TSTP Solution File: NUM401+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM401+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 08:26:29 EDT 2024
% Result : Theorem 6.21s 1.24s
% Output : Refutation 6.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 568
% Syntax : Number of formulae : 1874 ( 164 unt; 0 def)
% Number of atoms : 7013 ( 439 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 8398 (3259 ~;4382 |; 201 &)
% ( 512 <=>; 43 =>; 0 <=; 1 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 512 ( 510 usr; 497 prp; 0-3 aty)
% Number of functors : 24 ( 24 usr; 16 con; 0-3 aty)
% Number of variables : 2311 (2258 !; 53 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15758,plain,
$false,
inference(avatar_sat_refutation,[],[f278,f283,f288,f293,f298,f303,f308,f313,f318,f323,f328,f333,f338,f343,f348,f353,f358,f363,f368,f373,f378,f383,f388,f393,f398,f403,f408,f413,f418,f423,f428,f433,f438,f443,f448,f453,f458,f463,f468,f477,f478,f482,f486,f490,f494,f498,f502,f506,f510,f514,f518,f555,f564,f568,f572,f576,f580,f593,f599,f603,f607,f611,f615,f619,f623,f628,f632,f636,f640,f660,f670,f677,f684,f685,f686,f687,f688,f689,f705,f709,f713,f717,f721,f725,f729,f762,f766,f770,f786,f790,f794,f802,f806,f810,f814,f819,f823,f843,f848,f852,f856,f873,f882,f886,f895,f902,f935,f947,f952,f958,f963,f968,f974,f980,f985,f991,f997,f1002,f1008,f1021,f1027,f1028,f1035,f1040,f1045,f1049,f1071,f1075,f1079,f1083,f1099,f1103,f1112,f1116,f1143,f1147,f1151,f1155,f1159,f1163,f1193,f1197,f1211,f1215,f1219,f1223,f1227,f1275,f1279,f1287,f1291,f1311,f1315,f1319,f1360,f1378,f1396,f1400,f1409,f1413,f1432,f1436,f1440,f1444,f1448,f1538,f1563,f1567,f1571,f1647,f1651,f1655,f1659,f1663,f1667,f1671,f1777,f1781,f1785,f1872,f1876,f1881,f1956,f1960,f2097,f2107,f2137,f2141,f2162,f2193,f2204,f2208,f2233,f2242,f2286,f2295,f2301,f2307,f2313,f2317,f2322,f2331,f2332,f2342,f2374,f2379,f2384,f2398,f2416,f2420,f2424,f2428,f2432,f2436,f2441,f2536,f2540,f2560,f2564,f2568,f2572,f2576,f2580,f2584,f2588,f2592,f2605,f2612,f2713,f2718,f2729,f2733,f2737,f2741,f2745,f2749,f2753,f2757,f2854,f2858,f2880,f2884,f2888,f2893,f2943,f2947,f2951,f2955,f2959,f2963,f2964,f2968,f2972,f2976,f2980,f2984,f3211,f3215,f3219,f3305,f3309,f3313,f3317,f3321,f3325,f3329,f3419,f3423,f3427,f3442,f3476,f3488,f3489,f3561,f3565,f3569,f3573,f3577,f3581,f3585,f3592,f3596,f3600,f3604,f3608,f3612,f3616,f3620,f3624,f3628,f3629,f3633,f3637,f3641,f3645,f4085,f4178,f4182,f4186,f4238,f4242,f4246,f4250,f4254,f4258,f4262,f4266,f4270,f4275,f4279,f4283,f4287,f4291,f4295,f4299,f4303,f4307,f4311,f4315,f4320,f4324,f4328,f4332,f4336,f4340,f4344,f4383,f4458,f4996,f5000,f5010,f5014,f5018,f5022,f5026,f5030,f5034,f5085,f5317,f5321,f5325,f5329,f5338,f5342,f5346,f5350,f5354,f5358,f5362,f5456,f5666,f5670,f5678,f5682,f5686,f5690,f5694,f5698,f5776,f5886,f5890,f5894,f5898,f5902,f5906,f5910,f5914,f5918,f5922,f5926,f5930,f5934,f5938,f5942,f5946,f6040,f6044,f6048,f6052,f6056,f6060,f6064,f6068,f6195,f6495,f6618,f6835,f6926,f6930,f6934,f6938,f6942,f6943,f7017,f7082,f7086,f7090,f7094,f7098,f7102,f7106,f7110,f7115,f7120,f7124,f7128,f7132,f7136,f7140,f7144,f7148,f7152,f7156,f7161,f7166,f7170,f7174,f7178,f7182,f7443,f7483,f7489,f7495,f7677,f7798,f8220,f8263,f8272,f8460,f8473,f8478,f8489,f8693,f8694,f8698,f8702,f8706,f8710,f8714,f8718,f8722,f8726,f8730,f8742,f8746,f8750,f8754,f8758,f8762,f8766,f8770,f8774,f8778,f8790,f8794,f8798,f8802,f8806,f9018,f9601,f9606,f9610,f9614,f9618,f9622,f9626,f9630,f9634,f9638,f9642,f9647,f10331,f10335,f10339,f10343,f10347,f10351,f10355,f10359,f10363,f10367,f10371,f10379,f10383,f11668,f11672,f11676,f11680,f11684,f11967,f12723,f12727,f12731,f12735,f12739,f12743,f12748,f12752,f12756,f12760,f12764,f12768,f12772,f12776,f12780,f12784,f12789,f12793,f12797,f13659,f14058,f14062,f14066,f14343,f14347,f14351,f14355,f14359,f14363,f14367,f14371,f14375,f14379,f14383,f14387,f14736,f15757]) ).
fof(f15757,plain,
( ~ spl20_190
| ~ spl20_67
| ~ spl20_129 ),
inference(avatar_split_clause,[],[f8296,f1109,f630,f2239]) ).
fof(f2239,plain,
( spl20_190
<=> sK1 = sK2 ),
introduced(avatar_definition,[new_symbols(naming,[spl20_190])]) ).
fof(f630,plain,
( spl20_67
<=> ! [X0] : set_union2(X0,singleton(X0)) != X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl20_67])]) ).
fof(f1109,plain,
( spl20_129
<=> sK1 = set_union2(sK2,singleton(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_129])]) ).
fof(f8296,plain,
( sK1 != sK2
| ~ spl20_67
| ~ spl20_129 ),
inference(superposition,[],[f631,f1111]) ).
fof(f1111,plain,
( sK1 = set_union2(sK2,singleton(sK2))
| ~ spl20_129 ),
inference(avatar_component_clause,[],[f1109]) ).
fof(f631,plain,
( ! [X0] : set_union2(X0,singleton(X0)) != X0
| ~ spl20_67 ),
inference(avatar_component_clause,[],[f630]) ).
fof(f14736,plain,
( ~ spl20_52
| spl20_189
| ~ spl20_129
| ~ spl20_149 ),
inference(avatar_split_clause,[],[f2361,f1309,f1109,f2235,f552]) ).
fof(f552,plain,
( spl20_52
<=> epsilon_transitive(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_52])]) ).
fof(f2235,plain,
( spl20_189
<=> subset(sK2,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_189])]) ).
fof(f1309,plain,
( spl20_149
<=> ! [X0] :
( subset(X0,set_union2(X0,singleton(X0)))
| ~ epsilon_transitive(set_union2(X0,singleton(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_149])]) ).
fof(f2361,plain,
( subset(sK2,sK1)
| ~ epsilon_transitive(sK1)
| ~ spl20_129
| ~ spl20_149 ),
inference(superposition,[],[f1310,f1111]) ).
fof(f1310,plain,
( ! [X0] :
( subset(X0,set_union2(X0,singleton(X0)))
| ~ epsilon_transitive(set_union2(X0,singleton(X0))) )
| ~ spl20_149 ),
inference(avatar_component_clause,[],[f1309]) ).
fof(f14387,plain,
( spl20_496
| ~ spl20_141
| ~ spl20_175 ),
inference(avatar_split_clause,[],[f1864,f1783,f1217,f14385]) ).
fof(f14385,plain,
( spl20_496
<=> ! [X2,X0,X1] :
( subset(sK6(X0,sK4(powerset(X1)),X2),X0)
| in(sK6(X0,sK4(powerset(X1)),X2),X2)
| sP0(X0,sK4(powerset(X1)),X2)
| ~ epsilon_transitive(X0)
| element(sK6(X0,sK4(powerset(X1)),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_496])]) ).
fof(f1217,plain,
( spl20_141
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK4(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_141])]) ).
fof(f1783,plain,
( spl20_175
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| subset(sK6(X0,X1,X2),X0)
| ~ epsilon_transitive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_175])]) ).
fof(f1864,plain,
( ! [X2,X0,X1] :
( subset(sK6(X0,sK4(powerset(X1)),X2),X0)
| in(sK6(X0,sK4(powerset(X1)),X2),X2)
| sP0(X0,sK4(powerset(X1)),X2)
| ~ epsilon_transitive(X0)
| element(sK6(X0,sK4(powerset(X1)),X2),X1) )
| ~ spl20_141
| ~ spl20_175 ),
inference(resolution,[],[f1784,f1218]) ).
fof(f1218,plain,
( ! [X0,X1] :
( ~ in(X0,sK4(powerset(X1)))
| element(X0,X1) )
| ~ spl20_141 ),
inference(avatar_component_clause,[],[f1217]) ).
fof(f1784,plain,
( ! [X2,X0,X1] :
( subset(sK6(X0,X1,X2),X0)
| in(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ epsilon_transitive(X0) )
| ~ spl20_175 ),
inference(avatar_component_clause,[],[f1783]) ).
fof(f14383,plain,
( spl20_495
| ~ spl20_141
| ~ spl20_175 ),
inference(avatar_split_clause,[],[f1854,f1783,f1217,f14381]) ).
fof(f14381,plain,
( spl20_495
<=> ! [X2,X0,X1] :
( subset(sK6(X0,X1,sK4(powerset(X2))),X0)
| in(sK6(X0,X1,sK4(powerset(X2))),X1)
| sP0(X0,X1,sK4(powerset(X2)))
| ~ epsilon_transitive(X0)
| element(sK6(X0,X1,sK4(powerset(X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_495])]) ).
fof(f1854,plain,
( ! [X2,X0,X1] :
( subset(sK6(X0,X1,sK4(powerset(X2))),X0)
| in(sK6(X0,X1,sK4(powerset(X2))),X1)
| sP0(X0,X1,sK4(powerset(X2)))
| ~ epsilon_transitive(X0)
| element(sK6(X0,X1,sK4(powerset(X2))),X2) )
| ~ spl20_141
| ~ spl20_175 ),
inference(resolution,[],[f1784,f1218]) ).
fof(f14379,plain,
( spl20_494
| ~ spl20_141
| ~ spl20_174 ),
inference(avatar_split_clause,[],[f1837,f1779,f1217,f14377]) ).
fof(f14377,plain,
( spl20_494
<=> ! [X2,X0,X1] :
( subset(sK6(sK4(powerset(X0)),X1,X2),X1)
| in(sK6(sK4(powerset(X0)),X1,X2),X2)
| sP0(sK4(powerset(X0)),X1,X2)
| ~ epsilon_transitive(X1)
| element(sK6(sK4(powerset(X0)),X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_494])]) ).
fof(f1779,plain,
( spl20_174
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| subset(sK6(X0,X1,X2),X1)
| ~ epsilon_transitive(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_174])]) ).
fof(f1837,plain,
( ! [X2,X0,X1] :
( subset(sK6(sK4(powerset(X0)),X1,X2),X1)
| in(sK6(sK4(powerset(X0)),X1,X2),X2)
| sP0(sK4(powerset(X0)),X1,X2)
| ~ epsilon_transitive(X1)
| element(sK6(sK4(powerset(X0)),X1,X2),X0) )
| ~ spl20_141
| ~ spl20_174 ),
inference(resolution,[],[f1780,f1218]) ).
fof(f1780,plain,
( ! [X2,X0,X1] :
( subset(sK6(X0,X1,X2),X1)
| in(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ epsilon_transitive(X1) )
| ~ spl20_174 ),
inference(avatar_component_clause,[],[f1779]) ).
fof(f14375,plain,
( spl20_493
| ~ spl20_141
| ~ spl20_174 ),
inference(avatar_split_clause,[],[f1827,f1779,f1217,f14373]) ).
fof(f14373,plain,
( spl20_493
<=> ! [X2,X0,X1] :
( subset(sK6(X0,X1,sK4(powerset(X2))),X1)
| in(sK6(X0,X1,sK4(powerset(X2))),X0)
| sP0(X0,X1,sK4(powerset(X2)))
| ~ epsilon_transitive(X1)
| element(sK6(X0,X1,sK4(powerset(X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_493])]) ).
fof(f1827,plain,
( ! [X2,X0,X1] :
( subset(sK6(X0,X1,sK4(powerset(X2))),X1)
| in(sK6(X0,X1,sK4(powerset(X2))),X0)
| sP0(X0,X1,sK4(powerset(X2)))
| ~ epsilon_transitive(X1)
| element(sK6(X0,X1,sK4(powerset(X2))),X2) )
| ~ spl20_141
| ~ spl20_174 ),
inference(resolution,[],[f1780,f1218]) ).
fof(f14371,plain,
( spl20_492
| ~ spl20_141
| ~ spl20_173 ),
inference(avatar_split_clause,[],[f1808,f1775,f1217,f14369]) ).
fof(f14369,plain,
( spl20_492
<=> ! [X2,X0,X1] :
( subset(sK6(sK4(powerset(X0)),X1,X2),X2)
| in(sK6(sK4(powerset(X0)),X1,X2),X1)
| sP0(sK4(powerset(X0)),X1,X2)
| ~ epsilon_transitive(X2)
| element(sK6(sK4(powerset(X0)),X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_492])]) ).
fof(f1775,plain,
( spl20_173
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X1)
| in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| subset(sK6(X0,X1,X2),X2)
| ~ epsilon_transitive(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_173])]) ).
fof(f1808,plain,
( ! [X2,X0,X1] :
( subset(sK6(sK4(powerset(X0)),X1,X2),X2)
| in(sK6(sK4(powerset(X0)),X1,X2),X1)
| sP0(sK4(powerset(X0)),X1,X2)
| ~ epsilon_transitive(X2)
| element(sK6(sK4(powerset(X0)),X1,X2),X0) )
| ~ spl20_141
| ~ spl20_173 ),
inference(resolution,[],[f1776,f1218]) ).
fof(f1776,plain,
( ! [X2,X0,X1] :
( subset(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X1)
| in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ epsilon_transitive(X2) )
| ~ spl20_173 ),
inference(avatar_component_clause,[],[f1775]) ).
fof(f14367,plain,
( spl20_491
| ~ spl20_141
| ~ spl20_173 ),
inference(avatar_split_clause,[],[f1798,f1775,f1217,f14365]) ).
fof(f14365,plain,
( spl20_491
<=> ! [X2,X0,X1] :
( subset(sK6(X0,sK4(powerset(X1)),X2),X2)
| in(sK6(X0,sK4(powerset(X1)),X2),X0)
| sP0(X0,sK4(powerset(X1)),X2)
| ~ epsilon_transitive(X2)
| element(sK6(X0,sK4(powerset(X1)),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_491])]) ).
fof(f1798,plain,
( ! [X2,X0,X1] :
( subset(sK6(X0,sK4(powerset(X1)),X2),X2)
| in(sK6(X0,sK4(powerset(X1)),X2),X0)
| sP0(X0,sK4(powerset(X1)),X2)
| ~ epsilon_transitive(X2)
| element(sK6(X0,sK4(powerset(X1)),X2),X1) )
| ~ spl20_141
| ~ spl20_173 ),
inference(resolution,[],[f1776,f1218]) ).
fof(f14363,plain,
( spl20_490
| ~ spl20_150
| ~ spl20_165 ),
inference(avatar_split_clause,[],[f1636,f1569,f1313,f14361]) ).
fof(f14361,plain,
( spl20_490
<=> ! [X0,X3,X2,X1] :
( in(sK6(X0,set_union2(X1,X2),X3),X3)
| sP0(X0,set_union2(X1,X2),X3)
| ~ empty(X0)
| in(sK6(X0,set_union2(X1,X2),X3),X1)
| in(sK6(X0,set_union2(X1,X2),X3),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_490])]) ).
fof(f1313,plain,
( spl20_150
<=> ! [X2,X0,X1] :
( in(X0,X1)
| ~ in(X0,set_union2(X1,X2))
| in(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_150])]) ).
fof(f1569,plain,
( spl20_165
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_165])]) ).
fof(f1636,plain,
( ! [X2,X3,X0,X1] :
( in(sK6(X0,set_union2(X1,X2),X3),X3)
| sP0(X0,set_union2(X1,X2),X3)
| ~ empty(X0)
| in(sK6(X0,set_union2(X1,X2),X3),X1)
| in(sK6(X0,set_union2(X1,X2),X3),X2) )
| ~ spl20_150
| ~ spl20_165 ),
inference(resolution,[],[f1570,f1314]) ).
fof(f1314,plain,
( ! [X2,X0,X1] :
( ~ in(X0,set_union2(X1,X2))
| in(X0,X1)
| in(X0,X2) )
| ~ spl20_150 ),
inference(avatar_component_clause,[],[f1313]) ).
fof(f1570,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ empty(X0) )
| ~ spl20_165 ),
inference(avatar_component_clause,[],[f1569]) ).
fof(f14359,plain,
( spl20_489
| ~ spl20_150
| ~ spl20_165 ),
inference(avatar_split_clause,[],[f1626,f1569,f1313,f14357]) ).
fof(f14357,plain,
( spl20_489
<=> ! [X0,X3,X2,X1] :
( in(sK6(X0,X1,set_union2(X2,X3)),X1)
| sP0(X0,X1,set_union2(X2,X3))
| ~ empty(X0)
| in(sK6(X0,X1,set_union2(X2,X3)),X2)
| in(sK6(X0,X1,set_union2(X2,X3)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_489])]) ).
fof(f1626,plain,
( ! [X2,X3,X0,X1] :
( in(sK6(X0,X1,set_union2(X2,X3)),X1)
| sP0(X0,X1,set_union2(X2,X3))
| ~ empty(X0)
| in(sK6(X0,X1,set_union2(X2,X3)),X2)
| in(sK6(X0,X1,set_union2(X2,X3)),X3) )
| ~ spl20_150
| ~ spl20_165 ),
inference(resolution,[],[f1570,f1314]) ).
fof(f14355,plain,
( spl20_488
| ~ spl20_150
| ~ spl20_164 ),
inference(avatar_split_clause,[],[f1613,f1565,f1313,f14353]) ).
fof(f14353,plain,
( spl20_488
<=> ! [X0,X3,X2,X1] :
( in(sK6(set_union2(X0,X1),X2,X3),X3)
| sP0(set_union2(X0,X1),X2,X3)
| ~ empty(X2)
| in(sK6(set_union2(X0,X1),X2,X3),X0)
| in(sK6(set_union2(X0,X1),X2,X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_488])]) ).
fof(f1565,plain,
( spl20_164
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_164])]) ).
fof(f1613,plain,
( ! [X2,X3,X0,X1] :
( in(sK6(set_union2(X0,X1),X2,X3),X3)
| sP0(set_union2(X0,X1),X2,X3)
| ~ empty(X2)
| in(sK6(set_union2(X0,X1),X2,X3),X0)
| in(sK6(set_union2(X0,X1),X2,X3),X1) )
| ~ spl20_150
| ~ spl20_164 ),
inference(resolution,[],[f1566,f1314]) ).
fof(f1566,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ empty(X1) )
| ~ spl20_164 ),
inference(avatar_component_clause,[],[f1565]) ).
fof(f14351,plain,
( spl20_487
| ~ spl20_150
| ~ spl20_164 ),
inference(avatar_split_clause,[],[f1603,f1565,f1313,f14349]) ).
fof(f14349,plain,
( spl20_487
<=> ! [X0,X3,X2,X1] :
( in(sK6(X0,X1,set_union2(X2,X3)),X0)
| sP0(X0,X1,set_union2(X2,X3))
| ~ empty(X1)
| in(sK6(X0,X1,set_union2(X2,X3)),X2)
| in(sK6(X0,X1,set_union2(X2,X3)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_487])]) ).
fof(f1603,plain,
( ! [X2,X3,X0,X1] :
( in(sK6(X0,X1,set_union2(X2,X3)),X0)
| sP0(X0,X1,set_union2(X2,X3))
| ~ empty(X1)
| in(sK6(X0,X1,set_union2(X2,X3)),X2)
| in(sK6(X0,X1,set_union2(X2,X3)),X3) )
| ~ spl20_150
| ~ spl20_164 ),
inference(resolution,[],[f1566,f1314]) ).
fof(f14347,plain,
( spl20_486
| ~ spl20_150
| ~ spl20_163 ),
inference(avatar_split_clause,[],[f1588,f1561,f1313,f14345]) ).
fof(f14345,plain,
( spl20_486
<=> ! [X0,X3,X2,X1] :
( in(sK6(set_union2(X0,X1),X2,X3),X2)
| sP0(set_union2(X0,X1),X2,X3)
| ~ empty(X3)
| in(sK6(set_union2(X0,X1),X2,X3),X0)
| in(sK6(set_union2(X0,X1),X2,X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_486])]) ).
fof(f1561,plain,
( spl20_163
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X1)
| in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_163])]) ).
fof(f1588,plain,
( ! [X2,X3,X0,X1] :
( in(sK6(set_union2(X0,X1),X2,X3),X2)
| sP0(set_union2(X0,X1),X2,X3)
| ~ empty(X3)
| in(sK6(set_union2(X0,X1),X2,X3),X0)
| in(sK6(set_union2(X0,X1),X2,X3),X1) )
| ~ spl20_150
| ~ spl20_163 ),
inference(resolution,[],[f1562,f1314]) ).
fof(f1562,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X1)
| in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ empty(X2) )
| ~ spl20_163 ),
inference(avatar_component_clause,[],[f1561]) ).
fof(f14343,plain,
( spl20_485
| ~ spl20_150
| ~ spl20_163 ),
inference(avatar_split_clause,[],[f1578,f1561,f1313,f14341]) ).
fof(f14341,plain,
( spl20_485
<=> ! [X0,X3,X2,X1] :
( in(sK6(X0,set_union2(X1,X2),X3),X0)
| sP0(X0,set_union2(X1,X2),X3)
| ~ empty(X3)
| in(sK6(X0,set_union2(X1,X2),X3),X1)
| in(sK6(X0,set_union2(X1,X2),X3),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_485])]) ).
fof(f1578,plain,
( ! [X2,X3,X0,X1] :
( in(sK6(X0,set_union2(X1,X2),X3),X0)
| sP0(X0,set_union2(X1,X2),X3)
| ~ empty(X3)
| in(sK6(X0,set_union2(X1,X2),X3),X1)
| in(sK6(X0,set_union2(X1,X2),X3),X2) )
| ~ spl20_150
| ~ spl20_163 ),
inference(resolution,[],[f1562,f1314]) ).
fof(f14066,plain,
( spl20_484
| ~ spl20_89
| ~ spl20_175 ),
inference(avatar_split_clause,[],[f1844,f1783,f808,f14064]) ).
fof(f14064,plain,
( spl20_484
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ epsilon_transitive(X0)
| ordinal_subset(sK6(X0,X1,X2),X0)
| ~ ordinal(X0)
| ~ ordinal(sK6(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_484])]) ).
fof(f808,plain,
( spl20_89
<=> ! [X0,X1] :
( ordinal_subset(X0,X1)
| ~ subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_89])]) ).
fof(f1844,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ epsilon_transitive(X0)
| ordinal_subset(sK6(X0,X1,X2),X0)
| ~ ordinal(X0)
| ~ ordinal(sK6(X0,X1,X2)) )
| ~ spl20_89
| ~ spl20_175 ),
inference(resolution,[],[f1784,f809]) ).
fof(f809,plain,
( ! [X0,X1] :
( ~ subset(X0,X1)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) )
| ~ spl20_89 ),
inference(avatar_component_clause,[],[f808]) ).
fof(f14062,plain,
( spl20_483
| ~ spl20_89
| ~ spl20_174 ),
inference(avatar_split_clause,[],[f1817,f1779,f808,f14060]) ).
fof(f14060,plain,
( spl20_483
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ epsilon_transitive(X1)
| ordinal_subset(sK6(X0,X1,X2),X1)
| ~ ordinal(X1)
| ~ ordinal(sK6(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_483])]) ).
fof(f1817,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ epsilon_transitive(X1)
| ordinal_subset(sK6(X0,X1,X2),X1)
| ~ ordinal(X1)
| ~ ordinal(sK6(X0,X1,X2)) )
| ~ spl20_89
| ~ spl20_174 ),
inference(resolution,[],[f1780,f809]) ).
fof(f14058,plain,
( spl20_482
| ~ spl20_89
| ~ spl20_173 ),
inference(avatar_split_clause,[],[f1788,f1775,f808,f14056]) ).
fof(f14056,plain,
( spl20_482
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X1)
| in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ epsilon_transitive(X2)
| ordinal_subset(sK6(X0,X1,X2),X2)
| ~ ordinal(X2)
| ~ ordinal(sK6(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_482])]) ).
fof(f1788,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X1)
| in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ epsilon_transitive(X2)
| ordinal_subset(sK6(X0,X1,X2),X2)
| ~ ordinal(X2)
| ~ ordinal(sK6(X0,X1,X2)) )
| ~ spl20_89
| ~ spl20_173 ),
inference(resolution,[],[f1776,f809]) ).
fof(f13659,plain,
( ~ spl20_481
| ~ spl20_126
| spl20_368 ),
inference(avatar_split_clause,[],[f7672,f6615,f1097,f13656]) ).
fof(f13656,plain,
( spl20_481
<=> sK1 = singleton(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_481])]) ).
fof(f1097,plain,
( spl20_126
<=> ! [X0] : set_union2(sK8,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl20_126])]) ).
fof(f6615,plain,
( spl20_368
<=> sK1 = set_union2(sK8,singleton(sK8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_368])]) ).
fof(f7672,plain,
( sK1 != singleton(sK8)
| ~ spl20_126
| spl20_368 ),
inference(superposition,[],[f6616,f1098]) ).
fof(f1098,plain,
( ! [X0] : set_union2(sK8,X0) = X0
| ~ spl20_126 ),
inference(avatar_component_clause,[],[f1097]) ).
fof(f6616,plain,
( sK1 != set_union2(sK8,singleton(sK8))
| spl20_368 ),
inference(avatar_component_clause,[],[f6615]) ).
fof(f12797,plain,
( spl20_480
| ~ spl20_80
| ~ spl20_177 ),
inference(avatar_split_clause,[],[f1924,f1874,f727,f12795]) ).
fof(f12795,plain,
( spl20_480
<=> ! [X2,X0,X1] :
( in(sK6(singleton(X0),singleton(X1),X2),X2)
| sP0(singleton(X0),singleton(X1),X2)
| sK6(singleton(X0),singleton(X1),X2) = X1
| sK6(singleton(X0),singleton(X1),X2) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_480])]) ).
fof(f727,plain,
( spl20_80
<=> ! [X0,X3] :
( X0 = X3
| ~ in(X3,singleton(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_80])]) ).
fof(f1874,plain,
( spl20_177
<=> ! [X2,X0,X1] :
( in(sK6(X0,singleton(X1),X2),X2)
| in(sK6(X0,singleton(X1),X2),X0)
| sP0(X0,singleton(X1),X2)
| sK6(X0,singleton(X1),X2) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_177])]) ).
fof(f1924,plain,
( ! [X2,X0,X1] :
( in(sK6(singleton(X0),singleton(X1),X2),X2)
| sP0(singleton(X0),singleton(X1),X2)
| sK6(singleton(X0),singleton(X1),X2) = X1
| sK6(singleton(X0),singleton(X1),X2) = X0 )
| ~ spl20_80
| ~ spl20_177 ),
inference(resolution,[],[f1875,f728]) ).
fof(f728,plain,
( ! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 )
| ~ spl20_80 ),
inference(avatar_component_clause,[],[f727]) ).
fof(f1875,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,singleton(X1),X2),X2)
| in(sK6(X0,singleton(X1),X2),X0)
| sP0(X0,singleton(X1),X2)
| sK6(X0,singleton(X1),X2) = X1 )
| ~ spl20_177 ),
inference(avatar_component_clause,[],[f1874]) ).
fof(f12793,plain,
( spl20_479
| ~ spl20_80
| ~ spl20_176 ),
inference(avatar_split_clause,[],[f1899,f1870,f727,f12791]) ).
fof(f12791,plain,
( spl20_479
<=> ! [X2,X0,X1] :
( in(sK6(singleton(X0),X1,singleton(X2)),X1)
| sP0(singleton(X0),X1,singleton(X2))
| sK6(singleton(X0),X1,singleton(X2)) = X2
| sK6(singleton(X0),X1,singleton(X2)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_479])]) ).
fof(f1870,plain,
( spl20_176
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,singleton(X2)),X1)
| in(sK6(X0,X1,singleton(X2)),X0)
| sP0(X0,X1,singleton(X2))
| sK6(X0,X1,singleton(X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_176])]) ).
fof(f1899,plain,
( ! [X2,X0,X1] :
( in(sK6(singleton(X0),X1,singleton(X2)),X1)
| sP0(singleton(X0),X1,singleton(X2))
| sK6(singleton(X0),X1,singleton(X2)) = X2
| sK6(singleton(X0),X1,singleton(X2)) = X0 )
| ~ spl20_80
| ~ spl20_176 ),
inference(resolution,[],[f1871,f728]) ).
fof(f1871,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,singleton(X2)),X1)
| in(sK6(X0,X1,singleton(X2)),X0)
| sP0(X0,X1,singleton(X2))
| sK6(X0,X1,singleton(X2)) = X2 )
| ~ spl20_176 ),
inference(avatar_component_clause,[],[f1870]) ).
fof(f12789,plain,
( ~ spl20_478
| ~ spl20_129
| ~ spl20_205 ),
inference(avatar_split_clause,[],[f2515,f2430,f1109,f12786]) ).
fof(f12786,plain,
( spl20_478
<=> in(singleton(sK1),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_478])]) ).
fof(f2430,plain,
( spl20_205
<=> ! [X0,X1] : ~ in(singleton(set_union2(X0,X1)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_205])]) ).
fof(f2515,plain,
( ~ in(singleton(sK1),sK2)
| ~ spl20_129
| ~ spl20_205 ),
inference(superposition,[],[f2431,f1111]) ).
fof(f2431,plain,
( ! [X0,X1] : ~ in(singleton(set_union2(X0,X1)),X0)
| ~ spl20_205 ),
inference(avatar_component_clause,[],[f2430]) ).
fof(f12784,plain,
( spl20_477
| ~ spl20_80
| ~ spl20_176 ),
inference(avatar_split_clause,[],[f1889,f1870,f727,f12782]) ).
fof(f12782,plain,
( spl20_477
<=> ! [X2,X0,X1] :
( in(sK6(X0,singleton(X1),singleton(X2)),X0)
| sP0(X0,singleton(X1),singleton(X2))
| sK6(X0,singleton(X1),singleton(X2)) = X2
| sK6(X0,singleton(X1),singleton(X2)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_477])]) ).
fof(f1889,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,singleton(X1),singleton(X2)),X0)
| sP0(X0,singleton(X1),singleton(X2))
| sK6(X0,singleton(X1),singleton(X2)) = X2
| sK6(X0,singleton(X1),singleton(X2)) = X1 )
| ~ spl20_80
| ~ spl20_176 ),
inference(resolution,[],[f1871,f728]) ).
fof(f12780,plain,
( spl20_476
| ~ spl20_84
| ~ spl20_175 ),
inference(avatar_split_clause,[],[f1845,f1783,f784,f12778]) ).
fof(f12778,plain,
( spl20_476
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ epsilon_transitive(X0)
| sK6(X0,X1,X2) = X0
| ~ subset(X0,sK6(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_476])]) ).
fof(f784,plain,
( spl20_84
<=> ! [X0,X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_84])]) ).
fof(f1845,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ epsilon_transitive(X0)
| sK6(X0,X1,X2) = X0
| ~ subset(X0,sK6(X0,X1,X2)) )
| ~ spl20_84
| ~ spl20_175 ),
inference(resolution,[],[f1784,f785]) ).
fof(f785,plain,
( ! [X0,X1] :
( ~ subset(X1,X0)
| X0 = X1
| ~ subset(X0,X1) )
| ~ spl20_84 ),
inference(avatar_component_clause,[],[f784]) ).
fof(f12776,plain,
( spl20_475
| ~ spl20_84
| ~ spl20_174 ),
inference(avatar_split_clause,[],[f1818,f1779,f784,f12774]) ).
fof(f12774,plain,
( spl20_475
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ epsilon_transitive(X1)
| sK6(X0,X1,X2) = X1
| ~ subset(X1,sK6(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_475])]) ).
fof(f1818,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ epsilon_transitive(X1)
| sK6(X0,X1,X2) = X1
| ~ subset(X1,sK6(X0,X1,X2)) )
| ~ spl20_84
| ~ spl20_174 ),
inference(resolution,[],[f1780,f785]) ).
fof(f12772,plain,
( spl20_474
| ~ spl20_84
| ~ spl20_173 ),
inference(avatar_split_clause,[],[f1789,f1775,f784,f12770]) ).
fof(f12770,plain,
( spl20_474
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X1)
| in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ epsilon_transitive(X2)
| sK6(X0,X1,X2) = X2
| ~ subset(X2,sK6(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_474])]) ).
fof(f1789,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X1)
| in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ epsilon_transitive(X2)
| sK6(X0,X1,X2) = X2
| ~ subset(X2,sK6(X0,X1,X2)) )
| ~ spl20_84
| ~ spl20_173 ),
inference(resolution,[],[f1776,f785]) ).
fof(f12768,plain,
( spl20_473
| ~ spl20_141
| ~ spl20_171 ),
inference(avatar_split_clause,[],[f1763,f1665,f1217,f12766]) ).
fof(f12766,plain,
( spl20_473
<=> ! [X2,X0,X1] :
( element(sK6(X0,sK4(powerset(X1)),X2),X0)
| in(sK6(X0,sK4(powerset(X1)),X2),X2)
| sP0(X0,sK4(powerset(X1)),X2)
| element(sK6(X0,sK4(powerset(X1)),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_473])]) ).
fof(f1665,plain,
( spl20_171
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| element(sK6(X0,X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_171])]) ).
fof(f1763,plain,
( ! [X2,X0,X1] :
( element(sK6(X0,sK4(powerset(X1)),X2),X0)
| in(sK6(X0,sK4(powerset(X1)),X2),X2)
| sP0(X0,sK4(powerset(X1)),X2)
| element(sK6(X0,sK4(powerset(X1)),X2),X1) )
| ~ spl20_141
| ~ spl20_171 ),
inference(resolution,[],[f1666,f1218]) ).
fof(f1666,plain,
( ! [X2,X0,X1] :
( element(sK6(X0,X1,X2),X0)
| in(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2) )
| ~ spl20_171 ),
inference(avatar_component_clause,[],[f1665]) ).
fof(f12764,plain,
( spl20_472
| ~ spl20_141
| ~ spl20_171 ),
inference(avatar_split_clause,[],[f1753,f1665,f1217,f12762]) ).
fof(f12762,plain,
( spl20_472
<=> ! [X2,X0,X1] :
( element(sK6(X0,X1,sK4(powerset(X2))),X0)
| in(sK6(X0,X1,sK4(powerset(X2))),X1)
| sP0(X0,X1,sK4(powerset(X2)))
| element(sK6(X0,X1,sK4(powerset(X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_472])]) ).
fof(f1753,plain,
( ! [X2,X0,X1] :
( element(sK6(X0,X1,sK4(powerset(X2))),X0)
| in(sK6(X0,X1,sK4(powerset(X2))),X1)
| sP0(X0,X1,sK4(powerset(X2)))
| element(sK6(X0,X1,sK4(powerset(X2))),X2) )
| ~ spl20_141
| ~ spl20_171 ),
inference(resolution,[],[f1666,f1218]) ).
fof(f12760,plain,
( spl20_471
| ~ spl20_141
| ~ spl20_169 ),
inference(avatar_split_clause,[],[f1729,f1657,f1217,f12758]) ).
fof(f12758,plain,
( spl20_471
<=> ! [X2,X0,X1] :
( element(sK6(sK4(powerset(X0)),X1,X2),X1)
| in(sK6(sK4(powerset(X0)),X1,X2),X2)
| sP0(sK4(powerset(X0)),X1,X2)
| element(sK6(sK4(powerset(X0)),X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_471])]) ).
fof(f1657,plain,
( spl20_169
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| element(sK6(X0,X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_169])]) ).
fof(f1729,plain,
( ! [X2,X0,X1] :
( element(sK6(sK4(powerset(X0)),X1,X2),X1)
| in(sK6(sK4(powerset(X0)),X1,X2),X2)
| sP0(sK4(powerset(X0)),X1,X2)
| element(sK6(sK4(powerset(X0)),X1,X2),X0) )
| ~ spl20_141
| ~ spl20_169 ),
inference(resolution,[],[f1658,f1218]) ).
fof(f1658,plain,
( ! [X2,X0,X1] :
( element(sK6(X0,X1,X2),X1)
| in(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2) )
| ~ spl20_169 ),
inference(avatar_component_clause,[],[f1657]) ).
fof(f12756,plain,
( spl20_470
| ~ spl20_141
| ~ spl20_169 ),
inference(avatar_split_clause,[],[f1719,f1657,f1217,f12754]) ).
fof(f12754,plain,
( spl20_470
<=> ! [X2,X0,X1] :
( element(sK6(X0,X1,sK4(powerset(X2))),X1)
| in(sK6(X0,X1,sK4(powerset(X2))),X0)
| sP0(X0,X1,sK4(powerset(X2)))
| element(sK6(X0,X1,sK4(powerset(X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_470])]) ).
fof(f1719,plain,
( ! [X2,X0,X1] :
( element(sK6(X0,X1,sK4(powerset(X2))),X1)
| in(sK6(X0,X1,sK4(powerset(X2))),X0)
| sP0(X0,X1,sK4(powerset(X2)))
| element(sK6(X0,X1,sK4(powerset(X2))),X2) )
| ~ spl20_141
| ~ spl20_169 ),
inference(resolution,[],[f1658,f1218]) ).
fof(f12752,plain,
( spl20_469
| ~ spl20_141
| ~ spl20_167 ),
inference(avatar_split_clause,[],[f1694,f1649,f1217,f12750]) ).
fof(f12750,plain,
( spl20_469
<=> ! [X2,X0,X1] :
( element(sK6(sK4(powerset(X0)),X1,X2),X2)
| in(sK6(sK4(powerset(X0)),X1,X2),X1)
| sP0(sK4(powerset(X0)),X1,X2)
| element(sK6(sK4(powerset(X0)),X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_469])]) ).
fof(f1649,plain,
( spl20_167
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X1)
| in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| element(sK6(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_167])]) ).
fof(f1694,plain,
( ! [X2,X0,X1] :
( element(sK6(sK4(powerset(X0)),X1,X2),X2)
| in(sK6(sK4(powerset(X0)),X1,X2),X1)
| sP0(sK4(powerset(X0)),X1,X2)
| element(sK6(sK4(powerset(X0)),X1,X2),X0) )
| ~ spl20_141
| ~ spl20_167 ),
inference(resolution,[],[f1650,f1218]) ).
fof(f1650,plain,
( ! [X2,X0,X1] :
( element(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X1)
| in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2) )
| ~ spl20_167 ),
inference(avatar_component_clause,[],[f1649]) ).
fof(f12748,plain,
( spl20_468
| ~ spl20_141
| ~ spl20_167 ),
inference(avatar_split_clause,[],[f1684,f1649,f1217,f12746]) ).
fof(f12746,plain,
( spl20_468
<=> ! [X2,X0,X1] :
( element(sK6(X0,sK4(powerset(X1)),X2),X2)
| in(sK6(X0,sK4(powerset(X1)),X2),X0)
| sP0(X0,sK4(powerset(X1)),X2)
| element(sK6(X0,sK4(powerset(X1)),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_468])]) ).
fof(f1684,plain,
( ! [X2,X0,X1] :
( element(sK6(X0,sK4(powerset(X1)),X2),X2)
| in(sK6(X0,sK4(powerset(X1)),X2),X0)
| sP0(X0,sK4(powerset(X1)),X2)
| element(sK6(X0,sK4(powerset(X1)),X2),X1) )
| ~ spl20_141
| ~ spl20_167 ),
inference(resolution,[],[f1650,f1218]) ).
fof(f12743,plain,
( spl20_467
| ~ spl20_150
| ~ spl20_161 ),
inference(avatar_split_clause,[],[f1518,f1446,f1313,f12741]) ).
fof(f12741,plain,
( spl20_467
<=> ! [X2,X0,X1] :
( in(sK6(X0,X0,set_union2(X1,X2)),X0)
| sP0(X0,X0,set_union2(X1,X2))
| in(sK6(X0,X0,set_union2(X1,X2)),X1)
| in(sK6(X0,X0,set_union2(X1,X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_467])]) ).
fof(f1446,plain,
( spl20_161
<=> ! [X4,X5] :
( in(sK6(X4,X4,X5),X5)
| in(sK6(X4,X4,X5),X4)
| sP0(X4,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_161])]) ).
fof(f1518,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X0,set_union2(X1,X2)),X0)
| sP0(X0,X0,set_union2(X1,X2))
| in(sK6(X0,X0,set_union2(X1,X2)),X1)
| in(sK6(X0,X0,set_union2(X1,X2)),X2) )
| ~ spl20_150
| ~ spl20_161 ),
inference(resolution,[],[f1447,f1314]) ).
fof(f1447,plain,
( ! [X4,X5] :
( in(sK6(X4,X4,X5),X5)
| in(sK6(X4,X4,X5),X4)
| sP0(X4,X4,X5) )
| ~ spl20_161 ),
inference(avatar_component_clause,[],[f1446]) ).
fof(f12739,plain,
( spl20_466
| ~ spl20_150
| ~ spl20_160 ),
inference(avatar_split_clause,[],[f1495,f1442,f1313,f12737]) ).
fof(f12737,plain,
( spl20_466
<=> ! [X2,X0,X1] :
( in(sK6(X0,set_union2(X1,X2),X0),X0)
| sP0(X0,set_union2(X1,X2),X0)
| in(sK6(X0,set_union2(X1,X2),X0),X1)
| in(sK6(X0,set_union2(X1,X2),X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_466])]) ).
fof(f1442,plain,
( spl20_160
<=> ! [X2,X3] :
( in(sK6(X2,X3,X2),X2)
| in(sK6(X2,X3,X2),X3)
| sP0(X2,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_160])]) ).
fof(f1495,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,set_union2(X1,X2),X0),X0)
| sP0(X0,set_union2(X1,X2),X0)
| in(sK6(X0,set_union2(X1,X2),X0),X1)
| in(sK6(X0,set_union2(X1,X2),X0),X2) )
| ~ spl20_150
| ~ spl20_160 ),
inference(resolution,[],[f1443,f1314]) ).
fof(f1443,plain,
( ! [X2,X3] :
( in(sK6(X2,X3,X2),X3)
| in(sK6(X2,X3,X2),X2)
| sP0(X2,X3,X2) )
| ~ spl20_160 ),
inference(avatar_component_clause,[],[f1442]) ).
fof(f12735,plain,
( spl20_465
| ~ spl20_150
| ~ spl20_159 ),
inference(avatar_split_clause,[],[f1480,f1438,f1313,f12733]) ).
fof(f12733,plain,
( spl20_465
<=> ! [X2,X0,X1] :
( in(sK6(set_union2(X0,X1),X2,X2),X2)
| sP0(set_union2(X0,X1),X2,X2)
| in(sK6(set_union2(X0,X1),X2,X2),X0)
| in(sK6(set_union2(X0,X1),X2,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_465])]) ).
fof(f1438,plain,
( spl20_159
<=> ! [X0,X1] :
( in(sK6(X0,X1,X1),X1)
| in(sK6(X0,X1,X1),X0)
| sP0(X0,X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_159])]) ).
fof(f1480,plain,
( ! [X2,X0,X1] :
( in(sK6(set_union2(X0,X1),X2,X2),X2)
| sP0(set_union2(X0,X1),X2,X2)
| in(sK6(set_union2(X0,X1),X2,X2),X0)
| in(sK6(set_union2(X0,X1),X2,X2),X1) )
| ~ spl20_150
| ~ spl20_159 ),
inference(resolution,[],[f1439,f1314]) ).
fof(f1439,plain,
( ! [X0,X1] :
( in(sK6(X0,X1,X1),X1)
| in(sK6(X0,X1,X1),X0)
| sP0(X0,X1,X1) )
| ~ spl20_159 ),
inference(avatar_component_clause,[],[f1438]) ).
fof(f12731,plain,
( spl20_464
| ~ spl20_101
| ~ spl20_141 ),
inference(avatar_split_clause,[],[f1239,f1217,f900,f12729]) ).
fof(f12729,plain,
( spl20_464
<=> ! [X2,X0,X1] :
( element(sK6(sK4(powerset(X0)),X1,X2),X0)
| in(sK6(sK4(powerset(X0)),X1,X2),X2)
| in(sK6(sK4(powerset(X0)),X1,X2),X1)
| sP0(sK4(powerset(X0)),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_464])]) ).
fof(f900,plain,
( spl20_101
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(sK6(X0,X1,X2),X0)
| in(sK6(X0,X1,X2),X1)
| in(sK6(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_101])]) ).
fof(f1239,plain,
( ! [X2,X0,X1] :
( element(sK6(sK4(powerset(X0)),X1,X2),X0)
| in(sK6(sK4(powerset(X0)),X1,X2),X2)
| in(sK6(sK4(powerset(X0)),X1,X2),X1)
| sP0(sK4(powerset(X0)),X1,X2) )
| ~ spl20_101
| ~ spl20_141 ),
inference(resolution,[],[f1218,f901]) ).
fof(f901,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X1)
| in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2) )
| ~ spl20_101 ),
inference(avatar_component_clause,[],[f900]) ).
fof(f12727,plain,
( spl20_463
| ~ spl20_101
| ~ spl20_141 ),
inference(avatar_split_clause,[],[f1238,f1217,f900,f12725]) ).
fof(f12725,plain,
( spl20_463
<=> ! [X2,X0,X1] :
( element(sK6(X0,sK4(powerset(X1)),X2),X1)
| in(sK6(X0,sK4(powerset(X1)),X2),X2)
| in(sK6(X0,sK4(powerset(X1)),X2),X0)
| sP0(X0,sK4(powerset(X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_463])]) ).
fof(f1238,plain,
( ! [X2,X0,X1] :
( element(sK6(X0,sK4(powerset(X1)),X2),X1)
| in(sK6(X0,sK4(powerset(X1)),X2),X2)
| in(sK6(X0,sK4(powerset(X1)),X2),X0)
| sP0(X0,sK4(powerset(X1)),X2) )
| ~ spl20_101
| ~ spl20_141 ),
inference(resolution,[],[f1218,f901]) ).
fof(f12723,plain,
( spl20_462
| ~ spl20_101
| ~ spl20_141 ),
inference(avatar_split_clause,[],[f1237,f1217,f900,f12721]) ).
fof(f12721,plain,
( spl20_462
<=> ! [X2,X0,X1] :
( element(sK6(X0,X1,sK4(powerset(X2))),X2)
| in(sK6(X0,X1,sK4(powerset(X2))),X1)
| in(sK6(X0,X1,sK4(powerset(X2))),X0)
| sP0(X0,X1,sK4(powerset(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_462])]) ).
fof(f1237,plain,
( ! [X2,X0,X1] :
( element(sK6(X0,X1,sK4(powerset(X2))),X2)
| in(sK6(X0,X1,sK4(powerset(X2))),X1)
| in(sK6(X0,X1,sK4(powerset(X2))),X0)
| sP0(X0,X1,sK4(powerset(X2))) )
| ~ spl20_101
| ~ spl20_141 ),
inference(resolution,[],[f1218,f901]) ).
fof(f11967,plain,
( spl20_461
| ~ spl20_186
| ~ spl20_219 ),
inference(avatar_split_clause,[],[f8780,f2602,f2139,f11964]) ).
fof(f11964,plain,
( spl20_461
<=> element(sK2,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_461])]) ).
fof(f2139,plain,
( spl20_186
<=> ! [X0] :
( ~ in(X0,sK1)
| element(X0,sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_186])]) ).
fof(f2602,plain,
( spl20_219
<=> in(sK2,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_219])]) ).
fof(f8780,plain,
( element(sK2,sK2)
| ~ spl20_186
| ~ spl20_219 ),
inference(resolution,[],[f2604,f2140]) ).
fof(f2140,plain,
( ! [X0] :
( ~ in(X0,sK1)
| element(X0,sK2) )
| ~ spl20_186 ),
inference(avatar_component_clause,[],[f2139]) ).
fof(f2604,plain,
( in(sK2,sK1)
| ~ spl20_219 ),
inference(avatar_component_clause,[],[f2602]) ).
fof(f11684,plain,
( spl20_460
| ~ spl20_90
| ~ spl20_171 ),
inference(avatar_split_clause,[],[f1741,f1665,f812,f11682]) ).
fof(f11682,plain,
( spl20_460
<=> ! [X0,X3,X2,X1] :
( in(sK6(powerset(X0),X1,X2),X2)
| in(sK6(powerset(X0),X1,X2),X1)
| sP0(powerset(X0),X1,X2)
| element(X3,X0)
| ~ in(X3,sK6(powerset(X0),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_460])]) ).
fof(f812,plain,
( spl20_90
<=> ! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_90])]) ).
fof(f1741,plain,
( ! [X2,X3,X0,X1] :
( in(sK6(powerset(X0),X1,X2),X2)
| in(sK6(powerset(X0),X1,X2),X1)
| sP0(powerset(X0),X1,X2)
| element(X3,X0)
| ~ in(X3,sK6(powerset(X0),X1,X2)) )
| ~ spl20_90
| ~ spl20_171 ),
inference(resolution,[],[f1666,f813]) ).
fof(f813,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| element(X0,X2)
| ~ in(X0,X1) )
| ~ spl20_90 ),
inference(avatar_component_clause,[],[f812]) ).
fof(f11680,plain,
( spl20_459
| ~ spl20_90
| ~ spl20_169 ),
inference(avatar_split_clause,[],[f1707,f1657,f812,f11678]) ).
fof(f11678,plain,
( spl20_459
<=> ! [X0,X3,X2,X1] :
( in(sK6(X0,powerset(X1),X2),X2)
| in(sK6(X0,powerset(X1),X2),X0)
| sP0(X0,powerset(X1),X2)
| element(X3,X1)
| ~ in(X3,sK6(X0,powerset(X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_459])]) ).
fof(f1707,plain,
( ! [X2,X3,X0,X1] :
( in(sK6(X0,powerset(X1),X2),X2)
| in(sK6(X0,powerset(X1),X2),X0)
| sP0(X0,powerset(X1),X2)
| element(X3,X1)
| ~ in(X3,sK6(X0,powerset(X1),X2)) )
| ~ spl20_90
| ~ spl20_169 ),
inference(resolution,[],[f1658,f813]) ).
fof(f11676,plain,
( spl20_458
| ~ spl20_90
| ~ spl20_167 ),
inference(avatar_split_clause,[],[f1672,f1649,f812,f11674]) ).
fof(f11674,plain,
( spl20_458
<=> ! [X0,X3,X2,X1] :
( in(sK6(X0,X1,powerset(X2)),X1)
| in(sK6(X0,X1,powerset(X2)),X0)
| sP0(X0,X1,powerset(X2))
| element(X3,X2)
| ~ in(X3,sK6(X0,X1,powerset(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_458])]) ).
fof(f1672,plain,
( ! [X2,X3,X0,X1] :
( in(sK6(X0,X1,powerset(X2)),X1)
| in(sK6(X0,X1,powerset(X2)),X0)
| sP0(X0,X1,powerset(X2))
| element(X3,X2)
| ~ in(X3,sK6(X0,X1,powerset(X2))) )
| ~ spl20_90
| ~ spl20_167 ),
inference(resolution,[],[f1650,f813]) ).
fof(f11672,plain,
( spl20_457
| ~ spl20_98
| ~ spl20_153 ),
inference(avatar_split_clause,[],[f1392,f1376,f880,f11670]) ).
fof(f11670,plain,
( spl20_457
<=> ! [X2,X0,X1] :
( sK6(X1,X2,X0) = X0
| ~ ordinal(X0)
| ~ ordinal(sK6(X1,X2,X0))
| element(X0,sK6(X1,X2,X0))
| ~ in(sK6(X1,X2,X0),X2)
| sP0(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_457])]) ).
fof(f880,plain,
( spl20_98
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ in(sK6(X0,X1,X2),X1)
| ~ in(sK6(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_98])]) ).
fof(f1376,plain,
( spl20_153
<=> ! [X0,X1] :
( in(X1,X0)
| X0 = X1
| ~ ordinal(X0)
| ~ ordinal(X1)
| element(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_153])]) ).
fof(f1392,plain,
( ! [X2,X0,X1] :
( sK6(X1,X2,X0) = X0
| ~ ordinal(X0)
| ~ ordinal(sK6(X1,X2,X0))
| element(X0,sK6(X1,X2,X0))
| ~ in(sK6(X1,X2,X0),X2)
| sP0(X1,X2,X0) )
| ~ spl20_98
| ~ spl20_153 ),
inference(resolution,[],[f1377,f881]) ).
fof(f881,plain,
( ! [X2,X0,X1] :
( ~ in(sK6(X0,X1,X2),X2)
| ~ in(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2) )
| ~ spl20_98 ),
inference(avatar_component_clause,[],[f880]) ).
fof(f1377,plain,
( ! [X0,X1] :
( in(X1,X0)
| X0 = X1
| ~ ordinal(X0)
| ~ ordinal(X1)
| element(X0,X1) )
| ~ spl20_153 ),
inference(avatar_component_clause,[],[f1376]) ).
fof(f11668,plain,
( spl20_456
| ~ spl20_99
| ~ spl20_153 ),
inference(avatar_split_clause,[],[f1391,f1376,f884,f11666]) ).
fof(f11666,plain,
( spl20_456
<=> ! [X2,X0,X1] :
( sK6(X1,X2,X0) = X0
| ~ ordinal(X0)
| ~ ordinal(sK6(X1,X2,X0))
| element(X0,sK6(X1,X2,X0))
| ~ in(sK6(X1,X2,X0),X1)
| sP0(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_456])]) ).
fof(f884,plain,
( spl20_99
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ in(sK6(X0,X1,X2),X0)
| ~ in(sK6(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_99])]) ).
fof(f1391,plain,
( ! [X2,X0,X1] :
( sK6(X1,X2,X0) = X0
| ~ ordinal(X0)
| ~ ordinal(sK6(X1,X2,X0))
| element(X0,sK6(X1,X2,X0))
| ~ in(sK6(X1,X2,X0),X1)
| sP0(X1,X2,X0) )
| ~ spl20_99
| ~ spl20_153 ),
inference(resolution,[],[f1377,f885]) ).
fof(f885,plain,
( ! [X2,X0,X1] :
( ~ in(sK6(X0,X1,X2),X2)
| ~ in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2) )
| ~ spl20_99 ),
inference(avatar_component_clause,[],[f884]) ).
fof(f10383,plain,
( spl20_455
| ~ spl20_80
| ~ spl20_175 ),
inference(avatar_split_clause,[],[f1863,f1783,f727,f10381]) ).
fof(f10381,plain,
( spl20_455
<=> ! [X2,X0,X1] :
( subset(sK6(X0,singleton(X1),X2),X0)
| in(sK6(X0,singleton(X1),X2),X2)
| sP0(X0,singleton(X1),X2)
| ~ epsilon_transitive(X0)
| sK6(X0,singleton(X1),X2) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_455])]) ).
fof(f1863,plain,
( ! [X2,X0,X1] :
( subset(sK6(X0,singleton(X1),X2),X0)
| in(sK6(X0,singleton(X1),X2),X2)
| sP0(X0,singleton(X1),X2)
| ~ epsilon_transitive(X0)
| sK6(X0,singleton(X1),X2) = X1 )
| ~ spl20_80
| ~ spl20_175 ),
inference(resolution,[],[f1784,f728]) ).
fof(f10379,plain,
( spl20_454
| ~ spl20_80
| ~ spl20_175 ),
inference(avatar_split_clause,[],[f1853,f1783,f727,f10377]) ).
fof(f10377,plain,
( spl20_454
<=> ! [X2,X0,X1] :
( subset(sK6(X0,X1,singleton(X2)),X0)
| in(sK6(X0,X1,singleton(X2)),X1)
| sP0(X0,X1,singleton(X2))
| ~ epsilon_transitive(X0)
| sK6(X0,X1,singleton(X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_454])]) ).
fof(f1853,plain,
( ! [X2,X0,X1] :
( subset(sK6(X0,X1,singleton(X2)),X0)
| in(sK6(X0,X1,singleton(X2)),X1)
| sP0(X0,X1,singleton(X2))
| ~ epsilon_transitive(X0)
| sK6(X0,X1,singleton(X2)) = X2 )
| ~ spl20_80
| ~ spl20_175 ),
inference(resolution,[],[f1784,f728]) ).
fof(f10371,plain,
( spl20_453
| ~ spl20_80
| ~ spl20_174 ),
inference(avatar_split_clause,[],[f1836,f1779,f727,f10369]) ).
fof(f10369,plain,
( spl20_453
<=> ! [X2,X0,X1] :
( subset(sK6(singleton(X0),X1,X2),X1)
| in(sK6(singleton(X0),X1,X2),X2)
| sP0(singleton(X0),X1,X2)
| ~ epsilon_transitive(X1)
| sK6(singleton(X0),X1,X2) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_453])]) ).
fof(f1836,plain,
( ! [X2,X0,X1] :
( subset(sK6(singleton(X0),X1,X2),X1)
| in(sK6(singleton(X0),X1,X2),X2)
| sP0(singleton(X0),X1,X2)
| ~ epsilon_transitive(X1)
| sK6(singleton(X0),X1,X2) = X0 )
| ~ spl20_80
| ~ spl20_174 ),
inference(resolution,[],[f1780,f728]) ).
fof(f10367,plain,
( spl20_452
| ~ spl20_80
| ~ spl20_174 ),
inference(avatar_split_clause,[],[f1826,f1779,f727,f10365]) ).
fof(f10365,plain,
( spl20_452
<=> ! [X2,X0,X1] :
( subset(sK6(X0,X1,singleton(X2)),X1)
| in(sK6(X0,X1,singleton(X2)),X0)
| sP0(X0,X1,singleton(X2))
| ~ epsilon_transitive(X1)
| sK6(X0,X1,singleton(X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_452])]) ).
fof(f1826,plain,
( ! [X2,X0,X1] :
( subset(sK6(X0,X1,singleton(X2)),X1)
| in(sK6(X0,X1,singleton(X2)),X0)
| sP0(X0,X1,singleton(X2))
| ~ epsilon_transitive(X1)
| sK6(X0,X1,singleton(X2)) = X2 )
| ~ spl20_80
| ~ spl20_174 ),
inference(resolution,[],[f1780,f728]) ).
fof(f10363,plain,
( spl20_451
| ~ spl20_80
| ~ spl20_173 ),
inference(avatar_split_clause,[],[f1807,f1775,f727,f10361]) ).
fof(f10361,plain,
( spl20_451
<=> ! [X2,X0,X1] :
( subset(sK6(singleton(X0),X1,X2),X2)
| in(sK6(singleton(X0),X1,X2),X1)
| sP0(singleton(X0),X1,X2)
| ~ epsilon_transitive(X2)
| sK6(singleton(X0),X1,X2) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_451])]) ).
fof(f1807,plain,
( ! [X2,X0,X1] :
( subset(sK6(singleton(X0),X1,X2),X2)
| in(sK6(singleton(X0),X1,X2),X1)
| sP0(singleton(X0),X1,X2)
| ~ epsilon_transitive(X2)
| sK6(singleton(X0),X1,X2) = X0 )
| ~ spl20_80
| ~ spl20_173 ),
inference(resolution,[],[f1776,f728]) ).
fof(f10359,plain,
( spl20_450
| ~ spl20_80
| ~ spl20_173 ),
inference(avatar_split_clause,[],[f1797,f1775,f727,f10357]) ).
fof(f10357,plain,
( spl20_450
<=> ! [X2,X0,X1] :
( subset(sK6(X0,singleton(X1),X2),X2)
| in(sK6(X0,singleton(X1),X2),X0)
| sP0(X0,singleton(X1),X2)
| ~ epsilon_transitive(X2)
| sK6(X0,singleton(X1),X2) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_450])]) ).
fof(f1797,plain,
( ! [X2,X0,X1] :
( subset(sK6(X0,singleton(X1),X2),X2)
| in(sK6(X0,singleton(X1),X2),X0)
| sP0(X0,singleton(X1),X2)
| ~ epsilon_transitive(X2)
| sK6(X0,singleton(X1),X2) = X1 )
| ~ spl20_80
| ~ spl20_173 ),
inference(resolution,[],[f1776,f728]) ).
fof(f10355,plain,
( spl20_449
| ~ spl20_86
| ~ spl20_171 ),
inference(avatar_split_clause,[],[f1742,f1665,f792,f10353]) ).
fof(f10353,plain,
( spl20_449
<=> ! [X2,X0,X1,X3] :
( in(sK6(powerset(X0),X1,X2),X2)
| in(sK6(powerset(X0),X1,X2),X1)
| sP0(powerset(X0),X1,X2)
| ~ empty(X0)
| ~ in(X3,sK6(powerset(X0),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_449])]) ).
fof(f792,plain,
( spl20_86
<=> ! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_86])]) ).
fof(f1742,plain,
( ! [X2,X3,X0,X1] :
( in(sK6(powerset(X0),X1,X2),X2)
| in(sK6(powerset(X0),X1,X2),X1)
| sP0(powerset(X0),X1,X2)
| ~ empty(X0)
| ~ in(X3,sK6(powerset(X0),X1,X2)) )
| ~ spl20_86
| ~ spl20_171 ),
inference(resolution,[],[f1666,f793]) ).
fof(f793,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X0,X1) )
| ~ spl20_86 ),
inference(avatar_component_clause,[],[f792]) ).
fof(f10351,plain,
( spl20_448
| ~ spl20_86
| ~ spl20_169 ),
inference(avatar_split_clause,[],[f1708,f1657,f792,f10349]) ).
fof(f10349,plain,
( spl20_448
<=> ! [X2,X0,X1,X3] :
( in(sK6(X0,powerset(X1),X2),X2)
| in(sK6(X0,powerset(X1),X2),X0)
| sP0(X0,powerset(X1),X2)
| ~ empty(X1)
| ~ in(X3,sK6(X0,powerset(X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_448])]) ).
fof(f1708,plain,
( ! [X2,X3,X0,X1] :
( in(sK6(X0,powerset(X1),X2),X2)
| in(sK6(X0,powerset(X1),X2),X0)
| sP0(X0,powerset(X1),X2)
| ~ empty(X1)
| ~ in(X3,sK6(X0,powerset(X1),X2)) )
| ~ spl20_86
| ~ spl20_169 ),
inference(resolution,[],[f1658,f793]) ).
fof(f10347,plain,
( spl20_447
| ~ spl20_86
| ~ spl20_167 ),
inference(avatar_split_clause,[],[f1673,f1649,f792,f10345]) ).
fof(f10345,plain,
( spl20_447
<=> ! [X2,X0,X1,X3] :
( in(sK6(X0,X1,powerset(X2)),X1)
| in(sK6(X0,X1,powerset(X2)),X0)
| sP0(X0,X1,powerset(X2))
| ~ empty(X2)
| ~ in(X3,sK6(X0,X1,powerset(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_447])]) ).
fof(f1673,plain,
( ! [X2,X3,X0,X1] :
( in(sK6(X0,X1,powerset(X2)),X1)
| in(sK6(X0,X1,powerset(X2)),X0)
| sP0(X0,X1,powerset(X2))
| ~ empty(X2)
| ~ in(X3,sK6(X0,X1,powerset(X2))) )
| ~ spl20_86
| ~ spl20_167 ),
inference(resolution,[],[f1650,f793]) ).
fof(f10343,plain,
( spl20_446
| ~ spl20_141
| ~ spl20_161 ),
inference(avatar_split_clause,[],[f1530,f1446,f1217,f10341]) ).
fof(f10341,plain,
( spl20_446
<=> ! [X0,X1] :
( in(sK6(sK4(powerset(X0)),sK4(powerset(X0)),X1),X1)
| sP0(sK4(powerset(X0)),sK4(powerset(X0)),X1)
| element(sK6(sK4(powerset(X0)),sK4(powerset(X0)),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_446])]) ).
fof(f1530,plain,
( ! [X0,X1] :
( in(sK6(sK4(powerset(X0)),sK4(powerset(X0)),X1),X1)
| sP0(sK4(powerset(X0)),sK4(powerset(X0)),X1)
| element(sK6(sK4(powerset(X0)),sK4(powerset(X0)),X1),X0) )
| ~ spl20_141
| ~ spl20_161 ),
inference(resolution,[],[f1447,f1218]) ).
fof(f10339,plain,
( spl20_445
| ~ spl20_98
| ~ spl20_152 ),
inference(avatar_split_clause,[],[f1374,f1358,f880,f10337]) ).
fof(f10337,plain,
( spl20_445
<=> ! [X2,X0,X1] :
( sK6(X1,X2,X0) = X0
| ~ ordinal(X0)
| ~ ordinal(sK6(X1,X2,X0))
| ~ empty(sK6(X1,X2,X0))
| ~ in(sK6(X1,X2,X0),X2)
| sP0(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_445])]) ).
fof(f1358,plain,
( spl20_152
<=> ! [X0,X1] :
( in(X1,X0)
| X0 = X1
| ~ ordinal(X0)
| ~ ordinal(X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_152])]) ).
fof(f1374,plain,
( ! [X2,X0,X1] :
( sK6(X1,X2,X0) = X0
| ~ ordinal(X0)
| ~ ordinal(sK6(X1,X2,X0))
| ~ empty(sK6(X1,X2,X0))
| ~ in(sK6(X1,X2,X0),X2)
| sP0(X1,X2,X0) )
| ~ spl20_98
| ~ spl20_152 ),
inference(resolution,[],[f1359,f881]) ).
fof(f1359,plain,
( ! [X0,X1] :
( in(X1,X0)
| X0 = X1
| ~ ordinal(X0)
| ~ ordinal(X1)
| ~ empty(X1) )
| ~ spl20_152 ),
inference(avatar_component_clause,[],[f1358]) ).
fof(f10335,plain,
( spl20_444
| ~ spl20_99
| ~ spl20_152 ),
inference(avatar_split_clause,[],[f1373,f1358,f884,f10333]) ).
fof(f10333,plain,
( spl20_444
<=> ! [X2,X0,X1] :
( sK6(X1,X2,X0) = X0
| ~ ordinal(X0)
| ~ ordinal(sK6(X1,X2,X0))
| ~ empty(sK6(X1,X2,X0))
| ~ in(sK6(X1,X2,X0),X1)
| sP0(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_444])]) ).
fof(f1373,plain,
( ! [X2,X0,X1] :
( sK6(X1,X2,X0) = X0
| ~ ordinal(X0)
| ~ ordinal(sK6(X1,X2,X0))
| ~ empty(sK6(X1,X2,X0))
| ~ in(sK6(X1,X2,X0),X1)
| sP0(X1,X2,X0) )
| ~ spl20_99
| ~ spl20_152 ),
inference(resolution,[],[f1359,f885]) ).
fof(f10331,plain,
( spl20_443
| ~ spl20_186
| ~ spl20_400 ),
inference(avatar_split_clause,[],[f8462,f7486,f2139,f10328]) ).
fof(f10328,plain,
( spl20_443
<=> element(sK8,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_443])]) ).
fof(f7486,plain,
( spl20_400
<=> in(sK8,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_400])]) ).
fof(f8462,plain,
( element(sK8,sK2)
| ~ spl20_186
| ~ spl20_400 ),
inference(resolution,[],[f7487,f2140]) ).
fof(f7487,plain,
( in(sK8,sK1)
| ~ spl20_400 ),
inference(avatar_component_clause,[],[f7486]) ).
fof(f9647,plain,
( spl20_442
| ~ spl20_400
| ~ spl20_402 ),
inference(avatar_split_clause,[],[f8461,f7675,f7486,f9644]) ).
fof(f9644,plain,
( spl20_442
<=> element(sK8,sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_442])]) ).
fof(f7675,plain,
( spl20_402
<=> ! [X0] :
( element(X0,sK8)
| ~ in(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_402])]) ).
fof(f8461,plain,
( element(sK8,sK8)
| ~ spl20_400
| ~ spl20_402 ),
inference(resolution,[],[f7487,f7676]) ).
fof(f7676,plain,
( ! [X0] :
( ~ in(X0,sK1)
| element(X0,sK8) )
| ~ spl20_402 ),
inference(avatar_component_clause,[],[f7675]) ).
fof(f9642,plain,
( spl20_441
| ~ spl20_138
| ~ spl20_178 ),
inference(avatar_split_clause,[],[f1949,f1879,f1195,f9640]) ).
fof(f9640,plain,
( spl20_441
<=> ! [X2,X0,X1] :
( in(sK6(singleton(X0),sK4(powerset(X1)),X2),X2)
| sP0(singleton(X0),sK4(powerset(X1)),X2)
| sK6(singleton(X0),sK4(powerset(X1)),X2) = X0
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_441])]) ).
fof(f1195,plain,
( spl20_138
<=> ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK4(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_138])]) ).
fof(f1879,plain,
( spl20_178
<=> ! [X2,X0,X1] :
( in(sK6(singleton(X0),X1,X2),X2)
| in(sK6(singleton(X0),X1,X2),X1)
| sP0(singleton(X0),X1,X2)
| sK6(singleton(X0),X1,X2) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_178])]) ).
fof(f1949,plain,
( ! [X2,X0,X1] :
( in(sK6(singleton(X0),sK4(powerset(X1)),X2),X2)
| sP0(singleton(X0),sK4(powerset(X1)),X2)
| sK6(singleton(X0),sK4(powerset(X1)),X2) = X0
| ~ empty(X1) )
| ~ spl20_138
| ~ spl20_178 ),
inference(resolution,[],[f1880,f1196]) ).
fof(f1196,plain,
( ! [X0,X1] :
( ~ in(X1,sK4(powerset(X0)))
| ~ empty(X0) )
| ~ spl20_138 ),
inference(avatar_component_clause,[],[f1195]) ).
fof(f1880,plain,
( ! [X2,X0,X1] :
( in(sK6(singleton(X0),X1,X2),X2)
| in(sK6(singleton(X0),X1,X2),X1)
| sP0(singleton(X0),X1,X2)
| sK6(singleton(X0),X1,X2) = X0 )
| ~ spl20_178 ),
inference(avatar_component_clause,[],[f1879]) ).
fof(f9638,plain,
( spl20_440
| ~ spl20_138
| ~ spl20_178 ),
inference(avatar_split_clause,[],[f1939,f1879,f1195,f9636]) ).
fof(f9636,plain,
( spl20_440
<=> ! [X2,X0,X1] :
( in(sK6(singleton(X0),X1,sK4(powerset(X2))),X1)
| sP0(singleton(X0),X1,sK4(powerset(X2)))
| sK6(singleton(X0),X1,sK4(powerset(X2))) = X0
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_440])]) ).
fof(f1939,plain,
( ! [X2,X0,X1] :
( in(sK6(singleton(X0),X1,sK4(powerset(X2))),X1)
| sP0(singleton(X0),X1,sK4(powerset(X2)))
| sK6(singleton(X0),X1,sK4(powerset(X2))) = X0
| ~ empty(X2) )
| ~ spl20_138
| ~ spl20_178 ),
inference(resolution,[],[f1880,f1196]) ).
fof(f9634,plain,
( spl20_439
| ~ spl20_138
| ~ spl20_177 ),
inference(avatar_split_clause,[],[f1926,f1874,f1195,f9632]) ).
fof(f9632,plain,
( spl20_439
<=> ! [X2,X0,X1] :
( in(sK6(sK4(powerset(X0)),singleton(X1),X2),X2)
| sP0(sK4(powerset(X0)),singleton(X1),X2)
| sK6(sK4(powerset(X0)),singleton(X1),X2) = X1
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_439])]) ).
fof(f1926,plain,
( ! [X2,X0,X1] :
( in(sK6(sK4(powerset(X0)),singleton(X1),X2),X2)
| sP0(sK4(powerset(X0)),singleton(X1),X2)
| sK6(sK4(powerset(X0)),singleton(X1),X2) = X1
| ~ empty(X0) )
| ~ spl20_138
| ~ spl20_177 ),
inference(resolution,[],[f1875,f1196]) ).
fof(f9630,plain,
( spl20_438
| ~ spl20_138
| ~ spl20_177 ),
inference(avatar_split_clause,[],[f1916,f1874,f1195,f9628]) ).
fof(f9628,plain,
( spl20_438
<=> ! [X2,X0,X1] :
( in(sK6(X0,singleton(X1),sK4(powerset(X2))),X0)
| sP0(X0,singleton(X1),sK4(powerset(X2)))
| sK6(X0,singleton(X1),sK4(powerset(X2))) = X1
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_438])]) ).
fof(f1916,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,singleton(X1),sK4(powerset(X2))),X0)
| sP0(X0,singleton(X1),sK4(powerset(X2)))
| sK6(X0,singleton(X1),sK4(powerset(X2))) = X1
| ~ empty(X2) )
| ~ spl20_138
| ~ spl20_177 ),
inference(resolution,[],[f1875,f1196]) ).
fof(f9626,plain,
( spl20_437
| ~ spl20_138
| ~ spl20_176 ),
inference(avatar_split_clause,[],[f1901,f1870,f1195,f9624]) ).
fof(f9624,plain,
( spl20_437
<=> ! [X2,X0,X1] :
( in(sK6(sK4(powerset(X0)),X1,singleton(X2)),X1)
| sP0(sK4(powerset(X0)),X1,singleton(X2))
| sK6(sK4(powerset(X0)),X1,singleton(X2)) = X2
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_437])]) ).
fof(f1901,plain,
( ! [X2,X0,X1] :
( in(sK6(sK4(powerset(X0)),X1,singleton(X2)),X1)
| sP0(sK4(powerset(X0)),X1,singleton(X2))
| sK6(sK4(powerset(X0)),X1,singleton(X2)) = X2
| ~ empty(X0) )
| ~ spl20_138
| ~ spl20_176 ),
inference(resolution,[],[f1871,f1196]) ).
fof(f9622,plain,
( spl20_436
| ~ spl20_138
| ~ spl20_176 ),
inference(avatar_split_clause,[],[f1891,f1870,f1195,f9620]) ).
fof(f9620,plain,
( spl20_436
<=> ! [X2,X0,X1] :
( in(sK6(X0,sK4(powerset(X1)),singleton(X2)),X0)
| sP0(X0,sK4(powerset(X1)),singleton(X2))
| sK6(X0,sK4(powerset(X1)),singleton(X2)) = X2
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_436])]) ).
fof(f1891,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,sK4(powerset(X1)),singleton(X2)),X0)
| sP0(X0,sK4(powerset(X1)),singleton(X2))
| sK6(X0,sK4(powerset(X1)),singleton(X2)) = X2
| ~ empty(X1) )
| ~ spl20_138
| ~ spl20_176 ),
inference(resolution,[],[f1871,f1196]) ).
fof(f9618,plain,
( spl20_435
| ~ spl20_146
| ~ spl20_175 ),
inference(avatar_split_clause,[],[f1842,f1783,f1277,f9616]) ).
fof(f9616,plain,
( spl20_435
<=> ! [X0,X3,X2,X1] :
( in(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ epsilon_transitive(X0)
| ~ in(X3,sK6(X0,X1,X2))
| element(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_435])]) ).
fof(f1277,plain,
( spl20_146
<=> ! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_146])]) ).
fof(f1842,plain,
( ! [X2,X3,X0,X1] :
( in(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ epsilon_transitive(X0)
| ~ in(X3,sK6(X0,X1,X2))
| element(X3,X0) )
| ~ spl20_146
| ~ spl20_175 ),
inference(resolution,[],[f1784,f1278]) ).
fof(f1278,plain,
( ! [X2,X0,X1] :
( ~ subset(X2,X1)
| ~ in(X0,X2)
| element(X0,X1) )
| ~ spl20_146 ),
inference(avatar_component_clause,[],[f1277]) ).
fof(f9614,plain,
( spl20_434
| ~ spl20_146
| ~ spl20_174 ),
inference(avatar_split_clause,[],[f1815,f1779,f1277,f9612]) ).
fof(f9612,plain,
( spl20_434
<=> ! [X0,X3,X2,X1] :
( in(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ epsilon_transitive(X1)
| ~ in(X3,sK6(X0,X1,X2))
| element(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_434])]) ).
fof(f1815,plain,
( ! [X2,X3,X0,X1] :
( in(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ epsilon_transitive(X1)
| ~ in(X3,sK6(X0,X1,X2))
| element(X3,X1) )
| ~ spl20_146
| ~ spl20_174 ),
inference(resolution,[],[f1780,f1278]) ).
fof(f9610,plain,
( spl20_433
| ~ spl20_146
| ~ spl20_173 ),
inference(avatar_split_clause,[],[f1786,f1775,f1277,f9608]) ).
fof(f9608,plain,
( spl20_433
<=> ! [X0,X3,X2,X1] :
( in(sK6(X0,X1,X2),X1)
| in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ epsilon_transitive(X2)
| ~ in(X3,sK6(X0,X1,X2))
| element(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_433])]) ).
fof(f1786,plain,
( ! [X2,X3,X0,X1] :
( in(sK6(X0,X1,X2),X1)
| in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ epsilon_transitive(X2)
| ~ in(X3,sK6(X0,X1,X2))
| element(X3,X2) )
| ~ spl20_146
| ~ spl20_173 ),
inference(resolution,[],[f1776,f1278]) ).
fof(f9606,plain,
( spl20_432
| ~ spl20_97
| ~ spl20_150 ),
inference(avatar_split_clause,[],[f1334,f1313,f871,f9604]) ).
fof(f9604,plain,
( spl20_432
<=> ! [X2,X0,X1] :
( in(sK5(X0,set_union2(X1,X2)),X1)
| in(sK5(X0,set_union2(X1,X2)),X2)
| sK5(X0,set_union2(X1,X2)) = X0
| singleton(X0) = set_union2(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_432])]) ).
fof(f871,plain,
( spl20_97
<=> ! [X0,X1] :
( singleton(X0) = X1
| sK5(X0,X1) = X0
| in(sK5(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_97])]) ).
fof(f1334,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,set_union2(X1,X2)),X1)
| in(sK5(X0,set_union2(X1,X2)),X2)
| sK5(X0,set_union2(X1,X2)) = X0
| singleton(X0) = set_union2(X1,X2) )
| ~ spl20_97
| ~ spl20_150 ),
inference(resolution,[],[f1314,f872]) ).
fof(f872,plain,
( ! [X0,X1] :
( in(sK5(X0,X1),X1)
| sK5(X0,X1) = X0
| singleton(X0) = X1 )
| ~ spl20_97 ),
inference(avatar_component_clause,[],[f871]) ).
fof(f9601,plain,
( ~ spl20_210
| spl20_116
| ~ spl20_129 ),
inference(avatar_split_clause,[],[f8288,f1109,f1018,f2557]) ).
fof(f2557,plain,
( spl20_210
<=> subset(sK1,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_210])]) ).
fof(f1018,plain,
( spl20_116
<=> subset(sK1,set_union2(sK2,singleton(sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_116])]) ).
fof(f8288,plain,
( ~ subset(sK1,sK1)
| spl20_116
| ~ spl20_129 ),
inference(superposition,[],[f1019,f1111]) ).
fof(f1019,plain,
( ~ subset(sK1,set_union2(sK2,singleton(sK2)))
| spl20_116 ),
inference(avatar_component_clause,[],[f1018]) ).
fof(f9018,plain,
( spl20_207
| ~ spl20_129
| ~ spl20_196 ),
inference(avatar_split_clause,[],[f2623,f2339,f1109,f2438]) ).
fof(f2438,plain,
( spl20_207
<=> element(sK1,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_207])]) ).
fof(f2339,plain,
( spl20_196
<=> element(set_union2(sK2,singleton(sK2)),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_196])]) ).
fof(f2623,plain,
( element(sK1,sK1)
| ~ spl20_129
| ~ spl20_196 ),
inference(superposition,[],[f2341,f1111]) ).
fof(f2341,plain,
( element(set_union2(sK2,singleton(sK2)),sK1)
| ~ spl20_196 ),
inference(avatar_component_clause,[],[f2339]) ).
fof(f8806,plain,
( spl20_431
| ~ spl20_64
| ~ spl20_178 ),
inference(avatar_split_clause,[],[f1944,f1879,f617,f8804]) ).
fof(f8804,plain,
( spl20_431
<=> ! [X2,X0,X1] :
( in(sK6(singleton(X0),X1,X2),X2)
| sP0(singleton(X0),X1,X2)
| sK6(singleton(X0),X1,X2) = X0
| ~ in(X1,sK6(singleton(X0),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_431])]) ).
fof(f617,plain,
( spl20_64
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_64])]) ).
fof(f1944,plain,
( ! [X2,X0,X1] :
( in(sK6(singleton(X0),X1,X2),X2)
| sP0(singleton(X0),X1,X2)
| sK6(singleton(X0),X1,X2) = X0
| ~ in(X1,sK6(singleton(X0),X1,X2)) )
| ~ spl20_64
| ~ spl20_178 ),
inference(resolution,[],[f1880,f618]) ).
fof(f618,plain,
( ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) )
| ~ spl20_64 ),
inference(avatar_component_clause,[],[f617]) ).
fof(f8802,plain,
( spl20_430
| ~ spl20_64
| ~ spl20_178 ),
inference(avatar_split_clause,[],[f1934,f1879,f617,f8800]) ).
fof(f8800,plain,
( spl20_430
<=> ! [X2,X0,X1] :
( in(sK6(singleton(X0),X1,X2),X1)
| sP0(singleton(X0),X1,X2)
| sK6(singleton(X0),X1,X2) = X0
| ~ in(X2,sK6(singleton(X0),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_430])]) ).
fof(f1934,plain,
( ! [X2,X0,X1] :
( in(sK6(singleton(X0),X1,X2),X1)
| sP0(singleton(X0),X1,X2)
| sK6(singleton(X0),X1,X2) = X0
| ~ in(X2,sK6(singleton(X0),X1,X2)) )
| ~ spl20_64
| ~ spl20_178 ),
inference(resolution,[],[f1880,f618]) ).
fof(f8798,plain,
( spl20_429
| ~ spl20_64
| ~ spl20_177 ),
inference(avatar_split_clause,[],[f1921,f1874,f617,f8796]) ).
fof(f8796,plain,
( spl20_429
<=> ! [X2,X0,X1] :
( in(sK6(X0,singleton(X1),X2),X2)
| sP0(X0,singleton(X1),X2)
| sK6(X0,singleton(X1),X2) = X1
| ~ in(X0,sK6(X0,singleton(X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_429])]) ).
fof(f1921,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,singleton(X1),X2),X2)
| sP0(X0,singleton(X1),X2)
| sK6(X0,singleton(X1),X2) = X1
| ~ in(X0,sK6(X0,singleton(X1),X2)) )
| ~ spl20_64
| ~ spl20_177 ),
inference(resolution,[],[f1875,f618]) ).
fof(f8794,plain,
( spl20_428
| ~ spl20_64
| ~ spl20_177 ),
inference(avatar_split_clause,[],[f1911,f1874,f617,f8792]) ).
fof(f8792,plain,
( spl20_428
<=> ! [X2,X0,X1] :
( in(sK6(X0,singleton(X1),X2),X0)
| sP0(X0,singleton(X1),X2)
| sK6(X0,singleton(X1),X2) = X1
| ~ in(X2,sK6(X0,singleton(X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_428])]) ).
fof(f1911,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,singleton(X1),X2),X0)
| sP0(X0,singleton(X1),X2)
| sK6(X0,singleton(X1),X2) = X1
| ~ in(X2,sK6(X0,singleton(X1),X2)) )
| ~ spl20_64
| ~ spl20_177 ),
inference(resolution,[],[f1875,f618]) ).
fof(f8790,plain,
( spl20_427
| ~ spl20_64
| ~ spl20_176 ),
inference(avatar_split_clause,[],[f1896,f1870,f617,f8788]) ).
fof(f8788,plain,
( spl20_427
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,singleton(X2)),X1)
| sP0(X0,X1,singleton(X2))
| sK6(X0,X1,singleton(X2)) = X2
| ~ in(X0,sK6(X0,X1,singleton(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_427])]) ).
fof(f1896,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,singleton(X2)),X1)
| sP0(X0,X1,singleton(X2))
| sK6(X0,X1,singleton(X2)) = X2
| ~ in(X0,sK6(X0,X1,singleton(X2))) )
| ~ spl20_64
| ~ spl20_176 ),
inference(resolution,[],[f1871,f618]) ).
fof(f8778,plain,
( spl20_426
| ~ spl20_64
| ~ spl20_176 ),
inference(avatar_split_clause,[],[f1886,f1870,f617,f8776]) ).
fof(f8776,plain,
( spl20_426
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,singleton(X2)),X0)
| sP0(X0,X1,singleton(X2))
| sK6(X0,X1,singleton(X2)) = X2
| ~ in(X1,sK6(X0,X1,singleton(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_426])]) ).
fof(f1886,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,singleton(X2)),X0)
| sP0(X0,X1,singleton(X2))
| sK6(X0,X1,singleton(X2)) = X2
| ~ in(X1,sK6(X0,X1,singleton(X2))) )
| ~ spl20_64
| ~ spl20_176 ),
inference(resolution,[],[f1871,f618]) ).
fof(f8774,plain,
( spl20_425
| ~ spl20_138
| ~ spl20_175 ),
inference(avatar_split_clause,[],[f1865,f1783,f1195,f8772]) ).
fof(f8772,plain,
( spl20_425
<=> ! [X2,X0,X1] :
( subset(sK6(X0,sK4(powerset(X1)),X2),X0)
| in(sK6(X0,sK4(powerset(X1)),X2),X2)
| sP0(X0,sK4(powerset(X1)),X2)
| ~ epsilon_transitive(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_425])]) ).
fof(f1865,plain,
( ! [X2,X0,X1] :
( subset(sK6(X0,sK4(powerset(X1)),X2),X0)
| in(sK6(X0,sK4(powerset(X1)),X2),X2)
| sP0(X0,sK4(powerset(X1)),X2)
| ~ epsilon_transitive(X0)
| ~ empty(X1) )
| ~ spl20_138
| ~ spl20_175 ),
inference(resolution,[],[f1784,f1196]) ).
fof(f8770,plain,
( spl20_424
| ~ spl20_138
| ~ spl20_175 ),
inference(avatar_split_clause,[],[f1855,f1783,f1195,f8768]) ).
fof(f8768,plain,
( spl20_424
<=> ! [X2,X0,X1] :
( subset(sK6(X0,X1,sK4(powerset(X2))),X0)
| in(sK6(X0,X1,sK4(powerset(X2))),X1)
| sP0(X0,X1,sK4(powerset(X2)))
| ~ epsilon_transitive(X0)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_424])]) ).
fof(f1855,plain,
( ! [X2,X0,X1] :
( subset(sK6(X0,X1,sK4(powerset(X2))),X0)
| in(sK6(X0,X1,sK4(powerset(X2))),X1)
| sP0(X0,X1,sK4(powerset(X2)))
| ~ epsilon_transitive(X0)
| ~ empty(X2) )
| ~ spl20_138
| ~ spl20_175 ),
inference(resolution,[],[f1784,f1196]) ).
fof(f8766,plain,
( spl20_423
| ~ spl20_138
| ~ spl20_174 ),
inference(avatar_split_clause,[],[f1838,f1779,f1195,f8764]) ).
fof(f8764,plain,
( spl20_423
<=> ! [X2,X0,X1] :
( subset(sK6(sK4(powerset(X0)),X1,X2),X1)
| in(sK6(sK4(powerset(X0)),X1,X2),X2)
| sP0(sK4(powerset(X0)),X1,X2)
| ~ epsilon_transitive(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_423])]) ).
fof(f1838,plain,
( ! [X2,X0,X1] :
( subset(sK6(sK4(powerset(X0)),X1,X2),X1)
| in(sK6(sK4(powerset(X0)),X1,X2),X2)
| sP0(sK4(powerset(X0)),X1,X2)
| ~ epsilon_transitive(X1)
| ~ empty(X0) )
| ~ spl20_138
| ~ spl20_174 ),
inference(resolution,[],[f1780,f1196]) ).
fof(f8762,plain,
( spl20_422
| ~ spl20_81
| ~ spl20_174 ),
inference(avatar_split_clause,[],[f1831,f1779,f760,f8760]) ).
fof(f8760,plain,
( spl20_422
<=> ! [X2,X0,X1] :
( subset(sK6(X0,X1,X2),X1)
| in(sK6(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| ~ epsilon_transitive(X1)
| subset(sK6(X0,X1,X2),X0)
| ~ epsilon_transitive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_422])]) ).
fof(f760,plain,
( spl20_81
<=> ! [X2,X0] :
( subset(X2,X0)
| ~ in(X2,X0)
| ~ epsilon_transitive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_81])]) ).
fof(f1831,plain,
( ! [X2,X0,X1] :
( subset(sK6(X0,X1,X2),X1)
| in(sK6(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| ~ epsilon_transitive(X1)
| subset(sK6(X0,X1,X2),X0)
| ~ epsilon_transitive(X0) )
| ~ spl20_81
| ~ spl20_174 ),
inference(resolution,[],[f1780,f761]) ).
fof(f761,plain,
( ! [X2,X0] :
( ~ in(X2,X0)
| subset(X2,X0)
| ~ epsilon_transitive(X0) )
| ~ spl20_81 ),
inference(avatar_component_clause,[],[f760]) ).
fof(f8758,plain,
( spl20_421
| ~ spl20_138
| ~ spl20_174 ),
inference(avatar_split_clause,[],[f1828,f1779,f1195,f8756]) ).
fof(f8756,plain,
( spl20_421
<=> ! [X2,X0,X1] :
( subset(sK6(X0,X1,sK4(powerset(X2))),X1)
| in(sK6(X0,X1,sK4(powerset(X2))),X0)
| sP0(X0,X1,sK4(powerset(X2)))
| ~ epsilon_transitive(X1)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_421])]) ).
fof(f1828,plain,
( ! [X2,X0,X1] :
( subset(sK6(X0,X1,sK4(powerset(X2))),X1)
| in(sK6(X0,X1,sK4(powerset(X2))),X0)
| sP0(X0,X1,sK4(powerset(X2)))
| ~ epsilon_transitive(X1)
| ~ empty(X2) )
| ~ spl20_138
| ~ spl20_174 ),
inference(resolution,[],[f1780,f1196]) ).
fof(f8754,plain,
( spl20_420
| ~ spl20_138
| ~ spl20_173 ),
inference(avatar_split_clause,[],[f1809,f1775,f1195,f8752]) ).
fof(f8752,plain,
( spl20_420
<=> ! [X2,X0,X1] :
( subset(sK6(sK4(powerset(X0)),X1,X2),X2)
| in(sK6(sK4(powerset(X0)),X1,X2),X1)
| sP0(sK4(powerset(X0)),X1,X2)
| ~ epsilon_transitive(X2)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_420])]) ).
fof(f1809,plain,
( ! [X2,X0,X1] :
( subset(sK6(sK4(powerset(X0)),X1,X2),X2)
| in(sK6(sK4(powerset(X0)),X1,X2),X1)
| sP0(sK4(powerset(X0)),X1,X2)
| ~ epsilon_transitive(X2)
| ~ empty(X0) )
| ~ spl20_138
| ~ spl20_173 ),
inference(resolution,[],[f1776,f1196]) ).
fof(f8750,plain,
( spl20_419
| ~ spl20_81
| ~ spl20_173 ),
inference(avatar_split_clause,[],[f1802,f1775,f760,f8748]) ).
fof(f8748,plain,
( spl20_419
<=> ! [X2,X0,X1] :
( subset(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ epsilon_transitive(X2)
| subset(sK6(X0,X1,X2),X0)
| ~ epsilon_transitive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_419])]) ).
fof(f1802,plain,
( ! [X2,X0,X1] :
( subset(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ epsilon_transitive(X2)
| subset(sK6(X0,X1,X2),X0)
| ~ epsilon_transitive(X0) )
| ~ spl20_81
| ~ spl20_173 ),
inference(resolution,[],[f1776,f761]) ).
fof(f8746,plain,
( spl20_418
| ~ spl20_138
| ~ spl20_173 ),
inference(avatar_split_clause,[],[f1799,f1775,f1195,f8744]) ).
fof(f8744,plain,
( spl20_418
<=> ! [X2,X0,X1] :
( subset(sK6(X0,sK4(powerset(X1)),X2),X2)
| in(sK6(X0,sK4(powerset(X1)),X2),X0)
| sP0(X0,sK4(powerset(X1)),X2)
| ~ epsilon_transitive(X2)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_418])]) ).
fof(f1799,plain,
( ! [X2,X0,X1] :
( subset(sK6(X0,sK4(powerset(X1)),X2),X2)
| in(sK6(X0,sK4(powerset(X1)),X2),X0)
| sP0(X0,sK4(powerset(X1)),X2)
| ~ epsilon_transitive(X2)
| ~ empty(X1) )
| ~ spl20_138
| ~ spl20_173 ),
inference(resolution,[],[f1776,f1196]) ).
fof(f8742,plain,
( spl20_417
| ~ spl20_81
| ~ spl20_173 ),
inference(avatar_split_clause,[],[f1792,f1775,f760,f8740]) ).
fof(f8740,plain,
( spl20_417
<=> ! [X2,X0,X1] :
( subset(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ epsilon_transitive(X2)
| subset(sK6(X0,X1,X2),X1)
| ~ epsilon_transitive(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_417])]) ).
fof(f1792,plain,
( ! [X2,X0,X1] :
( subset(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ epsilon_transitive(X2)
| subset(sK6(X0,X1,X2),X1)
| ~ epsilon_transitive(X1) )
| ~ spl20_81
| ~ spl20_173 ),
inference(resolution,[],[f1776,f761]) ).
fof(f8730,plain,
( spl20_416
| ~ spl20_80
| ~ spl20_171 ),
inference(avatar_split_clause,[],[f1762,f1665,f727,f8728]) ).
fof(f8728,plain,
( spl20_416
<=> ! [X2,X0,X1] :
( element(sK6(X0,singleton(X1),X2),X0)
| in(sK6(X0,singleton(X1),X2),X2)
| sP0(X0,singleton(X1),X2)
| sK6(X0,singleton(X1),X2) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_416])]) ).
fof(f1762,plain,
( ! [X2,X0,X1] :
( element(sK6(X0,singleton(X1),X2),X0)
| in(sK6(X0,singleton(X1),X2),X2)
| sP0(X0,singleton(X1),X2)
| sK6(X0,singleton(X1),X2) = X1 )
| ~ spl20_80
| ~ spl20_171 ),
inference(resolution,[],[f1666,f728]) ).
fof(f8726,plain,
( spl20_415
| ~ spl20_80
| ~ spl20_171 ),
inference(avatar_split_clause,[],[f1752,f1665,f727,f8724]) ).
fof(f8724,plain,
( spl20_415
<=> ! [X2,X0,X1] :
( element(sK6(X0,X1,singleton(X2)),X0)
| in(sK6(X0,X1,singleton(X2)),X1)
| sP0(X0,X1,singleton(X2))
| sK6(X0,X1,singleton(X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_415])]) ).
fof(f1752,plain,
( ! [X2,X0,X1] :
( element(sK6(X0,X1,singleton(X2)),X0)
| in(sK6(X0,X1,singleton(X2)),X1)
| sP0(X0,X1,singleton(X2))
| sK6(X0,X1,singleton(X2)) = X2 )
| ~ spl20_80
| ~ spl20_171 ),
inference(resolution,[],[f1666,f728]) ).
fof(f8722,plain,
( spl20_414
| ~ spl20_74
| ~ spl20_171 ),
inference(avatar_split_clause,[],[f1743,f1665,f703,f8720]) ).
fof(f8720,plain,
( spl20_414
<=> ! [X2,X0,X1] :
( in(sK6(powerset(X0),X1,X2),X2)
| in(sK6(powerset(X0),X1,X2),X1)
| sP0(powerset(X0),X1,X2)
| subset(sK6(powerset(X0),X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_414])]) ).
fof(f703,plain,
( spl20_74
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_74])]) ).
fof(f1743,plain,
( ! [X2,X0,X1] :
( in(sK6(powerset(X0),X1,X2),X2)
| in(sK6(powerset(X0),X1,X2),X1)
| sP0(powerset(X0),X1,X2)
| subset(sK6(powerset(X0),X1,X2),X0) )
| ~ spl20_74
| ~ spl20_171 ),
inference(resolution,[],[f1666,f704]) ).
fof(f704,plain,
( ! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) )
| ~ spl20_74 ),
inference(avatar_component_clause,[],[f703]) ).
fof(f8718,plain,
( spl20_413
| ~ spl20_80
| ~ spl20_169 ),
inference(avatar_split_clause,[],[f1728,f1657,f727,f8716]) ).
fof(f8716,plain,
( spl20_413
<=> ! [X2,X0,X1] :
( element(sK6(singleton(X0),X1,X2),X1)
| in(sK6(singleton(X0),X1,X2),X2)
| sP0(singleton(X0),X1,X2)
| sK6(singleton(X0),X1,X2) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_413])]) ).
fof(f1728,plain,
( ! [X2,X0,X1] :
( element(sK6(singleton(X0),X1,X2),X1)
| in(sK6(singleton(X0),X1,X2),X2)
| sP0(singleton(X0),X1,X2)
| sK6(singleton(X0),X1,X2) = X0 )
| ~ spl20_80
| ~ spl20_169 ),
inference(resolution,[],[f1658,f728]) ).
fof(f8714,plain,
( spl20_412
| ~ spl20_80
| ~ spl20_169 ),
inference(avatar_split_clause,[],[f1718,f1657,f727,f8712]) ).
fof(f8712,plain,
( spl20_412
<=> ! [X2,X0,X1] :
( element(sK6(X0,X1,singleton(X2)),X1)
| in(sK6(X0,X1,singleton(X2)),X0)
| sP0(X0,X1,singleton(X2))
| sK6(X0,X1,singleton(X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_412])]) ).
fof(f1718,plain,
( ! [X2,X0,X1] :
( element(sK6(X0,X1,singleton(X2)),X1)
| in(sK6(X0,X1,singleton(X2)),X0)
| sP0(X0,X1,singleton(X2))
| sK6(X0,X1,singleton(X2)) = X2 )
| ~ spl20_80
| ~ spl20_169 ),
inference(resolution,[],[f1658,f728]) ).
fof(f8710,plain,
( spl20_411
| ~ spl20_74
| ~ spl20_169 ),
inference(avatar_split_clause,[],[f1709,f1657,f703,f8708]) ).
fof(f8708,plain,
( spl20_411
<=> ! [X2,X0,X1] :
( in(sK6(X0,powerset(X1),X2),X2)
| in(sK6(X0,powerset(X1),X2),X0)
| sP0(X0,powerset(X1),X2)
| subset(sK6(X0,powerset(X1),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_411])]) ).
fof(f1709,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,powerset(X1),X2),X2)
| in(sK6(X0,powerset(X1),X2),X0)
| sP0(X0,powerset(X1),X2)
| subset(sK6(X0,powerset(X1),X2),X1) )
| ~ spl20_74
| ~ spl20_169 ),
inference(resolution,[],[f1658,f704]) ).
fof(f8706,plain,
( spl20_410
| ~ spl20_80
| ~ spl20_167 ),
inference(avatar_split_clause,[],[f1693,f1649,f727,f8704]) ).
fof(f8704,plain,
( spl20_410
<=> ! [X2,X0,X1] :
( element(sK6(singleton(X0),X1,X2),X2)
| in(sK6(singleton(X0),X1,X2),X1)
| sP0(singleton(X0),X1,X2)
| sK6(singleton(X0),X1,X2) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_410])]) ).
fof(f1693,plain,
( ! [X2,X0,X1] :
( element(sK6(singleton(X0),X1,X2),X2)
| in(sK6(singleton(X0),X1,X2),X1)
| sP0(singleton(X0),X1,X2)
| sK6(singleton(X0),X1,X2) = X0 )
| ~ spl20_80
| ~ spl20_167 ),
inference(resolution,[],[f1650,f728]) ).
fof(f8702,plain,
( spl20_409
| ~ spl20_80
| ~ spl20_167 ),
inference(avatar_split_clause,[],[f1683,f1649,f727,f8700]) ).
fof(f8700,plain,
( spl20_409
<=> ! [X2,X0,X1] :
( element(sK6(X0,singleton(X1),X2),X2)
| in(sK6(X0,singleton(X1),X2),X0)
| sP0(X0,singleton(X1),X2)
| sK6(X0,singleton(X1),X2) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_409])]) ).
fof(f1683,plain,
( ! [X2,X0,X1] :
( element(sK6(X0,singleton(X1),X2),X2)
| in(sK6(X0,singleton(X1),X2),X0)
| sP0(X0,singleton(X1),X2)
| sK6(X0,singleton(X1),X2) = X1 )
| ~ spl20_80
| ~ spl20_167 ),
inference(resolution,[],[f1650,f728]) ).
fof(f8698,plain,
( spl20_408
| ~ spl20_74
| ~ spl20_167 ),
inference(avatar_split_clause,[],[f1674,f1649,f703,f8696]) ).
fof(f8696,plain,
( spl20_408
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,powerset(X2)),X1)
| in(sK6(X0,X1,powerset(X2)),X0)
| sP0(X0,X1,powerset(X2))
| subset(sK6(X0,X1,powerset(X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_408])]) ).
fof(f1674,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,powerset(X2)),X1)
| in(sK6(X0,X1,powerset(X2)),X0)
| sP0(X0,X1,powerset(X2))
| subset(sK6(X0,X1,powerset(X2)),X2) )
| ~ spl20_74
| ~ spl20_167 ),
inference(resolution,[],[f1650,f704]) ).
fof(f8694,plain,
( ~ spl20_184
| ~ spl20_56
| ~ spl20_312 ),
inference(avatar_split_clause,[],[f5006,f4380,f574,f2131]) ).
fof(f2131,plain,
( spl20_184
<=> empty(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_184])]) ).
fof(f574,plain,
( spl20_56
<=> ! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_56])]) ).
fof(f4380,plain,
( spl20_312
<=> in(sK4(sK1),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_312])]) ).
fof(f5006,plain,
( ~ empty(sK2)
| ~ spl20_56
| ~ spl20_312 ),
inference(resolution,[],[f4382,f575]) ).
fof(f575,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) )
| ~ spl20_56 ),
inference(avatar_component_clause,[],[f574]) ).
fof(f4382,plain,
( in(sK4(sK1),sK2)
| ~ spl20_312 ),
inference(avatar_component_clause,[],[f4380]) ).
fof(f8693,plain,
( spl20_407
| ~ spl20_150
| ~ spl20_157 ),
inference(avatar_split_clause,[],[f1454,f1430,f1313,f8691]) ).
fof(f8691,plain,
( spl20_407
<=> ! [X2,X0,X1] :
( singleton(X0) = set_union2(X1,X2)
| ~ ordinal(set_union2(X1,X2))
| ~ ordinal(singleton(X0))
| set_union2(X1,X2) = X0
| in(singleton(X0),X1)
| in(singleton(X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_407])]) ).
fof(f1430,plain,
( spl20_157
<=> ! [X0,X1] :
( in(singleton(X1),X0)
| singleton(X1) = X0
| ~ ordinal(X0)
| ~ ordinal(singleton(X1))
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_157])]) ).
fof(f1454,plain,
( ! [X2,X0,X1] :
( singleton(X0) = set_union2(X1,X2)
| ~ ordinal(set_union2(X1,X2))
| ~ ordinal(singleton(X0))
| set_union2(X1,X2) = X0
| in(singleton(X0),X1)
| in(singleton(X0),X2) )
| ~ spl20_150
| ~ spl20_157 ),
inference(resolution,[],[f1431,f1314]) ).
fof(f1431,plain,
( ! [X0,X1] :
( in(singleton(X1),X0)
| singleton(X1) = X0
| ~ ordinal(X0)
| ~ ordinal(singleton(X1))
| X0 = X1 )
| ~ spl20_157 ),
inference(avatar_component_clause,[],[f1430]) ).
fof(f8489,plain,
( ~ spl20_52
| spl20_406
| ~ spl20_81
| ~ spl20_400 ),
inference(avatar_split_clause,[],[f8465,f7486,f760,f8486,f552]) ).
fof(f8486,plain,
( spl20_406
<=> subset(sK8,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_406])]) ).
fof(f8465,plain,
( subset(sK8,sK1)
| ~ epsilon_transitive(sK1)
| ~ spl20_81
| ~ spl20_400 ),
inference(resolution,[],[f7487,f761]) ).
fof(f8478,plain,
( ~ spl20_405
| ~ spl20_64
| ~ spl20_400 ),
inference(avatar_split_clause,[],[f8467,f7486,f617,f8475]) ).
fof(f8475,plain,
( spl20_405
<=> in(sK1,sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_405])]) ).
fof(f8467,plain,
( ~ in(sK1,sK8)
| ~ spl20_64
| ~ spl20_400 ),
inference(resolution,[],[f7487,f618]) ).
fof(f8473,plain,
( spl20_404
| ~ spl20_65
| ~ spl20_400 ),
inference(avatar_split_clause,[],[f8466,f7486,f621,f8470]) ).
fof(f8470,plain,
( spl20_404
<=> element(sK8,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_404])]) ).
fof(f621,plain,
( spl20_65
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_65])]) ).
fof(f8466,plain,
( element(sK8,sK1)
| ~ spl20_65
| ~ spl20_400 ),
inference(resolution,[],[f7487,f622]) ).
fof(f622,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) )
| ~ spl20_65 ),
inference(avatar_component_clause,[],[f621]) ).
fof(f8460,plain,
( ~ spl20_10
| ~ spl20_112
| ~ spl20_1
| spl20_401
| ~ spl20_152
| spl20_400 ),
inference(avatar_split_clause,[],[f8275,f7486,f1358,f7492,f275,f994,f320]) ).
fof(f320,plain,
( spl20_10
<=> empty(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_10])]) ).
fof(f994,plain,
( spl20_112
<=> ordinal(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_112])]) ).
fof(f275,plain,
( spl20_1
<=> ordinal(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1])]) ).
fof(f7492,plain,
( spl20_401
<=> sK1 = sK8 ),
introduced(avatar_definition,[new_symbols(naming,[spl20_401])]) ).
fof(f8275,plain,
( sK1 = sK8
| ~ ordinal(sK1)
| ~ ordinal(sK8)
| ~ empty(sK8)
| ~ spl20_152
| spl20_400 ),
inference(resolution,[],[f7488,f1359]) ).
fof(f7488,plain,
( ~ in(sK8,sK1)
| spl20_400 ),
inference(avatar_component_clause,[],[f7486]) ).
fof(f8272,plain,
( ~ spl20_10
| spl20_192
| ~ spl20_401 ),
inference(avatar_split_clause,[],[f7799,f7492,f2310,f320]) ).
fof(f2310,plain,
( spl20_192
<=> empty(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_192])]) ).
fof(f7799,plain,
( ~ empty(sK8)
| spl20_192
| ~ spl20_401 ),
inference(forward_demodulation,[],[f2312,f7494]) ).
fof(f7494,plain,
( sK1 = sK8
| ~ spl20_401 ),
inference(avatar_component_clause,[],[f7492]) ).
fof(f2312,plain,
( ~ empty(sK1)
| spl20_192 ),
inference(avatar_component_clause,[],[f2310]) ).
fof(f8263,plain,
( ~ spl20_403
| spl20_400
| ~ spl20_401 ),
inference(avatar_split_clause,[],[f8221,f7492,f7486,f8260]) ).
fof(f8260,plain,
( spl20_403
<=> in(sK8,sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_403])]) ).
fof(f8221,plain,
( ~ in(sK8,sK8)
| spl20_400
| ~ spl20_401 ),
inference(forward_demodulation,[],[f7488,f7494]) ).
fof(f8220,plain,
( ~ spl20_10
| ~ spl20_57
| ~ spl20_374 ),
inference(avatar_split_clause,[],[f7028,f7014,f578,f320]) ).
fof(f578,plain,
( spl20_57
<=> ! [X0] : ~ empty(set_union2(X0,singleton(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_57])]) ).
fof(f7014,plain,
( spl20_374
<=> sK8 = set_union2(sK2,singleton(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_374])]) ).
fof(f7028,plain,
( ~ empty(sK8)
| ~ spl20_57
| ~ spl20_374 ),
inference(superposition,[],[f579,f7016]) ).
fof(f7016,plain,
( sK8 = set_union2(sK2,singleton(sK2))
| ~ spl20_374 ),
inference(avatar_component_clause,[],[f7014]) ).
fof(f579,plain,
( ! [X0] : ~ empty(set_union2(X0,singleton(X0)))
| ~ spl20_57 ),
inference(avatar_component_clause,[],[f578]) ).
fof(f7798,plain,
( ~ spl20_192
| ~ spl20_57
| ~ spl20_129 ),
inference(avatar_split_clause,[],[f2353,f1109,f578,f2310]) ).
fof(f2353,plain,
( ~ empty(sK1)
| ~ spl20_57
| ~ spl20_129 ),
inference(superposition,[],[f579,f1111]) ).
fof(f7677,plain,
( spl20_402
| ~ spl20_187
| ~ spl20_374 ),
inference(avatar_split_clause,[],[f7460,f7014,f2160,f7675]) ).
fof(f2160,plain,
( spl20_187
<=> ! [X0] :
( ~ in(X0,sK1)
| element(X0,set_union2(sK2,singleton(sK2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_187])]) ).
fof(f7460,plain,
( ! [X0] :
( element(X0,sK8)
| ~ in(X0,sK1) )
| ~ spl20_187
| ~ spl20_374 ),
inference(forward_demodulation,[],[f2161,f7016]) ).
fof(f2161,plain,
( ! [X0] :
( element(X0,set_union2(sK2,singleton(sK2)))
| ~ in(X0,sK1) )
| ~ spl20_187 ),
inference(avatar_component_clause,[],[f2160]) ).
fof(f7495,plain,
( spl20_401
| ~ spl20_129
| ~ spl20_374 ),
inference(avatar_split_clause,[],[f7464,f7014,f1109,f7492]) ).
fof(f7464,plain,
( sK1 = sK8
| ~ spl20_129
| ~ spl20_374 ),
inference(forward_demodulation,[],[f1111,f7016]) ).
fof(f7489,plain,
( ~ spl20_400
| spl20_94
| ~ spl20_374 ),
inference(avatar_split_clause,[],[f7444,f7014,f845,f7486]) ).
fof(f845,plain,
( spl20_94
<=> in(set_union2(sK2,singleton(sK2)),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_94])]) ).
fof(f7444,plain,
( ~ in(sK8,sK1)
| spl20_94
| ~ spl20_374 ),
inference(forward_demodulation,[],[f847,f7016]) ).
fof(f847,plain,
( ~ in(set_union2(sK2,singleton(sK2)),sK1)
| spl20_94 ),
inference(avatar_component_clause,[],[f845]) ).
fof(f7483,plain,
( ~ spl20_195
| spl20_94
| ~ spl20_129 ),
inference(avatar_split_clause,[],[f2343,f1109,f845,f2328]) ).
fof(f2328,plain,
( spl20_195
<=> in(sK1,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_195])]) ).
fof(f2343,plain,
( ~ in(sK1,sK1)
| spl20_94
| ~ spl20_129 ),
inference(forward_demodulation,[],[f847,f1111]) ).
fof(f7443,plain,
( ~ spl20_10
| ~ spl20_54
| ~ spl20_57
| ~ spl20_117
| ~ spl20_129
| ~ spl20_192 ),
inference(avatar_split_clause,[],[f7005,f2310,f1109,f1024,f578,f566,f320]) ).
fof(f566,plain,
( spl20_54
<=> ! [X0] :
( empty_set = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_54])]) ).
fof(f1024,plain,
( spl20_117
<=> empty_set = sK8 ),
introduced(avatar_definition,[new_symbols(naming,[spl20_117])]) ).
fof(f7005,plain,
( ~ empty(sK8)
| ~ spl20_54
| ~ spl20_57
| ~ spl20_117
| ~ spl20_129
| ~ spl20_192 ),
inference(forward_demodulation,[],[f2624,f6848]) ).
fof(f6848,plain,
( sK1 = sK8
| ~ spl20_54
| ~ spl20_117
| ~ spl20_192 ),
inference(forward_demodulation,[],[f6843,f1026]) ).
fof(f1026,plain,
( empty_set = sK8
| ~ spl20_117 ),
inference(avatar_component_clause,[],[f1024]) ).
fof(f6843,plain,
( empty_set = sK1
| ~ spl20_54
| ~ spl20_192 ),
inference(resolution,[],[f2311,f567]) ).
fof(f567,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = X0 )
| ~ spl20_54 ),
inference(avatar_component_clause,[],[f566]) ).
fof(f2311,plain,
( empty(sK1)
| ~ spl20_192 ),
inference(avatar_component_clause,[],[f2310]) ).
fof(f2624,plain,
( ~ empty(sK1)
| ~ spl20_57
| ~ spl20_129 ),
inference(superposition,[],[f579,f1111]) ).
fof(f7182,plain,
( spl20_399
| ~ spl20_64
| ~ spl20_175 ),
inference(avatar_split_clause,[],[f1860,f1783,f617,f7180]) ).
fof(f7180,plain,
( spl20_399
<=> ! [X2,X0,X1] :
( subset(sK6(X0,X1,X2),X0)
| in(sK6(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| ~ epsilon_transitive(X0)
| ~ in(X1,sK6(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_399])]) ).
fof(f1860,plain,
( ! [X2,X0,X1] :
( subset(sK6(X0,X1,X2),X0)
| in(sK6(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| ~ epsilon_transitive(X0)
| ~ in(X1,sK6(X0,X1,X2)) )
| ~ spl20_64
| ~ spl20_175 ),
inference(resolution,[],[f1784,f618]) ).
fof(f7178,plain,
( spl20_398
| ~ spl20_64
| ~ spl20_175 ),
inference(avatar_split_clause,[],[f1850,f1783,f617,f7176]) ).
fof(f7176,plain,
( spl20_398
<=> ! [X2,X0,X1] :
( subset(sK6(X0,X1,X2),X0)
| in(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ epsilon_transitive(X0)
| ~ in(X2,sK6(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_398])]) ).
fof(f1850,plain,
( ! [X2,X0,X1] :
( subset(sK6(X0,X1,X2),X0)
| in(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ epsilon_transitive(X0)
| ~ in(X2,sK6(X0,X1,X2)) )
| ~ spl20_64
| ~ spl20_175 ),
inference(resolution,[],[f1784,f618]) ).
fof(f7174,plain,
( spl20_397
| ~ spl20_64
| ~ spl20_174 ),
inference(avatar_split_clause,[],[f1833,f1779,f617,f7172]) ).
fof(f7172,plain,
( spl20_397
<=> ! [X2,X0,X1] :
( subset(sK6(X0,X1,X2),X1)
| in(sK6(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| ~ epsilon_transitive(X1)
| ~ in(X0,sK6(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_397])]) ).
fof(f1833,plain,
( ! [X2,X0,X1] :
( subset(sK6(X0,X1,X2),X1)
| in(sK6(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| ~ epsilon_transitive(X1)
| ~ in(X0,sK6(X0,X1,X2)) )
| ~ spl20_64
| ~ spl20_174 ),
inference(resolution,[],[f1780,f618]) ).
fof(f7170,plain,
( spl20_396
| ~ spl20_64
| ~ spl20_174 ),
inference(avatar_split_clause,[],[f1823,f1779,f617,f7168]) ).
fof(f7168,plain,
( spl20_396
<=> ! [X2,X0,X1] :
( subset(sK6(X0,X1,X2),X1)
| in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ epsilon_transitive(X1)
| ~ in(X2,sK6(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_396])]) ).
fof(f1823,plain,
( ! [X2,X0,X1] :
( subset(sK6(X0,X1,X2),X1)
| in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ epsilon_transitive(X1)
| ~ in(X2,sK6(X0,X1,X2)) )
| ~ spl20_64
| ~ spl20_174 ),
inference(resolution,[],[f1780,f618]) ).
fof(f7166,plain,
( spl20_395
| ~ spl20_64
| ~ spl20_173 ),
inference(avatar_split_clause,[],[f1804,f1775,f617,f7164]) ).
fof(f7164,plain,
( spl20_395
<=> ! [X2,X0,X1] :
( subset(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ epsilon_transitive(X2)
| ~ in(X0,sK6(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_395])]) ).
fof(f1804,plain,
( ! [X2,X0,X1] :
( subset(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ epsilon_transitive(X2)
| ~ in(X0,sK6(X0,X1,X2)) )
| ~ spl20_64
| ~ spl20_173 ),
inference(resolution,[],[f1776,f618]) ).
fof(f7161,plain,
( spl20_394
| ~ spl20_46
| ~ spl20_192 ),
inference(avatar_split_clause,[],[f6839,f2310,f496,f7158]) ).
fof(f7158,plain,
( spl20_394
<=> relation(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_394])]) ).
fof(f496,plain,
( spl20_46
<=> ! [X0] :
( relation(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_46])]) ).
fof(f6839,plain,
( relation(sK1)
| ~ spl20_46
| ~ spl20_192 ),
inference(resolution,[],[f2311,f497]) ).
fof(f497,plain,
( ! [X0] :
( ~ empty(X0)
| relation(X0) )
| ~ spl20_46 ),
inference(avatar_component_clause,[],[f496]) ).
fof(f7156,plain,
( spl20_393
| ~ spl20_64
| ~ spl20_173 ),
inference(avatar_split_clause,[],[f1794,f1775,f617,f7154]) ).
fof(f7154,plain,
( spl20_393
<=> ! [X2,X0,X1] :
( subset(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ epsilon_transitive(X2)
| ~ in(X1,sK6(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_393])]) ).
fof(f1794,plain,
( ! [X2,X0,X1] :
( subset(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ epsilon_transitive(X2)
| ~ in(X1,sK6(X0,X1,X2)) )
| ~ spl20_64
| ~ spl20_173 ),
inference(resolution,[],[f1776,f618]) ).
fof(f7152,plain,
( spl20_392
| ~ spl20_138
| ~ spl20_171 ),
inference(avatar_split_clause,[],[f1764,f1665,f1195,f7150]) ).
fof(f7150,plain,
( spl20_392
<=> ! [X2,X0,X1] :
( element(sK6(X0,sK4(powerset(X1)),X2),X0)
| in(sK6(X0,sK4(powerset(X1)),X2),X2)
| sP0(X0,sK4(powerset(X1)),X2)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_392])]) ).
fof(f1764,plain,
( ! [X2,X0,X1] :
( element(sK6(X0,sK4(powerset(X1)),X2),X0)
| in(sK6(X0,sK4(powerset(X1)),X2),X2)
| sP0(X0,sK4(powerset(X1)),X2)
| ~ empty(X1) )
| ~ spl20_138
| ~ spl20_171 ),
inference(resolution,[],[f1666,f1196]) ).
fof(f7148,plain,
( spl20_391
| ~ spl20_81
| ~ spl20_171 ),
inference(avatar_split_clause,[],[f1757,f1665,f760,f7146]) ).
fof(f7146,plain,
( spl20_391
<=> ! [X2,X0,X1] :
( element(sK6(X0,X1,X2),X0)
| in(sK6(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| subset(sK6(X0,X1,X2),X1)
| ~ epsilon_transitive(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_391])]) ).
fof(f1757,plain,
( ! [X2,X0,X1] :
( element(sK6(X0,X1,X2),X0)
| in(sK6(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| subset(sK6(X0,X1,X2),X1)
| ~ epsilon_transitive(X1) )
| ~ spl20_81
| ~ spl20_171 ),
inference(resolution,[],[f1666,f761]) ).
fof(f7144,plain,
( spl20_390
| ~ spl20_138
| ~ spl20_171 ),
inference(avatar_split_clause,[],[f1754,f1665,f1195,f7142]) ).
fof(f7142,plain,
( spl20_390
<=> ! [X2,X0,X1] :
( element(sK6(X0,X1,sK4(powerset(X2))),X0)
| in(sK6(X0,X1,sK4(powerset(X2))),X1)
| sP0(X0,X1,sK4(powerset(X2)))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_390])]) ).
fof(f1754,plain,
( ! [X2,X0,X1] :
( element(sK6(X0,X1,sK4(powerset(X2))),X0)
| in(sK6(X0,X1,sK4(powerset(X2))),X1)
| sP0(X0,X1,sK4(powerset(X2)))
| ~ empty(X2) )
| ~ spl20_138
| ~ spl20_171 ),
inference(resolution,[],[f1666,f1196]) ).
fof(f7140,plain,
( spl20_389
| ~ spl20_81
| ~ spl20_171 ),
inference(avatar_split_clause,[],[f1747,f1665,f760,f7138]) ).
fof(f7138,plain,
( spl20_389
<=> ! [X2,X0,X1] :
( element(sK6(X0,X1,X2),X0)
| in(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| subset(sK6(X0,X1,X2),X2)
| ~ epsilon_transitive(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_389])]) ).
fof(f1747,plain,
( ! [X2,X0,X1] :
( element(sK6(X0,X1,X2),X0)
| in(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| subset(sK6(X0,X1,X2),X2)
| ~ epsilon_transitive(X2) )
| ~ spl20_81
| ~ spl20_171 ),
inference(resolution,[],[f1666,f761]) ).
fof(f7136,plain,
( spl20_388
| ~ spl20_138
| ~ spl20_169 ),
inference(avatar_split_clause,[],[f1730,f1657,f1195,f7134]) ).
fof(f7134,plain,
( spl20_388
<=> ! [X2,X0,X1] :
( element(sK6(sK4(powerset(X0)),X1,X2),X1)
| in(sK6(sK4(powerset(X0)),X1,X2),X2)
| sP0(sK4(powerset(X0)),X1,X2)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_388])]) ).
fof(f1730,plain,
( ! [X2,X0,X1] :
( element(sK6(sK4(powerset(X0)),X1,X2),X1)
| in(sK6(sK4(powerset(X0)),X1,X2),X2)
| sP0(sK4(powerset(X0)),X1,X2)
| ~ empty(X0) )
| ~ spl20_138
| ~ spl20_169 ),
inference(resolution,[],[f1658,f1196]) ).
fof(f7132,plain,
( spl20_387
| ~ spl20_81
| ~ spl20_169 ),
inference(avatar_split_clause,[],[f1723,f1657,f760,f7130]) ).
fof(f7130,plain,
( spl20_387
<=> ! [X2,X0,X1] :
( element(sK6(X0,X1,X2),X1)
| in(sK6(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| subset(sK6(X0,X1,X2),X0)
| ~ epsilon_transitive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_387])]) ).
fof(f1723,plain,
( ! [X2,X0,X1] :
( element(sK6(X0,X1,X2),X1)
| in(sK6(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| subset(sK6(X0,X1,X2),X0)
| ~ epsilon_transitive(X0) )
| ~ spl20_81
| ~ spl20_169 ),
inference(resolution,[],[f1658,f761]) ).
fof(f7128,plain,
( spl20_386
| ~ spl20_138
| ~ spl20_169 ),
inference(avatar_split_clause,[],[f1720,f1657,f1195,f7126]) ).
fof(f7126,plain,
( spl20_386
<=> ! [X2,X0,X1] :
( element(sK6(X0,X1,sK4(powerset(X2))),X1)
| in(sK6(X0,X1,sK4(powerset(X2))),X0)
| sP0(X0,X1,sK4(powerset(X2)))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_386])]) ).
fof(f1720,plain,
( ! [X2,X0,X1] :
( element(sK6(X0,X1,sK4(powerset(X2))),X1)
| in(sK6(X0,X1,sK4(powerset(X2))),X0)
| sP0(X0,X1,sK4(powerset(X2)))
| ~ empty(X2) )
| ~ spl20_138
| ~ spl20_169 ),
inference(resolution,[],[f1658,f1196]) ).
fof(f7124,plain,
( spl20_385
| ~ spl20_81
| ~ spl20_169 ),
inference(avatar_split_clause,[],[f1713,f1657,f760,f7122]) ).
fof(f7122,plain,
( spl20_385
<=> ! [X2,X0,X1] :
( element(sK6(X0,X1,X2),X1)
| in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| subset(sK6(X0,X1,X2),X2)
| ~ epsilon_transitive(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_385])]) ).
fof(f1713,plain,
( ! [X2,X0,X1] :
( element(sK6(X0,X1,X2),X1)
| in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| subset(sK6(X0,X1,X2),X2)
| ~ epsilon_transitive(X2) )
| ~ spl20_81
| ~ spl20_169 ),
inference(resolution,[],[f1658,f761]) ).
fof(f7120,plain,
( spl20_384
| ~ spl20_138
| ~ spl20_167 ),
inference(avatar_split_clause,[],[f1695,f1649,f1195,f7118]) ).
fof(f7118,plain,
( spl20_384
<=> ! [X2,X0,X1] :
( element(sK6(sK4(powerset(X0)),X1,X2),X2)
| in(sK6(sK4(powerset(X0)),X1,X2),X1)
| sP0(sK4(powerset(X0)),X1,X2)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_384])]) ).
fof(f1695,plain,
( ! [X2,X0,X1] :
( element(sK6(sK4(powerset(X0)),X1,X2),X2)
| in(sK6(sK4(powerset(X0)),X1,X2),X1)
| sP0(sK4(powerset(X0)),X1,X2)
| ~ empty(X0) )
| ~ spl20_138
| ~ spl20_167 ),
inference(resolution,[],[f1650,f1196]) ).
fof(f7115,plain,
( spl20_383
| ~ spl20_45
| ~ spl20_192 ),
inference(avatar_split_clause,[],[f6838,f2310,f492,f7112]) ).
fof(f7112,plain,
( spl20_383
<=> function(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_383])]) ).
fof(f492,plain,
( spl20_45
<=> ! [X0] :
( function(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_45])]) ).
fof(f6838,plain,
( function(sK1)
| ~ spl20_45
| ~ spl20_192 ),
inference(resolution,[],[f2311,f493]) ).
fof(f493,plain,
( ! [X0] :
( ~ empty(X0)
| function(X0) )
| ~ spl20_45 ),
inference(avatar_component_clause,[],[f492]) ).
fof(f7110,plain,
( spl20_382
| ~ spl20_81
| ~ spl20_167 ),
inference(avatar_split_clause,[],[f1688,f1649,f760,f7108]) ).
fof(f7108,plain,
( spl20_382
<=> ! [X2,X0,X1] :
( element(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| subset(sK6(X0,X1,X2),X0)
| ~ epsilon_transitive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_382])]) ).
fof(f1688,plain,
( ! [X2,X0,X1] :
( element(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| subset(sK6(X0,X1,X2),X0)
| ~ epsilon_transitive(X0) )
| ~ spl20_81
| ~ spl20_167 ),
inference(resolution,[],[f1650,f761]) ).
fof(f7106,plain,
( spl20_381
| ~ spl20_138
| ~ spl20_167 ),
inference(avatar_split_clause,[],[f1685,f1649,f1195,f7104]) ).
fof(f7104,plain,
( spl20_381
<=> ! [X2,X0,X1] :
( element(sK6(X0,sK4(powerset(X1)),X2),X2)
| in(sK6(X0,sK4(powerset(X1)),X2),X0)
| sP0(X0,sK4(powerset(X1)),X2)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_381])]) ).
fof(f1685,plain,
( ! [X2,X0,X1] :
( element(sK6(X0,sK4(powerset(X1)),X2),X2)
| in(sK6(X0,sK4(powerset(X1)),X2),X0)
| sP0(X0,sK4(powerset(X1)),X2)
| ~ empty(X1) )
| ~ spl20_138
| ~ spl20_167 ),
inference(resolution,[],[f1650,f1196]) ).
fof(f7102,plain,
( spl20_380
| ~ spl20_81
| ~ spl20_167 ),
inference(avatar_split_clause,[],[f1678,f1649,f760,f7100]) ).
fof(f7100,plain,
( spl20_380
<=> ! [X2,X0,X1] :
( element(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| subset(sK6(X0,X1,X2),X1)
| ~ epsilon_transitive(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_380])]) ).
fof(f1678,plain,
( ! [X2,X0,X1] :
( element(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| subset(sK6(X0,X1,X2),X1)
| ~ epsilon_transitive(X1) )
| ~ spl20_81
| ~ spl20_167 ),
inference(resolution,[],[f1650,f761]) ).
fof(f7098,plain,
( spl20_379
| ~ spl20_141
| ~ spl20_165 ),
inference(avatar_split_clause,[],[f1638,f1569,f1217,f7096]) ).
fof(f7096,plain,
( spl20_379
<=> ! [X2,X0,X1] :
( in(sK6(X0,sK4(powerset(X1)),X2),X2)
| sP0(X0,sK4(powerset(X1)),X2)
| ~ empty(X0)
| element(sK6(X0,sK4(powerset(X1)),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_379])]) ).
fof(f1638,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,sK4(powerset(X1)),X2),X2)
| sP0(X0,sK4(powerset(X1)),X2)
| ~ empty(X0)
| element(sK6(X0,sK4(powerset(X1)),X2),X1) )
| ~ spl20_141
| ~ spl20_165 ),
inference(resolution,[],[f1570,f1218]) ).
fof(f7094,plain,
( spl20_378
| ~ spl20_141
| ~ spl20_165 ),
inference(avatar_split_clause,[],[f1628,f1569,f1217,f7092]) ).
fof(f7092,plain,
( spl20_378
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,sK4(powerset(X2))),X1)
| sP0(X0,X1,sK4(powerset(X2)))
| ~ empty(X0)
| element(sK6(X0,X1,sK4(powerset(X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_378])]) ).
fof(f1628,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,sK4(powerset(X2))),X1)
| sP0(X0,X1,sK4(powerset(X2)))
| ~ empty(X0)
| element(sK6(X0,X1,sK4(powerset(X2))),X2) )
| ~ spl20_141
| ~ spl20_165 ),
inference(resolution,[],[f1570,f1218]) ).
fof(f7090,plain,
( spl20_377
| ~ spl20_141
| ~ spl20_164 ),
inference(avatar_split_clause,[],[f1615,f1565,f1217,f7088]) ).
fof(f7088,plain,
( spl20_377
<=> ! [X2,X0,X1] :
( in(sK6(sK4(powerset(X0)),X1,X2),X2)
| sP0(sK4(powerset(X0)),X1,X2)
| ~ empty(X1)
| element(sK6(sK4(powerset(X0)),X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_377])]) ).
fof(f1615,plain,
( ! [X2,X0,X1] :
( in(sK6(sK4(powerset(X0)),X1,X2),X2)
| sP0(sK4(powerset(X0)),X1,X2)
| ~ empty(X1)
| element(sK6(sK4(powerset(X0)),X1,X2),X0) )
| ~ spl20_141
| ~ spl20_164 ),
inference(resolution,[],[f1566,f1218]) ).
fof(f7086,plain,
( spl20_376
| ~ spl20_141
| ~ spl20_164 ),
inference(avatar_split_clause,[],[f1605,f1565,f1217,f7084]) ).
fof(f7084,plain,
( spl20_376
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,sK4(powerset(X2))),X0)
| sP0(X0,X1,sK4(powerset(X2)))
| ~ empty(X1)
| element(sK6(X0,X1,sK4(powerset(X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_376])]) ).
fof(f1605,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,sK4(powerset(X2))),X0)
| sP0(X0,X1,sK4(powerset(X2)))
| ~ empty(X1)
| element(sK6(X0,X1,sK4(powerset(X2))),X2) )
| ~ spl20_141
| ~ spl20_164 ),
inference(resolution,[],[f1566,f1218]) ).
fof(f7082,plain,
( spl20_375
| ~ spl20_141
| ~ spl20_163 ),
inference(avatar_split_clause,[],[f1590,f1561,f1217,f7080]) ).
fof(f7080,plain,
( spl20_375
<=> ! [X2,X0,X1] :
( in(sK6(sK4(powerset(X0)),X1,X2),X1)
| sP0(sK4(powerset(X0)),X1,X2)
| ~ empty(X2)
| element(sK6(sK4(powerset(X0)),X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_375])]) ).
fof(f1590,plain,
( ! [X2,X0,X1] :
( in(sK6(sK4(powerset(X0)),X1,X2),X1)
| sP0(sK4(powerset(X0)),X1,X2)
| ~ empty(X2)
| element(sK6(sK4(powerset(X0)),X1,X2),X0) )
| ~ spl20_141
| ~ spl20_163 ),
inference(resolution,[],[f1562,f1218]) ).
fof(f7017,plain,
( spl20_374
| ~ spl20_54
| ~ spl20_117
| ~ spl20_129
| ~ spl20_192 ),
inference(avatar_split_clause,[],[f6959,f2310,f1109,f1024,f566,f7014]) ).
fof(f6959,plain,
( sK8 = set_union2(sK2,singleton(sK2))
| ~ spl20_54
| ~ spl20_117
| ~ spl20_129
| ~ spl20_192 ),
inference(forward_demodulation,[],[f1111,f6848]) ).
fof(f6943,plain,
( ~ spl20_192
| ~ spl20_57
| ~ spl20_368 ),
inference(avatar_split_clause,[],[f6621,f6615,f578,f2310]) ).
fof(f6621,plain,
( ~ empty(sK1)
| ~ spl20_57
| ~ spl20_368 ),
inference(superposition,[],[f579,f6617]) ).
fof(f6617,plain,
( sK1 = set_union2(sK8,singleton(sK8))
| ~ spl20_368 ),
inference(avatar_component_clause,[],[f6615]) ).
fof(f6942,plain,
( spl20_373
| ~ spl20_141
| ~ spl20_163 ),
inference(avatar_split_clause,[],[f1580,f1561,f1217,f6940]) ).
fof(f6940,plain,
( spl20_373
<=> ! [X2,X0,X1] :
( in(sK6(X0,sK4(powerset(X1)),X2),X0)
| sP0(X0,sK4(powerset(X1)),X2)
| ~ empty(X2)
| element(sK6(X0,sK4(powerset(X1)),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_373])]) ).
fof(f1580,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,sK4(powerset(X1)),X2),X0)
| sP0(X0,sK4(powerset(X1)),X2)
| ~ empty(X2)
| element(sK6(X0,sK4(powerset(X1)),X2),X1) )
| ~ spl20_141
| ~ spl20_163 ),
inference(resolution,[],[f1562,f1218]) ).
fof(f6938,plain,
( spl20_372
| ~ spl20_150
| ~ spl20_156 ),
inference(avatar_split_clause,[],[f1418,f1411,f1313,f6936]) ).
fof(f6936,plain,
( spl20_372
<=> ! [X2,X0,X1] :
( set_union2(X0,X1) = X2
| ~ ordinal(set_union2(X0,X1))
| ~ ordinal(X2)
| subset(set_union2(X0,X1),X2)
| ~ epsilon_transitive(X2)
| in(X2,X0)
| in(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_372])]) ).
fof(f1411,plain,
( spl20_156
<=> ! [X0,X1] :
( in(X1,X0)
| X0 = X1
| ~ ordinal(X0)
| ~ ordinal(X1)
| subset(X0,X1)
| ~ epsilon_transitive(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_156])]) ).
fof(f1418,plain,
( ! [X2,X0,X1] :
( set_union2(X0,X1) = X2
| ~ ordinal(set_union2(X0,X1))
| ~ ordinal(X2)
| subset(set_union2(X0,X1),X2)
| ~ epsilon_transitive(X2)
| in(X2,X0)
| in(X2,X1) )
| ~ spl20_150
| ~ spl20_156 ),
inference(resolution,[],[f1412,f1314]) ).
fof(f1412,plain,
( ! [X0,X1] :
( in(X1,X0)
| X0 = X1
| ~ ordinal(X0)
| ~ ordinal(X1)
| subset(X0,X1)
| ~ epsilon_transitive(X1) )
| ~ spl20_156 ),
inference(avatar_component_clause,[],[f1411]) ).
fof(f6934,plain,
( spl20_371
| ~ spl20_101
| ~ spl20_138 ),
inference(avatar_split_clause,[],[f1207,f1195,f900,f6932]) ).
fof(f6932,plain,
( spl20_371
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| in(sK6(sK4(powerset(X0)),X1,X2),X2)
| in(sK6(sK4(powerset(X0)),X1,X2),X1)
| sP0(sK4(powerset(X0)),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_371])]) ).
fof(f1207,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| in(sK6(sK4(powerset(X0)),X1,X2),X2)
| in(sK6(sK4(powerset(X0)),X1,X2),X1)
| sP0(sK4(powerset(X0)),X1,X2) )
| ~ spl20_101
| ~ spl20_138 ),
inference(resolution,[],[f1196,f901]) ).
fof(f6930,plain,
( spl20_370
| ~ spl20_101
| ~ spl20_138 ),
inference(avatar_split_clause,[],[f1206,f1195,f900,f6928]) ).
fof(f6928,plain,
( spl20_370
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| in(sK6(X1,sK4(powerset(X0)),X2),X2)
| in(sK6(X1,sK4(powerset(X0)),X2),X1)
| sP0(X1,sK4(powerset(X0)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_370])]) ).
fof(f1206,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| in(sK6(X1,sK4(powerset(X0)),X2),X2)
| in(sK6(X1,sK4(powerset(X0)),X2),X1)
| sP0(X1,sK4(powerset(X0)),X2) )
| ~ spl20_101
| ~ spl20_138 ),
inference(resolution,[],[f1196,f901]) ).
fof(f6926,plain,
( spl20_369
| ~ spl20_101
| ~ spl20_138 ),
inference(avatar_split_clause,[],[f1205,f1195,f900,f6924]) ).
fof(f6924,plain,
( spl20_369
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| in(sK6(X1,X2,sK4(powerset(X0))),X2)
| in(sK6(X1,X2,sK4(powerset(X0))),X1)
| sP0(X1,X2,sK4(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_369])]) ).
fof(f1205,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| in(sK6(X1,X2,sK4(powerset(X0))),X2)
| in(sK6(X1,X2,sK4(powerset(X0))),X1)
| sP0(X1,X2,sK4(powerset(X0))) )
| ~ spl20_101
| ~ spl20_138 ),
inference(resolution,[],[f1196,f901]) ).
fof(f6835,plain,
( spl20_192
| ~ spl20_136
| ~ spl20_185 ),
inference(avatar_split_clause,[],[f4410,f2135,f1161,f2310]) ).
fof(f1161,plain,
( spl20_136
<=> ! [X0] :
( empty(X0)
| in(sK4(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_136])]) ).
fof(f2135,plain,
( spl20_185
<=> ! [X0] : ~ in(X0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_185])]) ).
fof(f4410,plain,
( empty(sK1)
| ~ spl20_136
| ~ spl20_185 ),
inference(resolution,[],[f2136,f1162]) ).
fof(f1162,plain,
( ! [X0] :
( in(sK4(X0),X0)
| empty(X0) )
| ~ spl20_136 ),
inference(avatar_component_clause,[],[f1161]) ).
fof(f2136,plain,
( ! [X0] : ~ in(X0,sK1)
| ~ spl20_185 ),
inference(avatar_component_clause,[],[f2135]) ).
fof(f6618,plain,
( spl20_368
| ~ spl20_54
| ~ spl20_117
| ~ spl20_129
| ~ spl20_184 ),
inference(avatar_split_clause,[],[f6520,f2131,f1109,f1024,f566,f6615]) ).
fof(f6520,plain,
( sK1 = set_union2(sK8,singleton(sK8))
| ~ spl20_54
| ~ spl20_117
| ~ spl20_129
| ~ spl20_184 ),
inference(forward_demodulation,[],[f1111,f4394]) ).
fof(f4394,plain,
( sK2 = sK8
| ~ spl20_54
| ~ spl20_117
| ~ spl20_184 ),
inference(forward_demodulation,[],[f4389,f1026]) ).
fof(f4389,plain,
( empty_set = sK2
| ~ spl20_54
| ~ spl20_184 ),
inference(resolution,[],[f2132,f567]) ).
fof(f2132,plain,
( empty(sK2)
| ~ spl20_184 ),
inference(avatar_component_clause,[],[f2131]) ).
fof(f6495,plain,
( ~ spl20_134
| ~ spl20_367 ),
inference(avatar_contradiction_clause,[],[f6486]) ).
fof(f6486,plain,
( $false
| ~ spl20_134
| ~ spl20_367 ),
inference(resolution,[],[f6194,f1154]) ).
fof(f1154,plain,
( ! [X0] : ~ in(set_union2(X0,singleton(X0)),X0)
| ~ spl20_134 ),
inference(avatar_component_clause,[],[f1153]) ).
fof(f1153,plain,
( spl20_134
<=> ! [X0] : ~ in(set_union2(X0,singleton(X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_134])]) ).
fof(f6194,plain,
( in(set_union2(sK2,singleton(sK2)),sK2)
| ~ spl20_367 ),
inference(avatar_component_clause,[],[f6192]) ).
fof(f6192,plain,
( spl20_367
<=> in(set_union2(sK2,singleton(sK2)),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_367])]) ).
fof(f6195,plain,
( spl20_367
| spl20_184
| ~ spl20_82
| ~ spl20_294 ),
inference(avatar_split_clause,[],[f4316,f4272,f764,f2131,f6192]) ).
fof(f764,plain,
( spl20_82
<=> ! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_82])]) ).
fof(f4272,plain,
( spl20_294
<=> element(set_union2(sK2,singleton(sK2)),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_294])]) ).
fof(f4316,plain,
( empty(sK2)
| in(set_union2(sK2,singleton(sK2)),sK2)
| ~ spl20_82
| ~ spl20_294 ),
inference(resolution,[],[f4274,f765]) ).
fof(f765,plain,
( ! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) )
| ~ spl20_82 ),
inference(avatar_component_clause,[],[f764]) ).
fof(f4274,plain,
( element(set_union2(sK2,singleton(sK2)),sK2)
| ~ spl20_294 ),
inference(avatar_component_clause,[],[f4272]) ).
fof(f6068,plain,
( spl20_366
| ~ spl20_64
| ~ spl20_171 ),
inference(avatar_split_clause,[],[f1759,f1665,f617,f6066]) ).
fof(f6066,plain,
( spl20_366
<=> ! [X2,X0,X1] :
( element(sK6(X0,X1,X2),X0)
| in(sK6(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| ~ in(X1,sK6(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_366])]) ).
fof(f1759,plain,
( ! [X2,X0,X1] :
( element(sK6(X0,X1,X2),X0)
| in(sK6(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| ~ in(X1,sK6(X0,X1,X2)) )
| ~ spl20_64
| ~ spl20_171 ),
inference(resolution,[],[f1666,f618]) ).
fof(f6064,plain,
( spl20_365
| ~ spl20_64
| ~ spl20_171 ),
inference(avatar_split_clause,[],[f1749,f1665,f617,f6062]) ).
fof(f6062,plain,
( spl20_365
<=> ! [X2,X0,X1] :
( element(sK6(X0,X1,X2),X0)
| in(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ in(X2,sK6(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_365])]) ).
fof(f1749,plain,
( ! [X2,X0,X1] :
( element(sK6(X0,X1,X2),X0)
| in(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ in(X2,sK6(X0,X1,X2)) )
| ~ spl20_64
| ~ spl20_171 ),
inference(resolution,[],[f1666,f618]) ).
fof(f6060,plain,
( spl20_364
| ~ spl20_64
| ~ spl20_169 ),
inference(avatar_split_clause,[],[f1725,f1657,f617,f6058]) ).
fof(f6058,plain,
( spl20_364
<=> ! [X2,X0,X1] :
( element(sK6(X0,X1,X2),X1)
| in(sK6(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| ~ in(X0,sK6(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_364])]) ).
fof(f1725,plain,
( ! [X2,X0,X1] :
( element(sK6(X0,X1,X2),X1)
| in(sK6(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| ~ in(X0,sK6(X0,X1,X2)) )
| ~ spl20_64
| ~ spl20_169 ),
inference(resolution,[],[f1658,f618]) ).
fof(f6056,plain,
( spl20_363
| ~ spl20_65
| ~ spl20_169 ),
inference(avatar_split_clause,[],[f1724,f1657,f621,f6054]) ).
fof(f6054,plain,
( spl20_363
<=> ! [X2,X0,X1] :
( element(sK6(X0,X1,X2),X1)
| in(sK6(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| element(sK6(X0,X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_363])]) ).
fof(f1724,plain,
( ! [X2,X0,X1] :
( element(sK6(X0,X1,X2),X1)
| in(sK6(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| element(sK6(X0,X1,X2),X0) )
| ~ spl20_65
| ~ spl20_169 ),
inference(resolution,[],[f1658,f622]) ).
fof(f6052,plain,
( spl20_362
| ~ spl20_64
| ~ spl20_169 ),
inference(avatar_split_clause,[],[f1715,f1657,f617,f6050]) ).
fof(f6050,plain,
( spl20_362
<=> ! [X2,X0,X1] :
( element(sK6(X0,X1,X2),X1)
| in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ in(X2,sK6(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_362])]) ).
fof(f1715,plain,
( ! [X2,X0,X1] :
( element(sK6(X0,X1,X2),X1)
| in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ in(X2,sK6(X0,X1,X2)) )
| ~ spl20_64
| ~ spl20_169 ),
inference(resolution,[],[f1658,f618]) ).
fof(f6048,plain,
( spl20_361
| ~ spl20_64
| ~ spl20_167 ),
inference(avatar_split_clause,[],[f1690,f1649,f617,f6046]) ).
fof(f6046,plain,
( spl20_361
<=> ! [X2,X0,X1] :
( element(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ in(X0,sK6(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_361])]) ).
fof(f1690,plain,
( ! [X2,X0,X1] :
( element(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ in(X0,sK6(X0,X1,X2)) )
| ~ spl20_64
| ~ spl20_167 ),
inference(resolution,[],[f1650,f618]) ).
fof(f6044,plain,
( spl20_360
| ~ spl20_65
| ~ spl20_167 ),
inference(avatar_split_clause,[],[f1689,f1649,f621,f6042]) ).
fof(f6042,plain,
( spl20_360
<=> ! [X2,X0,X1] :
( element(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| element(sK6(X0,X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_360])]) ).
fof(f1689,plain,
( ! [X2,X0,X1] :
( element(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| element(sK6(X0,X1,X2),X0) )
| ~ spl20_65
| ~ spl20_167 ),
inference(resolution,[],[f1650,f622]) ).
fof(f6040,plain,
( spl20_359
| ~ spl20_64
| ~ spl20_167 ),
inference(avatar_split_clause,[],[f1680,f1649,f617,f6038]) ).
fof(f6038,plain,
( spl20_359
<=> ! [X2,X0,X1] :
( element(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ in(X1,sK6(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_359])]) ).
fof(f1680,plain,
( ! [X2,X0,X1] :
( element(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ in(X1,sK6(X0,X1,X2)) )
| ~ spl20_64
| ~ spl20_167 ),
inference(resolution,[],[f1650,f618]) ).
fof(f5946,plain,
( spl20_358
| ~ spl20_65
| ~ spl20_167 ),
inference(avatar_split_clause,[],[f1679,f1649,f621,f5944]) ).
fof(f5944,plain,
( spl20_358
<=> ! [X2,X0,X1] :
( element(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| element(sK6(X0,X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_358])]) ).
fof(f1679,plain,
( ! [X2,X0,X1] :
( element(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| element(sK6(X0,X1,X2),X1) )
| ~ spl20_65
| ~ spl20_167 ),
inference(resolution,[],[f1650,f622]) ).
fof(f5942,plain,
( spl20_357
| ~ spl20_80
| ~ spl20_161 ),
inference(avatar_split_clause,[],[f1529,f1446,f727,f5940]) ).
fof(f5940,plain,
( spl20_357
<=> ! [X0,X1] :
( in(sK6(singleton(X0),singleton(X0),X1),X1)
| sP0(singleton(X0),singleton(X0),X1)
| sK6(singleton(X0),singleton(X0),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_357])]) ).
fof(f1529,plain,
( ! [X0,X1] :
( in(sK6(singleton(X0),singleton(X0),X1),X1)
| sP0(singleton(X0),singleton(X0),X1)
| sK6(singleton(X0),singleton(X0),X1) = X0 )
| ~ spl20_80
| ~ spl20_161 ),
inference(resolution,[],[f1447,f728]) ).
fof(f5938,plain,
( spl20_356
| ~ spl20_141
| ~ spl20_161 ),
inference(avatar_split_clause,[],[f1520,f1446,f1217,f5936]) ).
fof(f5936,plain,
( spl20_356
<=> ! [X0,X1] :
( in(sK6(X0,X0,sK4(powerset(X1))),X0)
| sP0(X0,X0,sK4(powerset(X1)))
| element(sK6(X0,X0,sK4(powerset(X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_356])]) ).
fof(f1520,plain,
( ! [X0,X1] :
( in(sK6(X0,X0,sK4(powerset(X1))),X0)
| sP0(X0,X0,sK4(powerset(X1)))
| element(sK6(X0,X0,sK4(powerset(X1))),X1) )
| ~ spl20_141
| ~ spl20_161 ),
inference(resolution,[],[f1447,f1218]) ).
fof(f5934,plain,
( spl20_355
| ~ spl20_141
| ~ spl20_160 ),
inference(avatar_split_clause,[],[f1497,f1442,f1217,f5932]) ).
fof(f5932,plain,
( spl20_355
<=> ! [X0,X1] :
( in(sK6(X0,sK4(powerset(X1)),X0),X0)
| sP0(X0,sK4(powerset(X1)),X0)
| element(sK6(X0,sK4(powerset(X1)),X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_355])]) ).
fof(f1497,plain,
( ! [X0,X1] :
( in(sK6(X0,sK4(powerset(X1)),X0),X0)
| sP0(X0,sK4(powerset(X1)),X0)
| element(sK6(X0,sK4(powerset(X1)),X0),X1) )
| ~ spl20_141
| ~ spl20_160 ),
inference(resolution,[],[f1443,f1218]) ).
fof(f5930,plain,
( spl20_354
| ~ spl20_141
| ~ spl20_159 ),
inference(avatar_split_clause,[],[f1482,f1438,f1217,f5928]) ).
fof(f5928,plain,
( spl20_354
<=> ! [X0,X1] :
( in(sK6(sK4(powerset(X0)),X1,X1),X1)
| sP0(sK4(powerset(X0)),X1,X1)
| element(sK6(sK4(powerset(X0)),X1,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_354])]) ).
fof(f1482,plain,
( ! [X0,X1] :
( in(sK6(sK4(powerset(X0)),X1,X1),X1)
| sP0(sK4(powerset(X0)),X1,X1)
| element(sK6(sK4(powerset(X0)),X1,X1),X0) )
| ~ spl20_141
| ~ spl20_159 ),
inference(resolution,[],[f1439,f1218]) ).
fof(f5926,plain,
( spl20_353
| ~ spl20_89
| ~ spl20_158 ),
inference(avatar_split_clause,[],[f1462,f1434,f808,f5924]) ).
fof(f5924,plain,
( spl20_353
<=> ! [X0,X1] :
( singleton(X0) = X1
| sK5(X0,X1) = X0
| ~ epsilon_transitive(X1)
| ordinal_subset(sK5(X0,X1),X1)
| ~ ordinal(X1)
| ~ ordinal(sK5(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_353])]) ).
fof(f1434,plain,
( spl20_158
<=> ! [X0,X1] :
( sK5(X0,X1) = X0
| singleton(X0) = X1
| subset(sK5(X0,X1),X1)
| ~ epsilon_transitive(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_158])]) ).
fof(f1462,plain,
( ! [X0,X1] :
( singleton(X0) = X1
| sK5(X0,X1) = X0
| ~ epsilon_transitive(X1)
| ordinal_subset(sK5(X0,X1),X1)
| ~ ordinal(X1)
| ~ ordinal(sK5(X0,X1)) )
| ~ spl20_89
| ~ spl20_158 ),
inference(resolution,[],[f1435,f809]) ).
fof(f1435,plain,
( ! [X0,X1] :
( subset(sK5(X0,X1),X1)
| singleton(X0) = X1
| sK5(X0,X1) = X0
| ~ epsilon_transitive(X1) )
| ~ spl20_158 ),
inference(avatar_component_clause,[],[f1434]) ).
fof(f5922,plain,
( spl20_352
| ~ spl20_141
| ~ spl20_157 ),
inference(avatar_split_clause,[],[f1457,f1430,f1217,f5920]) ).
fof(f5920,plain,
( spl20_352
<=> ! [X0,X1] :
( singleton(X0) = sK4(powerset(X1))
| ~ ordinal(sK4(powerset(X1)))
| ~ ordinal(singleton(X0))
| sK4(powerset(X1)) = X0
| element(singleton(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_352])]) ).
fof(f1457,plain,
( ! [X0,X1] :
( singleton(X0) = sK4(powerset(X1))
| ~ ordinal(sK4(powerset(X1)))
| ~ ordinal(singleton(X0))
| sK4(powerset(X1)) = X0
| element(singleton(X0),X1) )
| ~ spl20_141
| ~ spl20_157 ),
inference(resolution,[],[f1431,f1218]) ).
fof(f5918,plain,
( spl20_351
| ~ spl20_150
| ~ spl20_153 ),
inference(avatar_split_clause,[],[f1383,f1376,f1313,f5916]) ).
fof(f5916,plain,
( spl20_351
<=> ! [X2,X0,X1] :
( set_union2(X0,X1) = X2
| ~ ordinal(set_union2(X0,X1))
| ~ ordinal(X2)
| element(set_union2(X0,X1),X2)
| in(X2,X0)
| in(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_351])]) ).
fof(f1383,plain,
( ! [X2,X0,X1] :
( set_union2(X0,X1) = X2
| ~ ordinal(set_union2(X0,X1))
| ~ ordinal(X2)
| element(set_union2(X0,X1),X2)
| in(X2,X0)
| in(X2,X1) )
| ~ spl20_150
| ~ spl20_153 ),
inference(resolution,[],[f1377,f1314]) ).
fof(f5914,plain,
( spl20_350
| ~ spl20_95
| ~ spl20_150 ),
inference(avatar_split_clause,[],[f1329,f1313,f850,f5912]) ).
fof(f5912,plain,
( spl20_350
<=> ! [X2,X0,X1] :
( in(X0,X1)
| in(X0,X2)
| in(set_union2(X1,X2),X0)
| set_union2(X1,X2) = X0
| ~ ordinal(set_union2(X1,X2))
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_350])]) ).
fof(f850,plain,
( spl20_95
<=> ! [X0,X1] :
( in(X1,X0)
| X0 = X1
| in(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_95])]) ).
fof(f1329,plain,
( ! [X2,X0,X1] :
( in(X0,X1)
| in(X0,X2)
| in(set_union2(X1,X2),X0)
| set_union2(X1,X2) = X0
| ~ ordinal(set_union2(X1,X2))
| ~ ordinal(X0) )
| ~ spl20_95
| ~ spl20_150 ),
inference(resolution,[],[f1314,f851]) ).
fof(f851,plain,
( ! [X0,X1] :
( in(X1,X0)
| in(X0,X1)
| X0 = X1
| ~ ordinal(X1)
| ~ ordinal(X0) )
| ~ spl20_95 ),
inference(avatar_component_clause,[],[f850]) ).
fof(f5910,plain,
( spl20_349
| ~ spl20_98
| ~ spl20_147 ),
inference(avatar_split_clause,[],[f1299,f1285,f880,f5908]) ).
fof(f5908,plain,
( spl20_349
<=> ! [X2,X0,X1] :
( empty(powerset(X0))
| ~ subset(sK6(X1,X2,powerset(X0)),X0)
| ~ in(sK6(X1,X2,powerset(X0)),X2)
| sP0(X1,X2,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_349])]) ).
fof(f1285,plain,
( spl20_147
<=> ! [X0,X1] :
( empty(powerset(X0))
| in(X1,powerset(X0))
| ~ subset(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_147])]) ).
fof(f1299,plain,
( ! [X2,X0,X1] :
( empty(powerset(X0))
| ~ subset(sK6(X1,X2,powerset(X0)),X0)
| ~ in(sK6(X1,X2,powerset(X0)),X2)
| sP0(X1,X2,powerset(X0)) )
| ~ spl20_98
| ~ spl20_147 ),
inference(resolution,[],[f1286,f881]) ).
fof(f1286,plain,
( ! [X0,X1] :
( in(X1,powerset(X0))
| empty(powerset(X0))
| ~ subset(X1,X0) )
| ~ spl20_147 ),
inference(avatar_component_clause,[],[f1285]) ).
fof(f5906,plain,
( spl20_348
| ~ spl20_146
| ~ spl20_334 ),
inference(avatar_split_clause,[],[f5671,f5453,f1277,f5904]) ).
fof(f5904,plain,
( spl20_348
<=> ! [X0] :
( ~ in(X0,sK4(sK1))
| element(X0,sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_348])]) ).
fof(f5453,plain,
( spl20_334
<=> subset(sK4(sK1),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_334])]) ).
fof(f5671,plain,
( ! [X0] :
( ~ in(X0,sK4(sK1))
| element(X0,sK2) )
| ~ spl20_146
| ~ spl20_334 ),
inference(resolution,[],[f5455,f1278]) ).
fof(f5455,plain,
( subset(sK4(sK1),sK2)
| ~ spl20_334 ),
inference(avatar_component_clause,[],[f5453]) ).
fof(f5902,plain,
( spl20_347
| ~ spl20_99
| ~ spl20_147 ),
inference(avatar_split_clause,[],[f1298,f1285,f884,f5900]) ).
fof(f5900,plain,
( spl20_347
<=> ! [X2,X0,X1] :
( empty(powerset(X0))
| ~ subset(sK6(X1,X2,powerset(X0)),X0)
| ~ in(sK6(X1,X2,powerset(X0)),X1)
| sP0(X1,X2,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_347])]) ).
fof(f1298,plain,
( ! [X2,X0,X1] :
( empty(powerset(X0))
| ~ subset(sK6(X1,X2,powerset(X0)),X0)
| ~ in(sK6(X1,X2,powerset(X0)),X1)
| sP0(X1,X2,powerset(X0)) )
| ~ spl20_99
| ~ spl20_147 ),
inference(resolution,[],[f1286,f885]) ).
fof(f5898,plain,
( spl20_346
| ~ spl20_98
| ~ spl20_143 ),
inference(avatar_split_clause,[],[f1260,f1225,f880,f5896]) ).
fof(f5896,plain,
( spl20_346
<=> ! [X0,X3,X2,X1] :
( ~ in(sK6(X0,X1,set_union2(X2,X3)),X3)
| ~ in(sK6(X0,X1,set_union2(X2,X3)),X1)
| sP0(X0,X1,set_union2(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_346])]) ).
fof(f1225,plain,
( spl20_143
<=> ! [X2,X0,X1] :
( ~ in(X0,X1)
| in(X0,set_union2(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_143])]) ).
fof(f1260,plain,
( ! [X2,X3,X0,X1] :
( ~ in(sK6(X0,X1,set_union2(X2,X3)),X3)
| ~ in(sK6(X0,X1,set_union2(X2,X3)),X1)
| sP0(X0,X1,set_union2(X2,X3)) )
| ~ spl20_98
| ~ spl20_143 ),
inference(resolution,[],[f1226,f881]) ).
fof(f1226,plain,
( ! [X2,X0,X1] :
( in(X0,set_union2(X2,X1))
| ~ in(X0,X1) )
| ~ spl20_143 ),
inference(avatar_component_clause,[],[f1225]) ).
fof(f5894,plain,
( spl20_345
| ~ spl20_99
| ~ spl20_143 ),
inference(avatar_split_clause,[],[f1259,f1225,f884,f5892]) ).
fof(f5892,plain,
( spl20_345
<=> ! [X0,X3,X2,X1] :
( ~ in(sK6(X0,X1,set_union2(X2,X3)),X3)
| ~ in(sK6(X0,X1,set_union2(X2,X3)),X0)
| sP0(X0,X1,set_union2(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_345])]) ).
fof(f1259,plain,
( ! [X2,X3,X0,X1] :
( ~ in(sK6(X0,X1,set_union2(X2,X3)),X3)
| ~ in(sK6(X0,X1,set_union2(X2,X3)),X0)
| sP0(X0,X1,set_union2(X2,X3)) )
| ~ spl20_99
| ~ spl20_143 ),
inference(resolution,[],[f1226,f885]) ).
fof(f5890,plain,
( spl20_344
| ~ spl20_98
| ~ spl20_142 ),
inference(avatar_split_clause,[],[f1247,f1221,f880,f5888]) ).
fof(f5888,plain,
( spl20_344
<=> ! [X0,X3,X2,X1] :
( ~ in(sK6(X0,X1,set_union2(X2,X3)),X2)
| ~ in(sK6(X0,X1,set_union2(X2,X3)),X1)
| sP0(X0,X1,set_union2(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_344])]) ).
fof(f1221,plain,
( spl20_142
<=> ! [X2,X0,X1] :
( ~ in(X0,X1)
| in(X0,set_union2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_142])]) ).
fof(f1247,plain,
( ! [X2,X3,X0,X1] :
( ~ in(sK6(X0,X1,set_union2(X2,X3)),X2)
| ~ in(sK6(X0,X1,set_union2(X2,X3)),X1)
| sP0(X0,X1,set_union2(X2,X3)) )
| ~ spl20_98
| ~ spl20_142 ),
inference(resolution,[],[f1222,f881]) ).
fof(f1222,plain,
( ! [X2,X0,X1] :
( in(X0,set_union2(X1,X2))
| ~ in(X0,X1) )
| ~ spl20_142 ),
inference(avatar_component_clause,[],[f1221]) ).
fof(f5886,plain,
( spl20_343
| ~ spl20_99
| ~ spl20_142 ),
inference(avatar_split_clause,[],[f1246,f1221,f884,f5884]) ).
fof(f5884,plain,
( spl20_343
<=> ! [X0,X3,X2,X1] :
( ~ in(sK6(X0,X1,set_union2(X2,X3)),X2)
| ~ in(sK6(X0,X1,set_union2(X2,X3)),X0)
| sP0(X0,X1,set_union2(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_343])]) ).
fof(f1246,plain,
( ! [X2,X3,X0,X1] :
( ~ in(sK6(X0,X1,set_union2(X2,X3)),X2)
| ~ in(sK6(X0,X1,set_union2(X2,X3)),X0)
| sP0(X0,X1,set_union2(X2,X3)) )
| ~ spl20_99
| ~ spl20_142 ),
inference(resolution,[],[f1222,f885]) ).
fof(f5776,plain,
( ~ spl20_2
| ~ spl20_1
| spl20_189
| ~ spl20_88
| ~ spl20_181 ),
inference(avatar_split_clause,[],[f2098,f2094,f804,f2235,f275,f280]) ).
fof(f280,plain,
( spl20_2
<=> ordinal(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_2])]) ).
fof(f804,plain,
( spl20_88
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_88])]) ).
fof(f2094,plain,
( spl20_181
<=> ordinal_subset(sK2,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_181])]) ).
fof(f2098,plain,
( subset(sK2,sK1)
| ~ ordinal(sK1)
| ~ ordinal(sK2)
| ~ spl20_88
| ~ spl20_181 ),
inference(resolution,[],[f2096,f805]) ).
fof(f805,plain,
( ! [X0,X1] :
( ~ ordinal_subset(X0,X1)
| subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) )
| ~ spl20_88 ),
inference(avatar_component_clause,[],[f804]) ).
fof(f2096,plain,
( ordinal_subset(sK2,sK1)
| ~ spl20_181 ),
inference(avatar_component_clause,[],[f2094]) ).
fof(f5698,plain,
( spl20_342
| ~ spl20_80
| ~ spl20_165 ),
inference(avatar_split_clause,[],[f1637,f1569,f727,f5696]) ).
fof(f5696,plain,
( spl20_342
<=> ! [X2,X0,X1] :
( in(sK6(X0,singleton(X1),X2),X2)
| sP0(X0,singleton(X1),X2)
| ~ empty(X0)
| sK6(X0,singleton(X1),X2) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_342])]) ).
fof(f1637,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,singleton(X1),X2),X2)
| sP0(X0,singleton(X1),X2)
| ~ empty(X0)
| sK6(X0,singleton(X1),X2) = X1 )
| ~ spl20_80
| ~ spl20_165 ),
inference(resolution,[],[f1570,f728]) ).
fof(f5694,plain,
( spl20_341
| ~ spl20_80
| ~ spl20_165 ),
inference(avatar_split_clause,[],[f1627,f1569,f727,f5692]) ).
fof(f5692,plain,
( spl20_341
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,singleton(X2)),X1)
| sP0(X0,X1,singleton(X2))
| ~ empty(X0)
| sK6(X0,X1,singleton(X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_341])]) ).
fof(f1627,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,singleton(X2)),X1)
| sP0(X0,X1,singleton(X2))
| ~ empty(X0)
| sK6(X0,X1,singleton(X2)) = X2 )
| ~ spl20_80
| ~ spl20_165 ),
inference(resolution,[],[f1570,f728]) ).
fof(f5690,plain,
( spl20_340
| ~ spl20_80
| ~ spl20_164 ),
inference(avatar_split_clause,[],[f1614,f1565,f727,f5688]) ).
fof(f5688,plain,
( spl20_340
<=> ! [X2,X0,X1] :
( in(sK6(singleton(X0),X1,X2),X2)
| sP0(singleton(X0),X1,X2)
| ~ empty(X1)
| sK6(singleton(X0),X1,X2) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_340])]) ).
fof(f1614,plain,
( ! [X2,X0,X1] :
( in(sK6(singleton(X0),X1,X2),X2)
| sP0(singleton(X0),X1,X2)
| ~ empty(X1)
| sK6(singleton(X0),X1,X2) = X0 )
| ~ spl20_80
| ~ spl20_164 ),
inference(resolution,[],[f1566,f728]) ).
fof(f5686,plain,
( spl20_339
| ~ spl20_80
| ~ spl20_164 ),
inference(avatar_split_clause,[],[f1604,f1565,f727,f5684]) ).
fof(f5684,plain,
( spl20_339
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,singleton(X2)),X0)
| sP0(X0,X1,singleton(X2))
| ~ empty(X1)
| sK6(X0,X1,singleton(X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_339])]) ).
fof(f1604,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,singleton(X2)),X0)
| sP0(X0,X1,singleton(X2))
| ~ empty(X1)
| sK6(X0,X1,singleton(X2)) = X2 )
| ~ spl20_80
| ~ spl20_164 ),
inference(resolution,[],[f1566,f728]) ).
fof(f5682,plain,
( spl20_338
| ~ spl20_80
| ~ spl20_163 ),
inference(avatar_split_clause,[],[f1589,f1561,f727,f5680]) ).
fof(f5680,plain,
( spl20_338
<=> ! [X2,X0,X1] :
( in(sK6(singleton(X0),X1,X2),X1)
| sP0(singleton(X0),X1,X2)
| ~ empty(X2)
| sK6(singleton(X0),X1,X2) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_338])]) ).
fof(f1589,plain,
( ! [X2,X0,X1] :
( in(sK6(singleton(X0),X1,X2),X1)
| sP0(singleton(X0),X1,X2)
| ~ empty(X2)
| sK6(singleton(X0),X1,X2) = X0 )
| ~ spl20_80
| ~ spl20_163 ),
inference(resolution,[],[f1562,f728]) ).
fof(f5678,plain,
( spl20_337
| ~ spl20_80
| ~ spl20_163 ),
inference(avatar_split_clause,[],[f1579,f1561,f727,f5676]) ).
fof(f5676,plain,
( spl20_337
<=> ! [X2,X0,X1] :
( in(sK6(X0,singleton(X1),X2),X0)
| sP0(X0,singleton(X1),X2)
| ~ empty(X2)
| sK6(X0,singleton(X1),X2) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_337])]) ).
fof(f1579,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,singleton(X1),X2),X0)
| sP0(X0,singleton(X1),X2)
| ~ empty(X2)
| sK6(X0,singleton(X1),X2) = X1 )
| ~ spl20_80
| ~ spl20_163 ),
inference(resolution,[],[f1562,f728]) ).
fof(f5670,plain,
( spl20_336
| ~ spl20_84
| ~ spl20_158 ),
inference(avatar_split_clause,[],[f1463,f1434,f784,f5668]) ).
fof(f5668,plain,
( spl20_336
<=> ! [X0,X1] :
( singleton(X0) = X1
| sK5(X0,X1) = X0
| ~ epsilon_transitive(X1)
| sK5(X0,X1) = X1
| ~ subset(X1,sK5(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_336])]) ).
fof(f1463,plain,
( ! [X0,X1] :
( singleton(X0) = X1
| sK5(X0,X1) = X0
| ~ epsilon_transitive(X1)
| sK5(X0,X1) = X1
| ~ subset(X1,sK5(X0,X1)) )
| ~ spl20_84
| ~ spl20_158 ),
inference(resolution,[],[f1435,f785]) ).
fof(f5666,plain,
( spl20_335
| ~ spl20_141
| ~ spl20_156 ),
inference(avatar_split_clause,[],[f1421,f1411,f1217,f5664]) ).
fof(f5664,plain,
( spl20_335
<=> ! [X0,X1] :
( sK4(powerset(X0)) = X1
| ~ ordinal(sK4(powerset(X0)))
| ~ ordinal(X1)
| subset(sK4(powerset(X0)),X1)
| ~ epsilon_transitive(X1)
| element(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_335])]) ).
fof(f1421,plain,
( ! [X0,X1] :
( sK4(powerset(X0)) = X1
| ~ ordinal(sK4(powerset(X0)))
| ~ ordinal(X1)
| subset(sK4(powerset(X0)),X1)
| ~ epsilon_transitive(X1)
| element(X1,X0) )
| ~ spl20_141
| ~ spl20_156 ),
inference(resolution,[],[f1412,f1218]) ).
fof(f5456,plain,
( ~ spl20_58
| spl20_334
| ~ spl20_81
| ~ spl20_312 ),
inference(avatar_split_clause,[],[f5003,f4380,f760,f5453,f590]) ).
fof(f590,plain,
( spl20_58
<=> epsilon_transitive(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_58])]) ).
fof(f5003,plain,
( subset(sK4(sK1),sK2)
| ~ epsilon_transitive(sK2)
| ~ spl20_81
| ~ spl20_312 ),
inference(resolution,[],[f4382,f761]) ).
fof(f5362,plain,
( spl20_333
| ~ spl20_81
| ~ spl20_165 ),
inference(avatar_split_clause,[],[f1632,f1569,f760,f5360]) ).
fof(f5360,plain,
( spl20_333
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| ~ empty(X0)
| subset(sK6(X0,X1,X2),X1)
| ~ epsilon_transitive(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_333])]) ).
fof(f1632,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| ~ empty(X0)
| subset(sK6(X0,X1,X2),X1)
| ~ epsilon_transitive(X1) )
| ~ spl20_81
| ~ spl20_165 ),
inference(resolution,[],[f1570,f761]) ).
fof(f5358,plain,
( spl20_332
| ~ spl20_81
| ~ spl20_165 ),
inference(avatar_split_clause,[],[f1622,f1569,f760,f5356]) ).
fof(f5356,plain,
( spl20_332
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ empty(X0)
| subset(sK6(X0,X1,X2),X2)
| ~ epsilon_transitive(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_332])]) ).
fof(f1622,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ empty(X0)
| subset(sK6(X0,X1,X2),X2)
| ~ epsilon_transitive(X2) )
| ~ spl20_81
| ~ spl20_165 ),
inference(resolution,[],[f1570,f761]) ).
fof(f5354,plain,
( spl20_331
| ~ spl20_81
| ~ spl20_164 ),
inference(avatar_split_clause,[],[f1609,f1565,f760,f5352]) ).
fof(f5352,plain,
( spl20_331
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| ~ empty(X1)
| subset(sK6(X0,X1,X2),X0)
| ~ epsilon_transitive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_331])]) ).
fof(f1609,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| ~ empty(X1)
| subset(sK6(X0,X1,X2),X0)
| ~ epsilon_transitive(X0) )
| ~ spl20_81
| ~ spl20_164 ),
inference(resolution,[],[f1566,f761]) ).
fof(f5350,plain,
( spl20_330
| ~ spl20_81
| ~ spl20_164 ),
inference(avatar_split_clause,[],[f1599,f1565,f760,f5348]) ).
fof(f5348,plain,
( spl20_330
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ empty(X1)
| subset(sK6(X0,X1,X2),X2)
| ~ epsilon_transitive(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_330])]) ).
fof(f1599,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ empty(X1)
| subset(sK6(X0,X1,X2),X2)
| ~ epsilon_transitive(X2) )
| ~ spl20_81
| ~ spl20_164 ),
inference(resolution,[],[f1566,f761]) ).
fof(f5346,plain,
( spl20_329
| ~ spl20_81
| ~ spl20_163 ),
inference(avatar_split_clause,[],[f1584,f1561,f760,f5344]) ).
fof(f5344,plain,
( spl20_329
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ empty(X2)
| subset(sK6(X0,X1,X2),X0)
| ~ epsilon_transitive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_329])]) ).
fof(f1584,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ empty(X2)
| subset(sK6(X0,X1,X2),X0)
| ~ epsilon_transitive(X0) )
| ~ spl20_81
| ~ spl20_163 ),
inference(resolution,[],[f1562,f761]) ).
fof(f5342,plain,
( spl20_328
| ~ spl20_81
| ~ spl20_163 ),
inference(avatar_split_clause,[],[f1574,f1561,f760,f5340]) ).
fof(f5340,plain,
( spl20_328
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ empty(X2)
| subset(sK6(X0,X1,X2),X1)
| ~ epsilon_transitive(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_328])]) ).
fof(f1574,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ empty(X2)
| subset(sK6(X0,X1,X2),X1)
| ~ epsilon_transitive(X1) )
| ~ spl20_81
| ~ spl20_163 ),
inference(resolution,[],[f1562,f761]) ).
fof(f5338,plain,
( spl20_327
| ~ spl20_138
| ~ spl20_161 ),
inference(avatar_split_clause,[],[f1531,f1446,f1195,f5336]) ).
fof(f5336,plain,
( spl20_327
<=> ! [X0,X1] :
( in(sK6(sK4(powerset(X0)),sK4(powerset(X0)),X1),X1)
| sP0(sK4(powerset(X0)),sK4(powerset(X0)),X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_327])]) ).
fof(f1531,plain,
( ! [X0,X1] :
( in(sK6(sK4(powerset(X0)),sK4(powerset(X0)),X1),X1)
| sP0(sK4(powerset(X0)),sK4(powerset(X0)),X1)
| ~ empty(X0) )
| ~ spl20_138
| ~ spl20_161 ),
inference(resolution,[],[f1447,f1196]) ).
fof(f5329,plain,
( spl20_326
| ~ spl20_138
| ~ spl20_157 ),
inference(avatar_split_clause,[],[f1458,f1430,f1195,f5327]) ).
fof(f5327,plain,
( spl20_326
<=> ! [X0,X1] :
( singleton(X0) = sK4(powerset(X1))
| ~ ordinal(sK4(powerset(X1)))
| ~ ordinal(singleton(X0))
| sK4(powerset(X1)) = X0
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_326])]) ).
fof(f1458,plain,
( ! [X0,X1] :
( singleton(X0) = sK4(powerset(X1))
| ~ ordinal(sK4(powerset(X1)))
| ~ ordinal(singleton(X0))
| sK4(powerset(X1)) = X0
| ~ empty(X1) )
| ~ spl20_138
| ~ spl20_157 ),
inference(resolution,[],[f1431,f1196]) ).
fof(f5325,plain,
( spl20_325
| ~ spl20_138
| ~ spl20_156 ),
inference(avatar_split_clause,[],[f1422,f1411,f1195,f5323]) ).
fof(f5323,plain,
( spl20_325
<=> ! [X0,X1] :
( sK4(powerset(X0)) = X1
| ~ ordinal(sK4(powerset(X0)))
| ~ ordinal(X1)
| subset(sK4(powerset(X0)),X1)
| ~ epsilon_transitive(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_325])]) ).
fof(f1422,plain,
( ! [X0,X1] :
( sK4(powerset(X0)) = X1
| ~ ordinal(sK4(powerset(X0)))
| ~ ordinal(X1)
| subset(sK4(powerset(X0)),X1)
| ~ epsilon_transitive(X1)
| ~ empty(X0) )
| ~ spl20_138
| ~ spl20_156 ),
inference(resolution,[],[f1412,f1196]) ).
fof(f5321,plain,
( spl20_324
| ~ spl20_90
| ~ spl20_154 ),
inference(avatar_split_clause,[],[f1401,f1394,f812,f5319]) ).
fof(f5319,plain,
( spl20_324
<=> ! [X2,X0,X1] :
( singleton(X0) = powerset(X1)
| sK5(X0,powerset(X1)) = X0
| element(X2,X1)
| ~ in(X2,sK5(X0,powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_324])]) ).
fof(f1394,plain,
( spl20_154
<=> ! [X0,X1] :
( sK5(X0,X1) = X0
| singleton(X0) = X1
| element(sK5(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_154])]) ).
fof(f1401,plain,
( ! [X2,X0,X1] :
( singleton(X0) = powerset(X1)
| sK5(X0,powerset(X1)) = X0
| element(X2,X1)
| ~ in(X2,sK5(X0,powerset(X1))) )
| ~ spl20_90
| ~ spl20_154 ),
inference(resolution,[],[f1395,f813]) ).
fof(f1395,plain,
( ! [X0,X1] :
( element(sK5(X0,X1),X1)
| singleton(X0) = X1
| sK5(X0,X1) = X0 )
| ~ spl20_154 ),
inference(avatar_component_clause,[],[f1394]) ).
fof(f5317,plain,
( spl20_323
| ~ spl20_97
| ~ spl20_141 ),
inference(avatar_split_clause,[],[f1236,f1217,f871,f5315]) ).
fof(f5315,plain,
( spl20_323
<=> ! [X0,X1] :
( element(sK5(X0,sK4(powerset(X1))),X1)
| sK5(X0,sK4(powerset(X1))) = X0
| singleton(X0) = sK4(powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_323])]) ).
fof(f1236,plain,
( ! [X0,X1] :
( element(sK5(X0,sK4(powerset(X1))),X1)
| sK5(X0,sK4(powerset(X1))) = X0
| singleton(X0) = sK4(powerset(X1)) )
| ~ spl20_97
| ~ spl20_141 ),
inference(resolution,[],[f1218,f872]) ).
fof(f5085,plain,
( ~ spl20_322
| ~ spl20_64
| ~ spl20_312 ),
inference(avatar_split_clause,[],[f5005,f4380,f617,f5082]) ).
fof(f5082,plain,
( spl20_322
<=> in(sK2,sK4(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_322])]) ).
fof(f5005,plain,
( ~ in(sK2,sK4(sK1))
| ~ spl20_64
| ~ spl20_312 ),
inference(resolution,[],[f4382,f618]) ).
fof(f5034,plain,
( spl20_321
| ~ spl20_80
| ~ spl20_161 ),
inference(avatar_split_clause,[],[f1519,f1446,f727,f5032]) ).
fof(f5032,plain,
( spl20_321
<=> ! [X0,X1] :
( in(sK6(X0,X0,singleton(X1)),X0)
| sP0(X0,X0,singleton(X1))
| sK6(X0,X0,singleton(X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_321])]) ).
fof(f1519,plain,
( ! [X0,X1] :
( in(sK6(X0,X0,singleton(X1)),X0)
| sP0(X0,X0,singleton(X1))
| sK6(X0,X0,singleton(X1)) = X1 )
| ~ spl20_80
| ~ spl20_161 ),
inference(resolution,[],[f1447,f728]) ).
fof(f5030,plain,
( spl20_320
| ~ spl20_80
| ~ spl20_160 ),
inference(avatar_split_clause,[],[f1496,f1442,f727,f5028]) ).
fof(f5028,plain,
( spl20_320
<=> ! [X0,X1] :
( in(sK6(X0,singleton(X1),X0),X0)
| sP0(X0,singleton(X1),X0)
| sK6(X0,singleton(X1),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_320])]) ).
fof(f1496,plain,
( ! [X0,X1] :
( in(sK6(X0,singleton(X1),X0),X0)
| sP0(X0,singleton(X1),X0)
| sK6(X0,singleton(X1),X0) = X1 )
| ~ spl20_80
| ~ spl20_160 ),
inference(resolution,[],[f1443,f728]) ).
fof(f5026,plain,
( spl20_319
| ~ spl20_80
| ~ spl20_159 ),
inference(avatar_split_clause,[],[f1481,f1438,f727,f5024]) ).
fof(f5024,plain,
( spl20_319
<=> ! [X0,X1] :
( in(sK6(singleton(X0),X1,X1),X1)
| sP0(singleton(X0),X1,X1)
| sK6(singleton(X0),X1,X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_319])]) ).
fof(f1481,plain,
( ! [X0,X1] :
( in(sK6(singleton(X0),X1,X1),X1)
| sP0(singleton(X0),X1,X1)
| sK6(singleton(X0),X1,X1) = X0 )
| ~ spl20_80
| ~ spl20_159 ),
inference(resolution,[],[f1439,f728]) ).
fof(f5022,plain,
( spl20_318
| ~ spl20_146
| ~ spl20_158 ),
inference(avatar_split_clause,[],[f1460,f1434,f1277,f5020]) ).
fof(f5020,plain,
( spl20_318
<=> ! [X2,X0,X1] :
( singleton(X0) = X1
| sK5(X0,X1) = X0
| ~ epsilon_transitive(X1)
| ~ in(X2,sK5(X0,X1))
| element(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_318])]) ).
fof(f1460,plain,
( ! [X2,X0,X1] :
( singleton(X0) = X1
| sK5(X0,X1) = X0
| ~ epsilon_transitive(X1)
| ~ in(X2,sK5(X0,X1))
| element(X2,X1) )
| ~ spl20_146
| ~ spl20_158 ),
inference(resolution,[],[f1435,f1278]) ).
fof(f5018,plain,
( spl20_317
| ~ spl20_80
| ~ spl20_157 ),
inference(avatar_split_clause,[],[f1455,f1430,f727,f5016]) ).
fof(f5016,plain,
( spl20_317
<=> ! [X0,X1] :
( singleton(X0) = singleton(X1)
| ~ ordinal(singleton(X1))
| ~ ordinal(singleton(X0))
| singleton(X1) = X0
| singleton(X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_317])]) ).
fof(f1455,plain,
( ! [X0,X1] :
( singleton(X0) = singleton(X1)
| ~ ordinal(singleton(X1))
| ~ ordinal(singleton(X0))
| singleton(X1) = X0
| singleton(X0) = X1 )
| ~ spl20_80
| ~ spl20_157 ),
inference(resolution,[],[f1431,f728]) ).
fof(f5014,plain,
( spl20_316
| ~ spl20_86
| ~ spl20_154 ),
inference(avatar_split_clause,[],[f1402,f1394,f792,f5012]) ).
fof(f5012,plain,
( spl20_316
<=> ! [X2,X0,X1] :
( singleton(X0) = powerset(X1)
| sK5(X0,powerset(X1)) = X0
| ~ empty(X1)
| ~ in(X2,sK5(X0,powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_316])]) ).
fof(f1402,plain,
( ! [X2,X0,X1] :
( singleton(X0) = powerset(X1)
| sK5(X0,powerset(X1)) = X0
| ~ empty(X1)
| ~ in(X2,sK5(X0,powerset(X1))) )
| ~ spl20_86
| ~ spl20_154 ),
inference(resolution,[],[f1395,f793]) ).
fof(f5010,plain,
( spl20_315
| ~ spl20_141
| ~ spl20_153 ),
inference(avatar_split_clause,[],[f1386,f1376,f1217,f5008]) ).
fof(f5008,plain,
( spl20_315
<=> ! [X0,X1] :
( sK4(powerset(X0)) = X1
| ~ ordinal(sK4(powerset(X0)))
| ~ ordinal(X1)
| element(sK4(powerset(X0)),X1)
| element(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_315])]) ).
fof(f1386,plain,
( ! [X0,X1] :
( sK4(powerset(X0)) = X1
| ~ ordinal(sK4(powerset(X0)))
| ~ ordinal(X1)
| element(sK4(powerset(X0)),X1)
| element(X1,X0) )
| ~ spl20_141
| ~ spl20_153 ),
inference(resolution,[],[f1377,f1218]) ).
fof(f5000,plain,
( spl20_314
| ~ spl20_150
| ~ spl20_152 ),
inference(avatar_split_clause,[],[f1365,f1358,f1313,f4998]) ).
fof(f4998,plain,
( spl20_314
<=> ! [X2,X0,X1] :
( set_union2(X0,X1) = X2
| ~ ordinal(set_union2(X0,X1))
| ~ ordinal(X2)
| ~ empty(X2)
| in(X2,X0)
| in(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_314])]) ).
fof(f1365,plain,
( ! [X2,X0,X1] :
( set_union2(X0,X1) = X2
| ~ ordinal(set_union2(X0,X1))
| ~ ordinal(X2)
| ~ empty(X2)
| in(X2,X0)
| in(X2,X1) )
| ~ spl20_150
| ~ spl20_152 ),
inference(resolution,[],[f1359,f1314]) ).
fof(f4996,plain,
( spl20_313
| ~ spl20_95
| ~ spl20_141 ),
inference(avatar_split_clause,[],[f1232,f1217,f850,f4994]) ).
fof(f4994,plain,
( spl20_313
<=> ! [X0,X1] :
( element(X0,X1)
| in(sK4(powerset(X1)),X0)
| sK4(powerset(X1)) = X0
| ~ ordinal(sK4(powerset(X1)))
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_313])]) ).
fof(f1232,plain,
( ! [X0,X1] :
( element(X0,X1)
| in(sK4(powerset(X1)),X0)
| sK4(powerset(X1)) = X0
| ~ ordinal(sK4(powerset(X1)))
| ~ ordinal(X0) )
| ~ spl20_95
| ~ spl20_141 ),
inference(resolution,[],[f1218,f851]) ).
fof(f4458,plain,
( ~ spl20_94
| ~ spl20_185 ),
inference(avatar_contradiction_clause,[],[f4405]) ).
fof(f4405,plain,
( $false
| ~ spl20_94
| ~ spl20_185 ),
inference(resolution,[],[f2136,f846]) ).
fof(f846,plain,
( in(set_union2(sK2,singleton(sK2)),sK1)
| ~ spl20_94 ),
inference(avatar_component_clause,[],[f845]) ).
fof(f4383,plain,
( spl20_312
| spl20_184
| ~ spl20_82
| ~ spl20_281 ),
inference(avatar_split_clause,[],[f4200,f4082,f764,f2131,f4380]) ).
fof(f4082,plain,
( spl20_281
<=> element(sK4(sK1),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_281])]) ).
fof(f4200,plain,
( empty(sK2)
| in(sK4(sK1),sK2)
| ~ spl20_82
| ~ spl20_281 ),
inference(resolution,[],[f4084,f765]) ).
fof(f4084,plain,
( element(sK4(sK1),sK2)
| ~ spl20_281 ),
inference(avatar_component_clause,[],[f4082]) ).
fof(f4344,plain,
( spl20_311
| ~ spl20_138
| ~ spl20_165 ),
inference(avatar_split_clause,[],[f1639,f1569,f1195,f4342]) ).
fof(f4342,plain,
( spl20_311
<=> ! [X2,X0,X1] :
( in(sK6(X0,sK4(powerset(X1)),X2),X2)
| sP0(X0,sK4(powerset(X1)),X2)
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_311])]) ).
fof(f1639,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,sK4(powerset(X1)),X2),X2)
| sP0(X0,sK4(powerset(X1)),X2)
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl20_138
| ~ spl20_165 ),
inference(resolution,[],[f1570,f1196]) ).
fof(f4340,plain,
( spl20_310
| ~ spl20_64
| ~ spl20_165 ),
inference(avatar_split_clause,[],[f1634,f1569,f617,f4338]) ).
fof(f4338,plain,
( spl20_310
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| ~ empty(X0)
| ~ in(X1,sK6(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_310])]) ).
fof(f1634,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| ~ empty(X0)
| ~ in(X1,sK6(X0,X1,X2)) )
| ~ spl20_64
| ~ spl20_165 ),
inference(resolution,[],[f1570,f618]) ).
fof(f4336,plain,
( spl20_309
| ~ spl20_65
| ~ spl20_165 ),
inference(avatar_split_clause,[],[f1633,f1569,f621,f4334]) ).
fof(f4334,plain,
( spl20_309
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| ~ empty(X0)
| element(sK6(X0,X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_309])]) ).
fof(f1633,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| ~ empty(X0)
| element(sK6(X0,X1,X2),X1) )
| ~ spl20_65
| ~ spl20_165 ),
inference(resolution,[],[f1570,f622]) ).
fof(f4332,plain,
( spl20_308
| ~ spl20_138
| ~ spl20_165 ),
inference(avatar_split_clause,[],[f1629,f1569,f1195,f4330]) ).
fof(f4330,plain,
( spl20_308
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,sK4(powerset(X2))),X1)
| sP0(X0,X1,sK4(powerset(X2)))
| ~ empty(X0)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_308])]) ).
fof(f1629,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,sK4(powerset(X2))),X1)
| sP0(X0,X1,sK4(powerset(X2)))
| ~ empty(X0)
| ~ empty(X2) )
| ~ spl20_138
| ~ spl20_165 ),
inference(resolution,[],[f1570,f1196]) ).
fof(f4328,plain,
( spl20_307
| ~ spl20_64
| ~ spl20_165 ),
inference(avatar_split_clause,[],[f1624,f1569,f617,f4326]) ).
fof(f4326,plain,
( spl20_307
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ empty(X0)
| ~ in(X2,sK6(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_307])]) ).
fof(f1624,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ empty(X0)
| ~ in(X2,sK6(X0,X1,X2)) )
| ~ spl20_64
| ~ spl20_165 ),
inference(resolution,[],[f1570,f618]) ).
fof(f4324,plain,
( spl20_306
| ~ spl20_65
| ~ spl20_165 ),
inference(avatar_split_clause,[],[f1623,f1569,f621,f4322]) ).
fof(f4322,plain,
( spl20_306
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ empty(X0)
| element(sK6(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_306])]) ).
fof(f1623,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ empty(X0)
| element(sK6(X0,X1,X2),X2) )
| ~ spl20_65
| ~ spl20_165 ),
inference(resolution,[],[f1570,f622]) ).
fof(f4320,plain,
( spl20_305
| ~ spl20_138
| ~ spl20_164 ),
inference(avatar_split_clause,[],[f1616,f1565,f1195,f4318]) ).
fof(f4318,plain,
( spl20_305
<=> ! [X2,X0,X1] :
( in(sK6(sK4(powerset(X0)),X1,X2),X2)
| sP0(sK4(powerset(X0)),X1,X2)
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_305])]) ).
fof(f1616,plain,
( ! [X2,X0,X1] :
( in(sK6(sK4(powerset(X0)),X1,X2),X2)
| sP0(sK4(powerset(X0)),X1,X2)
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl20_138
| ~ spl20_164 ),
inference(resolution,[],[f1566,f1196]) ).
fof(f4315,plain,
( spl20_304
| ~ spl20_64
| ~ spl20_164 ),
inference(avatar_split_clause,[],[f1611,f1565,f617,f4313]) ).
fof(f4313,plain,
( spl20_304
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| ~ empty(X1)
| ~ in(X0,sK6(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_304])]) ).
fof(f1611,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| ~ empty(X1)
| ~ in(X0,sK6(X0,X1,X2)) )
| ~ spl20_64
| ~ spl20_164 ),
inference(resolution,[],[f1566,f618]) ).
fof(f4311,plain,
( spl20_303
| ~ spl20_65
| ~ spl20_164 ),
inference(avatar_split_clause,[],[f1610,f1565,f621,f4309]) ).
fof(f4309,plain,
( spl20_303
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| ~ empty(X1)
| element(sK6(X0,X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_303])]) ).
fof(f1610,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| ~ empty(X1)
| element(sK6(X0,X1,X2),X0) )
| ~ spl20_65
| ~ spl20_164 ),
inference(resolution,[],[f1566,f622]) ).
fof(f4307,plain,
( spl20_302
| ~ spl20_138
| ~ spl20_164 ),
inference(avatar_split_clause,[],[f1606,f1565,f1195,f4305]) ).
fof(f4305,plain,
( spl20_302
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,sK4(powerset(X2))),X0)
| sP0(X0,X1,sK4(powerset(X2)))
| ~ empty(X1)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_302])]) ).
fof(f1606,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,sK4(powerset(X2))),X0)
| sP0(X0,X1,sK4(powerset(X2)))
| ~ empty(X1)
| ~ empty(X2) )
| ~ spl20_138
| ~ spl20_164 ),
inference(resolution,[],[f1566,f1196]) ).
fof(f4303,plain,
( spl20_301
| ~ spl20_64
| ~ spl20_164 ),
inference(avatar_split_clause,[],[f1601,f1565,f617,f4301]) ).
fof(f4301,plain,
( spl20_301
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ empty(X1)
| ~ in(X2,sK6(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_301])]) ).
fof(f1601,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ empty(X1)
| ~ in(X2,sK6(X0,X1,X2)) )
| ~ spl20_64
| ~ spl20_164 ),
inference(resolution,[],[f1566,f618]) ).
fof(f4299,plain,
( spl20_300
| ~ spl20_65
| ~ spl20_164 ),
inference(avatar_split_clause,[],[f1600,f1565,f621,f4297]) ).
fof(f4297,plain,
( spl20_300
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ empty(X1)
| element(sK6(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_300])]) ).
fof(f1600,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ empty(X1)
| element(sK6(X0,X1,X2),X2) )
| ~ spl20_65
| ~ spl20_164 ),
inference(resolution,[],[f1566,f622]) ).
fof(f4295,plain,
( spl20_299
| ~ spl20_138
| ~ spl20_163 ),
inference(avatar_split_clause,[],[f1591,f1561,f1195,f4293]) ).
fof(f4293,plain,
( spl20_299
<=> ! [X2,X0,X1] :
( in(sK6(sK4(powerset(X0)),X1,X2),X1)
| sP0(sK4(powerset(X0)),X1,X2)
| ~ empty(X2)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_299])]) ).
fof(f1591,plain,
( ! [X2,X0,X1] :
( in(sK6(sK4(powerset(X0)),X1,X2),X1)
| sP0(sK4(powerset(X0)),X1,X2)
| ~ empty(X2)
| ~ empty(X0) )
| ~ spl20_138
| ~ spl20_163 ),
inference(resolution,[],[f1562,f1196]) ).
fof(f4291,plain,
( spl20_298
| ~ spl20_64
| ~ spl20_163 ),
inference(avatar_split_clause,[],[f1586,f1561,f617,f4289]) ).
fof(f4289,plain,
( spl20_298
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ empty(X2)
| ~ in(X0,sK6(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_298])]) ).
fof(f1586,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ empty(X2)
| ~ in(X0,sK6(X0,X1,X2)) )
| ~ spl20_64
| ~ spl20_163 ),
inference(resolution,[],[f1562,f618]) ).
fof(f4287,plain,
( spl20_297
| ~ spl20_65
| ~ spl20_163 ),
inference(avatar_split_clause,[],[f1585,f1561,f621,f4285]) ).
fof(f4285,plain,
( spl20_297
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ empty(X2)
| element(sK6(X0,X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_297])]) ).
fof(f1585,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ empty(X2)
| element(sK6(X0,X1,X2),X0) )
| ~ spl20_65
| ~ spl20_163 ),
inference(resolution,[],[f1562,f622]) ).
fof(f4283,plain,
( spl20_296
| ~ spl20_138
| ~ spl20_163 ),
inference(avatar_split_clause,[],[f1581,f1561,f1195,f4281]) ).
fof(f4281,plain,
( spl20_296
<=> ! [X2,X0,X1] :
( in(sK6(X0,sK4(powerset(X1)),X2),X0)
| sP0(X0,sK4(powerset(X1)),X2)
| ~ empty(X2)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_296])]) ).
fof(f1581,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,sK4(powerset(X1)),X2),X0)
| sP0(X0,sK4(powerset(X1)),X2)
| ~ empty(X2)
| ~ empty(X1) )
| ~ spl20_138
| ~ spl20_163 ),
inference(resolution,[],[f1562,f1196]) ).
fof(f4279,plain,
( spl20_295
| ~ spl20_64
| ~ spl20_163 ),
inference(avatar_split_clause,[],[f1576,f1561,f617,f4277]) ).
fof(f4277,plain,
( spl20_295
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ empty(X2)
| ~ in(X1,sK6(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_295])]) ).
fof(f1576,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ empty(X2)
| ~ in(X1,sK6(X0,X1,X2)) )
| ~ spl20_64
| ~ spl20_163 ),
inference(resolution,[],[f1562,f618]) ).
fof(f4275,plain,
( spl20_294
| ~ spl20_94
| ~ spl20_186 ),
inference(avatar_split_clause,[],[f2333,f2139,f845,f4272]) ).
fof(f2333,plain,
( element(set_union2(sK2,singleton(sK2)),sK2)
| ~ spl20_94
| ~ spl20_186 ),
inference(resolution,[],[f846,f2140]) ).
fof(f4270,plain,
( spl20_293
| ~ spl20_65
| ~ spl20_163 ),
inference(avatar_split_clause,[],[f1575,f1561,f621,f4268]) ).
fof(f4268,plain,
( spl20_293
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ empty(X2)
| element(sK6(X0,X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_293])]) ).
fof(f1575,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ empty(X2)
| element(sK6(X0,X1,X2),X1) )
| ~ spl20_65
| ~ spl20_163 ),
inference(resolution,[],[f1562,f622]) ).
fof(f4266,plain,
( spl20_292
| ~ spl20_81
| ~ spl20_161 ),
inference(avatar_split_clause,[],[f1524,f1446,f760,f4264]) ).
fof(f4264,plain,
( spl20_292
<=> ! [X0,X1] :
( in(sK6(X0,X0,X1),X1)
| sP0(X0,X0,X1)
| subset(sK6(X0,X0,X1),X0)
| ~ epsilon_transitive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_292])]) ).
fof(f1524,plain,
( ! [X0,X1] :
( in(sK6(X0,X0,X1),X1)
| sP0(X0,X0,X1)
| subset(sK6(X0,X0,X1),X0)
| ~ epsilon_transitive(X0) )
| ~ spl20_81
| ~ spl20_161 ),
inference(resolution,[],[f1447,f761]) ).
fof(f4262,plain,
( spl20_291
| ~ spl20_81
| ~ spl20_161 ),
inference(avatar_split_clause,[],[f1514,f1446,f760,f4260]) ).
fof(f4260,plain,
( spl20_291
<=> ! [X0,X1] :
( in(sK6(X0,X0,X1),X0)
| sP0(X0,X0,X1)
| subset(sK6(X0,X0,X1),X1)
| ~ epsilon_transitive(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_291])]) ).
fof(f1514,plain,
( ! [X0,X1] :
( in(sK6(X0,X0,X1),X0)
| sP0(X0,X0,X1)
| subset(sK6(X0,X0,X1),X1)
| ~ epsilon_transitive(X1) )
| ~ spl20_81
| ~ spl20_161 ),
inference(resolution,[],[f1447,f761]) ).
fof(f4258,plain,
( spl20_290
| ~ spl20_81
| ~ spl20_160 ),
inference(avatar_split_clause,[],[f1491,f1442,f760,f4256]) ).
fof(f4256,plain,
( spl20_290
<=> ! [X0,X1] :
( in(sK6(X0,X1,X0),X0)
| sP0(X0,X1,X0)
| subset(sK6(X0,X1,X0),X1)
| ~ epsilon_transitive(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_290])]) ).
fof(f1491,plain,
( ! [X0,X1] :
( in(sK6(X0,X1,X0),X0)
| sP0(X0,X1,X0)
| subset(sK6(X0,X1,X0),X1)
| ~ epsilon_transitive(X1) )
| ~ spl20_81
| ~ spl20_160 ),
inference(resolution,[],[f1443,f761]) ).
fof(f4254,plain,
( spl20_289
| ~ spl20_81
| ~ spl20_159 ),
inference(avatar_split_clause,[],[f1476,f1438,f760,f4252]) ).
fof(f4252,plain,
( spl20_289
<=> ! [X0,X1] :
( in(sK6(X0,X1,X1),X1)
| sP0(X0,X1,X1)
| subset(sK6(X0,X1,X1),X0)
| ~ epsilon_transitive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_289])]) ).
fof(f1476,plain,
( ! [X0,X1] :
( in(sK6(X0,X1,X1),X1)
| sP0(X0,X1,X1)
| subset(sK6(X0,X1,X1),X0)
| ~ epsilon_transitive(X0) )
| ~ spl20_81
| ~ spl20_159 ),
inference(resolution,[],[f1439,f761]) ).
fof(f4250,plain,
( spl20_288
| ~ spl20_80
| ~ spl20_156 ),
inference(avatar_split_clause,[],[f1419,f1411,f727,f4248]) ).
fof(f4248,plain,
( spl20_288
<=> ! [X0,X1] :
( singleton(X0) = X1
| ~ ordinal(singleton(X0))
| ~ ordinal(X1)
| subset(singleton(X0),X1)
| ~ epsilon_transitive(X1)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_288])]) ).
fof(f1419,plain,
( ! [X0,X1] :
( singleton(X0) = X1
| ~ ordinal(singleton(X0))
| ~ ordinal(X1)
| subset(singleton(X0),X1)
| ~ epsilon_transitive(X1)
| X0 = X1 )
| ~ spl20_80
| ~ spl20_156 ),
inference(resolution,[],[f1412,f728]) ).
fof(f4246,plain,
( spl20_287
| ~ spl20_138
| ~ spl20_153 ),
inference(avatar_split_clause,[],[f1387,f1376,f1195,f4244]) ).
fof(f4244,plain,
( spl20_287
<=> ! [X0,X1] :
( sK4(powerset(X0)) = X1
| ~ ordinal(sK4(powerset(X0)))
| ~ ordinal(X1)
| element(sK4(powerset(X0)),X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_287])]) ).
fof(f1387,plain,
( ! [X0,X1] :
( sK4(powerset(X0)) = X1
| ~ ordinal(sK4(powerset(X0)))
| ~ ordinal(X1)
| element(sK4(powerset(X0)),X1)
| ~ empty(X0) )
| ~ spl20_138
| ~ spl20_153 ),
inference(resolution,[],[f1377,f1196]) ).
fof(f4242,plain,
( spl20_286
| ~ spl20_89
| ~ spl20_149 ),
inference(avatar_split_clause,[],[f1322,f1309,f808,f4240]) ).
fof(f4240,plain,
( spl20_286
<=> ! [X0] :
( ~ epsilon_transitive(set_union2(X0,singleton(X0)))
| ordinal_subset(X0,set_union2(X0,singleton(X0)))
| ~ ordinal(set_union2(X0,singleton(X0)))
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_286])]) ).
fof(f1322,plain,
( ! [X0] :
( ~ epsilon_transitive(set_union2(X0,singleton(X0)))
| ordinal_subset(X0,set_union2(X0,singleton(X0)))
| ~ ordinal(set_union2(X0,singleton(X0)))
| ~ ordinal(X0) )
| ~ spl20_89
| ~ spl20_149 ),
inference(resolution,[],[f1310,f809]) ).
fof(f4238,plain,
( spl20_285
| ~ spl20_95
| ~ spl20_138 ),
inference(avatar_split_clause,[],[f1200,f1195,f850,f4236]) ).
fof(f4236,plain,
( spl20_285
<=> ! [X0,X1] :
( ~ empty(X0)
| in(sK4(powerset(X0)),X1)
| sK4(powerset(X0)) = X1
| ~ ordinal(sK4(powerset(X0)))
| ~ ordinal(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_285])]) ).
fof(f1200,plain,
( ! [X0,X1] :
( ~ empty(X0)
| in(sK4(powerset(X0)),X1)
| sK4(powerset(X0)) = X1
| ~ ordinal(sK4(powerset(X0)))
| ~ ordinal(X1) )
| ~ spl20_95
| ~ spl20_138 ),
inference(resolution,[],[f1196,f851]) ).
fof(f4186,plain,
( spl20_284
| ~ spl20_81
| ~ spl20_156 ),
inference(avatar_split_clause,[],[f1414,f1411,f760,f4184]) ).
fof(f4184,plain,
( spl20_284
<=> ! [X0,X1] :
( X0 = X1
| ~ ordinal(X0)
| ~ ordinal(X1)
| subset(X0,X1)
| ~ epsilon_transitive(X1)
| subset(X1,X0)
| ~ epsilon_transitive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_284])]) ).
fof(f1414,plain,
( ! [X0,X1] :
( X0 = X1
| ~ ordinal(X0)
| ~ ordinal(X1)
| subset(X0,X1)
| ~ epsilon_transitive(X1)
| subset(X1,X0)
| ~ epsilon_transitive(X0) )
| ~ spl20_81
| ~ spl20_156 ),
inference(resolution,[],[f1412,f761]) ).
fof(f4182,plain,
( spl20_283
| ~ spl20_74
| ~ spl20_154 ),
inference(avatar_split_clause,[],[f1403,f1394,f703,f4180]) ).
fof(f4180,plain,
( spl20_283
<=> ! [X0,X1] :
( singleton(X0) = powerset(X1)
| sK5(X0,powerset(X1)) = X0
| subset(sK5(X0,powerset(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_283])]) ).
fof(f1403,plain,
( ! [X0,X1] :
( singleton(X0) = powerset(X1)
| sK5(X0,powerset(X1)) = X0
| subset(sK5(X0,powerset(X1)),X1) )
| ~ spl20_74
| ~ spl20_154 ),
inference(resolution,[],[f1395,f704]) ).
fof(f4178,plain,
( spl20_282
| ~ spl20_84
| ~ spl20_149 ),
inference(avatar_split_clause,[],[f1323,f1309,f784,f4176]) ).
fof(f4176,plain,
( spl20_282
<=> ! [X0] :
( ~ epsilon_transitive(set_union2(X0,singleton(X0)))
| set_union2(X0,singleton(X0)) = X0
| ~ subset(set_union2(X0,singleton(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_282])]) ).
fof(f1323,plain,
( ! [X0] :
( ~ epsilon_transitive(set_union2(X0,singleton(X0)))
| set_union2(X0,singleton(X0)) = X0
| ~ subset(set_union2(X0,singleton(X0)),X0) )
| ~ spl20_84
| ~ spl20_149 ),
inference(resolution,[],[f1310,f785]) ).
fof(f4085,plain,
( spl20_192
| spl20_281
| ~ spl20_136
| ~ spl20_186 ),
inference(avatar_split_clause,[],[f2251,f2139,f1161,f4082,f2310]) ).
fof(f2251,plain,
( element(sK4(sK1),sK2)
| empty(sK1)
| ~ spl20_136
| ~ spl20_186 ),
inference(resolution,[],[f2140,f1162]) ).
fof(f3645,plain,
( spl20_280
| ~ spl20_64
| ~ spl20_161 ),
inference(avatar_split_clause,[],[f1526,f1446,f617,f3643]) ).
fof(f3643,plain,
( spl20_280
<=> ! [X0,X1] :
( in(sK6(X0,X0,X1),X1)
| sP0(X0,X0,X1)
| ~ in(X0,sK6(X0,X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_280])]) ).
fof(f1526,plain,
( ! [X0,X1] :
( in(sK6(X0,X0,X1),X1)
| sP0(X0,X0,X1)
| ~ in(X0,sK6(X0,X0,X1)) )
| ~ spl20_64
| ~ spl20_161 ),
inference(resolution,[],[f1447,f618]) ).
fof(f3641,plain,
( spl20_279
| ~ spl20_65
| ~ spl20_161 ),
inference(avatar_split_clause,[],[f1525,f1446,f621,f3639]) ).
fof(f3639,plain,
( spl20_279
<=> ! [X0,X1] :
( in(sK6(X0,X0,X1),X1)
| sP0(X0,X0,X1)
| element(sK6(X0,X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_279])]) ).
fof(f1525,plain,
( ! [X0,X1] :
( in(sK6(X0,X0,X1),X1)
| sP0(X0,X0,X1)
| element(sK6(X0,X0,X1),X0) )
| ~ spl20_65
| ~ spl20_161 ),
inference(resolution,[],[f1447,f622]) ).
fof(f3637,plain,
( spl20_278
| ~ spl20_138
| ~ spl20_161 ),
inference(avatar_split_clause,[],[f1521,f1446,f1195,f3635]) ).
fof(f3635,plain,
( spl20_278
<=> ! [X0,X1] :
( in(sK6(X0,X0,sK4(powerset(X1))),X0)
| sP0(X0,X0,sK4(powerset(X1)))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_278])]) ).
fof(f1521,plain,
( ! [X0,X1] :
( in(sK6(X0,X0,sK4(powerset(X1))),X0)
| sP0(X0,X0,sK4(powerset(X1)))
| ~ empty(X1) )
| ~ spl20_138
| ~ spl20_161 ),
inference(resolution,[],[f1447,f1196]) ).
fof(f3633,plain,
( spl20_277
| ~ spl20_64
| ~ spl20_161 ),
inference(avatar_split_clause,[],[f1516,f1446,f617,f3631]) ).
fof(f3631,plain,
( spl20_277
<=> ! [X0,X1] :
( in(sK6(X0,X0,X1),X0)
| sP0(X0,X0,X1)
| ~ in(X1,sK6(X0,X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_277])]) ).
fof(f1516,plain,
( ! [X0,X1] :
( in(sK6(X0,X0,X1),X0)
| sP0(X0,X0,X1)
| ~ in(X1,sK6(X0,X0,X1)) )
| ~ spl20_64
| ~ spl20_161 ),
inference(resolution,[],[f1447,f618]) ).
fof(f3629,plain,
( spl20_183
| spl20_184
| ~ spl20_82
| ~ spl20_234 ),
inference(avatar_split_clause,[],[f3346,f2890,f764,f2131,f2104]) ).
fof(f2104,plain,
( spl20_183
<=> in(sK1,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_183])]) ).
fof(f2890,plain,
( spl20_234
<=> element(sK1,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_234])]) ).
fof(f3346,plain,
( empty(sK2)
| in(sK1,sK2)
| ~ spl20_82
| ~ spl20_234 ),
inference(resolution,[],[f2892,f765]) ).
fof(f2892,plain,
( element(sK1,sK2)
| ~ spl20_234 ),
inference(avatar_component_clause,[],[f2890]) ).
fof(f3628,plain,
( spl20_276
| ~ spl20_65
| ~ spl20_161 ),
inference(avatar_split_clause,[],[f1515,f1446,f621,f3626]) ).
fof(f3626,plain,
( spl20_276
<=> ! [X0,X1] :
( in(sK6(X0,X0,X1),X0)
| sP0(X0,X0,X1)
| element(sK6(X0,X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_276])]) ).
fof(f1515,plain,
( ! [X0,X1] :
( in(sK6(X0,X0,X1),X0)
| sP0(X0,X0,X1)
| element(sK6(X0,X0,X1),X1) )
| ~ spl20_65
| ~ spl20_161 ),
inference(resolution,[],[f1447,f622]) ).
fof(f3624,plain,
( spl20_275
| ~ spl20_99
| ~ spl20_160 ),
inference(avatar_split_clause,[],[f1511,f1442,f884,f3622]) ).
fof(f3622,plain,
( spl20_275
<=> ! [X0,X1] :
( in(sK6(X0,X1,X0),X1)
| sP0(X0,X1,X0)
| ~ in(sK6(X0,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_275])]) ).
fof(f1511,plain,
( ! [X0,X1] :
( in(sK6(X0,X1,X0),X1)
| sP0(X0,X1,X0)
| ~ in(sK6(X0,X1,X0),X0) )
| ~ spl20_99
| ~ spl20_160 ),
inference(duplicate_literal_removal,[],[f1499]) ).
fof(f1499,plain,
( ! [X0,X1] :
( in(sK6(X0,X1,X0),X1)
| sP0(X0,X1,X0)
| ~ in(sK6(X0,X1,X0),X0)
| sP0(X0,X1,X0) )
| ~ spl20_99
| ~ spl20_160 ),
inference(resolution,[],[f1443,f885]) ).
fof(f3620,plain,
( spl20_274
| ~ spl20_64
| ~ spl20_160 ),
inference(avatar_split_clause,[],[f1503,f1442,f617,f3618]) ).
fof(f3618,plain,
( spl20_274
<=> ! [X0,X1] :
( in(sK6(X0,X1,X0),X1)
| sP0(X0,X1,X0)
| ~ in(X0,sK6(X0,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_274])]) ).
fof(f1503,plain,
( ! [X0,X1] :
( in(sK6(X0,X1,X0),X1)
| sP0(X0,X1,X0)
| ~ in(X0,sK6(X0,X1,X0)) )
| ~ spl20_64
| ~ spl20_160 ),
inference(resolution,[],[f1443,f618]) ).
fof(f3616,plain,
( spl20_273
| ~ spl20_65
| ~ spl20_160 ),
inference(avatar_split_clause,[],[f1502,f1442,f621,f3614]) ).
fof(f3614,plain,
( spl20_273
<=> ! [X0,X1] :
( in(sK6(X0,X1,X0),X1)
| sP0(X0,X1,X0)
| element(sK6(X0,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_273])]) ).
fof(f1502,plain,
( ! [X0,X1] :
( in(sK6(X0,X1,X0),X1)
| sP0(X0,X1,X0)
| element(sK6(X0,X1,X0),X0) )
| ~ spl20_65
| ~ spl20_160 ),
inference(resolution,[],[f1443,f622]) ).
fof(f3612,plain,
( spl20_272
| ~ spl20_138
| ~ spl20_160 ),
inference(avatar_split_clause,[],[f1498,f1442,f1195,f3610]) ).
fof(f3610,plain,
( spl20_272
<=> ! [X0,X1] :
( in(sK6(X0,sK4(powerset(X1)),X0),X0)
| sP0(X0,sK4(powerset(X1)),X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_272])]) ).
fof(f1498,plain,
( ! [X0,X1] :
( in(sK6(X0,sK4(powerset(X1)),X0),X0)
| sP0(X0,sK4(powerset(X1)),X0)
| ~ empty(X1) )
| ~ spl20_138
| ~ spl20_160 ),
inference(resolution,[],[f1443,f1196]) ).
fof(f3608,plain,
( spl20_271
| ~ spl20_64
| ~ spl20_160 ),
inference(avatar_split_clause,[],[f1493,f1442,f617,f3606]) ).
fof(f3606,plain,
( spl20_271
<=> ! [X0,X1] :
( in(sK6(X0,X1,X0),X0)
| sP0(X0,X1,X0)
| ~ in(X1,sK6(X0,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_271])]) ).
fof(f1493,plain,
( ! [X0,X1] :
( in(sK6(X0,X1,X0),X0)
| sP0(X0,X1,X0)
| ~ in(X1,sK6(X0,X1,X0)) )
| ~ spl20_64
| ~ spl20_160 ),
inference(resolution,[],[f1443,f618]) ).
fof(f3604,plain,
( spl20_270
| ~ spl20_65
| ~ spl20_160 ),
inference(avatar_split_clause,[],[f1492,f1442,f621,f3602]) ).
fof(f3602,plain,
( spl20_270
<=> ! [X0,X1] :
( in(sK6(X0,X1,X0),X0)
| sP0(X0,X1,X0)
| element(sK6(X0,X1,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_270])]) ).
fof(f1492,plain,
( ! [X0,X1] :
( in(sK6(X0,X1,X0),X0)
| sP0(X0,X1,X0)
| element(sK6(X0,X1,X0),X1) )
| ~ spl20_65
| ~ spl20_160 ),
inference(resolution,[],[f1443,f622]) ).
fof(f3600,plain,
( spl20_269
| ~ spl20_98
| ~ spl20_159 ),
inference(avatar_split_clause,[],[f1485,f1438,f880,f3598]) ).
fof(f3598,plain,
( spl20_269
<=> ! [X0,X1] :
( in(sK6(X0,X1,X1),X0)
| sP0(X0,X1,X1)
| ~ in(sK6(X0,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_269])]) ).
fof(f1485,plain,
( ! [X0,X1] :
( in(sK6(X0,X1,X1),X0)
| sP0(X0,X1,X1)
| ~ in(sK6(X0,X1,X1),X1) )
| ~ spl20_98
| ~ spl20_159 ),
inference(duplicate_literal_removal,[],[f1465]) ).
fof(f1465,plain,
( ! [X0,X1] :
( in(sK6(X0,X1,X1),X0)
| sP0(X0,X1,X1)
| ~ in(sK6(X0,X1,X1),X1)
| sP0(X0,X1,X1) )
| ~ spl20_98
| ~ spl20_159 ),
inference(resolution,[],[f1439,f881]) ).
fof(f3596,plain,
( spl20_268
| ~ spl20_138
| ~ spl20_159 ),
inference(avatar_split_clause,[],[f1483,f1438,f1195,f3594]) ).
fof(f3594,plain,
( spl20_268
<=> ! [X0,X1] :
( in(sK6(sK4(powerset(X0)),X1,X1),X1)
| sP0(sK4(powerset(X0)),X1,X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_268])]) ).
fof(f1483,plain,
( ! [X0,X1] :
( in(sK6(sK4(powerset(X0)),X1,X1),X1)
| sP0(sK4(powerset(X0)),X1,X1)
| ~ empty(X0) )
| ~ spl20_138
| ~ spl20_159 ),
inference(resolution,[],[f1439,f1196]) ).
fof(f3592,plain,
( spl20_267
| ~ spl20_64
| ~ spl20_159 ),
inference(avatar_split_clause,[],[f1478,f1438,f617,f3590]) ).
fof(f3590,plain,
( spl20_267
<=> ! [X0,X1] :
( in(sK6(X0,X1,X1),X1)
| sP0(X0,X1,X1)
| ~ in(X0,sK6(X0,X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_267])]) ).
fof(f1478,plain,
( ! [X0,X1] :
( in(sK6(X0,X1,X1),X1)
| sP0(X0,X1,X1)
| ~ in(X0,sK6(X0,X1,X1)) )
| ~ spl20_64
| ~ spl20_159 ),
inference(resolution,[],[f1439,f618]) ).
fof(f3585,plain,
( spl20_266
| ~ spl20_65
| ~ spl20_159 ),
inference(avatar_split_clause,[],[f1477,f1438,f621,f3583]) ).
fof(f3583,plain,
( spl20_266
<=> ! [X0,X1] :
( in(sK6(X0,X1,X1),X1)
| sP0(X0,X1,X1)
| element(sK6(X0,X1,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_266])]) ).
fof(f1477,plain,
( ! [X0,X1] :
( in(sK6(X0,X1,X1),X1)
| sP0(X0,X1,X1)
| element(sK6(X0,X1,X1),X0) )
| ~ spl20_65
| ~ spl20_159 ),
inference(resolution,[],[f1439,f622]) ).
fof(f3581,plain,
( spl20_265
| ~ spl20_64
| ~ spl20_159 ),
inference(avatar_split_clause,[],[f1468,f1438,f617,f3579]) ).
fof(f3579,plain,
( spl20_265
<=> ! [X0,X1] :
( in(sK6(X0,X1,X1),X0)
| sP0(X0,X1,X1)
| ~ in(X1,sK6(X0,X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_265])]) ).
fof(f1468,plain,
( ! [X0,X1] :
( in(sK6(X0,X1,X1),X0)
| sP0(X0,X1,X1)
| ~ in(X1,sK6(X0,X1,X1)) )
| ~ spl20_64
| ~ spl20_159 ),
inference(resolution,[],[f1439,f618]) ).
fof(f3577,plain,
( spl20_264
| ~ spl20_65
| ~ spl20_159 ),
inference(avatar_split_clause,[],[f1467,f1438,f621,f3575]) ).
fof(f3575,plain,
( spl20_264
<=> ! [X0,X1] :
( in(sK6(X0,X1,X1),X0)
| sP0(X0,X1,X1)
| element(sK6(X0,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_264])]) ).
fof(f1467,plain,
( ! [X0,X1] :
( in(sK6(X0,X1,X1),X0)
| sP0(X0,X1,X1)
| element(sK6(X0,X1,X1),X1) )
| ~ spl20_65
| ~ spl20_159 ),
inference(resolution,[],[f1439,f622]) ).
fof(f3573,plain,
( spl20_263
| ~ spl20_80
| ~ spl20_153 ),
inference(avatar_split_clause,[],[f1384,f1376,f727,f3571]) ).
fof(f3571,plain,
( spl20_263
<=> ! [X0,X1] :
( singleton(X0) = X1
| ~ ordinal(singleton(X0))
| ~ ordinal(X1)
| element(singleton(X0),X1)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_263])]) ).
fof(f1384,plain,
( ! [X0,X1] :
( singleton(X0) = X1
| ~ ordinal(singleton(X0))
| ~ ordinal(X1)
| element(singleton(X0),X1)
| X0 = X1 )
| ~ spl20_80
| ~ spl20_153 ),
inference(resolution,[],[f1377,f728]) ).
fof(f3569,plain,
( spl20_262
| ~ spl20_141
| ~ spl20_152 ),
inference(avatar_split_clause,[],[f1368,f1358,f1217,f3567]) ).
fof(f3567,plain,
( spl20_262
<=> ! [X0,X1] :
( sK4(powerset(X0)) = X1
| ~ ordinal(sK4(powerset(X0)))
| ~ ordinal(X1)
| ~ empty(X1)
| element(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_262])]) ).
fof(f1368,plain,
( ! [X0,X1] :
( sK4(powerset(X0)) = X1
| ~ ordinal(sK4(powerset(X0)))
| ~ ordinal(X1)
| ~ empty(X1)
| element(X1,X0) )
| ~ spl20_141
| ~ spl20_152 ),
inference(resolution,[],[f1359,f1218]) ).
fof(f3565,plain,
( spl20_261
| ~ spl20_136
| ~ spl20_150 ),
inference(avatar_split_clause,[],[f1333,f1313,f1161,f3563]) ).
fof(f3563,plain,
( spl20_261
<=> ! [X0,X1] :
( in(sK4(set_union2(X0,X1)),X0)
| in(sK4(set_union2(X0,X1)),X1)
| empty(set_union2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_261])]) ).
fof(f1333,plain,
( ! [X0,X1] :
( in(sK4(set_union2(X0,X1)),X0)
| in(sK4(set_union2(X0,X1)),X1)
| empty(set_union2(X0,X1)) )
| ~ spl20_136
| ~ spl20_150 ),
inference(resolution,[],[f1314,f1162]) ).
fof(f3561,plain,
( spl20_260
| ~ spl20_60
| ~ spl20_150 ),
inference(avatar_split_clause,[],[f1332,f1313,f601,f3559]) ).
fof(f3559,plain,
( spl20_260
<=> ! [X0,X1] :
( in(sK3(set_union2(X0,X1)),X0)
| in(sK3(set_union2(X0,X1)),X1)
| epsilon_transitive(set_union2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_260])]) ).
fof(f601,plain,
( spl20_60
<=> ! [X0] :
( epsilon_transitive(X0)
| in(sK3(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_60])]) ).
fof(f1332,plain,
( ! [X0,X1] :
( in(sK3(set_union2(X0,X1)),X0)
| in(sK3(set_union2(X0,X1)),X1)
| epsilon_transitive(set_union2(X0,X1)) )
| ~ spl20_60
| ~ spl20_150 ),
inference(resolution,[],[f1314,f602]) ).
fof(f602,plain,
( ! [X0] :
( in(sK3(X0),X0)
| epsilon_transitive(X0) )
| ~ spl20_60 ),
inference(avatar_component_clause,[],[f601]) ).
fof(f3489,plain,
( spl20_219
| spl20_192
| ~ spl20_82
| ~ spl20_220 ),
inference(avatar_split_clause,[],[f3228,f2710,f764,f2310,f2602]) ).
fof(f2710,plain,
( spl20_220
<=> element(sK2,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_220])]) ).
fof(f3228,plain,
( empty(sK1)
| in(sK2,sK1)
| ~ spl20_82
| ~ spl20_220 ),
inference(resolution,[],[f2712,f765]) ).
fof(f2712,plain,
( element(sK2,sK1)
| ~ spl20_220 ),
inference(avatar_component_clause,[],[f2710]) ).
fof(f3488,plain,
( spl20_259
| ~ spl20_1
| ~ spl20_144
| spl20_116
| ~ spl20_148 ),
inference(avatar_split_clause,[],[f3466,f1289,f1018,f1268,f275,f3485]) ).
fof(f3485,plain,
( spl20_259
<=> ordinal_subset(set_union2(sK2,singleton(sK2)),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_259])]) ).
fof(f1268,plain,
( spl20_144
<=> ordinal(set_union2(sK2,singleton(sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_144])]) ).
fof(f1289,plain,
( spl20_148
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0)
| ordinal_subset(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_148])]) ).
fof(f3466,plain,
( ~ ordinal(set_union2(sK2,singleton(sK2)))
| ~ ordinal(sK1)
| ordinal_subset(set_union2(sK2,singleton(sK2)),sK1)
| spl20_116
| ~ spl20_148 ),
inference(resolution,[],[f1019,f1290]) ).
fof(f1290,plain,
( ! [X0,X1] :
( subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0)
| ordinal_subset(X1,X0) )
| ~ spl20_148 ),
inference(avatar_component_clause,[],[f1289]) ).
fof(f3476,plain,
( ~ spl20_40
| ~ spl20_64
| ~ spl20_94 ),
inference(avatar_split_clause,[],[f2609,f845,f617,f470]) ).
fof(f470,plain,
( spl20_40
<=> in(sK1,set_union2(sK2,singleton(sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_40])]) ).
fof(f2609,plain,
( ~ in(sK1,set_union2(sK2,singleton(sK2)))
| ~ spl20_64
| ~ spl20_94 ),
inference(resolution,[],[f846,f618]) ).
fof(f3442,plain,
( ~ spl20_58
| spl20_102
| ~ spl20_81
| ~ spl20_183 ),
inference(avatar_split_clause,[],[f2220,f2104,f760,f932,f590]) ).
fof(f932,plain,
( spl20_102
<=> subset(sK1,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_102])]) ).
fof(f2220,plain,
( subset(sK1,sK2)
| ~ epsilon_transitive(sK2)
| ~ spl20_81
| ~ spl20_183 ),
inference(resolution,[],[f2106,f761]) ).
fof(f2106,plain,
( in(sK1,sK2)
| ~ spl20_183 ),
inference(avatar_component_clause,[],[f2104]) ).
fof(f3427,plain,
( spl20_258
| ~ spl20_93
| ~ spl20_162 ),
inference(avatar_split_clause,[],[f1554,f1536,f841,f3425]) ).
fof(f3425,plain,
( spl20_258
<=> ! [X0,X1] :
( singleton(X0) = singleton(X1)
| ~ in(X0,singleton(X1))
| sK5(X0,singleton(X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_258])]) ).
fof(f841,plain,
( spl20_93
<=> ! [X0,X1] :
( singleton(X0) = X1
| sK5(X0,X1) != X0
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_93])]) ).
fof(f1536,plain,
( spl20_162
<=> ! [X0,X1] :
( sK5(X0,singleton(X1)) = X0
| singleton(X0) = singleton(X1)
| sK5(X0,singleton(X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_162])]) ).
fof(f1554,plain,
( ! [X0,X1] :
( singleton(X0) = singleton(X1)
| ~ in(X0,singleton(X1))
| sK5(X0,singleton(X1)) = X1 )
| ~ spl20_93
| ~ spl20_162 ),
inference(trivial_inequality_removal,[],[f1553]) ).
fof(f1553,plain,
( ! [X0,X1] :
( X0 != X0
| singleton(X0) = singleton(X1)
| ~ in(X0,singleton(X1))
| sK5(X0,singleton(X1)) = X1 )
| ~ spl20_93
| ~ spl20_162 ),
inference(duplicate_literal_removal,[],[f1550]) ).
fof(f1550,plain,
( ! [X0,X1] :
( X0 != X0
| singleton(X0) = singleton(X1)
| ~ in(X0,singleton(X1))
| sK5(X0,singleton(X1)) = X1
| singleton(X0) = singleton(X1) )
| ~ spl20_93
| ~ spl20_162 ),
inference(superposition,[],[f842,f1537]) ).
fof(f1537,plain,
( ! [X0,X1] :
( sK5(X0,singleton(X1)) = X1
| sK5(X0,singleton(X1)) = X0
| singleton(X0) = singleton(X1) )
| ~ spl20_162 ),
inference(avatar_component_clause,[],[f1536]) ).
fof(f842,plain,
( ! [X0,X1] :
( sK5(X0,X1) != X0
| singleton(X0) = X1
| ~ in(X0,X1) )
| ~ spl20_93 ),
inference(avatar_component_clause,[],[f841]) ).
fof(f3423,plain,
( spl20_257
| ~ spl20_81
| ~ spl20_153 ),
inference(avatar_split_clause,[],[f1379,f1376,f760,f3421]) ).
fof(f3421,plain,
( spl20_257
<=> ! [X0,X1] :
( X0 = X1
| ~ ordinal(X0)
| ~ ordinal(X1)
| element(X0,X1)
| subset(X1,X0)
| ~ epsilon_transitive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_257])]) ).
fof(f1379,plain,
( ! [X0,X1] :
( X0 = X1
| ~ ordinal(X0)
| ~ ordinal(X1)
| element(X0,X1)
| subset(X1,X0)
| ~ epsilon_transitive(X0) )
| ~ spl20_81
| ~ spl20_153 ),
inference(resolution,[],[f1377,f761]) ).
fof(f3419,plain,
( spl20_256
| ~ spl20_97
| ~ spl20_138 ),
inference(avatar_split_clause,[],[f1204,f1195,f871,f3417]) ).
fof(f3417,plain,
( spl20_256
<=> ! [X0,X1] :
( ~ empty(X0)
| sK5(X1,sK4(powerset(X0))) = X1
| singleton(X1) = sK4(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_256])]) ).
fof(f1204,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sK5(X1,sK4(powerset(X0))) = X1
| singleton(X1) = sK4(powerset(X0)) )
| ~ spl20_97
| ~ spl20_138 ),
inference(resolution,[],[f1196,f872]) ).
fof(f3329,plain,
( spl20_255
| ~ spl20_56
| ~ spl20_164 ),
inference(avatar_split_clause,[],[f1612,f1565,f574,f3327]) ).
fof(f3327,plain,
( spl20_255
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_255])]) ).
fof(f1612,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl20_56
| ~ spl20_164 ),
inference(resolution,[],[f1566,f575]) ).
fof(f3325,plain,
( spl20_254
| ~ spl20_56
| ~ spl20_163 ),
inference(avatar_split_clause,[],[f1587,f1561,f574,f3323]) ).
fof(f3323,plain,
( spl20_254
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ empty(X2)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_254])]) ).
fof(f1587,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ empty(X2)
| ~ empty(X0) )
| ~ spl20_56
| ~ spl20_163 ),
inference(resolution,[],[f1562,f575]) ).
fof(f3321,plain,
( spl20_253
| ~ spl20_56
| ~ spl20_163 ),
inference(avatar_split_clause,[],[f1577,f1561,f574,f3319]) ).
fof(f3319,plain,
( spl20_253
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ empty(X2)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_253])]) ).
fof(f1577,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ empty(X2)
| ~ empty(X1) )
| ~ spl20_56
| ~ spl20_163 ),
inference(resolution,[],[f1562,f575]) ).
fof(f3317,plain,
( spl20_252
| ~ spl20_162 ),
inference(avatar_split_clause,[],[f1552,f1536,f3315]) ).
fof(f3315,plain,
( spl20_252
<=> ! [X0,X1] :
( X0 != X1
| sK5(X0,singleton(X1)) = X1
| singleton(X0) = singleton(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_252])]) ).
fof(f1552,plain,
( ! [X0,X1] :
( X0 != X1
| sK5(X0,singleton(X1)) = X1
| singleton(X0) = singleton(X1) )
| ~ spl20_162 ),
inference(equality_factoring,[],[f1537]) ).
fof(f3313,plain,
( spl20_251
| ~ spl20_162 ),
inference(avatar_split_clause,[],[f1551,f1536,f3311]) ).
fof(f3311,plain,
( spl20_251
<=> ! [X0,X1] :
( X0 != X1
| sK5(X0,singleton(X1)) = X0
| singleton(X0) = singleton(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_251])]) ).
fof(f1551,plain,
( ! [X0,X1] :
( X0 != X1
| sK5(X0,singleton(X1)) = X0
| singleton(X0) = singleton(X1) )
| ~ spl20_162 ),
inference(equality_factoring,[],[f1537]) ).
fof(f3309,plain,
( spl20_250
| ~ spl20_80
| ~ spl20_152 ),
inference(avatar_split_clause,[],[f1366,f1358,f727,f3307]) ).
fof(f3307,plain,
( spl20_250
<=> ! [X0,X1] :
( singleton(X0) = X1
| ~ ordinal(singleton(X0))
| ~ ordinal(X1)
| ~ empty(X1)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_250])]) ).
fof(f1366,plain,
( ! [X0,X1] :
( singleton(X0) = X1
| ~ ordinal(singleton(X0))
| ~ ordinal(X1)
| ~ empty(X1)
| X0 = X1 )
| ~ spl20_80
| ~ spl20_152 ),
inference(resolution,[],[f1359,f728]) ).
fof(f3305,plain,
( spl20_249
| ~ spl20_81
| ~ spl20_152 ),
inference(avatar_split_clause,[],[f1361,f1358,f760,f3303]) ).
fof(f3303,plain,
( spl20_249
<=> ! [X0,X1] :
( X0 = X1
| ~ ordinal(X0)
| ~ ordinal(X1)
| ~ empty(X1)
| subset(X1,X0)
| ~ epsilon_transitive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_249])]) ).
fof(f1361,plain,
( ! [X0,X1] :
( X0 = X1
| ~ ordinal(X0)
| ~ ordinal(X1)
| ~ empty(X1)
| subset(X1,X0)
| ~ epsilon_transitive(X0) )
| ~ spl20_81
| ~ spl20_152 ),
inference(resolution,[],[f1359,f761]) ).
fof(f3219,plain,
( spl20_248
| ~ spl20_65
| ~ spl20_153 ),
inference(avatar_split_clause,[],[f1380,f1376,f621,f3217]) ).
fof(f3217,plain,
( spl20_248
<=> ! [X0,X1] :
( X0 = X1
| ~ ordinal(X0)
| ~ ordinal(X1)
| element(X0,X1)
| element(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_248])]) ).
fof(f1380,plain,
( ! [X0,X1] :
( X0 = X1
| ~ ordinal(X0)
| ~ ordinal(X1)
| element(X0,X1)
| element(X1,X0) )
| ~ spl20_65
| ~ spl20_153 ),
inference(resolution,[],[f1377,f622]) ).
fof(f3215,plain,
( spl20_247
| ~ spl20_146
| ~ spl20_148 ),
inference(avatar_split_clause,[],[f1300,f1289,f1277,f3213]) ).
fof(f3213,plain,
( spl20_247
<=> ! [X2,X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| ordinal_subset(X0,X1)
| ~ in(X2,X1)
| element(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_247])]) ).
fof(f1300,plain,
( ! [X2,X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| ordinal_subset(X0,X1)
| ~ in(X2,X1)
| element(X2,X0) )
| ~ spl20_146
| ~ spl20_148 ),
inference(resolution,[],[f1290,f1278]) ).
fof(f3211,plain,
( spl20_246
| ~ spl20_81
| ~ spl20_147 ),
inference(avatar_split_clause,[],[f1292,f1285,f760,f3209]) ).
fof(f3209,plain,
( spl20_246
<=> ! [X0,X1] :
( empty(powerset(X0))
| ~ subset(X1,X0)
| subset(X1,powerset(X0))
| ~ epsilon_transitive(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_246])]) ).
fof(f1292,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| ~ subset(X1,X0)
| subset(X1,powerset(X0))
| ~ epsilon_transitive(powerset(X0)) )
| ~ spl20_81
| ~ spl20_147 ),
inference(resolution,[],[f1286,f761]) ).
fof(f2984,plain,
( spl20_245
| ~ spl20_56
| ~ spl20_161 ),
inference(avatar_split_clause,[],[f1527,f1446,f574,f2982]) ).
fof(f2982,plain,
( spl20_245
<=> ! [X0,X1] :
( in(sK6(X0,X0,X1),X1)
| sP0(X0,X0,X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_245])]) ).
fof(f1527,plain,
( ! [X0,X1] :
( in(sK6(X0,X0,X1),X1)
| sP0(X0,X0,X1)
| ~ empty(X0) )
| ~ spl20_56
| ~ spl20_161 ),
inference(resolution,[],[f1447,f575]) ).
fof(f2980,plain,
( spl20_244
| ~ spl20_56
| ~ spl20_161 ),
inference(avatar_split_clause,[],[f1517,f1446,f574,f2978]) ).
fof(f2978,plain,
( spl20_244
<=> ! [X0,X1] :
( in(sK6(X0,X0,X1),X0)
| sP0(X0,X0,X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_244])]) ).
fof(f1517,plain,
( ! [X0,X1] :
( in(sK6(X0,X0,X1),X0)
| sP0(X0,X0,X1)
| ~ empty(X1) )
| ~ spl20_56
| ~ spl20_161 ),
inference(resolution,[],[f1447,f575]) ).
fof(f2976,plain,
( spl20_243
| ~ spl20_56
| ~ spl20_160 ),
inference(avatar_split_clause,[],[f1504,f1442,f574,f2974]) ).
fof(f2974,plain,
( spl20_243
<=> ! [X0,X1] :
( in(sK6(X0,X1,X0),X1)
| sP0(X0,X1,X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_243])]) ).
fof(f1504,plain,
( ! [X0,X1] :
( in(sK6(X0,X1,X0),X1)
| sP0(X0,X1,X0)
| ~ empty(X0) )
| ~ spl20_56
| ~ spl20_160 ),
inference(resolution,[],[f1443,f575]) ).
fof(f2972,plain,
( spl20_242
| ~ spl20_56
| ~ spl20_160 ),
inference(avatar_split_clause,[],[f1494,f1442,f574,f2970]) ).
fof(f2970,plain,
( spl20_242
<=> ! [X0,X1] :
( in(sK6(X0,X1,X0),X0)
| sP0(X0,X1,X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_242])]) ).
fof(f1494,plain,
( ! [X0,X1] :
( in(sK6(X0,X1,X0),X0)
| sP0(X0,X1,X0)
| ~ empty(X1) )
| ~ spl20_56
| ~ spl20_160 ),
inference(resolution,[],[f1443,f575]) ).
fof(f2968,plain,
( spl20_241
| ~ spl20_56
| ~ spl20_159 ),
inference(avatar_split_clause,[],[f1479,f1438,f574,f2966]) ).
fof(f2966,plain,
( spl20_241
<=> ! [X0,X1] :
( in(sK6(X0,X1,X1),X1)
| sP0(X0,X1,X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_241])]) ).
fof(f1479,plain,
( ! [X0,X1] :
( in(sK6(X0,X1,X1),X1)
| sP0(X0,X1,X1)
| ~ empty(X0) )
| ~ spl20_56
| ~ spl20_159 ),
inference(resolution,[],[f1439,f575]) ).
fof(f2964,plain,
( ~ spl20_219
| ~ spl20_64
| ~ spl20_183 ),
inference(avatar_split_clause,[],[f2222,f2104,f617,f2602]) ).
fof(f2222,plain,
( ~ in(sK2,sK1)
| ~ spl20_64
| ~ spl20_183 ),
inference(resolution,[],[f2106,f618]) ).
fof(f2963,plain,
( spl20_240
| ~ spl20_56
| ~ spl20_159 ),
inference(avatar_split_clause,[],[f1469,f1438,f574,f2961]) ).
fof(f2961,plain,
( spl20_240
<=> ! [X0,X1] :
( in(sK6(X0,X1,X1),X0)
| sP0(X0,X1,X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_240])]) ).
fof(f1469,plain,
( ! [X0,X1] :
( in(sK6(X0,X1,X1),X0)
| sP0(X0,X1,X1)
| ~ empty(X1) )
| ~ spl20_56
| ~ spl20_159 ),
inference(resolution,[],[f1439,f575]) ).
fof(f2959,plain,
( spl20_239
| ~ spl20_65
| ~ spl20_152 ),
inference(avatar_split_clause,[],[f1362,f1358,f621,f2957]) ).
fof(f2957,plain,
( spl20_239
<=> ! [X0,X1] :
( X0 = X1
| ~ ordinal(X0)
| ~ ordinal(X1)
| ~ empty(X1)
| element(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_239])]) ).
fof(f1362,plain,
( ! [X0,X1] :
( X0 = X1
| ~ ordinal(X0)
| ~ ordinal(X1)
| ~ empty(X1)
| element(X1,X0) )
| ~ spl20_65
| ~ spl20_152 ),
inference(resolution,[],[f1359,f622]) ).
fof(f2955,plain,
( spl20_238
| ~ spl20_140
| ~ spl20_148 ),
inference(avatar_split_clause,[],[f1301,f1289,f1213,f2953]) ).
fof(f2953,plain,
( spl20_238
<=> ! [X2,X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| ordinal_subset(X0,X1)
| ~ in(X2,X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_238])]) ).
fof(f1213,plain,
( spl20_140
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,X2)
| ~ subset(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_140])]) ).
fof(f1301,plain,
( ! [X2,X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| ordinal_subset(X0,X1)
| ~ in(X2,X1)
| ~ empty(X0) )
| ~ spl20_140
| ~ spl20_148 ),
inference(resolution,[],[f1290,f1214]) ).
fof(f1214,plain,
( ! [X2,X0,X1] :
( ~ subset(X2,X0)
| ~ in(X1,X2)
| ~ empty(X0) )
| ~ spl20_140 ),
inference(avatar_component_clause,[],[f1213]) ).
fof(f2951,plain,
( spl20_237
| ~ spl20_81
| ~ spl20_143 ),
inference(avatar_split_clause,[],[f1253,f1225,f760,f2949]) ).
fof(f2949,plain,
( spl20_237
<=> ! [X2,X0,X1] :
( ~ in(X0,X1)
| subset(X0,set_union2(X2,X1))
| ~ epsilon_transitive(set_union2(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_237])]) ).
fof(f1253,plain,
( ! [X2,X0,X1] :
( ~ in(X0,X1)
| subset(X0,set_union2(X2,X1))
| ~ epsilon_transitive(set_union2(X2,X1)) )
| ~ spl20_81
| ~ spl20_143 ),
inference(resolution,[],[f1226,f761]) ).
fof(f2947,plain,
( spl20_236
| ~ spl20_81
| ~ spl20_142 ),
inference(avatar_split_clause,[],[f1240,f1221,f760,f2945]) ).
fof(f2945,plain,
( spl20_236
<=> ! [X2,X0,X1] :
( ~ in(X0,X1)
| subset(X0,set_union2(X1,X2))
| ~ epsilon_transitive(set_union2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_236])]) ).
fof(f1240,plain,
( ! [X2,X0,X1] :
( ~ in(X0,X1)
| subset(X0,set_union2(X1,X2))
| ~ epsilon_transitive(set_union2(X1,X2)) )
| ~ spl20_81
| ~ spl20_142 ),
inference(resolution,[],[f1222,f761]) ).
fof(f2943,plain,
( spl20_235
| ~ spl20_89
| ~ spl20_137 ),
inference(avatar_split_clause,[],[f1198,f1191,f808,f2941]) ).
fof(f2941,plain,
( spl20_235
<=> ! [X0] :
( ~ epsilon_transitive(singleton(X0))
| ordinal_subset(X0,singleton(X0))
| ~ ordinal(singleton(X0))
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_235])]) ).
fof(f1191,plain,
( spl20_137
<=> ! [X0] :
( subset(X0,singleton(X0))
| ~ epsilon_transitive(singleton(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_137])]) ).
fof(f1198,plain,
( ! [X0] :
( ~ epsilon_transitive(singleton(X0))
| ordinal_subset(X0,singleton(X0))
| ~ ordinal(singleton(X0))
| ~ ordinal(X0) )
| ~ spl20_89
| ~ spl20_137 ),
inference(resolution,[],[f1192,f809]) ).
fof(f1192,plain,
( ! [X0] :
( subset(X0,singleton(X0))
| ~ epsilon_transitive(singleton(X0)) )
| ~ spl20_137 ),
inference(avatar_component_clause,[],[f1191]) ).
fof(f2893,plain,
( spl20_234
| ~ spl20_65
| ~ spl20_183 ),
inference(avatar_split_clause,[],[f2221,f2104,f621,f2890]) ).
fof(f2221,plain,
( element(sK1,sK2)
| ~ spl20_65
| ~ spl20_183 ),
inference(resolution,[],[f2106,f622]) ).
fof(f2888,plain,
( spl20_233
| ~ spl20_134
| ~ spl20_147 ),
inference(avatar_split_clause,[],[f1296,f1285,f1153,f2886]) ).
fof(f2886,plain,
( spl20_233
<=> ! [X0] :
( empty(powerset(X0))
| ~ subset(set_union2(powerset(X0),singleton(powerset(X0))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_233])]) ).
fof(f1296,plain,
( ! [X0] :
( empty(powerset(X0))
| ~ subset(set_union2(powerset(X0),singleton(powerset(X0))),X0) )
| ~ spl20_134
| ~ spl20_147 ),
inference(resolution,[],[f1286,f1154]) ).
fof(f2884,plain,
( spl20_232
| ~ spl20_84
| ~ spl20_137 ),
inference(avatar_split_clause,[],[f1199,f1191,f784,f2882]) ).
fof(f2882,plain,
( spl20_232
<=> ! [X0] :
( ~ epsilon_transitive(singleton(X0))
| singleton(X0) = X0
| ~ subset(singleton(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_232])]) ).
fof(f1199,plain,
( ! [X0] :
( ~ epsilon_transitive(singleton(X0))
| singleton(X0) = X0
| ~ subset(singleton(X0),X0) )
| ~ spl20_84
| ~ spl20_137 ),
inference(resolution,[],[f1192,f785]) ).
fof(f2880,plain,
( spl20_231
| ~ spl20_90
| ~ spl20_132 ),
inference(avatar_split_clause,[],[f1166,f1145,f812,f2878]) ).
fof(f2878,plain,
( spl20_231
<=> ! [X0,X1] :
( epsilon_transitive(powerset(X0))
| element(X1,X0)
| ~ in(X1,sK3(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_231])]) ).
fof(f1145,plain,
( spl20_132
<=> ! [X0] :
( element(sK3(X0),X0)
| epsilon_transitive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_132])]) ).
fof(f1166,plain,
( ! [X0,X1] :
( epsilon_transitive(powerset(X0))
| element(X1,X0)
| ~ in(X1,sK3(powerset(X0))) )
| ~ spl20_90
| ~ spl20_132 ),
inference(resolution,[],[f1146,f813]) ).
fof(f1146,plain,
( ! [X0] :
( element(sK3(X0),X0)
| epsilon_transitive(X0) )
| ~ spl20_132 ),
inference(avatar_component_clause,[],[f1145]) ).
fof(f2858,plain,
( ~ spl20_42
| spl20_210 ),
inference(avatar_contradiction_clause,[],[f2855]) ).
fof(f2855,plain,
( $false
| ~ spl20_42
| spl20_210 ),
inference(resolution,[],[f2559,f481]) ).
fof(f481,plain,
( ! [X0] : subset(X0,X0)
| ~ spl20_42 ),
inference(avatar_component_clause,[],[f480]) ).
fof(f480,plain,
( spl20_42
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_42])]) ).
fof(f2559,plain,
( ~ subset(sK1,sK1)
| spl20_210 ),
inference(avatar_component_clause,[],[f2557]) ).
fof(f2854,plain,
( spl20_230
| ~ spl20_89
| ~ spl20_127 ),
inference(avatar_split_clause,[],[f1133,f1101,f808,f2852]) ).
fof(f2852,plain,
( spl20_230
<=> ! [X0] :
( ordinal_subset(sK4(powerset(X0)),X0)
| ~ ordinal(X0)
| ~ ordinal(sK4(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_230])]) ).
fof(f1101,plain,
( spl20_127
<=> ! [X0] : subset(sK4(powerset(X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_127])]) ).
fof(f1133,plain,
( ! [X0] :
( ordinal_subset(sK4(powerset(X0)),X0)
| ~ ordinal(X0)
| ~ ordinal(sK4(powerset(X0))) )
| ~ spl20_89
| ~ spl20_127 ),
inference(resolution,[],[f1102,f809]) ).
fof(f1102,plain,
( ! [X0] : subset(sK4(powerset(X0)),X0)
| ~ spl20_127 ),
inference(avatar_component_clause,[],[f1101]) ).
fof(f2757,plain,
( spl20_229
| ~ spl20_64
| ~ spl20_147 ),
inference(avatar_split_clause,[],[f1294,f1285,f617,f2755]) ).
fof(f2755,plain,
( spl20_229
<=> ! [X0,X1] :
( empty(powerset(X0))
| ~ subset(X1,X0)
| ~ in(powerset(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_229])]) ).
fof(f1294,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| ~ subset(X1,X0)
| ~ in(powerset(X0),X1) )
| ~ spl20_64
| ~ spl20_147 ),
inference(resolution,[],[f1286,f618]) ).
fof(f2753,plain,
( spl20_228
| ~ spl20_137
| ~ spl20_146 ),
inference(avatar_split_clause,[],[f1281,f1277,f1191,f2751]) ).
fof(f2751,plain,
( spl20_228
<=> ! [X0,X1] :
( ~ in(X0,X1)
| element(X0,singleton(X1))
| ~ epsilon_transitive(singleton(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_228])]) ).
fof(f1281,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| element(X0,singleton(X1))
| ~ epsilon_transitive(singleton(X1)) )
| ~ spl20_137
| ~ spl20_146 ),
inference(resolution,[],[f1278,f1192]) ).
fof(f2749,plain,
( spl20_227
| ~ spl20_134
| ~ spl20_143 ),
inference(avatar_split_clause,[],[f1257,f1225,f1153,f2747]) ).
fof(f2747,plain,
( spl20_227
<=> ! [X0,X1] : ~ in(set_union2(set_union2(X0,X1),singleton(set_union2(X0,X1))),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_227])]) ).
fof(f1257,plain,
( ! [X0,X1] : ~ in(set_union2(set_union2(X0,X1),singleton(set_union2(X0,X1))),X1)
| ~ spl20_134
| ~ spl20_143 ),
inference(resolution,[],[f1226,f1154]) ).
fof(f2745,plain,
( spl20_226
| ~ spl20_134
| ~ spl20_142 ),
inference(avatar_split_clause,[],[f1244,f1221,f1153,f2743]) ).
fof(f2743,plain,
( spl20_226
<=> ! [X0,X1] : ~ in(set_union2(set_union2(X0,X1),singleton(set_union2(X0,X1))),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_226])]) ).
fof(f1244,plain,
( ! [X0,X1] : ~ in(set_union2(set_union2(X0,X1),singleton(set_union2(X0,X1))),X0)
| ~ spl20_134
| ~ spl20_142 ),
inference(resolution,[],[f1222,f1154]) ).
fof(f2741,plain,
( spl20_225
| ~ spl20_136
| ~ spl20_141 ),
inference(avatar_split_clause,[],[f1235,f1217,f1161,f2739]) ).
fof(f2739,plain,
( spl20_225
<=> ! [X0] :
( element(sK4(sK4(powerset(X0))),X0)
| empty(sK4(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_225])]) ).
fof(f1235,plain,
( ! [X0] :
( element(sK4(sK4(powerset(X0))),X0)
| empty(sK4(powerset(X0))) )
| ~ spl20_136
| ~ spl20_141 ),
inference(resolution,[],[f1218,f1162]) ).
fof(f2737,plain,
( spl20_224
| ~ spl20_60
| ~ spl20_141 ),
inference(avatar_split_clause,[],[f1234,f1217,f601,f2735]) ).
fof(f2735,plain,
( spl20_224
<=> ! [X0] :
( element(sK3(sK4(powerset(X0))),X0)
| epsilon_transitive(sK4(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_224])]) ).
fof(f1234,plain,
( ! [X0] :
( element(sK3(sK4(powerset(X0))),X0)
| epsilon_transitive(sK4(powerset(X0))) )
| ~ spl20_60
| ~ spl20_141 ),
inference(resolution,[],[f1218,f602]) ).
fof(f2733,plain,
( spl20_223
| ~ spl20_86
| ~ spl20_132 ),
inference(avatar_split_clause,[],[f1167,f1145,f792,f2731]) ).
fof(f2731,plain,
( spl20_223
<=> ! [X0,X1] :
( epsilon_transitive(powerset(X0))
| ~ empty(X0)
| ~ in(X1,sK3(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_223])]) ).
fof(f1167,plain,
( ! [X0,X1] :
( epsilon_transitive(powerset(X0))
| ~ empty(X0)
| ~ in(X1,sK3(powerset(X0))) )
| ~ spl20_86
| ~ spl20_132 ),
inference(resolution,[],[f1146,f793]) ).
fof(f2729,plain,
( spl20_222
| ~ spl20_84
| ~ spl20_127 ),
inference(avatar_split_clause,[],[f1134,f1101,f784,f2727]) ).
fof(f2727,plain,
( spl20_222
<=> ! [X0] :
( sK4(powerset(X0)) = X0
| ~ subset(X0,sK4(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_222])]) ).
fof(f1134,plain,
( ! [X0] :
( sK4(powerset(X0)) = X0
| ~ subset(X0,sK4(powerset(X0))) )
| ~ spl20_84
| ~ spl20_127 ),
inference(resolution,[],[f1102,f785]) ).
fof(f2718,plain,
( spl20_221
| ~ spl20_3
| ~ spl20_117
| ~ spl20_151 ),
inference(avatar_split_clause,[],[f1350,f1317,f1024,f285,f2716]) ).
fof(f2716,plain,
( spl20_221
<=> ! [X0] :
( sK5(X0,sK8) = X0
| singleton(X0) = sK8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_221])]) ).
fof(f285,plain,
( spl20_3
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_3])]) ).
fof(f1317,plain,
( spl20_151
<=> ! [X0,X1] :
( sK5(X0,X1) = X0
| singleton(X0) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_151])]) ).
fof(f1350,plain,
( ! [X0] :
( sK5(X0,sK8) = X0
| singleton(X0) = sK8 )
| ~ spl20_3
| ~ spl20_117
| ~ spl20_151 ),
inference(forward_demodulation,[],[f1349,f1026]) ).
fof(f1349,plain,
( ! [X0] :
( singleton(X0) = sK8
| sK5(X0,empty_set) = X0 )
| ~ spl20_3
| ~ spl20_117
| ~ spl20_151 ),
inference(forward_demodulation,[],[f1344,f1026]) ).
fof(f1344,plain,
( ! [X0] :
( singleton(X0) = empty_set
| sK5(X0,empty_set) = X0 )
| ~ spl20_3
| ~ spl20_151 ),
inference(resolution,[],[f1318,f287]) ).
fof(f287,plain,
( empty(empty_set)
| ~ spl20_3 ),
inference(avatar_component_clause,[],[f285]) ).
fof(f1318,plain,
( ! [X0,X1] :
( ~ empty(X1)
| singleton(X0) = X1
| sK5(X0,X1) = X0 )
| ~ spl20_151 ),
inference(avatar_component_clause,[],[f1317]) ).
fof(f2713,plain,
( spl20_220
| ~ spl20_129
| ~ spl20_133 ),
inference(avatar_split_clause,[],[f2359,f1149,f1109,f2710]) ).
fof(f1149,plain,
( spl20_133
<=> ! [X0] : element(X0,set_union2(X0,singleton(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_133])]) ).
fof(f2359,plain,
( element(sK2,sK1)
| ~ spl20_129
| ~ spl20_133 ),
inference(superposition,[],[f1150,f1111]) ).
fof(f1150,plain,
( ! [X0] : element(X0,set_union2(X0,singleton(X0)))
| ~ spl20_133 ),
inference(avatar_component_clause,[],[f1149]) ).
fof(f2612,plain,
( ~ spl20_52
| spl20_128
| ~ spl20_81
| ~ spl20_94 ),
inference(avatar_split_clause,[],[f2334,f845,f760,f1105,f552]) ).
fof(f1105,plain,
( spl20_128
<=> subset(set_union2(sK2,singleton(sK2)),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_128])]) ).
fof(f2334,plain,
( subset(set_union2(sK2,singleton(sK2)),sK1)
| ~ epsilon_transitive(sK1)
| ~ spl20_81
| ~ spl20_94 ),
inference(resolution,[],[f846,f761]) ).
fof(f2605,plain,
( spl20_219
| ~ spl20_68
| ~ spl20_129 ),
inference(avatar_split_clause,[],[f2355,f1109,f634,f2602]) ).
fof(f634,plain,
( spl20_68
<=> ! [X0] : in(X0,set_union2(X0,singleton(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_68])]) ).
fof(f2355,plain,
( in(sK2,sK1)
| ~ spl20_68
| ~ spl20_129 ),
inference(superposition,[],[f635,f1111]) ).
fof(f635,plain,
( ! [X0] : in(X0,set_union2(X0,singleton(X0)))
| ~ spl20_68 ),
inference(avatar_component_clause,[],[f634]) ).
fof(f2592,plain,
( spl20_218
| ~ spl20_122
| ~ spl20_147 ),
inference(avatar_split_clause,[],[f1297,f1285,f1069,f2590]) ).
fof(f2590,plain,
( spl20_218
<=> ! [X0] :
( empty(powerset(X0))
| ~ subset(singleton(powerset(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_218])]) ).
fof(f1069,plain,
( spl20_122
<=> ! [X0] : ~ in(singleton(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_122])]) ).
fof(f1297,plain,
( ! [X0] :
( empty(powerset(X0))
| ~ subset(singleton(powerset(X0)),X0) )
| ~ spl20_122
| ~ spl20_147 ),
inference(resolution,[],[f1286,f1070]) ).
fof(f1070,plain,
( ! [X0] : ~ in(singleton(X0),X0)
| ~ spl20_122 ),
inference(avatar_component_clause,[],[f1069]) ).
fof(f2588,plain,
( spl20_217
| ~ spl20_64
| ~ spl20_143 ),
inference(avatar_split_clause,[],[f1255,f1225,f617,f2586]) ).
fof(f2586,plain,
( spl20_217
<=> ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(set_union2(X2,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_217])]) ).
fof(f1255,plain,
( ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(set_union2(X2,X1),X0) )
| ~ spl20_64
| ~ spl20_143 ),
inference(resolution,[],[f1226,f618]) ).
fof(f2584,plain,
( spl20_216
| ~ spl20_65
| ~ spl20_143 ),
inference(avatar_split_clause,[],[f1254,f1225,f621,f2582]) ).
fof(f2582,plain,
( spl20_216
<=> ! [X2,X0,X1] :
( ~ in(X0,X1)
| element(X0,set_union2(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_216])]) ).
fof(f1254,plain,
( ! [X2,X0,X1] :
( ~ in(X0,X1)
| element(X0,set_union2(X2,X1)) )
| ~ spl20_65
| ~ spl20_143 ),
inference(resolution,[],[f1226,f622]) ).
fof(f2580,plain,
( spl20_215
| ~ spl20_64
| ~ spl20_142 ),
inference(avatar_split_clause,[],[f1242,f1221,f617,f2578]) ).
fof(f2578,plain,
( spl20_215
<=> ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(set_union2(X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_215])]) ).
fof(f1242,plain,
( ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(set_union2(X1,X2),X0) )
| ~ spl20_64
| ~ spl20_142 ),
inference(resolution,[],[f1222,f618]) ).
fof(f2576,plain,
( spl20_214
| ~ spl20_65
| ~ spl20_142 ),
inference(avatar_split_clause,[],[f1241,f1221,f621,f2574]) ).
fof(f2574,plain,
( spl20_214
<=> ! [X2,X0,X1] :
( ~ in(X0,X1)
| element(X0,set_union2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_214])]) ).
fof(f1241,plain,
( ! [X2,X0,X1] :
( ~ in(X0,X1)
| element(X0,set_union2(X1,X2)) )
| ~ spl20_65
| ~ spl20_142 ),
inference(resolution,[],[f1222,f622]) ).
fof(f2572,plain,
( spl20_213
| ~ spl20_80
| ~ spl20_136 ),
inference(avatar_split_clause,[],[f1189,f1161,f727,f2570]) ).
fof(f2570,plain,
( spl20_213
<=> ! [X0] :
( empty(singleton(X0))
| sK4(singleton(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_213])]) ).
fof(f1189,plain,
( ! [X0] :
( empty(singleton(X0))
| sK4(singleton(X0)) = X0 )
| ~ spl20_80
| ~ spl20_136 ),
inference(resolution,[],[f1162,f728]) ).
fof(f2568,plain,
( spl20_212
| ~ spl20_81
| ~ spl20_136 ),
inference(avatar_split_clause,[],[f1185,f1161,f760,f2566]) ).
fof(f2566,plain,
( spl20_212
<=> ! [X0] :
( empty(X0)
| subset(sK4(X0),X0)
| ~ epsilon_transitive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_212])]) ).
fof(f1185,plain,
( ! [X0] :
( empty(X0)
| subset(sK4(X0),X0)
| ~ epsilon_transitive(X0) )
| ~ spl20_81
| ~ spl20_136 ),
inference(resolution,[],[f1162,f761]) ).
fof(f2564,plain,
( spl20_211
| ~ spl20_74
| ~ spl20_132 ),
inference(avatar_split_clause,[],[f1168,f1145,f703,f2562]) ).
fof(f2562,plain,
( spl20_211
<=> ! [X0] :
( epsilon_transitive(powerset(X0))
| subset(sK3(powerset(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_211])]) ).
fof(f1168,plain,
( ! [X0] :
( epsilon_transitive(powerset(X0))
| subset(sK3(powerset(X0)),X0) )
| ~ spl20_74
| ~ spl20_132 ),
inference(resolution,[],[f1146,f704]) ).
fof(f2560,plain,
( ~ spl20_210
| spl20_128
| ~ spl20_129 ),
inference(avatar_split_clause,[],[f2348,f1109,f1105,f2557]) ).
fof(f2348,plain,
( ~ subset(sK1,sK1)
| spl20_128
| ~ spl20_129 ),
inference(superposition,[],[f1107,f1111]) ).
fof(f1107,plain,
( ~ subset(set_union2(sK2,singleton(sK2)),sK1)
| spl20_128 ),
inference(avatar_component_clause,[],[f1105]) ).
fof(f2540,plain,
( spl20_209
| ~ spl20_56
| ~ spl20_143 ),
inference(avatar_split_clause,[],[f1256,f1225,f574,f2538]) ).
fof(f2538,plain,
( spl20_209
<=> ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ empty(set_union2(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_209])]) ).
fof(f1256,plain,
( ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ empty(set_union2(X2,X1)) )
| ~ spl20_56
| ~ spl20_143 ),
inference(resolution,[],[f1226,f575]) ).
fof(f2536,plain,
( spl20_208
| ~ spl20_56
| ~ spl20_142 ),
inference(avatar_split_clause,[],[f1243,f1221,f574,f2534]) ).
fof(f2534,plain,
( spl20_208
<=> ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ empty(set_union2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_208])]) ).
fof(f1243,plain,
( ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ empty(set_union2(X1,X2)) )
| ~ spl20_56
| ~ spl20_142 ),
inference(resolution,[],[f1222,f575]) ).
fof(f2441,plain,
( ~ spl20_207
| spl20_100
| ~ spl20_129 ),
inference(avatar_split_clause,[],[f2345,f1109,f892,f2438]) ).
fof(f892,plain,
( spl20_100
<=> element(sK1,set_union2(sK2,singleton(sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_100])]) ).
fof(f2345,plain,
( ~ element(sK1,sK1)
| spl20_100
| ~ spl20_129 ),
inference(superposition,[],[f893,f1111]) ).
fof(f893,plain,
( ~ element(sK1,set_union2(sK2,singleton(sK2)))
| spl20_100 ),
inference(avatar_component_clause,[],[f892]) ).
fof(f2436,plain,
( spl20_206
| ~ spl20_122
| ~ spl20_143 ),
inference(avatar_split_clause,[],[f1258,f1225,f1069,f2434]) ).
fof(f2434,plain,
( spl20_206
<=> ! [X0,X1] : ~ in(singleton(set_union2(X0,X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_206])]) ).
fof(f1258,plain,
( ! [X0,X1] : ~ in(singleton(set_union2(X0,X1)),X1)
| ~ spl20_122
| ~ spl20_143 ),
inference(resolution,[],[f1226,f1070]) ).
fof(f2432,plain,
( spl20_205
| ~ spl20_122
| ~ spl20_142 ),
inference(avatar_split_clause,[],[f1245,f1221,f1069,f2430]) ).
fof(f1245,plain,
( ! [X0,X1] : ~ in(singleton(set_union2(X0,X1)),X0)
| ~ spl20_122
| ~ spl20_142 ),
inference(resolution,[],[f1222,f1070]) ).
fof(f2428,plain,
( spl20_204
| ~ spl20_136
| ~ spl20_138 ),
inference(avatar_split_clause,[],[f1203,f1195,f1161,f2426]) ).
fof(f2426,plain,
( spl20_204
<=> ! [X0] :
( ~ empty(X0)
| empty(sK4(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_204])]) ).
fof(f1203,plain,
( ! [X0] :
( ~ empty(X0)
| empty(sK4(powerset(X0))) )
| ~ spl20_136
| ~ spl20_138 ),
inference(resolution,[],[f1196,f1162]) ).
fof(f2424,plain,
( spl20_203
| ~ spl20_60
| ~ spl20_138 ),
inference(avatar_split_clause,[],[f1202,f1195,f601,f2422]) ).
fof(f2422,plain,
( spl20_203
<=> ! [X0] :
( ~ empty(X0)
| epsilon_transitive(sK4(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_203])]) ).
fof(f1202,plain,
( ! [X0] :
( ~ empty(X0)
| epsilon_transitive(sK4(powerset(X0))) )
| ~ spl20_60
| ~ spl20_138 ),
inference(resolution,[],[f1196,f602]) ).
fof(f2420,plain,
( spl20_202
| ~ spl20_64
| ~ spl20_136 ),
inference(avatar_split_clause,[],[f1187,f1161,f617,f2418]) ).
fof(f2418,plain,
( spl20_202
<=> ! [X0] :
( empty(X0)
| ~ in(X0,sK4(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_202])]) ).
fof(f1187,plain,
( ! [X0] :
( empty(X0)
| ~ in(X0,sK4(X0)) )
| ~ spl20_64
| ~ spl20_136 ),
inference(resolution,[],[f1162,f618]) ).
fof(f2416,plain,
( spl20_201
| ~ spl20_92
| ~ spl20_125 ),
inference(avatar_split_clause,[],[f1093,f1081,f821,f2414]) ).
fof(f2414,plain,
( spl20_201
<=> ! [X0,X1] :
( ~ in(X0,sK8)
| in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_201])]) ).
fof(f821,plain,
( spl20_92
<=> ! [X4,X0,X2,X1] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_92])]) ).
fof(f1081,plain,
( spl20_125
<=> ! [X0] : sP0(sK8,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_125])]) ).
fof(f1093,plain,
( ! [X0,X1] :
( ~ in(X0,sK8)
| in(X0,X1) )
| ~ spl20_92
| ~ spl20_125 ),
inference(resolution,[],[f1082,f822]) ).
fof(f822,plain,
( ! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| ~ in(X4,X0)
| in(X4,X2) )
| ~ spl20_92 ),
inference(avatar_component_clause,[],[f821]) ).
fof(f1082,plain,
( ! [X0] : sP0(sK8,X0,X0)
| ~ spl20_125 ),
inference(avatar_component_clause,[],[f1081]) ).
fof(f2398,plain,
( ~ spl20_112
| spl20_200
| ~ spl20_77
| ~ spl20_126 ),
inference(avatar_split_clause,[],[f1128,f1097,f715,f2395,f994]) ).
fof(f2395,plain,
( spl20_200
<=> ordinal(singleton(sK8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_200])]) ).
fof(f715,plain,
( spl20_77
<=> ! [X0] :
( ordinal(set_union2(X0,singleton(X0)))
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_77])]) ).
fof(f1128,plain,
( ordinal(singleton(sK8))
| ~ ordinal(sK8)
| ~ spl20_77
| ~ spl20_126 ),
inference(superposition,[],[f716,f1098]) ).
fof(f716,plain,
( ! [X0] :
( ordinal(set_union2(X0,singleton(X0)))
| ~ ordinal(X0) )
| ~ spl20_77 ),
inference(avatar_component_clause,[],[f715]) ).
fof(f2384,plain,
( ~ spl20_112
| spl20_199
| ~ spl20_78
| ~ spl20_126 ),
inference(avatar_split_clause,[],[f1127,f1097,f719,f2381,f994]) ).
fof(f2381,plain,
( spl20_199
<=> epsilon_connected(singleton(sK8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_199])]) ).
fof(f719,plain,
( spl20_78
<=> ! [X0] :
( epsilon_connected(set_union2(X0,singleton(X0)))
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_78])]) ).
fof(f1127,plain,
( epsilon_connected(singleton(sK8))
| ~ ordinal(sK8)
| ~ spl20_78
| ~ spl20_126 ),
inference(superposition,[],[f720,f1098]) ).
fof(f720,plain,
( ! [X0] :
( epsilon_connected(set_union2(X0,singleton(X0)))
| ~ ordinal(X0) )
| ~ spl20_78 ),
inference(avatar_component_clause,[],[f719]) ).
fof(f2379,plain,
( ~ spl20_112
| spl20_198
| ~ spl20_79
| ~ spl20_126 ),
inference(avatar_split_clause,[],[f1126,f1097,f723,f2376,f994]) ).
fof(f2376,plain,
( spl20_198
<=> epsilon_transitive(singleton(sK8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_198])]) ).
fof(f723,plain,
( spl20_79
<=> ! [X0] :
( epsilon_transitive(set_union2(X0,singleton(X0)))
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_79])]) ).
fof(f1126,plain,
( epsilon_transitive(singleton(sK8))
| ~ ordinal(sK8)
| ~ spl20_79
| ~ spl20_126 ),
inference(superposition,[],[f724,f1098]) ).
fof(f724,plain,
( ! [X0] :
( epsilon_transitive(set_union2(X0,singleton(X0)))
| ~ ordinal(X0) )
| ~ spl20_79 ),
inference(avatar_component_clause,[],[f723]) ).
fof(f2374,plain,
( spl20_197
| ~ spl20_53
| ~ spl20_117 ),
inference(avatar_split_clause,[],[f1056,f1024,f562,f2372]) ).
fof(f2372,plain,
( spl20_197
<=> ! [X0] : set_union2(X0,sK8) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl20_197])]) ).
fof(f562,plain,
( spl20_53
<=> ! [X0] : set_union2(X0,empty_set) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl20_53])]) ).
fof(f1056,plain,
( ! [X0] : set_union2(X0,sK8) = X0
| ~ spl20_53
| ~ spl20_117 ),
inference(superposition,[],[f563,f1026]) ).
fof(f563,plain,
( ! [X0] : set_union2(X0,empty_set) = X0
| ~ spl20_53 ),
inference(avatar_component_clause,[],[f562]) ).
fof(f2342,plain,
( spl20_196
| ~ spl20_65
| ~ spl20_94 ),
inference(avatar_split_clause,[],[f2335,f845,f621,f2339]) ).
fof(f2335,plain,
( element(set_union2(sK2,singleton(sK2)),sK1)
| ~ spl20_65
| ~ spl20_94 ),
inference(resolution,[],[f846,f622]) ).
fof(f2332,plain,
( ~ spl20_144
| ~ spl20_1
| spl20_129
| spl20_40
| spl20_94
| ~ spl20_95 ),
inference(avatar_split_clause,[],[f929,f850,f845,f470,f1109,f275,f1268]) ).
fof(f929,plain,
( in(sK1,set_union2(sK2,singleton(sK2)))
| sK1 = set_union2(sK2,singleton(sK2))
| ~ ordinal(sK1)
| ~ ordinal(set_union2(sK2,singleton(sK2)))
| spl20_94
| ~ spl20_95 ),
inference(resolution,[],[f847,f851]) ).
fof(f2331,plain,
( ~ spl20_195
| spl20_100
| ~ spl20_187 ),
inference(avatar_split_clause,[],[f2308,f2160,f892,f2328]) ).
fof(f2308,plain,
( ~ in(sK1,sK1)
| spl20_100
| ~ spl20_187 ),
inference(resolution,[],[f893,f2161]) ).
fof(f2322,plain,
( ~ spl20_194
| ~ spl20_67
| ~ spl20_126 ),
inference(avatar_split_clause,[],[f1130,f1097,f630,f2319]) ).
fof(f2319,plain,
( spl20_194
<=> sK8 = singleton(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_194])]) ).
fof(f1130,plain,
( sK8 != singleton(sK8)
| ~ spl20_67
| ~ spl20_126 ),
inference(superposition,[],[f631,f1098]) ).
fof(f2317,plain,
( spl20_193
| ~ spl20_69
| ~ spl20_126 ),
inference(avatar_split_clause,[],[f1123,f1097,f638,f2315]) ).
fof(f2315,plain,
( spl20_193
<=> ! [X0] : sP0(X0,sK8,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_193])]) ).
fof(f638,plain,
( spl20_69
<=> ! [X0,X1] : sP0(X1,X0,set_union2(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_69])]) ).
fof(f1123,plain,
( ! [X0] : sP0(X0,sK8,X0)
| ~ spl20_69
| ~ spl20_126 ),
inference(superposition,[],[f639,f1098]) ).
fof(f639,plain,
( ! [X0,X1] : sP0(X1,X0,set_union2(X0,X1))
| ~ spl20_69 ),
inference(avatar_component_clause,[],[f638]) ).
fof(f2313,plain,
( ~ spl20_192
| ~ spl20_1
| ~ spl20_144
| spl20_129
| spl20_40
| ~ spl20_152 ),
inference(avatar_split_clause,[],[f2113,f1358,f470,f1109,f1268,f275,f2310]) ).
fof(f2113,plain,
( sK1 = set_union2(sK2,singleton(sK2))
| ~ ordinal(set_union2(sK2,singleton(sK2)))
| ~ ordinal(sK1)
| ~ empty(sK1)
| spl20_40
| ~ spl20_152 ),
inference(resolution,[],[f472,f1359]) ).
fof(f472,plain,
( ~ in(sK1,set_union2(sK2,singleton(sK2)))
| spl20_40 ),
inference(avatar_component_clause,[],[f470]) ).
fof(f2307,plain,
( spl20_40
| spl20_191
| ~ spl20_82
| ~ spl20_100 ),
inference(avatar_split_clause,[],[f942,f892,f764,f2304,f470]) ).
fof(f2304,plain,
( spl20_191
<=> empty(set_union2(sK2,singleton(sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_191])]) ).
fof(f942,plain,
( empty(set_union2(sK2,singleton(sK2)))
| in(sK1,set_union2(sK2,singleton(sK2)))
| ~ spl20_82
| ~ spl20_100 ),
inference(resolution,[],[f894,f765]) ).
fof(f894,plain,
( element(sK1,set_union2(sK2,singleton(sK2)))
| ~ spl20_100 ),
inference(avatar_component_clause,[],[f892]) ).
fof(f2301,plain,
( spl20_187
| ~ spl20_116
| ~ spl20_146 ),
inference(avatar_split_clause,[],[f1282,f1277,f1018,f2160]) ).
fof(f1282,plain,
( ! [X0] :
( ~ in(X0,sK1)
| element(X0,set_union2(sK2,singleton(sK2))) )
| ~ spl20_116
| ~ spl20_146 ),
inference(resolution,[],[f1278,f1020]) ).
fof(f1020,plain,
( subset(sK1,set_union2(sK2,singleton(sK2)))
| ~ spl20_116 ),
inference(avatar_component_clause,[],[f1018]) ).
fof(f2295,plain,
( ~ spl20_183
| spl20_40
| ~ spl20_142 ),
inference(avatar_split_clause,[],[f2110,f1221,f470,f2104]) ).
fof(f2110,plain,
( ~ in(sK1,sK2)
| spl20_40
| ~ spl20_142 ),
inference(resolution,[],[f472,f1222]) ).
fof(f2286,plain,
( ~ spl20_1
| ~ spl20_2
| spl20_41
| ~ spl20_89
| ~ spl20_102 ),
inference(avatar_split_clause,[],[f2118,f932,f808,f474,f280,f275]) ).
fof(f474,plain,
( spl20_41
<=> ordinal_subset(sK1,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_41])]) ).
fof(f2118,plain,
( ordinal_subset(sK1,sK2)
| ~ ordinal(sK2)
| ~ ordinal(sK1)
| ~ spl20_89
| ~ spl20_102 ),
inference(resolution,[],[f934,f809]) ).
fof(f934,plain,
( subset(sK1,sK2)
| ~ spl20_102 ),
inference(avatar_component_clause,[],[f932]) ).
fof(f2242,plain,
( ~ spl20_189
| spl20_190
| ~ spl20_84
| ~ spl20_102 ),
inference(avatar_split_clause,[],[f2119,f932,f784,f2239,f2235]) ).
fof(f2119,plain,
( sK1 = sK2
| ~ subset(sK2,sK1)
| ~ spl20_84
| ~ spl20_102 ),
inference(resolution,[],[f934,f785]) ).
fof(f2233,plain,
( spl20_186
| ~ spl20_102
| ~ spl20_146 ),
inference(avatar_split_clause,[],[f2116,f1277,f932,f2139]) ).
fof(f2116,plain,
( ! [X0] :
( ~ in(X0,sK1)
| element(X0,sK2) )
| ~ spl20_102
| ~ spl20_146 ),
inference(resolution,[],[f934,f1278]) ).
fof(f2208,plain,
( ~ spl20_188
| spl20_41
| ~ spl20_80
| ~ spl20_182 ),
inference(avatar_split_clause,[],[f2197,f2100,f727,f474,f2190]) ).
fof(f2190,plain,
( spl20_188
<=> ordinal_subset(sK1,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_188])]) ).
fof(f2100,plain,
( spl20_182
<=> in(sK1,singleton(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_182])]) ).
fof(f2197,plain,
( ~ ordinal_subset(sK1,sK1)
| spl20_41
| ~ spl20_80
| ~ spl20_182 ),
inference(forward_demodulation,[],[f476,f2150]) ).
fof(f2150,plain,
( sK1 = sK2
| ~ spl20_80
| ~ spl20_182 ),
inference(resolution,[],[f2102,f728]) ).
fof(f2102,plain,
( in(sK1,singleton(sK2))
| ~ spl20_182 ),
inference(avatar_component_clause,[],[f2100]) ).
fof(f476,plain,
( ~ ordinal_subset(sK1,sK2)
| spl20_41 ),
inference(avatar_component_clause,[],[f474]) ).
fof(f2204,plain,
( ~ spl20_1
| ~ spl20_73
| spl20_188 ),
inference(avatar_split_clause,[],[f2201,f2190,f675,f275]) ).
fof(f675,plain,
( spl20_73
<=> ! [X0] :
( ordinal_subset(X0,X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_73])]) ).
fof(f2201,plain,
( ~ ordinal(sK1)
| ~ spl20_73
| spl20_188 ),
inference(resolution,[],[f2191,f676]) ).
fof(f676,plain,
( ! [X0] :
( ordinal_subset(X0,X0)
| ~ ordinal(X0) )
| ~ spl20_73 ),
inference(avatar_component_clause,[],[f675]) ).
fof(f2191,plain,
( ~ ordinal_subset(sK1,sK1)
| spl20_188 ),
inference(avatar_component_clause,[],[f2190]) ).
fof(f2193,plain,
( spl20_188
| ~ spl20_41
| ~ spl20_80
| ~ spl20_182 ),
inference(avatar_split_clause,[],[f2178,f2100,f727,f474,f2190]) ).
fof(f2178,plain,
( ordinal_subset(sK1,sK1)
| ~ spl20_41
| ~ spl20_80
| ~ spl20_182 ),
inference(forward_demodulation,[],[f475,f2150]) ).
fof(f475,plain,
( ordinal_subset(sK1,sK2)
| ~ spl20_41 ),
inference(avatar_component_clause,[],[f474]) ).
fof(f2162,plain,
( spl20_187
| ~ spl20_116
| ~ spl20_146 ),
inference(avatar_split_clause,[],[f1282,f1277,f1018,f2160]) ).
fof(f2141,plain,
( spl20_186
| ~ spl20_102
| ~ spl20_146 ),
inference(avatar_split_clause,[],[f2116,f1277,f932,f2139]) ).
fof(f2137,plain,
( ~ spl20_184
| spl20_185
| ~ spl20_102
| ~ spl20_140 ),
inference(avatar_split_clause,[],[f2117,f1213,f932,f2135,f2131]) ).
fof(f2117,plain,
( ! [X0] :
( ~ in(X0,sK1)
| ~ empty(sK2) )
| ~ spl20_102
| ~ spl20_140 ),
inference(resolution,[],[f934,f1214]) ).
fof(f2107,plain,
( spl20_182
| spl20_183
| ~ spl20_40
| ~ spl20_150 ),
inference(avatar_split_clause,[],[f1331,f1313,f470,f2104,f2100]) ).
fof(f1331,plain,
( in(sK1,sK2)
| in(sK1,singleton(sK2))
| ~ spl20_40
| ~ spl20_150 ),
inference(resolution,[],[f1314,f471]) ).
fof(f471,plain,
( in(sK1,set_union2(sK2,singleton(sK2)))
| ~ spl20_40 ),
inference(avatar_component_clause,[],[f470]) ).
fof(f2097,plain,
( spl20_181
| ~ spl20_1
| ~ spl20_2
| spl20_102
| ~ spl20_148 ),
inference(avatar_split_clause,[],[f1305,f1289,f932,f280,f275,f2094]) ).
fof(f1305,plain,
( ~ ordinal(sK2)
| ~ ordinal(sK1)
| ordinal_subset(sK2,sK1)
| spl20_102
| ~ spl20_148 ),
inference(resolution,[],[f1290,f933]) ).
fof(f933,plain,
( ~ subset(sK1,sK2)
| spl20_102 ),
inference(avatar_component_clause,[],[f932]) ).
fof(f1960,plain,
( spl20_180
| ~ spl20_95
| ~ spl20_99 ),
inference(avatar_split_clause,[],[f889,f884,f850,f1958]) ).
fof(f1958,plain,
( spl20_180
<=> ! [X2,X0,X1] :
( ~ in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| in(X2,sK6(X0,X1,X2))
| sK6(X0,X1,X2) = X2
| ~ ordinal(X2)
| ~ ordinal(sK6(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_180])]) ).
fof(f889,plain,
( ! [X2,X0,X1] :
( ~ in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| in(X2,sK6(X0,X1,X2))
| sK6(X0,X1,X2) = X2
| ~ ordinal(X2)
| ~ ordinal(sK6(X0,X1,X2)) )
| ~ spl20_95
| ~ spl20_99 ),
inference(resolution,[],[f885,f851]) ).
fof(f1956,plain,
( spl20_179
| ~ spl20_95
| ~ spl20_98 ),
inference(avatar_split_clause,[],[f887,f880,f850,f1954]) ).
fof(f1954,plain,
( spl20_179
<=> ! [X2,X0,X1] :
( ~ in(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| in(X2,sK6(X0,X1,X2))
| sK6(X0,X1,X2) = X2
| ~ ordinal(X2)
| ~ ordinal(sK6(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_179])]) ).
fof(f887,plain,
( ! [X2,X0,X1] :
( ~ in(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| in(X2,sK6(X0,X1,X2))
| sK6(X0,X1,X2) = X2
| ~ ordinal(X2)
| ~ ordinal(sK6(X0,X1,X2)) )
| ~ spl20_95
| ~ spl20_98 ),
inference(resolution,[],[f881,f851]) ).
fof(f1881,plain,
( spl20_178
| ~ spl20_80
| ~ spl20_101 ),
inference(avatar_split_clause,[],[f923,f900,f727,f1879]) ).
fof(f923,plain,
( ! [X2,X0,X1] :
( in(sK6(singleton(X0),X1,X2),X2)
| in(sK6(singleton(X0),X1,X2),X1)
| sP0(singleton(X0),X1,X2)
| sK6(singleton(X0),X1,X2) = X0 )
| ~ spl20_80
| ~ spl20_101 ),
inference(resolution,[],[f901,f728]) ).
fof(f1876,plain,
( spl20_177
| ~ spl20_80
| ~ spl20_101 ),
inference(avatar_split_clause,[],[f916,f900,f727,f1874]) ).
fof(f916,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,singleton(X1),X2),X2)
| in(sK6(X0,singleton(X1),X2),X0)
| sP0(X0,singleton(X1),X2)
| sK6(X0,singleton(X1),X2) = X1 )
| ~ spl20_80
| ~ spl20_101 ),
inference(resolution,[],[f901,f728]) ).
fof(f1872,plain,
( spl20_176
| ~ spl20_80
| ~ spl20_101 ),
inference(avatar_split_clause,[],[f909,f900,f727,f1870]) ).
fof(f909,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,singleton(X2)),X1)
| in(sK6(X0,X1,singleton(X2)),X0)
| sP0(X0,X1,singleton(X2))
| sK6(X0,X1,singleton(X2)) = X2 )
| ~ spl20_80
| ~ spl20_101 ),
inference(resolution,[],[f901,f728]) ).
fof(f1785,plain,
( spl20_175
| ~ spl20_81
| ~ spl20_101 ),
inference(avatar_split_clause,[],[f919,f900,f760,f1783]) ).
fof(f919,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| subset(sK6(X0,X1,X2),X0)
| ~ epsilon_transitive(X0) )
| ~ spl20_81
| ~ spl20_101 ),
inference(resolution,[],[f901,f761]) ).
fof(f1781,plain,
( spl20_174
| ~ spl20_81
| ~ spl20_101 ),
inference(avatar_split_clause,[],[f912,f900,f760,f1779]) ).
fof(f912,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| subset(sK6(X0,X1,X2),X1)
| ~ epsilon_transitive(X1) )
| ~ spl20_81
| ~ spl20_101 ),
inference(resolution,[],[f901,f761]) ).
fof(f1777,plain,
( spl20_173
| ~ spl20_81
| ~ spl20_101 ),
inference(avatar_split_clause,[],[f905,f900,f760,f1775]) ).
fof(f905,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X1)
| in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| subset(sK6(X0,X1,X2),X2)
| ~ epsilon_transitive(X2) )
| ~ spl20_81
| ~ spl20_101 ),
inference(resolution,[],[f901,f761]) ).
fof(f1671,plain,
( spl20_172
| ~ spl20_64
| ~ spl20_101 ),
inference(avatar_split_clause,[],[f921,f900,f617,f1669]) ).
fof(f1669,plain,
( spl20_172
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ in(X0,sK6(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_172])]) ).
fof(f921,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ in(X0,sK6(X0,X1,X2)) )
| ~ spl20_64
| ~ spl20_101 ),
inference(resolution,[],[f901,f618]) ).
fof(f1667,plain,
( spl20_171
| ~ spl20_65
| ~ spl20_101 ),
inference(avatar_split_clause,[],[f920,f900,f621,f1665]) ).
fof(f920,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| element(sK6(X0,X1,X2),X0) )
| ~ spl20_65
| ~ spl20_101 ),
inference(resolution,[],[f901,f622]) ).
fof(f1663,plain,
( spl20_170
| ~ spl20_64
| ~ spl20_101 ),
inference(avatar_split_clause,[],[f914,f900,f617,f1661]) ).
fof(f1661,plain,
( spl20_170
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ in(X1,sK6(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_170])]) ).
fof(f914,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ in(X1,sK6(X0,X1,X2)) )
| ~ spl20_64
| ~ spl20_101 ),
inference(resolution,[],[f901,f618]) ).
fof(f1659,plain,
( spl20_169
| ~ spl20_65
| ~ spl20_101 ),
inference(avatar_split_clause,[],[f913,f900,f621,f1657]) ).
fof(f913,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| element(sK6(X0,X1,X2),X1) )
| ~ spl20_65
| ~ spl20_101 ),
inference(resolution,[],[f901,f622]) ).
fof(f1655,plain,
( spl20_168
| ~ spl20_64
| ~ spl20_101 ),
inference(avatar_split_clause,[],[f907,f900,f617,f1653]) ).
fof(f1653,plain,
( spl20_168
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X1)
| in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ in(X2,sK6(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_168])]) ).
fof(f907,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X1)
| in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ in(X2,sK6(X0,X1,X2)) )
| ~ spl20_64
| ~ spl20_101 ),
inference(resolution,[],[f901,f618]) ).
fof(f1651,plain,
( spl20_167
| ~ spl20_65
| ~ spl20_101 ),
inference(avatar_split_clause,[],[f906,f900,f621,f1649]) ).
fof(f906,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X1)
| in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| element(sK6(X0,X1,X2),X2) )
| ~ spl20_65
| ~ spl20_101 ),
inference(resolution,[],[f901,f622]) ).
fof(f1647,plain,
( spl20_166
| ~ spl20_44
| ~ spl20_144 ),
inference(avatar_split_clause,[],[f1487,f1268,f488,f1644]) ).
fof(f1644,plain,
( spl20_166
<=> epsilon_connected(set_union2(sK2,singleton(sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_166])]) ).
fof(f488,plain,
( spl20_44
<=> ! [X0] :
( epsilon_connected(X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_44])]) ).
fof(f1487,plain,
( epsilon_connected(set_union2(sK2,singleton(sK2)))
| ~ spl20_44
| ~ spl20_144 ),
inference(resolution,[],[f1269,f489]) ).
fof(f489,plain,
( ! [X0] :
( ~ ordinal(X0)
| epsilon_connected(X0) )
| ~ spl20_44 ),
inference(avatar_component_clause,[],[f488]) ).
fof(f1269,plain,
( ordinal(set_union2(sK2,singleton(sK2)))
| ~ spl20_144 ),
inference(avatar_component_clause,[],[f1268]) ).
fof(f1571,plain,
( spl20_165
| ~ spl20_56
| ~ spl20_101 ),
inference(avatar_split_clause,[],[f922,f900,f574,f1569]) ).
fof(f922,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ empty(X0) )
| ~ spl20_56
| ~ spl20_101 ),
inference(resolution,[],[f901,f575]) ).
fof(f1567,plain,
( spl20_164
| ~ spl20_56
| ~ spl20_101 ),
inference(avatar_split_clause,[],[f915,f900,f574,f1565]) ).
fof(f915,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X2)
| in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ empty(X1) )
| ~ spl20_56
| ~ spl20_101 ),
inference(resolution,[],[f901,f575]) ).
fof(f1563,plain,
( spl20_163
| ~ spl20_56
| ~ spl20_101 ),
inference(avatar_split_clause,[],[f908,f900,f574,f1561]) ).
fof(f908,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X1)
| in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ empty(X2) )
| ~ spl20_56
| ~ spl20_101 ),
inference(resolution,[],[f901,f575]) ).
fof(f1538,plain,
( spl20_162
| ~ spl20_80
| ~ spl20_97 ),
inference(avatar_split_clause,[],[f878,f871,f727,f1536]) ).
fof(f878,plain,
( ! [X0,X1] :
( sK5(X0,singleton(X1)) = X0
| singleton(X0) = singleton(X1)
| sK5(X0,singleton(X1)) = X1 )
| ~ spl20_80
| ~ spl20_97 ),
inference(resolution,[],[f872,f728]) ).
fof(f1448,plain,
( spl20_161
| ~ spl20_101 ),
inference(avatar_split_clause,[],[f926,f900,f1446]) ).
fof(f926,plain,
( ! [X4,X5] :
( in(sK6(X4,X4,X5),X5)
| in(sK6(X4,X4,X5),X4)
| sP0(X4,X4,X5) )
| ~ spl20_101 ),
inference(factoring,[],[f901]) ).
fof(f1444,plain,
( spl20_160
| ~ spl20_101 ),
inference(avatar_split_clause,[],[f925,f900,f1442]) ).
fof(f925,plain,
( ! [X2,X3] :
( in(sK6(X2,X3,X2),X2)
| in(sK6(X2,X3,X2),X3)
| sP0(X2,X3,X2) )
| ~ spl20_101 ),
inference(factoring,[],[f901]) ).
fof(f1440,plain,
( spl20_159
| ~ spl20_101 ),
inference(avatar_split_clause,[],[f924,f900,f1438]) ).
fof(f924,plain,
( ! [X0,X1] :
( in(sK6(X0,X1,X1),X1)
| in(sK6(X0,X1,X1),X0)
| sP0(X0,X1,X1) )
| ~ spl20_101 ),
inference(factoring,[],[f901]) ).
fof(f1436,plain,
( spl20_158
| ~ spl20_81
| ~ spl20_97 ),
inference(avatar_split_clause,[],[f874,f871,f760,f1434]) ).
fof(f874,plain,
( ! [X0,X1] :
( sK5(X0,X1) = X0
| singleton(X0) = X1
| subset(sK5(X0,X1),X1)
| ~ epsilon_transitive(X1) )
| ~ spl20_81
| ~ spl20_97 ),
inference(resolution,[],[f872,f761]) ).
fof(f1432,plain,
( spl20_157
| ~ spl20_80
| ~ spl20_95 ),
inference(avatar_split_clause,[],[f861,f850,f727,f1430]) ).
fof(f861,plain,
( ! [X0,X1] :
( in(singleton(X1),X0)
| singleton(X1) = X0
| ~ ordinal(X0)
| ~ ordinal(singleton(X1))
| X0 = X1 )
| ~ spl20_80
| ~ spl20_95 ),
inference(resolution,[],[f851,f728]) ).
fof(f1413,plain,
( spl20_156
| ~ spl20_81
| ~ spl20_95 ),
inference(avatar_split_clause,[],[f857,f850,f760,f1411]) ).
fof(f857,plain,
( ! [X0,X1] :
( in(X1,X0)
| X0 = X1
| ~ ordinal(X0)
| ~ ordinal(X1)
| subset(X0,X1)
| ~ epsilon_transitive(X1) )
| ~ spl20_81
| ~ spl20_95 ),
inference(resolution,[],[f851,f761]) ).
fof(f1409,plain,
( ~ spl20_2
| ~ spl20_77
| spl20_144 ),
inference(avatar_split_clause,[],[f1325,f1268,f715,f280]) ).
fof(f1325,plain,
( ~ ordinal(sK2)
| ~ spl20_77
| spl20_144 ),
inference(resolution,[],[f1270,f716]) ).
fof(f1270,plain,
( ~ ordinal(set_union2(sK2,singleton(sK2)))
| spl20_144 ),
inference(avatar_component_clause,[],[f1268]) ).
fof(f1400,plain,
( spl20_155
| ~ spl20_64
| ~ spl20_97 ),
inference(avatar_split_clause,[],[f876,f871,f617,f1398]) ).
fof(f1398,plain,
( spl20_155
<=> ! [X0,X1] :
( sK5(X0,X1) = X0
| singleton(X0) = X1
| ~ in(X1,sK5(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_155])]) ).
fof(f876,plain,
( ! [X0,X1] :
( sK5(X0,X1) = X0
| singleton(X0) = X1
| ~ in(X1,sK5(X0,X1)) )
| ~ spl20_64
| ~ spl20_97 ),
inference(resolution,[],[f872,f618]) ).
fof(f1396,plain,
( spl20_154
| ~ spl20_65
| ~ spl20_97 ),
inference(avatar_split_clause,[],[f875,f871,f621,f1394]) ).
fof(f875,plain,
( ! [X0,X1] :
( sK5(X0,X1) = X0
| singleton(X0) = X1
| element(sK5(X0,X1),X1) )
| ~ spl20_65
| ~ spl20_97 ),
inference(resolution,[],[f872,f622]) ).
fof(f1378,plain,
( spl20_153
| ~ spl20_65
| ~ spl20_95 ),
inference(avatar_split_clause,[],[f858,f850,f621,f1376]) ).
fof(f858,plain,
( ! [X0,X1] :
( in(X1,X0)
| X0 = X1
| ~ ordinal(X0)
| ~ ordinal(X1)
| element(X0,X1) )
| ~ spl20_65
| ~ spl20_95 ),
inference(resolution,[],[f851,f622]) ).
fof(f1360,plain,
( spl20_152
| ~ spl20_56
| ~ spl20_95 ),
inference(avatar_split_clause,[],[f860,f850,f574,f1358]) ).
fof(f860,plain,
( ! [X0,X1] :
( in(X1,X0)
| X0 = X1
| ~ ordinal(X0)
| ~ ordinal(X1)
| ~ empty(X1) )
| ~ spl20_56
| ~ spl20_95 ),
inference(resolution,[],[f851,f575]) ).
fof(f1319,plain,
( spl20_151
| ~ spl20_56
| ~ spl20_97 ),
inference(avatar_split_clause,[],[f877,f871,f574,f1317]) ).
fof(f877,plain,
( ! [X0,X1] :
( sK5(X0,X1) = X0
| singleton(X0) = X1
| ~ empty(X1) )
| ~ spl20_56
| ~ spl20_97 ),
inference(resolution,[],[f872,f575]) ).
fof(f1315,plain,
( spl20_150
| ~ spl20_69
| ~ spl20_96 ),
inference(avatar_split_clause,[],[f869,f854,f638,f1313]) ).
fof(f854,plain,
( spl20_96
<=> ! [X2,X4,X0,X1] :
( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_96])]) ).
fof(f869,plain,
( ! [X2,X0,X1] :
( in(X0,X1)
| ~ in(X0,set_union2(X1,X2))
| in(X0,X2) )
| ~ spl20_69
| ~ spl20_96 ),
inference(resolution,[],[f855,f639]) ).
fof(f855,plain,
( ! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| in(X4,X1)
| ~ in(X4,X2)
| in(X4,X0) )
| ~ spl20_96 ),
inference(avatar_component_clause,[],[f854]) ).
fof(f1311,plain,
( spl20_149
| ~ spl20_68
| ~ spl20_81 ),
inference(avatar_split_clause,[],[f773,f760,f634,f1309]) ).
fof(f773,plain,
( ! [X0] :
( subset(X0,set_union2(X0,singleton(X0)))
| ~ epsilon_transitive(set_union2(X0,singleton(X0))) )
| ~ spl20_68
| ~ spl20_81 ),
inference(resolution,[],[f761,f635]) ).
fof(f1291,plain,
( spl20_148
| ~ spl20_87
| ~ spl20_88 ),
inference(avatar_split_clause,[],[f832,f804,f800,f1289]) ).
fof(f800,plain,
( spl20_87
<=> ! [X0,X1] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_87])]) ).
fof(f832,plain,
( ! [X0,X1] :
( subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0)
| ordinal_subset(X1,X0) )
| ~ spl20_87
| ~ spl20_88 ),
inference(duplicate_literal_removal,[],[f829]) ).
fof(f829,plain,
( ! [X0,X1] :
( subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0)
| ordinal_subset(X1,X0)
| ~ ordinal(X1)
| ~ ordinal(X0) )
| ~ spl20_87
| ~ spl20_88 ),
inference(resolution,[],[f805,f801]) ).
fof(f801,plain,
( ! [X0,X1] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) )
| ~ spl20_87 ),
inference(avatar_component_clause,[],[f800]) ).
fof(f1287,plain,
( spl20_147
| ~ spl20_75
| ~ spl20_82 ),
inference(avatar_split_clause,[],[f776,f764,f707,f1285]) ).
fof(f707,plain,
( spl20_75
<=> ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_75])]) ).
fof(f776,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| in(X1,powerset(X0))
| ~ subset(X1,X0) )
| ~ spl20_75
| ~ spl20_82 ),
inference(resolution,[],[f765,f708]) ).
fof(f708,plain,
( ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) )
| ~ spl20_75 ),
inference(avatar_component_clause,[],[f707]) ).
fof(f1279,plain,
( spl20_146
| ~ spl20_75
| ~ spl20_90 ),
inference(avatar_split_clause,[],[f837,f812,f707,f1277]) ).
fof(f837,plain,
( ! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,X1) )
| ~ spl20_75
| ~ spl20_90 ),
inference(resolution,[],[f813,f708]) ).
fof(f1275,plain,
( ~ spl20_1
| ~ spl20_144
| spl20_145
| ~ spl20_89
| ~ spl20_116 ),
inference(avatar_split_clause,[],[f1029,f1018,f808,f1272,f1268,f275]) ).
fof(f1272,plain,
( spl20_145
<=> ordinal_subset(sK1,set_union2(sK2,singleton(sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_145])]) ).
fof(f1029,plain,
( ordinal_subset(sK1,set_union2(sK2,singleton(sK2)))
| ~ ordinal(set_union2(sK2,singleton(sK2)))
| ~ ordinal(sK1)
| ~ spl20_89
| ~ spl20_116 ),
inference(resolution,[],[f1020,f809]) ).
fof(f1227,plain,
( spl20_143
| ~ spl20_69
| ~ spl20_92 ),
inference(avatar_split_clause,[],[f839,f821,f638,f1225]) ).
fof(f839,plain,
( ! [X2,X0,X1] :
( ~ in(X0,X1)
| in(X0,set_union2(X2,X1)) )
| ~ spl20_69
| ~ spl20_92 ),
inference(resolution,[],[f822,f639]) ).
fof(f1223,plain,
( spl20_142
| ~ spl20_69
| ~ spl20_91 ),
inference(avatar_split_clause,[],[f838,f817,f638,f1221]) ).
fof(f817,plain,
( spl20_91
<=> ! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_91])]) ).
fof(f838,plain,
( ! [X2,X0,X1] :
( ~ in(X0,X1)
| in(X0,set_union2(X1,X2)) )
| ~ spl20_69
| ~ spl20_91 ),
inference(resolution,[],[f818,f639]) ).
fof(f818,plain,
( ! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| ~ in(X4,X1)
| in(X4,X2) )
| ~ spl20_91 ),
inference(avatar_component_clause,[],[f817]) ).
fof(f1219,plain,
( spl20_141
| ~ spl20_50
| ~ spl20_90 ),
inference(avatar_split_clause,[],[f836,f812,f512,f1217]) ).
fof(f512,plain,
( spl20_50
<=> ! [X0] : element(sK4(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_50])]) ).
fof(f836,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK4(powerset(X1))) )
| ~ spl20_50
| ~ spl20_90 ),
inference(resolution,[],[f813,f513]) ).
fof(f513,plain,
( ! [X0] : element(sK4(X0),X0)
| ~ spl20_50 ),
inference(avatar_component_clause,[],[f512]) ).
fof(f1215,plain,
( spl20_140
| ~ spl20_75
| ~ spl20_86 ),
inference(avatar_split_clause,[],[f798,f792,f707,f1213]) ).
fof(f798,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,X2)
| ~ subset(X2,X0) )
| ~ spl20_75
| ~ spl20_86 ),
inference(resolution,[],[f793,f708]) ).
fof(f1211,plain,
( spl20_139
| ~ spl20_60
| ~ spl20_80 ),
inference(avatar_split_clause,[],[f758,f727,f601,f1209]) ).
fof(f1209,plain,
( spl20_139
<=> ! [X0] :
( sK3(singleton(X0)) = X0
| epsilon_transitive(singleton(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_139])]) ).
fof(f758,plain,
( ! [X0] :
( sK3(singleton(X0)) = X0
| epsilon_transitive(singleton(X0)) )
| ~ spl20_60
| ~ spl20_80 ),
inference(resolution,[],[f728,f602]) ).
fof(f1197,plain,
( spl20_138
| ~ spl20_50
| ~ spl20_86 ),
inference(avatar_split_clause,[],[f797,f792,f512,f1195]) ).
fof(f797,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK4(powerset(X0))) )
| ~ spl20_50
| ~ spl20_86 ),
inference(resolution,[],[f793,f513]) ).
fof(f1193,plain,
( spl20_137
| ~ spl20_51
| ~ spl20_81 ),
inference(avatar_split_clause,[],[f772,f760,f516,f1191]) ).
fof(f516,plain,
( spl20_51
<=> ! [X3] : in(X3,singleton(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_51])]) ).
fof(f772,plain,
( ! [X0] :
( subset(X0,singleton(X0))
| ~ epsilon_transitive(singleton(X0)) )
| ~ spl20_51
| ~ spl20_81 ),
inference(resolution,[],[f761,f517]) ).
fof(f517,plain,
( ! [X3] : in(X3,singleton(X3))
| ~ spl20_51 ),
inference(avatar_component_clause,[],[f516]) ).
fof(f1163,plain,
( spl20_136
| ~ spl20_50
| ~ spl20_82 ),
inference(avatar_split_clause,[],[f775,f764,f512,f1161]) ).
fof(f775,plain,
( ! [X0] :
( empty(X0)
| in(sK4(X0),X0) )
| ~ spl20_50
| ~ spl20_82 ),
inference(resolution,[],[f765,f513]) ).
fof(f1159,plain,
( spl20_135
| ~ spl20_69
| ~ spl20_71 ),
inference(avatar_split_clause,[],[f732,f668,f638,f1157]) ).
fof(f1157,plain,
( spl20_135
<=> ! [X0,X1] : sP0(X1,X0,set_union2(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_135])]) ).
fof(f668,plain,
( spl20_71
<=> ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_71])]) ).
fof(f732,plain,
( ! [X0,X1] : sP0(X1,X0,set_union2(X1,X0))
| ~ spl20_69
| ~ spl20_71 ),
inference(superposition,[],[f639,f669]) ).
fof(f669,plain,
( ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0)
| ~ spl20_71 ),
inference(avatar_component_clause,[],[f668]) ).
fof(f1155,plain,
( spl20_134
| ~ spl20_64
| ~ spl20_68 ),
inference(avatar_split_clause,[],[f662,f634,f617,f1153]) ).
fof(f662,plain,
( ! [X0] : ~ in(set_union2(X0,singleton(X0)),X0)
| ~ spl20_64
| ~ spl20_68 ),
inference(resolution,[],[f635,f618]) ).
fof(f1151,plain,
( spl20_133
| ~ spl20_65
| ~ spl20_68 ),
inference(avatar_split_clause,[],[f661,f634,f621,f1149]) ).
fof(f661,plain,
( ! [X0] : element(X0,set_union2(X0,singleton(X0)))
| ~ spl20_65
| ~ spl20_68 ),
inference(resolution,[],[f635,f622]) ).
fof(f1147,plain,
( spl20_132
| ~ spl20_60
| ~ spl20_65 ),
inference(avatar_split_clause,[],[f655,f621,f601,f1145]) ).
fof(f655,plain,
( ! [X0] :
( element(sK3(X0),X0)
| epsilon_transitive(X0) )
| ~ spl20_60
| ~ spl20_65 ),
inference(resolution,[],[f622,f602]) ).
fof(f1143,plain,
( spl20_131
| ~ spl20_60
| ~ spl20_64 ),
inference(avatar_split_clause,[],[f652,f617,f601,f1141]) ).
fof(f1141,plain,
( spl20_131
<=> ! [X0] :
( ~ in(X0,sK3(X0))
| epsilon_transitive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_131])]) ).
fof(f652,plain,
( ! [X0] :
( ~ in(X0,sK3(X0))
| epsilon_transitive(X0) )
| ~ spl20_60
| ~ spl20_64 ),
inference(resolution,[],[f618,f602]) ).
fof(f1116,plain,
( spl20_130
| ~ spl20_10
| ~ spl20_76 ),
inference(avatar_split_clause,[],[f747,f711,f320,f1114]) ).
fof(f1114,plain,
( spl20_130
<=> ! [X0] :
( sK8 = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_130])]) ).
fof(f711,plain,
( spl20_76
<=> ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_76])]) ).
fof(f747,plain,
( ! [X0] :
( sK8 = X0
| ~ empty(X0) )
| ~ spl20_10
| ~ spl20_76 ),
inference(resolution,[],[f712,f322]) ).
fof(f322,plain,
( empty(sK8)
| ~ spl20_10 ),
inference(avatar_component_clause,[],[f320]) ).
fof(f712,plain,
( ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) )
| ~ spl20_76 ),
inference(avatar_component_clause,[],[f711]) ).
fof(f1112,plain,
( ~ spl20_128
| spl20_129
| ~ spl20_84
| ~ spl20_116 ),
inference(avatar_split_clause,[],[f1030,f1018,f784,f1109,f1105]) ).
fof(f1030,plain,
( sK1 = set_union2(sK2,singleton(sK2))
| ~ subset(set_union2(sK2,singleton(sK2)),sK1)
| ~ spl20_84
| ~ spl20_116 ),
inference(resolution,[],[f1020,f785]) ).
fof(f1103,plain,
( spl20_127
| ~ spl20_50
| ~ spl20_74 ),
inference(avatar_split_clause,[],[f744,f703,f512,f1101]) ).
fof(f744,plain,
( ! [X0] : subset(sK4(powerset(X0)),X0)
| ~ spl20_50
| ~ spl20_74 ),
inference(resolution,[],[f704,f513]) ).
fof(f1099,plain,
( spl20_126
| ~ spl20_10
| ~ spl20_53
| ~ spl20_54
| ~ spl20_71 ),
inference(avatar_split_clause,[],[f740,f668,f566,f562,f320,f1097]) ).
fof(f740,plain,
( ! [X0] : set_union2(sK8,X0) = X0
| ~ spl20_10
| ~ spl20_53
| ~ spl20_54
| ~ spl20_71 ),
inference(forward_demodulation,[],[f730,f582]) ).
fof(f582,plain,
( empty_set = sK8
| ~ spl20_10
| ~ spl20_54 ),
inference(resolution,[],[f567,f322]) ).
fof(f730,plain,
( ! [X0] : set_union2(empty_set,X0) = X0
| ~ spl20_53
| ~ spl20_71 ),
inference(superposition,[],[f669,f563]) ).
fof(f1083,plain,
( spl20_125
| ~ spl20_10
| ~ spl20_53
| ~ spl20_54
| ~ spl20_69 ),
inference(avatar_split_clause,[],[f666,f638,f566,f562,f320,f1081]) ).
fof(f666,plain,
( ! [X0] : sP0(sK8,X0,X0)
| ~ spl20_10
| ~ spl20_53
| ~ spl20_54
| ~ spl20_69 ),
inference(forward_demodulation,[],[f664,f582]) ).
fof(f664,plain,
( ! [X0] : sP0(empty_set,X0,X0)
| ~ spl20_53
| ~ spl20_69 ),
inference(superposition,[],[f639,f563]) ).
fof(f1079,plain,
( spl20_124
| ~ spl20_55
| ~ spl20_69 ),
inference(avatar_split_clause,[],[f665,f638,f570,f1077]) ).
fof(f1077,plain,
( spl20_124
<=> ! [X0] : sP0(X0,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_124])]) ).
fof(f570,plain,
( spl20_55
<=> ! [X0] : set_union2(X0,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl20_55])]) ).
fof(f665,plain,
( ! [X0] : sP0(X0,X0,X0)
| ~ spl20_55
| ~ spl20_69 ),
inference(superposition,[],[f639,f571]) ).
fof(f571,plain,
( ! [X0] : set_union2(X0,X0) = X0
| ~ spl20_55 ),
inference(avatar_component_clause,[],[f570]) ).
fof(f1075,plain,
( spl20_123
| ~ spl20_51
| ~ spl20_65 ),
inference(avatar_split_clause,[],[f654,f621,f516,f1073]) ).
fof(f1073,plain,
( spl20_123
<=> ! [X0] : element(X0,singleton(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_123])]) ).
fof(f654,plain,
( ! [X0] : element(X0,singleton(X0))
| ~ spl20_51
| ~ spl20_65 ),
inference(resolution,[],[f622,f517]) ).
fof(f1071,plain,
( spl20_122
| ~ spl20_51
| ~ spl20_64 ),
inference(avatar_split_clause,[],[f651,f617,f516,f1069]) ).
fof(f651,plain,
( ! [X0] : ~ in(singleton(X0),X0)
| ~ spl20_51
| ~ spl20_64 ),
inference(resolution,[],[f618,f517]) ).
fof(f1049,plain,
( spl20_121
| ~ spl20_51
| ~ spl20_56 ),
inference(avatar_split_clause,[],[f595,f574,f516,f1047]) ).
fof(f1047,plain,
( spl20_121
<=> ! [X0] : ~ empty(singleton(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_121])]) ).
fof(f595,plain,
( ! [X0] : ~ empty(singleton(X0))
| ~ spl20_51
| ~ spl20_56 ),
inference(resolution,[],[f575,f517]) ).
fof(f1045,plain,
( spl20_120
| ~ spl20_10
| ~ spl20_38
| ~ spl20_54 ),
inference(avatar_split_clause,[],[f588,f566,f460,f320,f1042]) ).
fof(f1042,plain,
( spl20_120
<=> sK8 = sK19 ),
introduced(avatar_definition,[new_symbols(naming,[spl20_120])]) ).
fof(f460,plain,
( spl20_38
<=> empty(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_38])]) ).
fof(f588,plain,
( sK8 = sK19
| ~ spl20_10
| ~ spl20_38
| ~ spl20_54 ),
inference(forward_demodulation,[],[f585,f582]) ).
fof(f585,plain,
( empty_set = sK19
| ~ spl20_38
| ~ spl20_54 ),
inference(resolution,[],[f567,f462]) ).
fof(f462,plain,
( empty(sK19)
| ~ spl20_38 ),
inference(avatar_component_clause,[],[f460]) ).
fof(f1040,plain,
( spl20_119
| ~ spl20_10
| ~ spl20_33
| ~ spl20_54 ),
inference(avatar_split_clause,[],[f587,f566,f435,f320,f1037]) ).
fof(f1037,plain,
( spl20_119
<=> sK8 = sK18 ),
introduced(avatar_definition,[new_symbols(naming,[spl20_119])]) ).
fof(f435,plain,
( spl20_33
<=> empty(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_33])]) ).
fof(f587,plain,
( sK8 = sK18
| ~ spl20_10
| ~ spl20_33
| ~ spl20_54 ),
inference(forward_demodulation,[],[f584,f582]) ).
fof(f584,plain,
( empty_set = sK18
| ~ spl20_33
| ~ spl20_54 ),
inference(resolution,[],[f567,f437]) ).
fof(f437,plain,
( empty(sK18)
| ~ spl20_33 ),
inference(avatar_component_clause,[],[f435]) ).
fof(f1035,plain,
( spl20_118
| ~ spl20_10
| ~ spl20_20
| ~ spl20_54 ),
inference(avatar_split_clause,[],[f586,f566,f370,f320,f1032]) ).
fof(f1032,plain,
( spl20_118
<=> sK8 = sK12 ),
introduced(avatar_definition,[new_symbols(naming,[spl20_118])]) ).
fof(f370,plain,
( spl20_20
<=> empty(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_20])]) ).
fof(f586,plain,
( sK8 = sK12
| ~ spl20_10
| ~ spl20_20
| ~ spl20_54 ),
inference(forward_demodulation,[],[f583,f582]) ).
fof(f583,plain,
( empty_set = sK12
| ~ spl20_20
| ~ spl20_54 ),
inference(resolution,[],[f567,f372]) ).
fof(f372,plain,
( empty(sK12)
| ~ spl20_20 ),
inference(avatar_component_clause,[],[f370]) ).
fof(f1028,plain,
( ~ spl20_2
| ~ spl20_79
| spl20_115 ),
inference(avatar_split_clause,[],[f1022,f1014,f723,f280]) ).
fof(f1014,plain,
( spl20_115
<=> epsilon_transitive(set_union2(sK2,singleton(sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_115])]) ).
fof(f1022,plain,
( ~ ordinal(sK2)
| ~ spl20_79
| spl20_115 ),
inference(resolution,[],[f1016,f724]) ).
fof(f1016,plain,
( ~ epsilon_transitive(set_union2(sK2,singleton(sK2)))
| spl20_115 ),
inference(avatar_component_clause,[],[f1014]) ).
fof(f1027,plain,
( spl20_117
| ~ spl20_10
| ~ spl20_54 ),
inference(avatar_split_clause,[],[f582,f566,f320,f1024]) ).
fof(f1021,plain,
( ~ spl20_115
| spl20_116
| ~ spl20_40
| ~ spl20_81 ),
inference(avatar_split_clause,[],[f771,f760,f470,f1018,f1014]) ).
fof(f771,plain,
( subset(sK1,set_union2(sK2,singleton(sK2)))
| ~ epsilon_transitive(set_union2(sK2,singleton(sK2)))
| ~ spl20_40
| ~ spl20_81 ),
inference(resolution,[],[f761,f471]) ).
fof(f1008,plain,
( spl20_114
| ~ spl20_38
| ~ spl20_49 ),
inference(avatar_split_clause,[],[f560,f508,f460,f1005]) ).
fof(f1005,plain,
( spl20_114
<=> ordinal(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_114])]) ).
fof(f508,plain,
( spl20_49
<=> ! [X0] :
( ordinal(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_49])]) ).
fof(f560,plain,
( ordinal(sK19)
| ~ spl20_38
| ~ spl20_49 ),
inference(resolution,[],[f509,f462]) ).
fof(f509,plain,
( ! [X0] :
( ~ empty(X0)
| ordinal(X0) )
| ~ spl20_49 ),
inference(avatar_component_clause,[],[f508]) ).
fof(f1002,plain,
( spl20_113
| ~ spl20_20
| ~ spl20_49 ),
inference(avatar_split_clause,[],[f558,f508,f370,f999]) ).
fof(f999,plain,
( spl20_113
<=> ordinal(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_113])]) ).
fof(f558,plain,
( ordinal(sK12)
| ~ spl20_20
| ~ spl20_49 ),
inference(resolution,[],[f509,f372]) ).
fof(f997,plain,
( spl20_112
| ~ spl20_10
| ~ spl20_49 ),
inference(avatar_split_clause,[],[f557,f508,f320,f994]) ).
fof(f557,plain,
( ordinal(sK8)
| ~ spl20_10
| ~ spl20_49 ),
inference(resolution,[],[f509,f322]) ).
fof(f991,plain,
( spl20_111
| ~ spl20_38
| ~ spl20_48 ),
inference(avatar_split_clause,[],[f550,f504,f460,f988]) ).
fof(f988,plain,
( spl20_111
<=> epsilon_connected(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_111])]) ).
fof(f504,plain,
( spl20_48
<=> ! [X0] :
( epsilon_connected(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_48])]) ).
fof(f550,plain,
( epsilon_connected(sK19)
| ~ spl20_38
| ~ spl20_48 ),
inference(resolution,[],[f505,f462]) ).
fof(f505,plain,
( ! [X0] :
( ~ empty(X0)
| epsilon_connected(X0) )
| ~ spl20_48 ),
inference(avatar_component_clause,[],[f504]) ).
fof(f985,plain,
( spl20_110
| ~ spl20_20
| ~ spl20_48 ),
inference(avatar_split_clause,[],[f548,f504,f370,f982]) ).
fof(f982,plain,
( spl20_110
<=> epsilon_connected(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_110])]) ).
fof(f548,plain,
( epsilon_connected(sK12)
| ~ spl20_20
| ~ spl20_48 ),
inference(resolution,[],[f505,f372]) ).
fof(f980,plain,
( spl20_109
| ~ spl20_10
| ~ spl20_48 ),
inference(avatar_split_clause,[],[f547,f504,f320,f977]) ).
fof(f977,plain,
( spl20_109
<=> epsilon_connected(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_109])]) ).
fof(f547,plain,
( epsilon_connected(sK8)
| ~ spl20_10
| ~ spl20_48 ),
inference(resolution,[],[f505,f322]) ).
fof(f974,plain,
( spl20_108
| ~ spl20_38
| ~ spl20_47 ),
inference(avatar_split_clause,[],[f545,f500,f460,f971]) ).
fof(f971,plain,
( spl20_108
<=> epsilon_transitive(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_108])]) ).
fof(f500,plain,
( spl20_47
<=> ! [X0] :
( epsilon_transitive(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_47])]) ).
fof(f545,plain,
( epsilon_transitive(sK19)
| ~ spl20_38
| ~ spl20_47 ),
inference(resolution,[],[f501,f462]) ).
fof(f501,plain,
( ! [X0] :
( ~ empty(X0)
| epsilon_transitive(X0) )
| ~ spl20_47 ),
inference(avatar_component_clause,[],[f500]) ).
fof(f968,plain,
( spl20_107
| ~ spl20_20
| ~ spl20_47 ),
inference(avatar_split_clause,[],[f543,f500,f370,f965]) ).
fof(f965,plain,
( spl20_107
<=> epsilon_transitive(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_107])]) ).
fof(f543,plain,
( epsilon_transitive(sK12)
| ~ spl20_20
| ~ spl20_47 ),
inference(resolution,[],[f501,f372]) ).
fof(f963,plain,
( spl20_106
| ~ spl20_10
| ~ spl20_47 ),
inference(avatar_split_clause,[],[f542,f500,f320,f960]) ).
fof(f960,plain,
( spl20_106
<=> epsilon_transitive(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_106])]) ).
fof(f542,plain,
( epsilon_transitive(sK8)
| ~ spl20_10
| ~ spl20_47 ),
inference(resolution,[],[f501,f322]) ).
fof(f958,plain,
( spl20_105
| ~ spl20_10
| ~ spl20_46 ),
inference(avatar_split_clause,[],[f537,f496,f320,f955]) ).
fof(f955,plain,
( spl20_105
<=> relation(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_105])]) ).
fof(f537,plain,
( relation(sK8)
| ~ spl20_10
| ~ spl20_46 ),
inference(resolution,[],[f497,f322]) ).
fof(f952,plain,
( spl20_104
| ~ spl20_20
| ~ spl20_45 ),
inference(avatar_split_clause,[],[f533,f492,f370,f949]) ).
fof(f949,plain,
( spl20_104
<=> function(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_104])]) ).
fof(f533,plain,
( function(sK12)
| ~ spl20_20
| ~ spl20_45 ),
inference(resolution,[],[f493,f372]) ).
fof(f947,plain,
( spl20_103
| ~ spl20_10
| ~ spl20_45 ),
inference(avatar_split_clause,[],[f532,f492,f320,f944]) ).
fof(f944,plain,
( spl20_103
<=> function(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_103])]) ).
fof(f532,plain,
( function(sK8)
| ~ spl20_10
| ~ spl20_45 ),
inference(resolution,[],[f493,f322]) ).
fof(f935,plain,
( ~ spl20_1
| ~ spl20_2
| spl20_102
| ~ spl20_41
| ~ spl20_88 ),
inference(avatar_split_clause,[],[f896,f804,f474,f932,f280,f275]) ).
fof(f896,plain,
( subset(sK1,sK2)
| ~ ordinal(sK2)
| ~ ordinal(sK1)
| ~ spl20_41
| ~ spl20_88 ),
inference(resolution,[],[f475,f805]) ).
fof(f902,plain,
spl20_101,
inference(avatar_split_clause,[],[f221,f900]) ).
fof(f221,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(sK6(X0,X1,X2),X0)
| in(sK6(X0,X1,X2),X1)
| in(sK6(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f125]) ).
fof(f125,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ( ( ( ~ in(sK6(X0,X1,X2),X0)
& ~ in(sK6(X0,X1,X2),X1) )
| ~ in(sK6(X0,X1,X2),X2) )
& ( in(sK6(X0,X1,X2),X0)
| in(sK6(X0,X1,X2),X1)
| in(sK6(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X0)
& ~ in(X4,X1) ) )
& ( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f123,f124]) ).
fof(f124,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) )
=> ( ( ( ~ in(sK6(X0,X1,X2),X0)
& ~ in(sK6(X0,X1,X2),X1) )
| ~ in(sK6(X0,X1,X2),X2) )
& ( in(sK6(X0,X1,X2),X0)
| in(sK6(X0,X1,X2),X1)
| in(sK6(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f123,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X0)
& ~ in(X4,X1) ) )
& ( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f122]) ).
fof(f122,plain,
! [X1,X0,X2] :
( ( sP0(X1,X0,X2)
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2) ) )
| ~ sP0(X1,X0,X2) ) ),
inference(flattening,[],[f121]) ).
fof(f121,plain,
! [X1,X0,X2] :
( ( sP0(X1,X0,X2)
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2) ) )
| ~ sP0(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f100]) ).
fof(f100,plain,
! [X1,X0,X2] :
( sP0(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f895,plain,
( spl20_100
| ~ spl20_40
| ~ spl20_65 ),
inference(avatar_split_clause,[],[f653,f621,f470,f892]) ).
fof(f653,plain,
( element(sK1,set_union2(sK2,singleton(sK2)))
| ~ spl20_40
| ~ spl20_65 ),
inference(resolution,[],[f622,f471]) ).
fof(f886,plain,
spl20_99,
inference(avatar_split_clause,[],[f223,f884]) ).
fof(f223,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ in(sK6(X0,X1,X2),X0)
| ~ in(sK6(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f125]) ).
fof(f882,plain,
spl20_98,
inference(avatar_split_clause,[],[f222,f880]) ).
fof(f222,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ in(sK6(X0,X1,X2),X1)
| ~ in(sK6(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f125]) ).
fof(f873,plain,
spl20_97,
inference(avatar_split_clause,[],[f211,f871]) ).
fof(f211,plain,
! [X0,X1] :
( singleton(X0) = X1
| sK5(X0,X1) = X0
| in(sK5(X0,X1),X1) ),
inference(cnf_transformation,[],[f119]) ).
fof(f119,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ( ( sK5(X0,X1) != X0
| ~ in(sK5(X0,X1),X1) )
& ( sK5(X0,X1) = X0
| in(sK5(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f117,f118]) ).
fof(f118,plain,
! [X0,X1] :
( ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) )
=> ( ( sK5(X0,X1) != X0
| ~ in(sK5(X0,X1),X1) )
& ( sK5(X0,X1) = X0
| in(sK5(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f117,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(rectify,[],[f116]) ).
fof(f116,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X0 = X2
| ~ in(X2,X1) ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0,X1] :
( singleton(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f856,plain,
spl20_96,
inference(avatar_split_clause,[],[f218,f854]) ).
fof(f218,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f125]) ).
fof(f852,plain,
spl20_95,
inference(avatar_split_clause,[],[f179,f850]) ).
fof(f179,plain,
! [X0,X1] :
( in(X1,X0)
| X0 = X1
| in(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0] :
( ! [X1] :
( in(X1,X0)
| X0 = X1
| in(X0,X1)
| ~ ordinal(X1) )
| ~ ordinal(X0) ),
inference(flattening,[],[f70]) ).
fof(f70,plain,
! [X0] :
( ! [X1] :
( in(X1,X0)
| X0 = X1
| in(X0,X1)
| ~ ordinal(X1) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f46]) ).
fof(f46,axiom,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ~ ( ~ in(X1,X0)
& X0 != X1
& ~ in(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_ordinal1) ).
fof(f848,plain,
( ~ spl20_94
| ~ spl20_40
| ~ spl20_64 ),
inference(avatar_split_clause,[],[f650,f617,f470,f845]) ).
fof(f650,plain,
( ~ in(set_union2(sK2,singleton(sK2)),sK1)
| ~ spl20_40
| ~ spl20_64 ),
inference(resolution,[],[f618,f471]) ).
fof(f843,plain,
spl20_93,
inference(avatar_split_clause,[],[f273,f841]) ).
fof(f273,plain,
! [X0,X1] :
( singleton(X0) = X1
| sK5(X0,X1) != X0
| ~ in(X0,X1) ),
inference(inner_rewriting,[],[f212]) ).
fof(f212,plain,
! [X0,X1] :
( singleton(X0) = X1
| sK5(X0,X1) != X0
| ~ in(sK5(X0,X1),X1) ),
inference(cnf_transformation,[],[f119]) ).
fof(f823,plain,
spl20_92,
inference(avatar_split_clause,[],[f220,f821]) ).
fof(f220,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f125]) ).
fof(f819,plain,
spl20_91,
inference(avatar_split_clause,[],[f219,f817]) ).
fof(f219,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f125]) ).
fof(f814,plain,
spl20_90,
inference(avatar_split_clause,[],[f217,f812]) ).
fof(f217,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f98]) ).
fof(f98,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f97]) ).
fof(f97,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f51]) ).
fof(f51,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f810,plain,
spl20_89,
inference(avatar_split_clause,[],[f204,f808]) ).
fof(f204,plain,
! [X0,X1] :
( ordinal_subset(X0,X1)
| ~ subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f113]) ).
fof(f113,plain,
! [X0,X1] :
( ( ( ordinal_subset(X0,X1)
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ ordinal_subset(X0,X1) ) )
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(nnf_transformation,[],[f92]) ).
fof(f92,plain,
! [X0,X1] :
( ( ordinal_subset(X0,X1)
<=> subset(X0,X1) )
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(flattening,[],[f91]) ).
fof(f91,plain,
! [X0,X1] :
( ( ordinal_subset(X0,X1)
<=> subset(X0,X1) )
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f39]) ).
fof(f39,axiom,
! [X0,X1] :
( ( ordinal(X1)
& ordinal(X0) )
=> ( ordinal_subset(X0,X1)
<=> subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
fof(f806,plain,
spl20_88,
inference(avatar_split_clause,[],[f203,f804]) ).
fof(f203,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f113]) ).
fof(f802,plain,
spl20_87,
inference(avatar_split_clause,[],[f202,f800]) ).
fof(f202,plain,
! [X0,X1] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0,X1] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(flattening,[],[f89]) ).
fof(f89,plain,
! [X0,X1] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1] :
( ( ordinal(X1)
& ordinal(X0) )
=> ( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',connectedness_r1_ordinal1) ).
fof(f794,plain,
spl20_86,
inference(avatar_split_clause,[],[f226,f792]) ).
fof(f226,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f99]) ).
fof(f99,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f52]) ).
fof(f52,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f790,plain,
spl20_85,
inference(avatar_split_clause,[],[f225,f788]) ).
fof(f788,plain,
( spl20_85
<=> ! [X2,X0,X1] :
( set_union2(X0,X1) = X2
| ~ sP0(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_85])]) ).
fof(f225,plain,
! [X2,X0,X1] :
( set_union2(X0,X1) = X2
| ~ sP0(X1,X0,X2) ),
inference(cnf_transformation,[],[f126]) ).
fof(f126,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ~ sP0(X1,X0,X2) )
& ( sP0(X1,X0,X2)
| set_union2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f101]) ).
fof(f101,plain,
! [X0,X1,X2] :
( set_union2(X0,X1) = X2
<=> sP0(X1,X0,X2) ),
inference(definition_folding,[],[f14,f100]) ).
fof(f14,axiom,
! [X0,X1,X2] :
( set_union2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f786,plain,
spl20_84,
inference(avatar_split_clause,[],[f208,f784]) ).
fof(f208,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f115]) ).
fof(f115,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(flattening,[],[f114]) ).
fof(f114,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f770,plain,
spl20_83,
inference(avatar_split_clause,[],[f205,f768]) ).
fof(f768,plain,
( spl20_83
<=> ! [X0,X1] :
( relation(set_union2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_83])]) ).
fof(f205,plain,
! [X0,X1] :
( relation(set_union2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f94,plain,
! [X0,X1] :
( relation(set_union2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(flattening,[],[f93]) ).
fof(f93,plain,
! [X0,X1] :
( relation(set_union2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(set_union2(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_relat_1) ).
fof(f766,plain,
spl20_82,
inference(avatar_split_clause,[],[f198,f764]) ).
fof(f198,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f84,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f83]) ).
fof(f83,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f47]) ).
fof(f47,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f762,plain,
spl20_81,
inference(avatar_split_clause,[],[f189,f760]) ).
fof(f189,plain,
! [X2,X0] :
( subset(X2,X0)
| ~ in(X2,X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f110,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ( ~ subset(sK3(X0),X0)
& in(sK3(X0),X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f108,f109]) ).
fof(f109,plain,
! [X0] :
( ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) )
=> ( ~ subset(sK3(X0),X0)
& in(sK3(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f108,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(rectify,[],[f107]) ).
fof(f107,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) ) )
& ( ! [X1] :
( subset(X1,X0)
| ~ in(X1,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(nnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( subset(X1,X0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( in(X1,X0)
=> subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(f729,plain,
spl20_80,
inference(avatar_split_clause,[],[f271,f727]) ).
fof(f271,plain,
! [X3,X0] :
( X0 = X3
| ~ in(X3,singleton(X0)) ),
inference(equality_resolution,[],[f209]) ).
fof(f209,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f119]) ).
fof(f725,plain,
spl20_79,
inference(avatar_split_clause,[],[f265,f723]) ).
fof(f265,plain,
! [X0] :
( epsilon_transitive(set_union2(X0,singleton(X0)))
| ~ ordinal(X0) ),
inference(definition_unfolding,[],[f176,f172]) ).
fof(f172,plain,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_ordinal1) ).
fof(f176,plain,
! [X0] :
( epsilon_transitive(succ(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0] :
( ( ordinal(succ(X0))
& epsilon_connected(succ(X0))
& epsilon_transitive(succ(X0))
& ~ empty(succ(X0)) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0] :
( ordinal(X0)
=> ( ordinal(succ(X0))
& epsilon_connected(succ(X0))
& epsilon_transitive(succ(X0))
& ~ empty(succ(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_ordinal1) ).
fof(f721,plain,
spl20_78,
inference(avatar_split_clause,[],[f264,f719]) ).
fof(f264,plain,
! [X0] :
( epsilon_connected(set_union2(X0,singleton(X0)))
| ~ ordinal(X0) ),
inference(definition_unfolding,[],[f177,f172]) ).
fof(f177,plain,
! [X0] :
( epsilon_connected(succ(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f717,plain,
spl20_77,
inference(avatar_split_clause,[],[f263,f715]) ).
fof(f263,plain,
! [X0] :
( ordinal(set_union2(X0,singleton(X0)))
| ~ ordinal(X0) ),
inference(definition_unfolding,[],[f178,f172]) ).
fof(f178,plain,
! [X0] :
( ordinal(succ(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f713,plain,
spl20_76,
inference(avatar_split_clause,[],[f215,f711]) ).
fof(f215,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f95,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f55,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(f709,plain,
spl20_75,
inference(avatar_split_clause,[],[f214,f707]) ).
fof(f214,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f120]) ).
fof(f120,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f50]) ).
fof(f50,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f705,plain,
spl20_74,
inference(avatar_split_clause,[],[f213,f703]) ).
fof(f213,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f120]) ).
fof(f689,plain,
( ~ spl20_8
| ~ spl20_72 ),
inference(avatar_contradiction_clause,[],[f678]) ).
fof(f678,plain,
( $false
| ~ spl20_8
| ~ spl20_72 ),
inference(resolution,[],[f673,f312]) ).
fof(f312,plain,
( ordinal(empty_set)
| ~ spl20_8 ),
inference(avatar_component_clause,[],[f310]) ).
fof(f310,plain,
( spl20_8
<=> ordinal(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_8])]) ).
fof(f673,plain,
( ! [X1] : ~ ordinal(X1)
| ~ spl20_72 ),
inference(avatar_component_clause,[],[f672]) ).
fof(f672,plain,
( spl20_72
<=> ! [X1] : ~ ordinal(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_72])]) ).
fof(f688,plain,
( ~ spl20_1
| ~ spl20_72 ),
inference(avatar_contradiction_clause,[],[f679]) ).
fof(f679,plain,
( $false
| ~ spl20_1
| ~ spl20_72 ),
inference(resolution,[],[f673,f277]) ).
fof(f277,plain,
( ordinal(sK1)
| ~ spl20_1 ),
inference(avatar_component_clause,[],[f275]) ).
fof(f687,plain,
( ~ spl20_2
| ~ spl20_72 ),
inference(avatar_contradiction_clause,[],[f680]) ).
fof(f680,plain,
( $false
| ~ spl20_2
| ~ spl20_72 ),
inference(resolution,[],[f673,f282]) ).
fof(f282,plain,
( ordinal(sK2)
| ~ spl20_2 ),
inference(avatar_component_clause,[],[f280]) ).
fof(f686,plain,
( ~ spl20_14
| ~ spl20_72 ),
inference(avatar_contradiction_clause,[],[f681]) ).
fof(f681,plain,
( $false
| ~ spl20_14
| ~ spl20_72 ),
inference(resolution,[],[f673,f342]) ).
fof(f342,plain,
( ordinal(sK9)
| ~ spl20_14 ),
inference(avatar_component_clause,[],[f340]) ).
fof(f340,plain,
( spl20_14
<=> ordinal(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_14])]) ).
fof(f685,plain,
( ~ spl20_19
| ~ spl20_72 ),
inference(avatar_contradiction_clause,[],[f682]) ).
fof(f682,plain,
( $false
| ~ spl20_19
| ~ spl20_72 ),
inference(resolution,[],[f673,f367]) ).
fof(f367,plain,
( ordinal(sK11)
| ~ spl20_19 ),
inference(avatar_component_clause,[],[f365]) ).
fof(f365,plain,
( spl20_19
<=> ordinal(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_19])]) ).
fof(f684,plain,
( ~ spl20_36
| ~ spl20_72 ),
inference(avatar_contradiction_clause,[],[f683]) ).
fof(f683,plain,
( $false
| ~ spl20_36
| ~ spl20_72 ),
inference(resolution,[],[f673,f452]) ).
fof(f452,plain,
( ordinal(sK18)
| ~ spl20_36 ),
inference(avatar_component_clause,[],[f450]) ).
fof(f450,plain,
( spl20_36
<=> ordinal(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_36])]) ).
fof(f677,plain,
( spl20_72
| spl20_73 ),
inference(avatar_split_clause,[],[f201,f675,f672]) ).
fof(f201,plain,
! [X0,X1] :
( ordinal_subset(X0,X0)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0,X1] :
( ordinal_subset(X0,X0)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(flattening,[],[f87]) ).
fof(f87,plain,
! [X0,X1] :
( ordinal_subset(X0,X0)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,axiom,
! [X0,X1] :
( ( ordinal(X1)
& ordinal(X0) )
=> ordinal_subset(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_ordinal1) ).
fof(f670,plain,
spl20_71,
inference(avatar_split_clause,[],[f195,f668]) ).
fof(f195,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f660,plain,
( spl20_70
| ~ spl20_2
| ~ spl20_44 ),
inference(avatar_split_clause,[],[f527,f488,f280,f657]) ).
fof(f657,plain,
( spl20_70
<=> epsilon_connected(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_70])]) ).
fof(f527,plain,
( epsilon_connected(sK2)
| ~ spl20_2
| ~ spl20_44 ),
inference(resolution,[],[f489,f282]) ).
fof(f640,plain,
spl20_69,
inference(avatar_split_clause,[],[f272,f638]) ).
fof(f272,plain,
! [X0,X1] : sP0(X1,X0,set_union2(X0,X1)),
inference(equality_resolution,[],[f224]) ).
fof(f224,plain,
! [X2,X0,X1] :
( sP0(X1,X0,X2)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f126]) ).
fof(f636,plain,
spl20_68,
inference(avatar_split_clause,[],[f262,f634]) ).
fof(f262,plain,
! [X0] : in(X0,set_union2(X0,singleton(X0))),
inference(definition_unfolding,[],[f170,f172]) ).
fof(f170,plain,
! [X0] : in(X0,succ(X0)),
inference(cnf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0] : in(X0,succ(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_ordinal1) ).
fof(f632,plain,
spl20_67,
inference(avatar_split_clause,[],[f261,f630]) ).
fof(f261,plain,
! [X0] : set_union2(X0,singleton(X0)) != X0,
inference(definition_unfolding,[],[f169,f172]) ).
fof(f169,plain,
! [X0] : succ(X0) != X0,
inference(cnf_transformation,[],[f43]) ).
fof(f43,axiom,
! [X0] : succ(X0) != X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_ordinal1) ).
fof(f628,plain,
( spl20_66
| ~ spl20_1
| ~ spl20_44 ),
inference(avatar_split_clause,[],[f526,f488,f275,f625]) ).
fof(f625,plain,
( spl20_66
<=> epsilon_connected(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_66])]) ).
fof(f526,plain,
( epsilon_connected(sK1)
| ~ spl20_1
| ~ spl20_44 ),
inference(resolution,[],[f489,f277]) ).
fof(f623,plain,
spl20_65,
inference(avatar_split_clause,[],[f200,f621]) ).
fof(f200,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(f619,plain,
spl20_64,
inference(avatar_split_clause,[],[f199,f617]) ).
fof(f199,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f615,plain,
spl20_63,
inference(avatar_split_clause,[],[f197,f613]) ).
fof(f613,plain,
( spl20_63
<=> ! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_63])]) ).
fof(f197,plain,
! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).
fof(f611,plain,
spl20_62,
inference(avatar_split_clause,[],[f196,f609]) ).
fof(f609,plain,
( spl20_62
<=> ! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_62])]) ).
fof(f196,plain,
! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).
fof(f607,plain,
spl20_61,
inference(avatar_split_clause,[],[f191,f605]) ).
fof(f605,plain,
( spl20_61
<=> ! [X0] :
( epsilon_transitive(X0)
| ~ subset(sK3(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_61])]) ).
fof(f191,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ subset(sK3(X0),X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f603,plain,
spl20_60,
inference(avatar_split_clause,[],[f190,f601]) ).
fof(f190,plain,
! [X0] :
( epsilon_transitive(X0)
| in(sK3(X0),X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f599,plain,
spl20_59,
inference(avatar_split_clause,[],[f186,f597]) ).
fof(f597,plain,
( spl20_59
<=> ! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_59])]) ).
fof(f186,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(flattening,[],[f76]) ).
fof(f76,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( ( epsilon_connected(X0)
& epsilon_transitive(X0) )
=> ordinal(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_ordinal1) ).
fof(f593,plain,
( spl20_58
| ~ spl20_2
| ~ spl20_43 ),
inference(avatar_split_clause,[],[f521,f484,f280,f590]) ).
fof(f484,plain,
( spl20_43
<=> ! [X0] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_43])]) ).
fof(f521,plain,
( epsilon_transitive(sK2)
| ~ spl20_2
| ~ spl20_43 ),
inference(resolution,[],[f485,f282]) ).
fof(f485,plain,
( ! [X0] :
( ~ ordinal(X0)
| epsilon_transitive(X0) )
| ~ spl20_43 ),
inference(avatar_component_clause,[],[f484]) ).
fof(f580,plain,
spl20_57,
inference(avatar_split_clause,[],[f260,f578]) ).
fof(f260,plain,
! [X0] : ~ empty(set_union2(X0,singleton(X0))),
inference(definition_unfolding,[],[f168,f172]) ).
fof(f168,plain,
! [X0] : ~ empty(succ(X0)),
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0] : ~ empty(succ(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_ordinal1) ).
fof(f576,plain,
spl20_56,
inference(avatar_split_clause,[],[f216,f574]) ).
fof(f216,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f96]) ).
fof(f96,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f54]) ).
fof(f54,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f572,plain,
spl20_55,
inference(avatar_split_clause,[],[f194,f570]) ).
fof(f194,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(cnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(rectify,[],[f25]) ).
fof(f25,axiom,
! [X0,X1] : set_union2(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(f568,plain,
spl20_54,
inference(avatar_split_clause,[],[f182,f566]) ).
fof(f182,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f53]) ).
fof(f53,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f564,plain,
spl20_53,
inference(avatar_split_clause,[],[f171,f562]) ).
fof(f171,plain,
! [X0] : set_union2(X0,empty_set) = X0,
inference(cnf_transformation,[],[f44]) ).
fof(f44,axiom,
! [X0] : set_union2(X0,empty_set) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).
fof(f555,plain,
( spl20_52
| ~ spl20_1
| ~ spl20_43 ),
inference(avatar_split_clause,[],[f520,f484,f275,f552]) ).
fof(f520,plain,
( epsilon_transitive(sK1)
| ~ spl20_1
| ~ spl20_43 ),
inference(resolution,[],[f485,f277]) ).
fof(f518,plain,
spl20_51,
inference(avatar_split_clause,[],[f270,f516]) ).
fof(f270,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f269]) ).
fof(f269,plain,
! [X3,X1] :
( in(X3,X1)
| singleton(X3) != X1 ),
inference(equality_resolution,[],[f210]) ).
fof(f210,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f119]) ).
fof(f514,plain,
spl20_50,
inference(avatar_split_clause,[],[f192,f512]) ).
fof(f192,plain,
! [X0] : element(sK4(X0),X0),
inference(cnf_transformation,[],[f112]) ).
fof(f112,plain,
! [X0] : element(sK4(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f15,f111]) ).
fof(f111,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK4(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f15,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f510,plain,
spl20_49,
inference(avatar_split_clause,[],[f185,f508]) ).
fof(f185,plain,
! [X0] :
( ordinal(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0] :
( ( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] :
( empty(X0)
=> ( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_ordinal1) ).
fof(f506,plain,
spl20_48,
inference(avatar_split_clause,[],[f184,f504]) ).
fof(f184,plain,
! [X0] :
( epsilon_connected(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f502,plain,
spl20_47,
inference(avatar_split_clause,[],[f183,f500]) ).
fof(f183,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f498,plain,
spl20_46,
inference(avatar_split_clause,[],[f181,f496]) ).
fof(f181,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f73,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( empty(X0)
=> relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(f494,plain,
spl20_45,
inference(avatar_split_clause,[],[f180,f492]) ).
fof(f180,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( empty(X0)
=> function(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
fof(f490,plain,
spl20_44,
inference(avatar_split_clause,[],[f174,f488]) ).
fof(f174,plain,
! [X0] :
( epsilon_connected(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0] :
( ( epsilon_connected(X0)
& epsilon_transitive(X0) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( ordinal(X0)
=> ( epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_ordinal1) ).
fof(f486,plain,
spl20_43,
inference(avatar_split_clause,[],[f173,f484]) ).
fof(f173,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f482,plain,
spl20_42,
inference(avatar_split_clause,[],[f193,f480]) ).
fof(f193,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f41]) ).
fof(f41,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f478,plain,
( spl20_40
| spl20_41 ),
inference(avatar_split_clause,[],[f259,f474,f470]) ).
fof(f259,plain,
( ordinal_subset(sK1,sK2)
| in(sK1,set_union2(sK2,singleton(sK2))) ),
inference(definition_unfolding,[],[f155,f172]) ).
fof(f155,plain,
( ordinal_subset(sK1,sK2)
| in(sK1,succ(sK2)) ),
inference(cnf_transformation,[],[f106]) ).
fof(f106,plain,
( ( ~ ordinal_subset(sK1,sK2)
| ~ in(sK1,succ(sK2)) )
& ( ordinal_subset(sK1,sK2)
| in(sK1,succ(sK2)) )
& ordinal(sK2)
& ordinal(sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f103,f105,f104]) ).
fof(f104,plain,
( ? [X0] :
( ? [X1] :
( ( ~ ordinal_subset(X0,X1)
| ~ in(X0,succ(X1)) )
& ( ordinal_subset(X0,X1)
| in(X0,succ(X1)) )
& ordinal(X1) )
& ordinal(X0) )
=> ( ? [X1] :
( ( ~ ordinal_subset(sK1,X1)
| ~ in(sK1,succ(X1)) )
& ( ordinal_subset(sK1,X1)
| in(sK1,succ(X1)) )
& ordinal(X1) )
& ordinal(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f105,plain,
( ? [X1] :
( ( ~ ordinal_subset(sK1,X1)
| ~ in(sK1,succ(X1)) )
& ( ordinal_subset(sK1,X1)
| in(sK1,succ(X1)) )
& ordinal(X1) )
=> ( ( ~ ordinal_subset(sK1,sK2)
| ~ in(sK1,succ(sK2)) )
& ( ordinal_subset(sK1,sK2)
| in(sK1,succ(sK2)) )
& ordinal(sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f103,plain,
? [X0] :
( ? [X1] :
( ( ~ ordinal_subset(X0,X1)
| ~ in(X0,succ(X1)) )
& ( ordinal_subset(X0,X1)
| in(X0,succ(X1)) )
& ordinal(X1) )
& ordinal(X0) ),
inference(flattening,[],[f102]) ).
fof(f102,plain,
? [X0] :
( ? [X1] :
( ( ~ ordinal_subset(X0,X1)
| ~ in(X0,succ(X1)) )
& ( ordinal_subset(X0,X1)
| in(X0,succ(X1)) )
& ordinal(X1) )
& ordinal(X0) ),
inference(nnf_transformation,[],[f67]) ).
fof(f67,plain,
? [X0] :
( ? [X1] :
( ( in(X0,succ(X1))
<~> ordinal_subset(X0,X1) )
& ordinal(X1) )
& ordinal(X0) ),
inference(ennf_transformation,[],[f49]) ).
fof(f49,negated_conjecture,
~ ! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ( in(X0,succ(X1))
<=> ordinal_subset(X0,X1) ) ) ),
inference(negated_conjecture,[],[f48]) ).
fof(f48,conjecture,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ( in(X0,succ(X1))
<=> ordinal_subset(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_ordinal1) ).
fof(f477,plain,
( ~ spl20_40
| ~ spl20_41 ),
inference(avatar_split_clause,[],[f258,f474,f470]) ).
fof(f258,plain,
( ~ ordinal_subset(sK1,sK2)
| ~ in(sK1,set_union2(sK2,singleton(sK2))) ),
inference(definition_unfolding,[],[f156,f172]) ).
fof(f156,plain,
( ~ ordinal_subset(sK1,sK2)
| ~ in(sK1,succ(sK2)) ),
inference(cnf_transformation,[],[f106]) ).
fof(f468,plain,
spl20_39,
inference(avatar_split_clause,[],[f257,f465]) ).
fof(f465,plain,
( spl20_39
<=> function(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_39])]) ).
fof(f257,plain,
function(sK19),
inference(cnf_transformation,[],[f152]) ).
fof(f152,plain,
( function(sK19)
& empty(sK19)
& relation(sK19) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f30,f151]) ).
fof(f151,plain,
( ? [X0] :
( function(X0)
& empty(X0)
& relation(X0) )
=> ( function(sK19)
& empty(sK19)
& relation(sK19) ) ),
introduced(choice_axiom,[]) ).
fof(f30,axiom,
? [X0] :
( function(X0)
& empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(f463,plain,
spl20_38,
inference(avatar_split_clause,[],[f256,f460]) ).
fof(f256,plain,
empty(sK19),
inference(cnf_transformation,[],[f152]) ).
fof(f458,plain,
spl20_37,
inference(avatar_split_clause,[],[f255,f455]) ).
fof(f455,plain,
( spl20_37
<=> relation(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_37])]) ).
fof(f255,plain,
relation(sK19),
inference(cnf_transformation,[],[f152]) ).
fof(f453,plain,
spl20_36,
inference(avatar_split_clause,[],[f254,f450]) ).
fof(f254,plain,
ordinal(sK18),
inference(cnf_transformation,[],[f150]) ).
fof(f150,plain,
( ordinal(sK18)
& epsilon_connected(sK18)
& epsilon_transitive(sK18)
& empty(sK18)
& function(sK18)
& relation(sK18) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f63,f149]) ).
fof(f149,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& function(X0)
& relation(X0) )
=> ( ordinal(sK18)
& epsilon_connected(sK18)
& epsilon_transitive(sK18)
& empty(sK18)
& function(sK18)
& relation(sK18) ) ),
introduced(choice_axiom,[]) ).
fof(f63,plain,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f31]) ).
fof(f31,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_ordinal1) ).
fof(f448,plain,
spl20_35,
inference(avatar_split_clause,[],[f253,f445]) ).
fof(f445,plain,
( spl20_35
<=> epsilon_connected(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_35])]) ).
fof(f253,plain,
epsilon_connected(sK18),
inference(cnf_transformation,[],[f150]) ).
fof(f443,plain,
spl20_34,
inference(avatar_split_clause,[],[f252,f440]) ).
fof(f440,plain,
( spl20_34
<=> epsilon_transitive(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_34])]) ).
fof(f252,plain,
epsilon_transitive(sK18),
inference(cnf_transformation,[],[f150]) ).
fof(f438,plain,
spl20_33,
inference(avatar_split_clause,[],[f251,f435]) ).
fof(f251,plain,
empty(sK18),
inference(cnf_transformation,[],[f150]) ).
fof(f433,plain,
spl20_32,
inference(avatar_split_clause,[],[f250,f430]) ).
fof(f430,plain,
( spl20_32
<=> function(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_32])]) ).
fof(f250,plain,
function(sK18),
inference(cnf_transformation,[],[f150]) ).
fof(f428,plain,
spl20_31,
inference(avatar_split_clause,[],[f249,f425]) ).
fof(f425,plain,
( spl20_31
<=> relation(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_31])]) ).
fof(f249,plain,
relation(sK18),
inference(cnf_transformation,[],[f150]) ).
fof(f423,plain,
spl20_30,
inference(avatar_split_clause,[],[f248,f420]) ).
fof(f420,plain,
( spl20_30
<=> function(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_30])]) ).
fof(f248,plain,
function(sK17),
inference(cnf_transformation,[],[f148]) ).
fof(f148,plain,
( function(sK17)
& relation(sK17) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f64,f147]) ).
fof(f147,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK17)
& relation(sK17) ) ),
introduced(choice_axiom,[]) ).
fof(f64,plain,
? [X0] :
( function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f34]) ).
fof(f34,axiom,
? [X0] :
( one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).
fof(f418,plain,
spl20_29,
inference(avatar_split_clause,[],[f247,f415]) ).
fof(f415,plain,
( spl20_29
<=> relation(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_29])]) ).
fof(f247,plain,
relation(sK17),
inference(cnf_transformation,[],[f148]) ).
fof(f413,plain,
spl20_28,
inference(avatar_split_clause,[],[f246,f410]) ).
fof(f410,plain,
( spl20_28
<=> function(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_28])]) ).
fof(f246,plain,
function(sK16),
inference(cnf_transformation,[],[f146]) ).
fof(f146,plain,
( function(sK16)
& relation(sK16) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f26,f145]) ).
fof(f145,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK16)
& relation(sK16) ) ),
introduced(choice_axiom,[]) ).
fof(f26,axiom,
? [X0] :
( function(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
fof(f408,plain,
spl20_27,
inference(avatar_split_clause,[],[f245,f405]) ).
fof(f405,plain,
( spl20_27
<=> relation(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_27])]) ).
fof(f245,plain,
relation(sK16),
inference(cnf_transformation,[],[f146]) ).
fof(f403,plain,
spl20_26,
inference(avatar_split_clause,[],[f244,f400]) ).
fof(f400,plain,
( spl20_26
<=> function(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_26])]) ).
fof(f244,plain,
function(sK15),
inference(cnf_transformation,[],[f144]) ).
fof(f144,plain,
( function(sK15)
& relation(sK15) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f60,f143]) ).
fof(f143,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK15)
& relation(sK15) ) ),
introduced(choice_axiom,[]) ).
fof(f60,plain,
? [X0] :
( function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f37]) ).
fof(f37,axiom,
? [X0] :
( function(X0)
& relation_empty_yielding(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_funct_1) ).
fof(f398,plain,
spl20_25,
inference(avatar_split_clause,[],[f243,f395]) ).
fof(f395,plain,
( spl20_25
<=> relation(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_25])]) ).
fof(f243,plain,
relation(sK15),
inference(cnf_transformation,[],[f144]) ).
fof(f393,plain,
spl20_24,
inference(avatar_split_clause,[],[f242,f390]) ).
fof(f390,plain,
( spl20_24
<=> relation(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_24])]) ).
fof(f242,plain,
relation(sK14),
inference(cnf_transformation,[],[f142]) ).
fof(f142,plain,
relation(sK14),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f59,f141]) ).
fof(f141,plain,
( ? [X0] : relation(X0)
=> relation(sK14) ),
introduced(choice_axiom,[]) ).
fof(f59,plain,
? [X0] : relation(X0),
inference(pure_predicate_removal,[],[f36]) ).
fof(f36,axiom,
? [X0] :
( relation_empty_yielding(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).
fof(f388,plain,
spl20_23,
inference(avatar_split_clause,[],[f241,f385]) ).
fof(f385,plain,
( spl20_23
<=> function(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_23])]) ).
fof(f241,plain,
function(sK13),
inference(cnf_transformation,[],[f140]) ).
fof(f140,plain,
( function(sK13)
& relation(sK13) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f58,f139]) ).
fof(f139,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK13)
& relation(sK13) ) ),
introduced(choice_axiom,[]) ).
fof(f58,plain,
? [X0] :
( function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f38]) ).
fof(f38,axiom,
? [X0] :
( function(X0)
& relation_non_empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_funct_1) ).
fof(f383,plain,
spl20_22,
inference(avatar_split_clause,[],[f240,f380]) ).
fof(f380,plain,
( spl20_22
<=> relation(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_22])]) ).
fof(f240,plain,
relation(sK13),
inference(cnf_transformation,[],[f140]) ).
fof(f378,plain,
spl20_21,
inference(avatar_split_clause,[],[f239,f375]) ).
fof(f375,plain,
( spl20_21
<=> relation(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_21])]) ).
fof(f239,plain,
relation(sK12),
inference(cnf_transformation,[],[f138]) ).
fof(f138,plain,
( relation(sK12)
& empty(sK12) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f28,f137]) ).
fof(f137,plain,
( ? [X0] :
( relation(X0)
& empty(X0) )
=> ( relation(sK12)
& empty(sK12) ) ),
introduced(choice_axiom,[]) ).
fof(f28,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f373,plain,
spl20_20,
inference(avatar_split_clause,[],[f238,f370]) ).
fof(f238,plain,
empty(sK12),
inference(cnf_transformation,[],[f138]) ).
fof(f368,plain,
spl20_19,
inference(avatar_split_clause,[],[f237,f365]) ).
fof(f237,plain,
ordinal(sK11),
inference(cnf_transformation,[],[f136]) ).
fof(f136,plain,
( ordinal(sK11)
& epsilon_connected(sK11)
& epsilon_transitive(sK11) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f27,f135]) ).
fof(f135,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) )
=> ( ordinal(sK11)
& epsilon_connected(sK11)
& epsilon_transitive(sK11) ) ),
introduced(choice_axiom,[]) ).
fof(f27,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_ordinal1) ).
fof(f363,plain,
spl20_18,
inference(avatar_split_clause,[],[f236,f360]) ).
fof(f360,plain,
( spl20_18
<=> epsilon_connected(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_18])]) ).
fof(f236,plain,
epsilon_connected(sK11),
inference(cnf_transformation,[],[f136]) ).
fof(f358,plain,
spl20_17,
inference(avatar_split_clause,[],[f235,f355]) ).
fof(f355,plain,
( spl20_17
<=> epsilon_transitive(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_17])]) ).
fof(f235,plain,
epsilon_transitive(sK11),
inference(cnf_transformation,[],[f136]) ).
fof(f353,plain,
spl20_16,
inference(avatar_split_clause,[],[f234,f350]) ).
fof(f350,plain,
( spl20_16
<=> relation(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_16])]) ).
fof(f234,plain,
relation(sK10),
inference(cnf_transformation,[],[f134]) ).
fof(f134,plain,
( relation(sK10)
& ~ empty(sK10) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f32,f133]) ).
fof(f133,plain,
( ? [X0] :
( relation(X0)
& ~ empty(X0) )
=> ( relation(sK10)
& ~ empty(sK10) ) ),
introduced(choice_axiom,[]) ).
fof(f32,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f348,plain,
~ spl20_15,
inference(avatar_split_clause,[],[f233,f345]) ).
fof(f345,plain,
( spl20_15
<=> empty(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_15])]) ).
fof(f233,plain,
~ empty(sK10),
inference(cnf_transformation,[],[f134]) ).
fof(f343,plain,
spl20_14,
inference(avatar_split_clause,[],[f232,f340]) ).
fof(f232,plain,
ordinal(sK9),
inference(cnf_transformation,[],[f132]) ).
fof(f132,plain,
( ordinal(sK9)
& epsilon_connected(sK9)
& epsilon_transitive(sK9)
& ~ empty(sK9) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f35,f131]) ).
fof(f131,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) )
=> ( ordinal(sK9)
& epsilon_connected(sK9)
& epsilon_transitive(sK9)
& ~ empty(sK9) ) ),
introduced(choice_axiom,[]) ).
fof(f35,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_ordinal1) ).
fof(f338,plain,
spl20_13,
inference(avatar_split_clause,[],[f231,f335]) ).
fof(f335,plain,
( spl20_13
<=> epsilon_connected(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_13])]) ).
fof(f231,plain,
epsilon_connected(sK9),
inference(cnf_transformation,[],[f132]) ).
fof(f333,plain,
spl20_12,
inference(avatar_split_clause,[],[f230,f330]) ).
fof(f330,plain,
( spl20_12
<=> epsilon_transitive(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_12])]) ).
fof(f230,plain,
epsilon_transitive(sK9),
inference(cnf_transformation,[],[f132]) ).
fof(f328,plain,
~ spl20_11,
inference(avatar_split_clause,[],[f229,f325]) ).
fof(f325,plain,
( spl20_11
<=> empty(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_11])]) ).
fof(f229,plain,
~ empty(sK9),
inference(cnf_transformation,[],[f132]) ).
fof(f323,plain,
spl20_10,
inference(avatar_split_clause,[],[f228,f320]) ).
fof(f228,plain,
empty(sK8),
inference(cnf_transformation,[],[f130]) ).
fof(f130,plain,
empty(sK8),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f29,f129]) ).
fof(f129,plain,
( ? [X0] : empty(X0)
=> empty(sK8) ),
introduced(choice_axiom,[]) ).
fof(f29,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f318,plain,
~ spl20_9,
inference(avatar_split_clause,[],[f227,f315]) ).
fof(f315,plain,
( spl20_9
<=> empty(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_9])]) ).
fof(f227,plain,
~ empty(sK7),
inference(cnf_transformation,[],[f128]) ).
fof(f128,plain,
~ empty(sK7),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f33,f127]) ).
fof(f127,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK7) ),
introduced(choice_axiom,[]) ).
fof(f33,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f313,plain,
spl20_8,
inference(avatar_split_clause,[],[f167,f310]) ).
fof(f167,plain,
ordinal(empty_set),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& function(empty_set)
& relation(empty_set) ),
inference(pure_predicate_removal,[],[f61]) ).
fof(f61,plain,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation(empty_set) ),
inference(pure_predicate_removal,[],[f19]) ).
fof(f19,axiom,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation_empty_yielding(empty_set)
& relation(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_ordinal1) ).
fof(f308,plain,
spl20_7,
inference(avatar_split_clause,[],[f166,f305]) ).
fof(f305,plain,
( spl20_7
<=> epsilon_connected(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_7])]) ).
fof(f166,plain,
epsilon_connected(empty_set),
inference(cnf_transformation,[],[f66]) ).
fof(f303,plain,
spl20_6,
inference(avatar_split_clause,[],[f165,f300]) ).
fof(f300,plain,
( spl20_6
<=> epsilon_transitive(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_6])]) ).
fof(f165,plain,
epsilon_transitive(empty_set),
inference(cnf_transformation,[],[f66]) ).
fof(f298,plain,
spl20_5,
inference(avatar_split_clause,[],[f163,f295]) ).
fof(f295,plain,
( spl20_5
<=> function(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_5])]) ).
fof(f163,plain,
function(empty_set),
inference(cnf_transformation,[],[f66]) ).
fof(f293,plain,
spl20_4,
inference(avatar_split_clause,[],[f159,f290]) ).
fof(f290,plain,
( spl20_4
<=> relation(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_4])]) ).
fof(f159,plain,
relation(empty_set),
inference(cnf_transformation,[],[f24]) ).
fof(f24,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f288,plain,
spl20_3,
inference(avatar_split_clause,[],[f157,f285]) ).
fof(f157,plain,
empty(empty_set),
inference(cnf_transformation,[],[f18]) ).
fof(f18,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f283,plain,
spl20_2,
inference(avatar_split_clause,[],[f154,f280]) ).
fof(f154,plain,
ordinal(sK2),
inference(cnf_transformation,[],[f106]) ).
fof(f278,plain,
spl20_1,
inference(avatar_split_clause,[],[f153,f275]) ).
fof(f153,plain,
ordinal(sK1),
inference(cnf_transformation,[],[f106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM401+1 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n015.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri May 3 15:10:38 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.36 % (28053)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.37 % (28057)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.37 % (28056)WARNING: value z3 for option sas not known
% 0.22/0.37 % (28054)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.37 % (28055)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.37 % (28056)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)
% 0.22/0.38 % (28058)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)
% 0.22/0.38 % (28059)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)
% 0.22/0.38 % (28060)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)
% 0.22/0.38 TRYING [1]
% 0.22/0.38 TRYING [2]
% 0.22/0.38 TRYING [3]
% 0.22/0.38 TRYING [4]
% 0.22/0.39 TRYING [1]
% 0.22/0.39 TRYING [2]
% 0.22/0.39 TRYING [5]
% 0.22/0.40 TRYING [3]
% 0.22/0.42 TRYING [6]
% 0.22/0.46 TRYING [4]
% 0.22/0.47 TRYING [7]
% 0.22/0.53 TRYING [5]
% 1.38/0.54 TRYING [8]
% 2.29/0.67 TRYING [9]
% 2.29/0.69 TRYING [1]
% 2.29/0.69 TRYING [2]
% 2.29/0.69 TRYING [3]
% 2.29/0.69 TRYING [4]
% 2.29/0.70 TRYING [5]
% 2.29/0.72 TRYING [6]
% 2.29/0.72 TRYING [6]
% 2.80/0.76 TRYING [7]
% 3.43/0.84 TRYING [8]
% 3.65/0.86 TRYING [10]
% 4.43/0.99 TRYING [9]
% 5.63/1.15 TRYING [7]
% 5.63/1.15 TRYING [11]
% 5.83/1.22 % (28058)First to succeed.
% 6.21/1.23 % (28058)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-28053"
% 6.21/1.24 % (28058)Refutation found. Thanks to Tanya!
% 6.21/1.24 % SZS status Theorem for theBenchmark
% 6.21/1.24 % SZS output start Proof for theBenchmark
% See solution above
% 6.21/1.25 % (28058)------------------------------
% 6.21/1.25 % (28058)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 6.21/1.25 % (28058)Termination reason: Refutation
% 6.21/1.25
% 6.21/1.25 % (28058)Memory used [KB]: 10743
% 6.21/1.25 % (28058)Time elapsed: 0.860 s
% 6.21/1.25 % (28058)Instructions burned: 2616 (million)
% 6.21/1.25 % (28053)Success in time 0.859 s
%------------------------------------------------------------------------------