TSTP Solution File: SEU210+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU210+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 15:23:49 EDT 2024
% Result : Theorem 0.20s 0.47s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 286
% Syntax : Number of formulae : 951 ( 83 unt; 0 def)
% Number of atoms : 3528 ( 243 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 4722 (2145 ~;2216 |; 83 &)
% ( 251 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 249 ( 247 usr; 243 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 7 con; 0-3 aty)
% Number of variables : 1368 (1326 !; 42 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2907,plain,
$false,
inference(avatar_sat_refutation,[],[f159,f164,f169,f174,f179,f184,f189,f194,f199,f204,f209,f214,f218,f222,f226,f230,f234,f238,f242,f250,f254,f258,f262,f266,f270,f275,f287,f291,f295,f299,f303,f307,f311,f315,f328,f340,f344,f348,f363,f367,f373,f383,f393,f400,f404,f412,f423,f429,f433,f445,f450,f457,f470,f474,f479,f493,f498,f502,f512,f518,f524,f528,f532,f539,f544,f545,f546,f547,f553,f569,f599,f603,f607,f625,f629,f642,f646,f650,f654,f658,f663,f667,f708,f712,f716,f720,f751,f755,f759,f773,f784,f788,f792,f811,f815,f819,f823,f834,f855,f859,f863,f867,f880,f890,f900,f904,f908,f924,f934,f944,f949,f954,f959,f975,f980,f984,f993,f1005,f1009,f1013,f1041,f1045,f1049,f1053,f1057,f1087,f1091,f1095,f1099,f1103,f1154,f1158,f1162,f1166,f1170,f1174,f1183,f1205,f1210,f1229,f1242,f1246,f1250,f1254,f1258,f1262,f1266,f1292,f1342,f1346,f1350,f1354,f1358,f1362,f1367,f1371,f1375,f1379,f1436,f1455,f1459,f1463,f1467,f1471,f1475,f1479,f1606,f1610,f1614,f1618,f1622,f1626,f1681,f1685,f1752,f1756,f1760,f1764,f1768,f1772,f1776,f1780,f1784,f1788,f1792,f1910,f1914,f1918,f1922,f1926,f2018,f2028,f2032,f2036,f2085,f2089,f2157,f2161,f2165,f2169,f2285,f2289,f2293,f2297,f2370,f2374,f2378,f2382,f2486,f2490,f2494,f2498,f2527,f2547,f2567,f2575,f2579,f2583,f2587,f2623,f2636,f2640,f2665,f2670,f2690,f2698,f2706,f2720,f2724,f2728,f2734,f2755,f2759,f2780,f2784,f2788,f2848,f2852,f2856,f2860,f2864,f2868,f2886,f2906]) ).
fof(f2906,plain,
( spl14_78
| ~ spl14_54
| ~ spl14_138 ),
inference(avatar_split_clause,[],[f2899,f1208,f468,f660]) ).
fof(f660,plain,
( spl14_78
<=> sK0 = sK11 ),
introduced(avatar_definition,[new_symbols(naming,[spl14_78])]) ).
fof(f468,plain,
( spl14_54
<=> ! [X0] : ~ in(X0,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_54])]) ).
fof(f1208,plain,
( spl14_138
<=> ! [X0] :
( sK11 = X0
| in(sK3(sK11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_138])]) ).
fof(f2899,plain,
( sK0 = sK11
| ~ spl14_54
| ~ spl14_138 ),
inference(resolution,[],[f469,f1209]) ).
fof(f1209,plain,
( ! [X0] :
( in(sK3(sK11,X0),X0)
| sK11 = X0 )
| ~ spl14_138 ),
inference(avatar_component_clause,[],[f1208]) ).
fof(f469,plain,
( ! [X0] : ~ in(X0,sK0)
| ~ spl14_54 ),
inference(avatar_component_clause,[],[f468]) ).
fof(f2886,plain,
( spl14_54
| ~ spl14_41
| ~ spl14_230 ),
inference(avatar_split_clause,[],[f2817,f2726,f371,f468]) ).
fof(f371,plain,
( spl14_41
<=> ! [X0] :
( ~ in(X0,sK0)
| in(X0,relation_rng(sK1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_41])]) ).
fof(f2726,plain,
( spl14_230
<=> ! [X0] :
( ~ in(X0,relation_rng(sK1))
| ~ in(X0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_230])]) ).
fof(f2817,plain,
( ! [X0] : ~ in(X0,sK0)
| ~ spl14_41
| ~ spl14_230 ),
inference(duplicate_literal_removal,[],[f2789]) ).
fof(f2789,plain,
( ! [X0] :
( ~ in(X0,sK0)
| ~ in(X0,sK0) )
| ~ spl14_41
| ~ spl14_230 ),
inference(resolution,[],[f2727,f372]) ).
fof(f372,plain,
( ! [X0] :
( in(X0,relation_rng(sK1))
| ~ in(X0,sK0) )
| ~ spl14_41 ),
inference(avatar_component_clause,[],[f371]) ).
fof(f2727,plain,
( ! [X0] :
( ~ in(X0,relation_rng(sK1))
| ~ in(X0,sK0) )
| ~ spl14_230 ),
inference(avatar_component_clause,[],[f2726]) ).
fof(f2868,plain,
( spl14_242
| ~ spl14_27
| ~ spl14_138 ),
inference(avatar_split_clause,[],[f1213,f1208,f285,f2866]) ).
fof(f2866,plain,
( spl14_242
<=> ! [X0] :
( sK11 = X0
| ~ in(X0,sK3(sK11,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_242])]) ).
fof(f285,plain,
( spl14_27
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_27])]) ).
fof(f1213,plain,
( ! [X0] :
( sK11 = X0
| ~ in(X0,sK3(sK11,X0)) )
| ~ spl14_27
| ~ spl14_138 ),
inference(resolution,[],[f1209,f286]) ).
fof(f286,plain,
( ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) )
| ~ spl14_27 ),
inference(avatar_component_clause,[],[f285]) ).
fof(f2864,plain,
( spl14_241
| ~ spl14_28
| ~ spl14_138 ),
inference(avatar_split_clause,[],[f1212,f1208,f289,f2862]) ).
fof(f2862,plain,
( spl14_241
<=> ! [X0] :
( sK11 = X0
| element(sK3(sK11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_241])]) ).
fof(f289,plain,
( spl14_28
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_28])]) ).
fof(f1212,plain,
( ! [X0] :
( sK11 = X0
| element(sK3(sK11,X0),X0) )
| ~ spl14_28
| ~ spl14_138 ),
inference(resolution,[],[f1209,f290]) ).
fof(f290,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) )
| ~ spl14_28 ),
inference(avatar_component_clause,[],[f289]) ).
fof(f2860,plain,
( spl14_240
| ~ spl14_17
| ~ spl14_122 ),
inference(avatar_split_clause,[],[f1082,f1051,f232,f2858]) ).
fof(f2858,plain,
( spl14_240
<=> ! [X0,X1] :
( ~ empty(X0)
| ~ relation(X0)
| relation(relation_inverse_image(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_240])]) ).
fof(f232,plain,
( spl14_17
<=> ! [X0] :
( relation(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_17])]) ).
fof(f1051,plain,
( spl14_122
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| empty(relation_inverse_image(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_122])]) ).
fof(f1082,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ relation(X0)
| relation(relation_inverse_image(X0,X1)) )
| ~ spl14_17
| ~ spl14_122 ),
inference(resolution,[],[f1052,f233]) ).
fof(f233,plain,
( ! [X0] :
( ~ empty(X0)
| relation(X0) )
| ~ spl14_17 ),
inference(avatar_component_clause,[],[f232]) ).
fof(f1052,plain,
( ! [X0,X1] :
( empty(relation_inverse_image(X0,X1))
| ~ empty(X0)
| ~ relation(X0) )
| ~ spl14_122 ),
inference(avatar_component_clause,[],[f1051]) ).
fof(f2856,plain,
( spl14_239
| ~ spl14_17
| ~ spl14_121 ),
inference(avatar_split_clause,[],[f1075,f1047,f232,f2854]) ).
fof(f2854,plain,
( spl14_239
<=> ! [X0,X1] :
( ~ empty(X0)
| ~ relation(X1)
| relation(relation_inverse_image(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_239])]) ).
fof(f1047,plain,
( spl14_121
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| empty(relation_inverse_image(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_121])]) ).
fof(f1075,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ relation(X1)
| relation(relation_inverse_image(X1,X0)) )
| ~ spl14_17
| ~ spl14_121 ),
inference(resolution,[],[f1048,f233]) ).
fof(f1048,plain,
( ! [X0,X1] :
( empty(relation_inverse_image(X0,X1))
| ~ empty(X1)
| ~ relation(X0) )
| ~ spl14_121 ),
inference(avatar_component_clause,[],[f1047]) ).
fof(f2852,plain,
( spl14_238
| ~ spl14_22
| ~ spl14_117 ),
inference(avatar_split_clause,[],[f1022,f1007,f256,f2850]) ).
fof(f2850,plain,
( spl14_238
<=> ! [X0] :
( sK11 = relation_rng(relation_rng(relation_rng(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_238])]) ).
fof(f256,plain,
( spl14_22
<=> ! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_22])]) ).
fof(f1007,plain,
( spl14_117
<=> ! [X0] :
( sK11 = relation_rng(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_117])]) ).
fof(f1022,plain,
( ! [X0] :
( sK11 = relation_rng(relation_rng(relation_rng(X0)))
| ~ empty(X0) )
| ~ spl14_22
| ~ spl14_117 ),
inference(resolution,[],[f1008,f257]) ).
fof(f257,plain,
( ! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) )
| ~ spl14_22 ),
inference(avatar_component_clause,[],[f256]) ).
fof(f1008,plain,
( ! [X0] :
( ~ empty(X0)
| sK11 = relation_rng(relation_rng(X0)) )
| ~ spl14_117 ),
inference(avatar_component_clause,[],[f1007]) ).
fof(f2848,plain,
( spl14_237
| ~ spl14_68
| ~ spl14_114 ),
inference(avatar_split_clause,[],[f986,f982,f597,f2846]) ).
fof(f2846,plain,
( spl14_237
<=> ! [X0] :
( ~ empty(X0)
| sK11 = relation_rng(sK6(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_237])]) ).
fof(f597,plain,
( spl14_68
<=> ! [X0] :
( relation_rng(X0) = sK11
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_68])]) ).
fof(f982,plain,
( spl14_114
<=> ! [X0] :
( ~ empty(X0)
| empty(sK6(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_114])]) ).
fof(f986,plain,
( ! [X0] :
( ~ empty(X0)
| sK11 = relation_rng(sK6(powerset(X0))) )
| ~ spl14_68
| ~ spl14_114 ),
inference(resolution,[],[f983,f598]) ).
fof(f598,plain,
( ! [X0] :
( ~ empty(X0)
| relation_rng(X0) = sK11 )
| ~ spl14_68 ),
inference(avatar_component_clause,[],[f597]) ).
fof(f983,plain,
( ! [X0] :
( empty(sK6(powerset(X0)))
| ~ empty(X0) )
| ~ spl14_114 ),
inference(avatar_component_clause,[],[f982]) ).
fof(f2788,plain,
( spl14_236
| ~ spl14_116
| ~ spl14_138 ),
inference(avatar_split_clause,[],[f1218,f1208,f1003,f2786]) ).
fof(f2786,plain,
( spl14_236
<=> ! [X0] :
( sK11 = relation_inverse_image(X0,sK11)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_236])]) ).
fof(f1003,plain,
( spl14_116
<=> ! [X0,X1] :
( ~ in(X0,relation_inverse_image(X1,sK11))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_116])]) ).
fof(f1218,plain,
( ! [X0] :
( sK11 = relation_inverse_image(X0,sK11)
| ~ relation(X0) )
| ~ spl14_116
| ~ spl14_138 ),
inference(resolution,[],[f1209,f1004]) ).
fof(f1004,plain,
( ! [X0,X1] :
( ~ in(X0,relation_inverse_image(X1,sK11))
| ~ relation(X1) )
| ~ spl14_116 ),
inference(avatar_component_clause,[],[f1003]) ).
fof(f2784,plain,
( spl14_235
| ~ spl14_37
| ~ spl14_116 ),
inference(avatar_split_clause,[],[f1020,f1003,f342,f2782]) ).
fof(f2782,plain,
( spl14_235
<=> ! [X0,X1] :
( ~ relation(X0)
| subset(relation_inverse_image(X0,sK11),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_235])]) ).
fof(f342,plain,
( spl14_37
<=> ! [X0,X1] :
( subset(X0,X1)
| in(sK8(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_37])]) ).
fof(f1020,plain,
( ! [X0,X1] :
( ~ relation(X0)
| subset(relation_inverse_image(X0,sK11),X1) )
| ~ spl14_37
| ~ spl14_116 ),
inference(resolution,[],[f1004,f343]) ).
fof(f343,plain,
( ! [X0,X1] :
( in(sK8(X0,X1),X0)
| subset(X0,X1) )
| ~ spl14_37 ),
inference(avatar_component_clause,[],[f342]) ).
fof(f2780,plain,
( spl14_234
| ~ spl14_63
| ~ spl14_114 ),
inference(avatar_split_clause,[],[f987,f982,f526,f2778]) ).
fof(f2778,plain,
( spl14_234
<=> ! [X0] :
( ~ empty(X0)
| sK11 = sK6(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_234])]) ).
fof(f526,plain,
( spl14_63
<=> ! [X0] :
( sK11 = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_63])]) ).
fof(f987,plain,
( ! [X0] :
( ~ empty(X0)
| sK11 = sK6(powerset(X0)) )
| ~ spl14_63
| ~ spl14_114 ),
inference(resolution,[],[f983,f527]) ).
fof(f527,plain,
( ! [X0] :
( ~ empty(X0)
| sK11 = X0 )
| ~ spl14_63 ),
inference(avatar_component_clause,[],[f526]) ).
fof(f2759,plain,
( spl14_233
| ~ spl14_70
| ~ spl14_116 ),
inference(avatar_split_clause,[],[f1019,f1003,f605,f2757]) ).
fof(f2757,plain,
( spl14_233
<=> ! [X0] :
( ~ relation(X0)
| empty(relation_inverse_image(X0,sK11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_233])]) ).
fof(f605,plain,
( spl14_70
<=> ! [X0] :
( empty(X0)
| in(sK6(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_70])]) ).
fof(f1019,plain,
( ! [X0] :
( ~ relation(X0)
| empty(relation_inverse_image(X0,sK11)) )
| ~ spl14_70
| ~ spl14_116 ),
inference(resolution,[],[f1004,f606]) ).
fof(f606,plain,
( ! [X0] :
( in(sK6(X0),X0)
| empty(X0) )
| ~ spl14_70 ),
inference(avatar_component_clause,[],[f605]) ).
fof(f2755,plain,
( spl14_232
| ~ spl14_17
| ~ spl14_114 ),
inference(avatar_split_clause,[],[f989,f982,f232,f2753]) ).
fof(f2753,plain,
( spl14_232
<=> ! [X0] :
( ~ empty(X0)
| relation(sK6(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_232])]) ).
fof(f989,plain,
( ! [X0] :
( ~ empty(X0)
| relation(sK6(powerset(X0))) )
| ~ spl14_17
| ~ spl14_114 ),
inference(resolution,[],[f983,f233]) ).
fof(f2734,plain,
( spl14_231
| ~ spl14_41
| ~ spl14_207 ),
inference(avatar_split_clause,[],[f2462,f2380,f371,f2732]) ).
fof(f2732,plain,
( spl14_231
<=> ! [X0,X1] :
( ~ relation(X0)
| in(sK4(X0,X1),relation_inverse_image(X0,relation_rng(sK1)))
| in(sK3(X0,X1),X1)
| relation_rng(X0) = X1
| ~ in(sK3(X0,X1),sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_231])]) ).
fof(f2380,plain,
( spl14_207
<=> ! [X2,X0,X1] :
( in(sK3(X0,X1),X1)
| ~ relation(X0)
| in(sK4(X0,X1),relation_inverse_image(X0,X2))
| ~ in(sK3(X0,X1),X2)
| relation_rng(X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_207])]) ).
fof(f2462,plain,
( ! [X0,X1] :
( ~ relation(X0)
| in(sK4(X0,X1),relation_inverse_image(X0,relation_rng(sK1)))
| in(sK3(X0,X1),X1)
| relation_rng(X0) = X1
| ~ in(sK3(X0,X1),sK0) )
| ~ spl14_41
| ~ spl14_207 ),
inference(resolution,[],[f2381,f372]) ).
fof(f2381,plain,
( ! [X2,X0,X1] :
( ~ in(sK3(X0,X1),X2)
| ~ relation(X0)
| in(sK4(X0,X1),relation_inverse_image(X0,X2))
| in(sK3(X0,X1),X1)
| relation_rng(X0) = X1 )
| ~ spl14_207 ),
inference(avatar_component_clause,[],[f2380]) ).
fof(f2728,plain,
( spl14_230
| ~ spl14_66
| ~ spl14_225 ),
inference(avatar_split_clause,[],[f2699,f2696,f537,f2726]) ).
fof(f537,plain,
( spl14_66
<=> ! [X1] : ~ in(X1,sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_66])]) ).
fof(f2696,plain,
( spl14_225
<=> ! [X0] :
( in(sK5(sK1,X0),sK11)
| ~ in(X0,relation_rng(sK1))
| ~ in(X0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_225])]) ).
fof(f2699,plain,
( ! [X0] :
( ~ in(X0,relation_rng(sK1))
| ~ in(X0,sK0) )
| ~ spl14_66
| ~ spl14_225 ),
inference(resolution,[],[f2697,f538]) ).
fof(f538,plain,
( ! [X1] : ~ in(X1,sK11)
| ~ spl14_66 ),
inference(avatar_component_clause,[],[f537]) ).
fof(f2697,plain,
( ! [X0] :
( in(sK5(sK1,X0),sK11)
| ~ in(X0,relation_rng(sK1))
| ~ in(X0,sK0) )
| ~ spl14_225 ),
inference(avatar_component_clause,[],[f2696]) ).
fof(f2724,plain,
( spl14_229
| ~ spl14_41
| ~ spl14_189 ),
inference(avatar_split_clause,[],[f2021,f1924,f371,f2722]) ).
fof(f2722,plain,
( spl14_229
<=> ! [X2,X0,X1] :
( in(X0,relation_inverse_image(X1,relation_rng(sK1)))
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2))
| ~ in(sK9(X0,X2,X1),sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_229])]) ).
fof(f1924,plain,
( spl14_189
<=> ! [X0,X3,X2,X1] :
( ~ in(sK9(X0,X1,X2),X3)
| in(X0,relation_inverse_image(X2,X3))
| ~ relation(X2)
| ~ in(X0,relation_inverse_image(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_189])]) ).
fof(f2021,plain,
( ! [X2,X0,X1] :
( in(X0,relation_inverse_image(X1,relation_rng(sK1)))
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2))
| ~ in(sK9(X0,X2,X1),sK0) )
| ~ spl14_41
| ~ spl14_189 ),
inference(resolution,[],[f1925,f372]) ).
fof(f1925,plain,
( ! [X2,X3,X0,X1] :
( ~ in(sK9(X0,X1,X2),X3)
| in(X0,relation_inverse_image(X2,X3))
| ~ relation(X2)
| ~ in(X0,relation_inverse_image(X2,X1)) )
| ~ spl14_189 ),
inference(avatar_component_clause,[],[f1924]) ).
fof(f2720,plain,
( ~ spl14_227
| ~ spl14_1
| spl14_228
| ~ spl14_4
| ~ spl14_57
| ~ spl14_195 ),
inference(avatar_split_clause,[],[f2153,f2087,f490,f171,f2718,f156,f2714]) ).
fof(f2714,plain,
( spl14_227
<=> empty(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_227])]) ).
fof(f156,plain,
( spl14_1
<=> relation(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_1])]) ).
fof(f2718,plain,
( spl14_228
<=> ! [X0] :
( relation_rng(X0) = sK11
| ~ relation(X0)
| in(sK3(X0,sK11),relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_228])]) ).
fof(f171,plain,
( spl14_4
<=> empty_set = relation_inverse_image(sK1,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_4])]) ).
fof(f490,plain,
( spl14_57
<=> empty_set = sK11 ),
introduced(avatar_definition,[new_symbols(naming,[spl14_57])]) ).
fof(f2087,plain,
( spl14_195
<=> ! [X2,X0,X1] :
( in(sK3(X0,relation_inverse_image(X1,X2)),relation_rng(X0))
| ~ relation(X0)
| relation_rng(X0) = relation_inverse_image(X1,X2)
| ~ relation(X1)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_195])]) ).
fof(f2153,plain,
( ! [X0] :
( relation_rng(X0) = sK11
| in(sK3(X0,sK11),relation_rng(X0))
| ~ relation(X0)
| ~ relation(sK1)
| ~ empty(sK0) )
| ~ spl14_4
| ~ spl14_57
| ~ spl14_195 ),
inference(forward_demodulation,[],[f2152,f492]) ).
fof(f492,plain,
( empty_set = sK11
| ~ spl14_57 ),
inference(avatar_component_clause,[],[f490]) ).
fof(f2152,plain,
( ! [X0] :
( in(sK3(X0,sK11),relation_rng(X0))
| ~ relation(X0)
| relation_rng(X0) = empty_set
| ~ relation(sK1)
| ~ empty(sK0) )
| ~ spl14_4
| ~ spl14_57
| ~ spl14_195 ),
inference(forward_demodulation,[],[f2141,f492]) ).
fof(f2141,plain,
( ! [X0] :
( in(sK3(X0,empty_set),relation_rng(X0))
| ~ relation(X0)
| relation_rng(X0) = empty_set
| ~ relation(sK1)
| ~ empty(sK0) )
| ~ spl14_4
| ~ spl14_195 ),
inference(superposition,[],[f2088,f173]) ).
fof(f173,plain,
( empty_set = relation_inverse_image(sK1,sK0)
| ~ spl14_4 ),
inference(avatar_component_clause,[],[f171]) ).
fof(f2088,plain,
( ! [X2,X0,X1] :
( in(sK3(X0,relation_inverse_image(X1,X2)),relation_rng(X0))
| ~ relation(X0)
| relation_rng(X0) = relation_inverse_image(X1,X2)
| ~ relation(X1)
| ~ empty(X2) )
| ~ spl14_195 ),
inference(avatar_component_clause,[],[f2087]) ).
fof(f2706,plain,
( ~ spl14_1
| spl14_226
| ~ spl14_41
| ~ spl14_184 ),
inference(avatar_split_clause,[],[f1899,f1790,f371,f2704,f156]) ).
fof(f2704,plain,
( spl14_226
<=> ! [X0] :
( ~ in(sK3(sK1,X0),X0)
| ~ in(sK3(sK1,X0),sK0)
| relation_rng(sK1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_226])]) ).
fof(f1790,plain,
( spl14_184
<=> ! [X0,X1] :
( relation_rng(X0) = X1
| ~ in(sK3(X0,X1),X1)
| ~ relation(X0)
| ~ in(sK3(X0,X1),relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_184])]) ).
fof(f1899,plain,
( ! [X0] :
( ~ in(sK3(sK1,X0),X0)
| ~ relation(sK1)
| relation_rng(sK1) = X0
| ~ in(sK3(sK1,X0),sK0) )
| ~ spl14_41
| ~ spl14_184 ),
inference(resolution,[],[f1791,f372]) ).
fof(f1791,plain,
( ! [X0,X1] :
( ~ in(sK3(X0,X1),relation_rng(X0))
| ~ in(sK3(X0,X1),X1)
| ~ relation(X0)
| relation_rng(X0) = X1 )
| ~ spl14_184 ),
inference(avatar_component_clause,[],[f1790]) ).
fof(f2698,plain,
( ~ spl14_1
| spl14_225
| ~ spl14_4
| ~ spl14_57
| ~ spl14_173 ),
inference(avatar_split_clause,[],[f1747,f1683,f490,f171,f2696,f156]) ).
fof(f1683,plain,
( spl14_173
<=> ! [X2,X0,X1] :
( in(sK5(X0,X1),relation_inverse_image(X0,X2))
| ~ in(X1,X2)
| ~ in(X1,relation_rng(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_173])]) ).
fof(f1747,plain,
( ! [X0] :
( in(sK5(sK1,X0),sK11)
| ~ in(X0,sK0)
| ~ in(X0,relation_rng(sK1))
| ~ relation(sK1) )
| ~ spl14_4
| ~ spl14_57
| ~ spl14_173 ),
inference(forward_demodulation,[],[f1730,f492]) ).
fof(f1730,plain,
( ! [X0] :
( in(sK5(sK1,X0),empty_set)
| ~ in(X0,sK0)
| ~ in(X0,relation_rng(sK1))
| ~ relation(sK1) )
| ~ spl14_4
| ~ spl14_173 ),
inference(superposition,[],[f1684,f173]) ).
fof(f1684,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,X1),relation_inverse_image(X0,X2))
| ~ in(X1,X2)
| ~ in(X1,relation_rng(X0))
| ~ relation(X0) )
| ~ spl14_173 ),
inference(avatar_component_clause,[],[f1683]) ).
fof(f2690,plain,
( spl14_224
| ~ spl14_56
| ~ spl14_77 ),
inference(avatar_split_clause,[],[f692,f656,f477,f2688]) ).
fof(f2688,plain,
( spl14_224
<=> ! [X0,X1] :
( element(unordered_pair(singleton(sK4(sK6(powerset(X0)),X1)),unordered_pair(sK4(sK6(powerset(X0)),X1),sK3(sK6(powerset(X0)),X1))),X0)
| relation_rng(sK6(powerset(X0))) = X1
| in(sK3(sK6(powerset(X0)),X1),X1)
| ~ relation(sK6(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_224])]) ).
fof(f477,plain,
( spl14_56
<=> ! [X0,X1] :
( in(unordered_pair(singleton(sK4(X0,X1)),unordered_pair(sK4(X0,X1),sK3(X0,X1))),X0)
| relation_rng(X0) = X1
| in(sK3(X0,X1),X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_56])]) ).
fof(f656,plain,
( spl14_77
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK6(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_77])]) ).
fof(f692,plain,
( ! [X0,X1] :
( element(unordered_pair(singleton(sK4(sK6(powerset(X0)),X1)),unordered_pair(sK4(sK6(powerset(X0)),X1),sK3(sK6(powerset(X0)),X1))),X0)
| relation_rng(sK6(powerset(X0))) = X1
| in(sK3(sK6(powerset(X0)),X1),X1)
| ~ relation(sK6(powerset(X0))) )
| ~ spl14_56
| ~ spl14_77 ),
inference(resolution,[],[f657,f478]) ).
fof(f478,plain,
( ! [X0,X1] :
( in(unordered_pair(singleton(sK4(X0,X1)),unordered_pair(sK4(X0,X1),sK3(X0,X1))),X0)
| relation_rng(X0) = X1
| in(sK3(X0,X1),X1)
| ~ relation(X0) )
| ~ spl14_56 ),
inference(avatar_component_clause,[],[f477]) ).
fof(f657,plain,
( ! [X0,X1] :
( ~ in(X0,sK6(powerset(X1)))
| element(X0,X1) )
| ~ spl14_77 ),
inference(avatar_component_clause,[],[f656]) ).
fof(f2670,plain,
( spl14_223
| ~ spl14_5
| ~ spl14_57
| ~ spl14_212 ),
inference(avatar_split_clause,[],[f2600,f2525,f490,f176,f2667]) ).
fof(f2667,plain,
( spl14_223
<=> sK11 = relation_inverse_image(sK1,sK6(powerset(sK11))) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_223])]) ).
fof(f176,plain,
( spl14_5
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_5])]) ).
fof(f2525,plain,
( spl14_212
<=> ! [X0] :
( sK11 = relation_inverse_image(sK1,sK6(powerset(X0)))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_212])]) ).
fof(f2600,plain,
( sK11 = relation_inverse_image(sK1,sK6(powerset(sK11)))
| ~ spl14_5
| ~ spl14_57
| ~ spl14_212 ),
inference(forward_demodulation,[],[f2592,f492]) ).
fof(f2592,plain,
( sK11 = relation_inverse_image(sK1,sK6(powerset(empty_set)))
| ~ spl14_5
| ~ spl14_212 ),
inference(resolution,[],[f2526,f178]) ).
fof(f178,plain,
( empty(empty_set)
| ~ spl14_5 ),
inference(avatar_component_clause,[],[f176]) ).
fof(f2526,plain,
( ! [X0] :
( ~ empty(X0)
| sK11 = relation_inverse_image(sK1,sK6(powerset(X0))) )
| ~ spl14_212 ),
inference(avatar_component_clause,[],[f2525]) ).
fof(f2665,plain,
( spl14_222
| ~ spl14_42
| ~ spl14_103 ),
inference(avatar_split_clause,[],[f918,f902,f381,f2663]) ).
fof(f2663,plain,
( spl14_222
<=> ! [X2,X0,X1] :
( in(sK3(powerset(X0),X1),X1)
| ~ relation(powerset(X0))
| relation_rng(powerset(X0)) = X1
| element(X2,X0)
| ~ in(X2,unordered_pair(singleton(sK4(powerset(X0),X1)),unordered_pair(sK4(powerset(X0),X1),sK3(powerset(X0),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_222])]) ).
fof(f381,plain,
( spl14_42
<=> ! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_42])]) ).
fof(f902,plain,
( spl14_103
<=> ! [X0,X1] :
( relation_rng(X0) = X1
| in(sK3(X0,X1),X1)
| ~ relation(X0)
| element(unordered_pair(singleton(sK4(X0,X1)),unordered_pair(sK4(X0,X1),sK3(X0,X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_103])]) ).
fof(f918,plain,
( ! [X2,X0,X1] :
( in(sK3(powerset(X0),X1),X1)
| ~ relation(powerset(X0))
| relation_rng(powerset(X0)) = X1
| element(X2,X0)
| ~ in(X2,unordered_pair(singleton(sK4(powerset(X0),X1)),unordered_pair(sK4(powerset(X0),X1),sK3(powerset(X0),X1)))) )
| ~ spl14_42
| ~ spl14_103 ),
inference(resolution,[],[f903,f382]) ).
fof(f382,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| element(X0,X2)
| ~ in(X0,X1) )
| ~ spl14_42 ),
inference(avatar_component_clause,[],[f381]) ).
fof(f903,plain,
( ! [X0,X1] :
( element(unordered_pair(singleton(sK4(X0,X1)),unordered_pair(sK4(X0,X1),sK3(X0,X1))),X0)
| in(sK3(X0,X1),X1)
| ~ relation(X0)
| relation_rng(X0) = X1 )
| ~ spl14_103 ),
inference(avatar_component_clause,[],[f902]) ).
fof(f2640,plain,
( spl14_221
| ~ spl14_40
| ~ spl14_103 ),
inference(avatar_split_clause,[],[f917,f902,f365,f2638]) ).
fof(f2638,plain,
( spl14_221
<=> ! [X2,X0,X1] :
( in(sK3(powerset(X0),X1),X1)
| ~ relation(powerset(X0))
| relation_rng(powerset(X0)) = X1
| ~ empty(X0)
| ~ in(X2,unordered_pair(singleton(sK4(powerset(X0),X1)),unordered_pair(sK4(powerset(X0),X1),sK3(powerset(X0),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_221])]) ).
fof(f365,plain,
( spl14_40
<=> ! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_40])]) ).
fof(f917,plain,
( ! [X2,X0,X1] :
( in(sK3(powerset(X0),X1),X1)
| ~ relation(powerset(X0))
| relation_rng(powerset(X0)) = X1
| ~ empty(X0)
| ~ in(X2,unordered_pair(singleton(sK4(powerset(X0),X1)),unordered_pair(sK4(powerset(X0),X1),sK3(powerset(X0),X1)))) )
| ~ spl14_40
| ~ spl14_103 ),
inference(resolution,[],[f903,f366]) ).
fof(f366,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X0,X1) )
| ~ spl14_40 ),
inference(avatar_component_clause,[],[f365]) ).
fof(f2636,plain,
( spl14_220
| ~ spl14_56
| ~ spl14_81 ),
inference(avatar_split_clause,[],[f729,f710,f477,f2634]) ).
fof(f2634,plain,
( spl14_220
<=> ! [X0,X1] :
( element(unordered_pair(singleton(sK4(sK2(X0),X1)),unordered_pair(sK4(sK2(X0),X1),sK3(sK2(X0),X1))),X0)
| empty(X0)
| relation_rng(sK2(X0)) = X1
| in(sK3(sK2(X0),X1),X1)
| ~ relation(sK2(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_220])]) ).
fof(f710,plain,
( spl14_81
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK2(X1))
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_81])]) ).
fof(f729,plain,
( ! [X0,X1] :
( element(unordered_pair(singleton(sK4(sK2(X0),X1)),unordered_pair(sK4(sK2(X0),X1),sK3(sK2(X0),X1))),X0)
| empty(X0)
| relation_rng(sK2(X0)) = X1
| in(sK3(sK2(X0),X1),X1)
| ~ relation(sK2(X0)) )
| ~ spl14_56
| ~ spl14_81 ),
inference(resolution,[],[f711,f478]) ).
fof(f711,plain,
( ! [X0,X1] :
( ~ in(X0,sK2(X1))
| element(X0,X1)
| empty(X1) )
| ~ spl14_81 ),
inference(avatar_component_clause,[],[f710]) ).
fof(f2623,plain,
( spl14_219
| ~ spl14_32
| ~ spl14_103 ),
inference(avatar_split_clause,[],[f919,f902,f305,f2621]) ).
fof(f2621,plain,
( spl14_219
<=> ! [X0,X1] :
( in(sK3(powerset(X0),X1),X1)
| ~ relation(powerset(X0))
| relation_rng(powerset(X0)) = X1
| subset(unordered_pair(singleton(sK4(powerset(X0),X1)),unordered_pair(sK4(powerset(X0),X1),sK3(powerset(X0),X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_219])]) ).
fof(f305,plain,
( spl14_32
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_32])]) ).
fof(f919,plain,
( ! [X0,X1] :
( in(sK3(powerset(X0),X1),X1)
| ~ relation(powerset(X0))
| relation_rng(powerset(X0)) = X1
| subset(unordered_pair(singleton(sK4(powerset(X0),X1)),unordered_pair(sK4(powerset(X0),X1),sK3(powerset(X0),X1))),X0) )
| ~ spl14_32
| ~ spl14_103 ),
inference(resolution,[],[f903,f306]) ).
fof(f306,plain,
( ! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) )
| ~ spl14_32 ),
inference(avatar_component_clause,[],[f305]) ).
fof(f2587,plain,
( spl14_218
| ~ spl14_84
| ~ spl14_101 ),
inference(avatar_split_clause,[],[f893,f888,f749,f2585]) ).
fof(f2585,plain,
( spl14_218
<=> ! [X0,X3,X2,X1] :
( in(X0,relation_inverse_image(powerset(X1),X2))
| ~ in(X3,X2)
| ~ in(X3,relation_rng(powerset(X1)))
| ~ relation(powerset(X1))
| empty(powerset(X1))
| ~ subset(unordered_pair(singleton(X0),unordered_pair(X3,X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_218])]) ).
fof(f749,plain,
( spl14_84
<=> ! [X0,X1] :
( empty(powerset(X0))
| in(X1,powerset(X0))
| ~ subset(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_84])]) ).
fof(f888,plain,
( spl14_101
<=> ! [X0,X3,X2,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),X2)
| in(X0,relation_inverse_image(X2,X3))
| ~ in(X1,X3)
| ~ in(X1,relation_rng(X2))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_101])]) ).
fof(f893,plain,
( ! [X2,X3,X0,X1] :
( in(X0,relation_inverse_image(powerset(X1),X2))
| ~ in(X3,X2)
| ~ in(X3,relation_rng(powerset(X1)))
| ~ relation(powerset(X1))
| empty(powerset(X1))
| ~ subset(unordered_pair(singleton(X0),unordered_pair(X3,X0)),X1) )
| ~ spl14_84
| ~ spl14_101 ),
inference(resolution,[],[f889,f750]) ).
fof(f750,plain,
( ! [X0,X1] :
( in(X1,powerset(X0))
| empty(powerset(X0))
| ~ subset(X1,X0) )
| ~ spl14_84 ),
inference(avatar_component_clause,[],[f749]) ).
fof(f889,plain,
( ! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),X2)
| in(X0,relation_inverse_image(X2,X3))
| ~ in(X1,X3)
| ~ in(X1,relation_rng(X2))
| ~ relation(X2) )
| ~ spl14_101 ),
inference(avatar_component_clause,[],[f888]) ).
fof(f2583,plain,
( spl14_217
| ~ spl14_84
| ~ spl14_100 ),
inference(avatar_split_clause,[],[f883,f878,f749,f2581]) ).
fof(f2581,plain,
( spl14_217
<=> ! [X2,X0,X1] :
( relation_rng(powerset(X0)) = X1
| ~ in(sK3(powerset(X0),X1),X1)
| ~ relation(powerset(X0))
| empty(powerset(X0))
| ~ subset(unordered_pair(singleton(X2),unordered_pair(sK3(powerset(X0),X1),X2)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_217])]) ).
fof(f878,plain,
( spl14_100
<=> ! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(sK3(X1,X2),X0)),X1)
| relation_rng(X1) = X2
| ~ in(sK3(X1,X2),X2)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_100])]) ).
fof(f883,plain,
( ! [X2,X0,X1] :
( relation_rng(powerset(X0)) = X1
| ~ in(sK3(powerset(X0),X1),X1)
| ~ relation(powerset(X0))
| empty(powerset(X0))
| ~ subset(unordered_pair(singleton(X2),unordered_pair(sK3(powerset(X0),X1),X2)),X0) )
| ~ spl14_84
| ~ spl14_100 ),
inference(resolution,[],[f879,f750]) ).
fof(f879,plain,
( ! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(sK3(X1,X2),X0)),X1)
| relation_rng(X1) = X2
| ~ in(sK3(X1,X2),X2)
| ~ relation(X1) )
| ~ spl14_100 ),
inference(avatar_component_clause,[],[f878]) ).
fof(f2579,plain,
( spl14_216
| ~ spl14_52
| ~ spl14_84 ),
inference(avatar_split_clause,[],[f765,f749,f455,f2577]) ).
fof(f2577,plain,
( spl14_216
<=> ! [X0,X3,X2,X1] :
( empty(powerset(X0))
| ~ subset(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X0)
| in(X1,relation_inverse_image(powerset(X0),X3))
| ~ in(X2,X3)
| ~ in(X2,relation_rng(powerset(X0)))
| ~ relation(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_216])]) ).
fof(f455,plain,
( spl14_52
<=> ! [X0,X3,X2,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X3)),X2)
| in(X0,relation_inverse_image(X2,X1))
| ~ in(X3,X1)
| ~ in(X3,relation_rng(X2))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_52])]) ).
fof(f765,plain,
( ! [X2,X3,X0,X1] :
( empty(powerset(X0))
| ~ subset(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X0)
| in(X1,relation_inverse_image(powerset(X0),X3))
| ~ in(X2,X3)
| ~ in(X2,relation_rng(powerset(X0)))
| ~ relation(powerset(X0)) )
| ~ spl14_52
| ~ spl14_84 ),
inference(resolution,[],[f750,f456]) ).
fof(f456,plain,
( ! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X3)),X2)
| in(X0,relation_inverse_image(X2,X1))
| ~ in(X3,X1)
| ~ in(X3,relation_rng(X2))
| ~ relation(X2) )
| ~ spl14_52 ),
inference(avatar_component_clause,[],[f455]) ).
fof(f2575,plain,
( spl14_215
| ~ spl14_51
| ~ spl14_84 ),
inference(avatar_split_clause,[],[f764,f749,f448,f2573]) ).
fof(f2573,plain,
( spl14_215
<=> ! [X2,X0,X1] :
( empty(powerset(X0))
| ~ subset(unordered_pair(singleton(X1),unordered_pair(X1,sK3(powerset(X0),X2))),X0)
| relation_rng(powerset(X0)) = X2
| ~ in(sK3(powerset(X0),X2),X2)
| ~ relation(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_215])]) ).
fof(f448,plain,
( spl14_51
<=> ! [X0,X1,X3] :
( ~ in(unordered_pair(singleton(X3),unordered_pair(X3,sK3(X0,X1))),X0)
| relation_rng(X0) = X1
| ~ in(sK3(X0,X1),X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_51])]) ).
fof(f764,plain,
( ! [X2,X0,X1] :
( empty(powerset(X0))
| ~ subset(unordered_pair(singleton(X1),unordered_pair(X1,sK3(powerset(X0),X2))),X0)
| relation_rng(powerset(X0)) = X2
| ~ in(sK3(powerset(X0),X2),X2)
| ~ relation(powerset(X0)) )
| ~ spl14_51
| ~ spl14_84 ),
inference(resolution,[],[f750,f449]) ).
fof(f449,plain,
( ! [X3,X0,X1] :
( ~ in(unordered_pair(singleton(X3),unordered_pair(X3,sK3(X0,X1))),X0)
| relation_rng(X0) = X1
| ~ in(sK3(X0,X1),X1)
| ~ relation(X0) )
| ~ spl14_51 ),
inference(avatar_component_clause,[],[f448]) ).
fof(f2567,plain,
( spl14_214
| ~ spl14_49
| ~ spl14_77 ),
inference(avatar_split_clause,[],[f691,f656,f431,f2565]) ).
fof(f2565,plain,
( spl14_214
<=> ! [X0,X1] :
( element(unordered_pair(singleton(sK5(sK6(powerset(X0)),X1)),unordered_pair(X1,sK5(sK6(powerset(X0)),X1))),X0)
| ~ in(X1,relation_rng(sK6(powerset(X0))))
| ~ relation(sK6(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_214])]) ).
fof(f431,plain,
( spl14_49
<=> ! [X5,X0] :
( in(unordered_pair(singleton(sK5(X0,X5)),unordered_pair(X5,sK5(X0,X5))),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_49])]) ).
fof(f691,plain,
( ! [X0,X1] :
( element(unordered_pair(singleton(sK5(sK6(powerset(X0)),X1)),unordered_pair(X1,sK5(sK6(powerset(X0)),X1))),X0)
| ~ in(X1,relation_rng(sK6(powerset(X0))))
| ~ relation(sK6(powerset(X0))) )
| ~ spl14_49
| ~ spl14_77 ),
inference(resolution,[],[f657,f432]) ).
fof(f432,plain,
( ! [X0,X5] :
( in(unordered_pair(singleton(sK5(X0,X5)),unordered_pair(X5,sK5(X0,X5))),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) )
| ~ spl14_49 ),
inference(avatar_component_clause,[],[f431]) ).
fof(f2547,plain,
( spl14_213
| ~ spl14_42
| ~ spl14_98 ),
inference(avatar_split_clause,[],[f874,f861,f381,f2545]) ).
fof(f2545,plain,
( spl14_213
<=> ! [X2,X0,X1] :
( ~ relation(powerset(X0))
| ~ in(X1,relation_rng(powerset(X0)))
| element(X2,X0)
| ~ in(X2,unordered_pair(singleton(sK5(powerset(X0),X1)),unordered_pair(X1,sK5(powerset(X0),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_213])]) ).
fof(f861,plain,
( spl14_98
<=> ! [X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ relation(X1)
| element(unordered_pair(singleton(sK5(X1,X0)),unordered_pair(X0,sK5(X1,X0))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_98])]) ).
fof(f874,plain,
( ! [X2,X0,X1] :
( ~ relation(powerset(X0))
| ~ in(X1,relation_rng(powerset(X0)))
| element(X2,X0)
| ~ in(X2,unordered_pair(singleton(sK5(powerset(X0),X1)),unordered_pair(X1,sK5(powerset(X0),X1)))) )
| ~ spl14_42
| ~ spl14_98 ),
inference(resolution,[],[f862,f382]) ).
fof(f862,plain,
( ! [X0,X1] :
( element(unordered_pair(singleton(sK5(X1,X0)),unordered_pair(X0,sK5(X1,X0))),X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1)) )
| ~ spl14_98 ),
inference(avatar_component_clause,[],[f861]) ).
fof(f2527,plain,
( spl14_212
| ~ spl14_114
| ~ spl14_183 ),
inference(avatar_split_clause,[],[f1884,f1786,f982,f2525]) ).
fof(f1786,plain,
( spl14_183
<=> ! [X0] :
( sK11 = relation_inverse_image(sK1,X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_183])]) ).
fof(f1884,plain,
( ! [X0] :
( sK11 = relation_inverse_image(sK1,sK6(powerset(X0)))
| ~ empty(X0) )
| ~ spl14_114
| ~ spl14_183 ),
inference(resolution,[],[f1787,f983]) ).
fof(f1787,plain,
( ! [X0] :
( ~ empty(X0)
| sK11 = relation_inverse_image(sK1,X0) )
| ~ spl14_183 ),
inference(avatar_component_clause,[],[f1786]) ).
fof(f2498,plain,
( spl14_211
| ~ spl14_40
| ~ spl14_98 ),
inference(avatar_split_clause,[],[f873,f861,f365,f2496]) ).
fof(f2496,plain,
( spl14_211
<=> ! [X2,X0,X1] :
( ~ relation(powerset(X0))
| ~ in(X1,relation_rng(powerset(X0)))
| ~ empty(X0)
| ~ in(X2,unordered_pair(singleton(sK5(powerset(X0),X1)),unordered_pair(X1,sK5(powerset(X0),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_211])]) ).
fof(f873,plain,
( ! [X2,X0,X1] :
( ~ relation(powerset(X0))
| ~ in(X1,relation_rng(powerset(X0)))
| ~ empty(X0)
| ~ in(X2,unordered_pair(singleton(sK5(powerset(X0),X1)),unordered_pair(X1,sK5(powerset(X0),X1)))) )
| ~ spl14_40
| ~ spl14_98 ),
inference(resolution,[],[f862,f366]) ).
fof(f2494,plain,
( spl14_210
| ~ spl14_42
| ~ spl14_96 ),
inference(avatar_split_clause,[],[f869,f853,f381,f2492]) ).
fof(f2492,plain,
( spl14_210
<=> ! [X0,X3,X2,X1] :
( ~ relation(powerset(X0))
| ~ in(X1,relation_inverse_image(powerset(X0),X2))
| element(X3,X0)
| ~ in(X3,unordered_pair(singleton(X1),unordered_pair(X1,sK9(X1,X2,powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_210])]) ).
fof(f853,plain,
( spl14_96
<=> ! [X2,X0,X1] :
( ~ in(X0,relation_inverse_image(X1,X2))
| ~ relation(X1)
| element(unordered_pair(singleton(X0),unordered_pair(X0,sK9(X0,X2,X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_96])]) ).
fof(f869,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(powerset(X0))
| ~ in(X1,relation_inverse_image(powerset(X0),X2))
| element(X3,X0)
| ~ in(X3,unordered_pair(singleton(X1),unordered_pair(X1,sK9(X1,X2,powerset(X0))))) )
| ~ spl14_42
| ~ spl14_96 ),
inference(resolution,[],[f854,f382]) ).
fof(f854,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(X0),unordered_pair(X0,sK9(X0,X2,X1))),X1)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) )
| ~ spl14_96 ),
inference(avatar_component_clause,[],[f853]) ).
fof(f2490,plain,
( spl14_209
| ~ spl14_49
| ~ spl14_81 ),
inference(avatar_split_clause,[],[f728,f710,f431,f2488]) ).
fof(f2488,plain,
( spl14_209
<=> ! [X0,X1] :
( element(unordered_pair(singleton(sK5(sK2(X0),X1)),unordered_pair(X1,sK5(sK2(X0),X1))),X0)
| empty(X0)
| ~ in(X1,relation_rng(sK2(X0)))
| ~ relation(sK2(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_209])]) ).
fof(f728,plain,
( ! [X0,X1] :
( element(unordered_pair(singleton(sK5(sK2(X0),X1)),unordered_pair(X1,sK5(sK2(X0),X1))),X0)
| empty(X0)
| ~ in(X1,relation_rng(sK2(X0)))
| ~ relation(sK2(X0)) )
| ~ spl14_49
| ~ spl14_81 ),
inference(resolution,[],[f711,f432]) ).
fof(f2486,plain,
( spl14_208
| ~ spl14_48
| ~ spl14_77 ),
inference(avatar_split_clause,[],[f690,f656,f427,f2484]) ).
fof(f2484,plain,
( spl14_208
<=> ! [X2,X0,X1] :
( element(unordered_pair(singleton(X0),unordered_pair(X0,sK9(X0,X1,sK6(powerset(X2))))),X2)
| ~ in(X0,relation_inverse_image(sK6(powerset(X2)),X1))
| ~ relation(sK6(powerset(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_208])]) ).
fof(f427,plain,
( spl14_48
<=> ! [X2,X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK9(X0,X1,X2))),X2)
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_48])]) ).
fof(f690,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(X0),unordered_pair(X0,sK9(X0,X1,sK6(powerset(X2))))),X2)
| ~ in(X0,relation_inverse_image(sK6(powerset(X2)),X1))
| ~ relation(sK6(powerset(X2))) )
| ~ spl14_48
| ~ spl14_77 ),
inference(resolution,[],[f657,f428]) ).
fof(f428,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK9(X0,X1,X2))),X2)
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ relation(X2) )
| ~ spl14_48 ),
inference(avatar_component_clause,[],[f427]) ).
fof(f2382,plain,
( spl14_207
| ~ spl14_95
| ~ spl14_105 ),
inference(avatar_split_clause,[],[f930,f922,f832,f2380]) ).
fof(f832,plain,
( spl14_95
<=> ! [X0,X1] :
( relation_rng(X0) = X1
| in(sK3(X0,X1),X1)
| ~ relation(X0)
| in(sK3(X0,X1),relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_95])]) ).
fof(f922,plain,
( spl14_105
<=> ! [X2,X0,X1] :
( relation_rng(X0) = X1
| in(sK3(X0,X1),X1)
| ~ relation(X0)
| in(sK4(X0,X1),relation_inverse_image(X0,X2))
| ~ in(sK3(X0,X1),X2)
| ~ in(sK3(X0,X1),relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_105])]) ).
fof(f930,plain,
( ! [X2,X0,X1] :
( in(sK3(X0,X1),X1)
| ~ relation(X0)
| in(sK4(X0,X1),relation_inverse_image(X0,X2))
| ~ in(sK3(X0,X1),X2)
| relation_rng(X0) = X1 )
| ~ spl14_95
| ~ spl14_105 ),
inference(duplicate_literal_removal,[],[f925]) ).
fof(f925,plain,
( ! [X2,X0,X1] :
( in(sK3(X0,X1),X1)
| ~ relation(X0)
| in(sK4(X0,X1),relation_inverse_image(X0,X2))
| ~ in(sK3(X0,X1),X2)
| relation_rng(X0) = X1
| in(sK3(X0,X1),X1)
| ~ relation(X0)
| relation_rng(X0) = X1 )
| ~ spl14_95
| ~ spl14_105 ),
inference(resolution,[],[f923,f833]) ).
fof(f833,plain,
( ! [X0,X1] :
( in(sK3(X0,X1),relation_rng(X0))
| in(sK3(X0,X1),X1)
| ~ relation(X0)
| relation_rng(X0) = X1 )
| ~ spl14_95 ),
inference(avatar_component_clause,[],[f832]) ).
fof(f923,plain,
( ! [X2,X0,X1] :
( ~ in(sK3(X0,X1),relation_rng(X0))
| in(sK3(X0,X1),X1)
| ~ relation(X0)
| in(sK4(X0,X1),relation_inverse_image(X0,X2))
| ~ in(sK3(X0,X1),X2)
| relation_rng(X0) = X1 )
| ~ spl14_105 ),
inference(avatar_component_clause,[],[f922]) ).
fof(f2378,plain,
( spl14_206
| ~ spl14_40
| ~ spl14_96 ),
inference(avatar_split_clause,[],[f868,f853,f365,f2376]) ).
fof(f2376,plain,
( spl14_206
<=> ! [X2,X0,X1,X3] :
( ~ relation(powerset(X0))
| ~ in(X1,relation_inverse_image(powerset(X0),X2))
| ~ empty(X0)
| ~ in(X3,unordered_pair(singleton(X1),unordered_pair(X1,sK9(X1,X2,powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_206])]) ).
fof(f868,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(powerset(X0))
| ~ in(X1,relation_inverse_image(powerset(X0),X2))
| ~ empty(X0)
| ~ in(X3,unordered_pair(singleton(X1),unordered_pair(X1,sK9(X1,X2,powerset(X0))))) )
| ~ spl14_40
| ~ spl14_96 ),
inference(resolution,[],[f854,f366]) ).
fof(f2374,plain,
( spl14_205
| ~ spl14_77
| ~ spl14_95 ),
inference(avatar_split_clause,[],[f847,f832,f656,f2372]) ).
fof(f2372,plain,
( spl14_205
<=> ! [X0,X1] :
( in(sK3(X0,sK6(powerset(X1))),relation_rng(X0))
| ~ relation(X0)
| relation_rng(X0) = sK6(powerset(X1))
| element(sK3(X0,sK6(powerset(X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_205])]) ).
fof(f847,plain,
( ! [X0,X1] :
( in(sK3(X0,sK6(powerset(X1))),relation_rng(X0))
| ~ relation(X0)
| relation_rng(X0) = sK6(powerset(X1))
| element(sK3(X0,sK6(powerset(X1))),X1) )
| ~ spl14_77
| ~ spl14_95 ),
inference(resolution,[],[f833,f657]) ).
fof(f2370,plain,
( spl14_204
| ~ spl14_48
| ~ spl14_81 ),
inference(avatar_split_clause,[],[f727,f710,f427,f2368]) ).
fof(f2368,plain,
( spl14_204
<=> ! [X2,X0,X1] :
( element(unordered_pair(singleton(X0),unordered_pair(X0,sK9(X0,X1,sK2(X2)))),X2)
| empty(X2)
| ~ in(X0,relation_inverse_image(sK2(X2),X1))
| ~ relation(sK2(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_204])]) ).
fof(f727,plain,
( ! [X2,X0,X1] :
( element(unordered_pair(singleton(X0),unordered_pair(X0,sK9(X0,X1,sK2(X2)))),X2)
| empty(X2)
| ~ in(X0,relation_inverse_image(sK2(X2),X1))
| ~ relation(sK2(X2)) )
| ~ spl14_48
| ~ spl14_81 ),
inference(resolution,[],[f711,f428]) ).
fof(f2297,plain,
( spl14_203
| ~ spl14_32
| ~ spl14_98 ),
inference(avatar_split_clause,[],[f875,f861,f305,f2295]) ).
fof(f2295,plain,
( spl14_203
<=> ! [X0,X1] :
( ~ relation(powerset(X0))
| ~ in(X1,relation_rng(powerset(X0)))
| subset(unordered_pair(singleton(sK5(powerset(X0),X1)),unordered_pair(X1,sK5(powerset(X0),X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_203])]) ).
fof(f875,plain,
( ! [X0,X1] :
( ~ relation(powerset(X0))
| ~ in(X1,relation_rng(powerset(X0)))
| subset(unordered_pair(singleton(sK5(powerset(X0),X1)),unordered_pair(X1,sK5(powerset(X0),X1))),X0) )
| ~ spl14_32
| ~ spl14_98 ),
inference(resolution,[],[f862,f306]) ).
fof(f2293,plain,
( spl14_202
| ~ spl14_81
| ~ spl14_95 ),
inference(avatar_split_clause,[],[f846,f832,f710,f2291]) ).
fof(f2291,plain,
( spl14_202
<=> ! [X0,X1] :
( in(sK3(X0,sK2(X1)),relation_rng(X0))
| ~ relation(X0)
| relation_rng(X0) = sK2(X1)
| element(sK3(X0,sK2(X1)),X1)
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_202])]) ).
fof(f846,plain,
( ! [X0,X1] :
( in(sK3(X0,sK2(X1)),relation_rng(X0))
| ~ relation(X0)
| relation_rng(X0) = sK2(X1)
| element(sK3(X0,sK2(X1)),X1)
| empty(X1) )
| ~ spl14_81
| ~ spl14_95 ),
inference(resolution,[],[f833,f711]) ).
fof(f2289,plain,
( spl14_201
| ~ spl14_22
| ~ spl14_183 ),
inference(avatar_split_clause,[],[f1879,f1786,f256,f2287]) ).
fof(f2287,plain,
( spl14_201
<=> ! [X0] :
( sK11 = relation_inverse_image(sK1,relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_201])]) ).
fof(f1879,plain,
( ! [X0] :
( sK11 = relation_inverse_image(sK1,relation_rng(X0))
| ~ empty(X0) )
| ~ spl14_22
| ~ spl14_183 ),
inference(resolution,[],[f1787,f257]) ).
fof(f2285,plain,
( spl14_200
| ~ spl14_56
| ~ spl14_86 ),
inference(avatar_split_clause,[],[f776,f757,f477,f2283]) ).
fof(f2283,plain,
( spl14_200
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(relation_rng(X0))
| relation_rng(relation_inverse_image(X0,X1)) = X2
| in(sK3(relation_inverse_image(X0,X1),X2),X2)
| ~ relation(relation_inverse_image(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_200])]) ).
fof(f757,plain,
( spl14_86
<=> ! [X2,X0,X1] :
( ~ in(X0,relation_inverse_image(X1,X2))
| ~ relation(X1)
| ~ empty(relation_rng(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_86])]) ).
fof(f776,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(relation_rng(X0))
| relation_rng(relation_inverse_image(X0,X1)) = X2
| in(sK3(relation_inverse_image(X0,X1),X2),X2)
| ~ relation(relation_inverse_image(X0,X1)) )
| ~ spl14_56
| ~ spl14_86 ),
inference(resolution,[],[f758,f478]) ).
fof(f758,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_inverse_image(X1,X2))
| ~ relation(X1)
| ~ empty(relation_rng(X1)) )
| ~ spl14_86 ),
inference(avatar_component_clause,[],[f757]) ).
fof(f2169,plain,
( spl14_199
| ~ spl14_32
| ~ spl14_96 ),
inference(avatar_split_clause,[],[f870,f853,f305,f2167]) ).
fof(f2167,plain,
( spl14_199
<=> ! [X2,X0,X1] :
( ~ relation(powerset(X0))
| ~ in(X1,relation_inverse_image(powerset(X0),X2))
| subset(unordered_pair(singleton(X1),unordered_pair(X1,sK9(X1,X2,powerset(X0)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_199])]) ).
fof(f870,plain,
( ! [X2,X0,X1] :
( ~ relation(powerset(X0))
| ~ in(X1,relation_inverse_image(powerset(X0),X2))
| subset(unordered_pair(singleton(X1),unordered_pair(X1,sK9(X1,X2,powerset(X0)))),X0) )
| ~ spl14_32
| ~ spl14_96 ),
inference(resolution,[],[f854,f306]) ).
fof(f2165,plain,
( spl14_198
| ~ spl14_86
| ~ spl14_95 ),
inference(avatar_split_clause,[],[f843,f832,f757,f2163]) ).
fof(f2163,plain,
( spl14_198
<=> ! [X2,X0,X1] :
( in(sK3(X0,relation_inverse_image(X1,X2)),relation_rng(X0))
| ~ relation(X0)
| relation_rng(X0) = relation_inverse_image(X1,X2)
| ~ relation(X1)
| ~ empty(relation_rng(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_198])]) ).
fof(f843,plain,
( ! [X2,X0,X1] :
( in(sK3(X0,relation_inverse_image(X1,X2)),relation_rng(X0))
| ~ relation(X0)
| relation_rng(X0) = relation_inverse_image(X1,X2)
| ~ relation(X1)
| ~ empty(relation_rng(X1)) )
| ~ spl14_86
| ~ spl14_95 ),
inference(resolution,[],[f833,f758]) ).
fof(f2161,plain,
( spl14_197
| ~ spl14_56
| ~ spl14_83 ),
inference(avatar_split_clause,[],[f743,f718,f477,f2159]) ).
fof(f2159,plain,
( spl14_197
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| relation_rng(relation_inverse_image(X0,X1)) = X2
| in(sK3(relation_inverse_image(X0,X1),X2),X2)
| ~ relation(relation_inverse_image(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_197])]) ).
fof(f718,plain,
( spl14_83
<=> ! [X2,X0,X1] :
( ~ in(X0,relation_inverse_image(X1,X2))
| ~ relation(X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_83])]) ).
fof(f743,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| relation_rng(relation_inverse_image(X0,X1)) = X2
| in(sK3(relation_inverse_image(X0,X1),X2),X2)
| ~ relation(relation_inverse_image(X0,X1)) )
| ~ spl14_56
| ~ spl14_83 ),
inference(resolution,[],[f719,f478]) ).
fof(f719,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_inverse_image(X1,X2))
| ~ relation(X1)
| ~ empty(X1) )
| ~ spl14_83 ),
inference(avatar_component_clause,[],[f718]) ).
fof(f2157,plain,
( spl14_196
| ~ spl14_56
| ~ spl14_82 ),
inference(avatar_split_clause,[],[f735,f714,f477,f2155]) ).
fof(f2155,plain,
( spl14_196
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| relation_rng(relation_inverse_image(X0,X1)) = X2
| in(sK3(relation_inverse_image(X0,X1),X2),X2)
| ~ relation(relation_inverse_image(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_196])]) ).
fof(f714,plain,
( spl14_82
<=> ! [X2,X0,X1] :
( ~ in(X0,relation_inverse_image(X1,X2))
| ~ relation(X1)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_82])]) ).
fof(f735,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| relation_rng(relation_inverse_image(X0,X1)) = X2
| in(sK3(relation_inverse_image(X0,X1),X2),X2)
| ~ relation(relation_inverse_image(X0,X1)) )
| ~ spl14_56
| ~ spl14_82 ),
inference(resolution,[],[f715,f478]) ).
fof(f715,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_inverse_image(X1,X2))
| ~ relation(X1)
| ~ empty(X2) )
| ~ spl14_82 ),
inference(avatar_component_clause,[],[f714]) ).
fof(f2089,plain,
( spl14_195
| ~ spl14_82
| ~ spl14_95 ),
inference(avatar_split_clause,[],[f845,f832,f714,f2087]) ).
fof(f845,plain,
( ! [X2,X0,X1] :
( in(sK3(X0,relation_inverse_image(X1,X2)),relation_rng(X0))
| ~ relation(X0)
| relation_rng(X0) = relation_inverse_image(X1,X2)
| ~ relation(X1)
| ~ empty(X2) )
| ~ spl14_82
| ~ spl14_95 ),
inference(resolution,[],[f833,f715]) ).
fof(f2085,plain,
( spl14_194
| ~ spl14_83
| ~ spl14_95 ),
inference(avatar_split_clause,[],[f844,f832,f718,f2083]) ).
fof(f2083,plain,
( spl14_194
<=> ! [X2,X0,X1] :
( in(sK3(X0,relation_inverse_image(X1,X2)),relation_rng(X0))
| ~ relation(X0)
| relation_rng(X0) = relation_inverse_image(X1,X2)
| ~ relation(X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_194])]) ).
fof(f844,plain,
( ! [X2,X0,X1] :
( in(sK3(X0,relation_inverse_image(X1,X2)),relation_rng(X0))
| ~ relation(X0)
| relation_rng(X0) = relation_inverse_image(X1,X2)
| ~ relation(X1)
| ~ empty(X1) )
| ~ spl14_83
| ~ spl14_95 ),
inference(resolution,[],[f833,f719]) ).
fof(f2036,plain,
( spl14_193
| ~ spl14_84
| ~ spl14_93 ),
inference(avatar_split_clause,[],[f827,f817,f749,f2034]) ).
fof(f2034,plain,
( spl14_193
<=> ! [X2,X0,X1] :
( in(X0,relation_rng(powerset(X1)))
| ~ relation(powerset(X1))
| empty(powerset(X1))
| ~ subset(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_193])]) ).
fof(f817,plain,
( spl14_93
<=> ! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),X2)
| in(X1,relation_rng(X2))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_93])]) ).
fof(f827,plain,
( ! [X2,X0,X1] :
( in(X0,relation_rng(powerset(X1)))
| ~ relation(powerset(X1))
| empty(powerset(X1))
| ~ subset(unordered_pair(singleton(X2),unordered_pair(X0,X2)),X1) )
| ~ spl14_84
| ~ spl14_93 ),
inference(resolution,[],[f818,f750]) ).
fof(f818,plain,
( ! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),X2)
| in(X1,relation_rng(X2))
| ~ relation(X2) )
| ~ spl14_93 ),
inference(avatar_component_clause,[],[f817]) ).
fof(f2032,plain,
( spl14_192
| ~ spl14_46
| ~ spl14_84 ),
inference(avatar_split_clause,[],[f766,f749,f410,f2030]) ).
fof(f2030,plain,
( spl14_192
<=> ! [X2,X0,X1] :
( empty(powerset(X0))
| ~ subset(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X0)
| in(X2,relation_rng(powerset(X0)))
| ~ relation(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_192])]) ).
fof(f410,plain,
( spl14_46
<=> ! [X5,X0,X6] :
( ~ in(unordered_pair(singleton(X6),unordered_pair(X6,X5)),X0)
| in(X5,relation_rng(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_46])]) ).
fof(f766,plain,
( ! [X2,X0,X1] :
( empty(powerset(X0))
| ~ subset(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X0)
| in(X2,relation_rng(powerset(X0)))
| ~ relation(powerset(X0)) )
| ~ spl14_46
| ~ spl14_84 ),
inference(resolution,[],[f750,f411]) ).
fof(f411,plain,
( ! [X0,X6,X5] :
( ~ in(unordered_pair(singleton(X6),unordered_pair(X6,X5)),X0)
| in(X5,relation_rng(X0))
| ~ relation(X0) )
| ~ spl14_46 ),
inference(avatar_component_clause,[],[f410]) ).
fof(f2028,plain,
( spl14_191
| ~ spl14_56
| ~ spl14_72 ),
inference(avatar_split_clause,[],[f635,f627,f477,f2026]) ).
fof(f2026,plain,
( spl14_191
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_rng(sK6(powerset(X0))) = X1
| in(sK3(sK6(powerset(X0)),X1),X1)
| ~ relation(sK6(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_191])]) ).
fof(f627,plain,
( spl14_72
<=> ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK6(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_72])]) ).
fof(f635,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_rng(sK6(powerset(X0))) = X1
| in(sK3(sK6(powerset(X0)),X1),X1)
| ~ relation(sK6(powerset(X0))) )
| ~ spl14_56
| ~ spl14_72 ),
inference(resolution,[],[f628,f478]) ).
fof(f628,plain,
( ! [X0,X1] :
( ~ in(X1,sK6(powerset(X0)))
| ~ empty(X0) )
| ~ spl14_72 ),
inference(avatar_component_clause,[],[f627]) ).
fof(f2018,plain,
( spl14_190
| ~ spl14_5
| ~ spl14_57
| ~ spl14_183 ),
inference(avatar_split_clause,[],[f1888,f1786,f490,f176,f2015]) ).
fof(f2015,plain,
( spl14_190
<=> sK11 = relation_inverse_image(sK1,sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_190])]) ).
fof(f1888,plain,
( sK11 = relation_inverse_image(sK1,sK11)
| ~ spl14_5
| ~ spl14_57
| ~ spl14_183 ),
inference(forward_demodulation,[],[f1880,f492]) ).
fof(f1880,plain,
( sK11 = relation_inverse_image(sK1,empty_set)
| ~ spl14_5
| ~ spl14_183 ),
inference(resolution,[],[f1787,f178]) ).
fof(f1926,plain,
( spl14_189
| ~ spl14_44
| ~ spl14_102 ),
inference(avatar_split_clause,[],[f916,f898,f398,f1924]) ).
fof(f398,plain,
( spl14_44
<=> ! [X2,X0,X1] :
( in(sK9(X0,X1,X2),relation_rng(X2))
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_44])]) ).
fof(f898,plain,
( spl14_102
<=> ! [X0,X3,X2,X1] :
( in(X0,relation_inverse_image(X1,X2))
| ~ in(sK9(X0,X3,X1),X2)
| ~ in(sK9(X0,X3,X1),relation_rng(X1))
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_102])]) ).
fof(f916,plain,
( ! [X2,X3,X0,X1] :
( ~ in(sK9(X0,X1,X2),X3)
| in(X0,relation_inverse_image(X2,X3))
| ~ relation(X2)
| ~ in(X0,relation_inverse_image(X2,X1)) )
| ~ spl14_44
| ~ spl14_102 ),
inference(duplicate_literal_removal,[],[f912]) ).
fof(f912,plain,
( ! [X2,X3,X0,X1] :
( ~ in(sK9(X0,X1,X2),X3)
| in(X0,relation_inverse_image(X2,X3))
| ~ relation(X2)
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ relation(X2) )
| ~ spl14_44
| ~ spl14_102 ),
inference(resolution,[],[f899,f399]) ).
fof(f399,plain,
( ! [X2,X0,X1] :
( in(sK9(X0,X1,X2),relation_rng(X2))
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ relation(X2) )
| ~ spl14_44 ),
inference(avatar_component_clause,[],[f398]) ).
fof(f899,plain,
( ! [X2,X3,X0,X1] :
( ~ in(sK9(X0,X3,X1),relation_rng(X1))
| ~ in(sK9(X0,X3,X1),X2)
| in(X0,relation_inverse_image(X1,X2))
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X3)) )
| ~ spl14_102 ),
inference(avatar_component_clause,[],[f898]) ).
fof(f1922,plain,
( spl14_188
| ~ spl14_72
| ~ spl14_95 ),
inference(avatar_split_clause,[],[f848,f832,f627,f1920]) ).
fof(f1920,plain,
( spl14_188
<=> ! [X0,X1] :
( in(sK3(X0,sK6(powerset(X1))),relation_rng(X0))
| ~ relation(X0)
| relation_rng(X0) = sK6(powerset(X1))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_188])]) ).
fof(f848,plain,
( ! [X0,X1] :
( in(sK3(X0,sK6(powerset(X1))),relation_rng(X0))
| ~ relation(X0)
| relation_rng(X0) = sK6(powerset(X1))
| ~ empty(X1) )
| ~ spl14_72
| ~ spl14_95 ),
inference(resolution,[],[f833,f628]) ).
fof(f1918,plain,
( spl14_187
| ~ spl14_79
| ~ spl14_95 ),
inference(avatar_split_clause,[],[f842,f832,f665,f1916]) ).
fof(f1916,plain,
( spl14_187
<=> ! [X0,X1] :
( in(sK3(X0,relation_rng(X1)),relation_rng(X0))
| ~ relation(X0)
| relation_rng(X0) = relation_rng(X1)
| ~ relation(X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_187])]) ).
fof(f665,plain,
( spl14_79
<=> ! [X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ relation(X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_79])]) ).
fof(f842,plain,
( ! [X0,X1] :
( in(sK3(X0,relation_rng(X1)),relation_rng(X0))
| ~ relation(X0)
| relation_rng(X0) = relation_rng(X1)
| ~ relation(X1)
| ~ empty(X1) )
| ~ spl14_79
| ~ spl14_95 ),
inference(resolution,[],[f833,f666]) ).
fof(f666,plain,
( ! [X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ relation(X1)
| ~ empty(X1) )
| ~ spl14_79 ),
inference(avatar_component_clause,[],[f665]) ).
fof(f1914,plain,
( spl14_186
| ~ spl14_42
| ~ spl14_88 ),
inference(avatar_split_clause,[],[f794,f782,f381,f1912]) ).
fof(f1912,plain,
( spl14_186
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| ~ in(X1,relation_inverse_image(X0,powerset(X2)))
| element(X3,X2)
| ~ in(X3,sK9(X1,powerset(X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_186])]) ).
fof(f782,plain,
( spl14_88
<=> ! [X2,X0,X1] :
( ~ in(X0,relation_inverse_image(X1,X2))
| ~ relation(X1)
| element(sK9(X0,X2,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_88])]) ).
fof(f794,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| ~ in(X1,relation_inverse_image(X0,powerset(X2)))
| element(X3,X2)
| ~ in(X3,sK9(X1,powerset(X2),X0)) )
| ~ spl14_42
| ~ spl14_88 ),
inference(resolution,[],[f783,f382]) ).
fof(f783,plain,
( ! [X2,X0,X1] :
( element(sK9(X0,X2,X1),X2)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) )
| ~ spl14_88 ),
inference(avatar_component_clause,[],[f782]) ).
fof(f1910,plain,
( spl14_185
| ~ spl14_56
| ~ spl14_79 ),
inference(avatar_split_clause,[],[f699,f665,f477,f1908]) ).
fof(f1908,plain,
( spl14_185
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| relation_rng(relation_rng(X0)) = X1
| in(sK3(relation_rng(X0),X1),X1)
| ~ relation(relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_185])]) ).
fof(f699,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| relation_rng(relation_rng(X0)) = X1
| in(sK3(relation_rng(X0),X1),X1)
| ~ relation(relation_rng(X0)) )
| ~ spl14_56
| ~ spl14_79 ),
inference(resolution,[],[f666,f478]) ).
fof(f1792,plain,
( spl14_184
| ~ spl14_49
| ~ spl14_100 ),
inference(avatar_split_clause,[],[f886,f878,f431,f1790]) ).
fof(f886,plain,
( ! [X0,X1] :
( relation_rng(X0) = X1
| ~ in(sK3(X0,X1),X1)
| ~ relation(X0)
| ~ in(sK3(X0,X1),relation_rng(X0)) )
| ~ spl14_49
| ~ spl14_100 ),
inference(duplicate_literal_removal,[],[f881]) ).
fof(f881,plain,
( ! [X0,X1] :
( relation_rng(X0) = X1
| ~ in(sK3(X0,X1),X1)
| ~ relation(X0)
| ~ in(sK3(X0,X1),relation_rng(X0))
| ~ relation(X0) )
| ~ spl14_49
| ~ spl14_100 ),
inference(resolution,[],[f879,f432]) ).
fof(f1788,plain,
( ~ spl14_8
| spl14_183
| ~ spl14_6
| ~ spl14_57
| ~ spl14_111
| ~ spl14_169 ),
inference(avatar_split_clause,[],[f1707,f1616,f956,f490,f181,f1786,f191]) ).
fof(f191,plain,
( spl14_8
<=> empty(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_8])]) ).
fof(f181,plain,
( spl14_6
<=> relation(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_6])]) ).
fof(f956,plain,
( spl14_111
<=> sK11 = relation_rng(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_111])]) ).
fof(f1616,plain,
( spl14_169
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| relation_rng(X0) = relation_inverse_image(sK1,X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_169])]) ).
fof(f1707,plain,
( ! [X0] :
( sK11 = relation_inverse_image(sK1,X0)
| ~ empty(sK11)
| ~ empty(X0) )
| ~ spl14_6
| ~ spl14_57
| ~ spl14_111
| ~ spl14_169 ),
inference(forward_demodulation,[],[f1706,f958]) ).
fof(f958,plain,
( sK11 = relation_rng(sK11)
| ~ spl14_111 ),
inference(avatar_component_clause,[],[f956]) ).
fof(f1706,plain,
( ! [X0] :
( relation_rng(sK11) = relation_inverse_image(sK1,X0)
| ~ empty(sK11)
| ~ empty(X0) )
| ~ spl14_6
| ~ spl14_57
| ~ spl14_169 ),
inference(forward_demodulation,[],[f1705,f492]) ).
fof(f1705,plain,
( ! [X0] :
( ~ empty(sK11)
| relation_rng(empty_set) = relation_inverse_image(sK1,X0)
| ~ empty(X0) )
| ~ spl14_6
| ~ spl14_57
| ~ spl14_169 ),
inference(forward_demodulation,[],[f1700,f492]) ).
fof(f1700,plain,
( ! [X0] :
( ~ empty(empty_set)
| relation_rng(empty_set) = relation_inverse_image(sK1,X0)
| ~ empty(X0) )
| ~ spl14_6
| ~ spl14_169 ),
inference(resolution,[],[f1617,f183]) ).
fof(f183,plain,
( relation(empty_set)
| ~ spl14_6 ),
inference(avatar_component_clause,[],[f181]) ).
fof(f1617,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| relation_rng(X0) = relation_inverse_image(sK1,X1)
| ~ empty(X1) )
| ~ spl14_169 ),
inference(avatar_component_clause,[],[f1616]) ).
fof(f1784,plain,
( spl14_182
| ~ spl14_27
| ~ spl14_95 ),
inference(avatar_split_clause,[],[f841,f832,f285,f1782]) ).
fof(f1782,plain,
( spl14_182
<=> ! [X0,X1] :
( in(sK3(X0,X1),relation_rng(X0))
| ~ relation(X0)
| relation_rng(X0) = X1
| ~ in(X1,sK3(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_182])]) ).
fof(f841,plain,
( ! [X0,X1] :
( in(sK3(X0,X1),relation_rng(X0))
| ~ relation(X0)
| relation_rng(X0) = X1
| ~ in(X1,sK3(X0,X1)) )
| ~ spl14_27
| ~ spl14_95 ),
inference(resolution,[],[f833,f286]) ).
fof(f1780,plain,
( spl14_181
| ~ spl14_28
| ~ spl14_95 ),
inference(avatar_split_clause,[],[f840,f832,f289,f1778]) ).
fof(f1778,plain,
( spl14_181
<=> ! [X0,X1] :
( in(sK3(X0,X1),relation_rng(X0))
| ~ relation(X0)
| relation_rng(X0) = X1
| element(sK3(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_181])]) ).
fof(f840,plain,
( ! [X0,X1] :
( in(sK3(X0,X1),relation_rng(X0))
| ~ relation(X0)
| relation_rng(X0) = X1
| element(sK3(X0,X1),X1) )
| ~ spl14_28
| ~ spl14_95 ),
inference(resolution,[],[f833,f290]) ).
fof(f1776,plain,
( spl14_180
| ~ spl14_27
| ~ spl14_95 ),
inference(avatar_split_clause,[],[f838,f832,f285,f1774]) ).
fof(f1774,plain,
( spl14_180
<=> ! [X0,X1] :
( in(sK3(X0,X1),X1)
| ~ relation(X0)
| relation_rng(X0) = X1
| ~ in(relation_rng(X0),sK3(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_180])]) ).
fof(f838,plain,
( ! [X0,X1] :
( in(sK3(X0,X1),X1)
| ~ relation(X0)
| relation_rng(X0) = X1
| ~ in(relation_rng(X0),sK3(X0,X1)) )
| ~ spl14_27
| ~ spl14_95 ),
inference(resolution,[],[f833,f286]) ).
fof(f1772,plain,
( spl14_179
| ~ spl14_28
| ~ spl14_95 ),
inference(avatar_split_clause,[],[f837,f832,f289,f1770]) ).
fof(f1770,plain,
( spl14_179
<=> ! [X0,X1] :
( in(sK3(X0,X1),X1)
| ~ relation(X0)
| relation_rng(X0) = X1
| element(sK3(X0,X1),relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_179])]) ).
fof(f837,plain,
( ! [X0,X1] :
( in(sK3(X0,X1),X1)
| ~ relation(X0)
| relation_rng(X0) = X1
| element(sK3(X0,X1),relation_rng(X0)) )
| ~ spl14_28
| ~ spl14_95 ),
inference(resolution,[],[f833,f290]) ).
fof(f1768,plain,
( spl14_178
| ~ spl14_77
| ~ spl14_90 ),
inference(avatar_split_clause,[],[f805,f790,f656,f1766]) ).
fof(f1766,plain,
( spl14_178
<=> ! [X0,X1] :
( relation_rng(X0) = sK6(powerset(X1))
| ~ relation(X0)
| ~ empty(X0)
| element(sK3(X0,sK6(powerset(X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_178])]) ).
fof(f790,plain,
( spl14_90
<=> ! [X0,X1] :
( relation_rng(X0) = X1
| in(sK3(X0,X1),X1)
| ~ relation(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_90])]) ).
fof(f805,plain,
( ! [X0,X1] :
( relation_rng(X0) = sK6(powerset(X1))
| ~ relation(X0)
| ~ empty(X0)
| element(sK3(X0,sK6(powerset(X1))),X1) )
| ~ spl14_77
| ~ spl14_90 ),
inference(resolution,[],[f791,f657]) ).
fof(f791,plain,
( ! [X0,X1] :
( in(sK3(X0,X1),X1)
| relation_rng(X0) = X1
| ~ relation(X0)
| ~ empty(X0) )
| ~ spl14_90 ),
inference(avatar_component_clause,[],[f790]) ).
fof(f1764,plain,
( spl14_177
| ~ spl14_81
| ~ spl14_90 ),
inference(avatar_split_clause,[],[f804,f790,f710,f1762]) ).
fof(f1762,plain,
( spl14_177
<=> ! [X0,X1] :
( relation_rng(X0) = sK2(X1)
| ~ relation(X0)
| ~ empty(X0)
| element(sK3(X0,sK2(X1)),X1)
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_177])]) ).
fof(f804,plain,
( ! [X0,X1] :
( relation_rng(X0) = sK2(X1)
| ~ relation(X0)
| ~ empty(X0)
| element(sK3(X0,sK2(X1)),X1)
| empty(X1) )
| ~ spl14_81
| ~ spl14_90 ),
inference(resolution,[],[f791,f711]) ).
fof(f1760,plain,
( spl14_176
| ~ spl14_40
| ~ spl14_88 ),
inference(avatar_split_clause,[],[f793,f782,f365,f1758]) ).
fof(f1758,plain,
( spl14_176
<=> ! [X2,X0,X1,X3] :
( ~ relation(X0)
| ~ in(X1,relation_inverse_image(X0,powerset(X2)))
| ~ empty(X2)
| ~ in(X3,sK9(X1,powerset(X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_176])]) ).
fof(f793,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| ~ in(X1,relation_inverse_image(X0,powerset(X2)))
| ~ empty(X2)
| ~ in(X3,sK9(X1,powerset(X2),X0)) )
| ~ spl14_40
| ~ spl14_88 ),
inference(resolution,[],[f783,f366]) ).
fof(f1756,plain,
( spl14_175
| ~ spl14_43
| ~ spl14_81 ),
inference(avatar_split_clause,[],[f732,f710,f391,f1754]) ).
fof(f1754,plain,
( spl14_175
<=> ! [X2,X0,X1] :
( element(sK9(X0,sK2(X1),X2),X1)
| empty(X1)
| ~ in(X0,relation_inverse_image(X2,sK2(X1)))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_175])]) ).
fof(f391,plain,
( spl14_43
<=> ! [X2,X0,X1] :
( in(sK9(X0,X1,X2),X1)
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_43])]) ).
fof(f732,plain,
( ! [X2,X0,X1] :
( element(sK9(X0,sK2(X1),X2),X1)
| empty(X1)
| ~ in(X0,relation_inverse_image(X2,sK2(X1)))
| ~ relation(X2) )
| ~ spl14_43
| ~ spl14_81 ),
inference(resolution,[],[f711,f392]) ).
fof(f392,plain,
( ! [X2,X0,X1] :
( in(sK9(X0,X1,X2),X1)
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ relation(X2) )
| ~ spl14_43 ),
inference(avatar_component_clause,[],[f391]) ).
fof(f1752,plain,
( spl14_174
| ~ spl14_43
| ~ spl14_77 ),
inference(avatar_split_clause,[],[f695,f656,f391,f1750]) ).
fof(f1750,plain,
( spl14_174
<=> ! [X2,X0,X1] :
( element(sK9(X0,sK6(powerset(X1)),X2),X1)
| ~ in(X0,relation_inverse_image(X2,sK6(powerset(X1))))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_174])]) ).
fof(f695,plain,
( ! [X2,X0,X1] :
( element(sK9(X0,sK6(powerset(X1)),X2),X1)
| ~ in(X0,relation_inverse_image(X2,sK6(powerset(X1))))
| ~ relation(X2) )
| ~ spl14_43
| ~ spl14_77 ),
inference(resolution,[],[f657,f392]) ).
fof(f1685,plain,
( spl14_173
| ~ spl14_49
| ~ spl14_101 ),
inference(avatar_split_clause,[],[f896,f888,f431,f1683]) ).
fof(f896,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,X1),relation_inverse_image(X0,X2))
| ~ in(X1,X2)
| ~ in(X1,relation_rng(X0))
| ~ relation(X0) )
| ~ spl14_49
| ~ spl14_101 ),
inference(duplicate_literal_removal,[],[f891]) ).
fof(f891,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,X1),relation_inverse_image(X0,X2))
| ~ in(X1,X2)
| ~ in(X1,relation_rng(X0))
| ~ relation(X0)
| ~ in(X1,relation_rng(X0))
| ~ relation(X0) )
| ~ spl14_49
| ~ spl14_101 ),
inference(resolution,[],[f889,f432]) ).
fof(f1681,plain,
( spl14_172
| ~ spl14_48
| ~ spl14_86 ),
inference(avatar_split_clause,[],[f774,f757,f427,f1679]) ).
fof(f1679,plain,
( spl14_172
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| ~ empty(relation_rng(X0))
| ~ in(X1,relation_inverse_image(relation_inverse_image(X0,X2),X3))
| ~ relation(relation_inverse_image(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_172])]) ).
fof(f774,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| ~ empty(relation_rng(X0))
| ~ in(X1,relation_inverse_image(relation_inverse_image(X0,X2),X3))
| ~ relation(relation_inverse_image(X0,X2)) )
| ~ spl14_48
| ~ spl14_86 ),
inference(resolution,[],[f758,f428]) ).
fof(f1626,plain,
( spl14_171
| ~ spl14_86
| ~ spl14_90 ),
inference(avatar_split_clause,[],[f801,f790,f757,f1624]) ).
fof(f1624,plain,
( spl14_171
<=> ! [X2,X0,X1] :
( relation_rng(X0) = relation_inverse_image(X1,X2)
| ~ relation(X0)
| ~ empty(X0)
| ~ relation(X1)
| ~ empty(relation_rng(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_171])]) ).
fof(f801,plain,
( ! [X2,X0,X1] :
( relation_rng(X0) = relation_inverse_image(X1,X2)
| ~ relation(X0)
| ~ empty(X0)
| ~ relation(X1)
| ~ empty(relation_rng(X1)) )
| ~ spl14_86
| ~ spl14_90 ),
inference(resolution,[],[f791,f758]) ).
fof(f1622,plain,
( spl14_170
| ~ spl14_32
| ~ spl14_88 ),
inference(avatar_split_clause,[],[f795,f782,f305,f1620]) ).
fof(f1620,plain,
( spl14_170
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ in(X1,relation_inverse_image(X0,powerset(X2)))
| subset(sK9(X1,powerset(X2),X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_170])]) ).
fof(f795,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ in(X1,relation_inverse_image(X0,powerset(X2)))
| subset(sK9(X1,powerset(X2),X0),X2) )
| ~ spl14_32
| ~ spl14_88 ),
inference(resolution,[],[f783,f306]) ).
fof(f1618,plain,
( spl14_169
| ~ spl14_1
| ~ spl14_163 ),
inference(avatar_split_clause,[],[f1554,f1469,f156,f1616]) ).
fof(f1469,plain,
( spl14_163
<=> ! [X2,X0,X1] :
( relation_rng(X0) = relation_inverse_image(X1,X2)
| ~ relation(X0)
| ~ empty(X0)
| ~ relation(X1)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_163])]) ).
fof(f1554,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| relation_rng(X0) = relation_inverse_image(sK1,X1)
| ~ empty(X1) )
| ~ spl14_1
| ~ spl14_163 ),
inference(resolution,[],[f1470,f158]) ).
fof(f158,plain,
( relation(sK1)
| ~ spl14_1 ),
inference(avatar_component_clause,[],[f156]) ).
fof(f1470,plain,
( ! [X2,X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| ~ empty(X0)
| relation_rng(X0) = relation_inverse_image(X1,X2)
| ~ empty(X2) )
| ~ spl14_163 ),
inference(avatar_component_clause,[],[f1469]) ).
fof(f1614,plain,
( spl14_168
| ~ spl14_49
| ~ spl14_86 ),
inference(avatar_split_clause,[],[f775,f757,f431,f1612]) ).
fof(f1612,plain,
( spl14_168
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(relation_rng(X0))
| ~ in(X1,relation_rng(relation_inverse_image(X0,X2)))
| ~ relation(relation_inverse_image(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_168])]) ).
fof(f775,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(relation_rng(X0))
| ~ in(X1,relation_rng(relation_inverse_image(X0,X2)))
| ~ relation(relation_inverse_image(X0,X2)) )
| ~ spl14_49
| ~ spl14_86 ),
inference(resolution,[],[f758,f432]) ).
fof(f1610,plain,
( spl14_167
| ~ spl14_48
| ~ spl14_83 ),
inference(avatar_split_clause,[],[f741,f718,f427,f1608]) ).
fof(f1608,plain,
( spl14_167
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| ~ empty(X0)
| ~ in(X1,relation_inverse_image(relation_inverse_image(X0,X2),X3))
| ~ relation(relation_inverse_image(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_167])]) ).
fof(f741,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| ~ in(X1,relation_inverse_image(relation_inverse_image(X0,X2),X3))
| ~ relation(relation_inverse_image(X0,X2)) )
| ~ spl14_48
| ~ spl14_83 ),
inference(resolution,[],[f719,f428]) ).
fof(f1606,plain,
( spl14_166
| ~ spl14_48
| ~ spl14_82 ),
inference(avatar_split_clause,[],[f733,f714,f427,f1604]) ).
fof(f1604,plain,
( spl14_166
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| ~ empty(X1)
| ~ in(X2,relation_inverse_image(relation_inverse_image(X0,X1),X3))
| ~ relation(relation_inverse_image(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_166])]) ).
fof(f733,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| ~ in(X2,relation_inverse_image(relation_inverse_image(X0,X1),X3))
| ~ relation(relation_inverse_image(X0,X1)) )
| ~ spl14_48
| ~ spl14_82 ),
inference(resolution,[],[f715,f428]) ).
fof(f1479,plain,
( spl14_165
| ~ spl14_25
| ~ spl14_95 ),
inference(avatar_split_clause,[],[f839,f832,f268,f1477]) ).
fof(f1477,plain,
( spl14_165
<=> ! [X0,X1] :
( in(sK3(X0,X1),relation_rng(X0))
| ~ relation(X0)
| relation_rng(X0) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_165])]) ).
fof(f268,plain,
( spl14_25
<=> ! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_25])]) ).
fof(f839,plain,
( ! [X0,X1] :
( in(sK3(X0,X1),relation_rng(X0))
| ~ relation(X0)
| relation_rng(X0) = X1
| ~ empty(X1) )
| ~ spl14_25
| ~ spl14_95 ),
inference(resolution,[],[f833,f269]) ).
fof(f269,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) )
| ~ spl14_25 ),
inference(avatar_component_clause,[],[f268]) ).
fof(f1475,plain,
( spl14_164
| ~ spl14_25
| ~ spl14_95 ),
inference(avatar_split_clause,[],[f836,f832,f268,f1473]) ).
fof(f1473,plain,
( spl14_164
<=> ! [X0,X1] :
( in(sK3(X0,X1),X1)
| ~ relation(X0)
| relation_rng(X0) = X1
| ~ empty(relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_164])]) ).
fof(f836,plain,
( ! [X0,X1] :
( in(sK3(X0,X1),X1)
| ~ relation(X0)
| relation_rng(X0) = X1
| ~ empty(relation_rng(X0)) )
| ~ spl14_25
| ~ spl14_95 ),
inference(resolution,[],[f833,f269]) ).
fof(f1471,plain,
( spl14_163
| ~ spl14_82
| ~ spl14_90 ),
inference(avatar_split_clause,[],[f803,f790,f714,f1469]) ).
fof(f803,plain,
( ! [X2,X0,X1] :
( relation_rng(X0) = relation_inverse_image(X1,X2)
| ~ relation(X0)
| ~ empty(X0)
| ~ relation(X1)
| ~ empty(X2) )
| ~ spl14_82
| ~ spl14_90 ),
inference(resolution,[],[f791,f715]) ).
fof(f1467,plain,
( spl14_162
| ~ spl14_83
| ~ spl14_90 ),
inference(avatar_split_clause,[],[f802,f790,f718,f1465]) ).
fof(f1465,plain,
( spl14_162
<=> ! [X2,X0,X1] :
( relation_rng(X0) = relation_inverse_image(X1,X2)
| ~ relation(X0)
| ~ empty(X0)
| ~ relation(X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_162])]) ).
fof(f802,plain,
( ! [X2,X0,X1] :
( relation_rng(X0) = relation_inverse_image(X1,X2)
| ~ relation(X0)
| ~ empty(X0)
| ~ relation(X1)
| ~ empty(X1) )
| ~ spl14_83
| ~ spl14_90 ),
inference(resolution,[],[f791,f719]) ).
fof(f1463,plain,
( spl14_161
| ~ spl14_43
| ~ spl14_86 ),
inference(avatar_split_clause,[],[f779,f757,f391,f1461]) ).
fof(f1461,plain,
( spl14_161
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| ~ empty(relation_rng(X0))
| ~ in(X1,relation_inverse_image(X2,relation_inverse_image(X0,X3)))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_161])]) ).
fof(f779,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| ~ empty(relation_rng(X0))
| ~ in(X1,relation_inverse_image(X2,relation_inverse_image(X0,X3)))
| ~ relation(X2) )
| ~ spl14_43
| ~ spl14_86 ),
inference(resolution,[],[f758,f392]) ).
fof(f1459,plain,
( spl14_160
| ~ spl14_49
| ~ spl14_83 ),
inference(avatar_split_clause,[],[f742,f718,f431,f1457]) ).
fof(f1457,plain,
( spl14_160
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| ~ in(X1,relation_rng(relation_inverse_image(X0,X2)))
| ~ relation(relation_inverse_image(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_160])]) ).
fof(f742,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| ~ in(X1,relation_rng(relation_inverse_image(X0,X2)))
| ~ relation(relation_inverse_image(X0,X2)) )
| ~ spl14_49
| ~ spl14_83 ),
inference(resolution,[],[f719,f432]) ).
fof(f1455,plain,
( spl14_159
| ~ spl14_49
| ~ spl14_82 ),
inference(avatar_split_clause,[],[f734,f714,f431,f1453]) ).
fof(f1453,plain,
( spl14_159
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| ~ in(X2,relation_rng(relation_inverse_image(X0,X1)))
| ~ relation(relation_inverse_image(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_159])]) ).
fof(f734,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| ~ in(X2,relation_rng(relation_inverse_image(X0,X1)))
| ~ relation(relation_inverse_image(X0,X1)) )
| ~ spl14_49
| ~ spl14_82 ),
inference(resolution,[],[f715,f432]) ).
fof(f1436,plain,
( spl14_158
| ~ spl14_115
| ~ spl14_138 ),
inference(avatar_split_clause,[],[f1219,f1208,f991,f1434]) ).
fof(f1434,plain,
( spl14_158
<=> ! [X0] : sK11 = relation_inverse_image(sK11,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_158])]) ).
fof(f991,plain,
( spl14_115
<=> ! [X0,X1] : ~ in(X0,relation_inverse_image(sK11,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_115])]) ).
fof(f1219,plain,
( ! [X0] : sK11 = relation_inverse_image(sK11,X0)
| ~ spl14_115
| ~ spl14_138 ),
inference(resolution,[],[f1209,f992]) ).
fof(f992,plain,
( ! [X0,X1] : ~ in(X0,relation_inverse_image(sK11,X1))
| ~ spl14_115 ),
inference(avatar_component_clause,[],[f991]) ).
fof(f1379,plain,
( spl14_157
| ~ spl14_79
| ~ spl14_90 ),
inference(avatar_split_clause,[],[f800,f790,f665,f1377]) ).
fof(f1377,plain,
( spl14_157
<=> ! [X0,X1] :
( relation_rng(X0) = relation_rng(X1)
| ~ relation(X0)
| ~ empty(X0)
| ~ relation(X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_157])]) ).
fof(f800,plain,
( ! [X0,X1] :
( relation_rng(X0) = relation_rng(X1)
| ~ relation(X0)
| ~ empty(X0)
| ~ relation(X1)
| ~ empty(X1) )
| ~ spl14_79
| ~ spl14_90 ),
inference(resolution,[],[f791,f666]) ).
fof(f1375,plain,
( spl14_156
| ~ spl14_27
| ~ spl14_90 ),
inference(avatar_split_clause,[],[f799,f790,f285,f1373]) ).
fof(f1373,plain,
( spl14_156
<=> ! [X0,X1] :
( relation_rng(X0) = X1
| ~ relation(X0)
| ~ empty(X0)
| ~ in(X1,sK3(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_156])]) ).
fof(f799,plain,
( ! [X0,X1] :
( relation_rng(X0) = X1
| ~ relation(X0)
| ~ empty(X0)
| ~ in(X1,sK3(X0,X1)) )
| ~ spl14_27
| ~ spl14_90 ),
inference(resolution,[],[f791,f286]) ).
fof(f1371,plain,
( spl14_155
| ~ spl14_28
| ~ spl14_90 ),
inference(avatar_split_clause,[],[f798,f790,f289,f1369]) ).
fof(f1369,plain,
( spl14_155
<=> ! [X0,X1] :
( relation_rng(X0) = X1
| ~ relation(X0)
| ~ empty(X0)
| element(sK3(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_155])]) ).
fof(f798,plain,
( ! [X0,X1] :
( relation_rng(X0) = X1
| ~ relation(X0)
| ~ empty(X0)
| element(sK3(X0,X1),X1) )
| ~ spl14_28
| ~ spl14_90 ),
inference(resolution,[],[f791,f290]) ).
fof(f1367,plain,
( spl14_154
| ~ spl14_38
| ~ spl14_84 ),
inference(avatar_split_clause,[],[f763,f749,f346,f1365]) ).
fof(f1365,plain,
( spl14_154
<=> ! [X0,X1] :
( empty(powerset(X0))
| ~ subset(sK8(X1,powerset(X0)),X0)
| subset(X1,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_154])]) ).
fof(f346,plain,
( spl14_38
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ in(sK8(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_38])]) ).
fof(f763,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| ~ subset(sK8(X1,powerset(X0)),X0)
| subset(X1,powerset(X0)) )
| ~ spl14_38
| ~ spl14_84 ),
inference(resolution,[],[f750,f347]) ).
fof(f347,plain,
( ! [X0,X1] :
( ~ in(sK8(X0,X1),X1)
| subset(X0,X1) )
| ~ spl14_38 ),
inference(avatar_component_clause,[],[f346]) ).
fof(f1362,plain,
( spl14_153
| ~ spl14_37
| ~ spl14_115 ),
inference(avatar_split_clause,[],[f1000,f991,f342,f1360]) ).
fof(f1360,plain,
( spl14_153
<=> ! [X0,X1] : subset(relation_inverse_image(sK11,X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_153])]) ).
fof(f1000,plain,
( ! [X0,X1] : subset(relation_inverse_image(sK11,X0),X1)
| ~ spl14_37
| ~ spl14_115 ),
inference(resolution,[],[f992,f343]) ).
fof(f1358,plain,
( spl14_152
| ~ spl14_43
| ~ spl14_83 ),
inference(avatar_split_clause,[],[f746,f718,f391,f1356]) ).
fof(f1356,plain,
( spl14_152
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| ~ empty(X0)
| ~ in(X1,relation_inverse_image(X2,relation_inverse_image(X0,X3)))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_152])]) ).
fof(f746,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| ~ in(X1,relation_inverse_image(X2,relation_inverse_image(X0,X3)))
| ~ relation(X2) )
| ~ spl14_43
| ~ spl14_83 ),
inference(resolution,[],[f719,f392]) ).
fof(f1354,plain,
( spl14_151
| ~ spl14_43
| ~ spl14_82 ),
inference(avatar_split_clause,[],[f738,f714,f391,f1352]) ).
fof(f1352,plain,
( spl14_151
<=> ! [X0,X3,X2,X1] :
( ~ relation(X0)
| ~ empty(X1)
| ~ in(X2,relation_inverse_image(X3,relation_inverse_image(X0,X1)))
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_151])]) ).
fof(f738,plain,
( ! [X2,X3,X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| ~ in(X2,relation_inverse_image(X3,relation_inverse_image(X0,X1)))
| ~ relation(X3) )
| ~ spl14_43
| ~ spl14_82 ),
inference(resolution,[],[f715,f392]) ).
fof(f1350,plain,
( spl14_150
| ~ spl14_48
| ~ spl14_79 ),
inference(avatar_split_clause,[],[f697,f665,f427,f1348]) ).
fof(f1348,plain,
( spl14_150
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| ~ in(X1,relation_inverse_image(relation_rng(X0),X2))
| ~ relation(relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_150])]) ).
fof(f697,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| ~ in(X1,relation_inverse_image(relation_rng(X0),X2))
| ~ relation(relation_rng(X0)) )
| ~ spl14_48
| ~ spl14_79 ),
inference(resolution,[],[f666,f428]) ).
fof(f1346,plain,
( spl14_149
| ~ spl14_42
| ~ spl14_74 ),
inference(avatar_split_clause,[],[f681,f644,f381,f1344]) ).
fof(f1344,plain,
( spl14_149
<=> ! [X2,X0,X1] :
( subset(powerset(X0),X1)
| element(X2,X0)
| ~ in(X2,sK8(powerset(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_149])]) ).
fof(f644,plain,
( spl14_74
<=> ! [X0,X1] :
( subset(X0,X1)
| element(sK8(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_74])]) ).
fof(f681,plain,
( ! [X2,X0,X1] :
( subset(powerset(X0),X1)
| element(X2,X0)
| ~ in(X2,sK8(powerset(X0),X1)) )
| ~ spl14_42
| ~ spl14_74 ),
inference(resolution,[],[f645,f382]) ).
fof(f645,plain,
( ! [X0,X1] :
( element(sK8(X0,X1),X0)
| subset(X0,X1) )
| ~ spl14_74 ),
inference(avatar_component_clause,[],[f644]) ).
fof(f1342,plain,
( spl14_148
| ~ spl14_48
| ~ spl14_72 ),
inference(avatar_split_clause,[],[f633,f627,f427,f1340]) ).
fof(f1340,plain,
( spl14_148
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,relation_inverse_image(sK6(powerset(X0)),X2))
| ~ relation(sK6(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_148])]) ).
fof(f633,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,relation_inverse_image(sK6(powerset(X0)),X2))
| ~ relation(sK6(powerset(X0))) )
| ~ spl14_48
| ~ spl14_72 ),
inference(resolution,[],[f628,f428]) ).
fof(f1292,plain,
( spl14_147
| ~ spl14_70
| ~ spl14_115 ),
inference(avatar_split_clause,[],[f999,f991,f605,f1290]) ).
fof(f1290,plain,
( spl14_147
<=> ! [X0] : empty(relation_inverse_image(sK11,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_147])]) ).
fof(f999,plain,
( ! [X0] : empty(relation_inverse_image(sK11,X0))
| ~ spl14_70
| ~ spl14_115 ),
inference(resolution,[],[f992,f606]) ).
fof(f1266,plain,
( spl14_146
| ~ spl14_72
| ~ spl14_90 ),
inference(avatar_split_clause,[],[f806,f790,f627,f1264]) ).
fof(f1264,plain,
( spl14_146
<=> ! [X0,X1] :
( relation_rng(X0) = sK6(powerset(X1))
| ~ relation(X0)
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_146])]) ).
fof(f806,plain,
( ! [X0,X1] :
( relation_rng(X0) = sK6(powerset(X1))
| ~ relation(X0)
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl14_72
| ~ spl14_90 ),
inference(resolution,[],[f791,f628]) ).
fof(f1262,plain,
( spl14_145
| ~ spl14_37
| ~ spl14_81 ),
inference(avatar_split_clause,[],[f731,f710,f342,f1260]) ).
fof(f1260,plain,
( spl14_145
<=> ! [X0,X1] :
( element(sK8(sK2(X0),X1),X0)
| empty(X0)
| subset(sK2(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_145])]) ).
fof(f731,plain,
( ! [X0,X1] :
( element(sK8(sK2(X0),X1),X0)
| empty(X0)
| subset(sK2(X0),X1) )
| ~ spl14_37
| ~ spl14_81 ),
inference(resolution,[],[f711,f343]) ).
fof(f1258,plain,
( spl14_144
| ~ spl14_43
| ~ spl14_79 ),
inference(avatar_split_clause,[],[f703,f665,f391,f1256]) ).
fof(f1256,plain,
( spl14_144
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| ~ in(X1,relation_inverse_image(X2,relation_rng(X0)))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_144])]) ).
fof(f703,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| ~ in(X1,relation_inverse_image(X2,relation_rng(X0)))
| ~ relation(X2) )
| ~ spl14_43
| ~ spl14_79 ),
inference(resolution,[],[f666,f392]) ).
fof(f1254,plain,
( spl14_143
| ~ spl14_49
| ~ spl14_79 ),
inference(avatar_split_clause,[],[f698,f665,f431,f1252]) ).
fof(f1252,plain,
( spl14_143
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| ~ in(X1,relation_rng(relation_rng(X0)))
| ~ relation(relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_143])]) ).
fof(f698,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| ~ in(X1,relation_rng(relation_rng(X0)))
| ~ relation(relation_rng(X0)) )
| ~ spl14_49
| ~ spl14_79 ),
inference(resolution,[],[f666,f432]) ).
fof(f1250,plain,
( spl14_142
| ~ spl14_37
| ~ spl14_77 ),
inference(avatar_split_clause,[],[f694,f656,f342,f1248]) ).
fof(f1248,plain,
( spl14_142
<=> ! [X0,X1] :
( element(sK8(sK6(powerset(X0)),X1),X0)
| subset(sK6(powerset(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_142])]) ).
fof(f694,plain,
( ! [X0,X1] :
( element(sK8(sK6(powerset(X0)),X1),X0)
| subset(sK6(powerset(X0)),X1) )
| ~ spl14_37
| ~ spl14_77 ),
inference(resolution,[],[f657,f343]) ).
fof(f1246,plain,
( spl14_141
| ~ spl14_40
| ~ spl14_74 ),
inference(avatar_split_clause,[],[f680,f644,f365,f1244]) ).
fof(f1244,plain,
( spl14_141
<=> ! [X2,X0,X1] :
( subset(powerset(X0),X1)
| ~ empty(X0)
| ~ in(X2,sK8(powerset(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_141])]) ).
fof(f680,plain,
( ! [X2,X0,X1] :
( subset(powerset(X0),X1)
| ~ empty(X0)
| ~ in(X2,sK8(powerset(X0),X1)) )
| ~ spl14_40
| ~ spl14_74 ),
inference(resolution,[],[f645,f366]) ).
fof(f1242,plain,
( spl14_140
| ~ spl14_49
| ~ spl14_72 ),
inference(avatar_split_clause,[],[f634,f627,f431,f1240]) ).
fof(f1240,plain,
( spl14_140
<=> ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,relation_rng(sK6(powerset(X0))))
| ~ relation(sK6(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_140])]) ).
fof(f634,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,relation_rng(sK6(powerset(X0))))
| ~ relation(sK6(powerset(X0))) )
| ~ spl14_49
| ~ spl14_72 ),
inference(resolution,[],[f628,f432]) ).
fof(f1229,plain,
( spl14_139
| ~ spl14_43
| ~ spl14_72 ),
inference(avatar_split_clause,[],[f638,f627,f391,f1227]) ).
fof(f1227,plain,
( spl14_139
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,relation_inverse_image(X2,sK6(powerset(X0))))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_139])]) ).
fof(f638,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,relation_inverse_image(X2,sK6(powerset(X0))))
| ~ relation(X2) )
| ~ spl14_43
| ~ spl14_72 ),
inference(resolution,[],[f628,f392]) ).
fof(f1210,plain,
( spl14_138
| ~ spl14_111
| ~ spl14_137 ),
inference(avatar_split_clause,[],[f1206,f1203,f956,f1208]) ).
fof(f1203,plain,
( spl14_137
<=> ! [X0] :
( relation_rng(sK11) = X0
| in(sK3(sK11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_137])]) ).
fof(f1206,plain,
( ! [X0] :
( sK11 = X0
| in(sK3(sK11,X0),X0) )
| ~ spl14_111
| ~ spl14_137 ),
inference(forward_demodulation,[],[f1204,f958]) ).
fof(f1204,plain,
( ! [X0] :
( relation_rng(sK11) = X0
| in(sK3(sK11,X0),X0) )
| ~ spl14_137 ),
inference(avatar_component_clause,[],[f1203]) ).
fof(f1205,plain,
( ~ spl14_26
| spl14_137
| ~ spl14_56
| ~ spl14_66 ),
inference(avatar_split_clause,[],[f586,f537,f477,f1203,f272]) ).
fof(f272,plain,
( spl14_26
<=> relation(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_26])]) ).
fof(f586,plain,
( ! [X0] :
( relation_rng(sK11) = X0
| in(sK3(sK11,X0),X0)
| ~ relation(sK11) )
| ~ spl14_56
| ~ spl14_66 ),
inference(resolution,[],[f538,f478]) ).
fof(f1183,plain,
( ~ spl14_135
| spl14_136
| ~ spl14_16
| ~ spl14_123 ),
inference(avatar_split_clause,[],[f1113,f1055,f228,f1180,f1176]) ).
fof(f1176,plain,
( spl14_135
<=> in(powerset(relation_rng(sK1)),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_135])]) ).
fof(f1180,plain,
( spl14_136
<=> empty(powerset(relation_rng(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_136])]) ).
fof(f228,plain,
( spl14_16
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_16])]) ).
fof(f1055,plain,
( spl14_123
<=> ! [X0] :
( ~ in(powerset(X0),sK0)
| empty(powerset(X0))
| ~ subset(relation_rng(sK1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_123])]) ).
fof(f1113,plain,
( empty(powerset(relation_rng(sK1)))
| ~ in(powerset(relation_rng(sK1)),sK0)
| ~ spl14_16
| ~ spl14_123 ),
inference(resolution,[],[f1056,f229]) ).
fof(f229,plain,
( ! [X0] : subset(X0,X0)
| ~ spl14_16 ),
inference(avatar_component_clause,[],[f228]) ).
fof(f1056,plain,
( ! [X0] :
( ~ subset(relation_rng(sK1),X0)
| empty(powerset(X0))
| ~ in(powerset(X0),sK0) )
| ~ spl14_123 ),
inference(avatar_component_clause,[],[f1055]) ).
fof(f1174,plain,
( spl14_134
| ~ spl14_37
| ~ spl14_86 ),
inference(avatar_split_clause,[],[f778,f757,f342,f1172]) ).
fof(f1172,plain,
( spl14_134
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(relation_rng(X0))
| subset(relation_inverse_image(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_134])]) ).
fof(f778,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(relation_rng(X0))
| subset(relation_inverse_image(X0,X1),X2) )
| ~ spl14_37
| ~ spl14_86 ),
inference(resolution,[],[f758,f343]) ).
fof(f1170,plain,
( spl14_133
| ~ spl14_27
| ~ spl14_85 ),
inference(avatar_split_clause,[],[f769,f753,f285,f1168]) ).
fof(f1168,plain,
( spl14_133
<=> ! [X0] :
( empty(powerset(X0))
| empty(X0)
| ~ in(powerset(X0),sK2(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_133])]) ).
fof(f753,plain,
( spl14_85
<=> ! [X0] :
( empty(powerset(X0))
| in(sK2(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_85])]) ).
fof(f769,plain,
( ! [X0] :
( empty(powerset(X0))
| empty(X0)
| ~ in(powerset(X0),sK2(X0)) )
| ~ spl14_27
| ~ spl14_85 ),
inference(resolution,[],[f754,f286]) ).
fof(f754,plain,
( ! [X0] :
( in(sK2(X0),powerset(X0))
| empty(powerset(X0))
| empty(X0) )
| ~ spl14_85 ),
inference(avatar_component_clause,[],[f753]) ).
fof(f1166,plain,
( spl14_132
| ~ spl14_27
| ~ spl14_84 ),
inference(avatar_split_clause,[],[f762,f749,f285,f1164]) ).
fof(f1164,plain,
( spl14_132
<=> ! [X0,X1] :
( empty(powerset(X0))
| ~ subset(X1,X0)
| ~ in(powerset(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_132])]) ).
fof(f762,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| ~ subset(X1,X0)
| ~ in(powerset(X0),X1) )
| ~ spl14_27
| ~ spl14_84 ),
inference(resolution,[],[f750,f286]) ).
fof(f1162,plain,
( spl14_131
| ~ spl14_70
| ~ spl14_81 ),
inference(avatar_split_clause,[],[f730,f710,f605,f1160]) ).
fof(f1160,plain,
( spl14_131
<=> ! [X0] :
( element(sK6(sK2(X0)),X0)
| empty(X0)
| empty(sK2(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_131])]) ).
fof(f730,plain,
( ! [X0] :
( element(sK6(sK2(X0)),X0)
| empty(X0)
| empty(sK2(X0)) )
| ~ spl14_70
| ~ spl14_81 ),
inference(resolution,[],[f711,f606]) ).
fof(f1158,plain,
( spl14_130
| ~ spl14_70
| ~ spl14_77 ),
inference(avatar_split_clause,[],[f693,f656,f605,f1156]) ).
fof(f1156,plain,
( spl14_130
<=> ! [X0] :
( element(sK6(sK6(powerset(X0))),X0)
| empty(sK6(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_130])]) ).
fof(f693,plain,
( ! [X0] :
( element(sK6(sK6(powerset(X0))),X0)
| empty(sK6(powerset(X0))) )
| ~ spl14_70
| ~ spl14_77 ),
inference(resolution,[],[f657,f606]) ).
fof(f1154,plain,
( spl14_129
| ~ spl14_32
| ~ spl14_74 ),
inference(avatar_split_clause,[],[f682,f644,f305,f1152]) ).
fof(f1152,plain,
( spl14_129
<=> ! [X0,X1] :
( subset(powerset(X0),X1)
| subset(sK8(powerset(X0),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_129])]) ).
fof(f682,plain,
( ! [X0,X1] :
( subset(powerset(X0),X1)
| subset(sK8(powerset(X0),X1),X0) )
| ~ spl14_32
| ~ spl14_74 ),
inference(resolution,[],[f645,f306]) ).
fof(f1103,plain,
( spl14_128
| ~ spl14_70
| ~ spl14_86 ),
inference(avatar_split_clause,[],[f777,f757,f605,f1101]) ).
fof(f1101,plain,
( spl14_128
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ empty(relation_rng(X0))
| empty(relation_inverse_image(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_128])]) ).
fof(f777,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ empty(relation_rng(X0))
| empty(relation_inverse_image(X0,X1)) )
| ~ spl14_70
| ~ spl14_86 ),
inference(resolution,[],[f758,f606]) ).
fof(f1099,plain,
( spl14_127
| ~ spl14_37
| ~ spl14_83 ),
inference(avatar_split_clause,[],[f745,f718,f342,f1097]) ).
fof(f1097,plain,
( spl14_127
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| subset(relation_inverse_image(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_127])]) ).
fof(f745,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| subset(relation_inverse_image(X0,X1),X2) )
| ~ spl14_37
| ~ spl14_83 ),
inference(resolution,[],[f719,f343]) ).
fof(f1095,plain,
( spl14_126
| ~ spl14_37
| ~ spl14_82 ),
inference(avatar_split_clause,[],[f737,f714,f342,f1093]) ).
fof(f1093,plain,
( spl14_126
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| subset(relation_inverse_image(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_126])]) ).
fof(f737,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| subset(relation_inverse_image(X0,X1),X2) )
| ~ spl14_37
| ~ spl14_82 ),
inference(resolution,[],[f715,f343]) ).
fof(f1091,plain,
( spl14_125
| ~ spl14_22
| ~ spl14_73 ),
inference(avatar_split_clause,[],[f668,f640,f256,f1089]) ).
fof(f1089,plain,
( spl14_125
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_rng(relation_rng(X1)) = X0
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_125])]) ).
fof(f640,plain,
( spl14_73
<=> ! [X0,X1] :
( relation_rng(X1) = X0
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_73])]) ).
fof(f668,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_rng(relation_rng(X1)) = X0
| ~ empty(X1) )
| ~ spl14_22
| ~ spl14_73 ),
inference(resolution,[],[f641,f257]) ).
fof(f641,plain,
( ! [X0,X1] :
( ~ empty(X1)
| ~ empty(X0)
| relation_rng(X1) = X0 )
| ~ spl14_73 ),
inference(avatar_component_clause,[],[f640]) ).
fof(f1087,plain,
( spl14_124
| ~ spl14_39
| ~ spl14_69 ),
inference(avatar_split_clause,[],[f616,f601,f361,f1085]) ).
fof(f1085,plain,
( spl14_124
<=> ! [X0,X1] :
( empty(X0)
| ~ in(X1,sK2(X0))
| in(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_124])]) ).
fof(f361,plain,
( spl14_39
<=> ! [X0,X1,X3] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_39])]) ).
fof(f601,plain,
( spl14_69
<=> ! [X0] :
( subset(sK2(X0),X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_69])]) ).
fof(f616,plain,
( ! [X0,X1] :
( empty(X0)
| ~ in(X1,sK2(X0))
| in(X1,X0) )
| ~ spl14_39
| ~ spl14_69 ),
inference(resolution,[],[f602,f362]) ).
fof(f362,plain,
( ! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) )
| ~ spl14_39 ),
inference(avatar_component_clause,[],[f361]) ).
fof(f602,plain,
( ! [X0] :
( subset(sK2(X0),X0)
| empty(X0) )
| ~ spl14_69 ),
inference(avatar_component_clause,[],[f601]) ).
fof(f1057,plain,
( spl14_123
| ~ spl14_84
| ~ spl14_94 ),
inference(avatar_split_clause,[],[f910,f821,f749,f1055]) ).
fof(f821,plain,
( spl14_94
<=> ! [X0] :
( ~ in(X0,sK0)
| ~ in(relation_rng(sK1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_94])]) ).
fof(f910,plain,
( ! [X0] :
( ~ in(powerset(X0),sK0)
| empty(powerset(X0))
| ~ subset(relation_rng(sK1),X0) )
| ~ spl14_84
| ~ spl14_94 ),
inference(resolution,[],[f822,f750]) ).
fof(f822,plain,
( ! [X0] :
( ~ in(relation_rng(sK1),X0)
| ~ in(X0,sK0) )
| ~ spl14_94 ),
inference(avatar_component_clause,[],[f821]) ).
fof(f1053,plain,
( spl14_122
| ~ spl14_70
| ~ spl14_83 ),
inference(avatar_split_clause,[],[f744,f718,f605,f1051]) ).
fof(f744,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| empty(relation_inverse_image(X0,X1)) )
| ~ spl14_70
| ~ spl14_83 ),
inference(resolution,[],[f719,f606]) ).
fof(f1049,plain,
( spl14_121
| ~ spl14_70
| ~ spl14_82 ),
inference(avatar_split_clause,[],[f736,f714,f605,f1047]) ).
fof(f736,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| empty(relation_inverse_image(X0,X1)) )
| ~ spl14_70
| ~ spl14_82 ),
inference(resolution,[],[f715,f606]) ).
fof(f1045,plain,
( spl14_120
| ~ spl14_37
| ~ spl14_79 ),
inference(avatar_split_clause,[],[f701,f665,f342,f1043]) ).
fof(f1043,plain,
( spl14_120
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| subset(relation_rng(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_120])]) ).
fof(f701,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X0)
| subset(relation_rng(X0),X1) )
| ~ spl14_37
| ~ spl14_79 ),
inference(resolution,[],[f666,f343]) ).
fof(f1041,plain,
( spl14_119
| ~ spl14_39
| ~ spl14_62 ),
inference(avatar_split_clause,[],[f589,f522,f361,f1039]) ).
fof(f1039,plain,
( spl14_119
<=> ! [X0,X1] :
( ~ in(X0,sK6(powerset(X1)))
| in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_119])]) ).
fof(f522,plain,
( spl14_62
<=> ! [X0] : subset(sK6(powerset(X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_62])]) ).
fof(f589,plain,
( ! [X0,X1] :
( ~ in(X0,sK6(powerset(X1)))
| in(X0,X1) )
| ~ spl14_39
| ~ spl14_62 ),
inference(resolution,[],[f523,f362]) ).
fof(f523,plain,
( ! [X0] : subset(sK6(powerset(X0)),X0)
| ~ spl14_62 ),
inference(avatar_component_clause,[],[f522]) ).
fof(f1013,plain,
( spl14_118
| ~ spl14_37
| ~ spl14_72 ),
inference(avatar_split_clause,[],[f637,f627,f342,f1011]) ).
fof(f1011,plain,
( spl14_118
<=> ! [X0,X1] :
( ~ empty(X0)
| subset(sK6(powerset(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_118])]) ).
fof(f637,plain,
( ! [X0,X1] :
( ~ empty(X0)
| subset(sK6(powerset(X0)),X1) )
| ~ spl14_37
| ~ spl14_72 ),
inference(resolution,[],[f628,f343]) ).
fof(f1009,plain,
( spl14_117
| ~ spl14_22
| ~ spl14_68 ),
inference(avatar_split_clause,[],[f608,f597,f256,f1007]) ).
fof(f608,plain,
( ! [X0] :
( sK11 = relation_rng(relation_rng(X0))
| ~ empty(X0) )
| ~ spl14_22
| ~ spl14_68 ),
inference(resolution,[],[f598,f257]) ).
fof(f1005,plain,
( spl14_116
| ~ spl14_43
| ~ spl14_66 ),
inference(avatar_split_clause,[],[f588,f537,f391,f1003]) ).
fof(f588,plain,
( ! [X0,X1] :
( ~ in(X0,relation_inverse_image(X1,sK11))
| ~ relation(X1) )
| ~ spl14_43
| ~ spl14_66 ),
inference(resolution,[],[f538,f392]) ).
fof(f993,plain,
( ~ spl14_26
| spl14_115
| ~ spl14_48
| ~ spl14_66 ),
inference(avatar_split_clause,[],[f584,f537,f427,f991,f272]) ).
fof(f584,plain,
( ! [X0,X1] :
( ~ in(X0,relation_inverse_image(sK11,X1))
| ~ relation(sK11) )
| ~ spl14_48
| ~ spl14_66 ),
inference(resolution,[],[f538,f428]) ).
fof(f984,plain,
( spl14_114
| ~ spl14_70
| ~ spl14_72 ),
inference(avatar_split_clause,[],[f636,f627,f605,f982]) ).
fof(f636,plain,
( ! [X0] :
( ~ empty(X0)
| empty(sK6(powerset(X0))) )
| ~ spl14_70
| ~ spl14_72 ),
inference(resolution,[],[f628,f606]) ).
fof(f980,plain,
( spl14_113
| ~ spl14_27
| ~ spl14_70 ),
inference(avatar_split_clause,[],[f620,f605,f285,f978]) ).
fof(f978,plain,
( spl14_113
<=> ! [X0] :
( empty(X0)
| ~ in(X0,sK6(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_113])]) ).
fof(f620,plain,
( ! [X0] :
( empty(X0)
| ~ in(X0,sK6(X0)) )
| ~ spl14_27
| ~ spl14_70 ),
inference(resolution,[],[f606,f286]) ).
fof(f975,plain,
( ~ spl14_26
| spl14_112
| ~ spl14_49
| ~ spl14_66 ),
inference(avatar_split_clause,[],[f585,f537,f431,f973,f272]) ).
fof(f973,plain,
( spl14_112
<=> ! [X0] : ~ in(X0,relation_rng(sK11)) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_112])]) ).
fof(f585,plain,
( ! [X0] :
( ~ in(X0,relation_rng(sK11))
| ~ relation(sK11) )
| ~ spl14_49
| ~ spl14_66 ),
inference(resolution,[],[f538,f432]) ).
fof(f959,plain,
( spl14_111
| ~ spl14_5
| ~ spl14_57
| ~ spl14_68 ),
inference(avatar_split_clause,[],[f613,f597,f490,f176,f956]) ).
fof(f613,plain,
( sK11 = relation_rng(sK11)
| ~ spl14_5
| ~ spl14_57
| ~ spl14_68 ),
inference(forward_demodulation,[],[f609,f492]) ).
fof(f609,plain,
( sK11 = relation_rng(empty_set)
| ~ spl14_5
| ~ spl14_68 ),
inference(resolution,[],[f598,f178]) ).
fof(f954,plain,
( ~ spl14_110
| ~ spl14_41
| ~ spl14_94 ),
inference(avatar_split_clause,[],[f911,f821,f371,f951]) ).
fof(f951,plain,
( spl14_110
<=> in(relation_rng(sK1),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_110])]) ).
fof(f911,plain,
( ~ in(relation_rng(sK1),sK0)
| ~ spl14_41
| ~ spl14_94 ),
inference(duplicate_literal_removal,[],[f909]) ).
fof(f909,plain,
( ~ in(relation_rng(sK1),sK0)
| ~ in(relation_rng(sK1),sK0)
| ~ spl14_41
| ~ spl14_94 ),
inference(resolution,[],[f822,f372]) ).
fof(f949,plain,
( spl14_109
| ~ spl14_24
| ~ spl14_61 ),
inference(avatar_split_clause,[],[f519,f516,f264,f947]) ).
fof(f947,plain,
( spl14_109
<=> ! [X0] : element(sK11,powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_109])]) ).
fof(f264,plain,
( spl14_24
<=> ! [X0] : element(sK7(X0),powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_24])]) ).
fof(f516,plain,
( spl14_61
<=> ! [X0] : sK7(X0) = sK11 ),
introduced(avatar_definition,[new_symbols(naming,[spl14_61])]) ).
fof(f519,plain,
( ! [X0] : element(sK11,powerset(X0))
| ~ spl14_24
| ~ spl14_61 ),
inference(superposition,[],[f265,f517]) ).
fof(f517,plain,
( ! [X0] : sK7(X0) = sK11
| ~ spl14_61 ),
inference(avatar_component_clause,[],[f516]) ).
fof(f265,plain,
( ! [X0] : element(sK7(X0),powerset(X0))
| ~ spl14_24 ),
inference(avatar_component_clause,[],[f264]) ).
fof(f944,plain,
( ~ spl14_107
| spl14_108
| ~ spl14_41
| ~ spl14_46 ),
inference(avatar_split_clause,[],[f419,f410,f371,f942,f938]) ).
fof(f938,plain,
( spl14_107
<=> relation(relation_rng(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_107])]) ).
fof(f942,plain,
( spl14_108
<=> ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK0)
| in(X1,relation_rng(relation_rng(sK1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_108])]) ).
fof(f419,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK0)
| in(X1,relation_rng(relation_rng(sK1)))
| ~ relation(relation_rng(sK1)) )
| ~ spl14_41
| ~ spl14_46 ),
inference(resolution,[],[f372,f411]) ).
fof(f934,plain,
( spl14_106
| ~ spl14_38
| ~ spl14_41 ),
inference(avatar_split_clause,[],[f418,f371,f346,f932]) ).
fof(f932,plain,
( spl14_106
<=> ! [X0] :
( ~ in(sK8(X0,relation_rng(sK1)),sK0)
| subset(X0,relation_rng(sK1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_106])]) ).
fof(f418,plain,
( ! [X0] :
( ~ in(sK8(X0,relation_rng(sK1)),sK0)
| subset(X0,relation_rng(sK1)) )
| ~ spl14_38
| ~ spl14_41 ),
inference(resolution,[],[f372,f347]) ).
fof(f924,plain,
( spl14_105
| ~ spl14_52
| ~ spl14_56 ),
inference(avatar_split_clause,[],[f487,f477,f455,f922]) ).
fof(f487,plain,
( ! [X2,X0,X1] :
( relation_rng(X0) = X1
| in(sK3(X0,X1),X1)
| ~ relation(X0)
| in(sK4(X0,X1),relation_inverse_image(X0,X2))
| ~ in(sK3(X0,X1),X2)
| ~ in(sK3(X0,X1),relation_rng(X0)) )
| ~ spl14_52
| ~ spl14_56 ),
inference(duplicate_literal_removal,[],[f484]) ).
fof(f484,plain,
( ! [X2,X0,X1] :
( relation_rng(X0) = X1
| in(sK3(X0,X1),X1)
| ~ relation(X0)
| in(sK4(X0,X1),relation_inverse_image(X0,X2))
| ~ in(sK3(X0,X1),X2)
| ~ in(sK3(X0,X1),relation_rng(X0))
| ~ relation(X0) )
| ~ spl14_52
| ~ spl14_56 ),
inference(resolution,[],[f478,f456]) ).
fof(f908,plain,
( spl14_104
| ~ spl14_27
| ~ spl14_56 ),
inference(avatar_split_clause,[],[f482,f477,f285,f906]) ).
fof(f906,plain,
( spl14_104
<=> ! [X0,X1] :
( relation_rng(X0) = X1
| in(sK3(X0,X1),X1)
| ~ relation(X0)
| ~ in(X0,unordered_pair(singleton(sK4(X0,X1)),unordered_pair(sK4(X0,X1),sK3(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_104])]) ).
fof(f482,plain,
( ! [X0,X1] :
( relation_rng(X0) = X1
| in(sK3(X0,X1),X1)
| ~ relation(X0)
| ~ in(X0,unordered_pair(singleton(sK4(X0,X1)),unordered_pair(sK4(X0,X1),sK3(X0,X1)))) )
| ~ spl14_27
| ~ spl14_56 ),
inference(resolution,[],[f478,f286]) ).
fof(f904,plain,
( spl14_103
| ~ spl14_28
| ~ spl14_56 ),
inference(avatar_split_clause,[],[f481,f477,f289,f902]) ).
fof(f481,plain,
( ! [X0,X1] :
( relation_rng(X0) = X1
| in(sK3(X0,X1),X1)
| ~ relation(X0)
| element(unordered_pair(singleton(sK4(X0,X1)),unordered_pair(sK4(X0,X1),sK3(X0,X1))),X0) )
| ~ spl14_28
| ~ spl14_56 ),
inference(resolution,[],[f478,f290]) ).
fof(f900,plain,
( spl14_102
| ~ spl14_48
| ~ spl14_52 ),
inference(avatar_split_clause,[],[f462,f455,f427,f898]) ).
fof(f462,plain,
( ! [X2,X3,X0,X1] :
( in(X0,relation_inverse_image(X1,X2))
| ~ in(sK9(X0,X3,X1),X2)
| ~ in(sK9(X0,X3,X1),relation_rng(X1))
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X3)) )
| ~ spl14_48
| ~ spl14_52 ),
inference(duplicate_literal_removal,[],[f458]) ).
fof(f458,plain,
( ! [X2,X3,X0,X1] :
( in(X0,relation_inverse_image(X1,X2))
| ~ in(sK9(X0,X3,X1),X2)
| ~ in(sK9(X0,X3,X1),relation_rng(X1))
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X3))
| ~ relation(X1) )
| ~ spl14_48
| ~ spl14_52 ),
inference(resolution,[],[f456,f428]) ).
fof(f890,plain,
( spl14_101
| ~ spl14_31
| ~ spl14_52 ),
inference(avatar_split_clause,[],[f460,f455,f301,f888]) ).
fof(f301,plain,
( spl14_31
<=> ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_31])]) ).
fof(f460,plain,
( ! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),X2)
| in(X0,relation_inverse_image(X2,X3))
| ~ in(X1,X3)
| ~ in(X1,relation_rng(X2))
| ~ relation(X2) )
| ~ spl14_31
| ~ spl14_52 ),
inference(superposition,[],[f456,f302]) ).
fof(f302,plain,
( ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0)
| ~ spl14_31 ),
inference(avatar_component_clause,[],[f301]) ).
fof(f880,plain,
( spl14_100
| ~ spl14_31
| ~ spl14_51 ),
inference(avatar_split_clause,[],[f452,f448,f301,f878]) ).
fof(f452,plain,
( ! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(sK3(X1,X2),X0)),X1)
| relation_rng(X1) = X2
| ~ in(sK3(X1,X2),X2)
| ~ relation(X1) )
| ~ spl14_31
| ~ spl14_51 ),
inference(superposition,[],[f449,f302]) ).
fof(f867,plain,
( spl14_99
| ~ spl14_27
| ~ spl14_49 ),
inference(avatar_split_clause,[],[f440,f431,f285,f865]) ).
fof(f865,plain,
( spl14_99
<=> ! [X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ relation(X1)
| ~ in(X1,unordered_pair(singleton(sK5(X1,X0)),unordered_pair(X0,sK5(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_99])]) ).
fof(f440,plain,
( ! [X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ relation(X1)
| ~ in(X1,unordered_pair(singleton(sK5(X1,X0)),unordered_pair(X0,sK5(X1,X0)))) )
| ~ spl14_27
| ~ spl14_49 ),
inference(resolution,[],[f432,f286]) ).
fof(f863,plain,
( spl14_98
| ~ spl14_28
| ~ spl14_49 ),
inference(avatar_split_clause,[],[f439,f431,f289,f861]) ).
fof(f439,plain,
( ! [X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ relation(X1)
| element(unordered_pair(singleton(sK5(X1,X0)),unordered_pair(X0,sK5(X1,X0))),X1) )
| ~ spl14_28
| ~ spl14_49 ),
inference(resolution,[],[f432,f290]) ).
fof(f859,plain,
( spl14_97
| ~ spl14_27
| ~ spl14_48 ),
inference(avatar_split_clause,[],[f435,f427,f285,f857]) ).
fof(f857,plain,
( spl14_97
<=> ! [X2,X0,X1] :
( ~ in(X0,relation_inverse_image(X1,X2))
| ~ relation(X1)
| ~ in(X1,unordered_pair(singleton(X0),unordered_pair(X0,sK9(X0,X2,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_97])]) ).
fof(f435,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_inverse_image(X1,X2))
| ~ relation(X1)
| ~ in(X1,unordered_pair(singleton(X0),unordered_pair(X0,sK9(X0,X2,X1)))) )
| ~ spl14_27
| ~ spl14_48 ),
inference(resolution,[],[f428,f286]) ).
fof(f855,plain,
( spl14_96
| ~ spl14_28
| ~ spl14_48 ),
inference(avatar_split_clause,[],[f434,f427,f289,f853]) ).
fof(f434,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_inverse_image(X1,X2))
| ~ relation(X1)
| element(unordered_pair(singleton(X0),unordered_pair(X0,sK9(X0,X2,X1))),X1) )
| ~ spl14_28
| ~ spl14_48 ),
inference(resolution,[],[f428,f290]) ).
fof(f834,plain,
( spl14_95
| ~ spl14_46
| ~ spl14_56 ),
inference(avatar_split_clause,[],[f486,f477,f410,f832]) ).
fof(f486,plain,
( ! [X0,X1] :
( relation_rng(X0) = X1
| in(sK3(X0,X1),X1)
| ~ relation(X0)
| in(sK3(X0,X1),relation_rng(X0)) )
| ~ spl14_46
| ~ spl14_56 ),
inference(duplicate_literal_removal,[],[f485]) ).
fof(f485,plain,
( ! [X0,X1] :
( relation_rng(X0) = X1
| in(sK3(X0,X1),X1)
| ~ relation(X0)
| in(sK3(X0,X1),relation_rng(X0))
| ~ relation(X0) )
| ~ spl14_46
| ~ spl14_56 ),
inference(resolution,[],[f478,f411]) ).
fof(f823,plain,
( spl14_94
| ~ spl14_27
| ~ spl14_41 ),
inference(avatar_split_clause,[],[f416,f371,f285,f821]) ).
fof(f416,plain,
( ! [X0] :
( ~ in(X0,sK0)
| ~ in(relation_rng(sK1),X0) )
| ~ spl14_27
| ~ spl14_41 ),
inference(resolution,[],[f372,f286]) ).
fof(f819,plain,
( spl14_93
| ~ spl14_31
| ~ spl14_46 ),
inference(avatar_split_clause,[],[f413,f410,f301,f817]) ).
fof(f413,plain,
( ! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),X2)
| in(X1,relation_rng(X2))
| ~ relation(X2) )
| ~ spl14_31
| ~ spl14_46 ),
inference(superposition,[],[f411,f302]) ).
fof(f815,plain,
( spl14_92
| ~ spl14_27
| ~ spl14_44 ),
inference(avatar_split_clause,[],[f407,f398,f285,f813]) ).
fof(f813,plain,
( spl14_92
<=> ! [X2,X0,X1] :
( ~ in(X0,relation_inverse_image(X1,X2))
| ~ relation(X1)
| ~ in(relation_rng(X1),sK9(X0,X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_92])]) ).
fof(f407,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_inverse_image(X1,X2))
| ~ relation(X1)
| ~ in(relation_rng(X1),sK9(X0,X2,X1)) )
| ~ spl14_27
| ~ spl14_44 ),
inference(resolution,[],[f399,f286]) ).
fof(f811,plain,
( spl14_91
| ~ spl14_28
| ~ spl14_44 ),
inference(avatar_split_clause,[],[f406,f398,f289,f809]) ).
fof(f809,plain,
( spl14_91
<=> ! [X2,X0,X1] :
( ~ in(X0,relation_inverse_image(X1,X2))
| ~ relation(X1)
| element(sK9(X0,X2,X1),relation_rng(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_91])]) ).
fof(f406,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_inverse_image(X1,X2))
| ~ relation(X1)
| element(sK9(X0,X2,X1),relation_rng(X1)) )
| ~ spl14_28
| ~ spl14_44 ),
inference(resolution,[],[f399,f290]) ).
fof(f792,plain,
( spl14_90
| ~ spl14_25
| ~ spl14_56 ),
inference(avatar_split_clause,[],[f483,f477,f268,f790]) ).
fof(f483,plain,
( ! [X0,X1] :
( relation_rng(X0) = X1
| in(sK3(X0,X1),X1)
| ~ relation(X0)
| ~ empty(X0) )
| ~ spl14_25
| ~ spl14_56 ),
inference(resolution,[],[f478,f269]) ).
fof(f788,plain,
( spl14_89
| ~ spl14_27
| ~ spl14_43 ),
inference(avatar_split_clause,[],[f395,f391,f285,f786]) ).
fof(f786,plain,
( spl14_89
<=> ! [X2,X0,X1] :
( ~ in(X0,relation_inverse_image(X1,X2))
| ~ relation(X1)
| ~ in(X2,sK9(X0,X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_89])]) ).
fof(f395,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_inverse_image(X1,X2))
| ~ relation(X1)
| ~ in(X2,sK9(X0,X2,X1)) )
| ~ spl14_27
| ~ spl14_43 ),
inference(resolution,[],[f392,f286]) ).
fof(f784,plain,
( spl14_88
| ~ spl14_28
| ~ spl14_43 ),
inference(avatar_split_clause,[],[f394,f391,f289,f782]) ).
fof(f394,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_inverse_image(X1,X2))
| ~ relation(X1)
| element(sK9(X0,X2,X1),X2) )
| ~ spl14_28
| ~ spl14_43 ),
inference(resolution,[],[f392,f290]) ).
fof(f773,plain,
( spl14_87
| ~ spl14_28
| ~ spl14_41 ),
inference(avatar_split_clause,[],[f415,f371,f289,f771]) ).
fof(f771,plain,
( spl14_87
<=> ! [X0] :
( ~ in(X0,sK0)
| element(X0,relation_rng(sK1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_87])]) ).
fof(f415,plain,
( ! [X0] :
( ~ in(X0,sK0)
| element(X0,relation_rng(sK1)) )
| ~ spl14_28
| ~ spl14_41 ),
inference(resolution,[],[f372,f290]) ).
fof(f759,plain,
( spl14_86
| ~ spl14_25
| ~ spl14_44 ),
inference(avatar_split_clause,[],[f408,f398,f268,f757]) ).
fof(f408,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_inverse_image(X1,X2))
| ~ relation(X1)
| ~ empty(relation_rng(X1)) )
| ~ spl14_25
| ~ spl14_44 ),
inference(resolution,[],[f399,f269]) ).
fof(f755,plain,
( spl14_85
| ~ spl14_29
| ~ spl14_36 ),
inference(avatar_split_clause,[],[f350,f338,f293,f753]) ).
fof(f293,plain,
( spl14_29
<=> ! [X0] :
( element(sK2(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_29])]) ).
fof(f338,plain,
( spl14_36
<=> ! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_36])]) ).
fof(f350,plain,
( ! [X0] :
( empty(powerset(X0))
| in(sK2(X0),powerset(X0))
| empty(X0) )
| ~ spl14_29
| ~ spl14_36 ),
inference(resolution,[],[f339,f294]) ).
fof(f294,plain,
( ! [X0] :
( element(sK2(X0),powerset(X0))
| empty(X0) )
| ~ spl14_29 ),
inference(avatar_component_clause,[],[f293]) ).
fof(f339,plain,
( ! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) )
| ~ spl14_36 ),
inference(avatar_component_clause,[],[f338]) ).
fof(f751,plain,
( spl14_84
| ~ spl14_33
| ~ spl14_36 ),
inference(avatar_split_clause,[],[f349,f338,f309,f749]) ).
fof(f309,plain,
( spl14_33
<=> ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_33])]) ).
fof(f349,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| in(X1,powerset(X0))
| ~ subset(X1,X0) )
| ~ spl14_33
| ~ spl14_36 ),
inference(resolution,[],[f339,f310]) ).
fof(f310,plain,
( ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) )
| ~ spl14_33 ),
inference(avatar_component_clause,[],[f309]) ).
fof(f720,plain,
( spl14_83
| ~ spl14_25
| ~ spl14_48 ),
inference(avatar_split_clause,[],[f436,f427,f268,f718]) ).
fof(f436,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_inverse_image(X1,X2))
| ~ relation(X1)
| ~ empty(X1) )
| ~ spl14_25
| ~ spl14_48 ),
inference(resolution,[],[f428,f269]) ).
fof(f716,plain,
( spl14_82
| ~ spl14_25
| ~ spl14_43 ),
inference(avatar_split_clause,[],[f396,f391,f268,f714]) ).
fof(f396,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_inverse_image(X1,X2))
| ~ relation(X1)
| ~ empty(X2) )
| ~ spl14_25
| ~ spl14_43 ),
inference(resolution,[],[f392,f269]) ).
fof(f712,plain,
( spl14_81
| ~ spl14_29
| ~ spl14_42 ),
inference(avatar_split_clause,[],[f385,f381,f293,f710]) ).
fof(f385,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK2(X1))
| empty(X1) )
| ~ spl14_29
| ~ spl14_42 ),
inference(resolution,[],[f382,f294]) ).
fof(f708,plain,
( spl14_80
| ~ spl14_33
| ~ spl14_42 ),
inference(avatar_split_clause,[],[f384,f381,f309,f706]) ).
fof(f706,plain,
( spl14_80
<=> ! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_80])]) ).
fof(f384,plain,
( ! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,X1) )
| ~ spl14_33
| ~ spl14_42 ),
inference(resolution,[],[f382,f310]) ).
fof(f667,plain,
( spl14_79
| ~ spl14_25
| ~ spl14_49 ),
inference(avatar_split_clause,[],[f441,f431,f268,f665]) ).
fof(f441,plain,
( ! [X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ relation(X1)
| ~ empty(X1) )
| ~ spl14_25
| ~ spl14_49 ),
inference(resolution,[],[f432,f269]) ).
fof(f663,plain,
( ~ spl14_78
| spl14_2
| ~ spl14_57 ),
inference(avatar_split_clause,[],[f505,f490,f161,f660]) ).
fof(f161,plain,
( spl14_2
<=> empty_set = sK0 ),
introduced(avatar_definition,[new_symbols(naming,[spl14_2])]) ).
fof(f505,plain,
( sK0 != sK11
| spl14_2
| ~ spl14_57 ),
inference(superposition,[],[f163,f492]) ).
fof(f163,plain,
( empty_set != sK0
| spl14_2 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f658,plain,
( spl14_77
| ~ spl14_18
| ~ spl14_42 ),
inference(avatar_split_clause,[],[f386,f381,f236,f656]) ).
fof(f236,plain,
( spl14_18
<=> ! [X0] : element(sK6(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_18])]) ).
fof(f386,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK6(powerset(X1))) )
| ~ spl14_18
| ~ spl14_42 ),
inference(resolution,[],[f382,f237]) ).
fof(f237,plain,
( ! [X0] : element(sK6(X0),X0)
| ~ spl14_18 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f654,plain,
( spl14_76
| ~ spl14_33
| ~ spl14_40 ),
inference(avatar_split_clause,[],[f374,f365,f309,f652]) ).
fof(f652,plain,
( spl14_76
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,X2)
| ~ subset(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_76])]) ).
fof(f374,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,X2)
| ~ subset(X2,X0) )
| ~ spl14_33
| ~ spl14_40 ),
inference(resolution,[],[f366,f310]) ).
fof(f650,plain,
( spl14_75
| ~ spl14_27
| ~ spl14_37 ),
inference(avatar_split_clause,[],[f356,f342,f285,f648]) ).
fof(f648,plain,
( spl14_75
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ in(X0,sK8(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_75])]) ).
fof(f356,plain,
( ! [X0,X1] :
( subset(X0,X1)
| ~ in(X0,sK8(X0,X1)) )
| ~ spl14_27
| ~ spl14_37 ),
inference(resolution,[],[f343,f286]) ).
fof(f646,plain,
( spl14_74
| ~ spl14_28
| ~ spl14_37 ),
inference(avatar_split_clause,[],[f355,f342,f289,f644]) ).
fof(f355,plain,
( ! [X0,X1] :
( subset(X0,X1)
| element(sK8(X0,X1),X0) )
| ~ spl14_28
| ~ spl14_37 ),
inference(resolution,[],[f343,f290]) ).
fof(f642,plain,
( spl14_73
| ~ spl14_22
| ~ spl14_34 ),
inference(avatar_split_clause,[],[f330,f313,f256,f640]) ).
fof(f313,plain,
( spl14_34
<=> ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_34])]) ).
fof(f330,plain,
( ! [X0,X1] :
( relation_rng(X1) = X0
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl14_22
| ~ spl14_34 ),
inference(resolution,[],[f314,f257]) ).
fof(f314,plain,
( ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) )
| ~ spl14_34 ),
inference(avatar_component_clause,[],[f313]) ).
fof(f629,plain,
( spl14_72
| ~ spl14_18
| ~ spl14_40 ),
inference(avatar_split_clause,[],[f376,f365,f236,f627]) ).
fof(f376,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK6(powerset(X0))) )
| ~ spl14_18
| ~ spl14_40 ),
inference(resolution,[],[f366,f237]) ).
fof(f625,plain,
( spl14_71
| ~ spl14_8
| ~ spl14_15
| ~ spl14_21
| ~ spl14_24
| ~ spl14_36 ),
inference(avatar_split_clause,[],[f354,f338,f264,f252,f224,f191,f623]) ).
fof(f623,plain,
( spl14_71
<=> ! [X0] :
( in(sK11,powerset(X0))
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_71])]) ).
fof(f224,plain,
( spl14_15
<=> ! [X0] : empty(sK7(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_15])]) ).
fof(f252,plain,
( spl14_21
<=> ! [X0] :
( empty_set = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_21])]) ).
fof(f354,plain,
( ! [X0] :
( in(sK11,powerset(X0))
| empty(powerset(X0)) )
| ~ spl14_8
| ~ spl14_15
| ~ spl14_21
| ~ spl14_24
| ~ spl14_36 ),
inference(forward_demodulation,[],[f353,f278]) ).
fof(f278,plain,
( empty_set = sK11
| ~ spl14_8
| ~ spl14_21 ),
inference(resolution,[],[f253,f193]) ).
fof(f193,plain,
( empty(sK11)
| ~ spl14_8 ),
inference(avatar_component_clause,[],[f191]) ).
fof(f253,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = X0 )
| ~ spl14_21 ),
inference(avatar_component_clause,[],[f252]) ).
fof(f353,plain,
( ! [X0] :
( in(empty_set,powerset(X0))
| empty(powerset(X0)) )
| ~ spl14_15
| ~ spl14_21
| ~ spl14_24
| ~ spl14_36 ),
inference(forward_demodulation,[],[f352,f277]) ).
fof(f277,plain,
( ! [X0] : empty_set = sK7(X0)
| ~ spl14_15
| ~ spl14_21 ),
inference(resolution,[],[f253,f225]) ).
fof(f225,plain,
( ! [X0] : empty(sK7(X0))
| ~ spl14_15 ),
inference(avatar_component_clause,[],[f224]) ).
fof(f352,plain,
( ! [X0] :
( empty(powerset(X0))
| in(sK7(X0),powerset(X0)) )
| ~ spl14_24
| ~ spl14_36 ),
inference(resolution,[],[f339,f265]) ).
fof(f607,plain,
( spl14_70
| ~ spl14_18
| ~ spl14_36 ),
inference(avatar_split_clause,[],[f351,f338,f236,f605]) ).
fof(f351,plain,
( ! [X0] :
( empty(X0)
| in(sK6(X0),X0) )
| ~ spl14_18
| ~ spl14_36 ),
inference(resolution,[],[f339,f237]) ).
fof(f603,plain,
( spl14_69
| ~ spl14_29
| ~ spl14_32 ),
inference(avatar_split_clause,[],[f321,f305,f293,f601]) ).
fof(f321,plain,
( ! [X0] :
( subset(sK2(X0),X0)
| empty(X0) )
| ~ spl14_29
| ~ spl14_32 ),
inference(resolution,[],[f306,f294]) ).
fof(f599,plain,
( spl14_68
| ~ spl14_8
| ~ spl14_21
| ~ spl14_22 ),
inference(avatar_split_clause,[],[f283,f256,f252,f191,f597]) ).
fof(f283,plain,
( ! [X0] :
( relation_rng(X0) = sK11
| ~ empty(X0) )
| ~ spl14_8
| ~ spl14_21
| ~ spl14_22 ),
inference(forward_demodulation,[],[f281,f278]) ).
fof(f281,plain,
( ! [X0] :
( ~ empty(X0)
| relation_rng(X0) = empty_set )
| ~ spl14_21
| ~ spl14_22 ),
inference(resolution,[],[f257,f253]) ).
fof(f569,plain,
( spl14_63
| ~ spl14_21
| ~ spl14_57 ),
inference(avatar_split_clause,[],[f548,f490,f252,f526]) ).
fof(f548,plain,
( ! [X0] :
( sK11 = X0
| ~ empty(X0) )
| ~ spl14_21
| ~ spl14_57 ),
inference(forward_demodulation,[],[f253,f492]) ).
fof(f553,plain,
( ~ spl14_67
| ~ spl14_22
| spl14_53 ),
inference(avatar_split_clause,[],[f514,f464,f256,f550]) ).
fof(f550,plain,
( spl14_67
<=> empty(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_67])]) ).
fof(f464,plain,
( spl14_53
<=> empty(relation_rng(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_53])]) ).
fof(f514,plain,
( ~ empty(sK1)
| ~ spl14_22
| spl14_53 ),
inference(resolution,[],[f466,f257]) ).
fof(f466,plain,
( ~ empty(relation_rng(sK1))
| spl14_53 ),
inference(avatar_component_clause,[],[f464]) ).
fof(f547,plain,
( ~ spl14_5
| ~ spl14_65 ),
inference(avatar_contradiction_clause,[],[f540]) ).
fof(f540,plain,
( $false
| ~ spl14_5
| ~ spl14_65 ),
inference(resolution,[],[f535,f178]) ).
fof(f535,plain,
( ! [X0] : ~ empty(X0)
| ~ spl14_65 ),
inference(avatar_component_clause,[],[f534]) ).
fof(f534,plain,
( spl14_65
<=> ! [X0] : ~ empty(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_65])]) ).
fof(f546,plain,
( ~ spl14_15
| ~ spl14_65 ),
inference(avatar_contradiction_clause,[],[f541]) ).
fof(f541,plain,
( $false
| ~ spl14_15
| ~ spl14_65 ),
inference(resolution,[],[f535,f225]) ).
fof(f545,plain,
( ~ spl14_8
| ~ spl14_65 ),
inference(avatar_contradiction_clause,[],[f542]) ).
fof(f542,plain,
( $false
| ~ spl14_8
| ~ spl14_65 ),
inference(resolution,[],[f535,f193]) ).
fof(f544,plain,
( ~ spl14_11
| ~ spl14_65 ),
inference(avatar_contradiction_clause,[],[f543]) ).
fof(f543,plain,
( $false
| ~ spl14_11
| ~ spl14_65 ),
inference(resolution,[],[f535,f208]) ).
fof(f208,plain,
( empty(sK13)
| ~ spl14_11 ),
inference(avatar_component_clause,[],[f206]) ).
fof(f206,plain,
( spl14_11
<=> empty(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_11])]) ).
fof(f539,plain,
( spl14_65
| spl14_66
| ~ spl14_8
| ~ spl14_15
| ~ spl14_21
| ~ spl14_24
| ~ spl14_40 ),
inference(avatar_split_clause,[],[f379,f365,f264,f252,f224,f191,f537,f534]) ).
fof(f379,plain,
( ! [X0,X1] :
( ~ in(X1,sK11)
| ~ empty(X0) )
| ~ spl14_8
| ~ spl14_15
| ~ spl14_21
| ~ spl14_24
| ~ spl14_40 ),
inference(forward_demodulation,[],[f378,f278]) ).
fof(f378,plain,
( ! [X0,X1] :
( ~ in(X1,empty_set)
| ~ empty(X0) )
| ~ spl14_15
| ~ spl14_21
| ~ spl14_24
| ~ spl14_40 ),
inference(forward_demodulation,[],[f377,f277]) ).
fof(f377,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK7(X0)) )
| ~ spl14_24
| ~ spl14_40 ),
inference(resolution,[],[f366,f265]) ).
fof(f532,plain,
( spl14_64
| ~ spl14_25
| ~ spl14_37 ),
inference(avatar_split_clause,[],[f357,f342,f268,f530]) ).
fof(f530,plain,
( spl14_64
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_64])]) ).
fof(f357,plain,
( ! [X0,X1] :
( subset(X0,X1)
| ~ empty(X0) )
| ~ spl14_25
| ~ spl14_37 ),
inference(resolution,[],[f343,f269]) ).
fof(f528,plain,
( spl14_63
| ~ spl14_8
| ~ spl14_34 ),
inference(avatar_split_clause,[],[f333,f313,f191,f526]) ).
fof(f333,plain,
( ! [X0] :
( sK11 = X0
| ~ empty(X0) )
| ~ spl14_8
| ~ spl14_34 ),
inference(resolution,[],[f314,f193]) ).
fof(f524,plain,
( spl14_62
| ~ spl14_18
| ~ spl14_32 ),
inference(avatar_split_clause,[],[f319,f305,f236,f522]) ).
fof(f319,plain,
( ! [X0] : subset(sK6(powerset(X0)),X0)
| ~ spl14_18
| ~ spl14_32 ),
inference(resolution,[],[f306,f237]) ).
fof(f518,plain,
( spl14_61
| ~ spl14_57
| ~ spl14_60 ),
inference(avatar_split_clause,[],[f513,f510,f490,f516]) ).
fof(f510,plain,
( spl14_60
<=> ! [X0] : empty_set = sK7(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_60])]) ).
fof(f513,plain,
( ! [X0] : sK7(X0) = sK11
| ~ spl14_57
| ~ spl14_60 ),
inference(forward_demodulation,[],[f511,f492]) ).
fof(f511,plain,
( ! [X0] : empty_set = sK7(X0)
| ~ spl14_60 ),
inference(avatar_component_clause,[],[f510]) ).
fof(f512,plain,
( spl14_60
| ~ spl14_15
| ~ spl14_21 ),
inference(avatar_split_clause,[],[f277,f252,f224,f510]) ).
fof(f502,plain,
( spl14_59
| ~ spl14_8
| ~ spl14_15
| ~ spl14_21
| ~ spl14_24
| ~ spl14_32 ),
inference(avatar_split_clause,[],[f323,f305,f264,f252,f224,f191,f500]) ).
fof(f500,plain,
( spl14_59
<=> ! [X0] : subset(sK11,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_59])]) ).
fof(f323,plain,
( ! [X0] : subset(sK11,X0)
| ~ spl14_8
| ~ spl14_15
| ~ spl14_21
| ~ spl14_24
| ~ spl14_32 ),
inference(forward_demodulation,[],[f322,f278]) ).
fof(f322,plain,
( ! [X0] : subset(empty_set,X0)
| ~ spl14_15
| ~ spl14_21
| ~ spl14_24
| ~ spl14_32 ),
inference(forward_demodulation,[],[f320,f277]) ).
fof(f320,plain,
( ! [X0] : subset(sK7(X0),X0)
| ~ spl14_24
| ~ spl14_32 ),
inference(resolution,[],[f306,f265]) ).
fof(f498,plain,
( spl14_58
| ~ spl14_8
| ~ spl14_11
| ~ spl14_21 ),
inference(avatar_split_clause,[],[f280,f252,f206,f191,f495]) ).
fof(f495,plain,
( spl14_58
<=> sK11 = sK13 ),
introduced(avatar_definition,[new_symbols(naming,[spl14_58])]) ).
fof(f280,plain,
( sK11 = sK13
| ~ spl14_8
| ~ spl14_11
| ~ spl14_21 ),
inference(forward_demodulation,[],[f279,f278]) ).
fof(f279,plain,
( empty_set = sK13
| ~ spl14_11
| ~ spl14_21 ),
inference(resolution,[],[f253,f208]) ).
fof(f493,plain,
( spl14_57
| ~ spl14_8
| ~ spl14_21 ),
inference(avatar_split_clause,[],[f278,f252,f191,f490]) ).
fof(f479,plain,
( spl14_56
| ~ spl14_31
| ~ spl14_55 ),
inference(avatar_split_clause,[],[f475,f472,f301,f477]) ).
fof(f472,plain,
( spl14_55
<=> ! [X0,X1] :
( relation_rng(X0) = X1
| in(unordered_pair(unordered_pair(sK4(X0,X1),sK3(X0,X1)),singleton(sK4(X0,X1))),X0)
| in(sK3(X0,X1),X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_55])]) ).
fof(f475,plain,
( ! [X0,X1] :
( in(unordered_pair(singleton(sK4(X0,X1)),unordered_pair(sK4(X0,X1),sK3(X0,X1))),X0)
| relation_rng(X0) = X1
| in(sK3(X0,X1),X1)
| ~ relation(X0) )
| ~ spl14_31
| ~ spl14_55 ),
inference(forward_demodulation,[],[f473,f302]) ).
fof(f473,plain,
( ! [X0,X1] :
( relation_rng(X0) = X1
| in(unordered_pair(unordered_pair(sK4(X0,X1),sK3(X0,X1)),singleton(sK4(X0,X1))),X0)
| in(sK3(X0,X1),X1)
| ~ relation(X0) )
| ~ spl14_55 ),
inference(avatar_component_clause,[],[f472]) ).
fof(f474,plain,
spl14_55,
inference(avatar_split_clause,[],[f145,f472]) ).
fof(f145,plain,
! [X0,X1] :
( relation_rng(X0) = X1
| in(unordered_pair(unordered_pair(sK4(X0,X1),sK3(X0,X1)),singleton(sK4(X0,X1))),X0)
| in(sK3(X0,X1),X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f107,f121]) ).
fof(f121,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f107,plain,
! [X0,X1] :
( relation_rng(X0) = X1
| in(ordered_pair(sK4(X0,X1),sK3(X0,X1)),X0)
| in(sK3(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ( ( ! [X3] : ~ in(ordered_pair(X3,sK3(X0,X1)),X0)
| ~ in(sK3(X0,X1),X1) )
& ( in(ordered_pair(sK4(X0,X1),sK3(X0,X1)),X0)
| in(sK3(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( in(ordered_pair(sK5(X0,X5),X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f68,f71,f70,f69]) ).
fof(f69,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X4,X2),X0)
| in(X2,X1) ) )
=> ( ( ! [X3] : ~ in(ordered_pair(X3,sK3(X0,X1)),X0)
| ~ in(sK3(X0,X1),X1) )
& ( ? [X4] : in(ordered_pair(X4,sK3(X0,X1)),X0)
| in(sK3(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f70,plain,
! [X0,X1] :
( ? [X4] : in(ordered_pair(X4,sK3(X0,X1)),X0)
=> in(ordered_pair(sK4(X0,X1),sK3(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f71,plain,
! [X0,X5] :
( ? [X7] : in(ordered_pair(X7,X5),X0)
=> in(ordered_pair(sK5(X0,X5),X5),X0) ),
introduced(choice_axiom,[]) ).
fof(f68,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X4,X2),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( ? [X7] : in(ordered_pair(X7,X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f67]) ).
fof(f67,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).
fof(f470,plain,
( ~ spl14_53
| spl14_54
| ~ spl14_25
| ~ spl14_41 ),
inference(avatar_split_clause,[],[f417,f371,f268,f468,f464]) ).
fof(f417,plain,
( ! [X0] :
( ~ in(X0,sK0)
| ~ empty(relation_rng(sK1)) )
| ~ spl14_25
| ~ spl14_41 ),
inference(resolution,[],[f372,f269]) ).
fof(f457,plain,
spl14_52,
inference(avatar_split_clause,[],[f153,f455]) ).
fof(f153,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X3)),X2)
| in(X0,relation_inverse_image(X2,X1))
| ~ in(X3,X1)
| ~ in(X3,relation_rng(X2))
| ~ relation(X2) ),
inference(forward_demodulation,[],[f149,f120]) ).
fof(f120,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f149,plain,
! [X2,X3,X0,X1] :
( in(X0,relation_inverse_image(X2,X1))
| ~ in(X3,X1)
| ~ in(unordered_pair(unordered_pair(X0,X3),singleton(X0)),X2)
| ~ in(X3,relation_rng(X2))
| ~ relation(X2) ),
inference(definition_unfolding,[],[f135,f121]) ).
fof(f135,plain,
! [X2,X3,X0,X1] :
( in(X0,relation_inverse_image(X2,X1))
| ~ in(X3,X1)
| ~ in(ordered_pair(X0,X3),X2)
| ~ in(X3,relation_rng(X2))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_inverse_image(X2,X1))
| ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X0,X3),X2)
| ~ in(X3,relation_rng(X2)) ) )
& ( ( in(sK9(X0,X1,X2),X1)
& in(ordered_pair(X0,sK9(X0,X1,X2)),X2)
& in(sK9(X0,X1,X2),relation_rng(X2)) )
| ~ in(X0,relation_inverse_image(X2,X1)) ) )
| ~ relation(X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f83,f84]) ).
fof(f84,plain,
! [X0,X1,X2] :
( ? [X4] :
( in(X4,X1)
& in(ordered_pair(X0,X4),X2)
& in(X4,relation_rng(X2)) )
=> ( in(sK9(X0,X1,X2),X1)
& in(ordered_pair(X0,sK9(X0,X1,X2)),X2)
& in(sK9(X0,X1,X2),relation_rng(X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f83,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_inverse_image(X2,X1))
| ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X0,X3),X2)
| ~ in(X3,relation_rng(X2)) ) )
& ( ? [X4] :
( in(X4,X1)
& in(ordered_pair(X0,X4),X2)
& in(X4,relation_rng(X2)) )
| ~ in(X0,relation_inverse_image(X2,X1)) ) )
| ~ relation(X2) ),
inference(rectify,[],[f82]) ).
fof(f82,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_inverse_image(X2,X1))
| ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X0,X3),X2)
| ~ in(X3,relation_rng(X2)) ) )
& ( ? [X3] :
( in(X3,X1)
& in(ordered_pair(X0,X3),X2)
& in(X3,relation_rng(X2)) )
| ~ in(X0,relation_inverse_image(X2,X1)) ) )
| ~ relation(X2) ),
inference(nnf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0,X1,X2] :
( ( in(X0,relation_inverse_image(X2,X1))
<=> ? [X3] :
( in(X3,X1)
& in(ordered_pair(X0,X3),X2)
& in(X3,relation_rng(X2)) ) )
| ~ relation(X2) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_inverse_image(X2,X1))
<=> ? [X3] :
( in(X3,X1)
& in(ordered_pair(X0,X3),X2)
& in(X3,relation_rng(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t166_relat_1) ).
fof(f450,plain,
( spl14_51
| ~ spl14_31
| ~ spl14_50 ),
inference(avatar_split_clause,[],[f446,f443,f301,f448]) ).
fof(f443,plain,
( spl14_50
<=> ! [X0,X1,X3] :
( relation_rng(X0) = X1
| ~ in(unordered_pair(unordered_pair(X3,sK3(X0,X1)),singleton(X3)),X0)
| ~ in(sK3(X0,X1),X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_50])]) ).
fof(f446,plain,
( ! [X3,X0,X1] :
( ~ in(unordered_pair(singleton(X3),unordered_pair(X3,sK3(X0,X1))),X0)
| relation_rng(X0) = X1
| ~ in(sK3(X0,X1),X1)
| ~ relation(X0) )
| ~ spl14_31
| ~ spl14_50 ),
inference(forward_demodulation,[],[f444,f302]) ).
fof(f444,plain,
( ! [X3,X0,X1] :
( relation_rng(X0) = X1
| ~ in(unordered_pair(unordered_pair(X3,sK3(X0,X1)),singleton(X3)),X0)
| ~ in(sK3(X0,X1),X1)
| ~ relation(X0) )
| ~ spl14_50 ),
inference(avatar_component_clause,[],[f443]) ).
fof(f445,plain,
spl14_50,
inference(avatar_split_clause,[],[f144,f443]) ).
fof(f144,plain,
! [X3,X0,X1] :
( relation_rng(X0) = X1
| ~ in(unordered_pair(unordered_pair(X3,sK3(X0,X1)),singleton(X3)),X0)
| ~ in(sK3(X0,X1),X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f108,f121]) ).
fof(f108,plain,
! [X3,X0,X1] :
( relation_rng(X0) = X1
| ~ in(ordered_pair(X3,sK3(X0,X1)),X0)
| ~ in(sK3(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f433,plain,
( spl14_49
| ~ spl14_31
| ~ spl14_47 ),
inference(avatar_split_clause,[],[f425,f421,f301,f431]) ).
fof(f421,plain,
( spl14_47
<=> ! [X5,X0] :
( in(unordered_pair(unordered_pair(sK5(X0,X5),X5),singleton(sK5(X0,X5))),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_47])]) ).
fof(f425,plain,
( ! [X0,X5] :
( in(unordered_pair(singleton(sK5(X0,X5)),unordered_pair(X5,sK5(X0,X5))),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) )
| ~ spl14_31
| ~ spl14_47 ),
inference(forward_demodulation,[],[f424,f302]) ).
fof(f424,plain,
( ! [X0,X5] :
( in(unordered_pair(singleton(sK5(X0,X5)),unordered_pair(sK5(X0,X5),X5)),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) )
| ~ spl14_31
| ~ spl14_47 ),
inference(forward_demodulation,[],[f422,f302]) ).
fof(f422,plain,
( ! [X0,X5] :
( in(unordered_pair(unordered_pair(sK5(X0,X5),X5),singleton(sK5(X0,X5))),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) )
| ~ spl14_47 ),
inference(avatar_component_clause,[],[f421]) ).
fof(f429,plain,
spl14_48,
inference(avatar_split_clause,[],[f154,f427]) ).
fof(f154,plain,
! [X2,X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK9(X0,X1,X2))),X2)
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ relation(X2) ),
inference(forward_demodulation,[],[f150,f120]) ).
fof(f150,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(X0,sK9(X0,X1,X2)),singleton(X0)),X2)
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ relation(X2) ),
inference(definition_unfolding,[],[f133,f121]) ).
fof(f133,plain,
! [X2,X0,X1] :
( in(ordered_pair(X0,sK9(X0,X1,X2)),X2)
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f85]) ).
fof(f423,plain,
spl14_47,
inference(avatar_split_clause,[],[f152,f421]) ).
fof(f152,plain,
! [X0,X5] :
( in(unordered_pair(unordered_pair(sK5(X0,X5),X5),singleton(sK5(X0,X5))),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f147]) ).
fof(f147,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(sK5(X0,X5),X5),singleton(sK5(X0,X5))),X0)
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f105,f121]) ).
fof(f105,plain,
! [X0,X1,X5] :
( in(ordered_pair(sK5(X0,X5),X5),X0)
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f412,plain,
( spl14_46
| ~ spl14_31
| ~ spl14_45 ),
inference(avatar_split_clause,[],[f405,f402,f301,f410]) ).
fof(f402,plain,
( spl14_45
<=> ! [X5,X0,X6] :
( in(X5,relation_rng(X0))
| ~ in(unordered_pair(unordered_pair(X6,X5),singleton(X6)),X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_45])]) ).
fof(f405,plain,
( ! [X0,X6,X5] :
( ~ in(unordered_pair(singleton(X6),unordered_pair(X6,X5)),X0)
| in(X5,relation_rng(X0))
| ~ relation(X0) )
| ~ spl14_31
| ~ spl14_45 ),
inference(forward_demodulation,[],[f403,f302]) ).
fof(f403,plain,
( ! [X0,X6,X5] :
( in(X5,relation_rng(X0))
| ~ in(unordered_pair(unordered_pair(X6,X5),singleton(X6)),X0)
| ~ relation(X0) )
| ~ spl14_45 ),
inference(avatar_component_clause,[],[f402]) ).
fof(f404,plain,
spl14_45,
inference(avatar_split_clause,[],[f151,f402]) ).
fof(f151,plain,
! [X0,X6,X5] :
( in(X5,relation_rng(X0))
| ~ in(unordered_pair(unordered_pair(X6,X5),singleton(X6)),X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f146]) ).
fof(f146,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X6,X5),singleton(X6)),X0)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f106,f121]) ).
fof(f106,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X6,X5),X0)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f400,plain,
spl14_44,
inference(avatar_split_clause,[],[f132,f398]) ).
fof(f132,plain,
! [X2,X0,X1] :
( in(sK9(X0,X1,X2),relation_rng(X2))
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f85]) ).
fof(f393,plain,
spl14_43,
inference(avatar_split_clause,[],[f134,f391]) ).
fof(f134,plain,
! [X2,X0,X1] :
( in(sK9(X0,X1,X2),X1)
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f85]) ).
fof(f383,plain,
spl14_42,
inference(avatar_split_clause,[],[f136,f381]) ).
fof(f136,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f60]) ).
fof(f60,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f373,plain,
( spl14_41
| ~ spl14_3
| ~ spl14_39 ),
inference(avatar_split_clause,[],[f368,f361,f166,f371]) ).
fof(f166,plain,
( spl14_3
<=> subset(sK0,relation_rng(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_3])]) ).
fof(f368,plain,
( ! [X0] :
( ~ in(X0,sK0)
| in(X0,relation_rng(sK1)) )
| ~ spl14_3
| ~ spl14_39 ),
inference(resolution,[],[f362,f168]) ).
fof(f168,plain,
( subset(sK0,relation_rng(sK1))
| ~ spl14_3 ),
inference(avatar_component_clause,[],[f166]) ).
fof(f367,plain,
spl14_40,
inference(avatar_split_clause,[],[f137,f365]) ).
fof(f137,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f62,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/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f363,plain,
spl14_39,
inference(avatar_split_clause,[],[f125,f361]) ).
fof(f125,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK8(X0,X1),X1)
& in(sK8(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f78,f79]) ).
fof(f79,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK8(X0,X1),X1)
& in(sK8(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f78,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f77]) ).
fof(f77,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f348,plain,
spl14_38,
inference(avatar_split_clause,[],[f127,f346]) ).
fof(f127,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK8(X0,X1),X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f344,plain,
spl14_37,
inference(avatar_split_clause,[],[f126,f342]) ).
fof(f126,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK8(X0,X1),X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f340,plain,
spl14_36,
inference(avatar_split_clause,[],[f124,f338]) ).
fof(f124,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f54]) ).
fof(f54,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f328,plain,
( spl14_35
| ~ spl14_15
| ~ spl14_17 ),
inference(avatar_split_clause,[],[f244,f232,f224,f326]) ).
fof(f326,plain,
( spl14_35
<=> ! [X0] : relation(sK7(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_35])]) ).
fof(f244,plain,
( ! [X0] : relation(sK7(X0))
| ~ spl14_15
| ~ spl14_17 ),
inference(resolution,[],[f233,f225]) ).
fof(f315,plain,
spl14_34,
inference(avatar_split_clause,[],[f130,f313]) ).
fof(f130,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f57,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/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(f311,plain,
spl14_33,
inference(avatar_split_clause,[],[f129,f309]) ).
fof(f129,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f307,plain,
spl14_32,
inference(avatar_split_clause,[],[f128,f305]) ).
fof(f128,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f81]) ).
fof(f303,plain,
spl14_31,
inference(avatar_split_clause,[],[f120,f301]) ).
fof(f299,plain,
spl14_30,
inference(avatar_split_clause,[],[f113,f297]) ).
fof(f297,plain,
( spl14_30
<=> ! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_30])]) ).
fof(f113,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(flattening,[],[f50]) ).
fof(f50,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_rng(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_relat_1) ).
fof(f295,plain,
spl14_29,
inference(avatar_split_clause,[],[f103,f293]) ).
fof(f103,plain,
! [X0] :
( element(sK2(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0] :
( ( ~ empty(sK2(X0))
& element(sK2(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f45,f65]) ).
fof(f65,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( ~ empty(sK2(X0))
& element(sK2(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f45,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f291,plain,
spl14_28,
inference(avatar_split_clause,[],[f123,f289]) ).
fof(f123,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f53]) ).
fof(f53,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f287,plain,
spl14_27,
inference(avatar_split_clause,[],[f122,f285]) ).
fof(f122,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f275,plain,
( spl14_26
| ~ spl14_8
| ~ spl14_17 ),
inference(avatar_split_clause,[],[f245,f232,f191,f272]) ).
fof(f245,plain,
( relation(sK11)
| ~ spl14_8
| ~ spl14_17 ),
inference(resolution,[],[f233,f193]) ).
fof(f270,plain,
spl14_25,
inference(avatar_split_clause,[],[f131,f268]) ).
fof(f131,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f58]) ).
fof(f58,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/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f266,plain,
spl14_24,
inference(avatar_split_clause,[],[f115,f264]) ).
fof(f115,plain,
! [X0] : element(sK7(X0),powerset(X0)),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0] :
( empty(sK7(X0))
& element(sK7(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f28,f75]) ).
fof(f75,plain,
! [X0] :
( ? [X1] :
( empty(X1)
& element(X1,powerset(X0)) )
=> ( empty(sK7(X0))
& element(sK7(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f28,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f262,plain,
spl14_23,
inference(avatar_split_clause,[],[f112,f260]) ).
fof(f260,plain,
( spl14_23
<=> ! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_23])]) ).
fof(f112,plain,
! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0] :
( ( relation(relation_rng(X0))
& empty(relation_rng(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_rng(X0))
& empty(relation_rng(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).
fof(f258,plain,
spl14_22,
inference(avatar_split_clause,[],[f111,f256]) ).
fof(f111,plain,
! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f254,plain,
spl14_21,
inference(avatar_split_clause,[],[f110,f252]) ).
fof(f110,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f39]) ).
fof(f39,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f250,plain,
spl14_20,
inference(avatar_split_clause,[],[f104,f248]) ).
fof(f248,plain,
( spl14_20
<=> ! [X0] :
( ~ empty(sK2(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_20])]) ).
fof(f104,plain,
! [X0] :
( ~ empty(sK2(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f242,plain,
spl14_19,
inference(avatar_split_clause,[],[f119,f240]) ).
fof(f240,plain,
( spl14_19
<=> ! [X0,X1] : ~ empty(unordered_pair(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_19])]) ).
fof(f119,plain,
! [X0,X1] : ~ empty(unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0,X1] : ~ empty(unordered_pair(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_subset_1) ).
fof(f238,plain,
spl14_18,
inference(avatar_split_clause,[],[f114,f236]) ).
fof(f114,plain,
! [X0] : element(sK6(X0),X0),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
! [X0] : element(sK6(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f15,f73]) ).
fof(f73,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK6(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f15,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f234,plain,
spl14_17,
inference(avatar_split_clause,[],[f109,f232]) ).
fof(f109,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( empty(X0)
=> relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(f230,plain,
spl14_16,
inference(avatar_split_clause,[],[f117,f228]) ).
fof(f117,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f30]) ).
fof(f30,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f226,plain,
spl14_15,
inference(avatar_split_clause,[],[f116,f224]) ).
fof(f116,plain,
! [X0] : empty(sK7(X0)),
inference(cnf_transformation,[],[f76]) ).
fof(f222,plain,
spl14_14,
inference(avatar_split_clause,[],[f102,f220]) ).
fof(f220,plain,
( spl14_14
<=> ! [X0] : ~ empty(powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_14])]) ).
fof(f102,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f218,plain,
spl14_13,
inference(avatar_split_clause,[],[f101,f216]) ).
fof(f216,plain,
( spl14_13
<=> ! [X0] : ~ empty(singleton(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_13])]) ).
fof(f101,plain,
! [X0] : ~ empty(singleton(X0)),
inference(cnf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0] : ~ empty(singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).
fof(f214,plain,
spl14_12,
inference(avatar_split_clause,[],[f143,f211]) ).
fof(f211,plain,
( spl14_12
<=> relation(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_12])]) ).
fof(f143,plain,
relation(sK13),
inference(cnf_transformation,[],[f93]) ).
fof(f93,plain,
( relation(sK13)
& empty(sK13) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f24,f92]) ).
fof(f92,plain,
( ? [X0] :
( relation(X0)
& empty(X0) )
=> ( relation(sK13)
& empty(sK13) ) ),
introduced(choice_axiom,[]) ).
fof(f24,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f209,plain,
spl14_11,
inference(avatar_split_clause,[],[f142,f206]) ).
fof(f142,plain,
empty(sK13),
inference(cnf_transformation,[],[f93]) ).
fof(f204,plain,
spl14_10,
inference(avatar_split_clause,[],[f141,f201]) ).
fof(f201,plain,
( spl14_10
<=> relation(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_10])]) ).
fof(f141,plain,
relation(sK12),
inference(cnf_transformation,[],[f91]) ).
fof(f91,plain,
( relation(sK12)
& ~ empty(sK12) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f27,f90]) ).
fof(f90,plain,
( ? [X0] :
( relation(X0)
& ~ empty(X0) )
=> ( relation(sK12)
& ~ empty(sK12) ) ),
introduced(choice_axiom,[]) ).
fof(f27,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f199,plain,
~ spl14_9,
inference(avatar_split_clause,[],[f140,f196]) ).
fof(f196,plain,
( spl14_9
<=> empty(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_9])]) ).
fof(f140,plain,
~ empty(sK12),
inference(cnf_transformation,[],[f91]) ).
fof(f194,plain,
spl14_8,
inference(avatar_split_clause,[],[f139,f191]) ).
fof(f139,plain,
empty(sK11),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
empty(sK11),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f26,f88]) ).
fof(f88,plain,
( ? [X0] : empty(X0)
=> empty(sK11) ),
introduced(choice_axiom,[]) ).
fof(f26,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f189,plain,
~ spl14_7,
inference(avatar_split_clause,[],[f138,f186]) ).
fof(f186,plain,
( spl14_7
<=> empty(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_7])]) ).
fof(f138,plain,
~ empty(sK10),
inference(cnf_transformation,[],[f87]) ).
fof(f87,plain,
~ empty(sK10),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f29,f86]) ).
fof(f86,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK10) ),
introduced(choice_axiom,[]) ).
fof(f29,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f184,plain,
spl14_6,
inference(avatar_split_clause,[],[f100,f181]) ).
fof(f100,plain,
relation(empty_set),
inference(cnf_transformation,[],[f21]) ).
fof(f21,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f179,plain,
spl14_5,
inference(avatar_split_clause,[],[f98,f176]) ).
fof(f98,plain,
empty(empty_set),
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f174,plain,
spl14_4,
inference(avatar_split_clause,[],[f97,f171]) ).
fof(f97,plain,
empty_set = relation_inverse_image(sK1,sK0),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
( empty_set = relation_inverse_image(sK1,sK0)
& subset(sK0,relation_rng(sK1))
& empty_set != sK0
& relation(sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f44,f63]) ).
fof(f63,plain,
( ? [X0,X1] :
( empty_set = relation_inverse_image(X1,X0)
& subset(X0,relation_rng(X1))
& empty_set != X0
& relation(X1) )
=> ( empty_set = relation_inverse_image(sK1,sK0)
& subset(sK0,relation_rng(sK1))
& empty_set != sK0
& relation(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f44,plain,
? [X0,X1] :
( empty_set = relation_inverse_image(X1,X0)
& subset(X0,relation_rng(X1))
& empty_set != X0
& relation(X1) ),
inference(flattening,[],[f43]) ).
fof(f43,plain,
? [X0,X1] :
( empty_set = relation_inverse_image(X1,X0)
& subset(X0,relation_rng(X1))
& empty_set != X0
& relation(X1) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> ~ ( empty_set = relation_inverse_image(X1,X0)
& subset(X0,relation_rng(X1))
& empty_set != X0 ) ),
inference(negated_conjecture,[],[f32]) ).
fof(f32,conjecture,
! [X0,X1] :
( relation(X1)
=> ~ ( empty_set = relation_inverse_image(X1,X0)
& subset(X0,relation_rng(X1))
& empty_set != X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t174_relat_1) ).
fof(f169,plain,
spl14_3,
inference(avatar_split_clause,[],[f96,f166]) ).
fof(f96,plain,
subset(sK0,relation_rng(sK1)),
inference(cnf_transformation,[],[f64]) ).
fof(f164,plain,
~ spl14_2,
inference(avatar_split_clause,[],[f95,f161]) ).
fof(f95,plain,
empty_set != sK0,
inference(cnf_transformation,[],[f64]) ).
fof(f159,plain,
spl14_1,
inference(avatar_split_clause,[],[f94,f156]) ).
fof(f94,plain,
relation(sK1),
inference(cnf_transformation,[],[f64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU210+1 : TPTP v8.1.2. Released v3.3.0.
% 0.10/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35 % Computer : n006.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Apr 29 20:22:20 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % (24585)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.36 % (24587)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.37 % (24588)WARNING: value z3 for option sas not known
% 0.13/0.37 % (24586)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.37 % (24588)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)
% 0.13/0.37 % (24589)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.37 % (24590)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)
% 0.13/0.37 % (24591)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)
% 0.13/0.37 % (24592)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)
% 0.13/0.37 TRYING [1]
% 0.13/0.37 TRYING [2]
% 0.13/0.37 TRYING [3]
% 0.13/0.38 TRYING [1]
% 0.13/0.38 TRYING [2]
% 0.13/0.38 TRYING [1]
% 0.13/0.38 TRYING [2]
% 0.13/0.38 TRYING [3]
% 0.13/0.39 TRYING [4]
% 0.13/0.39 TRYING [3]
% 0.13/0.39 TRYING [4]
% 0.20/0.41 TRYING [5]
% 0.20/0.42 TRYING [5]
% 0.20/0.45 TRYING [4]
% 0.20/0.46 % (24590)First to succeed.
% 0.20/0.46 TRYING [6]
% 0.20/0.47 % (24590)Refutation found. Thanks to Tanya!
% 0.20/0.47 % SZS status Theorem for theBenchmark
% 0.20/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.48 % (24590)------------------------------
% 0.20/0.48 % (24590)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.20/0.48 % (24590)Termination reason: Refutation
% 0.20/0.48
% 0.20/0.48 % (24590)Memory used [KB]: 2569
% 0.20/0.48 % (24590)Time elapsed: 0.103 s
% 0.20/0.48 % (24590)Instructions burned: 189 (million)
% 0.20/0.48 % (24590)------------------------------
% 0.20/0.48 % (24590)------------------------------
% 0.20/0.48 % (24585)Success in time 0.122 s
%------------------------------------------------------------------------------