X0,X1] :
( ~ in(X0,sK5(X1))
| element(X0,X1)
| empty(X1) )
| ~ spl18_119 ),
inference(avatar_component_clause,[],[f1024]) ).
fof(f2176,plain,
( spl18_214
| ~ spl18_34
| ~ spl18_117 ),
inference(avatar_split_clause,[],[f1051,f1016,f370,f2174]) ).
fof(f2174,plain,
( spl18_214
<=> ! [X0,X1] :
( sK11 = relation_composition(X0,relation_rng(X1))
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_214])]) ).
fof(f1051,plain,
( ! [X0,X1] :
( sK11 = relation_composition(X0,relation_rng(X1))
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl18_34
| ~ spl18_117 ),
inference(resolution,[],[f1017,f371]) ).
fof(f2172,plain,
( spl18_213
| ~ spl18_36
| ~ spl18_117 ),
inference(avatar_split_clause,[],[f1050,f1016,f378,f2170]) ).
fof(f2170,plain,
( spl18_213
<=> ! [X0,X1] :
( sK11 = relation_composition(X0,relation_dom(X1))
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_213])]) ).
fof(f1050,plain,
( ! [X0,X1] :
( sK11 = relation_composition(X0,relation_dom(X1))
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl18_36
| ~ spl18_117 ),
inference(resolution,[],[f1017,f379]) ).
fof(f2168,plain,
( spl18_212
| ~ spl18_34
| ~ spl18_116 ),
inference(avatar_split_clause,[],[f1033,f1012,f370,f2166]) ).
fof(f2166,plain,
( spl18_212
<=> ! [X0,X1] :
( sK11 = relation_composition(relation_rng(X0),X1)
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_212])]) ).
fof(f1033,plain,
( ! [X0,X1] :
( sK11 = relation_composition(relation_rng(X0),X1)
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl18_34
| ~ spl18_116 ),
inference(resolution,[],[f1013,f371]) ).
fof(f2164,plain,
( spl18_211
| ~ spl18_36
| ~ spl18_116 ),
inference(avatar_split_clause,[],[f1032,f1012,f378,f2162]) ).
fof(f2162,plain,
( spl18_211
<=> ! [X0,X1] :
( sK11 = relation_composition(relation_dom(X0),X1)
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_211])]) ).
fof(f1032,plain,
( ! [X0,X1] :
( sK11 = relation_composition(relation_dom(X0),X1)
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl18_36
| ~ spl18_116 ),
inference(resolution,[],[f1013,f379]) ).
fof(f2160,plain,
( spl18_210
| ~ spl18_105
| ~ spl18_115 ),
inference(avatar_split_clause,[],[f1010,f970,f889,f2158]) ).
fof(f2158,plain,
( spl18_210
<=> ! [X0] :
( element(sK8(sK8(powerset(X0))),X0)
| empty(sK8(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_210])]) ).
fof(f970,plain,
( spl18_115
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK8(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_115])]) ).
fof(f1010,plain,
( ! [X0] :
( element(sK8(sK8(powerset(X0))),X0)
| empty(sK8(powerset(X0))) )
| ~ spl18_105
| ~ spl18_115 ),
inference(resolution,[],[f971,f890]) ).
fof(f971,plain,
( ! [X0,X1] :
( ~ in(X0,sK8(powerset(X1)))
| element(X0,X1) )
| ~ spl18_115 ),
inference(avatar_component_clause,[],[f970]) ).
fof(f2156,plain,
( spl18_209
| ~ spl18_54
| ~ spl18_98 ),
inference(avatar_split_clause,[],[f906,f858,f483,f2154]) ).
fof(f858,plain,
( spl18_98
<=> ! [X0] :
( relation_dom(X0) = sK11
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_98])]) ).
fof(f906,plain,
( ! [X0,X1] :
( sK11 = relation_dom(relation_composition(X0,X1))
| ~ relation(X0)
| ~ empty(X1) )
| ~ spl18_54
| ~ spl18_98 ),
inference(resolution,[],[f859,f484]) ).
fof(f859,plain,
( ! [X0] :
( ~ empty(X0)
| relation_dom(X0) = sK11 )
| ~ spl18_98 ),
inference(avatar_component_clause,[],[f858]) ).
fof(f2152,plain,
( spl18_208
| ~ spl18_57
| ~ spl18_98 ),
inference(avatar_split_clause,[],[f905,f858,f496,f2150]) ).
fof(f905,plain,
( ! [X0,X1] :
( sK11 = relation_dom(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) )
| ~ spl18_57
| ~ spl18_98 ),
inference(resolution,[],[f859,f497]) ).
fof(f2148,plain,
( spl18_207
| ~ spl18_116
| ~ spl18_139 ),
inference(avatar_split_clause,[],[f1377,f1270,f1012,f2146]) ).
fof(f1377,plain,
( ! [X0] :
( sK11 = relation_composition(function_inverse(sK4),X0)
| ~ empty(X0) )
| ~ spl18_116
| ~ spl18_139 ),
inference(resolution,[],[f1271,f1013]) ).
fof(f2144,plain,
( spl18_206
| ~ spl18_54
| ~ spl18_97 ),
inference(avatar_split_clause,[],[f893,f854,f483,f2142]) ).
fof(f854,plain,
( spl18_97
<=> ! [X0] :
( relation_rng(X0) = sK11
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_97])]) ).
fof(f893,plain,
( ! [X0,X1] :
( sK11 = relation_rng(relation_composition(X0,X1))
| ~ relation(X0)
| ~ empty(X1) )
| ~ spl18_54
| ~ spl18_97 ),
inference(resolution,[],[f855,f484]) ).
fof(f855,plain,
( ! [X0] :
( ~ empty(X0)
| relation_rng(X0) = sK11 )
| ~ spl18_97 ),
inference(avatar_component_clause,[],[f854]) ).
fof(f2140,plain,
( spl18_205
| ~ spl18_57
| ~ spl18_97 ),
inference(avatar_split_clause,[],[f892,f854,f496,f2138]) ).
fof(f892,plain,
( ! [X0,X1] :
( sK11 = relation_rng(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) )
| ~ spl18_57
| ~ spl18_97 ),
inference(resolution,[],[f855,f497]) ).
fof(f2024,plain,
( spl18_204
| ~ spl18_117
| ~ spl18_139 ),
inference(avatar_split_clause,[],[f1376,f1270,f1016,f2022]) ).
fof(f1376,plain,
( ! [X0] :
( sK11 = relation_composition(X0,function_inverse(sK4))
| ~ empty(X0) )
| ~ spl18_117
| ~ spl18_139 ),
inference(resolution,[],[f1271,f1017]) ).
fof(f1896,plain,
( spl18_203
| ~ spl18_6
| ~ spl18_85
| ~ spl18_126 ),
inference(avatar_split_clause,[],[f1136,f1096,f679,f230,f1894]) ).
fof(f1894,plain,
( spl18_203
<=> ! [X0,X1] :
( relation_composition(X0,sK11) = X1
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_203])]) ).
fof(f230,plain,
( spl18_6
<=> relation(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_6])]) ).
fof(f1136,plain,
( ! [X0,X1] :
( relation_composition(X0,sK11) = X1
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl18_6
| ~ spl18_85
| ~ spl18_126 ),
inference(forward_demodulation,[],[f1125,f681]) ).
fof(f1125,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_composition(X0,empty_set) = X1
| ~ empty(X1) )
| ~ spl18_6
| ~ spl18_126 ),
inference(resolution,[],[f1097,f232]) ).
fof(f232,plain,
( relation(empty_set)
| ~ spl18_6 ),
inference(avatar_component_clause,[],[f230]) ).
fof(f1892,plain,
( spl18_202
| ~ spl18_16
| ~ spl18_126 ),
inference(avatar_split_clause,[],[f1134,f1096,f280,f1890]) ).
fof(f1890,plain,
( spl18_202
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_composition(X0,sK16) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_202])]) ).
fof(f280,plain,
( spl18_16
<=> relation(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_16])]) ).
fof(f1134,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_composition(X0,sK16) = X1
| ~ empty(X1) )
| ~ spl18_16
| ~ spl18_126 ),
inference(resolution,[],[f1097,f282]) ).
fof(f282,plain,
( relation(sK16)
| ~ spl18_16 ),
inference(avatar_component_clause,[],[f280]) ).
fof(f1888,plain,
( spl18_201
| ~ spl18_14
| ~ spl18_126 ),
inference(avatar_split_clause,[],[f1133,f1096,f270,f1886]) ).
fof(f1886,plain,
( spl18_201
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_composition(X0,sK15) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_201])]) ).
fof(f270,plain,
( spl18_14
<=> relation(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_14])]) ).
fof(f1133,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_composition(X0,sK15) = X1
| ~ empty(X1) )
| ~ spl18_14
| ~ spl18_126 ),
inference(resolution,[],[f1097,f272]) ).
fof(f272,plain,
( relation(sK15)
| ~ spl18_14 ),
inference(avatar_component_clause,[],[f270]) ).
fof(f1884,plain,
( spl18_200
| ~ spl18_13
| ~ spl18_126 ),
inference(avatar_split_clause,[],[f1132,f1096,f265,f1882]) ).
fof(f1882,plain,
( spl18_200
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_composition(X0,sK14) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_200])]) ).
fof(f265,plain,
( spl18_13
<=> relation(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_13])]) ).
fof(f1132,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_composition(X0,sK14) = X1
| ~ empty(X1) )
| ~ spl18_13
| ~ spl18_126 ),
inference(resolution,[],[f1097,f267]) ).
fof(f267,plain,
( relation(sK14)
| ~ spl18_13 ),
inference(avatar_component_clause,[],[f265]) ).
fof(f1880,plain,
( spl18_199
| ~ spl18_33
| ~ spl18_129 ),
inference(avatar_split_clause,[],[f1222,f1150,f366,f1878]) ).
fof(f1878,plain,
( spl18_199
<=> ! [X0] :
( sK11 = relation_composition(relation_rng(X0),sK4)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_199])]) ).
fof(f1222,plain,
( ! [X0] :
( sK11 = relation_composition(relation_rng(X0),sK4)
| ~ empty(X0) )
| ~ spl18_33
| ~ spl18_129 ),
inference(resolution,[],[f1151,f367]) ).
fof(f1876,plain,
( spl18_198
| ~ spl18_10
| ~ spl18_126 ),
inference(avatar_split_clause,[],[f1130,f1096,f250,f1874]) ).
fof(f1874,plain,
( spl18_198
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_composition(X0,sK12) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_198])]) ).
fof(f250,plain,
( spl18_10
<=> relation(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_10])]) ).
fof(f1130,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_composition(X0,sK12) = X1
| ~ empty(X1) )
| ~ spl18_10
| ~ spl18_126 ),
inference(resolution,[],[f1097,f252]) ).
fof(f252,plain,
( relation(sK12)
| ~ spl18_10 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f1872,plain,
( spl18_197
| ~ spl18_6
| ~ spl18_85
| ~ spl18_125 ),
inference(avatar_split_clause,[],[f1118,f1092,f679,f230,f1870]) ).
fof(f1870,plain,
( spl18_197
<=> ! [X0,X1] :
( relation_composition(sK11,X0) = X1
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_197])]) ).
fof(f1118,plain,
( ! [X0,X1] :
( relation_composition(sK11,X0) = X1
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl18_6
| ~ spl18_85
| ~ spl18_125 ),
inference(forward_demodulation,[],[f1107,f681]) ).
fof(f1107,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_composition(empty_set,X0) = X1
| ~ empty(X1) )
| ~ spl18_6
| ~ spl18_125 ),
inference(resolution,[],[f1093,f232]) ).
fof(f1868,plain,
( spl18_196
| ~ spl18_16
| ~ spl18_125 ),
inference(avatar_split_clause,[],[f1116,f1092,f280,f1866]) ).
fof(f1866,plain,
( spl18_196
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_composition(sK16,X0) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_196])]) ).
fof(f1116,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_composition(sK16,X0) = X1
| ~ empty(X1) )
| ~ spl18_16
| ~ spl18_125 ),
inference(resolution,[],[f1093,f282]) ).
fof(f1864,plain,
( spl18_195
| ~ spl18_14
| ~ spl18_125 ),
inference(avatar_split_clause,[],[f1115,f1092,f270,f1862]) ).
fof(f1862,plain,
( spl18_195
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_composition(sK15,X0) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_195])]) ).
fof(f1115,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_composition(sK15,X0) = X1
| ~ empty(X1) )
| ~ spl18_14
| ~ spl18_125 ),
inference(resolution,[],[f1093,f272]) ).
fof(f1860,plain,
( spl18_194
| ~ spl18_13
| ~ spl18_125 ),
inference(avatar_split_clause,[],[f1114,f1092,f265,f1858]) ).
fof(f1858,plain,
( spl18_194
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_composition(sK14,X0) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_194])]) ).
fof(f1114,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_composition(sK14,X0) = X1
| ~ empty(X1) )
| ~ spl18_13
| ~ spl18_125 ),
inference(resolution,[],[f1093,f267]) ).
fof(f1856,plain,
( spl18_193
| ~ spl18_10
| ~ spl18_125 ),
inference(avatar_split_clause,[],[f1112,f1092,f250,f1854]) ).
fof(f1854,plain,
( spl18_193
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_composition(sK12,X0) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_193])]) ).
fof(f1112,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_composition(sK12,X0) = X1
| ~ empty(X1) )
| ~ spl18_10
| ~ spl18_125 ),
inference(resolution,[],[f1093,f252]) ).
fof(f1852,plain,
( spl18_192
| ~ spl18_33
| ~ spl18_109 ),
inference(avatar_split_clause,[],[f995,f945,f366,f1850]) ).
fof(f1850,plain,
( spl18_192
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_rng(relation_rng(X1)) = X0
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_192])]) ).
fof(f995,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_rng(relation_rng(X1)) = X0
| ~ empty(X1) )
| ~ spl18_33
| ~ spl18_109 ),
inference(resolution,[],[f946,f367]) ).
fof(f1848,plain,
( spl18_191
| ~ spl18_35
| ~ spl18_109 ),
inference(avatar_split_clause,[],[f994,f945,f374,f1846]) ).
fof(f1846,plain,
( spl18_191
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_rng(relation_dom(X1)) = X0
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_191])]) ).
fof(f994,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_rng(relation_dom(X1)) = X0
| ~ empty(X1) )
| ~ spl18_35
| ~ spl18_109 ),
inference(resolution,[],[f946,f375]) ).
fof(f1844,plain,
( spl18_190
| ~ spl18_33
| ~ spl18_108 ),
inference(avatar_split_clause,[],[f977,f941,f366,f1842]) ).
fof(f1842,plain,
( spl18_190
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_dom(relation_rng(X1)) = X0
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_190])]) ).
fof(f977,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_dom(relation_rng(X1)) = X0
| ~ empty(X1) )
| ~ spl18_33
| ~ spl18_108 ),
inference(resolution,[],[f942,f367]) ).
fof(f1840,plain,
( spl18_189
| ~ spl18_35
| ~ spl18_108 ),
inference(avatar_split_clause,[],[f976,f941,f374,f1838]) ).
fof(f1838,plain,
( spl18_189
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_dom(relation_dom(X1)) = X0
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_189])]) ).
fof(f976,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_dom(relation_dom(X1)) = X0
| ~ empty(X1) )
| ~ spl18_35
| ~ spl18_108 ),
inference(resolution,[],[f942,f375]) ).
fof(f1836,plain,
( spl18_188
| ~ spl18_35
| ~ spl18_129 ),
inference(avatar_split_clause,[],[f1221,f1150,f374,f1834]) ).
fof(f1221,plain,
( ! [X0] :
( sK11 = relation_composition(relation_dom(X0),sK4)
| ~ empty(X0) )
| ~ spl18_35
| ~ spl18_129 ),
inference(resolution,[],[f1151,f375]) ).
fof(f1824,plain,
( spl18_187
| ~ spl18_91
| ~ spl18_124 ),
inference(avatar_split_clause,[],[f1102,f1088,f738,f1822]) ).
fof(f1822,plain,
( spl18_187
<=> ! [X0] :
( ~ empty(relation_rng(X0))
| one_to_one(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_187])]) ).
fof(f1088,plain,
( spl18_124
<=> ! [X0] :
( ~ function(relation_rng(X0))
| ~ empty(relation_rng(X0))
| one_to_one(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_124])]) ).
fof(f1102,plain,
( ! [X0] :
( ~ empty(relation_rng(X0))
| one_to_one(relation_rng(X0))
| ~ empty(X0) )
| ~ spl18_91
| ~ spl18_124 ),
inference(duplicate_literal_removal,[],[f1101]) ).
fof(f1101,plain,
( ! [X0] :
( ~ empty(relation_rng(X0))
| one_to_one(relation_rng(X0))
| ~ empty(X0)
| ~ empty(X0) )
| ~ spl18_91
| ~ spl18_124 ),
inference(resolution,[],[f1089,f739]) ).
fof(f1089,plain,
( ! [X0] :
( ~ function(relation_rng(X0))
| ~ empty(relation_rng(X0))
| one_to_one(relation_rng(X0))
| ~ empty(X0) )
| ~ spl18_124 ),
inference(avatar_component_clause,[],[f1088]) ).
fof(f1820,plain,
( spl18_186
| ~ spl18_92
| ~ spl18_122 ),
inference(avatar_split_clause,[],[f1100,f1080,f742,f1818]) ).
fof(f1818,plain,
( spl18_186
<=> ! [X0] :
( ~ empty(relation_dom(X0))
| one_to_one(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_186])]) ).
fof(f1080,plain,
( spl18_122
<=> ! [X0] :
( ~ function(relation_dom(X0))
| ~ empty(relation_dom(X0))
| one_to_one(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_122])]) ).
fof(f1100,plain,
( ! [X0] :
( ~ empty(relation_dom(X0))
| one_to_one(relation_dom(X0))
| ~ empty(X0) )
| ~ spl18_92
| ~ spl18_122 ),
inference(duplicate_literal_removal,[],[f1099]) ).
fof(f1099,plain,
( ! [X0] :
( ~ empty(relation_dom(X0))
| one_to_one(relation_dom(X0))
| ~ empty(X0)
| ~ empty(X0) )
| ~ spl18_92
| ~ spl18_122 ),
inference(resolution,[],[f1081,f743]) ).
fof(f1081,plain,
( ! [X0] :
( ~ function(relation_dom(X0))
| ~ empty(relation_dom(X0))
| one_to_one(relation_dom(X0))
| ~ empty(X0) )
| ~ spl18_122 ),
inference(avatar_component_clause,[],[f1080]) ).
fof(f1732,plain,
( spl18_185
| ~ spl18_33
| ~ spl18_123 ),
inference(avatar_split_clause,[],[f1201,f1084,f366,f1730]) ).
fof(f1201,plain,
( ! [X0] :
( sK11 = relation_composition(sK4,relation_rng(X0))
| ~ empty(X0) )
| ~ spl18_33
| ~ spl18_123 ),
inference(resolution,[],[f1085,f367]) ).
fof(f1596,plain,
( spl18_184
| ~ spl18_6
| ~ spl18_85
| ~ spl18_117 ),
inference(avatar_split_clause,[],[f1060,f1016,f679,f230,f1594]) ).
fof(f1594,plain,
( spl18_184
<=> ! [X0] :
( sK11 = relation_composition(X0,sK11)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_184])]) ).
fof(f1060,plain,
( ! [X0] :
( sK11 = relation_composition(X0,sK11)
| ~ empty(X0) )
| ~ spl18_6
| ~ spl18_85
| ~ spl18_117 ),
inference(forward_demodulation,[],[f1049,f681]) ).
fof(f1049,plain,
( ! [X0] :
( sK11 = relation_composition(X0,empty_set)
| ~ empty(X0) )
| ~ spl18_6
| ~ spl18_117 ),
inference(resolution,[],[f1017,f232]) ).
fof(f1592,plain,
( spl18_183
| ~ spl18_16
| ~ spl18_117 ),
inference(avatar_split_clause,[],[f1058,f1016,f280,f1590]) ).
fof(f1590,plain,
( spl18_183
<=> ! [X0] :
( sK11 = relation_composition(X0,sK16)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_183])]) ).
fof(f1058,plain,
( ! [X0] :
( sK11 = relation_composition(X0,sK16)
| ~ empty(X0) )
| ~ spl18_16
| ~ spl18_117 ),
inference(resolution,[],[f1017,f282]) ).
fof(f1588,plain,
( spl18_182
| ~ spl18_35
| ~ spl18_123 ),
inference(avatar_split_clause,[],[f1200,f1084,f374,f1586]) ).
fof(f1200,plain,
( ! [X0] :
( sK11 = relation_composition(sK4,relation_dom(X0))
| ~ empty(X0) )
| ~ spl18_35
| ~ spl18_123 ),
inference(resolution,[],[f1085,f375]) ).
fof(f1584,plain,
( spl18_181
| ~ spl18_14
| ~ spl18_117 ),
inference(avatar_split_clause,[],[f1057,f1016,f270,f1582]) ).
fof(f1582,plain,
( spl18_181
<=> ! [X0] :
( sK11 = relation_composition(X0,sK15)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_181])]) ).
fof(f1057,plain,
( ! [X0] :
( sK11 = relation_composition(X0,sK15)
| ~ empty(X0) )
| ~ spl18_14
| ~ spl18_117 ),
inference(resolution,[],[f1017,f272]) ).
fof(f1580,plain,
( spl18_180
| ~ spl18_13
| ~ spl18_117 ),
inference(avatar_split_clause,[],[f1056,f1016,f265,f1578]) ).
fof(f1578,plain,
( spl18_180
<=> ! [X0] :
( sK11 = relation_composition(X0,sK14)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_180])]) ).
fof(f1056,plain,
( ! [X0] :
( sK11 = relation_composition(X0,sK14)
| ~ empty(X0) )
| ~ spl18_13
| ~ spl18_117 ),
inference(resolution,[],[f1017,f267]) ).
fof(f1576,plain,
( spl18_179
| ~ spl18_10
| ~ spl18_117 ),
inference(avatar_split_clause,[],[f1054,f1016,f250,f1574]) ).
fof(f1574,plain,
( spl18_179
<=> ! [X0] :
( sK11 = relation_composition(X0,sK12)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_179])]) ).
fof(f1054,plain,
( ! [X0] :
( sK11 = relation_composition(X0,sK12)
| ~ empty(X0) )
| ~ spl18_10
| ~ spl18_117 ),
inference(resolution,[],[f1017,f252]) ).
fof(f1572,plain,
( spl18_178
| ~ spl18_6
| ~ spl18_85
| ~ spl18_116 ),
inference(avatar_split_clause,[],[f1042,f1012,f679,f230,f1570]) ).
fof(f1570,plain,
( spl18_178
<=> ! [X0] :
( sK11 = relation_composition(sK11,X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_178])]) ).
fof(f1042,plain,
( ! [X0] :
( sK11 = relation_composition(sK11,X0)
| ~ empty(X0) )
| ~ spl18_6
| ~ spl18_85
| ~ spl18_116 ),
inference(forward_demodulation,[],[f1031,f681]) ).
fof(f1031,plain,
( ! [X0] :
( sK11 = relation_composition(empty_set,X0)
| ~ empty(X0) )
| ~ spl18_6
| ~ spl18_116 ),
inference(resolution,[],[f1013,f232]) ).
fof(f1568,plain,
( spl18_177
| ~ spl18_16
| ~ spl18_116 ),
inference(avatar_split_clause,[],[f1040,f1012,f280,f1566]) ).
fof(f1566,plain,
( spl18_177
<=> ! [X0] :
( sK11 = relation_composition(sK16,X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_177])]) ).
fof(f1040,plain,
( ! [X0] :
( sK11 = relation_composition(sK16,X0)
| ~ empty(X0) )
| ~ spl18_16
| ~ spl18_116 ),
inference(resolution,[],[f1013,f282]) ).
fof(f1564,plain,
( spl18_176
| ~ spl18_14
| ~ spl18_116 ),
inference(avatar_split_clause,[],[f1039,f1012,f270,f1562]) ).
fof(f1562,plain,
( spl18_176
<=> ! [X0] :
( sK11 = relation_composition(sK15,X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_176])]) ).
fof(f1039,plain,
( ! [X0] :
( sK11 = relation_composition(sK15,X0)
| ~ empty(X0) )
| ~ spl18_14
| ~ spl18_116 ),
inference(resolution,[],[f1013,f272]) ).
fof(f1560,plain,
( spl18_175
| ~ spl18_13
| ~ spl18_116 ),
inference(avatar_split_clause,[],[f1038,f1012,f265,f1558]) ).
fof(f1558,plain,
( spl18_175
<=> ! [X0] :
( sK11 = relation_composition(sK14,X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_175])]) ).
fof(f1038,plain,
( ! [X0] :
( sK11 = relation_composition(sK14,X0)
| ~ empty(X0) )
| ~ spl18_13
| ~ spl18_116 ),
inference(resolution,[],[f1013,f267]) ).
fof(f1556,plain,
( spl18_174
| ~ spl18_10
| ~ spl18_116 ),
inference(avatar_split_clause,[],[f1036,f1012,f250,f1554]) ).
fof(f1554,plain,
( spl18_174
<=> ! [X0] :
( sK11 = relation_composition(sK12,X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_174])]) ).
fof(f1036,plain,
( ! [X0] :
( sK11 = relation_composition(sK12,X0)
| ~ empty(X0) )
| ~ spl18_10
| ~ spl18_116 ),
inference(resolution,[],[f1013,f252]) ).
fof(f1552,plain,
( spl18_173
| ~ spl18_33
| ~ spl18_98 ),
inference(avatar_split_clause,[],[f909,f858,f366,f1550]) ).
fof(f1550,plain,
( spl18_173
<=> ! [X0] :
( sK11 = relation_dom(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_173])]) ).
fof(f909,plain,
( ! [X0] :
( sK11 = relation_dom(relation_rng(X0))
| ~ empty(X0) )
| ~ spl18_33
| ~ spl18_98 ),
inference(resolution,[],[f859,f367]) ).
fof(f1548,plain,
( spl18_172
| ~ spl18_35
| ~ spl18_98 ),
inference(avatar_split_clause,[],[f908,f858,f374,f1546]) ).
fof(f1546,plain,
( spl18_172
<=> ! [X0] :
( sK11 = relation_dom(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_172])]) ).
fof(f908,plain,
( ! [X0] :
( sK11 = relation_dom(relation_dom(X0))
| ~ empty(X0) )
| ~ spl18_35
| ~ spl18_98 ),
inference(resolution,[],[f859,f375]) ).
fof(f1534,plain,
( spl18_171
| ~ spl18_33
| ~ spl18_97 ),
inference(avatar_split_clause,[],[f896,f854,f366,f1532]) ).
fof(f1532,plain,
( spl18_171
<=> ! [X0] :
( sK11 = relation_rng(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_171])]) ).
fof(f896,plain,
( ! [X0] :
( sK11 = relation_rng(relation_rng(X0))
| ~ empty(X0) )
| ~ spl18_33
| ~ spl18_97 ),
inference(resolution,[],[f855,f367]) ).
fof(f1530,plain,
( spl18_170
| ~ spl18_35
| ~ spl18_97 ),
inference(avatar_split_clause,[],[f895,f854,f374,f1528]) ).
fof(f1528,plain,
( spl18_170
<=> ! [X0] :
( sK11 = relation_rng(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_170])]) ).
fof(f895,plain,
( ! [X0] :
( sK11 = relation_rng(relation_dom(X0))
| ~ empty(X0) )
| ~ spl18_35
| ~ spl18_97 ),
inference(resolution,[],[f855,f375]) ).
fof(f1514,plain,
( spl18_169
| ~ spl18_105
| ~ spl18_107 ),
inference(avatar_split_clause,[],[f939,f933,f889,f1512]) ).
fof(f933,plain,
( spl18_107
<=> ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK8(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_107])]) ).
fof(f939,plain,
( ! [X0] :
( ~ empty(X0)
| empty(sK8(powerset(X0))) )
| ~ spl18_105
| ~ spl18_107 ),
inference(resolution,[],[f934,f890]) ).
fof(f934,plain,
( ! [X0,X1] :
( ~ in(X1,sK8(powerset(X0)))
| ~ empty(X0) )
| ~ spl18_107 ),
inference(avatar_component_clause,[],[f933]) ).
fof(f1510,plain,
( spl18_168
| ~ spl18_40
| ~ spl18_105 ),
inference(avatar_split_clause,[],[f923,f889,f411,f1508]) ).
fof(f1508,plain,
( spl18_168
<=> ! [X0] :
( empty(X0)
| ~ in(X0,sK8(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_168])]) ).
fof(f923,plain,
( ! [X0] :
( empty(X0)
| ~ in(X0,sK8(X0)) )
| ~ spl18_40
| ~ spl18_105 ),
inference(resolution,[],[f890,f412]) ).
fof(f1486,plain,
( spl18_167
| ~ spl18_56
| ~ spl18_90 ),
inference(avatar_split_clause,[],[f719,f713,f492,f1484]) ).
fof(f1484,plain,
( spl18_167
<=> ! [X0,X1] :
( apply(relation_composition(X0,X1),apply(sK4,sK3)) = apply(relation_composition(sK4,relation_composition(X0,X1)),sK3)
| ~ function(relation_composition(X0,X1))
| ~ relation(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_167])]) ).
fof(f719,plain,
( ! [X0,X1] :
( apply(relation_composition(X0,X1),apply(sK4,sK3)) = apply(relation_composition(sK4,relation_composition(X0,X1)),sK3)
| ~ function(relation_composition(X0,X1))
| ~ relation(X0)
| ~ empty(X1) )
| ~ spl18_56
| ~ spl18_90 ),
inference(resolution,[],[f714,f493]) ).
fof(f1473,plain,
( spl18_166
| ~ spl18_58
| ~ spl18_90 ),
inference(avatar_split_clause,[],[f718,f713,f500,f1471]) ).
fof(f1471,plain,
( spl18_166
<=> ! [X0,X1] :
( apply(relation_composition(X0,X1),apply(sK4,sK3)) = apply(relation_composition(sK4,relation_composition(X0,X1)),sK3)
| ~ function(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_166])]) ).
fof(f718,plain,
( ! [X0,X1] :
( apply(relation_composition(X0,X1),apply(sK4,sK3)) = apply(relation_composition(sK4,relation_composition(X0,X1)),sK3)
| ~ function(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) )
| ~ spl18_58
| ~ spl18_90 ),
inference(resolution,[],[f714,f501]) ).
fof(f1469,plain,
( spl18_165
| ~ spl18_59
| ~ spl18_90 ),
inference(avatar_split_clause,[],[f717,f713,f504,f1467]) ).
fof(f1467,plain,
( spl18_165
<=> ! [X0,X1] :
( apply(relation_composition(X0,X1),apply(sK4,sK3)) = apply(relation_composition(sK4,relation_composition(X0,X1)),sK3)
| ~ function(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_165])]) ).
fof(f717,plain,
( ! [X0,X1] :
( apply(relation_composition(X0,X1),apply(sK4,sK3)) = apply(relation_composition(sK4,relation_composition(X0,X1)),sK3)
| ~ function(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl18_59
| ~ spl18_90 ),
inference(resolution,[],[f714,f505]) ).
fof(f1463,plain,
( spl18_164
| ~ spl18_51
| ~ spl18_159 ),
inference(avatar_split_clause,[],[f1444,f1433,f471,f1461]) ).
fof(f1461,plain,
( spl18_164
<=> ! [X0] :
( ~ in(apply(sK4,sK3),relation_rng(X0))
| apply(sK4,sK3) = apply(X0,sK3)
| ~ sP1(function_inverse(sK4),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_164])]) ).
fof(f471,plain,
( spl18_51
<=> ! [X4,X0,X5,X1] :
( sP0(X4,X5,X1,X0)
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_51])]) ).
fof(f1433,plain,
( spl18_159
<=> ! [X0] :
( ~ sP0(apply(sK4,sK3),sK3,X0,function_inverse(sK4))
| ~ in(apply(sK4,sK3),relation_rng(X0))
| apply(sK4,sK3) = apply(X0,sK3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_159])]) ).
fof(f1444,plain,
( ! [X0] :
( ~ in(apply(sK4,sK3),relation_rng(X0))
| apply(sK4,sK3) = apply(X0,sK3)
| ~ sP1(function_inverse(sK4),X0) )
| ~ spl18_51
| ~ spl18_159 ),
inference(resolution,[],[f1434,f472]) ).
fof(f472,plain,
( ! [X0,X1,X4,X5] :
( sP0(X4,X5,X1,X0)
| ~ sP1(X0,X1) )
| ~ spl18_51 ),
inference(avatar_component_clause,[],[f471]) ).
fof(f1434,plain,
( ! [X0] :
( ~ sP0(apply(sK4,sK3),sK3,X0,function_inverse(sK4))
| ~ in(apply(sK4,sK3),relation_rng(X0))
| apply(sK4,sK3) = apply(X0,sK3) )
| ~ spl18_159 ),
inference(avatar_component_clause,[],[f1433]) ).
fof(f1457,plain,
( spl18_163
| ~ spl18_25
| ~ spl18_128 ),
inference(avatar_split_clause,[],[f1411,f1144,f322,f1455]) ).
fof(f1455,plain,
( spl18_163
<=> ! [X0] :
( in(sK3,relation_dom(X0))
| ~ in(apply(sK4,sK3),relation_rng(X0))
| ~ sP1(function_inverse(sK4),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_163])]) ).
fof(f1411,plain,
( ! [X0] :
( in(sK3,relation_dom(X0))
| ~ in(apply(sK4,sK3),relation_rng(X0))
| ~ sP1(function_inverse(sK4),X0) )
| ~ spl18_25
| ~ spl18_128 ),
inference(superposition,[],[f1145,f323]) ).
fof(f1453,plain,
( ~ spl18_161
| ~ spl18_162
| ~ spl18_128
| spl18_156 ),
inference(avatar_split_clause,[],[f1423,f1416,f1144,f1450,f1446]) ).
fof(f1446,plain,
( spl18_161
<=> sP1(sK4,function_inverse(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_161])]) ).
fof(f1450,plain,
( spl18_162
<=> in(sK3,relation_rng(function_inverse(sK4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_162])]) ).
fof(f1416,plain,
( spl18_156
<=> in(apply(sK4,sK3),relation_dom(function_inverse(sK4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_156])]) ).
fof(f1423,plain,
( ~ in(sK3,relation_rng(function_inverse(sK4)))
| ~ sP1(sK4,function_inverse(sK4))
| ~ spl18_128
| spl18_156 ),
inference(resolution,[],[f1418,f1145]) ).
fof(f1418,plain,
( ~ in(apply(sK4,sK3),relation_dom(function_inverse(sK4)))
| spl18_156 ),
inference(avatar_component_clause,[],[f1416]) ).
fof(f1440,plain,
( spl18_160
| ~ spl18_5
| ~ spl18_85
| ~ spl18_129 ),
inference(avatar_split_clause,[],[f1227,f1150,f679,f225,f1437]) ).
fof(f1437,plain,
( spl18_160
<=> sK11 = relation_composition(sK11,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_160])]) ).
fof(f1227,plain,
( sK11 = relation_composition(sK11,sK4)
| ~ spl18_5
| ~ spl18_85
| ~ spl18_129 ),
inference(forward_demodulation,[],[f1220,f681]) ).
fof(f1220,plain,
( sK11 = relation_composition(empty_set,sK4)
| ~ spl18_5
| ~ spl18_129 ),
inference(resolution,[],[f1151,f227]) ).
fof(f1435,plain,
( spl18_159
| ~ spl18_25
| ~ spl18_74 ),
inference(avatar_split_clause,[],[f1412,f624,f322,f1433]) ).
fof(f624,plain,
( spl18_74
<=> ! [X2,X0,X3] :
( apply(X2,apply(X3,X0)) = X0
| ~ in(X0,relation_rng(X2))
| ~ sP0(X0,apply(X3,X0),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_74])]) ).
fof(f1412,plain,
( ! [X0] :
( ~ sP0(apply(sK4,sK3),sK3,X0,function_inverse(sK4))
| ~ in(apply(sK4,sK3),relation_rng(X0))
| apply(sK4,sK3) = apply(X0,sK3) )
| ~ spl18_25
| ~ spl18_74 ),
inference(superposition,[],[f625,f323]) ).
fof(f625,plain,
( ! [X2,X3,X0] :
( ~ sP0(X0,apply(X3,X0),X2,X3)
| ~ in(X0,relation_rng(X2))
| apply(X2,apply(X3,X0)) = X0 )
| ~ spl18_74 ),
inference(avatar_component_clause,[],[f624]) ).
fof(f1427,plain,
( spl18_158
| ~ spl18_25
| ~ spl18_73 ),
inference(avatar_split_clause,[],[f1413,f617,f322,f1425]) ).
fof(f1425,plain,
( spl18_158
<=> ! [X0] :
( ~ sP0(apply(sK4,sK3),sK3,X0,function_inverse(sK4))
| ~ in(apply(sK4,sK3),relation_rng(X0))
| in(sK3,relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_158])]) ).
fof(f617,plain,
( spl18_73
<=> ! [X2,X0,X3] :
( in(apply(X3,X0),relation_dom(X2))
| ~ in(X0,relation_rng(X2))
| ~ sP0(X0,apply(X3,X0),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_73])]) ).
fof(f1413,plain,
( ! [X0] :
( ~ sP0(apply(sK4,sK3),sK3,X0,function_inverse(sK4))
| ~ in(apply(sK4,sK3),relation_rng(X0))
| in(sK3,relation_dom(X0)) )
| ~ spl18_25
| ~ spl18_73 ),
inference(superposition,[],[f618,f323]) ).
fof(f618,plain,
( ! [X2,X3,X0] :
( ~ sP0(X0,apply(X3,X0),X2,X3)
| ~ in(X0,relation_rng(X2))
| in(apply(X3,X0),relation_dom(X2)) )
| ~ spl18_73 ),
inference(avatar_component_clause,[],[f617]) ).
fof(f1422,plain,
( ~ spl18_156
| spl18_157
| ~ spl18_25
| ~ spl18_67 ),
inference(avatar_split_clause,[],[f1414,f588,f322,f1420,f1416]) ).
fof(f1420,plain,
( spl18_157
<=> ! [X0] : sP0(sK3,apply(sK4,sK3),function_inverse(sK4),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_157])]) ).
fof(f588,plain,
( spl18_67
<=> ! [X2,X1,X3] :
( sP0(apply(X2,X1),X1,X2,X3)
| ~ in(X1,relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_67])]) ).
fof(f1414,plain,
( ! [X0] :
( sP0(sK3,apply(sK4,sK3),function_inverse(sK4),X0)
| ~ in(apply(sK4,sK3),relation_dom(function_inverse(sK4))) )
| ~ spl18_25
| ~ spl18_67 ),
inference(superposition,[],[f589,f323]) ).
fof(f589,plain,
( ! [X2,X3,X1] :
( sP0(apply(X2,X1),X1,X2,X3)
| ~ in(X1,relation_dom(X2)) )
| ~ spl18_67 ),
inference(avatar_component_clause,[],[f588]) ).
fof(f1410,plain,
( ~ spl18_138
| ~ spl18_1
| ~ spl18_2
| ~ spl18_3
| ~ spl18_139
| spl18_25
| ~ spl18_134
| ~ spl18_150 ),
inference(avatar_split_clause,[],[f1373,f1370,f1178,f322,f1270,f215,f210,f205,f1266]) ).
fof(f210,plain,
( spl18_2
<=> function(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_2])]) ).
fof(f215,plain,
( spl18_3
<=> one_to_one(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_3])]) ).
fof(f1370,plain,
( spl18_150
<=> ! [X0] :
( sK3 = apply(X0,apply(sK4,sK3))
| ~ sP1(X0,sK4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_150])]) ).
fof(f1373,plain,
( sK3 = apply(function_inverse(sK4),apply(sK4,sK3))
| ~ relation(function_inverse(sK4))
| ~ one_to_one(sK4)
| ~ function(sK4)
| ~ relation(sK4)
| ~ function(function_inverse(sK4))
| ~ spl18_134
| ~ spl18_150 ),
inference(resolution,[],[f1371,f1179]) ).
fof(f1371,plain,
( ! [X0] :
( ~ sP1(X0,sK4)
| sK3 = apply(X0,apply(sK4,sK3)) )
| ~ spl18_150 ),
inference(avatar_component_clause,[],[f1370]) ).
fof(f1405,plain,
( spl18_155
| ~ spl18_82
| ~ spl18_130 ),
inference(avatar_split_clause,[],[f1365,f1161,f664,f1403]) ).
fof(f1403,plain,
( spl18_155
<=> ! [X0] :
( apply(sK4,sK3) = apply(sK4,apply(X0,apply(sK4,sK3)))
| ~ sP1(X0,sK4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_155])]) ).
fof(f664,plain,
( spl18_82
<=> in(apply(sK4,sK3),relation_rng(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_82])]) ).
fof(f1365,plain,
( ! [X0] :
( apply(sK4,sK3) = apply(sK4,apply(X0,apply(sK4,sK3)))
| ~ sP1(X0,sK4) )
| ~ spl18_82
| ~ spl18_130 ),
inference(resolution,[],[f666,f1162]) ).
fof(f666,plain,
( in(apply(sK4,sK3),relation_rng(sK4))
| ~ spl18_82 ),
inference(avatar_component_clause,[],[f664]) ).
fof(f1401,plain,
( spl18_154
| ~ spl18_5
| ~ spl18_85
| ~ spl18_123 ),
inference(avatar_split_clause,[],[f1206,f1084,f679,f225,f1398]) ).
fof(f1398,plain,
( spl18_154
<=> sK11 = relation_composition(sK4,sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_154])]) ).
fof(f1206,plain,
( sK11 = relation_composition(sK4,sK11)
| ~ spl18_5
| ~ spl18_85
| ~ spl18_123 ),
inference(forward_demodulation,[],[f1199,f681]) ).
fof(f1199,plain,
( sK11 = relation_composition(sK4,empty_set)
| ~ spl18_5
| ~ spl18_123 ),
inference(resolution,[],[f1085,f227]) ).
fof(f1395,plain,
( ~ spl18_153
| ~ spl18_40
| ~ spl18_82 ),
inference(avatar_split_clause,[],[f1368,f664,f411,f1392]) ).
fof(f1392,plain,
( spl18_153
<=> in(relation_rng(sK4),apply(sK4,sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_153])]) ).
fof(f1368,plain,
( ~ in(relation_rng(sK4),apply(sK4,sK3))
| ~ spl18_40
| ~ spl18_82 ),
inference(resolution,[],[f666,f412]) ).
fof(f1390,plain,
( spl18_152
| ~ spl18_41
| ~ spl18_82 ),
inference(avatar_split_clause,[],[f1367,f664,f415,f1387]) ).
fof(f1387,plain,
( spl18_152
<=> element(apply(sK4,sK3),relation_rng(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_152])]) ).
fof(f1367,plain,
( element(apply(sK4,sK3),relation_rng(sK4))
| ~ spl18_41
| ~ spl18_82 ),
inference(resolution,[],[f666,f416]) ).
fof(f1384,plain,
( ~ spl18_151
| ~ spl18_38
| ~ spl18_82 ),
inference(avatar_split_clause,[],[f1366,f664,f386,f1381]) ).
fof(f1381,plain,
( spl18_151
<=> empty(relation_rng(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_151])]) ).
fof(f1366,plain,
( ~ empty(relation_rng(sK4))
| ~ spl18_38
| ~ spl18_82 ),
inference(resolution,[],[f666,f387]) ).
fof(f1372,plain,
( spl18_150
| ~ spl18_4
| ~ spl18_72 ),
inference(avatar_split_clause,[],[f615,f612,f220,f1370]) ).
fof(f220,plain,
( spl18_4
<=> in(sK3,relation_dom(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_4])]) ).
fof(f615,plain,
( ! [X0] :
( sK3 = apply(X0,apply(sK4,sK3))
| ~ sP1(X0,sK4) )
| ~ spl18_4
| ~ spl18_72 ),
inference(resolution,[],[f613,f222]) ).
fof(f222,plain,
( in(sK3,relation_dom(sK4))
| ~ spl18_4 ),
inference(avatar_component_clause,[],[f220]) ).
fof(f1364,plain,
( ~ spl18_1
| ~ spl18_2
| ~ spl18_46
| spl18_139 ),
inference(avatar_split_clause,[],[f1275,f1270,f438,f210,f205]) ).
fof(f1275,plain,
( ~ function(sK4)
| ~ relation(sK4)
| ~ spl18_46
| spl18_139 ),
inference(resolution,[],[f1272,f439]) ).
fof(f1272,plain,
( ~ relation(function_inverse(sK4))
| spl18_139 ),
inference(avatar_component_clause,[],[f1270]) ).
fof(f1363,plain,
( spl18_149
| ~ spl18_46
| ~ spl18_90 ),
inference(avatar_split_clause,[],[f716,f713,f438,f1361]) ).
fof(f1361,plain,
( spl18_149
<=> ! [X0] :
( apply(function_inverse(X0),apply(sK4,sK3)) = apply(relation_composition(sK4,function_inverse(X0)),sK3)
| ~ function(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_149])]) ).
fof(f716,plain,
( ! [X0] :
( apply(function_inverse(X0),apply(sK4,sK3)) = apply(relation_composition(sK4,function_inverse(X0)),sK3)
| ~ function(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl18_46
| ~ spl18_90 ),
inference(resolution,[],[f714,f439]) ).
fof(f1351,plain,
( spl18_148
| ~ spl18_34
| ~ spl18_90 ),
inference(avatar_split_clause,[],[f722,f713,f370,f1349]) ).
fof(f722,plain,
( ! [X0] :
( apply(relation_rng(X0),apply(sK4,sK3)) = apply(relation_composition(sK4,relation_rng(X0)),sK3)
| ~ function(relation_rng(X0))
| ~ empty(X0) )
| ~ spl18_34
| ~ spl18_90 ),
inference(resolution,[],[f714,f371]) ).
fof(f1347,plain,
( spl18_147
| ~ spl18_36
| ~ spl18_90 ),
inference(avatar_split_clause,[],[f721,f713,f378,f1345]) ).
fof(f721,plain,
( ! [X0] :
( apply(relation_dom(X0),apply(sK4,sK3)) = apply(relation_composition(sK4,relation_dom(X0)),sK3)
| ~ function(relation_dom(X0))
| ~ empty(X0) )
| ~ spl18_36
| ~ spl18_90 ),
inference(resolution,[],[f714,f379]) ).
fof(f1324,plain,
( spl18_146
| ~ spl18_5
| ~ spl18_85
| ~ spl18_98 ),
inference(avatar_split_clause,[],[f914,f858,f679,f225,f1321]) ).
fof(f1321,plain,
( spl18_146
<=> sK11 = relation_dom(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_146])]) ).
fof(f914,plain,
( sK11 = relation_dom(sK11)
| ~ spl18_5
| ~ spl18_85
| ~ spl18_98 ),
inference(forward_demodulation,[],[f907,f681]) ).
fof(f907,plain,
( sK11 = relation_dom(empty_set)
| ~ spl18_5
| ~ spl18_98 ),
inference(resolution,[],[f859,f227]) ).
fof(f1319,plain,
( ~ spl18_1
| ~ spl18_2
| ~ spl18_47
| spl18_138 ),
inference(avatar_split_clause,[],[f1274,f1266,f442,f210,f205]) ).
fof(f1274,plain,
( ~ function(sK4)
| ~ relation(sK4)
| ~ spl18_47
| spl18_138 ),
inference(resolution,[],[f1268,f443]) ).
fof(f1268,plain,
( ~ function(function_inverse(sK4))
| spl18_138 ),
inference(avatar_component_clause,[],[f1266]) ).
fof(f1318,plain,
( spl18_145
| ~ spl18_5
| ~ spl18_85
| ~ spl18_97 ),
inference(avatar_split_clause,[],[f901,f854,f679,f225,f1315]) ).
fof(f1315,plain,
( spl18_145
<=> sK11 = relation_rng(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_145])]) ).
fof(f901,plain,
( sK11 = relation_rng(sK11)
| ~ spl18_5
| ~ spl18_85
| ~ spl18_97 ),
inference(forward_demodulation,[],[f894,f681]) ).
fof(f894,plain,
( sK11 = relation_rng(empty_set)
| ~ spl18_5
| ~ spl18_97 ),
inference(resolution,[],[f855,f227]) ).
fof(f1313,plain,
( spl18_144
| ~ spl18_37
| ~ spl18_89 ),
inference(avatar_split_clause,[],[f710,f707,f382,f1311]) ).
fof(f1311,plain,
( spl18_144
<=> ! [X0] : element(sK11,powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_144])]) ).
fof(f382,plain,
( spl18_37
<=> ! [X0] : element(sK9(X0),powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_37])]) ).
fof(f707,plain,
( spl18_89
<=> ! [X0] : sK9(X0) = sK11 ),
introduced(avatar_definition,[new_symbols(naming,[spl18_89])]) ).
fof(f710,plain,
( ! [X0] : element(sK11,powerset(X0))
| ~ spl18_37
| ~ spl18_89 ),
inference(superposition,[],[f383,f708]) ).
fof(f708,plain,
( ! [X0] : sK9(X0) = sK11
| ~ spl18_89 ),
inference(avatar_component_clause,[],[f707]) ).
fof(f383,plain,
( ! [X0] : element(sK9(X0),powerset(X0))
| ~ spl18_37 ),
inference(avatar_component_clause,[],[f382]) ).
fof(f1304,plain,
( spl18_143
| ~ spl18_5
| ~ spl18_85
| ~ spl18_123
| ~ spl18_142 ),
inference(avatar_split_clause,[],[f1299,f1295,f1084,f679,f225,f1301]) ).
fof(f1295,plain,
( spl18_142
<=> apply(sK11,apply(sK4,sK3)) = apply(relation_composition(sK4,sK11),sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_142])]) ).
fof(f1299,plain,
( apply(sK11,apply(sK4,sK3)) = apply(sK11,sK3)
| ~ spl18_5
| ~ spl18_85
| ~ spl18_123
| ~ spl18_142 ),
inference(forward_demodulation,[],[f1297,f1206]) ).
fof(f1297,plain,
( apply(sK11,apply(sK4,sK3)) = apply(relation_composition(sK4,sK11),sK3)
| ~ spl18_142 ),
inference(avatar_component_clause,[],[f1295]) ).
fof(f1298,plain,
( spl18_142
| ~ spl18_39
| ~ spl18_6
| ~ spl18_85
| ~ spl18_90 ),
inference(avatar_split_clause,[],[f732,f713,f679,f230,f390,f1295]) ).
fof(f390,plain,
( spl18_39
<=> function(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_39])]) ).
fof(f732,plain,
( ~ function(sK11)
| apply(sK11,apply(sK4,sK3)) = apply(relation_composition(sK4,sK11),sK3)
| ~ spl18_6
| ~ spl18_85
| ~ spl18_90 ),
inference(forward_demodulation,[],[f731,f681]) ).
fof(f731,plain,
( apply(sK11,apply(sK4,sK3)) = apply(relation_composition(sK4,sK11),sK3)
| ~ function(empty_set)
| ~ spl18_6
| ~ spl18_85
| ~ spl18_90 ),
inference(forward_demodulation,[],[f720,f681]) ).
fof(f720,plain,
( apply(empty_set,apply(sK4,sK3)) = apply(relation_composition(sK4,empty_set),sK3)
| ~ function(empty_set)
| ~ spl18_6
| ~ spl18_90 ),
inference(resolution,[],[f714,f232]) ).
fof(f1289,plain,
( ~ spl18_17
| spl18_141
| ~ spl18_16
| ~ spl18_90 ),
inference(avatar_split_clause,[],[f729,f713,f280,f1286,f285]) ).
fof(f285,plain,
( spl18_17
<=> function(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_17])]) ).
fof(f1286,plain,
( spl18_141
<=> apply(sK16,apply(sK4,sK3)) = apply(relation_composition(sK4,sK16),sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_141])]) ).
fof(f729,plain,
( apply(sK16,apply(sK4,sK3)) = apply(relation_composition(sK4,sK16),sK3)
| ~ function(sK16)
| ~ spl18_16
| ~ spl18_90 ),
inference(resolution,[],[f714,f282]) ).
fof(f1280,plain,
( ~ spl18_15
| spl18_140
| ~ spl18_14
| ~ spl18_90 ),
inference(avatar_split_clause,[],[f728,f713,f270,f1277,f275]) ).
fof(f275,plain,
( spl18_15
<=> function(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_15])]) ).
fof(f1277,plain,
( spl18_140
<=> apply(sK15,apply(sK4,sK3)) = apply(relation_composition(sK4,sK15),sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_140])]) ).
fof(f728,plain,
( apply(sK15,apply(sK4,sK3)) = apply(relation_composition(sK4,sK15),sK3)
| ~ function(sK15)
| ~ spl18_14
| ~ spl18_90 ),
inference(resolution,[],[f714,f272]) ).
fof(f1273,plain,
( ~ spl18_138
| ~ spl18_1
| ~ spl18_2
| ~ spl18_3
| ~ spl18_139
| ~ spl18_81
| ~ spl18_134 ),
inference(avatar_split_clause,[],[f1211,f1178,f661,f1270,f215,f210,f205,f1266]) ).
fof(f661,plain,
( spl18_81
<=> ! [X0] : ~ sP1(X0,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_81])]) ).
fof(f1211,plain,
( ~ relation(function_inverse(sK4))
| ~ one_to_one(sK4)
| ~ function(sK4)
| ~ relation(sK4)
| ~ function(function_inverse(sK4))
| ~ spl18_81
| ~ spl18_134 ),
inference(resolution,[],[f1179,f662]) ).
fof(f662,plain,
( ! [X0] : ~ sP1(X0,sK4)
| ~ spl18_81 ),
inference(avatar_component_clause,[],[f661]) ).
fof(f1238,plain,
( spl18_137
| ~ spl18_1
| ~ spl18_126 ),
inference(avatar_split_clause,[],[f1128,f1096,f205,f1236]) ).
fof(f1128,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_composition(X0,sK4) = X1
| ~ empty(X1) )
| ~ spl18_1
| ~ spl18_126 ),
inference(resolution,[],[f1097,f207]) ).
fof(f1234,plain,
( spl18_136
| ~ spl18_1
| ~ spl18_125 ),
inference(avatar_split_clause,[],[f1110,f1092,f205,f1232]) ).
fof(f1110,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_composition(sK4,X0) = X1
| ~ empty(X1) )
| ~ spl18_1
| ~ spl18_125 ),
inference(resolution,[],[f1093,f207]) ).
fof(f1215,plain,
( spl18_135
| ~ spl18_63
| ~ spl18_69 ),
inference(avatar_split_clause,[],[f609,f596,f565,f1213]) ).
fof(f1213,plain,
( spl18_135
<=> ! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ sP1(X0,X1)
| function_inverse(X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_135])]) ).
fof(f565,plain,
( spl18_63
<=> ! [X0,X1] :
( function_inverse(X0) = X1
| ~ sP1(X1,X0)
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_63])]) ).
fof(f596,plain,
( spl18_69
<=> ! [X0,X1] :
( sP2(X0,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_69])]) ).
fof(f609,plain,
( ! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ sP1(X0,X1)
| function_inverse(X1) = X0 )
| ~ spl18_63
| ~ spl18_69 ),
inference(resolution,[],[f597,f566]) ).
fof(f566,plain,
( ! [X0,X1] :
( ~ sP2(X0,X1)
| ~ sP1(X1,X0)
| function_inverse(X0) = X1 )
| ~ spl18_63 ),
inference(avatar_component_clause,[],[f565]) ).
fof(f597,plain,
( ! [X0,X1] :
( sP2(X0,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) )
| ~ spl18_69 ),
inference(avatar_component_clause,[],[f596]) ).
fof(f1180,plain,
( spl18_134
| ~ spl18_60
| ~ spl18_69 ),
inference(avatar_split_clause,[],[f608,f596,f508,f1178]) ).
fof(f508,plain,
( spl18_60
<=> ! [X0] :
( sP1(function_inverse(X0),X0)
| ~ sP2(X0,function_inverse(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_60])]) ).
fof(f608,plain,
( ! [X0] :
( ~ function(function_inverse(X0))
| ~ relation(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0)
| sP1(function_inverse(X0),X0) )
| ~ spl18_60
| ~ spl18_69 ),
inference(resolution,[],[f597,f509]) ).
fof(f509,plain,
( ! [X0] :
( ~ sP2(X0,function_inverse(X0))
| sP1(function_inverse(X0),X0) )
| ~ spl18_60 ),
inference(avatar_component_clause,[],[f508]) ).
fof(f1176,plain,
( spl18_133
| ~ spl18_52
| ~ spl18_59 ),
inference(avatar_split_clause,[],[f549,f504,f475,f1174]) ).
fof(f549,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ function(relation_composition(X1,X0))
| ~ empty(relation_composition(X1,X0))
| one_to_one(relation_composition(X1,X0)) )
| ~ spl18_52
| ~ spl18_59 ),
inference(resolution,[],[f505,f476]) ).
fof(f1172,plain,
( spl18_132
| ~ spl18_52
| ~ spl18_58 ),
inference(avatar_split_clause,[],[f548,f500,f475,f1170]) ).
fof(f548,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| ~ function(relation_composition(X1,X0))
| ~ empty(relation_composition(X1,X0))
| one_to_one(relation_composition(X1,X0)) )
| ~ spl18_52
| ~ spl18_58 ),
inference(resolution,[],[f501,f476]) ).
fof(f1168,plain,
( spl18_131
| ~ spl18_52
| ~ spl18_56 ),
inference(avatar_split_clause,[],[f542,f492,f475,f1166]) ).
fof(f542,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| ~ function(relation_composition(X0,X1))
| ~ empty(relation_composition(X0,X1))
| one_to_one(relation_composition(X0,X1)) )
| ~ spl18_52
| ~ spl18_56 ),
inference(resolution,[],[f493,f476]) ).
fof(f1163,plain,
( spl18_130
| ~ spl18_51
| ~ spl18_74 ),
inference(avatar_split_clause,[],[f629,f624,f471,f1161]) ).
fof(f629,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_rng(X1))
| apply(X1,apply(X2,X0)) = X0
| ~ sP1(X2,X1) )
| ~ spl18_51
| ~ spl18_74 ),
inference(resolution,[],[f625,f472]) ).
fof(f1152,plain,
( spl18_129
| ~ spl18_1
| ~ spl18_117 ),
inference(avatar_split_clause,[],[f1052,f1016,f205,f1150]) ).
fof(f1052,plain,
( ! [X0] :
( sK11 = relation_composition(X0,sK4)
| ~ empty(X0) )
| ~ spl18_1
| ~ spl18_117 ),
inference(resolution,[],[f1017,f207]) ).
fof(f1146,plain,
( spl18_128
| ~ spl18_51
| ~ spl18_73 ),
inference(avatar_split_clause,[],[f622,f617,f471,f1144]) ).
fof(f622,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_rng(X1))
| in(apply(X2,X0),relation_dom(X1))
| ~ sP1(X2,X1) )
| ~ spl18_51
| ~ spl18_73 ),
inference(resolution,[],[f618,f472]) ).
fof(f1142,plain,
( spl18_127
| ~ spl18_46
| ~ spl18_52 ),
inference(avatar_split_clause,[],[f511,f475,f438,f1140]) ).
fof(f511,plain,
( ! [X0] :
( ~ function(function_inverse(X0))
| ~ empty(function_inverse(X0))
| one_to_one(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl18_46
| ~ spl18_52 ),
inference(resolution,[],[f476,f439]) ).
fof(f1098,plain,
( spl18_126
| ~ spl18_49
| ~ spl18_57 ),
inference(avatar_split_clause,[],[f543,f496,f450,f1096]) ).
fof(f450,plain,
( spl18_49
<=> ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_49])]) ).
fof(f543,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| relation_composition(X1,X0) = X2
| ~ empty(X2) )
| ~ spl18_49
| ~ spl18_57 ),
inference(resolution,[],[f497,f451]) ).
fof(f451,plain,
( ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) )
| ~ spl18_49 ),
inference(avatar_component_clause,[],[f450]) ).
fof(f1094,plain,
( spl18_125
| ~ spl18_49
| ~ spl18_54 ),
inference(avatar_split_clause,[],[f537,f483,f450,f1092]) ).
fof(f537,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| relation_composition(X0,X1) = X2
| ~ empty(X2) )
| ~ spl18_49
| ~ spl18_54 ),
inference(resolution,[],[f484,f451]) ).
fof(f1090,plain,
( spl18_124
| ~ spl18_34
| ~ spl18_52 ),
inference(avatar_split_clause,[],[f514,f475,f370,f1088]) ).
fof(f514,plain,
( ! [X0] :
( ~ function(relation_rng(X0))
| ~ empty(relation_rng(X0))
| one_to_one(relation_rng(X0))
| ~ empty(X0) )
| ~ spl18_34
| ~ spl18_52 ),
inference(resolution,[],[f476,f371]) ).
fof(f1086,plain,
( spl18_123
| ~ spl18_1
| ~ spl18_116 ),
inference(avatar_split_clause,[],[f1034,f1012,f205,f1084]) ).
fof(f1034,plain,
( ! [X0] :
( sK11 = relation_composition(sK4,X0)
| ~ empty(X0) )
| ~ spl18_1
| ~ spl18_116 ),
inference(resolution,[],[f1013,f207]) ).
fof(f1082,plain,
( spl18_122
| ~ spl18_36
| ~ spl18_52 ),
inference(avatar_split_clause,[],[f513,f475,f378,f1080]) ).
fof(f513,plain,
( ! [X0] :
( ~ function(relation_dom(X0))
| ~ empty(relation_dom(X0))
| one_to_one(relation_dom(X0))
| ~ empty(X0) )
| ~ spl18_36
| ~ spl18_52 ),
inference(resolution,[],[f476,f379]) ).
fof(f1072,plain,
( spl18_121
| ~ spl18_43
| ~ spl18_53 ),
inference(avatar_split_clause,[],[f532,f479,f426,f1070]) ).
fof(f426,plain,
( spl18_43
<=> ! [X0] :
( element(sK5(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_43])]) ).
fof(f479,plain,
( spl18_53
<=> ! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_53])]) ).
fof(f532,plain,
( ! [X0] :
( empty(powerset(X0))
| in(sK5(X0),powerset(X0))
| empty(X0) )
| ~ spl18_43
| ~ spl18_53 ),
inference(resolution,[],[f480,f427]) ).
fof(f427,plain,
( ! [X0] :
( element(sK5(X0),powerset(X0))
| empty(X0) )
| ~ spl18_43 ),
inference(avatar_component_clause,[],[f426]) ).
fof(f480,plain,
( ! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) )
| ~ spl18_53 ),
inference(avatar_component_clause,[],[f479]) ).
fof(f1068,plain,
( spl18_120
| ~ spl18_48
| ~ spl18_53 ),
inference(avatar_split_clause,[],[f531,f479,f446,f1066]) ).
fof(f446,plain,
( spl18_48
<=> ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_48])]) ).
fof(f531,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| in(X1,powerset(X0))
| ~ subset(X1,X0) )
| ~ spl18_48
| ~ spl18_53 ),
inference(resolution,[],[f480,f447]) ).
fof(f447,plain,
( ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) )
| ~ spl18_48 ),
inference(avatar_component_clause,[],[f446]) ).
fof(f1026,plain,
( spl18_119
| ~ spl18_43
| ~ spl18_66 ),
inference(avatar_split_clause,[],[f582,f578,f426,f1024]) ).
fof(f578,plain,
( spl18_66
<=> ! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_66])]) ).
fof(f582,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK5(X1))
| empty(X1) )
| ~ spl18_43
| ~ spl18_66 ),
inference(resolution,[],[f579,f427]) ).
fof(f579,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| element(X0,X2)
| ~ in(X0,X1) )
| ~ spl18_66 ),
inference(avatar_component_clause,[],[f578]) ).
fof(f1022,plain,
( spl18_118
| ~ spl18_48
| ~ spl18_66 ),
inference(avatar_split_clause,[],[f581,f578,f446,f1020]) ).
fof(f1020,plain,
( spl18_118
<=> ! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_118])]) ).
fof(f581,plain,
( ! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,X1) )
| ~ spl18_48
| ~ spl18_66 ),
inference(resolution,[],[f579,f447]) ).
fof(f1018,plain,
( spl18_117
| ~ spl18_8
| ~ spl18_32
| ~ spl18_57 ),
inference(avatar_split_clause,[],[f547,f496,f362,f240,f1016]) ).
fof(f240,plain,
( spl18_8
<=> empty(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_8])]) ).
fof(f362,plain,
( spl18_32
<=> ! [X0] :
( empty_set = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_32])]) ).
fof(f547,plain,
( ! [X0,X1] :
( relation_composition(X1,X0) = sK11
| ~ relation(X0)
| ~ empty(X1) )
| ~ spl18_8
| ~ spl18_32
| ~ spl18_57 ),
inference(forward_demodulation,[],[f544,f396]) ).
fof(f396,plain,
( empty_set = sK11
| ~ spl18_8
| ~ spl18_32 ),
inference(resolution,[],[f363,f242]) ).
fof(f242,plain,
( empty(sK11)
| ~ spl18_8 ),
inference(avatar_component_clause,[],[f240]) ).
fof(f363,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = X0 )
| ~ spl18_32 ),
inference(avatar_component_clause,[],[f362]) ).
fof(f544,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| relation_composition(X1,X0) = empty_set )
| ~ spl18_32
| ~ spl18_57 ),
inference(resolution,[],[f497,f363]) ).
fof(f1014,plain,
( spl18_116
| ~ spl18_8
| ~ spl18_32
| ~ spl18_54 ),
inference(avatar_split_clause,[],[f541,f483,f362,f240,f1012]) ).
fof(f541,plain,
( ! [X0,X1] :
( relation_composition(X0,X1) = sK11
| ~ relation(X0)
| ~ empty(X1) )
| ~ spl18_8
| ~ spl18_32
| ~ spl18_54 ),
inference(forward_demodulation,[],[f538,f396]) ).
fof(f538,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| relation_composition(X0,X1) = empty_set )
| ~ spl18_32
| ~ spl18_54 ),
inference(resolution,[],[f484,f363]) ).
fof(f972,plain,
( spl18_115
| ~ spl18_29
| ~ spl18_66 ),
inference(avatar_split_clause,[],[f583,f578,f339,f970]) ).
fof(f339,plain,
( spl18_29
<=> ! [X0] : element(sK8(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_29])]) ).
fof(f583,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK8(powerset(X1))) )
| ~ spl18_29
| ~ spl18_66 ),
inference(resolution,[],[f579,f340]) ).
fof(f340,plain,
( ! [X0] : element(sK8(X0),X0)
| ~ spl18_29 ),
inference(avatar_component_clause,[],[f339]) ).
fof(f968,plain,
( ~ spl18_113
| spl18_114
| ~ spl18_10
| ~ spl18_90 ),
inference(avatar_split_clause,[],[f725,f713,f250,f965,f961]) ).
fof(f961,plain,
( spl18_113
<=> function(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_113])]) ).
fof(f965,plain,
( spl18_114
<=> apply(sK12,apply(sK4,sK3)) = apply(relation_composition(sK4,sK12),sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_114])]) ).
fof(f725,plain,
( apply(sK12,apply(sK4,sK3)) = apply(relation_composition(sK4,sK12),sK3)
| ~ function(sK12)
| ~ spl18_10
| ~ spl18_90 ),
inference(resolution,[],[f714,f252]) ).
fof(f959,plain,
( spl18_112
| ~ spl18_48
| ~ spl18_62 ),
inference(avatar_split_clause,[],[f558,f555,f446,f957]) ).
fof(f957,plain,
( spl18_112
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,X2)
| ~ subset(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_112])]) ).
fof(f555,plain,
( spl18_62
<=> ! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_62])]) ).
fof(f558,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,X2)
| ~ subset(X2,X0) )
| ~ spl18_48
| ~ spl18_62 ),
inference(resolution,[],[f556,f447]) ).
fof(f556,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X0,X1) )
| ~ spl18_62 ),
inference(avatar_component_clause,[],[f555]) ).
fof(f955,plain,
( spl18_111
| ~ spl18_27
| ~ spl18_57 ),
inference(avatar_split_clause,[],[f546,f496,f331,f953]) ).
fof(f331,plain,
( spl18_27
<=> ! [X0] :
( function(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_27])]) ).
fof(f546,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| function(relation_composition(X1,X0)) )
| ~ spl18_27
| ~ spl18_57 ),
inference(resolution,[],[f497,f332]) ).
fof(f332,plain,
( ! [X0] :
( ~ empty(X0)
| function(X0) )
| ~ spl18_27 ),
inference(avatar_component_clause,[],[f331]) ).
fof(f951,plain,
( spl18_110
| ~ spl18_27
| ~ spl18_54 ),
inference(avatar_split_clause,[],[f540,f483,f331,f949]) ).
fof(f540,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| function(relation_composition(X0,X1)) )
| ~ spl18_27
| ~ spl18_54 ),
inference(resolution,[],[f484,f332]) ).
fof(f947,plain,
( spl18_109
| ~ spl18_33
| ~ spl18_49 ),
inference(avatar_split_clause,[],[f458,f450,f366,f945]) ).
fof(f458,plain,
( ! [X0,X1] :
( relation_rng(X1) = X0
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl18_33
| ~ spl18_49 ),
inference(resolution,[],[f451,f367]) ).
fof(f943,plain,
( spl18_108
| ~ spl18_35
| ~ spl18_49 ),
inference(avatar_split_clause,[],[f457,f450,f374,f941]) ).
fof(f457,plain,
( ! [X0,X1] :
( relation_dom(X1) = X0
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl18_35
| ~ spl18_49 ),
inference(resolution,[],[f451,f375]) ).
fof(f935,plain,
( spl18_107
| ~ spl18_29
| ~ spl18_62 ),
inference(avatar_split_clause,[],[f560,f555,f339,f933]) ).
fof(f560,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK8(powerset(X0))) )
| ~ spl18_29
| ~ spl18_62 ),
inference(resolution,[],[f556,f340]) ).
fof(f931,plain,
( spl18_106
| ~ spl18_8
| ~ spl18_23
| ~ spl18_32
| ~ spl18_37
| ~ spl18_53 ),
inference(avatar_split_clause,[],[f536,f479,f382,f362,f314,f240,f929]) ).
fof(f929,plain,
( spl18_106
<=> ! [X0] :
( in(sK11,powerset(X0))
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_106])]) ).
fof(f314,plain,
( spl18_23
<=> ! [X0] : empty(sK9(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_23])]) ).
fof(f536,plain,
( ! [X0] :
( in(sK11,powerset(X0))
| empty(powerset(X0)) )
| ~ spl18_8
| ~ spl18_23
| ~ spl18_32
| ~ spl18_37
| ~ spl18_53 ),
inference(forward_demodulation,[],[f535,f396]) ).
fof(f535,plain,
( ! [X0] :
( in(empty_set,powerset(X0))
| empty(powerset(X0)) )
| ~ spl18_23
| ~ spl18_32
| ~ spl18_37
| ~ spl18_53 ),
inference(forward_demodulation,[],[f534,f395]) ).
fof(f395,plain,
( ! [X0] : empty_set = sK9(X0)
| ~ spl18_23
| ~ spl18_32 ),
inference(resolution,[],[f363,f315]) ).
fof(f315,plain,
( ! [X0] : empty(sK9(X0))
| ~ spl18_23 ),
inference(avatar_component_clause,[],[f314]) ).
fof(f534,plain,
( ! [X0] :
( empty(powerset(X0))
| in(sK9(X0),powerset(X0)) )
| ~ spl18_37
| ~ spl18_53 ),
inference(resolution,[],[f480,f383]) ).
fof(f891,plain,
( spl18_105
| ~ spl18_29
| ~ spl18_53 ),
inference(avatar_split_clause,[],[f533,f479,f339,f889]) ).
fof(f533,plain,
( ! [X0] :
( empty(X0)
| in(sK8(X0),X0) )
| ~ spl18_29
| ~ spl18_53 ),
inference(resolution,[],[f480,f340]) ).
fof(f887,plain,
( ~ spl18_39
| ~ spl18_8
| spl18_104
| ~ spl18_6
| ~ spl18_8
| ~ spl18_32
| ~ spl18_52 ),
inference(avatar_split_clause,[],[f524,f475,f362,f240,f230,f884,f240,f390]) ).
fof(f884,plain,
( spl18_104
<=> one_to_one(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_104])]) ).
fof(f524,plain,
( one_to_one(sK11)
| ~ empty(sK11)
| ~ function(sK11)
| ~ spl18_6
| ~ spl18_8
| ~ spl18_32
| ~ spl18_52 ),
inference(forward_demodulation,[],[f523,f396]) ).
fof(f523,plain,
( ~ empty(sK11)
| ~ function(sK11)
| one_to_one(empty_set)
| ~ spl18_6
| ~ spl18_8
| ~ spl18_32
| ~ spl18_52 ),
inference(forward_demodulation,[],[f522,f396]) ).
fof(f522,plain,
( ~ function(sK11)
| ~ empty(empty_set)
| one_to_one(empty_set)
| ~ spl18_6
| ~ spl18_8
| ~ spl18_32
| ~ spl18_52 ),
inference(forward_demodulation,[],[f512,f396]) ).
fof(f512,plain,
( ~ function(empty_set)
| ~ empty(empty_set)
| one_to_one(empty_set)
| ~ spl18_6
| ~ spl18_52 ),
inference(resolution,[],[f476,f232]) ).
fof(f882,plain,
( spl18_102
| ~ spl18_103
| ~ spl18_15
| ~ spl18_14
| ~ spl18_52 ),
inference(avatar_split_clause,[],[f519,f475,f270,f275,f879,f875]) ).
fof(f875,plain,
( spl18_102
<=> one_to_one(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_102])]) ).
fof(f879,plain,
( spl18_103
<=> empty(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_103])]) ).
fof(f519,plain,
( ~ function(sK15)
| ~ empty(sK15)
| one_to_one(sK15)
| ~ spl18_14
| ~ spl18_52 ),
inference(resolution,[],[f476,f272]) ).
fof(f873,plain,
( spl18_99
| ~ spl18_100
| ~ spl18_101
| ~ spl18_13
| ~ spl18_52 ),
inference(avatar_split_clause,[],[f518,f475,f265,f870,f866,f862]) ).
fof(f862,plain,
( spl18_99
<=> one_to_one(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_99])]) ).
fof(f866,plain,
( spl18_100
<=> empty(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_100])]) ).
fof(f870,plain,
( spl18_101
<=> function(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_101])]) ).
fof(f518,plain,
( ~ function(sK14)
| ~ empty(sK14)
| one_to_one(sK14)
| ~ spl18_13
| ~ spl18_52 ),
inference(resolution,[],[f476,f267]) ).
fof(f860,plain,
( spl18_98
| ~ spl18_8
| ~ spl18_32
| ~ spl18_35 ),
inference(avatar_split_clause,[],[f408,f374,f362,f240,f858]) ).
fof(f408,plain,
( ! [X0] :
( relation_dom(X0) = sK11
| ~ empty(X0) )
| ~ spl18_8
| ~ spl18_32
| ~ spl18_35 ),
inference(forward_demodulation,[],[f405,f396]) ).
fof(f405,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = relation_dom(X0) )
| ~ spl18_32
| ~ spl18_35 ),
inference(resolution,[],[f375,f363]) ).
fof(f856,plain,
( spl18_97
| ~ spl18_8
| ~ spl18_32
| ~ spl18_33 ),
inference(avatar_split_clause,[],[f404,f366,f362,f240,f854]) ).
fof(f404,plain,
( ! [X0] :
( relation_rng(X0) = sK11
| ~ empty(X0) )
| ~ spl18_8
| ~ spl18_32
| ~ spl18_33 ),
inference(forward_demodulation,[],[f401,f396]) ).
fof(f401,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = relation_rng(X0) )
| ~ spl18_32
| ~ spl18_33 ),
inference(resolution,[],[f367,f363]) ).
fof(f792,plain,
( spl18_93
| ~ spl18_32
| ~ spl18_85 ),
inference(avatar_split_clause,[],[f771,f679,f362,f746]) ).
fof(f746,plain,
( spl18_93
<=> ! [X0] :
( sK11 = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_93])]) ).
fof(f771,plain,
( ! [X0] :
( sK11 = X0
| ~ empty(X0) )
| ~ spl18_32
| ~ spl18_85 ),
inference(forward_demodulation,[],[f363,f681]) ).
fof(f770,plain,
( ~ spl18_5
| ~ spl18_95 ),
inference(avatar_contradiction_clause,[],[f761]) ).
fof(f761,plain,
( $false
| ~ spl18_5
| ~ spl18_95 ),
inference(resolution,[],[f756,f227]) ).
fof(f756,plain,
( ! [X0] : ~ empty(X0)
| ~ spl18_95 ),
inference(avatar_component_clause,[],[f755]) ).
fof(f755,plain,
( spl18_95
<=> ! [X0] : ~ empty(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_95])]) ).
fof(f769,plain,
( ~ spl18_23
| ~ spl18_95 ),
inference(avatar_contradiction_clause,[],[f762]) ).
fof(f762,plain,
( $false
| ~ spl18_23
| ~ spl18_95 ),
inference(resolution,[],[f756,f315]) ).
fof(f768,plain,
( ~ spl18_8
| ~ spl18_95 ),
inference(avatar_contradiction_clause,[],[f763]) ).
fof(f763,plain,
( $false
| ~ spl18_8
| ~ spl18_95 ),
inference(resolution,[],[f756,f242]) ).
fof(f767,plain,
( ~ spl18_11
| ~ spl18_95 ),
inference(avatar_contradiction_clause,[],[f764]) ).
fof(f764,plain,
( $false
| ~ spl18_11
| ~ spl18_95 ),
inference(resolution,[],[f756,f257]) ).
fof(f257,plain,
( empty(sK13)
| ~ spl18_11 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f255,plain,
( spl18_11
<=> empty(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_11])]) ).
fof(f766,plain,
( ~ spl18_20
| ~ spl18_95 ),
inference(avatar_contradiction_clause,[],[f765]) ).
fof(f765,plain,
( $false
| ~ spl18_20
| ~ spl18_95 ),
inference(resolution,[],[f756,f302]) ).
fof(f302,plain,
( empty(sK17)
| ~ spl18_20 ),
inference(avatar_component_clause,[],[f300]) ).
fof(f300,plain,
( spl18_20
<=> empty(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_20])]) ).
fof(f760,plain,
( spl18_95
| spl18_96
| ~ spl18_8
| ~ spl18_23
| ~ spl18_32
| ~ spl18_37
| ~ spl18_62 ),
inference(avatar_split_clause,[],[f563,f555,f382,f362,f314,f240,f758,f755]) ).
fof(f758,plain,
( spl18_96
<=> ! [X1] : ~ in(X1,sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_96])]) ).
fof(f563,plain,
( ! [X0,X1] :
( ~ in(X1,sK11)
| ~ empty(X0) )
| ~ spl18_8
| ~ spl18_23
| ~ spl18_32
| ~ spl18_37
| ~ spl18_62 ),
inference(forward_demodulation,[],[f562,f396]) ).
fof(f562,plain,
( ! [X0,X1] :
( ~ in(X1,empty_set)
| ~ empty(X0) )
| ~ spl18_23
| ~ spl18_32
| ~ spl18_37
| ~ spl18_62 ),
inference(forward_demodulation,[],[f561,f395]) ).
fof(f561,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK9(X0)) )
| ~ spl18_37
| ~ spl18_62 ),
inference(resolution,[],[f556,f383]) ).
fof(f753,plain,
( ~ spl18_2
| spl18_94
| ~ spl18_1
| ~ spl18_90 ),
inference(avatar_split_clause,[],[f723,f713,f205,f750,f210]) ).
fof(f750,plain,
( spl18_94
<=> apply(sK4,apply(sK4,sK3)) = apply(relation_composition(sK4,sK4),sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_94])]) ).
fof(f723,plain,
( apply(sK4,apply(sK4,sK3)) = apply(relation_composition(sK4,sK4),sK3)
| ~ function(sK4)
| ~ spl18_1
| ~ spl18_90 ),
inference(resolution,[],[f714,f207]) ).
fof(f748,plain,
( spl18_93
| ~ spl18_8
| ~ spl18_49 ),
inference(avatar_split_clause,[],[f460,f450,f240,f746]) ).
fof(f460,plain,
( ! [X0] :
( sK11 = X0
| ~ empty(X0) )
| ~ spl18_8
| ~ spl18_49 ),
inference(resolution,[],[f451,f242]) ).
fof(f744,plain,
( spl18_92
| ~ spl18_27
| ~ spl18_35 ),
inference(avatar_split_clause,[],[f407,f374,f331,f742]) ).
fof(f407,plain,
( ! [X0] :
( ~ empty(X0)
| function(relation_dom(X0)) )
| ~ spl18_27
| ~ spl18_35 ),
inference(resolution,[],[f375,f332]) ).
fof(f740,plain,
( spl18_91
| ~ spl18_27
| ~ spl18_33 ),
inference(avatar_split_clause,[],[f403,f366,f331,f738]) ).
fof(f403,plain,
( ! [X0] :
( ~ empty(X0)
| function(relation_rng(X0)) )
| ~ spl18_27
| ~ spl18_33 ),
inference(resolution,[],[f367,f332]) ).
fof(f715,plain,
( ~ spl18_1
| ~ spl18_2
| spl18_90
| ~ spl18_4
| ~ spl18_76 ),
inference(avatar_split_clause,[],[f638,f635,f220,f713,f210,f205]) ).
fof(f638,plain,
( ! [X0] :
( apply(X0,apply(sK4,sK3)) = apply(relation_composition(sK4,X0),sK3)
| ~ function(X0)
| ~ relation(X0)
| ~ function(sK4)
| ~ relation(sK4) )
| ~ spl18_4
| ~ spl18_76 ),
inference(resolution,[],[f636,f222]) ).
fof(f709,plain,
( spl18_89
| ~ spl18_85
| ~ spl18_88 ),
inference(avatar_split_clause,[],[f705,f702,f679,f707]) ).
fof(f702,plain,
( spl18_88
<=> ! [X0] : empty_set = sK9(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_88])]) ).
fof(f705,plain,
( ! [X0] : sK9(X0) = sK11
| ~ spl18_85
| ~ spl18_88 ),
inference(forward_demodulation,[],[f703,f681]) ).
fof(f703,plain,
( ! [X0] : empty_set = sK9(X0)
| ~ spl18_88 ),
inference(avatar_component_clause,[],[f702]) ).
fof(f704,plain,
( spl18_88
| ~ spl18_23
| ~ spl18_32 ),
inference(avatar_split_clause,[],[f395,f362,f314,f702]) ).
fof(f692,plain,
( spl18_87
| ~ spl18_8
| ~ spl18_20
| ~ spl18_32 ),
inference(avatar_split_clause,[],[f400,f362,f300,f240,f689]) ).
fof(f689,plain,
( spl18_87
<=> sK11 = sK17 ),
introduced(avatar_definition,[new_symbols(naming,[spl18_87])]) ).
fof(f400,plain,
( sK11 = sK17
| ~ spl18_8
| ~ spl18_20
| ~ spl18_32 ),
inference(forward_demodulation,[],[f398,f396]) ).
fof(f398,plain,
( empty_set = sK17
| ~ spl18_20
| ~ spl18_32 ),
inference(resolution,[],[f363,f302]) ).
fof(f687,plain,
( spl18_86
| ~ spl18_8
| ~ spl18_11
| ~ spl18_32 ),
inference(avatar_split_clause,[],[f399,f362,f255,f240,f684]) ).
fof(f684,plain,
( spl18_86
<=> sK11 = sK13 ),
introduced(avatar_definition,[new_symbols(naming,[spl18_86])]) ).
fof(f399,plain,
( sK11 = sK13
| ~ spl18_8
| ~ spl18_11
| ~ spl18_32 ),
inference(forward_demodulation,[],[f397,f396]) ).
fof(f397,plain,
( empty_set = sK13
| ~ spl18_11
| ~ spl18_32 ),
inference(resolution,[],[f363,f257]) ).
fof(f682,plain,
( spl18_85
| ~ spl18_8
| ~ spl18_32 ),
inference(avatar_split_clause,[],[f396,f362,f240,f679]) ).
fof(f676,plain,
( spl18_84
| ~ spl18_23
| ~ spl18_28 ),
inference(avatar_split_clause,[],[f348,f335,f314,f674]) ).
fof(f674,plain,
( spl18_84
<=> ! [X0] : relation(sK9(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_84])]) ).
fof(f335,plain,
( spl18_28
<=> ! [X0] :
( relation(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_28])]) ).
fof(f348,plain,
( ! [X0] : relation(sK9(X0))
| ~ spl18_23
| ~ spl18_28 ),
inference(resolution,[],[f336,f315]) ).
fof(f336,plain,
( ! [X0] :
( ~ empty(X0)
| relation(X0) )
| ~ spl18_28 ),
inference(avatar_component_clause,[],[f335]) ).
fof(f671,plain,
( spl18_83
| ~ spl18_23
| ~ spl18_27 ),
inference(avatar_split_clause,[],[f343,f331,f314,f669]) ).
fof(f669,plain,
( spl18_83
<=> ! [X0] : function(sK9(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_83])]) ).
fof(f343,plain,
( ! [X0] : function(sK9(X0))
| ~ spl18_23
| ~ spl18_27 ),
inference(resolution,[],[f332,f315]) ).
fof(f667,plain,
( spl18_81
| spl18_82
| ~ spl18_4
| ~ spl18_71 ),
inference(avatar_split_clause,[],[f610,f605,f220,f664,f661]) ).
fof(f610,plain,
( ! [X0] :
( in(apply(sK4,sK3),relation_rng(sK4))
| ~ sP1(X0,sK4) )
| ~ spl18_4
| ~ spl18_71 ),
inference(resolution,[],[f606,f222]) ).
fof(f658,plain,
( spl18_80
| ~ spl18_8
| ~ spl18_28 ),
inference(avatar_split_clause,[],[f349,f335,f240,f655]) ).
fof(f655,plain,
( spl18_80
<=> relation(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_80])]) ).
fof(f349,plain,
( relation(sK11)
| ~ spl18_8
| ~ spl18_28 ),
inference(resolution,[],[f336,f242]) ).
fof(f652,plain,
( spl18_79
| ~ spl18_11
| ~ spl18_27 ),
inference(avatar_split_clause,[],[f345,f331,f255,f649]) ).
fof(f649,plain,
( spl18_79
<=> function(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_79])]) ).
fof(f345,plain,
( function(sK13)
| ~ spl18_11
| ~ spl18_27 ),
inference(resolution,[],[f332,f257]) ).
fof(f646,plain,
spl18_78,
inference(avatar_split_clause,[],[f153,f644]) ).
fof(f644,plain,
( spl18_78
<=> ! [X0,X1] :
( sP1(X0,X1)
| sK7(X0,X1) != apply(X0,sK6(X0,X1))
| ~ in(sK6(X0,X1),relation_rng(X1))
| ~ sP0(sK6(X0,X1),sK7(X0,X1),X1,X0)
| relation_dom(X0) != relation_rng(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_78])]) ).
fof(f153,plain,
! [X0,X1] :
( sP1(X0,X1)
| sK7(X0,X1) != apply(X0,sK6(X0,X1))
| ~ in(sK6(X0,X1),relation_rng(X1))
| ~ sP0(sK6(X0,X1),sK7(X0,X1),X1,X0)
| relation_dom(X0) != relation_rng(X1) ),
inference(cnf_transformation,[],[f97]) ).
fof(f97,plain,
! [X0,X1] :
( ( sP1(X0,X1)
| ( ( sK7(X0,X1) != apply(X0,sK6(X0,X1))
| ~ in(sK6(X0,X1),relation_rng(X1)) )
& sK6(X0,X1) = apply(X1,sK7(X0,X1))
& in(sK7(X0,X1),relation_dom(X1)) )
| ~ sP0(sK6(X0,X1),sK7(X0,X1),X1,X0)
| relation_dom(X0) != relation_rng(X1) )
& ( ( ! [X4,X5] :
( ( ( apply(X0,X4) = X5
& in(X4,relation_rng(X1)) )
| apply(X1,X5) != X4
| ~ in(X5,relation_dom(X1)) )
& sP0(X4,X5,X1,X0) )
& relation_dom(X0) = relation_rng(X1) )
| ~ sP1(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f95,f96]) ).
fof(f96,plain,
! [X0,X1] :
( ? [X2,X3] :
( ( ( apply(X0,X2) != X3
| ~ in(X2,relation_rng(X1)) )
& apply(X1,X3) = X2
& in(X3,relation_dom(X1)) )
| ~ sP0(X2,X3,X1,X0) )
=> ( ( ( sK7(X0,X1) != apply(X0,sK6(X0,X1))
| ~ in(sK6(X0,X1),relation_rng(X1)) )
& sK6(X0,X1) = apply(X1,sK7(X0,X1))
& in(sK7(X0,X1),relation_dom(X1)) )
| ~ sP0(sK6(X0,X1),sK7(X0,X1),X1,X0) ) ),
introduced(choice_axiom,[]) ).
fof(f95,plain,
! [X0,X1] :
( ( sP1(X0,X1)
| ? [X2,X3] :
( ( ( apply(X0,X2) != X3
| ~ in(X2,relation_rng(X1)) )
& apply(X1,X3) = X2
& in(X3,relation_dom(X1)) )
| ~ sP0(X2,X3,X1,X0) )
| relation_dom(X0) != relation_rng(X1) )
& ( ( ! [X4,X5] :
( ( ( apply(X0,X4) = X5
& in(X4,relation_rng(X1)) )
| apply(X1,X5) != X4
| ~ in(X5,relation_dom(X1)) )
& sP0(X4,X5,X1,X0) )
& relation_dom(X0) = relation_rng(X1) )
| ~ sP1(X0,X1) ) ),
inference(rectify,[],[f94]) ).
fof(f94,plain,
! [X1,X0] :
( ( sP1(X1,X0)
| ? [X2,X3] :
( ( ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) )
& apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| ~ sP0(X2,X3,X0,X1) )
| relation_rng(X0) != relation_dom(X1) )
& ( ( ! [X2,X3] :
( ( ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) )
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
& sP0(X2,X3,X0,X1) )
& relation_rng(X0) = relation_dom(X1) )
| ~ sP1(X1,X0) ) ),
inference(flattening,[],[f93]) ).
fof(f93,plain,
! [X1,X0] :
( ( sP1(X1,X0)
| ? [X2,X3] :
( ( ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) )
& apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| ~ sP0(X2,X3,X0,X1) )
| relation_rng(X0) != relation_dom(X1) )
& ( ( ! [X2,X3] :
( ( ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) )
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
& sP0(X2,X3,X0,X1) )
& relation_rng(X0) = relation_dom(X1) )
| ~ sP1(X1,X0) ) ),
inference(nnf_transformation,[],[f85]) ).
fof(f85,plain,
! [X1,X0] :
( sP1(X1,X0)
<=> ( ! [X2,X3] :
( ( ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) )
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
& sP0(X2,X3,X0,X1) )
& relation_rng(X0) = relation_dom(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f642,plain,
spl18_77,
inference(avatar_split_clause,[],[f152,f640]) ).
fof(f640,plain,
( spl18_77
<=> ! [X0,X1] :
( sP1(X0,X1)
| sK6(X0,X1) = apply(X1,sK7(X0,X1))
| ~ sP0(sK6(X0,X1),sK7(X0,X1),X1,X0)
| relation_dom(X0) != relation_rng(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_77])]) ).
fof(f152,plain,
! [X0,X1] :
( sP1(X0,X1)
| sK6(X0,X1) = apply(X1,sK7(X0,X1))
| ~ sP0(sK6(X0,X1),sK7(X0,X1),X1,X0)
| relation_dom(X0) != relation_rng(X1) ),
inference(cnf_transformation,[],[f97]) ).
fof(f637,plain,
spl18_76,
inference(avatar_split_clause,[],[f176,f635]) ).
fof(f176,plain,
! [X2,X0,X1] :
( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0,X1] :
( ! [X2] :
( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f74]) ).
fof(f74,plain,
! [X0,X1] :
( ! [X2] :
( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X0,relation_dom(X1))
=> apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_1) ).
fof(f633,plain,
spl18_75,
inference(avatar_split_clause,[],[f151,f631]) ).
fof(f631,plain,
( spl18_75
<=> ! [X0,X1] :
( sP1(X0,X1)
| in(sK7(X0,X1),relation_dom(X1))
| ~ sP0(sK6(X0,X1),sK7(X0,X1),X1,X0)
| relation_dom(X0) != relation_rng(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_75])]) ).
fof(f151,plain,
! [X0,X1] :
( sP1(X0,X1)
| in(sK7(X0,X1),relation_dom(X1))
| ~ sP0(sK6(X0,X1),sK7(X0,X1),X1,X0)
| relation_dom(X0) != relation_rng(X1) ),
inference(cnf_transformation,[],[f97]) ).
fof(f626,plain,
spl18_74,
inference(avatar_split_clause,[],[f202,f624]) ).
fof(f202,plain,
! [X2,X3,X0] :
( apply(X2,apply(X3,X0)) = X0
| ~ in(X0,relation_rng(X2))
| ~ sP0(X0,apply(X3,X0),X2,X3) ),
inference(equality_resolution,[],[f155]) ).
fof(f155,plain,
! [X2,X3,X0,X1] :
( apply(X2,X1) = X0
| apply(X3,X0) != X1
| ~ in(X0,relation_rng(X2))
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f100]) ).
fof(f100,plain,
! [X0,X1,X2,X3] :
( ( sP0(X0,X1,X2,X3)
| ( ( apply(X2,X1) != X0
| ~ in(X1,relation_dom(X2)) )
& apply(X3,X0) = X1
& in(X0,relation_rng(X2)) ) )
& ( ( apply(X2,X1) = X0
& in(X1,relation_dom(X2)) )
| apply(X3,X0) != X1
| ~ in(X0,relation_rng(X2))
| ~ sP0(X0,X1,X2,X3) ) ),
inference(rectify,[],[f99]) ).
fof(f99,plain,
! [X2,X3,X0,X1] :
( ( sP0(X2,X3,X0,X1)
| ( ( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
& apply(X1,X2) = X3
& in(X2,relation_rng(X0)) ) )
& ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0))
| ~ sP0(X2,X3,X0,X1) ) ),
inference(flattening,[],[f98]) ).
fof(f98,plain,
! [X2,X3,X0,X1] :
( ( sP0(X2,X3,X0,X1)
| ( ( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
& apply(X1,X2) = X3
& in(X2,relation_rng(X0)) ) )
& ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0))
| ~ sP0(X2,X3,X0,X1) ) ),
inference(nnf_transformation,[],[f84]) ).
fof(f84,plain,
! [X2,X3,X0,X1] :
( sP0(X2,X3,X0,X1)
<=> ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f619,plain,
spl18_73,
inference(avatar_split_clause,[],[f203,f617]) ).
fof(f203,plain,
! [X2,X3,X0] :
( in(apply(X3,X0),relation_dom(X2))
| ~ in(X0,relation_rng(X2))
| ~ sP0(X0,apply(X3,X0),X2,X3) ),
inference(equality_resolution,[],[f154]) ).
fof(f154,plain,
! [X2,X3,X0,X1] :
( in(X1,relation_dom(X2))
| apply(X3,X0) != X1
| ~ in(X0,relation_rng(X2))
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f100]) ).
fof(f614,plain,
spl18_72,
inference(avatar_split_clause,[],[f199,f612]) ).
fof(f199,plain,
! [X0,X1,X5] :
( apply(X0,apply(X1,X5)) = X5
| ~ in(X5,relation_dom(X1))
| ~ sP1(X0,X1) ),
inference(equality_resolution,[],[f150]) ).
fof(f150,plain,
! [X0,X1,X4,X5] :
( apply(X0,X4) = X5
| apply(X1,X5) != X4
| ~ in(X5,relation_dom(X1))
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f97]) ).
fof(f607,plain,
spl18_71,
inference(avatar_split_clause,[],[f200,f605]) ).
fof(f200,plain,
! [X0,X1,X5] :
( in(apply(X1,X5),relation_rng(X1))
| ~ in(X5,relation_dom(X1))
| ~ sP1(X0,X1) ),
inference(equality_resolution,[],[f149]) ).
fof(f149,plain,
! [X0,X1,X4,X5] :
( in(X4,relation_rng(X1))
| apply(X1,X5) != X4
| ~ in(X5,relation_dom(X1))
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f97]) ).
fof(f603,plain,
( spl18_70
| ~ spl18_4
| ~ spl18_41 ),
inference(avatar_split_clause,[],[f424,f415,f220,f600]) ).
fof(f600,plain,
( spl18_70
<=> element(sK3,relation_dom(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_70])]) ).
fof(f424,plain,
( element(sK3,relation_dom(sK4))
| ~ spl18_4
| ~ spl18_41 ),
inference(resolution,[],[f416,f222]) ).
fof(f598,plain,
spl18_69,
inference(avatar_split_clause,[],[f159,f596]) ).
fof(f159,plain,
! [X0,X1] :
( sP2(X0,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f87,plain,
! [X0] :
( ! [X1] :
( sP2(X0,X1)
| ~ function(X1)
| ~ relation(X1) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f61,f86,f85,f84]) ).
fof(f86,plain,
! [X0,X1] :
( ( function_inverse(X0) = X1
<=> sP1(X1,X0) )
| ~ sP2(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f61,plain,
! [X0] :
( ! [X1] :
( ( function_inverse(X0) = X1
<=> ( ! [X2,X3] :
( ( ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) )
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
& ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) ) )
& relation_rng(X0) = relation_dom(X1) ) )
| ~ function(X1)
| ~ relation(X1) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f60]) ).
fof(f60,plain,
! [X0] :
( ! [X1] :
( ( function_inverse(X0) = X1
<=> ( ! [X2,X3] :
( ( ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) )
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
& ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) ) )
& relation_rng(X0) = relation_dom(X1) ) )
| ~ function(X1)
| ~ relation(X1) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> ! [X1] :
( ( function(X1)
& relation(X1) )
=> ( function_inverse(X0) = X1
<=> ( ! [X2,X3] :
( ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
=> ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) ) )
& ( ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) )
=> ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) )
& relation_rng(X0) = relation_dom(X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_funct_1) ).
fof(f594,plain,
spl18_68,
inference(avatar_split_clause,[],[f175,f592]) ).
fof(f175,plain,
! [X0,X1] :
( function(relation_composition(X0,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f73,plain,
! [X0,X1] :
( ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) )
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f72]) ).
fof(f72,plain,
! [X0,X1] :
( ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) )
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1)
& function(X0)
& relation(X0) )
=> ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_1) ).
fof(f590,plain,
spl18_67,
inference(avatar_split_clause,[],[f201,f588]) ).
fof(f201,plain,
! [X2,X3,X1] :
( sP0(apply(X2,X1),X1,X2,X3)
| ~ in(X1,relation_dom(X2)) ),
inference(equality_resolution,[],[f158]) ).
fof(f158,plain,
! [X2,X3,X0,X1] :
( sP0(X0,X1,X2,X3)
| apply(X2,X1) != X0
| ~ in(X1,relation_dom(X2)) ),
inference(cnf_transformation,[],[f100]) ).
fof(f580,plain,
spl18_66,
inference(avatar_split_clause,[],[f181,f578]) ).
fof(f181,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f81]) ).
fof(f81,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f576,plain,
spl18_65,
inference(avatar_split_clause,[],[f157,f574]) ).
fof(f574,plain,
( spl18_65
<=> ! [X0,X3,X2,X1] :
( sP0(X0,X1,X2,X3)
| apply(X3,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_65])]) ).
fof(f157,plain,
! [X2,X3,X0,X1] :
( sP0(X0,X1,X2,X3)
| apply(X3,X0) = X1 ),
inference(cnf_transformation,[],[f100]) ).
fof(f572,plain,
( ~ spl18_64
| ~ spl18_4
| ~ spl18_40 ),
inference(avatar_split_clause,[],[f418,f411,f220,f569]) ).
fof(f569,plain,
( spl18_64
<=> in(relation_dom(sK4),sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_64])]) ).
fof(f418,plain,
( ~ in(relation_dom(sK4),sK3)
| ~ spl18_4
| ~ spl18_40 ),
inference(resolution,[],[f412,f222]) ).
fof(f567,plain,
spl18_63,
inference(avatar_split_clause,[],[f146,f565]) ).
fof(f146,plain,
! [X0,X1] :
( function_inverse(X0) = X1
| ~ sP1(X1,X0)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f92]) ).
fof(f92,plain,
! [X0,X1] :
( ( ( function_inverse(X0) = X1
| ~ sP1(X1,X0) )
& ( sP1(X1,X0)
| function_inverse(X0) != X1 ) )
| ~ sP2(X0,X1) ),
inference(nnf_transformation,[],[f86]) ).
fof(f557,plain,
spl18_62,
inference(avatar_split_clause,[],[f182,f555]) ).
fof(f182,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f553,plain,
spl18_61,
inference(avatar_split_clause,[],[f156,f551]) ).
fof(f551,plain,
( spl18_61
<=> ! [X0,X3,X2,X1] :
( sP0(X0,X1,X2,X3)
| in(X0,relation_rng(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_61])]) ).
fof(f156,plain,
! [X2,X3,X0,X1] :
( sP0(X0,X1,X2,X3)
| in(X0,relation_rng(X2)) ),
inference(cnf_transformation,[],[f100]) ).
fof(f510,plain,
spl18_60,
inference(avatar_split_clause,[],[f198,f508]) ).
fof(f198,plain,
! [X0] :
( sP1(function_inverse(X0),X0)
| ~ sP2(X0,function_inverse(X0)) ),
inference(equality_resolution,[],[f145]) ).
fof(f145,plain,
! [X0,X1] :
( sP1(X1,X0)
| function_inverse(X0) != X1
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f92]) ).
fof(f506,plain,
spl18_59,
inference(avatar_split_clause,[],[f177,f504]) ).
fof(f177,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(flattening,[],[f76]) ).
fof(f76,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f502,plain,
spl18_58,
inference(avatar_split_clause,[],[f173,f500]) ).
fof(f173,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& empty(relation_composition(X0,X1)) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(flattening,[],[f70]) ).
fof(f70,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& empty(relation_composition(X0,X1)) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0,X1] :
( ( relation(X1)
& empty(X0) )
=> ( relation(relation_composition(X0,X1))
& empty(relation_composition(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc9_relat_1) ).
fof(f498,plain,
spl18_57,
inference(avatar_split_clause,[],[f172,f496]) ).
fof(f172,plain,
! [X0,X1] :
( empty(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f494,plain,
spl18_56,
inference(avatar_split_clause,[],[f171,f492]) ).
fof(f171,plain,
! [X0,X1] :
( relation(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0,X1] :
( ( relation(relation_composition(X1,X0))
& empty(relation_composition(X1,X0)) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(flattening,[],[f68]) ).
fof(f68,plain,
! [X0,X1] :
( ( relation(relation_composition(X1,X0))
& empty(relation_composition(X1,X0)) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1] :
( ( relation(X1)
& empty(X0) )
=> ( relation(relation_composition(X1,X0))
& empty(relation_composition(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc10_relat_1) ).
fof(f490,plain,
( ~ spl18_55
| ~ spl18_35
| spl18_42 ),
inference(avatar_split_clause,[],[f454,f420,f374,f487]) ).
fof(f487,plain,
( spl18_55
<=> empty(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_55])]) ).
fof(f420,plain,
( spl18_42
<=> empty(relation_dom(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_42])]) ).
fof(f454,plain,
( ~ empty(sK4)
| ~ spl18_35
| spl18_42 ),
inference(resolution,[],[f422,f375]) ).
fof(f422,plain,
( ~ empty(relation_dom(sK4))
| spl18_42 ),
inference(avatar_component_clause,[],[f420]) ).
fof(f485,plain,
spl18_54,
inference(avatar_split_clause,[],[f170,f483]) ).
fof(f170,plain,
! [X0,X1] :
( empty(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f481,plain,
spl18_53,
inference(avatar_split_clause,[],[f169,f479]) ).
fof(f169,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f66]) ).
fof(f66,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f477,plain,
spl18_52,
inference(avatar_split_clause,[],[f162,f475]) ).
fof(f162,plain,
! [X0] :
( one_to_one(X0)
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0] :
( ( one_to_one(X0)
& function(X0)
& relation(X0) )
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ),
inference(flattening,[],[f62]) ).
fof(f62,plain,
! [X0] :
( ( one_to_one(X0)
& function(X0)
& relation(X0) )
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( ( function(X0)
& empty(X0)
& relation(X0) )
=> ( one_to_one(X0)
& function(X0)
& relation(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_funct_1) ).
fof(f473,plain,
spl18_51,
inference(avatar_split_clause,[],[f148,f471]) ).
fof(f148,plain,
! [X0,X1,X4,X5] :
( sP0(X4,X5,X1,X0)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f97]) ).
fof(f469,plain,
spl18_50,
inference(avatar_split_clause,[],[f147,f467]) ).
fof(f147,plain,
! [X0,X1] :
( relation_dom(X0) = relation_rng(X1)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f97]) ).
fof(f452,plain,
spl18_49,
inference(avatar_split_clause,[],[f179,f450]) ).
fof(f179,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f41,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(f448,plain,
spl18_48,
inference(avatar_split_clause,[],[f178,f446]) ).
fof(f178,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f43]) ).
fof(f43,plain,
! [X0,X1] :
( subset(X0,X1)
=> element(X0,powerset(X1)) ),
inference(unused_predicate_definition_removal,[],[f33]) ).
fof(f33,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f444,plain,
spl18_47,
inference(avatar_split_clause,[],[f144,f442]) ).
fof(f144,plain,
! [X0] :
( function(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0] :
( ( function(function_inverse(X0))
& relation(function_inverse(X0)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f58]) ).
fof(f58,plain,
! [X0] :
( ( function(function_inverse(X0))
& relation(function_inverse(X0)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( function(function_inverse(X0))
& relation(function_inverse(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_funct_1) ).
fof(f440,plain,
spl18_46,
inference(avatar_split_clause,[],[f143,f438]) ).
fof(f143,plain,
! [X0] :
( relation(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f436,plain,
spl18_45,
inference(avatar_split_clause,[],[f142,f434]) ).
fof(f434,plain,
( spl18_45
<=> ! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_45])]) ).
fof(f142,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,[],[f14]) ).
fof(f14,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_dom(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(f432,plain,
spl18_44,
inference(avatar_split_clause,[],[f141,f430]) ).
fof(f430,plain,
( spl18_44
<=> ! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_44])]) ).
fof(f141,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,[],[f15]) ).
fof(f15,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_rng(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).
fof(f428,plain,
spl18_43,
inference(avatar_split_clause,[],[f132,f426]) ).
fof(f132,plain,
! [X0] :
( element(sK5(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f91,plain,
! [X0] :
( ( ~ empty(sK5(X0))
& element(sK5(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f48,f90]) ).
fof(f90,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( ~ empty(sK5(X0))
& element(sK5(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f48,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f423,plain,
( ~ spl18_42
| ~ spl18_4
| ~ spl18_38 ),
inference(avatar_split_clause,[],[f409,f386,f220,f420]) ).
fof(f409,plain,
( ~ empty(relation_dom(sK4))
| ~ spl18_4
| ~ spl18_38 ),
inference(resolution,[],[f387,f222]) ).
fof(f417,plain,
spl18_41,
inference(avatar_split_clause,[],[f168,f415]) ).
fof(f168,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(f413,plain,
spl18_40,
inference(avatar_split_clause,[],[f167,f411]) ).
fof(f167,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f393,plain,
( spl18_39
| ~ spl18_8
| ~ spl18_27 ),
inference(avatar_split_clause,[],[f344,f331,f240,f390]) ).
fof(f344,plain,
( function(sK11)
| ~ spl18_8
| ~ spl18_27 ),
inference(resolution,[],[f332,f242]) ).
fof(f388,plain,
spl18_38,
inference(avatar_split_clause,[],[f180,f386]) ).
fof(f180,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f384,plain,
spl18_37,
inference(avatar_split_clause,[],[f164,f382]) ).
fof(f164,plain,
! [X0] : element(sK9(X0),powerset(X0)),
inference(cnf_transformation,[],[f104]) ).
fof(f104,plain,
! [X0] :
( empty(sK9(X0))
& element(sK9(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f25,f103]) ).
fof(f103,plain,
! [X0] :
( ? [X1] :
( empty(X1)
& element(X1,powerset(X0)) )
=> ( empty(sK9(X0))
& element(sK9(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f25,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f380,plain,
spl18_36,
inference(avatar_split_clause,[],[f140,f378]) ).
fof(f140,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,[],[f16]) ).
fof(f16,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(f376,plain,
spl18_35,
inference(avatar_split_clause,[],[f139,f374]) ).
fof(f139,plain,
! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f372,plain,
spl18_34,
inference(avatar_split_clause,[],[f138,f370]) ).
fof(f138,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,[],[f17]) ).
fof(f17,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_rng(X0))
& empty(relation_rng(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).
fof(f368,plain,
spl18_33,
inference(avatar_split_clause,[],[f137,f366]) ).
fof(f137,plain,
! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f364,plain,
spl18_32,
inference(avatar_split_clause,[],[f136,f362]) ).
fof(f136,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f39]) ).
fof(f39,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f360,plain,
spl18_31,
inference(avatar_split_clause,[],[f133,f358]) ).
fof(f358,plain,
( spl18_31
<=> ! [X0] :
( ~ empty(sK5(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_31])]) ).
fof(f133,plain,
! [X0] :
( ~ empty(sK5(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f356,plain,
( spl18_30
| ~ spl18_5
| ~ spl18_27 ),
inference(avatar_split_clause,[],[f342,f331,f225,f353]) ).
fof(f353,plain,
( spl18_30
<=> function(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_30])]) ).
fof(f342,plain,
( function(empty_set)
| ~ spl18_5
| ~ spl18_27 ),
inference(resolution,[],[f332,f227]) ).
fof(f341,plain,
spl18_29,
inference(avatar_split_clause,[],[f163,f339]) ).
fof(f163,plain,
! [X0] : element(sK8(X0),X0),
inference(cnf_transformation,[],[f102]) ).
fof(f102,plain,
! [X0] : element(sK8(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f7,f101]) ).
fof(f101,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK8(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f7,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f337,plain,
spl18_28,
inference(avatar_split_clause,[],[f135,f335]) ).
fof(f135,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/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(f333,plain,
spl18_27,
inference(avatar_split_clause,[],[f134,f331]) ).
fof(f134,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/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
fof(f329,plain,
( ~ spl18_25
| ~ spl18_26 ),
inference(avatar_split_clause,[],[f125,f326,f322]) ).
fof(f125,plain,
( sK3 != apply(relation_composition(sK4,function_inverse(sK4)),sK3)
| sK3 != apply(function_inverse(sK4),apply(sK4,sK3)) ),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
( ( sK3 != apply(relation_composition(sK4,function_inverse(sK4)),sK3)
| sK3 != apply(function_inverse(sK4),apply(sK4,sK3)) )
& in(sK3,relation_dom(sK4))
& one_to_one(sK4)
& function(sK4)
& relation(sK4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f47,f88]) ).
fof(f88,plain,
( ? [X0,X1] :
( ( apply(relation_composition(X1,function_inverse(X1)),X0) != X0
| apply(function_inverse(X1),apply(X1,X0)) != X0 )
& in(X0,relation_dom(X1))
& one_to_one(X1)
& function(X1)
& relation(X1) )
=> ( ( sK3 != apply(relation_composition(sK4,function_inverse(sK4)),sK3)
| sK3 != apply(function_inverse(sK4),apply(sK4,sK3)) )
& in(sK3,relation_dom(sK4))
& one_to_one(sK4)
& function(sK4)
& relation(sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f47,plain,
? [X0,X1] :
( ( apply(relation_composition(X1,function_inverse(X1)),X0) != X0
| apply(function_inverse(X1),apply(X1,X0)) != X0 )
& in(X0,relation_dom(X1))
& one_to_one(X1)
& function(X1)
& relation(X1) ),
inference(flattening,[],[f46]) ).
fof(f46,plain,
? [X0,X1] :
( ( apply(relation_composition(X1,function_inverse(X1)),X0) != X0
| apply(function_inverse(X1),apply(X1,X0)) != X0 )
& in(X0,relation_dom(X1))
& one_to_one(X1)
& function(X1)
& relation(X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,negated_conjecture,
~ ! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( ( in(X0,relation_dom(X1))
& one_to_one(X1) )
=> ( apply(relation_composition(X1,function_inverse(X1)),X0) = X0
& apply(function_inverse(X1),apply(X1,X0)) = X0 ) ) ),
inference(negated_conjecture,[],[f36]) ).
fof(f36,conjecture,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( ( in(X0,relation_dom(X1))
& one_to_one(X1) )
=> ( apply(relation_composition(X1,function_inverse(X1)),X0) = X0
& apply(function_inverse(X1),apply(X1,X0)) = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_funct_1) ).
fof(f320,plain,
spl18_24,
inference(avatar_split_clause,[],[f166,f318]) ).
fof(f318,plain,
( spl18_24
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_24])]) ).
fof(f166,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f29]) ).
fof(f29,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f316,plain,
spl18_23,
inference(avatar_split_clause,[],[f165,f314]) ).
fof(f165,plain,
! [X0] : empty(sK9(X0)),
inference(cnf_transformation,[],[f104]) ).
fof(f312,plain,
spl18_22,
inference(avatar_split_clause,[],[f131,f310]) ).
fof(f310,plain,
( spl18_22
<=> ! [X0] : ~ empty(powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_22])]) ).
fof(f131,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f308,plain,
spl18_21,
inference(avatar_split_clause,[],[f197,f305]) ).
fof(f305,plain,
( spl18_21
<=> function(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_21])]) ).
fof(f197,plain,
function(sK17),
inference(cnf_transformation,[],[f120]) ).
fof(f120,plain,
( function(sK17)
& empty(sK17)
& relation(sK17) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f23,f119]) ).
fof(f119,plain,
( ? [X0] :
( function(X0)
& empty(X0)
& relation(X0) )
=> ( function(sK17)
& empty(sK17)
& relation(sK17) ) ),
introduced(choice_axiom,[]) ).
fof(f23,axiom,
? [X0] :
( function(X0)
& empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(f303,plain,
spl18_20,
inference(avatar_split_clause,[],[f196,f300]) ).
fof(f196,plain,
empty(sK17),
inference(cnf_transformation,[],[f120]) ).
fof(f298,plain,
spl18_19,
inference(avatar_split_clause,[],[f195,f295]) ).
fof(f295,plain,
( spl18_19
<=> relation(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_19])]) ).
fof(f195,plain,
relation(sK17),
inference(cnf_transformation,[],[f120]) ).
fof(f293,plain,
spl18_18,
inference(avatar_split_clause,[],[f194,f290]) ).
fof(f290,plain,
( spl18_18
<=> one_to_one(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_18])]) ).
fof(f194,plain,
one_to_one(sK16),
inference(cnf_transformation,[],[f118]) ).
fof(f118,plain,
( one_to_one(sK16)
& function(sK16)
& relation(sK16) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f27,f117]) ).
fof(f117,plain,
( ? [X0] :
( one_to_one(X0)
& function(X0)
& relation(X0) )
=> ( one_to_one(sK16)
& function(sK16)
& relation(sK16) ) ),
introduced(choice_axiom,[]) ).
fof(f27,axiom,
? [X0] :
( one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).
fof(f288,plain,
spl18_17,
inference(avatar_split_clause,[],[f193,f285]) ).
fof(f193,plain,
function(sK16),
inference(cnf_transformation,[],[f118]) ).
fof(f283,plain,
spl18_16,
inference(avatar_split_clause,[],[f192,f280]) ).
fof(f192,plain,
relation(sK16),
inference(cnf_transformation,[],[f118]) ).
fof(f278,plain,
spl18_15,
inference(avatar_split_clause,[],[f191,f275]) ).
fof(f191,plain,
function(sK15),
inference(cnf_transformation,[],[f116]) ).
fof(f116,plain,
( function(sK15)
& relation(sK15) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f19,f115]) ).
fof(f115,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK15)
& relation(sK15) ) ),
introduced(choice_axiom,[]) ).
fof(f19,axiom,
? [X0] :
( function(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
fof(f273,plain,
spl18_14,
inference(avatar_split_clause,[],[f190,f270]) ).
fof(f190,plain,
relation(sK15),
inference(cnf_transformation,[],[f116]) ).
fof(f268,plain,
spl18_13,
inference(avatar_split_clause,[],[f189,f265]) ).
fof(f189,plain,
relation(sK14),
inference(cnf_transformation,[],[f114]) ).
fof(f114,plain,
relation(sK14),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f44,f113]) ).
fof(f113,plain,
( ? [X0] : relation(X0)
=> relation(sK14) ),
introduced(choice_axiom,[]) ).
fof(f44,plain,
? [X0] : relation(X0),
inference(pure_predicate_removal,[],[f28]) ).
fof(f28,axiom,
? [X0] :
( relation_empty_yielding(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).
fof(f263,plain,
spl18_12,
inference(avatar_split_clause,[],[f188,f260]) ).
fof(f260,plain,
( spl18_12
<=> relation(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_12])]) ).
fof(f188,plain,
relation(sK13),
inference(cnf_transformation,[],[f112]) ).
fof(f112,plain,
( relation(sK13)
& empty(sK13) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f20,f111]) ).
fof(f111,plain,
( ? [X0] :
( relation(X0)
& empty(X0) )
=> ( relation(sK13)
& empty(sK13) ) ),
introduced(choice_axiom,[]) ).
fof(f20,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f258,plain,
spl18_11,
inference(avatar_split_clause,[],[f187,f255]) ).
fof(f187,plain,
empty(sK13),
inference(cnf_transformation,[],[f112]) ).
fof(f253,plain,
spl18_10,
inference(avatar_split_clause,[],[f186,f250]) ).
fof(f186,plain,
relation(sK12),
inference(cnf_transformation,[],[f110]) ).
fof(f110,plain,
( relation(sK12)
& ~ empty(sK12) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f24,f109]) ).
fof(f109,plain,
( ? [X0] :
( relation(X0)
& ~ empty(X0) )
=> ( relation(sK12)
& ~ empty(sK12) ) ),
introduced(choice_axiom,[]) ).
fof(f24,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f248,plain,
~ spl18_9,
inference(avatar_split_clause,[],[f185,f245]) ).
fof(f245,plain,
( spl18_9
<=> empty(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_9])]) ).
fof(f185,plain,
~ empty(sK12),
inference(cnf_transformation,[],[f110]) ).
fof(f243,plain,
spl18_8,
inference(avatar_split_clause,[],[f184,f240]) ).
fof(f184,plain,
empty(sK11),
inference(cnf_transformation,[],[f108]) ).
fof(f108,plain,
empty(sK11),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f22,f107]) ).
fof(f107,plain,
( ? [X0] : empty(X0)
=> empty(sK11) ),
introduced(choice_axiom,[]) ).
fof(f22,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f238,plain,
~ spl18_7,
inference(avatar_split_clause,[],[f183,f235]) ).
fof(f235,plain,
( spl18_7
<=> empty(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_7])]) ).
fof(f183,plain,
~ empty(sK10),
inference(cnf_transformation,[],[f106]) ).
fof(f106,plain,
~ empty(sK10),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f26,f105]) ).
fof(f105,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK10) ),
introduced(choice_axiom,[]) ).
fof(f26,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f233,plain,
spl18_6,
inference(avatar_split_clause,[],[f128,f230]) ).
fof(f128,plain,
relation(empty_set),
inference(cnf_transformation,[],[f13]) ).
fof(f13,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f228,plain,
spl18_5,
inference(avatar_split_clause,[],[f126,f225]) ).
fof(f126,plain,
empty(empty_set),
inference(cnf_transformation,[],[f12]) ).
fof(f12,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f223,plain,
spl18_4,
inference(avatar_split_clause,[],[f124,f220]) ).
fof(f124,plain,
in(sK3,relation_dom(sK4)),
inference(cnf_transformation,[],[f89]) ).
fof(f218,plain,
spl18_3,
inference(avatar_split_clause,[],[f123,f215]) ).
fof(f123,plain,
one_to_one(sK4),
inference(cnf_transformation,[],[f89]) ).
fof(f213,plain,
spl18_2,
inference(avatar_split_clause,[],[f122,f210]) ).
fof(f122,plain,
function(sK4),
inference(cnf_transformation,[],[f89]) ).
fof(f208,plain,
spl18_1,
inference(avatar_split_clause,[],[f121,f205]) ).
fof(f121,plain,
relation(sK4),
inference(cnf_transformation,[],[f89]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU023+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.16/0.36 % Computer : n008.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Fri May 3 10:59:12 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.16/0.37 % (32143)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.39 % (32146)WARNING: value z3 for option sas not known
% 0.16/0.39 % (32144)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.39 % (32145)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.39 % (32147)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.39 % (32146)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)
% 0.16/0.39 % (32148)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)
% 0.16/0.39 % (32149)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)
% 0.16/0.39 % (32150)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)
% 0.16/0.39 TRYING [1]
% 0.16/0.39 TRYING [2]
% 0.16/0.40 TRYING [3]
% 0.22/0.41 TRYING [1]
% 0.22/0.41 TRYING [2]
% 0.22/0.41 TRYING [4]
% 0.22/0.45 TRYING [3]
% 0.22/0.46 TRYING [5]
% 0.22/0.48 TRYING [1]
% 0.22/0.48 TRYING [2]
% 0.22/0.48 TRYING [3]
% 0.22/0.49 TRYING [4]
% 0.22/0.50 TRYING [4]
% 0.22/0.51 % (32148)First to succeed.
% 0.22/0.52 TRYING [5]
% 0.22/0.52 % (32148)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-32143"
% 0.22/0.52 % (32148)Refutation found. Thanks to Tanya!
% 0.22/0.52 % SZS status Theorem for theBenchmark
% 0.22/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.53 % (32148)------------------------------
% 0.22/0.53 % (32148)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.53 % (32148)Termination reason: Refutation
% 0.22/0.53
% 0.22/0.53 % (32148)Memory used [KB]: 2938
% 0.22/0.53 % (32148)Time elapsed: 0.135 s
% 0.22/0.53 % (32148)Instructions burned: 285 (million)
% 0.22/0.53 % (32143)Success in time 0.157 s
%------------------------------------------------------------------------------