TSTP Solution File: NUM401+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM401+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 20:10:15 EDT 2023
% Result : Theorem 49.12s 7.40s
% Output : Refutation 49.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1201
% Syntax : Number of formulae : 4001 ( 174 unt; 0 def)
% Number of atoms : 17675 ( 946 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 22796 (9122 ~;12279 |; 207 &)
% (1143 <=>; 44 =>; 0 <=; 1 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 1143 (1141 usr;1128 prp; 0-3 aty)
% Number of functors : 24 ( 24 usr; 16 con; 0-3 aty)
% Number of variables : 5888 (;5840 !; 48 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f43164,plain,
$false,
inference(avatar_sat_refutation,[],[f263,f268,f277,f282,f287,f292,f297,f302,f307,f312,f317,f322,f327,f332,f337,f342,f347,f352,f357,f362,f367,f372,f377,f382,f387,f392,f397,f402,f407,f412,f417,f422,f427,f432,f437,f442,f447,f452,f457,f462,f467,f472,f477,f482,f487,f492,f497,f501,f505,f509,f513,f517,f521,f525,f529,f533,f537,f541,f545,f586,f590,f594,f599,f603,f607,f611,f615,f630,f635,f639,f643,f647,f651,f655,f659,f663,f673,f687,f691,f698,f703,f710,f711,f712,f713,f714,f715,f734,f738,f742,f770,f774,f778,f782,f813,f817,f821,f825,f840,f844,f848,f852,f856,f860,f864,f868,f888,f892,f897,f901,f917,f925,f929,f937,f967,f972,f978,f983,f988,f994,f1000,f1005,f1011,f1021,f1026,f1031,f1037,f1047,f1052,f1057,f1062,f1087,f1091,f1098,f1102,f1106,f1129,f1133,f1142,f1155,f1164,f1173,f1178,f1182,f1186,f1211,f1215,f1219,f1223,f1228,f1232,f1236,f1261,f1265,f1269,f1285,f1289,f1293,f1314,f1318,f1322,f1340,f1357,f1373,f1389,f1393,f1405,f1422,f1426,f1430,f1434,f1438,f1450,f1464,f1559,f1563,f1567,f1647,f1651,f1655,f1659,f1663,f1667,f1671,f1794,f1798,f1802,f1913,f1917,f1922,f2043,f2048,f2052,f2056,f2060,f2082,f2087,f2112,f2113,f2121,f2144,f2148,f2152,f2156,f2193,f2198,f2202,f2206,f2210,f2215,f2220,f2224,f2228,f2285,f2290,f2294,f2308,f2312,f2316,f2320,f2324,f2328,f2333,f2396,f2400,f2404,f2408,f2409,f2498,f2502,f2506,f2510,f2514,f2518,f2523,f2527,f2531,f2535,f2674,f2723,f2727,f2731,f2806,f2810,f2814,f2818,f2822,f2902,f2906,f2938,f2942,f2946,f2950,f2954,f2962,f2966,f2970,f2974,f2978,f2982,f2986,f2990,f2994,f2998,f3010,f3014,f3018,f3022,f3026,f3442,f3446,f3450,f3480,f3516,f3520,f3524,f3528,f3532,f3536,f3540,f3544,f3548,f3552,f3556,f3560,f3564,f3568,f3572,f3576,f3580,f3584,f3588,f3593,f3619,f3623,f3627,f3631,f3635,f3639,f3677,f4072,f4104,f4108,f4112,f4116,f4120,f4124,f4128,f4164,f4374,f4378,f4389,f4393,f4397,f4401,f4405,f4409,f4413,f4417,f4697,f4701,f4708,f4712,f4716,f4720,f4724,f4728,f4901,f4905,f4909,f4913,f4917,f4921,f4926,f4930,f4934,f4938,f4942,f4946,f4950,f4954,f4958,f4962,f4966,f5274,f5278,f5282,f5286,f5297,f5301,f5305,f5309,f5313,f5317,f5321,f5325,f5329,f5333,f5338,f5349,f5353,f5357,f5361,f5365,f5369,f5373,f5377,f5381,f5385,f5407,f5411,f5415,f5701,f5998,f6200,f6204,f6208,f6212,f6216,f6220,f6224,f6228,f6232,f6243,f6247,f6251,f6255,f6259,f6263,f6267,f6271,f6275,f6279,f6284,f6288,f7041,f7045,f7049,f7467,f7473,f7477,f7481,f7485,f7489,f7493,f7497,f7501,f7505,f7509,f7519,f8715,f8719,f8723,f8727,f8731,f9268,f9707,f9711,f9715,f9719,f9723,f9727,f9731,f9738,f9742,f9746,f9750,f9754,f10104,f10347,f10351,f10362,f10605,f10609,f10613,f10617,f10621,f10625,f10626,f10929,f10933,f11558,f11562,f11566,f11570,f11574,f11578,f12090,f12094,f12276,f12311,f12322,f12334,f12338,f12342,f12512,f12540,f12559,f12561,f12571,f12574,f12575,f12581,f12588,f12594,f12616,f12618,f12628,f12813,f12825,f12832,f12855,f12861,f12866,f12870,f12875,f12887,f12903,f12908,f12914,f12921,f12925,f12926,f12935,f12939,f12943,f12947,f12951,f12955,f13130,f13172,f13176,f13180,f13184,f13188,f13193,f13197,f13421,f13425,f13429,f13434,f13438,f13442,f13446,f13450,f13454,f13458,f13679,f13731,f13735,f13739,f13770,f13774,f13778,f13782,f13786,f13790,f13913,f13917,f13921,f13925,f13929,f14271,f14275,f14279,f14283,f14287,f14291,f14295,f14300,f14304,f14308,f14312,f14316,f14320,f14324,f14328,f14332,f14336,f14340,f14351,f14355,f14496,f14523,f14529,f14535,f14650,f14693,f14697,f14701,f14705,f14710,f14714,f14718,f14722,f14761,f14766,f14770,f14774,f14778,f14782,f14786,f14790,f14794,f14798,f14802,f14806,f14811,f14815,f14819,f14823,f14827,f14831,f14835,f14839,f14843,f14847,f14851,f14856,f14860,f14864,f15224,f15407,f15425,f15429,f15433,f15437,f15441,f15449,f15453,f15457,f15461,f15465,f15469,f16092,f16096,f16100,f16110,f16114,f16118,f16122,f16126,f16130,f16134,f16138,f16142,f16146,f16156,f16160,f16164,f16168,f16172,f16176,f16180,f16644,f16648,f16652,f16657,f16661,f16665,f16669,f16673,f16677,f16681,f16685,f16689,f16693,f16706,f16710,f16714,f16718,f16722,f16726,f16882,f16984,f16988,f16992,f16996,f17000,f17005,f17009,f17013,f17017,f17021,f17025,f17029,f17033,f17037,f17041,f17045,f17050,f17054,f17058,f17062,f17066,f17070,f17074,f17078,f17082,f17086,f17090,f17095,f17099,f17103,f17107,f17111,f17115,f17119,f17123,f17127,f17131,f17135,f17155,f17159,f17163,f17167,f17171,f17175,f17267,f18208,f18212,f18216,f18221,f18225,f18229,f18233,f18237,f18241,f18245,f18249,f18253,f18257,f18261,f18266,f18270,f18274,f18278,f18282,f18286,f18290,f18294,f18298,f18302,f18306,f18311,f18315,f18319,f18323,f18327,f18331,f18335,f18468,f18670,f18943,f19005,f19009,f19013,f19017,f19021,f19026,f19030,f19034,f19038,f19042,f19046,f19050,f19054,f19058,f19062,f19066,f19071,f19075,f19079,f19083,f19087,f19091,f19095,f19099,f19103,f19107,f19111,f19116,f19120,f19124,f19128,f19132,f19136,f19140,f19144,f19148,f19152,f19156,f19161,f19819,f19997,f20001,f20005,f20072,f20076,f20080,f20084,f20088,f20092,f20096,f20100,f20104,f20108,f20109,f20115,f20119,f20123,f20127,f20131,f20135,f20139,f20143,f20147,f20151,f20155,f20159,f20163,f20167,f20171,f20175,f20196,f20200,f20204,f20208,f20212,f20216,f20220,f20224,f20228,f20232,f20237,f20241,f20245,f20249,f20253,f20257,f20261,f20265,f20269,f20273,f20284,f20288,f20292,f20296,f20300,f20304,f20308,f20312,f20316,f20320,f20325,f20329,f20333,f20337,f20341,f20345,f20349,f20353,f20357,f20361,f20376,f20380,f20384,f23408,f23876,f24008,f24012,f24016,f24020,f24024,f24037,f24041,f24045,f24049,f24053,f24057,f24061,f24065,f24069,f24073,f24078,f24082,f24086,f24090,f24094,f24098,f24102,f24106,f24110,f24114,f24118,f24129,f24133,f24137,f24141,f24145,f24149,f24153,f24157,f24161,f24165,f24169,f24173,f24177,f24181,f24185,f24189,f24193,f24197,f24201,f24205,f24209,f24214,f24218,f24222,f24226,f24230,f24841,f26459,f27172,f27176,f27180,f27184,f27188,f27192,f27196,f27201,f27205,f27209,f27213,f27217,f27221,f27225,f27229,f27233,f27237,f27241,f27252,f27256,f27260,f27264,f27268,f27272,f27276,f27280,f27284,f27288,f27332,f27336,f27340,f27344,f27348,f27352,f27356,f27360,f27364,f27368,f27369,f27378,f27382,f27386,f27390,f27394,f27398,f27402,f27406,f27410,f27411,f27415,f27419,f27423,f27427,f27431,f27435,f27439,f27443,f27447,f27451,f27456,f27460,f27464,f27468,f27472,f27476,f27480,f27593,f27815,f30000,f30782,f31350,f31354,f31358,f31362,f31366,f31370,f31374,f31378,f31382,f31386,f31390,f31402,f31406,f31410,f31414,f31418,f31422,f31426,f31430,f31434,f31438,f31443,f31447,f31451,f31455,f31459,f31463,f31467,f31471,f31475,f31479,f31483,f31494,f31498,f31502,f31506,f31510,f31514,f31518,f31522,f31526,f31530,f31576,f31580,f31584,f31588,f31592,f31596,f31600,f31604,f31608,f31612,f31617,f31621,f31625,f31629,f31633,f31637,f31641,f31645,f31649,f31653,f31657,f31668,f31672,f31676,f31680,f31684,f31688,f31692,f31696,f31700,f31704,f31705,f34046,f35128,f35711,f35715,f35719,f35723,f35727,f35731,f35735,f35739,f35743,f35747,f35751,f35755,f35759,f35763,f35767,f35771,f35775,f35779,f35783,f35787,f35791,f35795,f35799,f35803,f35807,f35811,f35815,f35819,f35823,f35827,f35831,f35835,f35839,f35844,f35848,f35852,f35856,f35860,f35864,f35868,f35872,f35876,f35880,f35884,f35914,f35918,f35922,f35926,f35930,f35934,f35938,f35942,f35946,f35950,f35951,f35965,f35969,f35973,f35977,f35981,f35985,f35989,f35993,f35997,f35998,f36002,f36006,f36010,f36014,f36018,f36022,f36026,f36030,f36034,f36038,f36039,f36050,f36054,f36058,f36062,f36066,f36070,f36074,f36078,f36082,f36086,f36087,f36111,f36339,f36343,f36347,f36351,f36355,f36359,f36360,f36416,f36420,f36424,f36428,f36432,f36436,f36440,f36444,f36448,f36546,f36575,f36592,f36811,f36864,f37116,f39210,f39673,f39734,f41972,f42023,f42024,f42207,f42304,f42309,f42314,f42319,f42334,f42381,f42385,f42389,f42390,f42436,f42442,f42452,f42492,f42704,f42713,f42714,f42720,f42734,f42775,f42877,f43145,f43149,f43154,f43161,f43163]) ).
fof(f43163,plain,
( spl20_181
| ~ spl20_146
| ~ spl20_162 ),
inference(avatar_split_clause,[],[f42893,f1312,f1180,f1640]) ).
fof(f1640,plain,
( spl20_181
<=> empty(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_181])]) ).
fof(f1180,plain,
( spl20_146
<=> ! [X0] :
( empty(X0)
| in(sK4(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_146])]) ).
fof(f1312,plain,
( spl20_162
<=> ! [X4] : ~ in(X4,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_162])]) ).
fof(f42893,plain,
( empty(sK1)
| ~ spl20_146
| ~ spl20_162 ),
inference(resolution,[],[f1313,f1181]) ).
fof(f1181,plain,
( ! [X0] :
( in(sK4(X0),X0)
| empty(X0) )
| ~ spl20_146 ),
inference(avatar_component_clause,[],[f1180]) ).
fof(f1313,plain,
( ! [X4] : ~ in(X4,sK1)
| ~ spl20_162 ),
inference(avatar_component_clause,[],[f1312]) ).
fof(f43161,plain,
( spl20_1127
| ~ spl20_203
| ~ spl20_533
| ~ spl20_1126 ),
inference(avatar_split_clause,[],[f43156,f43151,f14532,f2084,f43158]) ).
fof(f43158,plain,
( spl20_1127
<=> ordinal_subset(singleton(sK8),sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1127])]) ).
fof(f2084,plain,
( spl20_203
<=> singleton(sK8) = succ(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_203])]) ).
fof(f14532,plain,
( spl20_533
<=> sK2 = sK8 ),
introduced(avatar_definition,[new_symbols(naming,[spl20_533])]) ).
fof(f43151,plain,
( spl20_1126
<=> ordinal_subset(succ(sK2),sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1126])]) ).
fof(f43156,plain,
( ordinal_subset(singleton(sK8),sK8)
| ~ spl20_203
| ~ spl20_533
| ~ spl20_1126 ),
inference(forward_demodulation,[],[f43155,f2086]) ).
fof(f2086,plain,
( singleton(sK8) = succ(sK8)
| ~ spl20_203 ),
inference(avatar_component_clause,[],[f2084]) ).
fof(f43155,plain,
( ordinal_subset(succ(sK8),sK8)
| ~ spl20_533
| ~ spl20_1126 ),
inference(forward_demodulation,[],[f43153,f14534]) ).
fof(f14534,plain,
( sK2 = sK8
| ~ spl20_533 ),
inference(avatar_component_clause,[],[f14532]) ).
fof(f43153,plain,
( ordinal_subset(succ(sK2),sK8)
| ~ spl20_1126 ),
inference(avatar_component_clause,[],[f43151]) ).
fof(f43154,plain,
( spl20_1126
| ~ spl20_122
| ~ spl20_196
| ~ spl20_164
| spl20_1123 ),
inference(avatar_split_clause,[],[f42705,f42701,f1320,f2036,f1023,f43151]) ).
fof(f1023,plain,
( spl20_122
<=> ordinal(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_122])]) ).
fof(f2036,plain,
( spl20_196
<=> ordinal(succ(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_196])]) ).
fof(f1320,plain,
( spl20_164
<=> ! [X2,X1] :
( subset(X1,X2)
| ~ ordinal(X2)
| ~ ordinal(X1)
| ordinal_subset(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_164])]) ).
fof(f42701,plain,
( spl20_1123
<=> subset(sK8,succ(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1123])]) ).
fof(f42705,plain,
( ~ ordinal(succ(sK2))
| ~ ordinal(sK8)
| ordinal_subset(succ(sK2),sK8)
| ~ spl20_164
| spl20_1123 ),
inference(resolution,[],[f42703,f1321]) ).
fof(f1321,plain,
( ! [X2,X1] :
( subset(X1,X2)
| ~ ordinal(X2)
| ~ ordinal(X1)
| ordinal_subset(X2,X1) )
| ~ spl20_164 ),
inference(avatar_component_clause,[],[f1320]) ).
fof(f42703,plain,
( ~ subset(sK8,succ(sK2))
| spl20_1123 ),
inference(avatar_component_clause,[],[f42701]) ).
fof(f43149,plain,
( ~ spl20_698
| spl20_176
| ~ spl20_203
| ~ spl20_533 ),
inference(avatar_split_clause,[],[f43148,f14532,f2084,f1447,f18465]) ).
fof(f18465,plain,
( spl20_698
<=> element(sK1,singleton(sK8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_698])]) ).
fof(f1447,plain,
( spl20_176
<=> element(sK1,succ(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_176])]) ).
fof(f43148,plain,
( ~ element(sK1,singleton(sK8))
| spl20_176
| ~ spl20_203
| ~ spl20_533 ),
inference(forward_demodulation,[],[f43147,f2086]) ).
fof(f43147,plain,
( ~ element(sK1,succ(sK8))
| spl20_176
| ~ spl20_533 ),
inference(forward_demodulation,[],[f1448,f14534]) ).
fof(f1448,plain,
( ~ element(sK1,succ(sK2))
| spl20_176 ),
inference(avatar_component_clause,[],[f1447]) ).
fof(f43145,plain,
( spl20_3
| spl20_461
| ~ spl20_89
| ~ spl20_176 ),
inference(avatar_split_clause,[],[f12589,f1447,f776,f12807,f270]) ).
fof(f270,plain,
( spl20_3
<=> in(sK1,succ(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_3])]) ).
fof(f12807,plain,
( spl20_461
<=> empty(succ(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_461])]) ).
fof(f776,plain,
( spl20_89
<=> ! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_89])]) ).
fof(f12589,plain,
( empty(succ(sK2))
| in(sK1,succ(sK2))
| ~ spl20_89
| ~ spl20_176 ),
inference(resolution,[],[f1449,f777]) ).
fof(f777,plain,
( ! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) )
| ~ spl20_89 ),
inference(avatar_component_clause,[],[f776]) ).
fof(f1449,plain,
( element(sK1,succ(sK2))
| ~ spl20_176 ),
inference(avatar_component_clause,[],[f1447]) ).
fof(f42877,plain,
( ~ spl20_181
| ~ spl20_68
| ~ spl20_277 ),
inference(avatar_split_clause,[],[f10358,f3477,f613,f1640]) ).
fof(f613,plain,
( spl20_68
<=> ! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_68])]) ).
fof(f3477,plain,
( spl20_277
<=> in(succ(sK2),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_277])]) ).
fof(f10358,plain,
( ~ empty(sK1)
| ~ spl20_68
| ~ spl20_277 ),
inference(resolution,[],[f3479,f614]) ).
fof(f614,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) )
| ~ spl20_68 ),
inference(avatar_component_clause,[],[f613]) ).
fof(f3479,plain,
( in(succ(sK2),sK1)
| ~ spl20_277 ),
inference(avatar_component_clause,[],[f3477]) ).
fof(f42775,plain,
( ~ spl20_14
| ~ spl20_49
| ~ spl20_1125 ),
inference(avatar_split_clause,[],[f42750,f42731,f499,f324]) ).
fof(f324,plain,
( spl20_14
<=> empty(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_14])]) ).
fof(f499,plain,
( spl20_49
<=> ! [X0] : ~ empty(succ(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_49])]) ).
fof(f42731,plain,
( spl20_1125
<=> succ(sK2) = sK8 ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1125])]) ).
fof(f42750,plain,
( ~ empty(sK8)
| ~ spl20_49
| ~ spl20_1125 ),
inference(superposition,[],[f500,f42733]) ).
fof(f42733,plain,
( succ(sK2) = sK8
| ~ spl20_1125 ),
inference(avatar_component_clause,[],[f42731]) ).
fof(f500,plain,
( ! [X0] : ~ empty(succ(X0))
| ~ spl20_49 ),
inference(avatar_component_clause,[],[f499]) ).
fof(f42734,plain,
( ~ spl20_196
| spl20_1125
| ~ spl20_122
| ~ spl20_14
| spl20_3
| ~ spl20_166
| ~ spl20_297 ),
inference(avatar_split_clause,[],[f42688,f3590,f1355,f270,f324,f1023,f42731,f2036]) ).
fof(f1355,plain,
( spl20_166
<=> ! [X6,X7] :
( in(X7,X6)
| X6 = X7
| ~ ordinal(X6)
| ~ ordinal(X7)
| ~ empty(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_166])]) ).
fof(f3590,plain,
( spl20_297
<=> sK1 = sK8 ),
introduced(avatar_definition,[new_symbols(naming,[spl20_297])]) ).
fof(f42688,plain,
( ~ empty(sK8)
| ~ ordinal(sK8)
| succ(sK2) = sK8
| ~ ordinal(succ(sK2))
| spl20_3
| ~ spl20_166
| ~ spl20_297 ),
inference(forward_demodulation,[],[f42687,f3592]) ).
fof(f3592,plain,
( sK1 = sK8
| ~ spl20_297 ),
inference(avatar_component_clause,[],[f3590]) ).
fof(f42687,plain,
( ~ ordinal(sK8)
| succ(sK2) = sK8
| ~ ordinal(succ(sK2))
| ~ empty(sK1)
| spl20_3
| ~ spl20_166
| ~ spl20_297 ),
inference(forward_demodulation,[],[f42686,f3592]) ).
fof(f42686,plain,
( succ(sK2) = sK8
| ~ ordinal(succ(sK2))
| ~ ordinal(sK1)
| ~ empty(sK1)
| spl20_3
| ~ spl20_166
| ~ spl20_297 ),
inference(forward_demodulation,[],[f1367,f3592]) ).
fof(f1367,plain,
( sK1 = succ(sK2)
| ~ ordinal(succ(sK2))
| ~ ordinal(sK1)
| ~ empty(sK1)
| spl20_3
| ~ spl20_166 ),
inference(resolution,[],[f1356,f271]) ).
fof(f271,plain,
( ~ in(sK1,succ(sK2))
| spl20_3 ),
inference(avatar_component_clause,[],[f270]) ).
fof(f1356,plain,
( ! [X6,X7] :
( in(X7,X6)
| X6 = X7
| ~ ordinal(X6)
| ~ ordinal(X7)
| ~ empty(X7) )
| ~ spl20_166 ),
inference(avatar_component_clause,[],[f1355]) ).
fof(f42720,plain,
( spl20_461
| spl20_1124
| ~ spl20_89
| ~ spl20_176
| ~ spl20_297 ),
inference(avatar_split_clause,[],[f42499,f3590,f1447,f776,f42717,f12807]) ).
fof(f42717,plain,
( spl20_1124
<=> in(sK8,succ(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1124])]) ).
fof(f42499,plain,
( in(sK8,succ(sK2))
| empty(succ(sK2))
| ~ spl20_89
| ~ spl20_176
| ~ spl20_297 ),
inference(forward_demodulation,[],[f12589,f3592]) ).
fof(f42714,plain,
( spl20_175
| ~ spl20_105
| ~ spl20_160 ),
inference(avatar_split_clause,[],[f1305,f1291,f894,f1436]) ).
fof(f1436,plain,
( spl20_175
<=> ! [X4] :
( ~ in(X4,sK1)
| element(X4,sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_175])]) ).
fof(f894,plain,
( spl20_105
<=> subset(sK1,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_105])]) ).
fof(f1291,plain,
( spl20_160
<=> ! [X2,X4,X3] :
( element(X2,X3)
| ~ in(X2,X4)
| ~ subset(X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_160])]) ).
fof(f1305,plain,
( ! [X4] :
( ~ in(X4,sK1)
| element(X4,sK2) )
| ~ spl20_105
| ~ spl20_160 ),
inference(resolution,[],[f1292,f896]) ).
fof(f896,plain,
( subset(sK1,sK2)
| ~ spl20_105 ),
inference(avatar_component_clause,[],[f894]) ).
fof(f1292,plain,
( ! [X2,X3,X4] :
( ~ subset(X4,X3)
| ~ in(X2,X4)
| element(X2,X3) )
| ~ spl20_160 ),
inference(avatar_component_clause,[],[f1291]) ).
fof(f42713,plain,
( ~ spl20_120
| spl20_121
| ~ spl20_91
| ~ spl20_105 ),
inference(avatar_split_clause,[],[f939,f894,f811,f1018,f1014]) ).
fof(f1014,plain,
( spl20_120
<=> subset(sK2,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_120])]) ).
fof(f1018,plain,
( spl20_121
<=> sK1 = sK2 ),
introduced(avatar_definition,[new_symbols(naming,[spl20_121])]) ).
fof(f811,plain,
( spl20_91
<=> ! [X0,X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_91])]) ).
fof(f939,plain,
( sK1 = sK2
| ~ subset(sK2,sK1)
| ~ spl20_91
| ~ spl20_105 ),
inference(resolution,[],[f896,f812]) ).
fof(f812,plain,
( ! [X0,X1] :
( ~ subset(X1,X0)
| X0 = X1
| ~ subset(X0,X1) )
| ~ spl20_91 ),
inference(avatar_component_clause,[],[f811]) ).
fof(f42704,plain,
( ~ spl20_1123
| ~ spl20_297
| spl20_458 ),
inference(avatar_split_clause,[],[f42511,f12591,f3590,f42701]) ).
fof(f12591,plain,
( spl20_458
<=> subset(sK1,succ(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_458])]) ).
fof(f42511,plain,
( ~ subset(sK8,succ(sK2))
| ~ spl20_297
| spl20_458 ),
inference(forward_demodulation,[],[f12592,f3592]) ).
fof(f12592,plain,
( ~ subset(sK1,succ(sK2))
| spl20_458 ),
inference(avatar_component_clause,[],[f12591]) ).
fof(f42492,plain,
( ~ spl20_3
| ~ spl20_4 ),
inference(avatar_split_clause,[],[f147,f274,f270]) ).
fof(f274,plain,
( spl20_4
<=> ordinal_subset(sK1,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_4])]) ).
fof(f147,plain,
( ~ ordinal_subset(sK1,sK2)
| ~ in(sK1,succ(sK2)) ),
inference(cnf_transformation,[],[f97]) ).
fof(f97,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])],[f94,f96,f95]) ).
fof(f95,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(f96,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(f94,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,[],[f93]) ).
fof(f93,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,[],[f58]) ).
fof(f58,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/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',t34_ordinal1) ).
fof(f42452,plain,
( ~ spl20_52
| spl20_1122 ),
inference(avatar_contradiction_clause,[],[f42443]) ).
fof(f42443,plain,
( $false
| ~ spl20_52
| spl20_1122 ),
inference(resolution,[],[f42441,f512]) ).
fof(f512,plain,
( ! [X0] : in(X0,succ(X0))
| ~ spl20_52 ),
inference(avatar_component_clause,[],[f511]) ).
fof(f511,plain,
( spl20_52
<=> ! [X0] : in(X0,succ(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_52])]) ).
fof(f42441,plain,
( ~ in(sK1,succ(sK1))
| spl20_1122 ),
inference(avatar_component_clause,[],[f42439]) ).
fof(f42439,plain,
( spl20_1122
<=> in(sK1,succ(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1122])]) ).
fof(f42442,plain,
( ~ spl20_1113
| ~ spl20_1122
| ~ spl20_121 ),
inference(avatar_split_clause,[],[f42392,f1018,f42439,f42020]) ).
fof(f42020,plain,
( spl20_1113
<=> ordinal_subset(sK1,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1113])]) ).
fof(f42392,plain,
( ~ in(sK1,succ(sK1))
| ~ ordinal_subset(sK1,sK1)
| ~ spl20_121 ),
inference(forward_demodulation,[],[f42391,f1020]) ).
fof(f1020,plain,
( sK1 = sK2
| ~ spl20_121 ),
inference(avatar_component_clause,[],[f1018]) ).
fof(f42391,plain,
( ~ ordinal_subset(sK1,sK1)
| ~ in(sK1,succ(sK2))
| ~ spl20_121 ),
inference(forward_demodulation,[],[f147,f1020]) ).
fof(f42436,plain,
( ~ spl20_1113
| ~ spl20_121
| spl20_456 ),
inference(avatar_split_clause,[],[f42209,f12556,f1018,f42020]) ).
fof(f12556,plain,
( spl20_456
<=> ordinal_subset(sK2,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_456])]) ).
fof(f42209,plain,
( ~ ordinal_subset(sK1,sK1)
| ~ spl20_121
| spl20_456 ),
inference(forward_demodulation,[],[f12557,f1020]) ).
fof(f12557,plain,
( ~ ordinal_subset(sK2,sK1)
| spl20_456 ),
inference(avatar_component_clause,[],[f12556]) ).
fof(f42390,plain,
( ~ spl20_1
| ~ spl20_82
| spl20_1113 ),
inference(avatar_split_clause,[],[f42210,f42020,f696,f260]) ).
fof(f260,plain,
( spl20_1
<=> ordinal(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1])]) ).
fof(f696,plain,
( spl20_82
<=> ! [X0] :
( ordinal_subset(X0,X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_82])]) ).
fof(f42210,plain,
( ~ ordinal(sK1)
| ~ spl20_82
| spl20_1113 ),
inference(resolution,[],[f42022,f697]) ).
fof(f697,plain,
( ! [X0] :
( ordinal_subset(X0,X0)
| ~ ordinal(X0) )
| ~ spl20_82 ),
inference(avatar_component_clause,[],[f696]) ).
fof(f42022,plain,
( ~ ordinal_subset(sK1,sK1)
| spl20_1113 ),
inference(avatar_component_clause,[],[f42020]) ).
fof(f42389,plain,
( spl20_1121
| ~ spl20_231
| ~ spl20_251 ),
inference(avatar_split_clause,[],[f2888,f2820,f2402,f42387]) ).
fof(f42387,plain,
( spl20_1121
<=> ! [X31,X33,X30,X32] :
( sP0(X30,X31,set_union2(X32,X33))
| ~ empty(X31)
| ~ empty(X30)
| in(sK6(X30,X31,set_union2(X32,X33)),X32)
| in(sK6(X30,X31,set_union2(X32,X33)),X33) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1121])]) ).
fof(f2402,plain,
( spl20_231
<=> ! [X2,X0,X1] :
( in(X0,X1)
| ~ in(X0,set_union2(X1,X2))
| in(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_231])]) ).
fof(f2820,plain,
( spl20_251
<=> ! [X13,X14,X15] :
( in(sK6(X13,X14,X15),X15)
| sP0(X13,X14,X15)
| ~ empty(X14)
| ~ empty(X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_251])]) ).
fof(f2888,plain,
( ! [X31,X32,X30,X33] :
( sP0(X30,X31,set_union2(X32,X33))
| ~ empty(X31)
| ~ empty(X30)
| in(sK6(X30,X31,set_union2(X32,X33)),X32)
| in(sK6(X30,X31,set_union2(X32,X33)),X33) )
| ~ spl20_231
| ~ spl20_251 ),
inference(resolution,[],[f2821,f2403]) ).
fof(f2403,plain,
( ! [X2,X0,X1] :
( ~ in(X0,set_union2(X1,X2))
| in(X0,X1)
| in(X0,X2) )
| ~ spl20_231 ),
inference(avatar_component_clause,[],[f2402]) ).
fof(f2821,plain,
( ! [X14,X15,X13] :
( in(sK6(X13,X14,X15),X15)
| sP0(X13,X14,X15)
| ~ empty(X14)
| ~ empty(X13) )
| ~ spl20_251 ),
inference(avatar_component_clause,[],[f2820]) ).
fof(f42385,plain,
( spl20_1120
| ~ spl20_231
| ~ spl20_250 ),
inference(avatar_split_clause,[],[f2867,f2816,f2402,f42383]) ).
fof(f42383,plain,
( spl20_1120
<=> ! [X31,X29,X32,X30] :
( sP0(X29,set_union2(X30,X31),X32)
| ~ empty(X32)
| ~ empty(X29)
| in(sK6(X29,set_union2(X30,X31),X32),X30)
| in(sK6(X29,set_union2(X30,X31),X32),X31) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1120])]) ).
fof(f2816,plain,
( spl20_250
<=> ! [X13,X14,X15] :
( in(sK6(X13,X14,X15),X14)
| sP0(X13,X14,X15)
| ~ empty(X15)
| ~ empty(X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_250])]) ).
fof(f2867,plain,
( ! [X31,X29,X32,X30] :
( sP0(X29,set_union2(X30,X31),X32)
| ~ empty(X32)
| ~ empty(X29)
| in(sK6(X29,set_union2(X30,X31),X32),X30)
| in(sK6(X29,set_union2(X30,X31),X32),X31) )
| ~ spl20_231
| ~ spl20_250 ),
inference(resolution,[],[f2817,f2403]) ).
fof(f2817,plain,
( ! [X14,X15,X13] :
( in(sK6(X13,X14,X15),X14)
| sP0(X13,X14,X15)
| ~ empty(X15)
| ~ empty(X13) )
| ~ spl20_250 ),
inference(avatar_component_clause,[],[f2816]) ).
fof(f42381,plain,
( spl20_1119
| ~ spl20_231
| ~ spl20_249 ),
inference(avatar_split_clause,[],[f2846,f2812,f2402,f42379]) ).
fof(f42379,plain,
( spl20_1119
<=> ! [X31,X29,X32,X30] :
( sP0(set_union2(X29,X30),X31,X32)
| ~ empty(X32)
| ~ empty(X31)
| in(sK6(set_union2(X29,X30),X31,X32),X29)
| in(sK6(set_union2(X29,X30),X31,X32),X30) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1119])]) ).
fof(f2812,plain,
( spl20_249
<=> ! [X13,X14,X15] :
( in(sK6(X13,X14,X15),X13)
| sP0(X13,X14,X15)
| ~ empty(X15)
| ~ empty(X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_249])]) ).
fof(f2846,plain,
( ! [X31,X29,X32,X30] :
( sP0(set_union2(X29,X30),X31,X32)
| ~ empty(X32)
| ~ empty(X31)
| in(sK6(set_union2(X29,X30),X31,X32),X29)
| in(sK6(set_union2(X29,X30),X31,X32),X30) )
| ~ spl20_231
| ~ spl20_249 ),
inference(resolution,[],[f2813,f2403]) ).
fof(f2813,plain,
( ! [X14,X15,X13] :
( in(sK6(X13,X14,X15),X13)
| sP0(X13,X14,X15)
| ~ empty(X15)
| ~ empty(X14) )
| ~ spl20_249 ),
inference(avatar_component_clause,[],[f2812]) ).
fof(f42334,plain,
( spl20_1118
| ~ spl20_121
| ~ spl20_532 ),
inference(avatar_split_clause,[],[f42009,f14526,f1018,f42331]) ).
fof(f42331,plain,
( spl20_1118
<=> relation(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1118])]) ).
fof(f14526,plain,
( spl20_532
<=> relation(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_532])]) ).
fof(f42009,plain,
( relation(sK1)
| ~ spl20_121
| ~ spl20_532 ),
inference(superposition,[],[f14528,f1020]) ).
fof(f14528,plain,
( relation(sK2)
| ~ spl20_532 ),
inference(avatar_component_clause,[],[f14526]) ).
fof(f42319,plain,
( spl20_1117
| ~ spl20_121
| ~ spl20_460 ),
inference(avatar_split_clause,[],[f42001,f12625,f1018,f42316]) ).
fof(f42316,plain,
( spl20_1117
<=> ordinal_subset(sK1,succ(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1117])]) ).
fof(f12625,plain,
( spl20_460
<=> ordinal_subset(sK1,succ(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_460])]) ).
fof(f42001,plain,
( ordinal_subset(sK1,succ(sK1))
| ~ spl20_121
| ~ spl20_460 ),
inference(superposition,[],[f12627,f1020]) ).
fof(f12627,plain,
( ordinal_subset(sK1,succ(sK2))
| ~ spl20_460 ),
inference(avatar_component_clause,[],[f12625]) ).
fof(f42314,plain,
( spl20_1116
| ~ spl20_121
| ~ spl20_458 ),
inference(avatar_split_clause,[],[f41999,f12591,f1018,f42311]) ).
fof(f42311,plain,
( spl20_1116
<=> subset(sK1,succ(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1116])]) ).
fof(f41999,plain,
( subset(sK1,succ(sK1))
| ~ spl20_121
| ~ spl20_458 ),
inference(superposition,[],[f12593,f1020]) ).
fof(f12593,plain,
( subset(sK1,succ(sK2))
| ~ spl20_458 ),
inference(avatar_component_clause,[],[f12591]) ).
fof(f42309,plain,
( ~ spl20_1115
| ~ spl20_121
| spl20_205 ),
inference(avatar_split_clause,[],[f41986,f2118,f1018,f42306]) ).
fof(f42306,plain,
( spl20_1115
<=> subset(succ(sK1),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1115])]) ).
fof(f2118,plain,
( spl20_205
<=> subset(succ(sK2),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_205])]) ).
fof(f41986,plain,
( ~ subset(succ(sK1),sK1)
| ~ spl20_121
| spl20_205 ),
inference(superposition,[],[f2119,f1020]) ).
fof(f2119,plain,
( ~ subset(succ(sK2),sK1)
| spl20_205 ),
inference(avatar_component_clause,[],[f2118]) ).
fof(f42304,plain,
( ~ spl20_1114
| ~ spl20_121
| spl20_195 ),
inference(avatar_split_clause,[],[f41983,f2032,f1018,f42301]) ).
fof(f42301,plain,
( spl20_1114
<=> element(succ(sK1),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1114])]) ).
fof(f2032,plain,
( spl20_195
<=> element(succ(sK2),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_195])]) ).
fof(f41983,plain,
( ~ element(succ(sK1),sK1)
| ~ spl20_121
| spl20_195 ),
inference(superposition,[],[f2033,f1020]) ).
fof(f2033,plain,
( ~ element(succ(sK2),sK1)
| spl20_195 ),
inference(avatar_component_clause,[],[f2032]) ).
fof(f42207,plain,
( spl20_1113
| ~ spl20_121
| ~ spl20_456 ),
inference(avatar_split_clause,[],[f41997,f12556,f1018,f42020]) ).
fof(f41997,plain,
( ordinal_subset(sK1,sK1)
| ~ spl20_121
| ~ spl20_456 ),
inference(superposition,[],[f12558,f1020]) ).
fof(f12558,plain,
( ordinal_subset(sK2,sK1)
| ~ spl20_456 ),
inference(avatar_component_clause,[],[f12556]) ).
fof(f42024,plain,
( ~ spl20_452
| spl20_105
| ~ spl20_121 ),
inference(avatar_split_clause,[],[f41978,f1018,f894,f12308]) ).
fof(f12308,plain,
( spl20_452
<=> subset(sK1,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_452])]) ).
fof(f41978,plain,
( ~ subset(sK1,sK1)
| spl20_105
| ~ spl20_121 ),
inference(superposition,[],[f895,f1020]) ).
fof(f895,plain,
( ~ subset(sK1,sK2)
| spl20_105 ),
inference(avatar_component_clause,[],[f894]) ).
fof(f42023,plain,
( ~ spl20_1113
| spl20_4
| ~ spl20_121 ),
inference(avatar_split_clause,[],[f41975,f1018,f274,f42020]) ).
fof(f41975,plain,
( ~ ordinal_subset(sK1,sK1)
| spl20_4
| ~ spl20_121 ),
inference(superposition,[],[f275,f1020]) ).
fof(f275,plain,
( ~ ordinal_subset(sK1,sK2)
| spl20_4 ),
inference(avatar_component_clause,[],[f274]) ).
fof(f41972,plain,
( spl20_121
| ~ spl20_153
| ~ spl20_1043 ),
inference(avatar_split_clause,[],[f35889,f35841,f1230,f1018]) ).
fof(f1230,plain,
( spl20_153
<=> ! [X0,X1] :
( ~ in(X0,singleton(X1))
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_153])]) ).
fof(f35841,plain,
( spl20_1043
<=> in(sK1,singleton(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1043])]) ).
fof(f35889,plain,
( sK1 = sK2
| ~ spl20_153
| ~ spl20_1043 ),
inference(resolution,[],[f35843,f1231]) ).
fof(f1231,plain,
( ! [X0,X1] :
( ~ in(X0,singleton(X1))
| X0 = X1 )
| ~ spl20_153 ),
inference(avatar_component_clause,[],[f1230]) ).
fof(f35843,plain,
( in(sK1,singleton(sK2))
| ~ spl20_1043 ),
inference(avatar_component_clause,[],[f35841]) ).
fof(f39734,plain,
( spl20_228
| ~ spl20_121
| ~ spl20_312 ),
inference(avatar_split_clause,[],[f12530,f4161,f1018,f2330]) ).
fof(f2330,plain,
( spl20_228
<=> element(sK1,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_228])]) ).
fof(f4161,plain,
( spl20_312
<=> element(sK2,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_312])]) ).
fof(f12530,plain,
( element(sK1,sK1)
| ~ spl20_121
| ~ spl20_312 ),
inference(superposition,[],[f4163,f1020]) ).
fof(f4163,plain,
( element(sK2,sK1)
| ~ spl20_312 ),
inference(avatar_component_clause,[],[f4161]) ).
fof(f39673,plain,
( spl20_1112
| ~ spl20_121
| ~ spl20_219 ),
inference(avatar_split_clause,[],[f12526,f2282,f1018,f39670]) ).
fof(f39670,plain,
( spl20_1112
<=> epsilon_transitive(succ(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1112])]) ).
fof(f2282,plain,
( spl20_219
<=> epsilon_transitive(succ(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_219])]) ).
fof(f12526,plain,
( epsilon_transitive(succ(sK1))
| ~ spl20_121
| ~ spl20_219 ),
inference(superposition,[],[f2284,f1020]) ).
fof(f2284,plain,
( epsilon_transitive(succ(sK2))
| ~ spl20_219 ),
inference(avatar_component_clause,[],[f2282]) ).
fof(f39210,plain,
( spl20_1111
| ~ spl20_121
| ~ spl20_215 ),
inference(avatar_split_clause,[],[f12525,f2212,f1018,f39207]) ).
fof(f39207,plain,
( spl20_1111
<=> epsilon_connected(succ(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1111])]) ).
fof(f2212,plain,
( spl20_215
<=> epsilon_connected(succ(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_215])]) ).
fof(f12525,plain,
( epsilon_connected(succ(sK1))
| ~ spl20_121
| ~ spl20_215 ),
inference(superposition,[],[f2214,f1020]) ).
fof(f2214,plain,
( epsilon_connected(succ(sK2))
| ~ spl20_215 ),
inference(avatar_component_clause,[],[f2212]) ).
fof(f37116,plain,
( ~ spl20_181
| ~ spl20_68
| ~ spl20_935 ),
inference(avatar_split_clause,[],[f31391,f31347,f613,f1640]) ).
fof(f31347,plain,
( spl20_935
<=> in(sK4(sK2),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_935])]) ).
fof(f31391,plain,
( ~ empty(sK1)
| ~ spl20_68
| ~ spl20_935 ),
inference(resolution,[],[f31349,f614]) ).
fof(f31349,plain,
( in(sK4(sK2),sK1)
| ~ spl20_935 ),
inference(avatar_component_clause,[],[f31347]) ).
fof(f36864,plain,
( spl20_1110
| ~ spl20_121
| ~ spl20_196 ),
inference(avatar_split_clause,[],[f12523,f2036,f1018,f36861]) ).
fof(f36861,plain,
( spl20_1110
<=> ordinal(succ(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1110])]) ).
fof(f12523,plain,
( ordinal(succ(sK1))
| ~ spl20_121
| ~ spl20_196 ),
inference(superposition,[],[f2037,f1020]) ).
fof(f2037,plain,
( ordinal(succ(sK2))
| ~ spl20_196 ),
inference(avatar_component_clause,[],[f2036]) ).
fof(f36811,plain,
( ~ spl20_304
| ~ spl20_1109 ),
inference(avatar_contradiction_clause,[],[f36602]) ).
fof(f36602,plain,
( $false
| ~ spl20_304
| ~ spl20_1109 ),
inference(resolution,[],[f36591,f4070]) ).
fof(f4070,plain,
( in(sK1,sK2)
| ~ spl20_304 ),
inference(avatar_component_clause,[],[f4069]) ).
fof(f4069,plain,
( spl20_304
<=> in(sK1,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_304])]) ).
fof(f36591,plain,
( ! [X1] : ~ in(X1,sK2)
| ~ spl20_1109 ),
inference(avatar_component_clause,[],[f36590]) ).
fof(f36590,plain,
( spl20_1109
<=> ! [X1] : ~ in(X1,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1109])]) ).
fof(f36592,plain,
( spl20_1109
| ~ spl20_14
| ~ spl20_120
| ~ spl20_156
| ~ spl20_297 ),
inference(avatar_split_clause,[],[f36408,f3590,f1263,f1014,f324,f36590]) ).
fof(f1263,plain,
( spl20_156
<=> ! [X2,X3,X4] :
( ~ empty(X2)
| ~ in(X3,X4)
| ~ subset(X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_156])]) ).
fof(f36408,plain,
( ! [X1] :
( ~ empty(sK8)
| ~ in(X1,sK2) )
| ~ spl20_120
| ~ spl20_156
| ~ spl20_297 ),
inference(forward_demodulation,[],[f12563,f3592]) ).
fof(f12563,plain,
( ! [X1] :
( ~ in(X1,sK2)
| ~ empty(sK1) )
| ~ spl20_120
| ~ spl20_156 ),
inference(resolution,[],[f1015,f1264]) ).
fof(f1264,plain,
( ! [X2,X3,X4] :
( ~ subset(X4,X2)
| ~ in(X3,X4)
| ~ empty(X2) )
| ~ spl20_156 ),
inference(avatar_component_clause,[],[f1263]) ).
fof(f1015,plain,
( subset(sK2,sK1)
| ~ spl20_120 ),
inference(avatar_component_clause,[],[f1014]) ).
fof(f36575,plain,
( ~ spl20_1108
| spl20_182
| ~ spl20_297 ),
inference(avatar_split_clause,[],[f36570,f3590,f1644,f36572]) ).
fof(f36572,plain,
( spl20_1108
<=> element(sK4(sK8),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1108])]) ).
fof(f1644,plain,
( spl20_182
<=> element(sK4(sK1),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_182])]) ).
fof(f36570,plain,
( ~ element(sK4(sK8),sK2)
| spl20_182
| ~ spl20_297 ),
inference(forward_demodulation,[],[f1645,f3592]) ).
fof(f1645,plain,
( ~ element(sK4(sK1),sK2)
| spl20_182 ),
inference(avatar_component_clause,[],[f1644]) ).
fof(f36546,plain,
( ~ spl20_14
| ~ spl20_68
| ~ spl20_297
| ~ spl20_867 ),
inference(avatar_split_clause,[],[f36393,f26456,f3590,f613,f324]) ).
fof(f26456,plain,
( spl20_867
<=> in(sK4(sK1),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_867])]) ).
fof(f36393,plain,
( ~ empty(sK8)
| ~ spl20_68
| ~ spl20_297
| ~ spl20_867 ),
inference(forward_demodulation,[],[f26939,f3592]) ).
fof(f26939,plain,
( ~ empty(sK1)
| ~ spl20_68
| ~ spl20_867 ),
inference(resolution,[],[f26458,f614]) ).
fof(f26458,plain,
( in(sK4(sK1),sK1)
| ~ spl20_867 ),
inference(avatar_component_clause,[],[f26456]) ).
fof(f36448,plain,
( spl20_1107
| ~ spl20_223
| ~ spl20_369 ),
inference(avatar_split_clause,[],[f6139,f5371,f2310,f36446]) ).
fof(f36446,plain,
( spl20_1107
<=> ! [X44,X43,X42] :
( element(sK6(X42,sK4(powerset(X43)),sK3(powerset(X44))),X42)
| sP0(X42,sK4(powerset(X43)),sK3(powerset(X44)))
| ~ empty(X43)
| ~ empty(X44)
| epsilon_transitive(powerset(X44)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1107])]) ).
fof(f2310,plain,
( spl20_223
<=> ! [X2,X3] :
( epsilon_transitive(powerset(X2))
| ~ empty(X2)
| ~ in(X3,sK3(powerset(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_223])]) ).
fof(f5371,plain,
( spl20_369
<=> ! [X25,X24,X26] :
( element(sK6(X24,sK4(powerset(X25)),X26),X24)
| in(sK6(X24,sK4(powerset(X25)),X26),X26)
| sP0(X24,sK4(powerset(X25)),X26)
| ~ empty(X25) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_369])]) ).
fof(f6139,plain,
( ! [X44,X42,X43] :
( element(sK6(X42,sK4(powerset(X43)),sK3(powerset(X44))),X42)
| sP0(X42,sK4(powerset(X43)),sK3(powerset(X44)))
| ~ empty(X43)
| ~ empty(X44)
| epsilon_transitive(powerset(X44)) )
| ~ spl20_223
| ~ spl20_369 ),
inference(resolution,[],[f5372,f2311]) ).
fof(f2311,plain,
( ! [X2,X3] :
( ~ in(X3,sK3(powerset(X2)))
| ~ empty(X2)
| epsilon_transitive(powerset(X2)) )
| ~ spl20_223 ),
inference(avatar_component_clause,[],[f2310]) ).
fof(f5372,plain,
( ! [X26,X24,X25] :
( element(sK6(X24,sK4(powerset(X25)),X26),X24)
| in(sK6(X24,sK4(powerset(X25)),X26),X26)
| sP0(X24,sK4(powerset(X25)),X26)
| ~ empty(X25) )
| ~ spl20_369 ),
inference(avatar_component_clause,[],[f5371]) ).
fof(f36444,plain,
( spl20_1106
| ~ spl20_234
| ~ spl20_369 ),
inference(avatar_split_clause,[],[f6130,f5371,f2500,f36442]) ).
fof(f36442,plain,
( spl20_1106
<=> ! [X17,X14,X16,X15] :
( element(sK6(X14,sK4(powerset(X15)),X16),X14)
| sP0(X14,sK4(powerset(X15)),X16)
| ~ empty(X15)
| ~ ordinal(X16)
| ordinal_subset(X17,X16)
| ~ ordinal(X17)
| ~ empty(X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1106])]) ).
fof(f2500,plain,
( spl20_234
<=> ! [X6,X4,X5] :
( ~ ordinal(X4)
| ~ ordinal(X5)
| ordinal_subset(X4,X5)
| ~ in(X6,X5)
| ~ empty(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_234])]) ).
fof(f6130,plain,
( ! [X16,X14,X17,X15] :
( element(sK6(X14,sK4(powerset(X15)),X16),X14)
| sP0(X14,sK4(powerset(X15)),X16)
| ~ empty(X15)
| ~ ordinal(X16)
| ordinal_subset(X17,X16)
| ~ ordinal(X17)
| ~ empty(X17) )
| ~ spl20_234
| ~ spl20_369 ),
inference(resolution,[],[f5372,f2501]) ).
fof(f2501,plain,
( ! [X6,X4,X5] :
( ~ in(X6,X5)
| ~ ordinal(X5)
| ordinal_subset(X4,X5)
| ~ ordinal(X4)
| ~ empty(X4) )
| ~ spl20_234 ),
inference(avatar_component_clause,[],[f2500]) ).
fof(f36440,plain,
( spl20_1105
| ~ spl20_223
| ~ spl20_367 ),
inference(avatar_split_clause,[],[f6077,f5363,f2310,f36438]) ).
fof(f36438,plain,
( spl20_1105
<=> ! [X41,X43,X42] :
( element(sK6(X41,sK3(powerset(X42)),sK4(powerset(X43))),X41)
| sP0(X41,sK3(powerset(X42)),sK4(powerset(X43)))
| ~ empty(X43)
| ~ empty(X42)
| epsilon_transitive(powerset(X42)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1105])]) ).
fof(f5363,plain,
( spl20_367
<=> ! [X27,X28,X26] :
( element(sK6(X26,X27,sK4(powerset(X28))),X26)
| in(sK6(X26,X27,sK4(powerset(X28))),X27)
| sP0(X26,X27,sK4(powerset(X28)))
| ~ empty(X28) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_367])]) ).
fof(f6077,plain,
( ! [X41,X42,X43] :
( element(sK6(X41,sK3(powerset(X42)),sK4(powerset(X43))),X41)
| sP0(X41,sK3(powerset(X42)),sK4(powerset(X43)))
| ~ empty(X43)
| ~ empty(X42)
| epsilon_transitive(powerset(X42)) )
| ~ spl20_223
| ~ spl20_367 ),
inference(resolution,[],[f5364,f2311]) ).
fof(f5364,plain,
( ! [X28,X26,X27] :
( element(sK6(X26,X27,sK4(powerset(X28))),X26)
| in(sK6(X26,X27,sK4(powerset(X28))),X27)
| sP0(X26,X27,sK4(powerset(X28)))
| ~ empty(X28) )
| ~ spl20_367 ),
inference(avatar_component_clause,[],[f5363]) ).
fof(f36436,plain,
( spl20_1104
| ~ spl20_234
| ~ spl20_367 ),
inference(avatar_split_clause,[],[f6068,f5363,f2500,f36434]) ).
fof(f36434,plain,
( spl20_1104
<=> ! [X13,X14,X16,X15] :
( element(sK6(X13,X14,sK4(powerset(X15))),X13)
| sP0(X13,X14,sK4(powerset(X15)))
| ~ empty(X15)
| ~ ordinal(X14)
| ordinal_subset(X16,X14)
| ~ ordinal(X16)
| ~ empty(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1104])]) ).
fof(f6068,plain,
( ! [X16,X14,X15,X13] :
( element(sK6(X13,X14,sK4(powerset(X15))),X13)
| sP0(X13,X14,sK4(powerset(X15)))
| ~ empty(X15)
| ~ ordinal(X14)
| ordinal_subset(X16,X14)
| ~ ordinal(X16)
| ~ empty(X16) )
| ~ spl20_234
| ~ spl20_367 ),
inference(resolution,[],[f5364,f2501]) ).
fof(f36432,plain,
( spl20_1103
| ~ spl20_223
| ~ spl20_365 ),
inference(avatar_split_clause,[],[f6017,f5355,f2310,f36430]) ).
fof(f36430,plain,
( spl20_1103
<=> ! [X43,X44,X42] :
( element(sK6(sK4(powerset(X42)),X43,sK3(powerset(X44))),X43)
| sP0(sK4(powerset(X42)),X43,sK3(powerset(X44)))
| ~ empty(X42)
| ~ empty(X44)
| epsilon_transitive(powerset(X44)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1103])]) ).
fof(f5355,plain,
( spl20_365
<=> ! [X25,X24,X26] :
( element(sK6(sK4(powerset(X24)),X25,X26),X25)
| in(sK6(sK4(powerset(X24)),X25,X26),X26)
| sP0(sK4(powerset(X24)),X25,X26)
| ~ empty(X24) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_365])]) ).
fof(f6017,plain,
( ! [X44,X42,X43] :
( element(sK6(sK4(powerset(X42)),X43,sK3(powerset(X44))),X43)
| sP0(sK4(powerset(X42)),X43,sK3(powerset(X44)))
| ~ empty(X42)
| ~ empty(X44)
| epsilon_transitive(powerset(X44)) )
| ~ spl20_223
| ~ spl20_365 ),
inference(resolution,[],[f5356,f2311]) ).
fof(f5356,plain,
( ! [X26,X24,X25] :
( element(sK6(sK4(powerset(X24)),X25,X26),X25)
| in(sK6(sK4(powerset(X24)),X25,X26),X26)
| sP0(sK4(powerset(X24)),X25,X26)
| ~ empty(X24) )
| ~ spl20_365 ),
inference(avatar_component_clause,[],[f5355]) ).
fof(f36428,plain,
( spl20_1102
| ~ spl20_234
| ~ spl20_365 ),
inference(avatar_split_clause,[],[f6008,f5355,f2500,f36426]) ).
fof(f36426,plain,
( spl20_1102
<=> ! [X17,X14,X16,X15] :
( element(sK6(sK4(powerset(X14)),X15,X16),X15)
| sP0(sK4(powerset(X14)),X15,X16)
| ~ empty(X14)
| ~ ordinal(X16)
| ordinal_subset(X17,X16)
| ~ ordinal(X17)
| ~ empty(X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1102])]) ).
fof(f6008,plain,
( ! [X16,X14,X17,X15] :
( element(sK6(sK4(powerset(X14)),X15,X16),X15)
| sP0(sK4(powerset(X14)),X15,X16)
| ~ empty(X14)
| ~ ordinal(X16)
| ordinal_subset(X17,X16)
| ~ ordinal(X17)
| ~ empty(X17) )
| ~ spl20_234
| ~ spl20_365 ),
inference(resolution,[],[f5356,f2501]) ).
fof(f36424,plain,
( spl20_1101
| ~ spl20_223
| ~ spl20_363 ),
inference(avatar_split_clause,[],[f5954,f5347,f2310,f36422]) ).
fof(f36422,plain,
( spl20_1101
<=> ! [X41,X43,X42] :
( element(sK6(sK3(powerset(X41)),X42,sK4(powerset(X43))),X42)
| sP0(sK3(powerset(X41)),X42,sK4(powerset(X43)))
| ~ empty(X43)
| ~ empty(X41)
| epsilon_transitive(powerset(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1101])]) ).
fof(f5347,plain,
( spl20_363
<=> ! [X27,X28,X26] :
( element(sK6(X26,X27,sK4(powerset(X28))),X27)
| in(sK6(X26,X27,sK4(powerset(X28))),X26)
| sP0(X26,X27,sK4(powerset(X28)))
| ~ empty(X28) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_363])]) ).
fof(f5954,plain,
( ! [X41,X42,X43] :
( element(sK6(sK3(powerset(X41)),X42,sK4(powerset(X43))),X42)
| sP0(sK3(powerset(X41)),X42,sK4(powerset(X43)))
| ~ empty(X43)
| ~ empty(X41)
| epsilon_transitive(powerset(X41)) )
| ~ spl20_223
| ~ spl20_363 ),
inference(resolution,[],[f5348,f2311]) ).
fof(f5348,plain,
( ! [X28,X26,X27] :
( element(sK6(X26,X27,sK4(powerset(X28))),X27)
| in(sK6(X26,X27,sK4(powerset(X28))),X26)
| sP0(X26,X27,sK4(powerset(X28)))
| ~ empty(X28) )
| ~ spl20_363 ),
inference(avatar_component_clause,[],[f5347]) ).
fof(f36420,plain,
( spl20_1100
| ~ spl20_234
| ~ spl20_363 ),
inference(avatar_split_clause,[],[f5945,f5347,f2500,f36418]) ).
fof(f36418,plain,
( spl20_1100
<=> ! [X13,X14,X16,X15] :
( element(sK6(X13,X14,sK4(powerset(X15))),X14)
| sP0(X13,X14,sK4(powerset(X15)))
| ~ empty(X15)
| ~ ordinal(X13)
| ordinal_subset(X16,X13)
| ~ ordinal(X16)
| ~ empty(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1100])]) ).
fof(f5945,plain,
( ! [X16,X14,X15,X13] :
( element(sK6(X13,X14,sK4(powerset(X15))),X14)
| sP0(X13,X14,sK4(powerset(X15)))
| ~ empty(X15)
| ~ ordinal(X13)
| ordinal_subset(X16,X13)
| ~ ordinal(X16)
| ~ empty(X16) )
| ~ spl20_234
| ~ spl20_363 ),
inference(resolution,[],[f5348,f2501]) ).
fof(f36416,plain,
( spl20_1099
| ~ spl20_223
| ~ spl20_360 ),
inference(avatar_split_clause,[],[f5894,f5327,f2310,f36414]) ).
fof(f36414,plain,
( spl20_1099
<=> ! [X41,X43,X42] :
( element(sK6(sK4(powerset(X41)),sK3(powerset(X42)),X43),X43)
| sP0(sK4(powerset(X41)),sK3(powerset(X42)),X43)
| ~ empty(X41)
| ~ empty(X42)
| epsilon_transitive(powerset(X42)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1099])]) ).
fof(f5327,plain,
( spl20_360
<=> ! [X25,X24,X26] :
( element(sK6(sK4(powerset(X24)),X25,X26),X26)
| in(sK6(sK4(powerset(X24)),X25,X26),X25)
| sP0(sK4(powerset(X24)),X25,X26)
| ~ empty(X24) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_360])]) ).
fof(f5894,plain,
( ! [X41,X42,X43] :
( element(sK6(sK4(powerset(X41)),sK3(powerset(X42)),X43),X43)
| sP0(sK4(powerset(X41)),sK3(powerset(X42)),X43)
| ~ empty(X41)
| ~ empty(X42)
| epsilon_transitive(powerset(X42)) )
| ~ spl20_223
| ~ spl20_360 ),
inference(resolution,[],[f5328,f2311]) ).
fof(f5328,plain,
( ! [X26,X24,X25] :
( element(sK6(sK4(powerset(X24)),X25,X26),X26)
| in(sK6(sK4(powerset(X24)),X25,X26),X25)
| sP0(sK4(powerset(X24)),X25,X26)
| ~ empty(X24) )
| ~ spl20_360 ),
inference(avatar_component_clause,[],[f5327]) ).
fof(f36360,plain,
( ~ spl20_181
| ~ spl20_68
| ~ spl20_555 ),
inference(avatar_split_clause,[],[f16152,f14808,f613,f1640]) ).
fof(f14808,plain,
( spl20_555
<=> in(sK8,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_555])]) ).
fof(f16152,plain,
( ~ empty(sK1)
| ~ spl20_68
| ~ spl20_555 ),
inference(resolution,[],[f14810,f614]) ).
fof(f14810,plain,
( in(sK8,sK1)
| ~ spl20_555 ),
inference(avatar_component_clause,[],[f14808]) ).
fof(f36359,plain,
( spl20_1098
| ~ spl20_234
| ~ spl20_360 ),
inference(avatar_split_clause,[],[f5885,f5327,f2500,f36357]) ).
fof(f36357,plain,
( spl20_1098
<=> ! [X13,X14,X16,X15] :
( element(sK6(sK4(powerset(X13)),X14,X15),X15)
| sP0(sK4(powerset(X13)),X14,X15)
| ~ empty(X13)
| ~ ordinal(X14)
| ordinal_subset(X16,X14)
| ~ ordinal(X16)
| ~ empty(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1098])]) ).
fof(f5885,plain,
( ! [X16,X14,X15,X13] :
( element(sK6(sK4(powerset(X13)),X14,X15),X15)
| sP0(sK4(powerset(X13)),X14,X15)
| ~ empty(X13)
| ~ ordinal(X14)
| ordinal_subset(X16,X14)
| ~ ordinal(X16)
| ~ empty(X16) )
| ~ spl20_234
| ~ spl20_360 ),
inference(resolution,[],[f5328,f2501]) ).
fof(f36355,plain,
( spl20_1097
| ~ spl20_223
| ~ spl20_358 ),
inference(avatar_split_clause,[],[f5832,f5319,f2310,f36353]) ).
fof(f36353,plain,
( spl20_1097
<=> ! [X41,X43,X42] :
( element(sK6(sK3(powerset(X41)),sK4(powerset(X42)),X43),X43)
| sP0(sK3(powerset(X41)),sK4(powerset(X42)),X43)
| ~ empty(X42)
| ~ empty(X41)
| epsilon_transitive(powerset(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1097])]) ).
fof(f5319,plain,
( spl20_358
<=> ! [X25,X24,X26] :
( element(sK6(X24,sK4(powerset(X25)),X26),X26)
| in(sK6(X24,sK4(powerset(X25)),X26),X24)
| sP0(X24,sK4(powerset(X25)),X26)
| ~ empty(X25) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_358])]) ).
fof(f5832,plain,
( ! [X41,X42,X43] :
( element(sK6(sK3(powerset(X41)),sK4(powerset(X42)),X43),X43)
| sP0(sK3(powerset(X41)),sK4(powerset(X42)),X43)
| ~ empty(X42)
| ~ empty(X41)
| epsilon_transitive(powerset(X41)) )
| ~ spl20_223
| ~ spl20_358 ),
inference(resolution,[],[f5320,f2311]) ).
fof(f5320,plain,
( ! [X26,X24,X25] :
( element(sK6(X24,sK4(powerset(X25)),X26),X26)
| in(sK6(X24,sK4(powerset(X25)),X26),X24)
| sP0(X24,sK4(powerset(X25)),X26)
| ~ empty(X25) )
| ~ spl20_358 ),
inference(avatar_component_clause,[],[f5319]) ).
fof(f36351,plain,
( spl20_1096
| ~ spl20_234
| ~ spl20_358 ),
inference(avatar_split_clause,[],[f5823,f5319,f2500,f36349]) ).
fof(f36349,plain,
( spl20_1096
<=> ! [X13,X14,X16,X15] :
( element(sK6(X13,sK4(powerset(X14)),X15),X15)
| sP0(X13,sK4(powerset(X14)),X15)
| ~ empty(X14)
| ~ ordinal(X13)
| ordinal_subset(X16,X13)
| ~ ordinal(X16)
| ~ empty(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1096])]) ).
fof(f5823,plain,
( ! [X16,X14,X15,X13] :
( element(sK6(X13,sK4(powerset(X14)),X15),X15)
| sP0(X13,sK4(powerset(X14)),X15)
| ~ empty(X14)
| ~ ordinal(X13)
| ordinal_subset(X16,X13)
| ~ ordinal(X16)
| ~ empty(X16) )
| ~ spl20_234
| ~ spl20_358 ),
inference(resolution,[],[f5320,f2501]) ).
fof(f36347,plain,
( spl20_1095
| ~ spl20_223
| ~ spl20_356 ),
inference(avatar_split_clause,[],[f5770,f5311,f2310,f36345]) ).
fof(f36345,plain,
( spl20_1095
<=> ! [X43,X44,X42] :
( element(sK6(X42,sK4(powerset(X43)),sK3(powerset(X44))),X43)
| ~ empty(X42)
| sP0(X42,sK4(powerset(X43)),sK3(powerset(X44)))
| ~ empty(X44)
| epsilon_transitive(powerset(X44)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1095])]) ).
fof(f5311,plain,
( spl20_356
<=> ! [X22,X21,X23] :
( in(sK6(X21,sK4(powerset(X22)),X23),X23)
| sP0(X21,sK4(powerset(X22)),X23)
| ~ empty(X21)
| element(sK6(X21,sK4(powerset(X22)),X23),X22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_356])]) ).
fof(f5770,plain,
( ! [X44,X42,X43] :
( element(sK6(X42,sK4(powerset(X43)),sK3(powerset(X44))),X43)
| ~ empty(X42)
| sP0(X42,sK4(powerset(X43)),sK3(powerset(X44)))
| ~ empty(X44)
| epsilon_transitive(powerset(X44)) )
| ~ spl20_223
| ~ spl20_356 ),
inference(resolution,[],[f5312,f2311]) ).
fof(f5312,plain,
( ! [X21,X22,X23] :
( element(sK6(X21,sK4(powerset(X22)),X23),X22)
| in(sK6(X21,sK4(powerset(X22)),X23),X23)
| ~ empty(X21)
| sP0(X21,sK4(powerset(X22)),X23) )
| ~ spl20_356 ),
inference(avatar_component_clause,[],[f5311]) ).
fof(f36343,plain,
( spl20_1094
| ~ spl20_234
| ~ spl20_356 ),
inference(avatar_split_clause,[],[f5761,f5311,f2500,f36341]) ).
fof(f36341,plain,
( spl20_1094
<=> ! [X17,X14,X16,X15] :
( element(sK6(X14,sK4(powerset(X15)),X16),X15)
| ~ empty(X14)
| sP0(X14,sK4(powerset(X15)),X16)
| ~ ordinal(X16)
| ordinal_subset(X17,X16)
| ~ ordinal(X17)
| ~ empty(X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1094])]) ).
fof(f5761,plain,
( ! [X16,X14,X17,X15] :
( element(sK6(X14,sK4(powerset(X15)),X16),X15)
| ~ empty(X14)
| sP0(X14,sK4(powerset(X15)),X16)
| ~ ordinal(X16)
| ordinal_subset(X17,X16)
| ~ ordinal(X17)
| ~ empty(X17) )
| ~ spl20_234
| ~ spl20_356 ),
inference(resolution,[],[f5312,f2501]) ).
fof(f36339,plain,
( spl20_1093
| ~ spl20_223
| ~ spl20_355 ),
inference(avatar_split_clause,[],[f5742,f5307,f2310,f36337]) ).
fof(f36337,plain,
( spl20_1093
<=> ! [X41,X43,X42] :
( element(sK6(X41,sK3(powerset(X42)),sK4(powerset(X43))),X43)
| ~ empty(X41)
| sP0(X41,sK3(powerset(X42)),sK4(powerset(X43)))
| ~ empty(X42)
| epsilon_transitive(powerset(X42)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1093])]) ).
fof(f5307,plain,
( spl20_355
<=> ! [X25,X24,X23] :
( in(sK6(X23,X24,sK4(powerset(X25))),X24)
| sP0(X23,X24,sK4(powerset(X25)))
| ~ empty(X23)
| element(sK6(X23,X24,sK4(powerset(X25))),X25) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_355])]) ).
fof(f5742,plain,
( ! [X41,X42,X43] :
( element(sK6(X41,sK3(powerset(X42)),sK4(powerset(X43))),X43)
| ~ empty(X41)
| sP0(X41,sK3(powerset(X42)),sK4(powerset(X43)))
| ~ empty(X42)
| epsilon_transitive(powerset(X42)) )
| ~ spl20_223
| ~ spl20_355 ),
inference(resolution,[],[f5308,f2311]) ).
fof(f5308,plain,
( ! [X24,X25,X23] :
( element(sK6(X23,X24,sK4(powerset(X25))),X25)
| in(sK6(X23,X24,sK4(powerset(X25))),X24)
| ~ empty(X23)
| sP0(X23,X24,sK4(powerset(X25))) )
| ~ spl20_355 ),
inference(avatar_component_clause,[],[f5307]) ).
fof(f36111,plain,
( spl20_455
| ~ spl20_120
| ~ spl20_160 ),
inference(avatar_split_clause,[],[f12562,f1291,f1014,f12340]) ).
fof(f12340,plain,
( spl20_455
<=> ! [X1] :
( element(X1,sK1)
| ~ in(X1,sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_455])]) ).
fof(f12562,plain,
( ! [X0] :
( ~ in(X0,sK2)
| element(X0,sK1) )
| ~ spl20_120
| ~ spl20_160 ),
inference(resolution,[],[f1015,f1292]) ).
fof(f36087,plain,
( ~ spl20_181
| ~ spl20_68
| ~ spl20_935 ),
inference(avatar_split_clause,[],[f31391,f31347,f613,f1640]) ).
fof(f36086,plain,
( spl20_1092
| ~ spl20_234
| ~ spl20_355 ),
inference(avatar_split_clause,[],[f5733,f5307,f2500,f36084]) ).
fof(f36084,plain,
( spl20_1092
<=> ! [X13,X14,X16,X15] :
( element(sK6(X13,X14,sK4(powerset(X15))),X15)
| ~ empty(X13)
| sP0(X13,X14,sK4(powerset(X15)))
| ~ ordinal(X14)
| ordinal_subset(X16,X14)
| ~ ordinal(X16)
| ~ empty(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1092])]) ).
fof(f5733,plain,
( ! [X16,X14,X15,X13] :
( element(sK6(X13,X14,sK4(powerset(X15))),X15)
| ~ empty(X13)
| sP0(X13,X14,sK4(powerset(X15)))
| ~ ordinal(X14)
| ordinal_subset(X16,X14)
| ~ ordinal(X16)
| ~ empty(X16) )
| ~ spl20_234
| ~ spl20_355 ),
inference(resolution,[],[f5308,f2501]) ).
fof(f36082,plain,
( spl20_1091
| ~ spl20_223
| ~ spl20_354 ),
inference(avatar_split_clause,[],[f5684,f5303,f2310,f36080]) ).
fof(f36080,plain,
( spl20_1091
<=> ! [X44,X43,X42] :
( element(sK6(sK4(powerset(X42)),X43,sK3(powerset(X44))),X42)
| ~ empty(X43)
| sP0(sK4(powerset(X42)),X43,sK3(powerset(X44)))
| ~ empty(X44)
| epsilon_transitive(powerset(X44)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1091])]) ).
fof(f5303,plain,
( spl20_354
<=> ! [X22,X21,X23] :
( in(sK6(sK4(powerset(X21)),X22,X23),X23)
| sP0(sK4(powerset(X21)),X22,X23)
| ~ empty(X22)
| element(sK6(sK4(powerset(X21)),X22,X23),X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_354])]) ).
fof(f5684,plain,
( ! [X44,X42,X43] :
( element(sK6(sK4(powerset(X42)),X43,sK3(powerset(X44))),X42)
| ~ empty(X43)
| sP0(sK4(powerset(X42)),X43,sK3(powerset(X44)))
| ~ empty(X44)
| epsilon_transitive(powerset(X44)) )
| ~ spl20_223
| ~ spl20_354 ),
inference(resolution,[],[f5304,f2311]) ).
fof(f5304,plain,
( ! [X21,X22,X23] :
( element(sK6(sK4(powerset(X21)),X22,X23),X21)
| in(sK6(sK4(powerset(X21)),X22,X23),X23)
| ~ empty(X22)
| sP0(sK4(powerset(X21)),X22,X23) )
| ~ spl20_354 ),
inference(avatar_component_clause,[],[f5303]) ).
fof(f36078,plain,
( spl20_1090
| ~ spl20_234
| ~ spl20_354 ),
inference(avatar_split_clause,[],[f5675,f5303,f2500,f36076]) ).
fof(f36076,plain,
( spl20_1090
<=> ! [X17,X14,X16,X15] :
( element(sK6(sK4(powerset(X14)),X15,X16),X14)
| ~ empty(X15)
| sP0(sK4(powerset(X14)),X15,X16)
| ~ ordinal(X16)
| ordinal_subset(X17,X16)
| ~ ordinal(X17)
| ~ empty(X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1090])]) ).
fof(f5675,plain,
( ! [X16,X14,X17,X15] :
( element(sK6(sK4(powerset(X14)),X15,X16),X14)
| ~ empty(X15)
| sP0(sK4(powerset(X14)),X15,X16)
| ~ ordinal(X16)
| ordinal_subset(X17,X16)
| ~ ordinal(X17)
| ~ empty(X17) )
| ~ spl20_234
| ~ spl20_354 ),
inference(resolution,[],[f5304,f2501]) ).
fof(f36074,plain,
( spl20_1089
| ~ spl20_223
| ~ spl20_353 ),
inference(avatar_split_clause,[],[f5653,f5299,f2310,f36072]) ).
fof(f36072,plain,
( spl20_1089
<=> ! [X41,X43,X42] :
( element(sK6(sK3(powerset(X41)),X42,sK4(powerset(X43))),X43)
| ~ empty(X42)
| sP0(sK3(powerset(X41)),X42,sK4(powerset(X43)))
| ~ empty(X41)
| epsilon_transitive(powerset(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1089])]) ).
fof(f5299,plain,
( spl20_353
<=> ! [X24,X25,X23] :
( in(sK6(X23,X24,sK4(powerset(X25))),X23)
| sP0(X23,X24,sK4(powerset(X25)))
| ~ empty(X24)
| element(sK6(X23,X24,sK4(powerset(X25))),X25) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_353])]) ).
fof(f5653,plain,
( ! [X41,X42,X43] :
( element(sK6(sK3(powerset(X41)),X42,sK4(powerset(X43))),X43)
| ~ empty(X42)
| sP0(sK3(powerset(X41)),X42,sK4(powerset(X43)))
| ~ empty(X41)
| epsilon_transitive(powerset(X41)) )
| ~ spl20_223
| ~ spl20_353 ),
inference(resolution,[],[f5300,f2311]) ).
fof(f5300,plain,
( ! [X24,X25,X23] :
( element(sK6(X23,X24,sK4(powerset(X25))),X25)
| in(sK6(X23,X24,sK4(powerset(X25))),X23)
| ~ empty(X24)
| sP0(X23,X24,sK4(powerset(X25))) )
| ~ spl20_353 ),
inference(avatar_component_clause,[],[f5299]) ).
fof(f36070,plain,
( spl20_1088
| ~ spl20_234
| ~ spl20_353 ),
inference(avatar_split_clause,[],[f5644,f5299,f2500,f36068]) ).
fof(f36068,plain,
( spl20_1088
<=> ! [X13,X14,X16,X15] :
( element(sK6(X13,X14,sK4(powerset(X15))),X15)
| ~ empty(X14)
| sP0(X13,X14,sK4(powerset(X15)))
| ~ ordinal(X13)
| ordinal_subset(X16,X13)
| ~ ordinal(X16)
| ~ empty(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1088])]) ).
fof(f5644,plain,
( ! [X16,X14,X15,X13] :
( element(sK6(X13,X14,sK4(powerset(X15))),X15)
| ~ empty(X14)
| sP0(X13,X14,sK4(powerset(X15)))
| ~ ordinal(X13)
| ordinal_subset(X16,X13)
| ~ ordinal(X16)
| ~ empty(X16) )
| ~ spl20_234
| ~ spl20_353 ),
inference(resolution,[],[f5300,f2501]) ).
fof(f36066,plain,
( spl20_1087
| ~ spl20_223
| ~ spl20_352 ),
inference(avatar_split_clause,[],[f5622,f5295,f2310,f36064]) ).
fof(f36064,plain,
( spl20_1087
<=> ! [X41,X43,X42] :
( element(sK6(sK4(powerset(X41)),sK3(powerset(X42)),X43),X41)
| ~ empty(X43)
| sP0(sK4(powerset(X41)),sK3(powerset(X42)),X43)
| ~ empty(X42)
| epsilon_transitive(powerset(X42)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1087])]) ).
fof(f5295,plain,
( spl20_352
<=> ! [X22,X21,X23] :
( in(sK6(sK4(powerset(X21)),X22,X23),X22)
| sP0(sK4(powerset(X21)),X22,X23)
| ~ empty(X23)
| element(sK6(sK4(powerset(X21)),X22,X23),X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_352])]) ).
fof(f5622,plain,
( ! [X41,X42,X43] :
( element(sK6(sK4(powerset(X41)),sK3(powerset(X42)),X43),X41)
| ~ empty(X43)
| sP0(sK4(powerset(X41)),sK3(powerset(X42)),X43)
| ~ empty(X42)
| epsilon_transitive(powerset(X42)) )
| ~ spl20_223
| ~ spl20_352 ),
inference(resolution,[],[f5296,f2311]) ).
fof(f5296,plain,
( ! [X21,X22,X23] :
( element(sK6(sK4(powerset(X21)),X22,X23),X21)
| in(sK6(sK4(powerset(X21)),X22,X23),X22)
| ~ empty(X23)
| sP0(sK4(powerset(X21)),X22,X23) )
| ~ spl20_352 ),
inference(avatar_component_clause,[],[f5295]) ).
fof(f36062,plain,
( spl20_1086
| ~ spl20_234
| ~ spl20_352 ),
inference(avatar_split_clause,[],[f5613,f5295,f2500,f36060]) ).
fof(f36060,plain,
( spl20_1086
<=> ! [X13,X14,X16,X15] :
( element(sK6(sK4(powerset(X13)),X14,X15),X13)
| ~ empty(X15)
| sP0(sK4(powerset(X13)),X14,X15)
| ~ ordinal(X14)
| ordinal_subset(X16,X14)
| ~ ordinal(X16)
| ~ empty(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1086])]) ).
fof(f5613,plain,
( ! [X16,X14,X15,X13] :
( element(sK6(sK4(powerset(X13)),X14,X15),X13)
| ~ empty(X15)
| sP0(sK4(powerset(X13)),X14,X15)
| ~ ordinal(X14)
| ordinal_subset(X16,X14)
| ~ ordinal(X16)
| ~ empty(X16) )
| ~ spl20_234
| ~ spl20_352 ),
inference(resolution,[],[f5296,f2501]) ).
fof(f36058,plain,
( spl20_1085
| ~ spl20_223
| ~ spl20_351 ),
inference(avatar_split_clause,[],[f5591,f5284,f2310,f36056]) ).
fof(f36056,plain,
( spl20_1085
<=> ! [X41,X43,X42] :
( element(sK6(sK3(powerset(X41)),sK4(powerset(X42)),X43),X42)
| ~ empty(X43)
| sP0(sK3(powerset(X41)),sK4(powerset(X42)),X43)
| ~ empty(X41)
| epsilon_transitive(powerset(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1085])]) ).
fof(f5284,plain,
( spl20_351
<=> ! [X22,X21,X23] :
( in(sK6(X21,sK4(powerset(X22)),X23),X21)
| sP0(X21,sK4(powerset(X22)),X23)
| ~ empty(X23)
| element(sK6(X21,sK4(powerset(X22)),X23),X22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_351])]) ).
fof(f5591,plain,
( ! [X41,X42,X43] :
( element(sK6(sK3(powerset(X41)),sK4(powerset(X42)),X43),X42)
| ~ empty(X43)
| sP0(sK3(powerset(X41)),sK4(powerset(X42)),X43)
| ~ empty(X41)
| epsilon_transitive(powerset(X41)) )
| ~ spl20_223
| ~ spl20_351 ),
inference(resolution,[],[f5285,f2311]) ).
fof(f5285,plain,
( ! [X21,X22,X23] :
( element(sK6(X21,sK4(powerset(X22)),X23),X22)
| in(sK6(X21,sK4(powerset(X22)),X23),X21)
| ~ empty(X23)
| sP0(X21,sK4(powerset(X22)),X23) )
| ~ spl20_351 ),
inference(avatar_component_clause,[],[f5284]) ).
fof(f36054,plain,
( spl20_1084
| ~ spl20_234
| ~ spl20_351 ),
inference(avatar_split_clause,[],[f5582,f5284,f2500,f36052]) ).
fof(f36052,plain,
( spl20_1084
<=> ! [X13,X14,X16,X15] :
( element(sK6(X13,sK4(powerset(X14)),X15),X14)
| ~ empty(X15)
| sP0(X13,sK4(powerset(X14)),X15)
| ~ ordinal(X13)
| ordinal_subset(X16,X13)
| ~ ordinal(X16)
| ~ empty(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1084])]) ).
fof(f5582,plain,
( ! [X16,X14,X15,X13] :
( element(sK6(X13,sK4(powerset(X14)),X15),X14)
| ~ empty(X15)
| sP0(X13,sK4(powerset(X14)),X15)
| ~ ordinal(X13)
| ordinal_subset(X16,X13)
| ~ ordinal(X16)
| ~ empty(X16) )
| ~ spl20_234
| ~ spl20_351 ),
inference(resolution,[],[f5285,f2501]) ).
fof(f36050,plain,
( spl20_1083
| ~ spl20_223
| ~ spl20_350 ),
inference(avatar_split_clause,[],[f5555,f5280,f2310,f36048]) ).
fof(f36048,plain,
( spl20_1083
<=> ! [X41,X43,X42] :
( in(sK6(sK4(powerset(X41)),sK3(powerset(X42)),X43),X43)
| ~ empty(X41)
| sP0(sK4(powerset(X41)),sK3(powerset(X42)),X43)
| ~ empty(X42)
| epsilon_transitive(powerset(X42)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1083])]) ).
fof(f5280,plain,
( spl20_350
<=> ! [X16,X14,X15] :
( ~ empty(X14)
| in(sK6(sK4(powerset(X14)),X15,X16),X16)
| in(sK6(sK4(powerset(X14)),X15,X16),X15)
| sP0(sK4(powerset(X14)),X15,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_350])]) ).
fof(f5555,plain,
( ! [X41,X42,X43] :
( in(sK6(sK4(powerset(X41)),sK3(powerset(X42)),X43),X43)
| ~ empty(X41)
| sP0(sK4(powerset(X41)),sK3(powerset(X42)),X43)
| ~ empty(X42)
| epsilon_transitive(powerset(X42)) )
| ~ spl20_223
| ~ spl20_350 ),
inference(resolution,[],[f5281,f2311]) ).
fof(f5281,plain,
( ! [X16,X14,X15] :
( in(sK6(sK4(powerset(X14)),X15,X16),X16)
| in(sK6(sK4(powerset(X14)),X15,X16),X15)
| ~ empty(X14)
| sP0(sK4(powerset(X14)),X15,X16) )
| ~ spl20_350 ),
inference(avatar_component_clause,[],[f5280]) ).
fof(f36039,plain,
( spl20_228
| ~ spl20_304
| ~ spl20_455 ),
inference(avatar_split_clause,[],[f35953,f12340,f4069,f2330]) ).
fof(f35953,plain,
( element(sK1,sK1)
| ~ spl20_304
| ~ spl20_455 ),
inference(resolution,[],[f4070,f12341]) ).
fof(f12341,plain,
( ! [X1] :
( ~ in(X1,sK2)
| element(X1,sK1) )
| ~ spl20_455 ),
inference(avatar_component_clause,[],[f12340]) ).
fof(f36038,plain,
( spl20_1082
| ~ spl20_234
| ~ spl20_350 ),
inference(avatar_split_clause,[],[f5546,f5280,f2500,f36036]) ).
fof(f36036,plain,
( spl20_1082
<=> ! [X13,X14,X16,X15] :
( in(sK6(sK4(powerset(X13)),X14,X15),X15)
| ~ empty(X13)
| sP0(sK4(powerset(X13)),X14,X15)
| ~ ordinal(X14)
| ordinal_subset(X16,X14)
| ~ ordinal(X16)
| ~ empty(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1082])]) ).
fof(f5546,plain,
( ! [X16,X14,X15,X13] :
( in(sK6(sK4(powerset(X13)),X14,X15),X15)
| ~ empty(X13)
| sP0(sK4(powerset(X13)),X14,X15)
| ~ ordinal(X14)
| ordinal_subset(X16,X14)
| ~ ordinal(X16)
| ~ empty(X16) )
| ~ spl20_234
| ~ spl20_350 ),
inference(resolution,[],[f5281,f2501]) ).
fof(f36034,plain,
( spl20_1081
| ~ spl20_223
| ~ spl20_350 ),
inference(avatar_split_clause,[],[f5535,f5280,f2310,f36032]) ).
fof(f36032,plain,
( spl20_1081
<=> ! [X43,X44,X42] :
( in(sK6(sK4(powerset(X42)),X43,sK3(powerset(X44))),X43)
| ~ empty(X42)
| sP0(sK4(powerset(X42)),X43,sK3(powerset(X44)))
| ~ empty(X44)
| epsilon_transitive(powerset(X44)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1081])]) ).
fof(f5535,plain,
( ! [X44,X42,X43] :
( in(sK6(sK4(powerset(X42)),X43,sK3(powerset(X44))),X43)
| ~ empty(X42)
| sP0(sK4(powerset(X42)),X43,sK3(powerset(X44)))
| ~ empty(X44)
| epsilon_transitive(powerset(X44)) )
| ~ spl20_223
| ~ spl20_350 ),
inference(resolution,[],[f5281,f2311]) ).
fof(f36030,plain,
( spl20_1080
| ~ spl20_234
| ~ spl20_350 ),
inference(avatar_split_clause,[],[f5526,f5280,f2500,f36028]) ).
fof(f36028,plain,
( spl20_1080
<=> ! [X17,X14,X16,X15] :
( in(sK6(sK4(powerset(X14)),X15,X16),X15)
| ~ empty(X14)
| sP0(sK4(powerset(X14)),X15,X16)
| ~ ordinal(X16)
| ordinal_subset(X17,X16)
| ~ ordinal(X17)
| ~ empty(X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1080])]) ).
fof(f5526,plain,
( ! [X16,X14,X17,X15] :
( in(sK6(sK4(powerset(X14)),X15,X16),X15)
| ~ empty(X14)
| sP0(sK4(powerset(X14)),X15,X16)
| ~ ordinal(X16)
| ordinal_subset(X17,X16)
| ~ ordinal(X17)
| ~ empty(X17) )
| ~ spl20_234
| ~ spl20_350 ),
inference(resolution,[],[f5281,f2501]) ).
fof(f36026,plain,
( spl20_1079
| ~ spl20_223
| ~ spl20_349 ),
inference(avatar_split_clause,[],[f5503,f5276,f2310,f36024]) ).
fof(f36024,plain,
( spl20_1079
<=> ! [X41,X43,X42] :
( in(sK6(sK3(powerset(X41)),sK4(powerset(X42)),X43),X43)
| ~ empty(X42)
| sP0(sK3(powerset(X41)),sK4(powerset(X42)),X43)
| ~ empty(X41)
| epsilon_transitive(powerset(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1079])]) ).
fof(f5276,plain,
( spl20_349
<=> ! [X13,X12,X11] :
( ~ empty(X11)
| in(sK6(X12,sK4(powerset(X11)),X13),X13)
| in(sK6(X12,sK4(powerset(X11)),X13),X12)
| sP0(X12,sK4(powerset(X11)),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_349])]) ).
fof(f5503,plain,
( ! [X41,X42,X43] :
( in(sK6(sK3(powerset(X41)),sK4(powerset(X42)),X43),X43)
| ~ empty(X42)
| sP0(sK3(powerset(X41)),sK4(powerset(X42)),X43)
| ~ empty(X41)
| epsilon_transitive(powerset(X41)) )
| ~ spl20_223
| ~ spl20_349 ),
inference(resolution,[],[f5277,f2311]) ).
fof(f5277,plain,
( ! [X11,X12,X13] :
( in(sK6(X12,sK4(powerset(X11)),X13),X13)
| in(sK6(X12,sK4(powerset(X11)),X13),X12)
| ~ empty(X11)
| sP0(X12,sK4(powerset(X11)),X13) )
| ~ spl20_349 ),
inference(avatar_component_clause,[],[f5276]) ).
fof(f36022,plain,
( spl20_1078
| ~ spl20_234
| ~ spl20_349 ),
inference(avatar_split_clause,[],[f5494,f5276,f2500,f36020]) ).
fof(f36020,plain,
( spl20_1078
<=> ! [X13,X14,X16,X15] :
( in(sK6(X13,sK4(powerset(X14)),X15),X15)
| ~ empty(X14)
| sP0(X13,sK4(powerset(X14)),X15)
| ~ ordinal(X13)
| ordinal_subset(X16,X13)
| ~ ordinal(X16)
| ~ empty(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1078])]) ).
fof(f5494,plain,
( ! [X16,X14,X15,X13] :
( in(sK6(X13,sK4(powerset(X14)),X15),X15)
| ~ empty(X14)
| sP0(X13,sK4(powerset(X14)),X15)
| ~ ordinal(X13)
| ordinal_subset(X16,X13)
| ~ ordinal(X16)
| ~ empty(X16) )
| ~ spl20_234
| ~ spl20_349 ),
inference(resolution,[],[f5277,f2501]) ).
fof(f36018,plain,
( spl20_1077
| ~ spl20_223
| ~ spl20_349 ),
inference(avatar_split_clause,[],[f5483,f5276,f2310,f36016]) ).
fof(f36016,plain,
( spl20_1077
<=> ! [X44,X43,X42] :
( in(sK6(X42,sK4(powerset(X43)),sK3(powerset(X44))),X42)
| ~ empty(X43)
| sP0(X42,sK4(powerset(X43)),sK3(powerset(X44)))
| ~ empty(X44)
| epsilon_transitive(powerset(X44)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1077])]) ).
fof(f5483,plain,
( ! [X44,X42,X43] :
( in(sK6(X42,sK4(powerset(X43)),sK3(powerset(X44))),X42)
| ~ empty(X43)
| sP0(X42,sK4(powerset(X43)),sK3(powerset(X44)))
| ~ empty(X44)
| epsilon_transitive(powerset(X44)) )
| ~ spl20_223
| ~ spl20_349 ),
inference(resolution,[],[f5277,f2311]) ).
fof(f36014,plain,
( spl20_1076
| ~ spl20_234
| ~ spl20_349 ),
inference(avatar_split_clause,[],[f5474,f5276,f2500,f36012]) ).
fof(f36012,plain,
( spl20_1076
<=> ! [X17,X14,X16,X15] :
( in(sK6(X14,sK4(powerset(X15)),X16),X14)
| ~ empty(X15)
| sP0(X14,sK4(powerset(X15)),X16)
| ~ ordinal(X16)
| ordinal_subset(X17,X16)
| ~ ordinal(X17)
| ~ empty(X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1076])]) ).
fof(f5474,plain,
( ! [X16,X14,X17,X15] :
( in(sK6(X14,sK4(powerset(X15)),X16),X14)
| ~ empty(X15)
| sP0(X14,sK4(powerset(X15)),X16)
| ~ ordinal(X16)
| ordinal_subset(X17,X16)
| ~ ordinal(X17)
| ~ empty(X17) )
| ~ spl20_234
| ~ spl20_349 ),
inference(resolution,[],[f5277,f2501]) ).
fof(f36010,plain,
( spl20_1075
| ~ spl20_223
| ~ spl20_348 ),
inference(avatar_split_clause,[],[f5450,f5272,f2310,f36008]) ).
fof(f36008,plain,
( spl20_1075
<=> ! [X41,X43,X42] :
( in(sK6(sK3(powerset(X41)),X42,sK4(powerset(X43))),X42)
| ~ empty(X43)
| sP0(sK3(powerset(X41)),X42,sK4(powerset(X43)))
| ~ empty(X41)
| epsilon_transitive(powerset(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1075])]) ).
fof(f5272,plain,
( spl20_348
<=> ! [X9,X8,X10] :
( ~ empty(X8)
| in(sK6(X9,X10,sK4(powerset(X8))),X10)
| in(sK6(X9,X10,sK4(powerset(X8))),X9)
| sP0(X9,X10,sK4(powerset(X8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_348])]) ).
fof(f5450,plain,
( ! [X41,X42,X43] :
( in(sK6(sK3(powerset(X41)),X42,sK4(powerset(X43))),X42)
| ~ empty(X43)
| sP0(sK3(powerset(X41)),X42,sK4(powerset(X43)))
| ~ empty(X41)
| epsilon_transitive(powerset(X41)) )
| ~ spl20_223
| ~ spl20_348 ),
inference(resolution,[],[f5273,f2311]) ).
fof(f5273,plain,
( ! [X10,X8,X9] :
( in(sK6(X9,X10,sK4(powerset(X8))),X10)
| in(sK6(X9,X10,sK4(powerset(X8))),X9)
| ~ empty(X8)
| sP0(X9,X10,sK4(powerset(X8))) )
| ~ spl20_348 ),
inference(avatar_component_clause,[],[f5272]) ).
fof(f36006,plain,
( spl20_1074
| ~ spl20_234
| ~ spl20_348 ),
inference(avatar_split_clause,[],[f5441,f5272,f2500,f36004]) ).
fof(f36004,plain,
( spl20_1074
<=> ! [X13,X14,X16,X15] :
( in(sK6(X13,X14,sK4(powerset(X15))),X14)
| ~ empty(X15)
| sP0(X13,X14,sK4(powerset(X15)))
| ~ ordinal(X13)
| ordinal_subset(X16,X13)
| ~ ordinal(X16)
| ~ empty(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1074])]) ).
fof(f5441,plain,
( ! [X16,X14,X15,X13] :
( in(sK6(X13,X14,sK4(powerset(X15))),X14)
| ~ empty(X15)
| sP0(X13,X14,sK4(powerset(X15)))
| ~ ordinal(X13)
| ordinal_subset(X16,X13)
| ~ ordinal(X16)
| ~ empty(X16) )
| ~ spl20_234
| ~ spl20_348 ),
inference(resolution,[],[f5273,f2501]) ).
fof(f36002,plain,
( spl20_1073
| ~ spl20_223
| ~ spl20_348 ),
inference(avatar_split_clause,[],[f5430,f5272,f2310,f36000]) ).
fof(f36000,plain,
( spl20_1073
<=> ! [X41,X43,X42] :
( in(sK6(X41,sK3(powerset(X42)),sK4(powerset(X43))),X41)
| ~ empty(X43)
| sP0(X41,sK3(powerset(X42)),sK4(powerset(X43)))
| ~ empty(X42)
| epsilon_transitive(powerset(X42)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1073])]) ).
fof(f5430,plain,
( ! [X41,X42,X43] :
( in(sK6(X41,sK3(powerset(X42)),sK4(powerset(X43))),X41)
| ~ empty(X43)
| sP0(X41,sK3(powerset(X42)),sK4(powerset(X43)))
| ~ empty(X42)
| epsilon_transitive(powerset(X42)) )
| ~ spl20_223
| ~ spl20_348 ),
inference(resolution,[],[f5273,f2311]) ).
fof(f35998,plain,
( ~ spl20_304
| ~ spl20_75
| ~ spl20_243 ),
inference(avatar_split_clause,[],[f6238,f2671,f653,f4069]) ).
fof(f653,plain,
( spl20_75
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_75])]) ).
fof(f2671,plain,
( spl20_243
<=> in(sK2,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_243])]) ).
fof(f6238,plain,
( ~ in(sK1,sK2)
| ~ spl20_75
| ~ spl20_243 ),
inference(resolution,[],[f2673,f654]) ).
fof(f654,plain,
( ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) )
| ~ spl20_75 ),
inference(avatar_component_clause,[],[f653]) ).
fof(f2673,plain,
( in(sK2,sK1)
| ~ spl20_243 ),
inference(avatar_component_clause,[],[f2671]) ).
fof(f35997,plain,
( spl20_1072
| ~ spl20_234
| ~ spl20_348 ),
inference(avatar_split_clause,[],[f5421,f5272,f2500,f35995]) ).
fof(f35995,plain,
( spl20_1072
<=> ! [X13,X14,X16,X15] :
( in(sK6(X13,X14,sK4(powerset(X15))),X13)
| ~ empty(X15)
| sP0(X13,X14,sK4(powerset(X15)))
| ~ ordinal(X14)
| ordinal_subset(X16,X14)
| ~ ordinal(X16)
| ~ empty(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1072])]) ).
fof(f5421,plain,
( ! [X16,X14,X15,X13] :
( in(sK6(X13,X14,sK4(powerset(X15))),X13)
| ~ empty(X15)
| sP0(X13,X14,sK4(powerset(X15)))
| ~ ordinal(X14)
| ordinal_subset(X16,X14)
| ~ ordinal(X16)
| ~ empty(X16) )
| ~ spl20_234
| ~ spl20_348 ),
inference(resolution,[],[f5273,f2501]) ).
fof(f35993,plain,
( spl20_1071
| ~ spl20_234
| ~ spl20_344 ),
inference(avatar_split_clause,[],[f5227,f4952,f2500,f35991]) ).
fof(f35991,plain,
( spl20_1071
<=> ! [X17,X14,X16,X15] :
( element(sK6(X14,X15,X16),X15)
| element(sK6(X14,X15,X16),X14)
| sP0(X14,X15,X16)
| ~ ordinal(X16)
| ordinal_subset(X17,X16)
| ~ ordinal(X17)
| ~ empty(X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1071])]) ).
fof(f4952,plain,
( spl20_344
<=> ! [X9,X8,X7] :
( element(sK6(X7,X8,X9),X8)
| in(sK6(X7,X8,X9),X9)
| sP0(X7,X8,X9)
| element(sK6(X7,X8,X9),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_344])]) ).
fof(f5227,plain,
( ! [X16,X14,X17,X15] :
( element(sK6(X14,X15,X16),X15)
| element(sK6(X14,X15,X16),X14)
| sP0(X14,X15,X16)
| ~ ordinal(X16)
| ordinal_subset(X17,X16)
| ~ ordinal(X17)
| ~ empty(X17) )
| ~ spl20_234
| ~ spl20_344 ),
inference(resolution,[],[f4953,f2501]) ).
fof(f4953,plain,
( ! [X8,X9,X7] :
( element(sK6(X7,X8,X9),X8)
| element(sK6(X7,X8,X9),X7)
| in(sK6(X7,X8,X9),X9)
| sP0(X7,X8,X9) )
| ~ spl20_344 ),
inference(avatar_component_clause,[],[f4952]) ).
fof(f35989,plain,
( spl20_1070
| ~ spl20_234
| ~ spl20_341 ),
inference(avatar_split_clause,[],[f5174,f4940,f2500,f35987]) ).
fof(f35987,plain,
( spl20_1070
<=> ! [X13,X14,X16,X15] :
( element(sK6(X13,X14,X15),X15)
| element(sK6(X13,X14,X15),X13)
| sP0(X13,X14,X15)
| ~ ordinal(X14)
| ordinal_subset(X16,X14)
| ~ ordinal(X16)
| ~ empty(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1070])]) ).
fof(f4940,plain,
( spl20_341
<=> ! [X9,X8,X7] :
( element(sK6(X7,X8,X9),X9)
| in(sK6(X7,X8,X9),X8)
| sP0(X7,X8,X9)
| element(sK6(X7,X8,X9),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_341])]) ).
fof(f5174,plain,
( ! [X16,X14,X15,X13] :
( element(sK6(X13,X14,X15),X15)
| element(sK6(X13,X14,X15),X13)
| sP0(X13,X14,X15)
| ~ ordinal(X14)
| ordinal_subset(X16,X14)
| ~ ordinal(X16)
| ~ empty(X16) )
| ~ spl20_234
| ~ spl20_341 ),
inference(resolution,[],[f4941,f2501]) ).
fof(f4941,plain,
( ! [X8,X9,X7] :
( element(sK6(X7,X8,X9),X9)
| element(sK6(X7,X8,X9),X7)
| in(sK6(X7,X8,X9),X8)
| sP0(X7,X8,X9) )
| ~ spl20_341 ),
inference(avatar_component_clause,[],[f4940]) ).
fof(f35985,plain,
( spl20_1069
| ~ spl20_234
| ~ spl20_339 ),
inference(avatar_split_clause,[],[f5133,f4932,f2500,f35983]) ).
fof(f35983,plain,
( spl20_1069
<=> ! [X13,X14,X16,X15] :
( element(sK6(X13,X14,X15),X15)
| element(sK6(X13,X14,X15),X14)
| sP0(X13,X14,X15)
| ~ ordinal(X13)
| ordinal_subset(X16,X13)
| ~ ordinal(X16)
| ~ empty(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1069])]) ).
fof(f4932,plain,
( spl20_339
<=> ! [X9,X8,X7] :
( element(sK6(X7,X8,X9),X9)
| in(sK6(X7,X8,X9),X7)
| sP0(X7,X8,X9)
| element(sK6(X7,X8,X9),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_339])]) ).
fof(f5133,plain,
( ! [X16,X14,X15,X13] :
( element(sK6(X13,X14,X15),X15)
| element(sK6(X13,X14,X15),X14)
| sP0(X13,X14,X15)
| ~ ordinal(X13)
| ordinal_subset(X16,X13)
| ~ ordinal(X16)
| ~ empty(X16) )
| ~ spl20_234
| ~ spl20_339 ),
inference(resolution,[],[f4933,f2501]) ).
fof(f4933,plain,
( ! [X8,X9,X7] :
( element(sK6(X7,X8,X9),X9)
| element(sK6(X7,X8,X9),X8)
| in(sK6(X7,X8,X9),X7)
| sP0(X7,X8,X9) )
| ~ spl20_339 ),
inference(avatar_component_clause,[],[f4932]) ).
fof(f35981,plain,
( spl20_1068
| ~ spl20_84
| ~ spl20_336 ),
inference(avatar_split_clause,[],[f5070,f4919,f732,f35979]) ).
fof(f35979,plain,
( spl20_1068
<=> ! [X6,X7] :
( in(sK6(X6,X6,sK4(powerset(powerset(X7)))),X6)
| sP0(X6,X6,sK4(powerset(powerset(X7))))
| subset(sK6(X6,X6,sK4(powerset(powerset(X7)))),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1068])]) ).
fof(f732,plain,
( spl20_84
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_84])]) ).
fof(f4919,plain,
( spl20_336
<=> ! [X16,X15] :
( in(sK6(X15,X15,sK4(powerset(X16))),X15)
| sP0(X15,X15,sK4(powerset(X16)))
| element(sK6(X15,X15,sK4(powerset(X16))),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_336])]) ).
fof(f5070,plain,
( ! [X6,X7] :
( in(sK6(X6,X6,sK4(powerset(powerset(X7)))),X6)
| sP0(X6,X6,sK4(powerset(powerset(X7))))
| subset(sK6(X6,X6,sK4(powerset(powerset(X7)))),X7) )
| ~ spl20_84
| ~ spl20_336 ),
inference(resolution,[],[f4920,f733]) ).
fof(f733,plain,
( ! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) )
| ~ spl20_84 ),
inference(avatar_component_clause,[],[f732]) ).
fof(f4920,plain,
( ! [X16,X15] :
( element(sK6(X15,X15,sK4(powerset(X16))),X16)
| in(sK6(X15,X15,sK4(powerset(X16))),X15)
| sP0(X15,X15,sK4(powerset(X16))) )
| ~ spl20_336 ),
inference(avatar_component_clause,[],[f4919]) ).
fof(f35977,plain,
( spl20_1067
| ~ spl20_84
| ~ spl20_335 ),
inference(avatar_split_clause,[],[f5042,f4915,f732,f35975]) ).
fof(f35975,plain,
( spl20_1067
<=> ! [X6,X7] :
( in(sK6(X6,sK4(powerset(powerset(X7))),X6),X6)
| sP0(X6,sK4(powerset(powerset(X7))),X6)
| subset(sK6(X6,sK4(powerset(powerset(X7))),X6),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1067])]) ).
fof(f4915,plain,
( spl20_335
<=> ! [X13,X14] :
( in(sK6(X13,sK4(powerset(X14)),X13),X13)
| sP0(X13,sK4(powerset(X14)),X13)
| element(sK6(X13,sK4(powerset(X14)),X13),X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_335])]) ).
fof(f5042,plain,
( ! [X6,X7] :
( in(sK6(X6,sK4(powerset(powerset(X7))),X6),X6)
| sP0(X6,sK4(powerset(powerset(X7))),X6)
| subset(sK6(X6,sK4(powerset(powerset(X7))),X6),X7) )
| ~ spl20_84
| ~ spl20_335 ),
inference(resolution,[],[f4916,f733]) ).
fof(f4916,plain,
( ! [X14,X13] :
( element(sK6(X13,sK4(powerset(X14)),X13),X14)
| in(sK6(X13,sK4(powerset(X14)),X13),X13)
| sP0(X13,sK4(powerset(X14)),X13) )
| ~ spl20_335 ),
inference(avatar_component_clause,[],[f4915]) ).
fof(f35973,plain,
( spl20_1066
| ~ spl20_84
| ~ spl20_334 ),
inference(avatar_split_clause,[],[f5014,f4911,f732,f35971]) ).
fof(f35971,plain,
( spl20_1066
<=> ! [X6,X7] :
( in(sK6(sK4(powerset(powerset(X6))),X7,X7),X7)
| sP0(sK4(powerset(powerset(X6))),X7,X7)
| subset(sK6(sK4(powerset(powerset(X6))),X7,X7),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1066])]) ).
fof(f4911,plain,
( spl20_334
<=> ! [X13,X14] :
( in(sK6(sK4(powerset(X13)),X14,X14),X14)
| sP0(sK4(powerset(X13)),X14,X14)
| element(sK6(sK4(powerset(X13)),X14,X14),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_334])]) ).
fof(f5014,plain,
( ! [X6,X7] :
( in(sK6(sK4(powerset(powerset(X6))),X7,X7),X7)
| sP0(sK4(powerset(powerset(X6))),X7,X7)
| subset(sK6(sK4(powerset(powerset(X6))),X7,X7),X6) )
| ~ spl20_84
| ~ spl20_334 ),
inference(resolution,[],[f4912,f733]) ).
fof(f4912,plain,
( ! [X14,X13] :
( element(sK6(sK4(powerset(X13)),X14,X14),X13)
| in(sK6(sK4(powerset(X13)),X14,X14),X14)
| sP0(sK4(powerset(X13)),X14,X14) )
| ~ spl20_334 ),
inference(avatar_component_clause,[],[f4911]) ).
fof(f35969,plain,
( spl20_1065
| ~ spl20_94
| ~ spl20_313 ),
inference(avatar_split_clause,[],[f4419,f4372,f823,f35967]) ).
fof(f35967,plain,
( spl20_1065
<=> ! [X4,X5,X3] :
( sK5(X3,sK4(powerset(powerset(X4)))) = X3
| singleton(X3) = sK4(powerset(powerset(X4)))
| ~ empty(X4)
| ~ in(X5,sK5(X3,sK4(powerset(powerset(X4))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1065])]) ).
fof(f823,plain,
( spl20_94
<=> ! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_94])]) ).
fof(f4372,plain,
( spl20_313
<=> ! [X6,X7] :
( element(sK5(X6,sK4(powerset(X7))),X7)
| sK5(X6,sK4(powerset(X7))) = X6
| singleton(X6) = sK4(powerset(X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_313])]) ).
fof(f4419,plain,
( ! [X3,X4,X5] :
( sK5(X3,sK4(powerset(powerset(X4)))) = X3
| singleton(X3) = sK4(powerset(powerset(X4)))
| ~ empty(X4)
| ~ in(X5,sK5(X3,sK4(powerset(powerset(X4))))) )
| ~ spl20_94
| ~ spl20_313 ),
inference(resolution,[],[f4373,f824]) ).
fof(f824,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X0,X1) )
| ~ spl20_94 ),
inference(avatar_component_clause,[],[f823]) ).
fof(f4373,plain,
( ! [X6,X7] :
( element(sK5(X6,sK4(powerset(X7))),X7)
| sK5(X6,sK4(powerset(X7))) = X6
| singleton(X6) = sK4(powerset(X7)) )
| ~ spl20_313 ),
inference(avatar_component_clause,[],[f4372]) ).
fof(f35965,plain,
( spl20_1064
| ~ spl20_223
| ~ spl20_311 ),
inference(avatar_split_clause,[],[f4362,f4126,f2310,f35963]) ).
fof(f35963,plain,
( spl20_1064
<=> ! [X29,X28] :
( sP0(sK3(powerset(X28)),sK3(powerset(X28)),singleton(X29))
| sK6(sK3(powerset(X28)),sK3(powerset(X28)),singleton(X29)) = X29
| ~ empty(X28)
| epsilon_transitive(powerset(X28)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1064])]) ).
fof(f4126,plain,
( spl20_311
<=> ! [X13,X12] :
( in(sK6(X12,X12,singleton(X13)),X12)
| sP0(X12,X12,singleton(X13))
| sK6(X12,X12,singleton(X13)) = X13 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_311])]) ).
fof(f4362,plain,
( ! [X28,X29] :
( sP0(sK3(powerset(X28)),sK3(powerset(X28)),singleton(X29))
| sK6(sK3(powerset(X28)),sK3(powerset(X28)),singleton(X29)) = X29
| ~ empty(X28)
| epsilon_transitive(powerset(X28)) )
| ~ spl20_223
| ~ spl20_311 ),
inference(resolution,[],[f4127,f2311]) ).
fof(f4127,plain,
( ! [X12,X13] :
( in(sK6(X12,X12,singleton(X13)),X12)
| sP0(X12,X12,singleton(X13))
| sK6(X12,X12,singleton(X13)) = X13 )
| ~ spl20_311 ),
inference(avatar_component_clause,[],[f4126]) ).
fof(f35951,plain,
( spl20_121
| ~ spl20_153
| ~ spl20_1043 ),
inference(avatar_split_clause,[],[f35889,f35841,f1230,f1018]) ).
fof(f35950,plain,
( spl20_1063
| ~ spl20_153
| ~ spl20_311 ),
inference(avatar_split_clause,[],[f4359,f4126,f1230,f35948]) ).
fof(f35948,plain,
( spl20_1063
<=> ! [X24,X23] :
( sP0(singleton(X23),singleton(X23),singleton(X24))
| sK6(singleton(X23),singleton(X23),singleton(X24)) = X24
| sK6(singleton(X23),singleton(X23),singleton(X24)) = X23 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1063])]) ).
fof(f4359,plain,
( ! [X24,X23] :
( sP0(singleton(X23),singleton(X23),singleton(X24))
| sK6(singleton(X23),singleton(X23),singleton(X24)) = X24
| sK6(singleton(X23),singleton(X23),singleton(X24)) = X23 )
| ~ spl20_153
| ~ spl20_311 ),
inference(resolution,[],[f4127,f1231]) ).
fof(f35946,plain,
( spl20_1062
| ~ spl20_241
| ~ spl20_307 ),
inference(avatar_split_clause,[],[f4225,f4110,f2529,f35944]) ).
fof(f35944,plain,
( spl20_1062
<=> ! [X197,X195,X196] :
( sK5(X195,powerset(X196)) = X195
| ~ empty(X196)
| powerset(X196) = singleton(X195)
| sP0(sK5(X195,powerset(X196)),sK5(X195,powerset(X196)),X197)
| ~ empty(X197) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1062])]) ).
fof(f2529,plain,
( spl20_241
<=> ! [X11,X10] :
( in(sK6(X10,X10,X11),X10)
| sP0(X10,X10,X11)
| ~ empty(X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_241])]) ).
fof(f4110,plain,
( spl20_307
<=> ! [X4,X5,X3] :
( powerset(X4) = singleton(X3)
| sK5(X3,powerset(X4)) = X3
| ~ empty(X4)
| ~ in(X5,sK5(X3,powerset(X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_307])]) ).
fof(f4225,plain,
( ! [X195,X196,X197] :
( sK5(X195,powerset(X196)) = X195
| ~ empty(X196)
| powerset(X196) = singleton(X195)
| sP0(sK5(X195,powerset(X196)),sK5(X195,powerset(X196)),X197)
| ~ empty(X197) )
| ~ spl20_241
| ~ spl20_307 ),
inference(resolution,[],[f4111,f2530]) ).
fof(f2530,plain,
( ! [X10,X11] :
( in(sK6(X10,X10,X11),X10)
| sP0(X10,X10,X11)
| ~ empty(X11) )
| ~ spl20_241 ),
inference(avatar_component_clause,[],[f2529]) ).
fof(f4111,plain,
( ! [X3,X4,X5] :
( ~ in(X5,sK5(X3,powerset(X4)))
| sK5(X3,powerset(X4)) = X3
| ~ empty(X4)
| powerset(X4) = singleton(X3) )
| ~ spl20_307 ),
inference(avatar_component_clause,[],[f4110]) ).
fof(f35942,plain,
( spl20_1061
| ~ spl20_100
| ~ spl20_306 ),
inference(avatar_split_clause,[],[f4166,f4106,f858,f35940]) ).
fof(f35940,plain,
( spl20_1061
<=> ! [X2,X0,X1] :
( ~ ordinal(sK4(powerset(X0)))
| ~ ordinal(powerset(X1))
| powerset(X1) = sK4(powerset(X0))
| element(powerset(X1),X0)
| element(X2,X1)
| ~ in(X2,sK4(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1061])]) ).
fof(f858,plain,
( spl20_100
<=> ! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_100])]) ).
fof(f4106,plain,
( spl20_306
<=> ! [X11,X12] :
( sK4(powerset(X11)) = X12
| ~ ordinal(sK4(powerset(X11)))
| ~ ordinal(X12)
| element(sK4(powerset(X11)),X12)
| element(X12,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_306])]) ).
fof(f4166,plain,
( ! [X2,X0,X1] :
( ~ ordinal(sK4(powerset(X0)))
| ~ ordinal(powerset(X1))
| powerset(X1) = sK4(powerset(X0))
| element(powerset(X1),X0)
| element(X2,X1)
| ~ in(X2,sK4(powerset(X0))) )
| ~ spl20_100
| ~ spl20_306 ),
inference(resolution,[],[f4107,f859]) ).
fof(f859,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| element(X0,X2)
| ~ in(X0,X1) )
| ~ spl20_100 ),
inference(avatar_component_clause,[],[f858]) ).
fof(f4107,plain,
( ! [X11,X12] :
( element(sK4(powerset(X11)),X12)
| ~ ordinal(sK4(powerset(X11)))
| ~ ordinal(X12)
| sK4(powerset(X11)) = X12
| element(X12,X11) )
| ~ spl20_306 ),
inference(avatar_component_clause,[],[f4106]) ).
fof(f35938,plain,
( spl20_1060
| ~ spl20_157
| ~ spl20_305 ),
inference(avatar_split_clause,[],[f4141,f4102,f1267,f35936]) ).
fof(f35936,plain,
( spl20_1060
<=> ! [X25,X26] :
( element(sK4(powerset(X25)),X26)
| sK4(powerset(X25)) = sK4(powerset(X26))
| ~ ordinal(sK4(powerset(X26)))
| ~ ordinal(sK4(powerset(X25)))
| element(sK4(powerset(X26)),X25) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1060])]) ).
fof(f1267,plain,
( spl20_157
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK4(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_157])]) ).
fof(f4102,plain,
( spl20_305
<=> ! [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_305])]) ).
fof(f4141,plain,
( ! [X26,X25] :
( element(sK4(powerset(X25)),X26)
| sK4(powerset(X25)) = sK4(powerset(X26))
| ~ ordinal(sK4(powerset(X26)))
| ~ ordinal(sK4(powerset(X25)))
| element(sK4(powerset(X26)),X25) )
| ~ spl20_157
| ~ spl20_305 ),
inference(resolution,[],[f4103,f1268]) ).
fof(f1268,plain,
( ! [X0,X1] :
( ~ in(X0,sK4(powerset(X1)))
| element(X0,X1) )
| ~ spl20_157 ),
inference(avatar_component_clause,[],[f1267]) ).
fof(f4103,plain,
( ! [X0,X1] :
( in(sK4(powerset(X1)),X0)
| element(X0,X1)
| sK4(powerset(X1)) = X0
| ~ ordinal(sK4(powerset(X1)))
| ~ ordinal(X0) )
| ~ spl20_305 ),
inference(avatar_component_clause,[],[f4102]) ).
fof(f35934,plain,
( spl20_1059
| ~ spl20_223
| ~ spl20_305 ),
inference(avatar_split_clause,[],[f4140,f4102,f2310,f35932]) ).
fof(f35932,plain,
( spl20_1059
<=> ! [X24,X23] :
( element(sK3(powerset(X23)),X24)
| sK4(powerset(X24)) = sK3(powerset(X23))
| ~ ordinal(sK4(powerset(X24)))
| ~ ordinal(sK3(powerset(X23)))
| ~ empty(X23)
| epsilon_transitive(powerset(X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1059])]) ).
fof(f4140,plain,
( ! [X24,X23] :
( element(sK3(powerset(X23)),X24)
| sK4(powerset(X24)) = sK3(powerset(X23))
| ~ ordinal(sK4(powerset(X24)))
| ~ ordinal(sK3(powerset(X23)))
| ~ empty(X23)
| epsilon_transitive(powerset(X23)) )
| ~ spl20_223
| ~ spl20_305 ),
inference(resolution,[],[f4103,f2311]) ).
fof(f35930,plain,
( spl20_1058
| ~ spl20_230
| ~ spl20_303 ),
inference(avatar_split_clause,[],[f4093,f3637,f2398,f35928]) ).
fof(f35928,plain,
( spl20_1058
<=> ! [X41,X40,X39] :
( sP0(X39,sK4(powerset(X40)),sK3(powerset(X41)))
| ~ empty(X39)
| ~ empty(X40)
| element(sK6(X39,sK4(powerset(X40)),sK3(powerset(X41))),X41)
| epsilon_transitive(powerset(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1058])]) ).
fof(f2398,plain,
( spl20_230
<=> ! [X0,X1] :
( epsilon_transitive(powerset(X0))
| element(X1,X0)
| ~ in(X1,sK3(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_230])]) ).
fof(f3637,plain,
( spl20_303
<=> ! [X25,X24,X26] :
( in(sK6(X24,sK4(powerset(X25)),X26),X26)
| sP0(X24,sK4(powerset(X25)),X26)
| ~ empty(X24)
| ~ empty(X25) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_303])]) ).
fof(f4093,plain,
( ! [X40,X41,X39] :
( sP0(X39,sK4(powerset(X40)),sK3(powerset(X41)))
| ~ empty(X39)
| ~ empty(X40)
| element(sK6(X39,sK4(powerset(X40)),sK3(powerset(X41))),X41)
| epsilon_transitive(powerset(X41)) )
| ~ spl20_230
| ~ spl20_303 ),
inference(resolution,[],[f3638,f2399]) ).
fof(f2399,plain,
( ! [X0,X1] :
( ~ in(X1,sK3(powerset(X0)))
| element(X1,X0)
| epsilon_transitive(powerset(X0)) )
| ~ spl20_230 ),
inference(avatar_component_clause,[],[f2398]) ).
fof(f3638,plain,
( ! [X26,X24,X25] :
( in(sK6(X24,sK4(powerset(X25)),X26),X26)
| sP0(X24,sK4(powerset(X25)),X26)
| ~ empty(X24)
| ~ empty(X25) )
| ~ spl20_303 ),
inference(avatar_component_clause,[],[f3637]) ).
fof(f35926,plain,
( spl20_1057
| ~ spl20_245
| ~ spl20_303 ),
inference(avatar_split_clause,[],[f4084,f3637,f2725,f35924]) ).
fof(f35924,plain,
( spl20_1057
<=> ! [X10,X11,X13,X12] :
( sP0(X10,sK4(powerset(X11)),X12)
| ~ empty(X10)
| ~ empty(X11)
| ~ ordinal(X12)
| ordinal_subset(X13,X12)
| ~ ordinal(X13)
| element(sK6(X10,sK4(powerset(X11)),X12),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1057])]) ).
fof(f2725,plain,
( spl20_245
<=> ! [X2,X1,X3] :
( ~ ordinal(X1)
| ~ ordinal(X2)
| ordinal_subset(X1,X2)
| ~ in(X3,X2)
| element(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_245])]) ).
fof(f4084,plain,
( ! [X10,X11,X12,X13] :
( sP0(X10,sK4(powerset(X11)),X12)
| ~ empty(X10)
| ~ empty(X11)
| ~ ordinal(X12)
| ordinal_subset(X13,X12)
| ~ ordinal(X13)
| element(sK6(X10,sK4(powerset(X11)),X12),X13) )
| ~ spl20_245
| ~ spl20_303 ),
inference(resolution,[],[f3638,f2726]) ).
fof(f2726,plain,
( ! [X2,X3,X1] :
( ~ in(X3,X2)
| ~ ordinal(X2)
| ordinal_subset(X1,X2)
| ~ ordinal(X1)
| element(X3,X1) )
| ~ spl20_245 ),
inference(avatar_component_clause,[],[f2725]) ).
fof(f35922,plain,
( spl20_1056
| ~ spl20_245
| ~ spl20_301 ),
inference(avatar_split_clause,[],[f4051,f3629,f2725,f35920]) ).
fof(f35920,plain,
( spl20_1056
<=> ! [X10,X11,X13,X12] :
( element(sK6(X10,X11,X12),X11)
| ~ empty(X10)
| sP0(X10,X11,X12)
| ~ ordinal(X12)
| ordinal_subset(X13,X12)
| ~ ordinal(X13)
| element(sK6(X10,X11,X12),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1056])]) ).
fof(f3629,plain,
( spl20_301
<=> ! [X9,X8,X7] :
( in(sK6(X7,X8,X9),X9)
| sP0(X7,X8,X9)
| ~ empty(X7)
| element(sK6(X7,X8,X9),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_301])]) ).
fof(f4051,plain,
( ! [X10,X11,X12,X13] :
( element(sK6(X10,X11,X12),X11)
| ~ empty(X10)
| sP0(X10,X11,X12)
| ~ ordinal(X12)
| ordinal_subset(X13,X12)
| ~ ordinal(X13)
| element(sK6(X10,X11,X12),X13) )
| ~ spl20_245
| ~ spl20_301 ),
inference(resolution,[],[f3630,f2726]) ).
fof(f3630,plain,
( ! [X8,X9,X7] :
( element(sK6(X7,X8,X9),X8)
| in(sK6(X7,X8,X9),X9)
| ~ empty(X7)
| sP0(X7,X8,X9) )
| ~ spl20_301 ),
inference(avatar_component_clause,[],[f3629]) ).
fof(f35918,plain,
( spl20_1055
| ~ spl20_230
| ~ spl20_300 ),
inference(avatar_split_clause,[],[f4035,f3625,f2398,f35916]) ).
fof(f35916,plain,
( spl20_1055
<=> ! [X38,X39,X40] :
( sP0(X38,sK3(powerset(X39)),sK4(powerset(X40)))
| ~ empty(X38)
| ~ empty(X40)
| element(sK6(X38,sK3(powerset(X39)),sK4(powerset(X40))),X39)
| epsilon_transitive(powerset(X39)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1055])]) ).
fof(f3625,plain,
( spl20_300
<=> ! [X27,X28,X26] :
( in(sK6(X26,X27,sK4(powerset(X28))),X27)
| sP0(X26,X27,sK4(powerset(X28)))
| ~ empty(X26)
| ~ empty(X28) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_300])]) ).
fof(f4035,plain,
( ! [X40,X38,X39] :
( sP0(X38,sK3(powerset(X39)),sK4(powerset(X40)))
| ~ empty(X38)
| ~ empty(X40)
| element(sK6(X38,sK3(powerset(X39)),sK4(powerset(X40))),X39)
| epsilon_transitive(powerset(X39)) )
| ~ spl20_230
| ~ spl20_300 ),
inference(resolution,[],[f3626,f2399]) ).
fof(f3626,plain,
( ! [X28,X26,X27] :
( in(sK6(X26,X27,sK4(powerset(X28))),X27)
| sP0(X26,X27,sK4(powerset(X28)))
| ~ empty(X26)
| ~ empty(X28) )
| ~ spl20_300 ),
inference(avatar_component_clause,[],[f3625]) ).
fof(f35914,plain,
( spl20_1054
| ~ spl20_245
| ~ spl20_300 ),
inference(avatar_split_clause,[],[f4026,f3625,f2725,f35912]) ).
fof(f35912,plain,
( spl20_1054
<=> ! [X10,X11,X12,X9] :
( sP0(X9,X10,sK4(powerset(X11)))
| ~ empty(X9)
| ~ empty(X11)
| ~ ordinal(X10)
| ordinal_subset(X12,X10)
| ~ ordinal(X12)
| element(sK6(X9,X10,sK4(powerset(X11))),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1054])]) ).
fof(f4026,plain,
( ! [X10,X11,X9,X12] :
( sP0(X9,X10,sK4(powerset(X11)))
| ~ empty(X9)
| ~ empty(X11)
| ~ ordinal(X10)
| ordinal_subset(X12,X10)
| ~ ordinal(X12)
| element(sK6(X9,X10,sK4(powerset(X11))),X12) )
| ~ spl20_245
| ~ spl20_300 ),
inference(resolution,[],[f3626,f2726]) ).
fof(f35884,plain,
( spl20_1053
| ~ spl20_245
| ~ spl20_298 ),
inference(avatar_split_clause,[],[f3998,f3617,f2725,f35882]) ).
fof(f35882,plain,
( spl20_1053
<=> ! [X10,X11,X12,X9] :
( element(sK6(X9,X10,X11),X11)
| ~ empty(X9)
| sP0(X9,X10,X11)
| ~ ordinal(X10)
| ordinal_subset(X12,X10)
| ~ ordinal(X12)
| element(sK6(X9,X10,X11),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1053])]) ).
fof(f3617,plain,
( spl20_298
<=> ! [X9,X11,X10] :
( in(sK6(X9,X10,X11),X10)
| sP0(X9,X10,X11)
| ~ empty(X9)
| element(sK6(X9,X10,X11),X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_298])]) ).
fof(f3998,plain,
( ! [X10,X11,X9,X12] :
( element(sK6(X9,X10,X11),X11)
| ~ empty(X9)
| sP0(X9,X10,X11)
| ~ ordinal(X10)
| ordinal_subset(X12,X10)
| ~ ordinal(X12)
| element(sK6(X9,X10,X11),X12) )
| ~ spl20_245
| ~ spl20_298 ),
inference(resolution,[],[f3618,f2726]) ).
fof(f3618,plain,
( ! [X10,X11,X9] :
( element(sK6(X9,X10,X11),X11)
| in(sK6(X9,X10,X11),X10)
| ~ empty(X9)
| sP0(X9,X10,X11) )
| ~ spl20_298 ),
inference(avatar_component_clause,[],[f3617]) ).
fof(f35880,plain,
( spl20_1052
| ~ spl20_230
| ~ spl20_296 ),
inference(avatar_split_clause,[],[f3982,f3586,f2398,f35878]) ).
fof(f35878,plain,
( spl20_1052
<=> ! [X41,X40,X39] :
( sP0(sK4(powerset(X39)),X40,sK3(powerset(X41)))
| ~ empty(X40)
| ~ empty(X39)
| element(sK6(sK4(powerset(X39)),X40,sK3(powerset(X41))),X41)
| epsilon_transitive(powerset(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1052])]) ).
fof(f3586,plain,
( spl20_296
<=> ! [X25,X24,X26] :
( in(sK6(sK4(powerset(X24)),X25,X26),X26)
| sP0(sK4(powerset(X24)),X25,X26)
| ~ empty(X25)
| ~ empty(X24) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_296])]) ).
fof(f3982,plain,
( ! [X40,X41,X39] :
( sP0(sK4(powerset(X39)),X40,sK3(powerset(X41)))
| ~ empty(X40)
| ~ empty(X39)
| element(sK6(sK4(powerset(X39)),X40,sK3(powerset(X41))),X41)
| epsilon_transitive(powerset(X41)) )
| ~ spl20_230
| ~ spl20_296 ),
inference(resolution,[],[f3587,f2399]) ).
fof(f3587,plain,
( ! [X26,X24,X25] :
( in(sK6(sK4(powerset(X24)),X25,X26),X26)
| sP0(sK4(powerset(X24)),X25,X26)
| ~ empty(X25)
| ~ empty(X24) )
| ~ spl20_296 ),
inference(avatar_component_clause,[],[f3586]) ).
fof(f35876,plain,
( spl20_1051
| ~ spl20_245
| ~ spl20_296 ),
inference(avatar_split_clause,[],[f3973,f3586,f2725,f35874]) ).
fof(f35874,plain,
( spl20_1051
<=> ! [X10,X11,X13,X12] :
( sP0(sK4(powerset(X10)),X11,X12)
| ~ empty(X11)
| ~ empty(X10)
| ~ ordinal(X12)
| ordinal_subset(X13,X12)
| ~ ordinal(X13)
| element(sK6(sK4(powerset(X10)),X11,X12),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1051])]) ).
fof(f3973,plain,
( ! [X10,X11,X12,X13] :
( sP0(sK4(powerset(X10)),X11,X12)
| ~ empty(X11)
| ~ empty(X10)
| ~ ordinal(X12)
| ordinal_subset(X13,X12)
| ~ ordinal(X13)
| element(sK6(sK4(powerset(X10)),X11,X12),X13) )
| ~ spl20_245
| ~ spl20_296 ),
inference(resolution,[],[f3587,f2726]) ).
fof(f35872,plain,
( spl20_1050
| ~ spl20_245
| ~ spl20_294 ),
inference(avatar_split_clause,[],[f3945,f3578,f2725,f35870]) ).
fof(f35870,plain,
( spl20_1050
<=> ! [X10,X11,X13,X12] :
( element(sK6(X10,X11,X12),X10)
| ~ empty(X11)
| sP0(X10,X11,X12)
| ~ ordinal(X12)
| ordinal_subset(X13,X12)
| ~ ordinal(X13)
| element(sK6(X10,X11,X12),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1050])]) ).
fof(f3578,plain,
( spl20_294
<=> ! [X9,X8,X7] :
( in(sK6(X7,X8,X9),X9)
| sP0(X7,X8,X9)
| ~ empty(X8)
| element(sK6(X7,X8,X9),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_294])]) ).
fof(f3945,plain,
( ! [X10,X11,X12,X13] :
( element(sK6(X10,X11,X12),X10)
| ~ empty(X11)
| sP0(X10,X11,X12)
| ~ ordinal(X12)
| ordinal_subset(X13,X12)
| ~ ordinal(X13)
| element(sK6(X10,X11,X12),X13) )
| ~ spl20_245
| ~ spl20_294 ),
inference(resolution,[],[f3579,f2726]) ).
fof(f3579,plain,
( ! [X8,X9,X7] :
( element(sK6(X7,X8,X9),X7)
| in(sK6(X7,X8,X9),X9)
| ~ empty(X8)
| sP0(X7,X8,X9) )
| ~ spl20_294 ),
inference(avatar_component_clause,[],[f3578]) ).
fof(f35868,plain,
( spl20_1049
| ~ spl20_230
| ~ spl20_293 ),
inference(avatar_split_clause,[],[f3929,f3574,f2398,f35866]) ).
fof(f35866,plain,
( spl20_1049
<=> ! [X38,X39,X40] :
( sP0(sK3(powerset(X38)),X39,sK4(powerset(X40)))
| ~ empty(X39)
| ~ empty(X40)
| element(sK6(sK3(powerset(X38)),X39,sK4(powerset(X40))),X38)
| epsilon_transitive(powerset(X38)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1049])]) ).
fof(f3574,plain,
( spl20_293
<=> ! [X27,X28,X26] :
( in(sK6(X26,X27,sK4(powerset(X28))),X26)
| sP0(X26,X27,sK4(powerset(X28)))
| ~ empty(X27)
| ~ empty(X28) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_293])]) ).
fof(f3929,plain,
( ! [X40,X38,X39] :
( sP0(sK3(powerset(X38)),X39,sK4(powerset(X40)))
| ~ empty(X39)
| ~ empty(X40)
| element(sK6(sK3(powerset(X38)),X39,sK4(powerset(X40))),X38)
| epsilon_transitive(powerset(X38)) )
| ~ spl20_230
| ~ spl20_293 ),
inference(resolution,[],[f3575,f2399]) ).
fof(f3575,plain,
( ! [X28,X26,X27] :
( in(sK6(X26,X27,sK4(powerset(X28))),X26)
| sP0(X26,X27,sK4(powerset(X28)))
| ~ empty(X27)
| ~ empty(X28) )
| ~ spl20_293 ),
inference(avatar_component_clause,[],[f3574]) ).
fof(f35864,plain,
( spl20_1048
| ~ spl20_245
| ~ spl20_293 ),
inference(avatar_split_clause,[],[f3920,f3574,f2725,f35862]) ).
fof(f35862,plain,
( spl20_1048
<=> ! [X10,X11,X12,X9] :
( sP0(X9,X10,sK4(powerset(X11)))
| ~ empty(X10)
| ~ empty(X11)
| ~ ordinal(X9)
| ordinal_subset(X12,X9)
| ~ ordinal(X12)
| element(sK6(X9,X10,sK4(powerset(X11))),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1048])]) ).
fof(f3920,plain,
( ! [X10,X11,X9,X12] :
( sP0(X9,X10,sK4(powerset(X11)))
| ~ empty(X10)
| ~ empty(X11)
| ~ ordinal(X9)
| ordinal_subset(X12,X9)
| ~ ordinal(X12)
| element(sK6(X9,X10,sK4(powerset(X11))),X12) )
| ~ spl20_245
| ~ spl20_293 ),
inference(resolution,[],[f3575,f2726]) ).
fof(f35860,plain,
( spl20_1047
| ~ spl20_245
| ~ spl20_291 ),
inference(avatar_split_clause,[],[f3892,f3566,f2725,f35858]) ).
fof(f35858,plain,
( spl20_1047
<=> ! [X10,X11,X12,X9] :
( element(sK6(X9,X10,X11),X11)
| ~ empty(X10)
| sP0(X9,X10,X11)
| ~ ordinal(X9)
| ordinal_subset(X12,X9)
| ~ ordinal(X12)
| element(sK6(X9,X10,X11),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1047])]) ).
fof(f3566,plain,
( spl20_291
<=> ! [X9,X11,X10] :
( in(sK6(X9,X10,X11),X9)
| sP0(X9,X10,X11)
| ~ empty(X10)
| element(sK6(X9,X10,X11),X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_291])]) ).
fof(f3892,plain,
( ! [X10,X11,X9,X12] :
( element(sK6(X9,X10,X11),X11)
| ~ empty(X10)
| sP0(X9,X10,X11)
| ~ ordinal(X9)
| ordinal_subset(X12,X9)
| ~ ordinal(X12)
| element(sK6(X9,X10,X11),X12) )
| ~ spl20_245
| ~ spl20_291 ),
inference(resolution,[],[f3567,f2726]) ).
fof(f3567,plain,
( ! [X10,X11,X9] :
( element(sK6(X9,X10,X11),X11)
| in(sK6(X9,X10,X11),X9)
| ~ empty(X10)
| sP0(X9,X10,X11) )
| ~ spl20_291 ),
inference(avatar_component_clause,[],[f3566]) ).
fof(f35856,plain,
( spl20_1046
| ~ spl20_230
| ~ spl20_290 ),
inference(avatar_split_clause,[],[f3876,f3562,f2398,f35854]) ).
fof(f35854,plain,
( spl20_1046
<=> ! [X38,X39,X40] :
( sP0(sK4(powerset(X38)),sK3(powerset(X39)),X40)
| ~ empty(X40)
| ~ empty(X38)
| element(sK6(sK4(powerset(X38)),sK3(powerset(X39)),X40),X39)
| epsilon_transitive(powerset(X39)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1046])]) ).
fof(f3562,plain,
( spl20_290
<=> ! [X25,X24,X26] :
( in(sK6(sK4(powerset(X24)),X25,X26),X25)
| sP0(sK4(powerset(X24)),X25,X26)
| ~ empty(X26)
| ~ empty(X24) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_290])]) ).
fof(f3876,plain,
( ! [X40,X38,X39] :
( sP0(sK4(powerset(X38)),sK3(powerset(X39)),X40)
| ~ empty(X40)
| ~ empty(X38)
| element(sK6(sK4(powerset(X38)),sK3(powerset(X39)),X40),X39)
| epsilon_transitive(powerset(X39)) )
| ~ spl20_230
| ~ spl20_290 ),
inference(resolution,[],[f3563,f2399]) ).
fof(f3563,plain,
( ! [X26,X24,X25] :
( in(sK6(sK4(powerset(X24)),X25,X26),X25)
| sP0(sK4(powerset(X24)),X25,X26)
| ~ empty(X26)
| ~ empty(X24) )
| ~ spl20_290 ),
inference(avatar_component_clause,[],[f3562]) ).
fof(f35852,plain,
( spl20_1045
| ~ spl20_245
| ~ spl20_290 ),
inference(avatar_split_clause,[],[f3867,f3562,f2725,f35850]) ).
fof(f35850,plain,
( spl20_1045
<=> ! [X10,X11,X12,X9] :
( sP0(sK4(powerset(X9)),X10,X11)
| ~ empty(X11)
| ~ empty(X9)
| ~ ordinal(X10)
| ordinal_subset(X12,X10)
| ~ ordinal(X12)
| element(sK6(sK4(powerset(X9)),X10,X11),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1045])]) ).
fof(f3867,plain,
( ! [X10,X11,X9,X12] :
( sP0(sK4(powerset(X9)),X10,X11)
| ~ empty(X11)
| ~ empty(X9)
| ~ ordinal(X10)
| ordinal_subset(X12,X10)
| ~ ordinal(X12)
| element(sK6(sK4(powerset(X9)),X10,X11),X12) )
| ~ spl20_245
| ~ spl20_290 ),
inference(resolution,[],[f3563,f2726]) ).
fof(f35848,plain,
( spl20_1044
| ~ spl20_245
| ~ spl20_288 ),
inference(avatar_split_clause,[],[f3839,f3554,f2725,f35846]) ).
fof(f35846,plain,
( spl20_1044
<=> ! [X10,X11,X12,X9] :
( element(sK6(X9,X10,X11),X9)
| ~ empty(X11)
| sP0(X9,X10,X11)
| ~ ordinal(X10)
| ordinal_subset(X12,X10)
| ~ ordinal(X12)
| element(sK6(X9,X10,X11),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1044])]) ).
fof(f3554,plain,
( spl20_288
<=> ! [X9,X8,X7] :
( in(sK6(X7,X8,X9),X8)
| sP0(X7,X8,X9)
| ~ empty(X9)
| element(sK6(X7,X8,X9),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_288])]) ).
fof(f3839,plain,
( ! [X10,X11,X9,X12] :
( element(sK6(X9,X10,X11),X9)
| ~ empty(X11)
| sP0(X9,X10,X11)
| ~ ordinal(X10)
| ordinal_subset(X12,X10)
| ~ ordinal(X12)
| element(sK6(X9,X10,X11),X12) )
| ~ spl20_245
| ~ spl20_288 ),
inference(resolution,[],[f3555,f2726]) ).
fof(f3555,plain,
( ! [X8,X9,X7] :
( element(sK6(X7,X8,X9),X7)
| in(sK6(X7,X8,X9),X8)
| ~ empty(X9)
| sP0(X7,X8,X9) )
| ~ spl20_288 ),
inference(avatar_component_clause,[],[f3554]) ).
fof(f35844,plain,
( spl20_1043
| spl20_304
| ~ spl20_3
| ~ spl20_506 ),
inference(avatar_split_clause,[],[f13939,f13911,f270,f4069,f35841]) ).
fof(f13911,plain,
( spl20_506
<=> ! [X0,X1] :
( in(X0,X1)
| ~ in(X0,succ(X1))
| in(X0,singleton(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_506])]) ).
fof(f13939,plain,
( in(sK1,sK2)
| in(sK1,singleton(sK2))
| ~ spl20_3
| ~ spl20_506 ),
inference(resolution,[],[f13912,f272]) ).
fof(f272,plain,
( in(sK1,succ(sK2))
| ~ spl20_3 ),
inference(avatar_component_clause,[],[f270]) ).
fof(f13912,plain,
( ! [X0,X1] :
( ~ in(X0,succ(X1))
| in(X0,X1)
| in(X0,singleton(X1)) )
| ~ spl20_506 ),
inference(avatar_component_clause,[],[f13911]) ).
fof(f35839,plain,
( spl20_1042
| ~ spl20_230
| ~ spl20_287 ),
inference(avatar_split_clause,[],[f3823,f3550,f2398,f35837]) ).
fof(f35837,plain,
( spl20_1042
<=> ! [X38,X39,X40] :
( sP0(sK3(powerset(X38)),sK4(powerset(X39)),X40)
| ~ empty(X40)
| ~ empty(X39)
| element(sK6(sK3(powerset(X38)),sK4(powerset(X39)),X40),X38)
| epsilon_transitive(powerset(X38)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1042])]) ).
fof(f3550,plain,
( spl20_287
<=> ! [X25,X24,X26] :
( in(sK6(X24,sK4(powerset(X25)),X26),X24)
| sP0(X24,sK4(powerset(X25)),X26)
| ~ empty(X26)
| ~ empty(X25) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_287])]) ).
fof(f3823,plain,
( ! [X40,X38,X39] :
( sP0(sK3(powerset(X38)),sK4(powerset(X39)),X40)
| ~ empty(X40)
| ~ empty(X39)
| element(sK6(sK3(powerset(X38)),sK4(powerset(X39)),X40),X38)
| epsilon_transitive(powerset(X38)) )
| ~ spl20_230
| ~ spl20_287 ),
inference(resolution,[],[f3551,f2399]) ).
fof(f3551,plain,
( ! [X26,X24,X25] :
( in(sK6(X24,sK4(powerset(X25)),X26),X24)
| sP0(X24,sK4(powerset(X25)),X26)
| ~ empty(X26)
| ~ empty(X25) )
| ~ spl20_287 ),
inference(avatar_component_clause,[],[f3550]) ).
fof(f35835,plain,
( spl20_1041
| ~ spl20_245
| ~ spl20_287 ),
inference(avatar_split_clause,[],[f3814,f3550,f2725,f35833]) ).
fof(f35833,plain,
( spl20_1041
<=> ! [X10,X11,X12,X9] :
( sP0(X9,sK4(powerset(X10)),X11)
| ~ empty(X11)
| ~ empty(X10)
| ~ ordinal(X9)
| ordinal_subset(X12,X9)
| ~ ordinal(X12)
| element(sK6(X9,sK4(powerset(X10)),X11),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1041])]) ).
fof(f3814,plain,
( ! [X10,X11,X9,X12] :
( sP0(X9,sK4(powerset(X10)),X11)
| ~ empty(X11)
| ~ empty(X10)
| ~ ordinal(X9)
| ordinal_subset(X12,X9)
| ~ ordinal(X12)
| element(sK6(X9,sK4(powerset(X10)),X11),X12) )
| ~ spl20_245
| ~ spl20_287 ),
inference(resolution,[],[f3551,f2726]) ).
fof(f35831,plain,
( spl20_1040
| ~ spl20_245
| ~ spl20_285 ),
inference(avatar_split_clause,[],[f3786,f3542,f2725,f35829]) ).
fof(f35829,plain,
( spl20_1040
<=> ! [X10,X11,X12,X9] :
( element(sK6(X9,X10,X11),X10)
| ~ empty(X11)
| sP0(X9,X10,X11)
| ~ ordinal(X9)
| ordinal_subset(X12,X9)
| ~ ordinal(X12)
| element(sK6(X9,X10,X11),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1040])]) ).
fof(f3542,plain,
( spl20_285
<=> ! [X9,X7,X8] :
( in(sK6(X7,X8,X9),X7)
| sP0(X7,X8,X9)
| ~ empty(X9)
| element(sK6(X7,X8,X9),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_285])]) ).
fof(f3786,plain,
( ! [X10,X11,X9,X12] :
( element(sK6(X9,X10,X11),X10)
| ~ empty(X11)
| sP0(X9,X10,X11)
| ~ ordinal(X9)
| ordinal_subset(X12,X9)
| ~ ordinal(X12)
| element(sK6(X9,X10,X11),X12) )
| ~ spl20_245
| ~ spl20_285 ),
inference(resolution,[],[f3543,f2726]) ).
fof(f3543,plain,
( ! [X8,X9,X7] :
( element(sK6(X7,X8,X9),X8)
| in(sK6(X7,X8,X9),X7)
| ~ empty(X9)
| sP0(X7,X8,X9) )
| ~ spl20_285 ),
inference(avatar_component_clause,[],[f3542]) ).
fof(f35827,plain,
( spl20_1039
| ~ spl20_245
| ~ spl20_284 ),
inference(avatar_split_clause,[],[f3761,f3538,f2725,f35825]) ).
fof(f35825,plain,
( spl20_1039
<=> ! [X6,X7,X8] :
( subset(sK6(X6,X6,X7),X6)
| sP0(X6,X6,X7)
| ~ epsilon_transitive(X6)
| ~ ordinal(X7)
| ordinal_subset(X8,X7)
| ~ ordinal(X8)
| element(sK6(X6,X6,X7),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1039])]) ).
fof(f3538,plain,
( spl20_284
<=> ! [X2,X3] :
( in(sK6(X2,X2,X3),X3)
| sP0(X2,X2,X3)
| subset(sK6(X2,X2,X3),X2)
| ~ epsilon_transitive(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_284])]) ).
fof(f3761,plain,
( ! [X8,X6,X7] :
( subset(sK6(X6,X6,X7),X6)
| sP0(X6,X6,X7)
| ~ epsilon_transitive(X6)
| ~ ordinal(X7)
| ordinal_subset(X8,X7)
| ~ ordinal(X8)
| element(sK6(X6,X6,X7),X8) )
| ~ spl20_245
| ~ spl20_284 ),
inference(resolution,[],[f3539,f2726]) ).
fof(f3539,plain,
( ! [X2,X3] :
( subset(sK6(X2,X2,X3),X2)
| in(sK6(X2,X2,X3),X3)
| sP0(X2,X2,X3)
| ~ epsilon_transitive(X2) )
| ~ spl20_284 ),
inference(avatar_component_clause,[],[f3538]) ).
fof(f35823,plain,
( spl20_1038
| ~ spl20_97
| ~ spl20_284 ),
inference(avatar_split_clause,[],[f3755,f3538,f846,f35821]) ).
fof(f35821,plain,
( spl20_1038
<=> ! [X6,X7] :
( in(sK6(X6,X6,X7),X7)
| sP0(X6,X6,X7)
| ~ epsilon_transitive(X6)
| ordinal_subset(sK6(X6,X6,X7),X6)
| ~ ordinal(X6)
| ~ ordinal(sK6(X6,X6,X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1038])]) ).
fof(f846,plain,
( spl20_97
<=> ! [X0,X1] :
( ordinal_subset(X0,X1)
| ~ subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_97])]) ).
fof(f3755,plain,
( ! [X6,X7] :
( in(sK6(X6,X6,X7),X7)
| sP0(X6,X6,X7)
| ~ epsilon_transitive(X6)
| ordinal_subset(sK6(X6,X6,X7),X6)
| ~ ordinal(X6)
| ~ ordinal(sK6(X6,X6,X7)) )
| ~ spl20_97
| ~ spl20_284 ),
inference(resolution,[],[f3539,f847]) ).
fof(f847,plain,
( ! [X0,X1] :
( ~ subset(X0,X1)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) )
| ~ spl20_97 ),
inference(avatar_component_clause,[],[f846]) ).
fof(f35819,plain,
( spl20_1037
| ~ spl20_223
| ~ spl20_283 ),
inference(avatar_split_clause,[],[f3746,f3534,f2310,f35817]) ).
fof(f35817,plain,
( spl20_1037
<=> ! [X29,X28] :
( subset(sK6(sK3(powerset(X28)),sK3(powerset(X28)),X29),X29)
| sP0(sK3(powerset(X28)),sK3(powerset(X28)),X29)
| ~ epsilon_transitive(X29)
| ~ empty(X28)
| epsilon_transitive(powerset(X28)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1037])]) ).
fof(f3534,plain,
( spl20_283
<=> ! [X4,X5] :
( in(sK6(X4,X4,X5),X4)
| sP0(X4,X4,X5)
| subset(sK6(X4,X4,X5),X5)
| ~ epsilon_transitive(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_283])]) ).
fof(f3746,plain,
( ! [X28,X29] :
( subset(sK6(sK3(powerset(X28)),sK3(powerset(X28)),X29),X29)
| sP0(sK3(powerset(X28)),sK3(powerset(X28)),X29)
| ~ epsilon_transitive(X29)
| ~ empty(X28)
| epsilon_transitive(powerset(X28)) )
| ~ spl20_223
| ~ spl20_283 ),
inference(resolution,[],[f3535,f2311]) ).
fof(f3535,plain,
( ! [X4,X5] :
( subset(sK6(X4,X4,X5),X5)
| in(sK6(X4,X4,X5),X4)
| sP0(X4,X4,X5)
| ~ epsilon_transitive(X5) )
| ~ spl20_283 ),
inference(avatar_component_clause,[],[f3534]) ).
fof(f35815,plain,
( spl20_1036
| ~ spl20_245
| ~ spl20_283 ),
inference(avatar_split_clause,[],[f3736,f3534,f2725,f35813]) ).
fof(f35813,plain,
( spl20_1036
<=> ! [X6,X7,X8] :
( subset(sK6(X6,X6,X7),X7)
| sP0(X6,X6,X7)
| ~ epsilon_transitive(X7)
| ~ ordinal(X6)
| ordinal_subset(X8,X6)
| ~ ordinal(X8)
| element(sK6(X6,X6,X7),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1036])]) ).
fof(f3736,plain,
( ! [X8,X6,X7] :
( subset(sK6(X6,X6,X7),X7)
| sP0(X6,X6,X7)
| ~ epsilon_transitive(X7)
| ~ ordinal(X6)
| ordinal_subset(X8,X6)
| ~ ordinal(X8)
| element(sK6(X6,X6,X7),X8) )
| ~ spl20_245
| ~ spl20_283 ),
inference(resolution,[],[f3535,f2726]) ).
fof(f35811,plain,
( spl20_1035
| ~ spl20_97
| ~ spl20_283 ),
inference(avatar_split_clause,[],[f3730,f3534,f846,f35809]) ).
fof(f35809,plain,
( spl20_1035
<=> ! [X6,X7] :
( in(sK6(X6,X6,X7),X6)
| sP0(X6,X6,X7)
| ~ epsilon_transitive(X7)
| ordinal_subset(sK6(X6,X6,X7),X7)
| ~ ordinal(X7)
| ~ ordinal(sK6(X6,X6,X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1035])]) ).
fof(f3730,plain,
( ! [X6,X7] :
( in(sK6(X6,X6,X7),X6)
| sP0(X6,X6,X7)
| ~ epsilon_transitive(X7)
| ordinal_subset(sK6(X6,X6,X7),X7)
| ~ ordinal(X7)
| ~ ordinal(sK6(X6,X6,X7)) )
| ~ spl20_97
| ~ spl20_283 ),
inference(resolution,[],[f3535,f847]) ).
fof(f35807,plain,
( spl20_1034
| ~ spl20_97
| ~ spl20_282 ),
inference(avatar_split_clause,[],[f3705,f3530,f846,f35805]) ).
fof(f35805,plain,
( spl20_1034
<=> ! [X6,X7] :
( in(sK6(X6,X7,X6),X6)
| sP0(X6,X7,X6)
| ~ epsilon_transitive(X7)
| ordinal_subset(sK6(X6,X7,X6),X7)
| ~ ordinal(X7)
| ~ ordinal(sK6(X6,X7,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1034])]) ).
fof(f3530,plain,
( spl20_282
<=> ! [X2,X3] :
( in(sK6(X2,X3,X2),X2)
| sP0(X2,X3,X2)
| subset(sK6(X2,X3,X2),X3)
| ~ epsilon_transitive(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_282])]) ).
fof(f3705,plain,
( ! [X6,X7] :
( in(sK6(X6,X7,X6),X6)
| sP0(X6,X7,X6)
| ~ epsilon_transitive(X7)
| ordinal_subset(sK6(X6,X7,X6),X7)
| ~ ordinal(X7)
| ~ ordinal(sK6(X6,X7,X6)) )
| ~ spl20_97
| ~ spl20_282 ),
inference(resolution,[],[f3531,f847]) ).
fof(f3531,plain,
( ! [X2,X3] :
( subset(sK6(X2,X3,X2),X3)
| in(sK6(X2,X3,X2),X2)
| sP0(X2,X3,X2)
| ~ epsilon_transitive(X3) )
| ~ spl20_282 ),
inference(avatar_component_clause,[],[f3530]) ).
fof(f35803,plain,
( spl20_1033
| ~ spl20_97
| ~ spl20_281 ),
inference(avatar_split_clause,[],[f3680,f3526,f846,f35801]) ).
fof(f35801,plain,
( spl20_1033
<=> ! [X6,X7] :
( in(sK6(X6,X7,X7),X7)
| sP0(X6,X7,X7)
| ~ epsilon_transitive(X6)
| ordinal_subset(sK6(X6,X7,X7),X6)
| ~ ordinal(X6)
| ~ ordinal(sK6(X6,X7,X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1033])]) ).
fof(f3526,plain,
( spl20_281
<=> ! [X2,X3] :
( in(sK6(X2,X3,X3),X3)
| sP0(X2,X3,X3)
| subset(sK6(X2,X3,X3),X2)
| ~ epsilon_transitive(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_281])]) ).
fof(f3680,plain,
( ! [X6,X7] :
( in(sK6(X6,X7,X7),X7)
| sP0(X6,X7,X7)
| ~ epsilon_transitive(X6)
| ordinal_subset(sK6(X6,X7,X7),X6)
| ~ ordinal(X6)
| ~ ordinal(sK6(X6,X7,X7)) )
| ~ spl20_97
| ~ spl20_281 ),
inference(resolution,[],[f3527,f847]) ).
fof(f3527,plain,
( ! [X2,X3] :
( subset(sK6(X2,X3,X3),X2)
| in(sK6(X2,X3,X3),X3)
| sP0(X2,X3,X3)
| ~ epsilon_transitive(X2) )
| ~ spl20_281 ),
inference(avatar_component_clause,[],[f3526]) ).
fof(f35799,plain,
( spl20_1032
| ~ spl20_462
| ~ spl20_478 ),
inference(avatar_split_clause,[],[f13160,f12953,f12811,f35797]) ).
fof(f35797,plain,
( spl20_1032
<=> ! [X16] : ~ in(succ(set_union2(succ(sK2),X16)),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1032])]) ).
fof(f12811,plain,
( spl20_462
<=> ! [X0] :
( ~ in(X0,sK1)
| in(X0,succ(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_462])]) ).
fof(f12953,plain,
( spl20_478
<=> ! [X13,X12] : ~ in(succ(set_union2(X12,X13)),X12) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_478])]) ).
fof(f13160,plain,
( ! [X16] : ~ in(succ(set_union2(succ(sK2),X16)),sK1)
| ~ spl20_462
| ~ spl20_478 ),
inference(resolution,[],[f12954,f12812]) ).
fof(f12812,plain,
( ! [X0] :
( in(X0,succ(sK2))
| ~ in(X0,sK1) )
| ~ spl20_462 ),
inference(avatar_component_clause,[],[f12811]) ).
fof(f12954,plain,
( ! [X12,X13] : ~ in(succ(set_union2(X12,X13)),X12)
| ~ spl20_478 ),
inference(avatar_component_clause,[],[f12953]) ).
fof(f35795,plain,
( spl20_1031
| ~ spl20_230
| ~ spl20_278 ),
inference(avatar_split_clause,[],[f3650,f3514,f2398,f35793]) ).
fof(f35793,plain,
( spl20_1031
<=> ! [X22,X21] :
( ~ empty(X21)
| sK4(powerset(X21)) = sK3(powerset(X22))
| ~ ordinal(sK4(powerset(X21)))
| ~ ordinal(sK3(powerset(X22)))
| element(sK4(powerset(X21)),X22)
| epsilon_transitive(powerset(X22)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1031])]) ).
fof(f3514,plain,
( spl20_278
<=> ! [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_278])]) ).
fof(f3650,plain,
( ! [X21,X22] :
( ~ empty(X21)
| sK4(powerset(X21)) = sK3(powerset(X22))
| ~ ordinal(sK4(powerset(X21)))
| ~ ordinal(sK3(powerset(X22)))
| element(sK4(powerset(X21)),X22)
| epsilon_transitive(powerset(X22)) )
| ~ spl20_230
| ~ spl20_278 ),
inference(resolution,[],[f3515,f2399]) ).
fof(f3515,plain,
( ! [X0,X1] :
( in(sK4(powerset(X0)),X1)
| ~ empty(X0)
| sK4(powerset(X0)) = X1
| ~ ordinal(sK4(powerset(X0)))
| ~ ordinal(X1) )
| ~ spl20_278 ),
inference(avatar_component_clause,[],[f3514]) ).
fof(f35791,plain,
( spl20_1030
| ~ spl20_230
| ~ spl20_272 ),
inference(avatar_split_clause,[],[f3425,f3020,f2398,f35789]) ).
fof(f35789,plain,
( spl20_1030
<=> ! [X27,X26] :
( element(sK6(X26,X26,sK3(powerset(X27))),X26)
| sP0(X26,X26,sK3(powerset(X27)))
| element(sK6(X26,X26,sK3(powerset(X27))),X27)
| epsilon_transitive(powerset(X27)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1030])]) ).
fof(f3020,plain,
( spl20_272
<=> ! [X4,X5] :
( in(sK6(X4,X4,X5),X5)
| sP0(X4,X4,X5)
| element(sK6(X4,X4,X5),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_272])]) ).
fof(f3425,plain,
( ! [X26,X27] :
( element(sK6(X26,X26,sK3(powerset(X27))),X26)
| sP0(X26,X26,sK3(powerset(X27)))
| element(sK6(X26,X26,sK3(powerset(X27))),X27)
| epsilon_transitive(powerset(X27)) )
| ~ spl20_230
| ~ spl20_272 ),
inference(resolution,[],[f3021,f2399]) ).
fof(f3021,plain,
( ! [X4,X5] :
( element(sK6(X4,X4,X5),X4)
| in(sK6(X4,X4,X5),X5)
| sP0(X4,X4,X5) )
| ~ spl20_272 ),
inference(avatar_component_clause,[],[f3020]) ).
fof(f35787,plain,
( spl20_1029
| ~ spl20_100
| ~ spl20_272 ),
inference(avatar_split_clause,[],[f3408,f3020,f858,f35785]) ).
fof(f35785,plain,
( spl20_1029
<=> ! [X2,X0,X1] :
( in(sK6(powerset(X0),powerset(X0),X1),X1)
| sP0(powerset(X0),powerset(X0),X1)
| element(X2,X0)
| ~ in(X2,sK6(powerset(X0),powerset(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1029])]) ).
fof(f3408,plain,
( ! [X2,X0,X1] :
( in(sK6(powerset(X0),powerset(X0),X1),X1)
| sP0(powerset(X0),powerset(X0),X1)
| element(X2,X0)
| ~ in(X2,sK6(powerset(X0),powerset(X0),X1)) )
| ~ spl20_100
| ~ spl20_272 ),
inference(resolution,[],[f3021,f859]) ).
fof(f35783,plain,
( spl20_1028
| ~ spl20_230
| ~ spl20_254 ),
inference(avatar_split_clause,[],[f3037,f2936,f2398,f35781]) ).
fof(f35781,plain,
( spl20_1028
<=> ! [X22,X21] :
( sK3(powerset(X21)) = X22
| singleton(X22) = sK3(powerset(X21))
| ~ ordinal(singleton(X22))
| ~ ordinal(sK3(powerset(X21)))
| element(singleton(X22),X21)
| epsilon_transitive(powerset(X21)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1028])]) ).
fof(f2936,plain,
( spl20_254
<=> ! [X0,X1] :
( X0 = X1
| in(singleton(X1),X0)
| singleton(X1) = X0
| ~ ordinal(singleton(X1))
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_254])]) ).
fof(f3037,plain,
( ! [X21,X22] :
( sK3(powerset(X21)) = X22
| singleton(X22) = sK3(powerset(X21))
| ~ ordinal(singleton(X22))
| ~ ordinal(sK3(powerset(X21)))
| element(singleton(X22),X21)
| epsilon_transitive(powerset(X21)) )
| ~ spl20_230
| ~ spl20_254 ),
inference(resolution,[],[f2937,f2399]) ).
fof(f2937,plain,
( ! [X0,X1] :
( in(singleton(X1),X0)
| X0 = X1
| singleton(X1) = X0
| ~ ordinal(singleton(X1))
| ~ ordinal(X0) )
| ~ spl20_254 ),
inference(avatar_component_clause,[],[f2936]) ).
fof(f35779,plain,
( spl20_1027
| ~ spl20_179
| ~ spl20_245 ),
inference(avatar_split_clause,[],[f2768,f2725,f1561,f35777]) ).
fof(f35777,plain,
( spl20_1027
<=> ! [X102,X104,X103,X101] :
( ~ ordinal(X101)
| ordinal_subset(X102,X101)
| ~ ordinal(X102)
| element(sK6(X101,X103,X104),X102)
| in(sK6(X101,X103,X104),X104)
| sP0(X101,X103,X104)
| ~ empty(X103) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1027])]) ).
fof(f1561,plain,
( spl20_179
<=> ! [X13,X14,X15] :
( in(sK6(X13,X14,X15),X15)
| in(sK6(X13,X14,X15),X13)
| sP0(X13,X14,X15)
| ~ empty(X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_179])]) ).
fof(f2768,plain,
( ! [X101,X104,X102,X103] :
( ~ ordinal(X101)
| ordinal_subset(X102,X101)
| ~ ordinal(X102)
| element(sK6(X101,X103,X104),X102)
| in(sK6(X101,X103,X104),X104)
| sP0(X101,X103,X104)
| ~ empty(X103) )
| ~ spl20_179
| ~ spl20_245 ),
inference(resolution,[],[f2726,f1562]) ).
fof(f1562,plain,
( ! [X14,X15,X13] :
( in(sK6(X13,X14,X15),X15)
| in(sK6(X13,X14,X15),X13)
| sP0(X13,X14,X15)
| ~ empty(X14) )
| ~ spl20_179 ),
inference(avatar_component_clause,[],[f1561]) ).
fof(f35775,plain,
( spl20_1026
| ~ spl20_178
| ~ spl20_245 ),
inference(avatar_split_clause,[],[f2767,f2725,f1557,f35773]) ).
fof(f35773,plain,
( spl20_1026
<=> ! [X99,X98,X100,X97] :
( ~ ordinal(X97)
| ordinal_subset(X98,X97)
| ~ ordinal(X98)
| element(sK6(X97,X99,X100),X98)
| in(sK6(X97,X99,X100),X99)
| sP0(X97,X99,X100)
| ~ empty(X100) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1026])]) ).
fof(f1557,plain,
( spl20_178
<=> ! [X16,X17,X15] :
( in(sK6(X15,X16,X17),X16)
| in(sK6(X15,X16,X17),X15)
| sP0(X15,X16,X17)
| ~ empty(X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_178])]) ).
fof(f2767,plain,
( ! [X98,X99,X97,X100] :
( ~ ordinal(X97)
| ordinal_subset(X98,X97)
| ~ ordinal(X98)
| element(sK6(X97,X99,X100),X98)
| in(sK6(X97,X99,X100),X99)
| sP0(X97,X99,X100)
| ~ empty(X100) )
| ~ spl20_178
| ~ spl20_245 ),
inference(resolution,[],[f2726,f1558]) ).
fof(f1558,plain,
( ! [X16,X17,X15] :
( in(sK6(X15,X16,X17),X16)
| in(sK6(X15,X16,X17),X15)
| sP0(X15,X16,X17)
| ~ empty(X17) )
| ~ spl20_178 ),
inference(avatar_component_clause,[],[f1557]) ).
fof(f35771,plain,
( spl20_1025
| ~ spl20_180
| ~ spl20_245 ),
inference(avatar_split_clause,[],[f2761,f2725,f1565,f35769]) ).
fof(f35769,plain,
( spl20_1025
<=> ! [X74,X75,X76,X73] :
( ~ ordinal(X73)
| ordinal_subset(X74,X73)
| ~ ordinal(X74)
| element(sK6(X75,X73,X76),X74)
| in(sK6(X75,X73,X76),X76)
| sP0(X75,X73,X76)
| ~ empty(X75) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1025])]) ).
fof(f1565,plain,
( spl20_180
<=> ! [X13,X14,X15] :
( in(sK6(X13,X14,X15),X15)
| in(sK6(X13,X14,X15),X14)
| sP0(X13,X14,X15)
| ~ empty(X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_180])]) ).
fof(f2761,plain,
( ! [X73,X76,X74,X75] :
( ~ ordinal(X73)
| ordinal_subset(X74,X73)
| ~ ordinal(X74)
| element(sK6(X75,X73,X76),X74)
| in(sK6(X75,X73,X76),X76)
| sP0(X75,X73,X76)
| ~ empty(X75) )
| ~ spl20_180
| ~ spl20_245 ),
inference(resolution,[],[f2726,f1566]) ).
fof(f1566,plain,
( ! [X14,X15,X13] :
( in(sK6(X13,X14,X15),X15)
| in(sK6(X13,X14,X15),X14)
| sP0(X13,X14,X15)
| ~ empty(X13) )
| ~ spl20_180 ),
inference(avatar_component_clause,[],[f1565]) ).
fof(f35767,plain,
( spl20_1024
| ~ spl20_178
| ~ spl20_245 ),
inference(avatar_split_clause,[],[f2760,f2725,f1557,f35765]) ).
fof(f35765,plain,
( spl20_1024
<=> ! [X69,X71,X70,X72] :
( ~ ordinal(X69)
| ordinal_subset(X70,X69)
| ~ ordinal(X70)
| element(sK6(X71,X69,X72),X70)
| in(sK6(X71,X69,X72),X71)
| sP0(X71,X69,X72)
| ~ empty(X72) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1024])]) ).
fof(f2760,plain,
( ! [X72,X70,X71,X69] :
( ~ ordinal(X69)
| ordinal_subset(X70,X69)
| ~ ordinal(X70)
| element(sK6(X71,X69,X72),X70)
| in(sK6(X71,X69,X72),X71)
| sP0(X71,X69,X72)
| ~ empty(X72) )
| ~ spl20_178
| ~ spl20_245 ),
inference(resolution,[],[f2726,f1558]) ).
fof(f35763,plain,
( spl20_1023
| ~ spl20_180
| ~ spl20_245 ),
inference(avatar_split_clause,[],[f2754,f2725,f1565,f35761]) ).
fof(f35761,plain,
( spl20_1023
<=> ! [X48,X47,X46,X45] :
( ~ ordinal(X45)
| ordinal_subset(X46,X45)
| ~ ordinal(X46)
| element(sK6(X47,X48,X45),X46)
| in(sK6(X47,X48,X45),X48)
| sP0(X47,X48,X45)
| ~ empty(X47) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1023])]) ).
fof(f2754,plain,
( ! [X48,X46,X47,X45] :
( ~ ordinal(X45)
| ordinal_subset(X46,X45)
| ~ ordinal(X46)
| element(sK6(X47,X48,X45),X46)
| in(sK6(X47,X48,X45),X48)
| sP0(X47,X48,X45)
| ~ empty(X47) )
| ~ spl20_180
| ~ spl20_245 ),
inference(resolution,[],[f2726,f1566]) ).
fof(f35759,plain,
( spl20_1022
| ~ spl20_179
| ~ spl20_245 ),
inference(avatar_split_clause,[],[f2753,f2725,f1561,f35757]) ).
fof(f35757,plain,
( spl20_1022
<=> ! [X41,X42,X44,X43] :
( ~ ordinal(X41)
| ordinal_subset(X42,X41)
| ~ ordinal(X42)
| element(sK6(X43,X44,X41),X42)
| in(sK6(X43,X44,X41),X43)
| sP0(X43,X44,X41)
| ~ empty(X44) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1022])]) ).
fof(f2753,plain,
( ! [X41,X44,X42,X43] :
( ~ ordinal(X41)
| ordinal_subset(X42,X41)
| ~ ordinal(X42)
| element(sK6(X43,X44,X41),X42)
| in(sK6(X43,X44,X41),X43)
| sP0(X43,X44,X41)
| ~ empty(X44) )
| ~ spl20_179
| ~ spl20_245 ),
inference(resolution,[],[f2726,f1562]) ).
fof(f35755,plain,
( spl20_1021
| ~ spl20_462
| ~ spl20_477 ),
inference(avatar_split_clause,[],[f13143,f12949,f12811,f35753]) ).
fof(f35753,plain,
( spl20_1021
<=> ! [X16] : ~ in(succ(set_union2(X16,succ(sK2))),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1021])]) ).
fof(f12949,plain,
( spl20_477
<=> ! [X13,X12] : ~ in(succ(set_union2(X12,X13)),X13) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_477])]) ).
fof(f13143,plain,
( ! [X16] : ~ in(succ(set_union2(X16,succ(sK2))),sK1)
| ~ spl20_462
| ~ spl20_477 ),
inference(resolution,[],[f12950,f12812]) ).
fof(f12950,plain,
( ! [X12,X13] : ~ in(succ(set_union2(X12,X13)),X13)
| ~ spl20_477 ),
inference(avatar_component_clause,[],[f12949]) ).
fof(f35751,plain,
( spl20_1020
| ~ spl20_185
| ~ spl20_234 ),
inference(avatar_split_clause,[],[f2571,f2500,f1657,f35749]) ).
fof(f35749,plain,
( spl20_1020
<=> ! [X112,X110,X111,X109] :
( ~ ordinal(X109)
| ordinal_subset(X110,X109)
| ~ ordinal(X110)
| ~ empty(X110)
| element(sK6(X109,X111,X112),X111)
| in(sK6(X109,X111,X112),X112)
| sP0(X109,X111,X112) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1020])]) ).
fof(f1657,plain,
( spl20_185
<=> ! [X9,X8,X7] :
( in(sK6(X7,X8,X9),X9)
| in(sK6(X7,X8,X9),X7)
| sP0(X7,X8,X9)
| element(sK6(X7,X8,X9),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_185])]) ).
fof(f2571,plain,
( ! [X111,X109,X112,X110] :
( ~ ordinal(X109)
| ordinal_subset(X110,X109)
| ~ ordinal(X110)
| ~ empty(X110)
| element(sK6(X109,X111,X112),X111)
| in(sK6(X109,X111,X112),X112)
| sP0(X109,X111,X112) )
| ~ spl20_185
| ~ spl20_234 ),
inference(resolution,[],[f2501,f1658]) ).
fof(f1658,plain,
( ! [X8,X9,X7] :
( element(sK6(X7,X8,X9),X8)
| in(sK6(X7,X8,X9),X9)
| in(sK6(X7,X8,X9),X7)
| sP0(X7,X8,X9) )
| ~ spl20_185 ),
inference(avatar_component_clause,[],[f1657]) ).
fof(f35747,plain,
( spl20_1019
| ~ spl20_183
| ~ spl20_234 ),
inference(avatar_split_clause,[],[f2570,f2500,f1649,f35745]) ).
fof(f35745,plain,
( spl20_1019
<=> ! [X105,X106,X108,X107] :
( ~ ordinal(X105)
| ordinal_subset(X106,X105)
| ~ ordinal(X106)
| ~ empty(X106)
| element(sK6(X105,X107,X108),X108)
| in(sK6(X105,X107,X108),X107)
| sP0(X105,X107,X108) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1019])]) ).
fof(f1649,plain,
( spl20_183
<=> ! [X9,X11,X10] :
( in(sK6(X9,X10,X11),X10)
| in(sK6(X9,X10,X11),X9)
| sP0(X9,X10,X11)
| element(sK6(X9,X10,X11),X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_183])]) ).
fof(f2570,plain,
( ! [X108,X106,X107,X105] :
( ~ ordinal(X105)
| ordinal_subset(X106,X105)
| ~ ordinal(X106)
| ~ empty(X106)
| element(sK6(X105,X107,X108),X108)
| in(sK6(X105,X107,X108),X107)
| sP0(X105,X107,X108) )
| ~ spl20_183
| ~ spl20_234 ),
inference(resolution,[],[f2501,f1650]) ).
fof(f1650,plain,
( ! [X10,X11,X9] :
( element(sK6(X9,X10,X11),X11)
| in(sK6(X9,X10,X11),X10)
| in(sK6(X9,X10,X11),X9)
| sP0(X9,X10,X11) )
| ~ spl20_183 ),
inference(avatar_component_clause,[],[f1649]) ).
fof(f35743,plain,
( spl20_1018
| ~ spl20_110
| ~ spl20_234 ),
inference(avatar_split_clause,[],[f2567,f2500,f935,f35741]) ).
fof(f35741,plain,
( spl20_1018
<=> ! [X94,X95,X93,X96] :
( ~ ordinal(X93)
| ordinal_subset(X94,X93)
| ~ ordinal(X94)
| ~ empty(X94)
| in(sK6(X93,X95,X96),X96)
| in(sK6(X93,X95,X96),X95)
| sP0(X93,X95,X96) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1018])]) ).
fof(f935,plain,
( spl20_110
<=> ! [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_110])]) ).
fof(f2567,plain,
( ! [X96,X94,X95,X93] :
( ~ ordinal(X93)
| ordinal_subset(X94,X93)
| ~ ordinal(X94)
| ~ empty(X94)
| in(sK6(X93,X95,X96),X96)
| in(sK6(X93,X95,X96),X95)
| sP0(X93,X95,X96) )
| ~ spl20_110
| ~ spl20_234 ),
inference(resolution,[],[f2501,f936]) ).
fof(f936,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_110 ),
inference(avatar_component_clause,[],[f935]) ).
fof(f35739,plain,
( spl20_1017
| ~ spl20_187
| ~ spl20_234 ),
inference(avatar_split_clause,[],[f2564,f2500,f1665,f35737]) ).
fof(f35737,plain,
( spl20_1017
<=> ! [X82,X81,X84,X83] :
( ~ ordinal(X81)
| ordinal_subset(X82,X81)
| ~ ordinal(X82)
| ~ empty(X82)
| element(sK6(X83,X81,X84),X83)
| in(sK6(X83,X81,X84),X84)
| sP0(X83,X81,X84) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1017])]) ).
fof(f1665,plain,
( spl20_187
<=> ! [X9,X8,X7] :
( in(sK6(X7,X8,X9),X9)
| in(sK6(X7,X8,X9),X8)
| sP0(X7,X8,X9)
| element(sK6(X7,X8,X9),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_187])]) ).
fof(f2564,plain,
( ! [X82,X83,X81,X84] :
( ~ ordinal(X81)
| ordinal_subset(X82,X81)
| ~ ordinal(X82)
| ~ empty(X82)
| element(sK6(X83,X81,X84),X83)
| in(sK6(X83,X81,X84),X84)
| sP0(X83,X81,X84) )
| ~ spl20_187
| ~ spl20_234 ),
inference(resolution,[],[f2501,f1666]) ).
fof(f1666,plain,
( ! [X8,X9,X7] :
( element(sK6(X7,X8,X9),X7)
| in(sK6(X7,X8,X9),X9)
| in(sK6(X7,X8,X9),X8)
| sP0(X7,X8,X9) )
| ~ spl20_187 ),
inference(avatar_component_clause,[],[f1665]) ).
fof(f35735,plain,
( spl20_1016
| ~ spl20_183
| ~ spl20_234 ),
inference(avatar_split_clause,[],[f2563,f2500,f1649,f35733]) ).
fof(f35733,plain,
( spl20_1016
<=> ! [X77,X78,X80,X79] :
( ~ ordinal(X77)
| ordinal_subset(X78,X77)
| ~ ordinal(X78)
| ~ empty(X78)
| element(sK6(X79,X77,X80),X80)
| in(sK6(X79,X77,X80),X79)
| sP0(X79,X77,X80) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1016])]) ).
fof(f2563,plain,
( ! [X80,X78,X79,X77] :
( ~ ordinal(X77)
| ordinal_subset(X78,X77)
| ~ ordinal(X78)
| ~ empty(X78)
| element(sK6(X79,X77,X80),X80)
| in(sK6(X79,X77,X80),X79)
| sP0(X79,X77,X80) )
| ~ spl20_183
| ~ spl20_234 ),
inference(resolution,[],[f2501,f1650]) ).
fof(f35731,plain,
( spl20_1015
| ~ spl20_110
| ~ spl20_234 ),
inference(avatar_split_clause,[],[f2560,f2500,f935,f35729]) ).
fof(f35729,plain,
( spl20_1015
<=> ! [X65,X68,X67,X66] :
( ~ ordinal(X65)
| ordinal_subset(X66,X65)
| ~ ordinal(X66)
| ~ empty(X66)
| in(sK6(X67,X65,X68),X68)
| in(sK6(X67,X65,X68),X67)
| sP0(X67,X65,X68) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1015])]) ).
fof(f2560,plain,
( ! [X65,X68,X66,X67] :
( ~ ordinal(X65)
| ordinal_subset(X66,X65)
| ~ ordinal(X66)
| ~ empty(X66)
| in(sK6(X67,X65,X68),X68)
| in(sK6(X67,X65,X68),X67)
| sP0(X67,X65,X68) )
| ~ spl20_110
| ~ spl20_234 ),
inference(resolution,[],[f2501,f936]) ).
fof(f35727,plain,
( spl20_1014
| ~ spl20_187
| ~ spl20_234 ),
inference(avatar_split_clause,[],[f2557,f2500,f1665,f35725]) ).
fof(f35725,plain,
( spl20_1014
<=> ! [X55,X54,X53,X56] :
( ~ ordinal(X53)
| ordinal_subset(X54,X53)
| ~ ordinal(X54)
| ~ empty(X54)
| element(sK6(X55,X56,X53),X55)
| in(sK6(X55,X56,X53),X56)
| sP0(X55,X56,X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1014])]) ).
fof(f2557,plain,
( ! [X56,X54,X55,X53] :
( ~ ordinal(X53)
| ordinal_subset(X54,X53)
| ~ ordinal(X54)
| ~ empty(X54)
| element(sK6(X55,X56,X53),X55)
| in(sK6(X55,X56,X53),X56)
| sP0(X55,X56,X53) )
| ~ spl20_187
| ~ spl20_234 ),
inference(resolution,[],[f2501,f1666]) ).
fof(f35723,plain,
( spl20_1013
| ~ spl20_185
| ~ spl20_234 ),
inference(avatar_split_clause,[],[f2556,f2500,f1657,f35721]) ).
fof(f35721,plain,
( spl20_1013
<=> ! [X51,X50,X49,X52] :
( ~ ordinal(X49)
| ordinal_subset(X50,X49)
| ~ ordinal(X50)
| ~ empty(X50)
| element(sK6(X51,X52,X49),X52)
| in(sK6(X51,X52,X49),X51)
| sP0(X51,X52,X49) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1013])]) ).
fof(f2556,plain,
( ! [X50,X51,X49,X52] :
( ~ ordinal(X49)
| ordinal_subset(X50,X49)
| ~ ordinal(X50)
| ~ empty(X50)
| element(sK6(X51,X52,X49),X52)
| in(sK6(X51,X52,X49),X51)
| sP0(X51,X52,X49) )
| ~ spl20_185
| ~ spl20_234 ),
inference(resolution,[],[f2501,f1658]) ).
fof(f35719,plain,
( spl20_1012
| ~ spl20_110
| ~ spl20_234 ),
inference(avatar_split_clause,[],[f2553,f2500,f935,f35717]) ).
fof(f35717,plain,
( spl20_1012
<=> ! [X38,X40,X39,X37] :
( ~ ordinal(X37)
| ordinal_subset(X38,X37)
| ~ ordinal(X38)
| ~ empty(X38)
| in(sK6(X39,X40,X37),X40)
| in(sK6(X39,X40,X37),X39)
| sP0(X39,X40,X37) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1012])]) ).
fof(f2553,plain,
( ! [X40,X38,X39,X37] :
( ~ ordinal(X37)
| ordinal_subset(X38,X37)
| ~ ordinal(X38)
| ~ empty(X38)
| in(sK6(X39,X40,X37),X40)
| in(sK6(X39,X40,X37),X39)
| sP0(X39,X40,X37) )
| ~ spl20_110
| ~ spl20_234 ),
inference(resolution,[],[f2501,f936]) ).
fof(f35715,plain,
( spl20_1011
| ~ spl20_177
| ~ spl20_230 ),
inference(avatar_split_clause,[],[f2445,f2398,f1462,f35713]) ).
fof(f35713,plain,
( spl20_1011
<=> ! [X86,X85] :
( element(sK6(X85,X85,sK3(powerset(X86))),X86)
| epsilon_transitive(powerset(X86))
| in(sK6(X85,X85,sK3(powerset(X86))),X85)
| sP0(X85,X85,sK3(powerset(X86))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1011])]) ).
fof(f1462,plain,
( spl20_177
<=> ! [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_177])]) ).
fof(f2445,plain,
( ! [X86,X85] :
( element(sK6(X85,X85,sK3(powerset(X86))),X86)
| epsilon_transitive(powerset(X86))
| in(sK6(X85,X85,sK3(powerset(X86))),X85)
| sP0(X85,X85,sK3(powerset(X86))) )
| ~ spl20_177
| ~ spl20_230 ),
inference(resolution,[],[f2399,f1463]) ).
fof(f1463,plain,
( ! [X4,X5] :
( in(sK6(X4,X4,X5),X5)
| in(sK6(X4,X4,X5),X4)
| sP0(X4,X4,X5) )
| ~ spl20_177 ),
inference(avatar_component_clause,[],[f1462]) ).
fof(f35711,plain,
( spl20_1010
| ~ spl20_75
| ~ spl20_462 ),
inference(avatar_split_clause,[],[f12838,f12811,f653,f35709]) ).
fof(f35709,plain,
( spl20_1010
<=> ! [X7] :
( ~ in(X7,sK1)
| ~ in(succ(sK2),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1010])]) ).
fof(f12838,plain,
( ! [X7] :
( ~ in(X7,sK1)
| ~ in(succ(sK2),X7) )
| ~ spl20_75
| ~ spl20_462 ),
inference(resolution,[],[f12812,f654]) ).
fof(f35128,plain,
( ~ spl20_64
| spl20_1009
| ~ spl20_88
| ~ spl20_935 ),
inference(avatar_split_clause,[],[f31394,f31347,f772,f35125,f596]) ).
fof(f596,plain,
( spl20_64
<=> epsilon_transitive(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_64])]) ).
fof(f35125,plain,
( spl20_1009
<=> subset(sK4(sK2),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1009])]) ).
fof(f772,plain,
( spl20_88
<=> ! [X2,X0] :
( subset(X2,X0)
| ~ in(X2,X0)
| ~ epsilon_transitive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_88])]) ).
fof(f31394,plain,
( subset(sK4(sK2),sK1)
| ~ epsilon_transitive(sK1)
| ~ spl20_88
| ~ spl20_935 ),
inference(resolution,[],[f31349,f773]) ).
fof(f773,plain,
( ! [X2,X0] :
( ~ in(X2,X0)
| subset(X2,X0)
| ~ epsilon_transitive(X0) )
| ~ spl20_88 ),
inference(avatar_component_clause,[],[f772]) ).
fof(f34046,plain,
( ~ spl20_64
| spl20_1008
| ~ spl20_88
| ~ spl20_867 ),
inference(avatar_split_clause,[],[f26942,f26456,f772,f34043,f596]) ).
fof(f34043,plain,
( spl20_1008
<=> subset(sK4(sK1),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1008])]) ).
fof(f26942,plain,
( subset(sK4(sK1),sK1)
| ~ epsilon_transitive(sK1)
| ~ spl20_88
| ~ spl20_867 ),
inference(resolution,[],[f26458,f773]) ).
fof(f31705,plain,
( spl20_431
| ~ spl20_206
| ~ spl20_933 ),
inference(avatar_split_clause,[],[f31542,f29997,f2142,f10101]) ).
fof(f10101,plain,
( spl20_431
<=> sP0(singleton(sK2),sK2,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_431])]) ).
fof(f2142,plain,
( spl20_206
<=> ! [X2,X1] : sP0(X2,X1,set_union2(X2,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_206])]) ).
fof(f29997,plain,
( spl20_933
<=> sK1 = set_union2(singleton(sK2),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_933])]) ).
fof(f31542,plain,
( sP0(singleton(sK2),sK2,sK1)
| ~ spl20_206
| ~ spl20_933 ),
inference(superposition,[],[f2143,f29999]) ).
fof(f29999,plain,
( sK1 = set_union2(singleton(sK2),sK2)
| ~ spl20_933 ),
inference(avatar_component_clause,[],[f29997]) ).
fof(f2143,plain,
( ! [X2,X1] : sP0(X2,X1,set_union2(X2,X1))
| ~ spl20_206 ),
inference(avatar_component_clause,[],[f2142]) ).
fof(f31704,plain,
( spl20_1007
| ~ spl20_151
| ~ spl20_396 ),
inference(avatar_split_clause,[],[f7000,f6282,f1221,f31702]) ).
fof(f31702,plain,
( spl20_1007
<=> ! [X49,X48,X47] :
( subset(sK6(X47,sK4(powerset(X48)),sK4(powerset(X49))),X47)
| sP0(X47,sK4(powerset(X48)),sK4(powerset(X49)))
| ~ epsilon_transitive(X47)
| ~ empty(X49)
| ~ empty(X48) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1007])]) ).
fof(f1221,plain,
( spl20_151
<=> ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK4(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_151])]) ).
fof(f6282,plain,
( spl20_396
<=> ! [X27,X28,X26] :
( subset(sK6(X26,X27,sK4(powerset(X28))),X26)
| in(sK6(X26,X27,sK4(powerset(X28))),X27)
| sP0(X26,X27,sK4(powerset(X28)))
| ~ epsilon_transitive(X26)
| ~ empty(X28) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_396])]) ).
fof(f7000,plain,
( ! [X48,X49,X47] :
( subset(sK6(X47,sK4(powerset(X48)),sK4(powerset(X49))),X47)
| sP0(X47,sK4(powerset(X48)),sK4(powerset(X49)))
| ~ epsilon_transitive(X47)
| ~ empty(X49)
| ~ empty(X48) )
| ~ spl20_151
| ~ spl20_396 ),
inference(resolution,[],[f6283,f1222]) ).
fof(f1222,plain,
( ! [X0,X1] :
( ~ in(X1,sK4(powerset(X0)))
| ~ empty(X0) )
| ~ spl20_151 ),
inference(avatar_component_clause,[],[f1221]) ).
fof(f6283,plain,
( ! [X28,X26,X27] :
( subset(sK6(X26,X27,sK4(powerset(X28))),X26)
| in(sK6(X26,X27,sK4(powerset(X28))),X27)
| sP0(X26,X27,sK4(powerset(X28)))
| ~ epsilon_transitive(X26)
| ~ empty(X28) )
| ~ spl20_396 ),
inference(avatar_component_clause,[],[f6282]) ).
fof(f31700,plain,
( spl20_1006
| ~ spl20_151
| ~ spl20_393 ),
inference(avatar_split_clause,[],[f6903,f6269,f1221,f31698]) ).
fof(f31698,plain,
( spl20_1006
<=> ! [X48,X47,X49] :
( subset(sK6(sK4(powerset(X47)),X48,sK4(powerset(X49))),X48)
| sP0(sK4(powerset(X47)),X48,sK4(powerset(X49)))
| ~ epsilon_transitive(X48)
| ~ empty(X49)
| ~ empty(X47) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1006])]) ).
fof(f6269,plain,
( spl20_393
<=> ! [X27,X28,X26] :
( subset(sK6(X26,X27,sK4(powerset(X28))),X27)
| in(sK6(X26,X27,sK4(powerset(X28))),X26)
| sP0(X26,X27,sK4(powerset(X28)))
| ~ epsilon_transitive(X27)
| ~ empty(X28) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_393])]) ).
fof(f6903,plain,
( ! [X48,X49,X47] :
( subset(sK6(sK4(powerset(X47)),X48,sK4(powerset(X49))),X48)
| sP0(sK4(powerset(X47)),X48,sK4(powerset(X49)))
| ~ epsilon_transitive(X48)
| ~ empty(X49)
| ~ empty(X47) )
| ~ spl20_151
| ~ spl20_393 ),
inference(resolution,[],[f6270,f1222]) ).
fof(f6270,plain,
( ! [X28,X26,X27] :
( subset(sK6(X26,X27,sK4(powerset(X28))),X27)
| in(sK6(X26,X27,sK4(powerset(X28))),X26)
| sP0(X26,X27,sK4(powerset(X28)))
| ~ epsilon_transitive(X27)
| ~ empty(X28) )
| ~ spl20_393 ),
inference(avatar_component_clause,[],[f6269]) ).
fof(f31696,plain,
( spl20_1005
| ~ spl20_151
| ~ spl20_390 ),
inference(avatar_split_clause,[],[f6811,f6257,f1221,f31694]) ).
fof(f31694,plain,
( spl20_1005
<=> ! [X48,X47,X49] :
( subset(sK6(sK4(powerset(X47)),sK4(powerset(X48)),X49),X49)
| sP0(sK4(powerset(X47)),sK4(powerset(X48)),X49)
| ~ epsilon_transitive(X49)
| ~ empty(X48)
| ~ empty(X47) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1005])]) ).
fof(f6257,plain,
( spl20_390
<=> ! [X25,X24,X26] :
( subset(sK6(X24,sK4(powerset(X25)),X26),X26)
| in(sK6(X24,sK4(powerset(X25)),X26),X24)
| sP0(X24,sK4(powerset(X25)),X26)
| ~ epsilon_transitive(X26)
| ~ empty(X25) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_390])]) ).
fof(f6811,plain,
( ! [X48,X49,X47] :
( subset(sK6(sK4(powerset(X47)),sK4(powerset(X48)),X49),X49)
| sP0(sK4(powerset(X47)),sK4(powerset(X48)),X49)
| ~ epsilon_transitive(X49)
| ~ empty(X48)
| ~ empty(X47) )
| ~ spl20_151
| ~ spl20_390 ),
inference(resolution,[],[f6258,f1222]) ).
fof(f6258,plain,
( ! [X26,X24,X25] :
( subset(sK6(X24,sK4(powerset(X25)),X26),X26)
| in(sK6(X24,sK4(powerset(X25)),X26),X24)
| sP0(X24,sK4(powerset(X25)),X26)
| ~ epsilon_transitive(X26)
| ~ empty(X25) )
| ~ spl20_390 ),
inference(avatar_component_clause,[],[f6257]) ).
fof(f31692,plain,
( spl20_1004
| ~ spl20_75
| ~ spl20_369 ),
inference(avatar_split_clause,[],[f6133,f5371,f653,f31690]) ).
fof(f31690,plain,
( spl20_1004
<=> ! [X25,X24,X26] :
( element(sK6(X24,sK4(powerset(X25)),X26),X24)
| sP0(X24,sK4(powerset(X25)),X26)
| ~ empty(X25)
| ~ in(X26,sK6(X24,sK4(powerset(X25)),X26)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1004])]) ).
fof(f6133,plain,
( ! [X26,X24,X25] :
( element(sK6(X24,sK4(powerset(X25)),X26),X24)
| sP0(X24,sK4(powerset(X25)),X26)
| ~ empty(X25)
| ~ in(X26,sK6(X24,sK4(powerset(X25)),X26)) )
| ~ spl20_75
| ~ spl20_369 ),
inference(resolution,[],[f5372,f654]) ).
fof(f31688,plain,
( spl20_1003
| ~ spl20_75
| ~ spl20_368 ),
inference(avatar_split_clause,[],[f6105,f5367,f653,f31686]) ).
fof(f31686,plain,
( spl20_1003
<=> ! [X25,X24,X26] :
( element(sK6(X24,X25,X26),X24)
| subset(sK6(X24,X25,X26),X25)
| sP0(X24,X25,X26)
| ~ epsilon_transitive(X25)
| ~ in(X26,sK6(X24,X25,X26)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1003])]) ).
fof(f5367,plain,
( spl20_368
<=> ! [X6,X4,X5] :
( element(sK6(X4,X5,X6),X4)
| in(sK6(X4,X5,X6),X6)
| sP0(X4,X5,X6)
| subset(sK6(X4,X5,X6),X5)
| ~ epsilon_transitive(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_368])]) ).
fof(f6105,plain,
( ! [X26,X24,X25] :
( element(sK6(X24,X25,X26),X24)
| subset(sK6(X24,X25,X26),X25)
| sP0(X24,X25,X26)
| ~ epsilon_transitive(X25)
| ~ in(X26,sK6(X24,X25,X26)) )
| ~ spl20_75
| ~ spl20_368 ),
inference(resolution,[],[f5368,f654]) ).
fof(f5368,plain,
( ! [X6,X4,X5] :
( element(sK6(X4,X5,X6),X4)
| subset(sK6(X4,X5,X6),X5)
| in(sK6(X4,X5,X6),X6)
| sP0(X4,X5,X6)
| ~ epsilon_transitive(X5) )
| ~ spl20_368 ),
inference(avatar_component_clause,[],[f5367]) ).
fof(f31684,plain,
( spl20_1002
| ~ spl20_75
| ~ spl20_367 ),
inference(avatar_split_clause,[],[f6071,f5363,f653,f31682]) ).
fof(f31682,plain,
( spl20_1002
<=> ! [X24,X25,X23] :
( element(sK6(X23,X24,sK4(powerset(X25))),X23)
| sP0(X23,X24,sK4(powerset(X25)))
| ~ empty(X25)
| ~ in(X24,sK6(X23,X24,sK4(powerset(X25)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1002])]) ).
fof(f6071,plain,
( ! [X24,X25,X23] :
( element(sK6(X23,X24,sK4(powerset(X25))),X23)
| sP0(X23,X24,sK4(powerset(X25)))
| ~ empty(X25)
| ~ in(X24,sK6(X23,X24,sK4(powerset(X25)))) )
| ~ spl20_75
| ~ spl20_367 ),
inference(resolution,[],[f5364,f654]) ).
fof(f31680,plain,
( spl20_1001
| ~ spl20_75
| ~ spl20_366 ),
inference(avatar_split_clause,[],[f6043,f5359,f653,f31678]) ).
fof(f31678,plain,
( spl20_1001
<=> ! [X24,X25,X23] :
( element(sK6(X23,X24,X25),X23)
| subset(sK6(X23,X24,X25),X25)
| sP0(X23,X24,X25)
| ~ epsilon_transitive(X25)
| ~ in(X24,sK6(X23,X24,X25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1001])]) ).
fof(f5359,plain,
( spl20_366
<=> ! [X6,X8,X7] :
( element(sK6(X6,X7,X8),X6)
| in(sK6(X6,X7,X8),X7)
| sP0(X6,X7,X8)
| subset(sK6(X6,X7,X8),X8)
| ~ epsilon_transitive(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_366])]) ).
fof(f6043,plain,
( ! [X24,X25,X23] :
( element(sK6(X23,X24,X25),X23)
| subset(sK6(X23,X24,X25),X25)
| sP0(X23,X24,X25)
| ~ epsilon_transitive(X25)
| ~ in(X24,sK6(X23,X24,X25)) )
| ~ spl20_75
| ~ spl20_366 ),
inference(resolution,[],[f5360,f654]) ).
fof(f5360,plain,
( ! [X8,X6,X7] :
( element(sK6(X6,X7,X8),X6)
| subset(sK6(X6,X7,X8),X8)
| in(sK6(X6,X7,X8),X7)
| sP0(X6,X7,X8)
| ~ epsilon_transitive(X8) )
| ~ spl20_366 ),
inference(avatar_component_clause,[],[f5359]) ).
fof(f31676,plain,
( spl20_1000
| ~ spl20_75
| ~ spl20_365 ),
inference(avatar_split_clause,[],[f6011,f5355,f653,f31674]) ).
fof(f31674,plain,
( spl20_1000
<=> ! [X25,X24,X26] :
( element(sK6(sK4(powerset(X24)),X25,X26),X25)
| sP0(sK4(powerset(X24)),X25,X26)
| ~ empty(X24)
| ~ in(X26,sK6(sK4(powerset(X24)),X25,X26)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1000])]) ).
fof(f6011,plain,
( ! [X26,X24,X25] :
( element(sK6(sK4(powerset(X24)),X25,X26),X25)
| sP0(sK4(powerset(X24)),X25,X26)
| ~ empty(X24)
| ~ in(X26,sK6(sK4(powerset(X24)),X25,X26)) )
| ~ spl20_75
| ~ spl20_365 ),
inference(resolution,[],[f5356,f654]) ).
fof(f31672,plain,
( spl20_999
| ~ spl20_75
| ~ spl20_364 ),
inference(avatar_split_clause,[],[f5982,f5351,f653,f31670]) ).
fof(f31670,plain,
( spl20_999
<=> ! [X25,X24,X26] :
( element(sK6(X24,X25,X26),X25)
| subset(sK6(X24,X25,X26),X24)
| sP0(X24,X25,X26)
| ~ epsilon_transitive(X24)
| ~ in(X26,sK6(X24,X25,X26)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_999])]) ).
fof(f5351,plain,
( spl20_364
<=> ! [X6,X4,X5] :
( element(sK6(X4,X5,X6),X5)
| in(sK6(X4,X5,X6),X6)
| sP0(X4,X5,X6)
| subset(sK6(X4,X5,X6),X4)
| ~ epsilon_transitive(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_364])]) ).
fof(f5982,plain,
( ! [X26,X24,X25] :
( element(sK6(X24,X25,X26),X25)
| subset(sK6(X24,X25,X26),X24)
| sP0(X24,X25,X26)
| ~ epsilon_transitive(X24)
| ~ in(X26,sK6(X24,X25,X26)) )
| ~ spl20_75
| ~ spl20_364 ),
inference(resolution,[],[f5352,f654]) ).
fof(f5352,plain,
( ! [X6,X4,X5] :
( element(sK6(X4,X5,X6),X5)
| subset(sK6(X4,X5,X6),X4)
| in(sK6(X4,X5,X6),X6)
| sP0(X4,X5,X6)
| ~ epsilon_transitive(X4) )
| ~ spl20_364 ),
inference(avatar_component_clause,[],[f5351]) ).
fof(f31668,plain,
( spl20_998
| ~ spl20_75
| ~ spl20_363 ),
inference(avatar_split_clause,[],[f5948,f5347,f653,f31666]) ).
fof(f31666,plain,
( spl20_998
<=> ! [X25,X24,X23] :
( element(sK6(X23,X24,sK4(powerset(X25))),X24)
| sP0(X23,X24,sK4(powerset(X25)))
| ~ empty(X25)
| ~ in(X23,sK6(X23,X24,sK4(powerset(X25)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_998])]) ).
fof(f5948,plain,
( ! [X24,X25,X23] :
( element(sK6(X23,X24,sK4(powerset(X25))),X24)
| sP0(X23,X24,sK4(powerset(X25)))
| ~ empty(X25)
| ~ in(X23,sK6(X23,X24,sK4(powerset(X25)))) )
| ~ spl20_75
| ~ spl20_363 ),
inference(resolution,[],[f5348,f654]) ).
fof(f31657,plain,
( spl20_997
| ~ spl20_75
| ~ spl20_361 ),
inference(avatar_split_clause,[],[f5920,f5331,f653,f31655]) ).
fof(f31655,plain,
( spl20_997
<=> ! [X25,X24,X23] :
( element(sK6(X23,X24,X25),X24)
| subset(sK6(X23,X24,X25),X25)
| sP0(X23,X24,X25)
| ~ epsilon_transitive(X25)
| ~ in(X23,sK6(X23,X24,X25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_997])]) ).
fof(f5331,plain,
( spl20_361
<=> ! [X6,X7,X8] :
( element(sK6(X6,X7,X8),X7)
| in(sK6(X6,X7,X8),X6)
| sP0(X6,X7,X8)
| subset(sK6(X6,X7,X8),X8)
| ~ epsilon_transitive(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_361])]) ).
fof(f5920,plain,
( ! [X24,X25,X23] :
( element(sK6(X23,X24,X25),X24)
| subset(sK6(X23,X24,X25),X25)
| sP0(X23,X24,X25)
| ~ epsilon_transitive(X25)
| ~ in(X23,sK6(X23,X24,X25)) )
| ~ spl20_75
| ~ spl20_361 ),
inference(resolution,[],[f5332,f654]) ).
fof(f5332,plain,
( ! [X8,X6,X7] :
( element(sK6(X6,X7,X8),X7)
| subset(sK6(X6,X7,X8),X8)
| in(sK6(X6,X7,X8),X6)
| sP0(X6,X7,X8)
| ~ epsilon_transitive(X8) )
| ~ spl20_361 ),
inference(avatar_component_clause,[],[f5331]) ).
fof(f31653,plain,
( spl20_996
| ~ spl20_75
| ~ spl20_360 ),
inference(avatar_split_clause,[],[f5888,f5327,f653,f31651]) ).
fof(f31651,plain,
( spl20_996
<=> ! [X25,X24,X23] :
( element(sK6(sK4(powerset(X23)),X24,X25),X25)
| sP0(sK4(powerset(X23)),X24,X25)
| ~ empty(X23)
| ~ in(X24,sK6(sK4(powerset(X23)),X24,X25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_996])]) ).
fof(f5888,plain,
( ! [X24,X25,X23] :
( element(sK6(sK4(powerset(X23)),X24,X25),X25)
| sP0(sK4(powerset(X23)),X24,X25)
| ~ empty(X23)
| ~ in(X24,sK6(sK4(powerset(X23)),X24,X25)) )
| ~ spl20_75
| ~ spl20_360 ),
inference(resolution,[],[f5328,f654]) ).
fof(f31649,plain,
( spl20_995
| ~ spl20_75
| ~ spl20_359 ),
inference(avatar_split_clause,[],[f5860,f5323,f653,f31647]) ).
fof(f31647,plain,
( spl20_995
<=> ! [X25,X24,X23] :
( element(sK6(X23,X24,X25),X25)
| subset(sK6(X23,X24,X25),X23)
| sP0(X23,X24,X25)
| ~ epsilon_transitive(X23)
| ~ in(X24,sK6(X23,X24,X25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_995])]) ).
fof(f5323,plain,
( spl20_359
<=> ! [X6,X4,X5] :
( element(sK6(X4,X5,X6),X6)
| in(sK6(X4,X5,X6),X5)
| sP0(X4,X5,X6)
| subset(sK6(X4,X5,X6),X4)
| ~ epsilon_transitive(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_359])]) ).
fof(f5860,plain,
( ! [X24,X25,X23] :
( element(sK6(X23,X24,X25),X25)
| subset(sK6(X23,X24,X25),X23)
| sP0(X23,X24,X25)
| ~ epsilon_transitive(X23)
| ~ in(X24,sK6(X23,X24,X25)) )
| ~ spl20_75
| ~ spl20_359 ),
inference(resolution,[],[f5324,f654]) ).
fof(f5324,plain,
( ! [X6,X4,X5] :
( element(sK6(X4,X5,X6),X6)
| subset(sK6(X4,X5,X6),X4)
| in(sK6(X4,X5,X6),X5)
| sP0(X4,X5,X6)
| ~ epsilon_transitive(X4) )
| ~ spl20_359 ),
inference(avatar_component_clause,[],[f5323]) ).
fof(f31645,plain,
( spl20_994
| ~ spl20_75
| ~ spl20_358 ),
inference(avatar_split_clause,[],[f5826,f5319,f653,f31643]) ).
fof(f31643,plain,
( spl20_994
<=> ! [X25,X24,X23] :
( element(sK6(X23,sK4(powerset(X24)),X25),X25)
| sP0(X23,sK4(powerset(X24)),X25)
| ~ empty(X24)
| ~ in(X23,sK6(X23,sK4(powerset(X24)),X25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_994])]) ).
fof(f5826,plain,
( ! [X24,X25,X23] :
( element(sK6(X23,sK4(powerset(X24)),X25),X25)
| sP0(X23,sK4(powerset(X24)),X25)
| ~ empty(X24)
| ~ in(X23,sK6(X23,sK4(powerset(X24)),X25)) )
| ~ spl20_75
| ~ spl20_358 ),
inference(resolution,[],[f5320,f654]) ).
fof(f31641,plain,
( spl20_993
| ~ spl20_75
| ~ spl20_357 ),
inference(avatar_split_clause,[],[f5798,f5315,f653,f31639]) ).
fof(f31639,plain,
( spl20_993
<=> ! [X25,X24,X23] :
( element(sK6(X23,X24,X25),X25)
| subset(sK6(X23,X24,X25),X24)
| sP0(X23,X24,X25)
| ~ epsilon_transitive(X24)
| ~ in(X23,sK6(X23,X24,X25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_993])]) ).
fof(f5315,plain,
( spl20_357
<=> ! [X6,X4,X5] :
( element(sK6(X4,X5,X6),X6)
| in(sK6(X4,X5,X6),X4)
| sP0(X4,X5,X6)
| subset(sK6(X4,X5,X6),X5)
| ~ epsilon_transitive(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_357])]) ).
fof(f5798,plain,
( ! [X24,X25,X23] :
( element(sK6(X23,X24,X25),X25)
| subset(sK6(X23,X24,X25),X24)
| sP0(X23,X24,X25)
| ~ epsilon_transitive(X24)
| ~ in(X23,sK6(X23,X24,X25)) )
| ~ spl20_75
| ~ spl20_357 ),
inference(resolution,[],[f5316,f654]) ).
fof(f5316,plain,
( ! [X6,X4,X5] :
( element(sK6(X4,X5,X6),X6)
| subset(sK6(X4,X5,X6),X5)
| in(sK6(X4,X5,X6),X4)
| sP0(X4,X5,X6)
| ~ epsilon_transitive(X5) )
| ~ spl20_357 ),
inference(avatar_component_clause,[],[f5315]) ).
fof(f31637,plain,
( spl20_992
| ~ spl20_75
| ~ spl20_356 ),
inference(avatar_split_clause,[],[f5764,f5311,f653,f31635]) ).
fof(f31635,plain,
( spl20_992
<=> ! [X25,X24,X26] :
( element(sK6(X24,sK4(powerset(X25)),X26),X25)
| ~ empty(X24)
| sP0(X24,sK4(powerset(X25)),X26)
| ~ in(X26,sK6(X24,sK4(powerset(X25)),X26)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_992])]) ).
fof(f5764,plain,
( ! [X26,X24,X25] :
( element(sK6(X24,sK4(powerset(X25)),X26),X25)
| ~ empty(X24)
| sP0(X24,sK4(powerset(X25)),X26)
| ~ in(X26,sK6(X24,sK4(powerset(X25)),X26)) )
| ~ spl20_75
| ~ spl20_356 ),
inference(resolution,[],[f5312,f654]) ).
fof(f31633,plain,
( spl20_991
| ~ spl20_75
| ~ spl20_355 ),
inference(avatar_split_clause,[],[f5736,f5307,f653,f31631]) ).
fof(f31631,plain,
( spl20_991
<=> ! [X25,X24,X23] :
( element(sK6(X23,X24,sK4(powerset(X25))),X25)
| ~ empty(X23)
| sP0(X23,X24,sK4(powerset(X25)))
| ~ in(X24,sK6(X23,X24,sK4(powerset(X25)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_991])]) ).
fof(f5736,plain,
( ! [X24,X25,X23] :
( element(sK6(X23,X24,sK4(powerset(X25))),X25)
| ~ empty(X23)
| sP0(X23,X24,sK4(powerset(X25)))
| ~ in(X24,sK6(X23,X24,sK4(powerset(X25)))) )
| ~ spl20_75
| ~ spl20_355 ),
inference(resolution,[],[f5308,f654]) ).
fof(f31629,plain,
( spl20_990
| ~ spl20_75
| ~ spl20_354 ),
inference(avatar_split_clause,[],[f5678,f5303,f653,f31627]) ).
fof(f31627,plain,
( spl20_990
<=> ! [X25,X24,X26] :
( element(sK6(sK4(powerset(X24)),X25,X26),X24)
| ~ empty(X25)
| sP0(sK4(powerset(X24)),X25,X26)
| ~ in(X26,sK6(sK4(powerset(X24)),X25,X26)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_990])]) ).
fof(f5678,plain,
( ! [X26,X24,X25] :
( element(sK6(sK4(powerset(X24)),X25,X26),X24)
| ~ empty(X25)
| sP0(sK4(powerset(X24)),X25,X26)
| ~ in(X26,sK6(sK4(powerset(X24)),X25,X26)) )
| ~ spl20_75
| ~ spl20_354 ),
inference(resolution,[],[f5304,f654]) ).
fof(f31625,plain,
( spl20_989
| ~ spl20_75
| ~ spl20_353 ),
inference(avatar_split_clause,[],[f5647,f5299,f653,f31623]) ).
fof(f31623,plain,
( spl20_989
<=> ! [X25,X24,X23] :
( element(sK6(X23,X24,sK4(powerset(X25))),X25)
| ~ empty(X24)
| sP0(X23,X24,sK4(powerset(X25)))
| ~ in(X23,sK6(X23,X24,sK4(powerset(X25)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_989])]) ).
fof(f5647,plain,
( ! [X24,X25,X23] :
( element(sK6(X23,X24,sK4(powerset(X25))),X25)
| ~ empty(X24)
| sP0(X23,X24,sK4(powerset(X25)))
| ~ in(X23,sK6(X23,X24,sK4(powerset(X25)))) )
| ~ spl20_75
| ~ spl20_353 ),
inference(resolution,[],[f5300,f654]) ).
fof(f31621,plain,
( spl20_988
| ~ spl20_75
| ~ spl20_352 ),
inference(avatar_split_clause,[],[f5616,f5295,f653,f31619]) ).
fof(f31619,plain,
( spl20_988
<=> ! [X24,X25,X23] :
( element(sK6(sK4(powerset(X23)),X24,X25),X23)
| ~ empty(X25)
| sP0(sK4(powerset(X23)),X24,X25)
| ~ in(X24,sK6(sK4(powerset(X23)),X24,X25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_988])]) ).
fof(f5616,plain,
( ! [X24,X25,X23] :
( element(sK6(sK4(powerset(X23)),X24,X25),X23)
| ~ empty(X25)
| sP0(sK4(powerset(X23)),X24,X25)
| ~ in(X24,sK6(sK4(powerset(X23)),X24,X25)) )
| ~ spl20_75
| ~ spl20_352 ),
inference(resolution,[],[f5296,f654]) ).
fof(f31617,plain,
( ~ spl20_987
| ~ spl20_477
| ~ spl20_933 ),
inference(avatar_split_clause,[],[f31546,f29997,f12949,f31614]) ).
fof(f31614,plain,
( spl20_987
<=> in(succ(sK1),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_987])]) ).
fof(f31546,plain,
( ~ in(succ(sK1),sK2)
| ~ spl20_477
| ~ spl20_933 ),
inference(superposition,[],[f12950,f29999]) ).
fof(f31612,plain,
( spl20_986
| ~ spl20_75
| ~ spl20_351 ),
inference(avatar_split_clause,[],[f5585,f5284,f653,f31610]) ).
fof(f31610,plain,
( spl20_986
<=> ! [X25,X24,X23] :
( element(sK6(X23,sK4(powerset(X24)),X25),X24)
| ~ empty(X25)
| sP0(X23,sK4(powerset(X24)),X25)
| ~ in(X23,sK6(X23,sK4(powerset(X24)),X25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_986])]) ).
fof(f5585,plain,
( ! [X24,X25,X23] :
( element(sK6(X23,sK4(powerset(X24)),X25),X24)
| ~ empty(X25)
| sP0(X23,sK4(powerset(X24)),X25)
| ~ in(X23,sK6(X23,sK4(powerset(X24)),X25)) )
| ~ spl20_75
| ~ spl20_351 ),
inference(resolution,[],[f5285,f654]) ).
fof(f31608,plain,
( spl20_985
| ~ spl20_75
| ~ spl20_350 ),
inference(avatar_split_clause,[],[f5549,f5280,f653,f31606]) ).
fof(f31606,plain,
( spl20_985
<=> ! [X25,X24,X23] :
( in(sK6(sK4(powerset(X23)),X24,X25),X25)
| ~ empty(X23)
| sP0(sK4(powerset(X23)),X24,X25)
| ~ in(X24,sK6(sK4(powerset(X23)),X24,X25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_985])]) ).
fof(f5549,plain,
( ! [X24,X25,X23] :
( in(sK6(sK4(powerset(X23)),X24,X25),X25)
| ~ empty(X23)
| sP0(sK4(powerset(X23)),X24,X25)
| ~ in(X24,sK6(sK4(powerset(X23)),X24,X25)) )
| ~ spl20_75
| ~ spl20_350 ),
inference(resolution,[],[f5281,f654]) ).
fof(f31604,plain,
( spl20_984
| ~ spl20_75
| ~ spl20_350 ),
inference(avatar_split_clause,[],[f5529,f5280,f653,f31602]) ).
fof(f31602,plain,
( spl20_984
<=> ! [X25,X24,X26] :
( in(sK6(sK4(powerset(X24)),X25,X26),X25)
| ~ empty(X24)
| sP0(sK4(powerset(X24)),X25,X26)
| ~ in(X26,sK6(sK4(powerset(X24)),X25,X26)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_984])]) ).
fof(f5529,plain,
( ! [X26,X24,X25] :
( in(sK6(sK4(powerset(X24)),X25,X26),X25)
| ~ empty(X24)
| sP0(sK4(powerset(X24)),X25,X26)
| ~ in(X26,sK6(sK4(powerset(X24)),X25,X26)) )
| ~ spl20_75
| ~ spl20_350 ),
inference(resolution,[],[f5281,f654]) ).
fof(f31600,plain,
( spl20_983
| ~ spl20_75
| ~ spl20_349 ),
inference(avatar_split_clause,[],[f5497,f5276,f653,f31598]) ).
fof(f31598,plain,
( spl20_983
<=> ! [X25,X24,X23] :
( in(sK6(X23,sK4(powerset(X24)),X25),X25)
| ~ empty(X24)
| sP0(X23,sK4(powerset(X24)),X25)
| ~ in(X23,sK6(X23,sK4(powerset(X24)),X25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_983])]) ).
fof(f5497,plain,
( ! [X24,X25,X23] :
( in(sK6(X23,sK4(powerset(X24)),X25),X25)
| ~ empty(X24)
| sP0(X23,sK4(powerset(X24)),X25)
| ~ in(X23,sK6(X23,sK4(powerset(X24)),X25)) )
| ~ spl20_75
| ~ spl20_349 ),
inference(resolution,[],[f5277,f654]) ).
fof(f31596,plain,
( spl20_982
| ~ spl20_75
| ~ spl20_349 ),
inference(avatar_split_clause,[],[f5477,f5276,f653,f31594]) ).
fof(f31594,plain,
( spl20_982
<=> ! [X25,X24,X26] :
( in(sK6(X24,sK4(powerset(X25)),X26),X24)
| ~ empty(X25)
| sP0(X24,sK4(powerset(X25)),X26)
| ~ in(X26,sK6(X24,sK4(powerset(X25)),X26)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_982])]) ).
fof(f5477,plain,
( ! [X26,X24,X25] :
( in(sK6(X24,sK4(powerset(X25)),X26),X24)
| ~ empty(X25)
| sP0(X24,sK4(powerset(X25)),X26)
| ~ in(X26,sK6(X24,sK4(powerset(X25)),X26)) )
| ~ spl20_75
| ~ spl20_349 ),
inference(resolution,[],[f5277,f654]) ).
fof(f31592,plain,
( spl20_981
| ~ spl20_75
| ~ spl20_348 ),
inference(avatar_split_clause,[],[f5444,f5272,f653,f31590]) ).
fof(f31590,plain,
( spl20_981
<=> ! [X25,X24,X23] :
( in(sK6(X23,X24,sK4(powerset(X25))),X24)
| ~ empty(X25)
| sP0(X23,X24,sK4(powerset(X25)))
| ~ in(X23,sK6(X23,X24,sK4(powerset(X25)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_981])]) ).
fof(f5444,plain,
( ! [X24,X25,X23] :
( in(sK6(X23,X24,sK4(powerset(X25))),X24)
| ~ empty(X25)
| sP0(X23,X24,sK4(powerset(X25)))
| ~ in(X23,sK6(X23,X24,sK4(powerset(X25)))) )
| ~ spl20_75
| ~ spl20_348 ),
inference(resolution,[],[f5273,f654]) ).
fof(f31588,plain,
( spl20_980
| ~ spl20_75
| ~ spl20_348 ),
inference(avatar_split_clause,[],[f5424,f5272,f653,f31586]) ).
fof(f31586,plain,
( spl20_980
<=> ! [X24,X25,X23] :
( in(sK6(X23,X24,sK4(powerset(X25))),X23)
| ~ empty(X25)
| sP0(X23,X24,sK4(powerset(X25)))
| ~ in(X24,sK6(X23,X24,sK4(powerset(X25)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_980])]) ).
fof(f5424,plain,
( ! [X24,X25,X23] :
( in(sK6(X23,X24,sK4(powerset(X25))),X23)
| ~ empty(X25)
| sP0(X23,X24,sK4(powerset(X25)))
| ~ in(X24,sK6(X23,X24,sK4(powerset(X25)))) )
| ~ spl20_75
| ~ spl20_348 ),
inference(resolution,[],[f5273,f654]) ).
fof(f31584,plain,
( spl20_979
| ~ spl20_151
| ~ spl20_344 ),
inference(avatar_split_clause,[],[f5238,f4952,f1221,f31582]) ).
fof(f31582,plain,
( spl20_979
<=> ! [X50,X48,X49] :
( element(sK6(X48,X49,sK4(powerset(X50))),X49)
| element(sK6(X48,X49,sK4(powerset(X50))),X48)
| sP0(X48,X49,sK4(powerset(X50)))
| ~ empty(X50) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_979])]) ).
fof(f5238,plain,
( ! [X50,X48,X49] :
( element(sK6(X48,X49,sK4(powerset(X50))),X49)
| element(sK6(X48,X49,sK4(powerset(X50))),X48)
| sP0(X48,X49,sK4(powerset(X50)))
| ~ empty(X50) )
| ~ spl20_151
| ~ spl20_344 ),
inference(resolution,[],[f4953,f1222]) ).
fof(f31580,plain,
( spl20_978
| ~ spl20_88
| ~ spl20_344 ),
inference(avatar_split_clause,[],[f5228,f4952,f772,f31578]) ).
fof(f31578,plain,
( spl20_978
<=> ! [X20,X18,X19] :
( element(sK6(X18,X19,X20),X19)
| element(sK6(X18,X19,X20),X18)
| sP0(X18,X19,X20)
| subset(sK6(X18,X19,X20),X20)
| ~ epsilon_transitive(X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_978])]) ).
fof(f5228,plain,
( ! [X18,X19,X20] :
( element(sK6(X18,X19,X20),X19)
| element(sK6(X18,X19,X20),X18)
| sP0(X18,X19,X20)
| subset(sK6(X18,X19,X20),X20)
| ~ epsilon_transitive(X20) )
| ~ spl20_88
| ~ spl20_344 ),
inference(resolution,[],[f4953,f773]) ).
fof(f31576,plain,
( spl20_977
| ~ spl20_151
| ~ spl20_341 ),
inference(avatar_split_clause,[],[f5185,f4940,f1221,f31574]) ).
fof(f31574,plain,
( spl20_977
<=> ! [X48,X47,X49] :
( element(sK6(X47,sK4(powerset(X48)),X49),X49)
| element(sK6(X47,sK4(powerset(X48)),X49),X47)
| sP0(X47,sK4(powerset(X48)),X49)
| ~ empty(X48) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_977])]) ).
fof(f5185,plain,
( ! [X48,X49,X47] :
( element(sK6(X47,sK4(powerset(X48)),X49),X49)
| element(sK6(X47,sK4(powerset(X48)),X49),X47)
| sP0(X47,sK4(powerset(X48)),X49)
| ~ empty(X48) )
| ~ spl20_151
| ~ spl20_341 ),
inference(resolution,[],[f4941,f1222]) ).
fof(f31530,plain,
( spl20_976
| ~ spl20_88
| ~ spl20_341 ),
inference(avatar_split_clause,[],[f5175,f4940,f772,f31528]) ).
fof(f31528,plain,
( spl20_976
<=> ! [X18,X17,X19] :
( element(sK6(X17,X18,X19),X19)
| element(sK6(X17,X18,X19),X17)
| sP0(X17,X18,X19)
| subset(sK6(X17,X18,X19),X18)
| ~ epsilon_transitive(X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_976])]) ).
fof(f5175,plain,
( ! [X18,X19,X17] :
( element(sK6(X17,X18,X19),X19)
| element(sK6(X17,X18,X19),X17)
| sP0(X17,X18,X19)
| subset(sK6(X17,X18,X19),X18)
| ~ epsilon_transitive(X18) )
| ~ spl20_88
| ~ spl20_341 ),
inference(resolution,[],[f4941,f773]) ).
fof(f31526,plain,
( spl20_975
| ~ spl20_151
| ~ spl20_339 ),
inference(avatar_split_clause,[],[f5144,f4932,f1221,f31524]) ).
fof(f31524,plain,
( spl20_975
<=> ! [X48,X47,X49] :
( element(sK6(sK4(powerset(X47)),X48,X49),X49)
| element(sK6(sK4(powerset(X47)),X48,X49),X48)
| sP0(sK4(powerset(X47)),X48,X49)
| ~ empty(X47) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_975])]) ).
fof(f5144,plain,
( ! [X48,X49,X47] :
( element(sK6(sK4(powerset(X47)),X48,X49),X49)
| element(sK6(sK4(powerset(X47)),X48,X49),X48)
| sP0(sK4(powerset(X47)),X48,X49)
| ~ empty(X47) )
| ~ spl20_151
| ~ spl20_339 ),
inference(resolution,[],[f4933,f1222]) ).
fof(f31522,plain,
( spl20_974
| ~ spl20_88
| ~ spl20_339 ),
inference(avatar_split_clause,[],[f5134,f4932,f772,f31520]) ).
fof(f31520,plain,
( spl20_974
<=> ! [X18,X17,X19] :
( element(sK6(X17,X18,X19),X19)
| element(sK6(X17,X18,X19),X18)
| sP0(X17,X18,X19)
| subset(sK6(X17,X18,X19),X17)
| ~ epsilon_transitive(X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_974])]) ).
fof(f5134,plain,
( ! [X18,X19,X17] :
( element(sK6(X17,X18,X19),X19)
| element(sK6(X17,X18,X19),X18)
| sP0(X17,X18,X19)
| subset(sK6(X17,X18,X19),X17)
| ~ epsilon_transitive(X17) )
| ~ spl20_88
| ~ spl20_339 ),
inference(resolution,[],[f4933,f773]) ).
fof(f31518,plain,
( spl20_973
| ~ spl20_89
| ~ spl20_336 ),
inference(avatar_split_clause,[],[f5071,f4919,f776,f31516]) ).
fof(f31516,plain,
( spl20_973
<=> ! [X9,X8] :
( in(sK6(X8,X8,sK4(powerset(X9))),X8)
| sP0(X8,X8,sK4(powerset(X9)))
| empty(X9)
| in(sK6(X8,X8,sK4(powerset(X9))),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_973])]) ).
fof(f5071,plain,
( ! [X8,X9] :
( in(sK6(X8,X8,sK4(powerset(X9))),X8)
| sP0(X8,X8,sK4(powerset(X9)))
| empty(X9)
| in(sK6(X8,X8,sK4(powerset(X9))),X9) )
| ~ spl20_89
| ~ spl20_336 ),
inference(resolution,[],[f4920,f777]) ).
fof(f31514,plain,
( spl20_972
| ~ spl20_89
| ~ spl20_335 ),
inference(avatar_split_clause,[],[f5043,f4915,f776,f31512]) ).
fof(f31512,plain,
( spl20_972
<=> ! [X9,X8] :
( in(sK6(X8,sK4(powerset(X9)),X8),X8)
| sP0(X8,sK4(powerset(X9)),X8)
| empty(X9)
| in(sK6(X8,sK4(powerset(X9)),X8),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_972])]) ).
fof(f5043,plain,
( ! [X8,X9] :
( in(sK6(X8,sK4(powerset(X9)),X8),X8)
| sP0(X8,sK4(powerset(X9)),X8)
| empty(X9)
| in(sK6(X8,sK4(powerset(X9)),X8),X9) )
| ~ spl20_89
| ~ spl20_335 ),
inference(resolution,[],[f4916,f777]) ).
fof(f31510,plain,
( spl20_971
| ~ spl20_89
| ~ spl20_334 ),
inference(avatar_split_clause,[],[f5015,f4911,f776,f31508]) ).
fof(f31508,plain,
( spl20_971
<=> ! [X9,X8] :
( in(sK6(sK4(powerset(X8)),X9,X9),X9)
| sP0(sK4(powerset(X8)),X9,X9)
| empty(X8)
| in(sK6(sK4(powerset(X8)),X9,X9),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_971])]) ).
fof(f5015,plain,
( ! [X8,X9] :
( in(sK6(sK4(powerset(X8)),X9,X9),X9)
| sP0(sK4(powerset(X8)),X9,X9)
| empty(X8)
| in(sK6(sK4(powerset(X8)),X9,X9),X8) )
| ~ spl20_89
| ~ spl20_334 ),
inference(resolution,[],[f4912,f777]) ).
fof(f31506,plain,
( spl20_970
| ~ spl20_153
| ~ spl20_329 ),
inference(avatar_split_clause,[],[f4861,f4722,f1230,f31504]) ).
fof(f31504,plain,
( spl20_970
<=> ! [X34,X35,X33] :
( sP0(X33,singleton(X34),singleton(X35))
| ~ empty(X33)
| sK6(X33,singleton(X34),singleton(X35)) = X35
| sK6(X33,singleton(X34),singleton(X35)) = X34 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_970])]) ).
fof(f4722,plain,
( spl20_329
<=> ! [X20,X18,X19] :
( in(sK6(X18,X19,singleton(X20)),X19)
| sP0(X18,X19,singleton(X20))
| ~ empty(X18)
| sK6(X18,X19,singleton(X20)) = X20 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_329])]) ).
fof(f4861,plain,
( ! [X34,X35,X33] :
( sP0(X33,singleton(X34),singleton(X35))
| ~ empty(X33)
| sK6(X33,singleton(X34),singleton(X35)) = X35
| sK6(X33,singleton(X34),singleton(X35)) = X34 )
| ~ spl20_153
| ~ spl20_329 ),
inference(resolution,[],[f4723,f1231]) ).
fof(f4723,plain,
( ! [X18,X19,X20] :
( in(sK6(X18,X19,singleton(X20)),X19)
| sP0(X18,X19,singleton(X20))
| ~ empty(X18)
| sK6(X18,X19,singleton(X20)) = X20 )
| ~ spl20_329 ),
inference(avatar_component_clause,[],[f4722]) ).
fof(f31502,plain,
( spl20_969
| ~ spl20_153
| ~ spl20_327 ),
inference(avatar_split_clause,[],[f4813,f4714,f1230,f31500]) ).
fof(f31500,plain,
( spl20_969
<=> ! [X34,X35,X33] :
( sP0(singleton(X33),X34,singleton(X35))
| ~ empty(X34)
| sK6(singleton(X33),X34,singleton(X35)) = X35
| sK6(singleton(X33),X34,singleton(X35)) = X33 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_969])]) ).
fof(f4714,plain,
( spl20_327
<=> ! [X20,X18,X19] :
( in(sK6(X18,X19,singleton(X20)),X18)
| sP0(X18,X19,singleton(X20))
| ~ empty(X19)
| sK6(X18,X19,singleton(X20)) = X20 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_327])]) ).
fof(f4813,plain,
( ! [X34,X35,X33] :
( sP0(singleton(X33),X34,singleton(X35))
| ~ empty(X34)
| sK6(singleton(X33),X34,singleton(X35)) = X35
| sK6(singleton(X33),X34,singleton(X35)) = X33 )
| ~ spl20_153
| ~ spl20_327 ),
inference(resolution,[],[f4715,f1231]) ).
fof(f4715,plain,
( ! [X18,X19,X20] :
( in(sK6(X18,X19,singleton(X20)),X18)
| sP0(X18,X19,singleton(X20))
| ~ empty(X19)
| sK6(X18,X19,singleton(X20)) = X20 )
| ~ spl20_327 ),
inference(avatar_component_clause,[],[f4714]) ).
fof(f31498,plain,
( spl20_968
| ~ spl20_153
| ~ spl20_325 ),
inference(avatar_split_clause,[],[f4765,f4706,f1230,f31496]) ).
fof(f31496,plain,
( spl20_968
<=> ! [X34,X35,X33] :
( sP0(singleton(X33),singleton(X34),X35)
| ~ empty(X35)
| sK6(singleton(X33),singleton(X34),X35) = X34
| sK6(singleton(X33),singleton(X34),X35) = X33 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_968])]) ).
fof(f4706,plain,
( spl20_325
<=> ! [X18,X16,X17] :
( in(sK6(X16,singleton(X17),X18),X16)
| sP0(X16,singleton(X17),X18)
| ~ empty(X18)
| sK6(X16,singleton(X17),X18) = X17 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_325])]) ).
fof(f4765,plain,
( ! [X34,X35,X33] :
( sP0(singleton(X33),singleton(X34),X35)
| ~ empty(X35)
| sK6(singleton(X33),singleton(X34),X35) = X34
| sK6(singleton(X33),singleton(X34),X35) = X33 )
| ~ spl20_153
| ~ spl20_325 ),
inference(resolution,[],[f4707,f1231]) ).
fof(f4707,plain,
( ! [X18,X16,X17] :
( in(sK6(X16,singleton(X17),X18),X16)
| sP0(X16,singleton(X17),X18)
| ~ empty(X18)
| sK6(X16,singleton(X17),X18) = X17 )
| ~ spl20_325 ),
inference(avatar_component_clause,[],[f4706]) ).
fof(f31494,plain,
( spl20_967
| ~ spl20_160
| ~ spl20_323 ),
inference(avatar_split_clause,[],[f4729,f4695,f1291,f31492]) ).
fof(f31492,plain,
( spl20_967
<=> ! [X2,X0,X1] :
( ~ ordinal(sK4(powerset(X0)))
| ~ ordinal(X1)
| sK4(powerset(X0)) = X1
| ~ epsilon_transitive(X1)
| element(X1,X0)
| ~ in(X2,sK4(powerset(X0)))
| element(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_967])]) ).
fof(f4695,plain,
( spl20_323
<=> ! [X11,X12] :
( sK4(powerset(X11)) = X12
| ~ ordinal(sK4(powerset(X11)))
| ~ ordinal(X12)
| subset(sK4(powerset(X11)),X12)
| ~ epsilon_transitive(X12)
| element(X12,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_323])]) ).
fof(f4729,plain,
( ! [X2,X0,X1] :
( ~ ordinal(sK4(powerset(X0)))
| ~ ordinal(X1)
| sK4(powerset(X0)) = X1
| ~ epsilon_transitive(X1)
| element(X1,X0)
| ~ in(X2,sK4(powerset(X0)))
| element(X2,X1) )
| ~ spl20_160
| ~ spl20_323 ),
inference(resolution,[],[f4696,f1292]) ).
fof(f4696,plain,
( ! [X11,X12] :
( subset(sK4(powerset(X11)),X12)
| ~ ordinal(sK4(powerset(X11)))
| ~ ordinal(X12)
| sK4(powerset(X11)) = X12
| ~ epsilon_transitive(X12)
| element(X12,X11) )
| ~ spl20_323 ),
inference(avatar_component_clause,[],[f4695]) ).
fof(f31483,plain,
( spl20_966
| ~ spl20_157
| ~ spl20_316 ),
inference(avatar_split_clause,[],[f4517,f4391,f1267,f31481]) ).
fof(f31481,plain,
( spl20_966
<=> ! [X30,X31] :
( sP0(sK4(powerset(X30)),sK4(powerset(X30)),sK4(powerset(X31)))
| ~ empty(X30)
| element(sK6(sK4(powerset(X30)),sK4(powerset(X30)),sK4(powerset(X31))),X31) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_966])]) ).
fof(f4391,plain,
( spl20_316
<=> ! [X16,X15] :
( in(sK6(sK4(powerset(X15)),sK4(powerset(X15)),X16),X16)
| sP0(sK4(powerset(X15)),sK4(powerset(X15)),X16)
| ~ empty(X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_316])]) ).
fof(f4517,plain,
( ! [X31,X30] :
( sP0(sK4(powerset(X30)),sK4(powerset(X30)),sK4(powerset(X31)))
| ~ empty(X30)
| element(sK6(sK4(powerset(X30)),sK4(powerset(X30)),sK4(powerset(X31))),X31) )
| ~ spl20_157
| ~ spl20_316 ),
inference(resolution,[],[f4392,f1268]) ).
fof(f4392,plain,
( ! [X16,X15] :
( in(sK6(sK4(powerset(X15)),sK4(powerset(X15)),X16),X16)
| sP0(sK4(powerset(X15)),sK4(powerset(X15)),X16)
| ~ empty(X15) )
| ~ spl20_316 ),
inference(avatar_component_clause,[],[f4391]) ).
fof(f31479,plain,
( spl20_965
| ~ spl20_249
| ~ spl20_307 ),
inference(avatar_split_clause,[],[f4214,f4110,f2812,f31477]) ).
fof(f31477,plain,
( spl20_965
<=> ! [X160,X159,X157,X158] :
( sK5(X157,powerset(X158)) = X157
| ~ empty(X158)
| powerset(X158) = singleton(X157)
| sP0(sK5(X157,powerset(X158)),X159,X160)
| ~ empty(X160)
| ~ empty(X159) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_965])]) ).
fof(f4214,plain,
( ! [X160,X158,X159,X157] :
( sK5(X157,powerset(X158)) = X157
| ~ empty(X158)
| powerset(X158) = singleton(X157)
| sP0(sK5(X157,powerset(X158)),X159,X160)
| ~ empty(X160)
| ~ empty(X159) )
| ~ spl20_249
| ~ spl20_307 ),
inference(resolution,[],[f4111,f2813]) ).
fof(f31475,plain,
( spl20_964
| ~ spl20_250
| ~ spl20_307 ),
inference(avatar_split_clause,[],[f4204,f4110,f2816,f31473]) ).
fof(f31473,plain,
( spl20_964
<=> ! [X119,X118,X117,X120] :
( sK5(X117,powerset(X118)) = X117
| ~ empty(X118)
| powerset(X118) = singleton(X117)
| sP0(X119,sK5(X117,powerset(X118)),X120)
| ~ empty(X120)
| ~ empty(X119) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_964])]) ).
fof(f4204,plain,
( ! [X120,X118,X119,X117] :
( sK5(X117,powerset(X118)) = X117
| ~ empty(X118)
| powerset(X118) = singleton(X117)
| sP0(X119,sK5(X117,powerset(X118)),X120)
| ~ empty(X120)
| ~ empty(X119) )
| ~ spl20_250
| ~ spl20_307 ),
inference(resolution,[],[f4111,f2817]) ).
fof(f31471,plain,
( spl20_963
| ~ spl20_251
| ~ spl20_307 ),
inference(avatar_split_clause,[],[f4194,f4110,f2820,f31469]) ).
fof(f31469,plain,
( spl20_963
<=> ! [X77,X78,X80,X79] :
( sK5(X77,powerset(X78)) = X77
| ~ empty(X78)
| powerset(X78) = singleton(X77)
| sP0(X79,X80,sK5(X77,powerset(X78)))
| ~ empty(X80)
| ~ empty(X79) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_963])]) ).
fof(f4194,plain,
( ! [X80,X78,X79,X77] :
( sK5(X77,powerset(X78)) = X77
| ~ empty(X78)
| powerset(X78) = singleton(X77)
| sP0(X79,X80,sK5(X77,powerset(X78)))
| ~ empty(X80)
| ~ empty(X79) )
| ~ spl20_251
| ~ spl20_307 ),
inference(resolution,[],[f4111,f2821]) ).
fof(f31467,plain,
( spl20_962
| ~ spl20_94
| ~ spl20_306 ),
inference(avatar_split_clause,[],[f4167,f4106,f823,f31465]) ).
fof(f31465,plain,
( spl20_962
<=> ! [X4,X5,X3] :
( ~ ordinal(sK4(powerset(X3)))
| ~ ordinal(powerset(X4))
| powerset(X4) = sK4(powerset(X3))
| element(powerset(X4),X3)
| ~ empty(X4)
| ~ in(X5,sK4(powerset(X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_962])]) ).
fof(f4167,plain,
( ! [X3,X4,X5] :
( ~ ordinal(sK4(powerset(X3)))
| ~ ordinal(powerset(X4))
| powerset(X4) = sK4(powerset(X3))
| element(powerset(X4),X3)
| ~ empty(X4)
| ~ in(X5,sK4(powerset(X3))) )
| ~ spl20_94
| ~ spl20_306 ),
inference(resolution,[],[f4107,f824]) ).
fof(f31463,plain,
( spl20_961
| ~ spl20_245
| ~ spl20_305 ),
inference(avatar_split_clause,[],[f4159,f4102,f2725,f31461]) ).
fof(f31461,plain,
( spl20_961
<=> ! [X2,X0,X1] :
( element(X0,X1)
| sK4(powerset(X1)) = X0
| ~ ordinal(sK4(powerset(X1)))
| ~ ordinal(X0)
| ordinal_subset(X2,X0)
| ~ ordinal(X2)
| element(sK4(powerset(X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_961])]) ).
fof(f4159,plain,
( ! [X2,X0,X1] :
( element(X0,X1)
| sK4(powerset(X1)) = X0
| ~ ordinal(sK4(powerset(X1)))
| ~ ordinal(X0)
| ordinal_subset(X2,X0)
| ~ ordinal(X2)
| element(sK4(powerset(X1)),X2) )
| ~ spl20_245
| ~ spl20_305 ),
inference(duplicate_literal_removal,[],[f4129]) ).
fof(f4129,plain,
( ! [X2,X0,X1] :
( element(X0,X1)
| sK4(powerset(X1)) = X0
| ~ ordinal(sK4(powerset(X1)))
| ~ ordinal(X0)
| ~ ordinal(X0)
| ordinal_subset(X2,X0)
| ~ ordinal(X2)
| element(sK4(powerset(X1)),X2) )
| ~ spl20_245
| ~ spl20_305 ),
inference(resolution,[],[f4103,f2726]) ).
fof(f31459,plain,
( spl20_960
| ~ spl20_157
| ~ spl20_301 ),
inference(avatar_split_clause,[],[f4062,f3629,f1267,f31457]) ).
fof(f31457,plain,
( spl20_960
<=> ! [X45,X46,X47] :
( element(sK6(X45,X46,sK4(powerset(X47))),X46)
| ~ empty(X45)
| sP0(X45,X46,sK4(powerset(X47)))
| element(sK6(X45,X46,sK4(powerset(X47))),X47) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_960])]) ).
fof(f4062,plain,
( ! [X46,X47,X45] :
( element(sK6(X45,X46,sK4(powerset(X47))),X46)
| ~ empty(X45)
| sP0(X45,X46,sK4(powerset(X47)))
| element(sK6(X45,X46,sK4(powerset(X47))),X47) )
| ~ spl20_157
| ~ spl20_301 ),
inference(resolution,[],[f3630,f1268]) ).
fof(f31455,plain,
( spl20_959
| ~ spl20_100
| ~ spl20_301 ),
inference(avatar_split_clause,[],[f4043,f3629,f858,f31453]) ).
fof(f31453,plain,
( spl20_959
<=> ! [X0,X3,X2,X1] :
( in(sK6(X0,powerset(X1),X2),X2)
| ~ empty(X0)
| sP0(X0,powerset(X1),X2)
| element(X3,X1)
| ~ in(X3,sK6(X0,powerset(X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_959])]) ).
fof(f4043,plain,
( ! [X2,X3,X0,X1] :
( in(sK6(X0,powerset(X1),X2),X2)
| ~ empty(X0)
| sP0(X0,powerset(X1),X2)
| element(X3,X1)
| ~ in(X3,sK6(X0,powerset(X1),X2)) )
| ~ spl20_100
| ~ spl20_301 ),
inference(resolution,[],[f3630,f859]) ).
fof(f31451,plain,
( spl20_958
| ~ spl20_157
| ~ spl20_298 ),
inference(avatar_split_clause,[],[f4009,f3617,f1267,f31449]) ).
fof(f31449,plain,
( spl20_958
<=> ! [X45,X44,X46] :
( element(sK6(X44,sK4(powerset(X45)),X46),X46)
| ~ empty(X44)
| sP0(X44,sK4(powerset(X45)),X46)
| element(sK6(X44,sK4(powerset(X45)),X46),X45) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_958])]) ).
fof(f4009,plain,
( ! [X46,X44,X45] :
( element(sK6(X44,sK4(powerset(X45)),X46),X46)
| ~ empty(X44)
| sP0(X44,sK4(powerset(X45)),X46)
| element(sK6(X44,sK4(powerset(X45)),X46),X45) )
| ~ spl20_157
| ~ spl20_298 ),
inference(resolution,[],[f3618,f1268]) ).
fof(f31447,plain,
( spl20_957
| ~ spl20_100
| ~ spl20_298 ),
inference(avatar_split_clause,[],[f3990,f3617,f858,f31445]) ).
fof(f31445,plain,
( spl20_957
<=> ! [X0,X3,X2,X1] :
( in(sK6(X0,X1,powerset(X2)),X1)
| ~ empty(X0)
| sP0(X0,X1,powerset(X2))
| element(X3,X2)
| ~ in(X3,sK6(X0,X1,powerset(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_957])]) ).
fof(f3990,plain,
( ! [X2,X3,X0,X1] :
( in(sK6(X0,X1,powerset(X2)),X1)
| ~ empty(X0)
| sP0(X0,X1,powerset(X2))
| element(X3,X2)
| ~ in(X3,sK6(X0,X1,powerset(X2))) )
| ~ spl20_100
| ~ spl20_298 ),
inference(resolution,[],[f3618,f859]) ).
fof(f31443,plain,
( ~ spl20_956
| ~ spl20_75
| ~ spl20_935 ),
inference(avatar_split_clause,[],[f31392,f31347,f653,f31440]) ).
fof(f31440,plain,
( spl20_956
<=> in(sK1,sK4(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_956])]) ).
fof(f31392,plain,
( ~ in(sK1,sK4(sK2))
| ~ spl20_75
| ~ spl20_935 ),
inference(resolution,[],[f31349,f654]) ).
fof(f31438,plain,
( spl20_955
| ~ spl20_157
| ~ spl20_294 ),
inference(avatar_split_clause,[],[f3956,f3578,f1267,f31436]) ).
fof(f31436,plain,
( spl20_955
<=> ! [X45,X46,X47] :
( element(sK6(X45,X46,sK4(powerset(X47))),X45)
| ~ empty(X46)
| sP0(X45,X46,sK4(powerset(X47)))
| element(sK6(X45,X46,sK4(powerset(X47))),X47) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_955])]) ).
fof(f3956,plain,
( ! [X46,X47,X45] :
( element(sK6(X45,X46,sK4(powerset(X47))),X45)
| ~ empty(X46)
| sP0(X45,X46,sK4(powerset(X47)))
| element(sK6(X45,X46,sK4(powerset(X47))),X47) )
| ~ spl20_157
| ~ spl20_294 ),
inference(resolution,[],[f3579,f1268]) ).
fof(f31434,plain,
( spl20_954
| ~ spl20_100
| ~ spl20_294 ),
inference(avatar_split_clause,[],[f3937,f3578,f858,f31432]) ).
fof(f31432,plain,
( spl20_954
<=> ! [X0,X3,X2,X1] :
( in(sK6(powerset(X0),X1,X2),X2)
| ~ empty(X1)
| sP0(powerset(X0),X1,X2)
| element(X3,X0)
| ~ in(X3,sK6(powerset(X0),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_954])]) ).
fof(f3937,plain,
( ! [X2,X3,X0,X1] :
( in(sK6(powerset(X0),X1,X2),X2)
| ~ empty(X1)
| sP0(powerset(X0),X1,X2)
| element(X3,X0)
| ~ in(X3,sK6(powerset(X0),X1,X2)) )
| ~ spl20_100
| ~ spl20_294 ),
inference(resolution,[],[f3579,f859]) ).
fof(f31430,plain,
( spl20_953
| ~ spl20_157
| ~ spl20_291 ),
inference(avatar_split_clause,[],[f3903,f3566,f1267,f31428]) ).
fof(f31428,plain,
( spl20_953
<=> ! [X45,X44,X46] :
( element(sK6(sK4(powerset(X44)),X45,X46),X46)
| ~ empty(X45)
| sP0(sK4(powerset(X44)),X45,X46)
| element(sK6(sK4(powerset(X44)),X45,X46),X44) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_953])]) ).
fof(f3903,plain,
( ! [X46,X44,X45] :
( element(sK6(sK4(powerset(X44)),X45,X46),X46)
| ~ empty(X45)
| sP0(sK4(powerset(X44)),X45,X46)
| element(sK6(sK4(powerset(X44)),X45,X46),X44) )
| ~ spl20_157
| ~ spl20_291 ),
inference(resolution,[],[f3567,f1268]) ).
fof(f31426,plain,
( spl20_952
| ~ spl20_100
| ~ spl20_291 ),
inference(avatar_split_clause,[],[f3884,f3566,f858,f31424]) ).
fof(f31424,plain,
( spl20_952
<=> ! [X0,X3,X2,X1] :
( in(sK6(X0,X1,powerset(X2)),X0)
| ~ empty(X1)
| sP0(X0,X1,powerset(X2))
| element(X3,X2)
| ~ in(X3,sK6(X0,X1,powerset(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_952])]) ).
fof(f3884,plain,
( ! [X2,X3,X0,X1] :
( in(sK6(X0,X1,powerset(X2)),X0)
| ~ empty(X1)
| sP0(X0,X1,powerset(X2))
| element(X3,X2)
| ~ in(X3,sK6(X0,X1,powerset(X2))) )
| ~ spl20_100
| ~ spl20_291 ),
inference(resolution,[],[f3567,f859]) ).
fof(f31422,plain,
( spl20_951
| ~ spl20_157
| ~ spl20_288 ),
inference(avatar_split_clause,[],[f3850,f3554,f1267,f31420]) ).
fof(f31420,plain,
( spl20_951
<=> ! [X45,X44,X46] :
( element(sK6(X44,sK4(powerset(X45)),X46),X44)
| ~ empty(X46)
| sP0(X44,sK4(powerset(X45)),X46)
| element(sK6(X44,sK4(powerset(X45)),X46),X45) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_951])]) ).
fof(f3850,plain,
( ! [X46,X44,X45] :
( element(sK6(X44,sK4(powerset(X45)),X46),X44)
| ~ empty(X46)
| sP0(X44,sK4(powerset(X45)),X46)
| element(sK6(X44,sK4(powerset(X45)),X46),X45) )
| ~ spl20_157
| ~ spl20_288 ),
inference(resolution,[],[f3555,f1268]) ).
fof(f31418,plain,
( spl20_950
| ~ spl20_100
| ~ spl20_288 ),
inference(avatar_split_clause,[],[f3831,f3554,f858,f31416]) ).
fof(f31416,plain,
( spl20_950
<=> ! [X0,X3,X2,X1] :
( in(sK6(powerset(X0),X1,X2),X1)
| ~ empty(X2)
| sP0(powerset(X0),X1,X2)
| element(X3,X0)
| ~ in(X3,sK6(powerset(X0),X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_950])]) ).
fof(f3831,plain,
( ! [X2,X3,X0,X1] :
( in(sK6(powerset(X0),X1,X2),X1)
| ~ empty(X2)
| sP0(powerset(X0),X1,X2)
| element(X3,X0)
| ~ in(X3,sK6(powerset(X0),X1,X2)) )
| ~ spl20_100
| ~ spl20_288 ),
inference(resolution,[],[f3555,f859]) ).
fof(f31414,plain,
( spl20_949
| ~ spl20_157
| ~ spl20_285 ),
inference(avatar_split_clause,[],[f3797,f3542,f1267,f31412]) ).
fof(f31412,plain,
( spl20_949
<=> ! [X45,X44,X46] :
( element(sK6(sK4(powerset(X44)),X45,X46),X45)
| ~ empty(X46)
| sP0(sK4(powerset(X44)),X45,X46)
| element(sK6(sK4(powerset(X44)),X45,X46),X44) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_949])]) ).
fof(f3797,plain,
( ! [X46,X44,X45] :
( element(sK6(sK4(powerset(X44)),X45,X46),X45)
| ~ empty(X46)
| sP0(sK4(powerset(X44)),X45,X46)
| element(sK6(sK4(powerset(X44)),X45,X46),X44) )
| ~ spl20_157
| ~ spl20_285 ),
inference(resolution,[],[f3543,f1268]) ).
fof(f31410,plain,
( spl20_948
| ~ spl20_100
| ~ spl20_285 ),
inference(avatar_split_clause,[],[f3778,f3542,f858,f31408]) ).
fof(f31408,plain,
( spl20_948
<=> ! [X0,X3,X2,X1] :
( in(sK6(X0,powerset(X1),X2),X0)
| ~ empty(X2)
| sP0(X0,powerset(X1),X2)
| element(X3,X1)
| ~ in(X3,sK6(X0,powerset(X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_948])]) ).
fof(f3778,plain,
( ! [X2,X3,X0,X1] :
( in(sK6(X0,powerset(X1),X2),X0)
| ~ empty(X2)
| sP0(X0,powerset(X1),X2)
| element(X3,X1)
| ~ in(X3,sK6(X0,powerset(X1),X2)) )
| ~ spl20_100
| ~ spl20_285 ),
inference(resolution,[],[f3543,f859]) ).
fof(f31406,plain,
( spl20_947
| ~ spl20_157
| ~ spl20_284 ),
inference(avatar_split_clause,[],[f3772,f3538,f1267,f31404]) ).
fof(f31404,plain,
( spl20_947
<=> ! [X30,X31] :
( subset(sK6(X30,X30,sK4(powerset(X31))),X30)
| sP0(X30,X30,sK4(powerset(X31)))
| ~ epsilon_transitive(X30)
| element(sK6(X30,X30,sK4(powerset(X31))),X31) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_947])]) ).
fof(f3772,plain,
( ! [X31,X30] :
( subset(sK6(X30,X30,sK4(powerset(X31))),X30)
| sP0(X30,X30,sK4(powerset(X31)))
| ~ epsilon_transitive(X30)
| element(sK6(X30,X30,sK4(powerset(X31))),X31) )
| ~ spl20_157
| ~ spl20_284 ),
inference(resolution,[],[f3539,f1268]) ).
fof(f31402,plain,
( spl20_946
| ~ spl20_91
| ~ spl20_284 ),
inference(avatar_split_clause,[],[f3756,f3538,f811,f31400]) ).
fof(f31400,plain,
( spl20_946
<=> ! [X9,X8] :
( in(sK6(X8,X8,X9),X9)
| sP0(X8,X8,X9)
| ~ epsilon_transitive(X8)
| sK6(X8,X8,X9) = X8
| ~ subset(X8,sK6(X8,X8,X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_946])]) ).
fof(f3756,plain,
( ! [X8,X9] :
( in(sK6(X8,X8,X9),X9)
| sP0(X8,X8,X9)
| ~ epsilon_transitive(X8)
| sK6(X8,X8,X9) = X8
| ~ subset(X8,sK6(X8,X8,X9)) )
| ~ spl20_91
| ~ spl20_284 ),
inference(resolution,[],[f3539,f812]) ).
fof(f31390,plain,
( spl20_945
| ~ spl20_153
| ~ spl20_283 ),
inference(avatar_split_clause,[],[f3743,f3534,f1230,f31388]) ).
fof(f31388,plain,
( spl20_945
<=> ! [X24,X23] :
( subset(sK6(singleton(X23),singleton(X23),X24),X24)
| sP0(singleton(X23),singleton(X23),X24)
| ~ epsilon_transitive(X24)
| sK6(singleton(X23),singleton(X23),X24) = X23 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_945])]) ).
fof(f3743,plain,
( ! [X24,X23] :
( subset(sK6(singleton(X23),singleton(X23),X24),X24)
| sP0(singleton(X23),singleton(X23),X24)
| ~ epsilon_transitive(X24)
| sK6(singleton(X23),singleton(X23),X24) = X23 )
| ~ spl20_153
| ~ spl20_283 ),
inference(resolution,[],[f3535,f1231]) ).
fof(f31386,plain,
( spl20_944
| ~ spl20_91
| ~ spl20_283 ),
inference(avatar_split_clause,[],[f3731,f3534,f811,f31384]) ).
fof(f31384,plain,
( spl20_944
<=> ! [X9,X8] :
( in(sK6(X8,X8,X9),X8)
| sP0(X8,X8,X9)
| ~ epsilon_transitive(X9)
| sK6(X8,X8,X9) = X9
| ~ subset(X9,sK6(X8,X8,X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_944])]) ).
fof(f3731,plain,
( ! [X8,X9] :
( in(sK6(X8,X8,X9),X8)
| sP0(X8,X8,X9)
| ~ epsilon_transitive(X9)
| sK6(X8,X8,X9) = X9
| ~ subset(X9,sK6(X8,X8,X9)) )
| ~ spl20_91
| ~ spl20_283 ),
inference(resolution,[],[f3535,f812]) ).
fof(f31382,plain,
( spl20_943
| ~ spl20_91
| ~ spl20_282 ),
inference(avatar_split_clause,[],[f3706,f3530,f811,f31380]) ).
fof(f31380,plain,
( spl20_943
<=> ! [X9,X8] :
( in(sK6(X8,X9,X8),X8)
| sP0(X8,X9,X8)
| ~ epsilon_transitive(X9)
| sK6(X8,X9,X8) = X9
| ~ subset(X9,sK6(X8,X9,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_943])]) ).
fof(f3706,plain,
( ! [X8,X9] :
( in(sK6(X8,X9,X8),X8)
| sP0(X8,X9,X8)
| ~ epsilon_transitive(X9)
| sK6(X8,X9,X8) = X9
| ~ subset(X9,sK6(X8,X9,X8)) )
| ~ spl20_91
| ~ spl20_282 ),
inference(resolution,[],[f3531,f812]) ).
fof(f31378,plain,
( spl20_942
| ~ spl20_91
| ~ spl20_281 ),
inference(avatar_split_clause,[],[f3681,f3526,f811,f31376]) ).
fof(f31376,plain,
( spl20_942
<=> ! [X9,X8] :
( in(sK6(X8,X9,X9),X9)
| sP0(X8,X9,X9)
| ~ epsilon_transitive(X8)
| sK6(X8,X9,X9) = X8
| ~ subset(X8,sK6(X8,X9,X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_942])]) ).
fof(f3681,plain,
( ! [X8,X9] :
( in(sK6(X8,X9,X9),X9)
| sP0(X8,X9,X9)
| ~ epsilon_transitive(X8)
| sK6(X8,X9,X9) = X8
| ~ subset(X8,sK6(X8,X9,X9)) )
| ~ spl20_91
| ~ spl20_281 ),
inference(resolution,[],[f3527,f812]) ).
fof(f31374,plain,
( spl20_941
| ~ spl20_97
| ~ spl20_275 ),
inference(avatar_split_clause,[],[f3474,f3444,f846,f31372]) ).
fof(f31372,plain,
( spl20_941
<=> ! [X6,X7] :
( sK5(X6,powerset(X7)) = X6
| singleton(X6) = powerset(X7)
| ordinal_subset(sK5(X6,powerset(X7)),X7)
| ~ ordinal(X7)
| ~ ordinal(sK5(X6,powerset(X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_941])]) ).
fof(f3444,plain,
( spl20_275
<=> ! [X6,X7] :
( singleton(X6) = powerset(X7)
| sK5(X6,powerset(X7)) = X6
| subset(sK5(X6,powerset(X7)),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_275])]) ).
fof(f3474,plain,
( ! [X6,X7] :
( sK5(X6,powerset(X7)) = X6
| singleton(X6) = powerset(X7)
| ordinal_subset(sK5(X6,powerset(X7)),X7)
| ~ ordinal(X7)
| ~ ordinal(sK5(X6,powerset(X7))) )
| ~ spl20_97
| ~ spl20_275 ),
inference(resolution,[],[f3445,f847]) ).
fof(f3445,plain,
( ! [X6,X7] :
( subset(sK5(X6,powerset(X7)),X7)
| sK5(X6,powerset(X7)) = X6
| singleton(X6) = powerset(X7) )
| ~ spl20_275 ),
inference(avatar_component_clause,[],[f3444]) ).
fof(f31370,plain,
( spl20_940
| ~ spl20_94
| ~ spl20_272 ),
inference(avatar_split_clause,[],[f3409,f3020,f823,f31368]) ).
fof(f31368,plain,
( spl20_940
<=> ! [X4,X5,X3] :
( in(sK6(powerset(X3),powerset(X3),X4),X4)
| sP0(powerset(X3),powerset(X3),X4)
| ~ empty(X3)
| ~ in(X5,sK6(powerset(X3),powerset(X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_940])]) ).
fof(f3409,plain,
( ! [X3,X4,X5] :
( in(sK6(powerset(X3),powerset(X3),X4),X4)
| sP0(powerset(X3),powerset(X3),X4)
| ~ empty(X3)
| ~ in(X5,sK6(powerset(X3),powerset(X3),X4)) )
| ~ spl20_94
| ~ spl20_272 ),
inference(resolution,[],[f3021,f824]) ).
fof(f31366,plain,
( spl20_939
| ~ spl20_157
| ~ spl20_271 ),
inference(avatar_split_clause,[],[f3402,f3016,f1267,f31364]) ).
fof(f31364,plain,
( spl20_939
<=> ! [X30,X31] :
( sP0(sK4(powerset(X30)),sK4(powerset(X30)),sK4(powerset(X31)))
| ~ empty(X31)
| element(sK6(sK4(powerset(X30)),sK4(powerset(X30)),sK4(powerset(X31))),X30) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_939])]) ).
fof(f3016,plain,
( spl20_271
<=> ! [X18,X17] :
( in(sK6(X17,X17,sK4(powerset(X18))),X17)
| sP0(X17,X17,sK4(powerset(X18)))
| ~ empty(X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_271])]) ).
fof(f3402,plain,
( ! [X31,X30] :
( sP0(sK4(powerset(X30)),sK4(powerset(X30)),sK4(powerset(X31)))
| ~ empty(X31)
| element(sK6(sK4(powerset(X30)),sK4(powerset(X30)),sK4(powerset(X31))),X30) )
| ~ spl20_157
| ~ spl20_271 ),
inference(resolution,[],[f3017,f1268]) ).
fof(f3017,plain,
( ! [X18,X17] :
( in(sK6(X17,X17,sK4(powerset(X18))),X17)
| sP0(X17,X17,sK4(powerset(X18)))
| ~ empty(X18) )
| ~ spl20_271 ),
inference(avatar_component_clause,[],[f3016]) ).
fof(f31362,plain,
( spl20_938
| ~ spl20_231
| ~ spl20_242 ),
inference(avatar_split_clause,[],[f2709,f2533,f2402,f31360]) ).
fof(f31360,plain,
( spl20_938
<=> ! [X18,X17,X19] :
( sP0(X17,X17,set_union2(X18,X19))
| ~ empty(X17)
| in(sK6(X17,X17,set_union2(X18,X19)),X18)
| in(sK6(X17,X17,set_union2(X18,X19)),X19) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_938])]) ).
fof(f2533,plain,
( spl20_242
<=> ! [X9,X8] :
( in(sK6(X8,X8,X9),X9)
| sP0(X8,X8,X9)
| ~ empty(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_242])]) ).
fof(f2709,plain,
( ! [X18,X19,X17] :
( sP0(X17,X17,set_union2(X18,X19))
| ~ empty(X17)
| in(sK6(X17,X17,set_union2(X18,X19)),X18)
| in(sK6(X17,X17,set_union2(X18,X19)),X19) )
| ~ spl20_231
| ~ spl20_242 ),
inference(resolution,[],[f2534,f2403]) ).
fof(f2534,plain,
( ! [X8,X9] :
( in(sK6(X8,X8,X9),X9)
| sP0(X8,X8,X9)
| ~ empty(X8) )
| ~ spl20_242 ),
inference(avatar_component_clause,[],[f2533]) ).
fof(f31358,plain,
( spl20_937
| ~ spl20_170
| ~ spl20_231 ),
inference(avatar_split_clause,[],[f2449,f2402,f1403,f31356]) ).
fof(f31356,plain,
( spl20_937
<=> ! [X6,X7,X8] :
( in(X6,X7)
| in(X6,X8)
| set_union2(X7,X8) = X6
| ~ ordinal(set_union2(X7,X8))
| ~ ordinal(X6)
| subset(set_union2(X7,X8),X6)
| ~ epsilon_transitive(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_937])]) ).
fof(f1403,plain,
( spl20_170
<=> ! [X0,X1] :
( in(X1,X0)
| X0 = X1
| ~ ordinal(X0)
| ~ ordinal(X1)
| subset(X0,X1)
| ~ epsilon_transitive(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_170])]) ).
fof(f2449,plain,
( ! [X8,X6,X7] :
( in(X6,X7)
| in(X6,X8)
| set_union2(X7,X8) = X6
| ~ ordinal(set_union2(X7,X8))
| ~ ordinal(X6)
| subset(set_union2(X7,X8),X6)
| ~ epsilon_transitive(X6) )
| ~ spl20_170
| ~ spl20_231 ),
inference(resolution,[],[f2403,f1404]) ).
fof(f1404,plain,
( ! [X0,X1] :
( in(X1,X0)
| X0 = X1
| ~ ordinal(X0)
| ~ ordinal(X1)
| subset(X0,X1)
| ~ epsilon_transitive(X1) )
| ~ spl20_170 ),
inference(avatar_component_clause,[],[f1403]) ).
fof(f31354,plain,
( spl20_936
| ~ spl20_170
| ~ spl20_230 ),
inference(avatar_split_clause,[],[f2412,f2398,f1403,f31352]) ).
fof(f31352,plain,
( spl20_936
<=> ! [X0,X1] :
( element(X0,X1)
| epsilon_transitive(powerset(X1))
| sK3(powerset(X1)) = X0
| ~ ordinal(sK3(powerset(X1)))
| ~ ordinal(X0)
| subset(sK3(powerset(X1)),X0)
| ~ epsilon_transitive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_936])]) ).
fof(f2412,plain,
( ! [X0,X1] :
( element(X0,X1)
| epsilon_transitive(powerset(X1))
| sK3(powerset(X1)) = X0
| ~ ordinal(sK3(powerset(X1)))
| ~ ordinal(X0)
| subset(sK3(powerset(X1)),X0)
| ~ epsilon_transitive(X0) )
| ~ spl20_170
| ~ spl20_230 ),
inference(resolution,[],[f2399,f1404]) ).
fof(f31350,plain,
( spl20_935
| spl20_181
| ~ spl20_89
| ~ spl20_866 ),
inference(avatar_split_clause,[],[f25911,f24838,f776,f1640,f31347]) ).
fof(f24838,plain,
( spl20_866
<=> element(sK4(sK2),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_866])]) ).
fof(f25911,plain,
( empty(sK1)
| in(sK4(sK2),sK1)
| ~ spl20_89
| ~ spl20_866 ),
inference(resolution,[],[f24840,f777]) ).
fof(f24840,plain,
( element(sK4(sK2),sK1)
| ~ spl20_866 ),
inference(avatar_component_clause,[],[f24838]) ).
fof(f30782,plain,
( ~ spl20_69
| spl20_934
| ~ spl20_88
| ~ spl20_813 ),
inference(avatar_split_clause,[],[f24029,f23873,f772,f30779,f627]) ).
fof(f627,plain,
( spl20_69
<=> epsilon_transitive(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_69])]) ).
fof(f30779,plain,
( spl20_934
<=> subset(sK4(sK1),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_934])]) ).
fof(f23873,plain,
( spl20_813
<=> in(sK4(sK1),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_813])]) ).
fof(f24029,plain,
( subset(sK4(sK1),sK2)
| ~ epsilon_transitive(sK2)
| ~ spl20_88
| ~ spl20_813 ),
inference(resolution,[],[f23875,f773]) ).
fof(f23875,plain,
( in(sK4(sK1),sK2)
| ~ spl20_813 ),
inference(avatar_component_clause,[],[f23873]) ).
fof(f30000,plain,
( spl20_933
| ~ spl20_93
| ~ spl20_484 ),
inference(avatar_split_clause,[],[f13753,f13190,f819,f29997]) ).
fof(f819,plain,
( spl20_93
<=> ! [X2,X0,X1] :
( set_union2(X0,X1) = X2
| ~ sP0(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_93])]) ).
fof(f13190,plain,
( spl20_484
<=> sP0(sK2,singleton(sK2),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_484])]) ).
fof(f13753,plain,
( sK1 = set_union2(singleton(sK2),sK2)
| ~ spl20_93
| ~ spl20_484 ),
inference(resolution,[],[f13192,f820]) ).
fof(f820,plain,
( ! [X2,X0,X1] :
( ~ sP0(X1,X0,X2)
| set_union2(X0,X1) = X2 )
| ~ spl20_93 ),
inference(avatar_component_clause,[],[f819]) ).
fof(f13192,plain,
( sP0(sK2,singleton(sK2),sK1)
| ~ spl20_484 ),
inference(avatar_component_clause,[],[f13190]) ).
fof(f27815,plain,
( ~ spl20_129
| ~ spl20_932 ),
inference(avatar_contradiction_clause,[],[f27804]) ).
fof(f27804,plain,
( $false
| ~ spl20_129
| ~ spl20_932 ),
inference(resolution,[],[f27592,f1086]) ).
fof(f1086,plain,
( ! [X0] : ~ in(succ(X0),X0)
| ~ spl20_129 ),
inference(avatar_component_clause,[],[f1085]) ).
fof(f1085,plain,
( spl20_129
<=> ! [X0] : ~ in(succ(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_129])]) ).
fof(f27592,plain,
( in(succ(sK2),sK2)
| ~ spl20_932 ),
inference(avatar_component_clause,[],[f27590]) ).
fof(f27590,plain,
( spl20_932
<=> in(succ(sK2),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_932])]) ).
fof(f27593,plain,
( spl20_932
| spl20_161
| ~ spl20_89
| ~ spl20_362 ),
inference(avatar_split_clause,[],[f11244,f5335,f776,f1308,f27590]) ).
fof(f1308,plain,
( spl20_161
<=> empty(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_161])]) ).
fof(f5335,plain,
( spl20_362
<=> element(succ(sK2),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_362])]) ).
fof(f11244,plain,
( empty(sK2)
| in(succ(sK2),sK2)
| ~ spl20_89
| ~ spl20_362 ),
inference(resolution,[],[f5337,f777]) ).
fof(f5337,plain,
( element(succ(sK2),sK2)
| ~ spl20_362 ),
inference(avatar_component_clause,[],[f5335]) ).
fof(f27480,plain,
( spl20_931
| ~ spl20_447 ),
inference(avatar_split_clause,[],[f11955,f11572,f27478]) ).
fof(f27478,plain,
( spl20_931
<=> ! [X0,X1] :
( in(X0,sK6(X0,X1,X0))
| sK6(X0,X1,X0) = X0
| ~ ordinal(X0)
| ~ ordinal(sK6(X0,X1,X0))
| sP0(X0,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_931])]) ).
fof(f11572,plain,
( spl20_447
<=> ! [X69,X68,X67] :
( sP0(X67,X68,X69)
| in(X69,sK6(X67,X68,X69))
| sK6(X67,X68,X69) = X69
| ~ ordinal(X69)
| ~ ordinal(sK6(X67,X68,X69))
| in(X67,sK6(X67,X68,X69))
| sK6(X67,X68,X69) = X67
| ~ ordinal(X67) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_447])]) ).
fof(f11955,plain,
( ! [X0,X1] :
( in(X0,sK6(X0,X1,X0))
| sK6(X0,X1,X0) = X0
| ~ ordinal(X0)
| ~ ordinal(sK6(X0,X1,X0))
| sP0(X0,X1,X0) )
| ~ spl20_447 ),
inference(duplicate_literal_removal,[],[f11954]) ).
fof(f11954,plain,
( ! [X0,X1] :
( in(X0,sK6(X0,X1,X0))
| sK6(X0,X1,X0) = X0
| ~ ordinal(X0)
| ~ ordinal(sK6(X0,X1,X0))
| sP0(X0,X1,X0)
| sK6(X0,X1,X0) = X0
| ~ ordinal(X0) )
| ~ spl20_447 ),
inference(factoring,[],[f11573]) ).
fof(f11573,plain,
( ! [X68,X69,X67] :
( in(X69,sK6(X67,X68,X69))
| in(X67,sK6(X67,X68,X69))
| sK6(X67,X68,X69) = X69
| ~ ordinal(X69)
| ~ ordinal(sK6(X67,X68,X69))
| sP0(X67,X68,X69)
| sK6(X67,X68,X69) = X67
| ~ ordinal(X67) )
| ~ spl20_447 ),
inference(avatar_component_clause,[],[f11572]) ).
fof(f27476,plain,
( spl20_930
| ~ spl20_444 ),
inference(avatar_split_clause,[],[f11701,f11560,f27474]) ).
fof(f27474,plain,
( spl20_930
<=> ! [X0,X1] :
( in(X0,sK6(X1,X0,X0))
| sK6(X1,X0,X0) = X0
| ~ ordinal(X0)
| ~ ordinal(sK6(X1,X0,X0))
| sP0(X1,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_930])]) ).
fof(f11560,plain,
( spl20_444
<=> ! [X69,X68,X67] :
( sP0(X67,X68,X69)
| in(X69,sK6(X67,X68,X69))
| sK6(X67,X68,X69) = X69
| ~ ordinal(X69)
| ~ ordinal(sK6(X67,X68,X69))
| in(X68,sK6(X67,X68,X69))
| sK6(X67,X68,X69) = X68
| ~ ordinal(X68) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_444])]) ).
fof(f11701,plain,
( ! [X0,X1] :
( in(X0,sK6(X1,X0,X0))
| sK6(X1,X0,X0) = X0
| ~ ordinal(X0)
| ~ ordinal(sK6(X1,X0,X0))
| sP0(X1,X0,X0) )
| ~ spl20_444 ),
inference(duplicate_literal_removal,[],[f11700]) ).
fof(f11700,plain,
( ! [X0,X1] :
( in(X0,sK6(X1,X0,X0))
| sK6(X1,X0,X0) = X0
| ~ ordinal(X0)
| ~ ordinal(sK6(X1,X0,X0))
| sP0(X1,X0,X0)
| sK6(X1,X0,X0) = X0
| ~ ordinal(X0) )
| ~ spl20_444 ),
inference(factoring,[],[f11561]) ).
fof(f11561,plain,
( ! [X68,X69,X67] :
( in(X69,sK6(X67,X68,X69))
| in(X68,sK6(X67,X68,X69))
| sK6(X67,X68,X69) = X69
| ~ ordinal(X69)
| ~ ordinal(sK6(X67,X68,X69))
| sP0(X67,X68,X69)
| sK6(X67,X68,X69) = X68
| ~ ordinal(X68) )
| ~ spl20_444 ),
inference(avatar_component_clause,[],[f11560]) ).
fof(f27472,plain,
( spl20_929
| ~ spl20_223
| ~ spl20_338 ),
inference(avatar_split_clause,[],[f5110,f4928,f2310,f27470]) ).
fof(f27470,plain,
( spl20_929
<=> ! [X29,X28] :
( sP0(singleton(X28),singleton(X28),sK3(powerset(X29)))
| sK6(singleton(X28),singleton(X28),sK3(powerset(X29))) = X28
| ~ empty(X29)
| epsilon_transitive(powerset(X29)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_929])]) ).
fof(f4928,plain,
( spl20_338
<=> ! [X11,X10] :
( in(sK6(singleton(X10),singleton(X10),X11),X11)
| sP0(singleton(X10),singleton(X10),X11)
| sK6(singleton(X10),singleton(X10),X11) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_338])]) ).
fof(f5110,plain,
( ! [X28,X29] :
( sP0(singleton(X28),singleton(X28),sK3(powerset(X29)))
| sK6(singleton(X28),singleton(X28),sK3(powerset(X29))) = X28
| ~ empty(X29)
| epsilon_transitive(powerset(X29)) )
| ~ spl20_223
| ~ spl20_338 ),
inference(resolution,[],[f4929,f2311]) ).
fof(f4929,plain,
( ! [X10,X11] :
( in(sK6(singleton(X10),singleton(X10),X11),X11)
| sP0(singleton(X10),singleton(X10),X11)
| sK6(singleton(X10),singleton(X10),X11) = X10 )
| ~ spl20_338 ),
inference(avatar_component_clause,[],[f4928]) ).
fof(f27468,plain,
( spl20_928
| ~ spl20_234
| ~ spl20_338 ),
inference(avatar_split_clause,[],[f5101,f4928,f2500,f27466]) ).
fof(f27466,plain,
( spl20_928
<=> ! [X9,X11,X10] :
( sP0(singleton(X9),singleton(X9),X10)
| sK6(singleton(X9),singleton(X9),X10) = X9
| ~ ordinal(X10)
| ordinal_subset(X11,X10)
| ~ ordinal(X11)
| ~ empty(X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_928])]) ).
fof(f5101,plain,
( ! [X10,X11,X9] :
( sP0(singleton(X9),singleton(X9),X10)
| sK6(singleton(X9),singleton(X9),X10) = X9
| ~ ordinal(X10)
| ordinal_subset(X11,X10)
| ~ ordinal(X11)
| ~ empty(X11) )
| ~ spl20_234
| ~ spl20_338 ),
inference(resolution,[],[f4929,f2501]) ).
fof(f27464,plain,
( spl20_927
| ~ spl20_234
| ~ spl20_336 ),
inference(avatar_split_clause,[],[f5077,f4919,f2500,f27462]) ).
fof(f27462,plain,
( spl20_927
<=> ! [X9,X11,X10] :
( element(sK6(X9,X9,sK4(powerset(X10))),X10)
| sP0(X9,X9,sK4(powerset(X10)))
| ~ ordinal(X9)
| ordinal_subset(X11,X9)
| ~ ordinal(X11)
| ~ empty(X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_927])]) ).
fof(f5077,plain,
( ! [X10,X11,X9] :
( element(sK6(X9,X9,sK4(powerset(X10))),X10)
| sP0(X9,X9,sK4(powerset(X10)))
| ~ ordinal(X9)
| ordinal_subset(X11,X9)
| ~ ordinal(X11)
| ~ empty(X11) )
| ~ spl20_234
| ~ spl20_336 ),
inference(resolution,[],[f4920,f2501]) ).
fof(f27460,plain,
( spl20_926
| ~ spl20_223
| ~ spl20_330 ),
inference(avatar_split_clause,[],[f4888,f4726,f2310,f27458]) ).
fof(f27458,plain,
( spl20_926
<=> ! [X44,X43,X42] :
( sP0(X42,singleton(X43),sK3(powerset(X44)))
| ~ empty(X42)
| sK6(X42,singleton(X43),sK3(powerset(X44))) = X43
| ~ empty(X44)
| epsilon_transitive(powerset(X44)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_926])]) ).
fof(f4726,plain,
( spl20_330
<=> ! [X18,X16,X17] :
( in(sK6(X16,singleton(X17),X18),X18)
| sP0(X16,singleton(X17),X18)
| ~ empty(X16)
| sK6(X16,singleton(X17),X18) = X17 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_330])]) ).
fof(f4888,plain,
( ! [X44,X42,X43] :
( sP0(X42,singleton(X43),sK3(powerset(X44)))
| ~ empty(X42)
| sK6(X42,singleton(X43),sK3(powerset(X44))) = X43
| ~ empty(X44)
| epsilon_transitive(powerset(X44)) )
| ~ spl20_223
| ~ spl20_330 ),
inference(resolution,[],[f4727,f2311]) ).
fof(f4727,plain,
( ! [X18,X16,X17] :
( in(sK6(X16,singleton(X17),X18),X18)
| sP0(X16,singleton(X17),X18)
| ~ empty(X16)
| sK6(X16,singleton(X17),X18) = X17 )
| ~ spl20_330 ),
inference(avatar_component_clause,[],[f4726]) ).
fof(f27456,plain,
( spl20_925
| ~ spl20_234
| ~ spl20_330 ),
inference(avatar_split_clause,[],[f4879,f4726,f2500,f27454]) ).
fof(f27454,plain,
( spl20_925
<=> ! [X17,X14,X16,X15] :
( sP0(X14,singleton(X15),X16)
| ~ empty(X14)
| sK6(X14,singleton(X15),X16) = X15
| ~ ordinal(X16)
| ordinal_subset(X17,X16)
| ~ ordinal(X17)
| ~ empty(X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_925])]) ).
fof(f4879,plain,
( ! [X16,X14,X17,X15] :
( sP0(X14,singleton(X15),X16)
| ~ empty(X14)
| sK6(X14,singleton(X15),X16) = X15
| ~ ordinal(X16)
| ordinal_subset(X17,X16)
| ~ ordinal(X17)
| ~ empty(X17) )
| ~ spl20_234
| ~ spl20_330 ),
inference(resolution,[],[f4727,f2501]) ).
fof(f27451,plain,
( spl20_924
| ~ spl20_223
| ~ spl20_329 ),
inference(avatar_split_clause,[],[f4864,f4722,f2310,f27449]) ).
fof(f27449,plain,
( spl20_924
<=> ! [X41,X43,X42] :
( sP0(X41,sK3(powerset(X42)),singleton(X43))
| ~ empty(X41)
| sK6(X41,sK3(powerset(X42)),singleton(X43)) = X43
| ~ empty(X42)
| epsilon_transitive(powerset(X42)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_924])]) ).
fof(f4864,plain,
( ! [X41,X42,X43] :
( sP0(X41,sK3(powerset(X42)),singleton(X43))
| ~ empty(X41)
| sK6(X41,sK3(powerset(X42)),singleton(X43)) = X43
| ~ empty(X42)
| epsilon_transitive(powerset(X42)) )
| ~ spl20_223
| ~ spl20_329 ),
inference(resolution,[],[f4723,f2311]) ).
fof(f27447,plain,
( spl20_923
| ~ spl20_234
| ~ spl20_329 ),
inference(avatar_split_clause,[],[f4855,f4722,f2500,f27445]) ).
fof(f27445,plain,
( spl20_923
<=> ! [X13,X14,X16,X15] :
( sP0(X13,X14,singleton(X15))
| ~ empty(X13)
| sK6(X13,X14,singleton(X15)) = X15
| ~ ordinal(X14)
| ordinal_subset(X16,X14)
| ~ ordinal(X16)
| ~ empty(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_923])]) ).
fof(f4855,plain,
( ! [X16,X14,X15,X13] :
( sP0(X13,X14,singleton(X15))
| ~ empty(X13)
| sK6(X13,X14,singleton(X15)) = X15
| ~ ordinal(X14)
| ordinal_subset(X16,X14)
| ~ ordinal(X16)
| ~ empty(X16) )
| ~ spl20_234
| ~ spl20_329 ),
inference(resolution,[],[f4723,f2501]) ).
fof(f27443,plain,
( spl20_922
| ~ spl20_223
| ~ spl20_328 ),
inference(avatar_split_clause,[],[f4840,f4718,f2310,f27441]) ).
fof(f27441,plain,
( spl20_922
<=> ! [X44,X43,X42] :
( sP0(singleton(X42),X43,sK3(powerset(X44)))
| ~ empty(X43)
| sK6(singleton(X42),X43,sK3(powerset(X44))) = X42
| ~ empty(X44)
| epsilon_transitive(powerset(X44)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_922])]) ).
fof(f4718,plain,
( spl20_328
<=> ! [X18,X16,X17] :
( in(sK6(singleton(X16),X17,X18),X18)
| sP0(singleton(X16),X17,X18)
| ~ empty(X17)
| sK6(singleton(X16),X17,X18) = X16 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_328])]) ).
fof(f4840,plain,
( ! [X44,X42,X43] :
( sP0(singleton(X42),X43,sK3(powerset(X44)))
| ~ empty(X43)
| sK6(singleton(X42),X43,sK3(powerset(X44))) = X42
| ~ empty(X44)
| epsilon_transitive(powerset(X44)) )
| ~ spl20_223
| ~ spl20_328 ),
inference(resolution,[],[f4719,f2311]) ).
fof(f4719,plain,
( ! [X18,X16,X17] :
( in(sK6(singleton(X16),X17,X18),X18)
| sP0(singleton(X16),X17,X18)
| ~ empty(X17)
| sK6(singleton(X16),X17,X18) = X16 )
| ~ spl20_328 ),
inference(avatar_component_clause,[],[f4718]) ).
fof(f27439,plain,
( spl20_921
| ~ spl20_234
| ~ spl20_328 ),
inference(avatar_split_clause,[],[f4831,f4718,f2500,f27437]) ).
fof(f27437,plain,
( spl20_921
<=> ! [X17,X14,X16,X15] :
( sP0(singleton(X14),X15,X16)
| ~ empty(X15)
| sK6(singleton(X14),X15,X16) = X14
| ~ ordinal(X16)
| ordinal_subset(X17,X16)
| ~ ordinal(X17)
| ~ empty(X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_921])]) ).
fof(f4831,plain,
( ! [X16,X14,X17,X15] :
( sP0(singleton(X14),X15,X16)
| ~ empty(X15)
| sK6(singleton(X14),X15,X16) = X14
| ~ ordinal(X16)
| ordinal_subset(X17,X16)
| ~ ordinal(X17)
| ~ empty(X17) )
| ~ spl20_234
| ~ spl20_328 ),
inference(resolution,[],[f4719,f2501]) ).
fof(f27435,plain,
( spl20_920
| ~ spl20_223
| ~ spl20_327 ),
inference(avatar_split_clause,[],[f4816,f4714,f2310,f27433]) ).
fof(f27433,plain,
( spl20_920
<=> ! [X41,X43,X42] :
( sP0(sK3(powerset(X41)),X42,singleton(X43))
| ~ empty(X42)
| sK6(sK3(powerset(X41)),X42,singleton(X43)) = X43
| ~ empty(X41)
| epsilon_transitive(powerset(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_920])]) ).
fof(f4816,plain,
( ! [X41,X42,X43] :
( sP0(sK3(powerset(X41)),X42,singleton(X43))
| ~ empty(X42)
| sK6(sK3(powerset(X41)),X42,singleton(X43)) = X43
| ~ empty(X41)
| epsilon_transitive(powerset(X41)) )
| ~ spl20_223
| ~ spl20_327 ),
inference(resolution,[],[f4715,f2311]) ).
fof(f27431,plain,
( spl20_919
| ~ spl20_234
| ~ spl20_327 ),
inference(avatar_split_clause,[],[f4807,f4714,f2500,f27429]) ).
fof(f27429,plain,
( spl20_919
<=> ! [X13,X14,X16,X15] :
( sP0(X13,X14,singleton(X15))
| ~ empty(X14)
| sK6(X13,X14,singleton(X15)) = X15
| ~ ordinal(X13)
| ordinal_subset(X16,X13)
| ~ ordinal(X16)
| ~ empty(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_919])]) ).
fof(f4807,plain,
( ! [X16,X14,X15,X13] :
( sP0(X13,X14,singleton(X15))
| ~ empty(X14)
| sK6(X13,X14,singleton(X15)) = X15
| ~ ordinal(X13)
| ordinal_subset(X16,X13)
| ~ ordinal(X16)
| ~ empty(X16) )
| ~ spl20_234
| ~ spl20_327 ),
inference(resolution,[],[f4715,f2501]) ).
fof(f27427,plain,
( spl20_918
| ~ spl20_223
| ~ spl20_326 ),
inference(avatar_split_clause,[],[f4792,f4710,f2310,f27425]) ).
fof(f27425,plain,
( spl20_918
<=> ! [X41,X43,X42] :
( sP0(singleton(X41),sK3(powerset(X42)),X43)
| ~ empty(X43)
| sK6(singleton(X41),sK3(powerset(X42)),X43) = X41
| ~ empty(X42)
| epsilon_transitive(powerset(X42)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_918])]) ).
fof(f4710,plain,
( spl20_326
<=> ! [X18,X16,X17] :
( in(sK6(singleton(X16),X17,X18),X17)
| sP0(singleton(X16),X17,X18)
| ~ empty(X18)
| sK6(singleton(X16),X17,X18) = X16 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_326])]) ).
fof(f4792,plain,
( ! [X41,X42,X43] :
( sP0(singleton(X41),sK3(powerset(X42)),X43)
| ~ empty(X43)
| sK6(singleton(X41),sK3(powerset(X42)),X43) = X41
| ~ empty(X42)
| epsilon_transitive(powerset(X42)) )
| ~ spl20_223
| ~ spl20_326 ),
inference(resolution,[],[f4711,f2311]) ).
fof(f4711,plain,
( ! [X18,X16,X17] :
( in(sK6(singleton(X16),X17,X18),X17)
| sP0(singleton(X16),X17,X18)
| ~ empty(X18)
| sK6(singleton(X16),X17,X18) = X16 )
| ~ spl20_326 ),
inference(avatar_component_clause,[],[f4710]) ).
fof(f27423,plain,
( spl20_917
| ~ spl20_234
| ~ spl20_326 ),
inference(avatar_split_clause,[],[f4783,f4710,f2500,f27421]) ).
fof(f27421,plain,
( spl20_917
<=> ! [X13,X14,X16,X15] :
( sP0(singleton(X13),X14,X15)
| ~ empty(X15)
| sK6(singleton(X13),X14,X15) = X13
| ~ ordinal(X14)
| ordinal_subset(X16,X14)
| ~ ordinal(X16)
| ~ empty(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_917])]) ).
fof(f4783,plain,
( ! [X16,X14,X15,X13] :
( sP0(singleton(X13),X14,X15)
| ~ empty(X15)
| sK6(singleton(X13),X14,X15) = X13
| ~ ordinal(X14)
| ordinal_subset(X16,X14)
| ~ ordinal(X16)
| ~ empty(X16) )
| ~ spl20_234
| ~ spl20_326 ),
inference(resolution,[],[f4711,f2501]) ).
fof(f27419,plain,
( spl20_916
| ~ spl20_223
| ~ spl20_325 ),
inference(avatar_split_clause,[],[f4768,f4706,f2310,f27417]) ).
fof(f27417,plain,
( spl20_916
<=> ! [X41,X43,X42] :
( sP0(sK3(powerset(X41)),singleton(X42),X43)
| ~ empty(X43)
| sK6(sK3(powerset(X41)),singleton(X42),X43) = X42
| ~ empty(X41)
| epsilon_transitive(powerset(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_916])]) ).
fof(f4768,plain,
( ! [X41,X42,X43] :
( sP0(sK3(powerset(X41)),singleton(X42),X43)
| ~ empty(X43)
| sK6(sK3(powerset(X41)),singleton(X42),X43) = X42
| ~ empty(X41)
| epsilon_transitive(powerset(X41)) )
| ~ spl20_223
| ~ spl20_325 ),
inference(resolution,[],[f4707,f2311]) ).
fof(f27415,plain,
( spl20_915
| ~ spl20_234
| ~ spl20_325 ),
inference(avatar_split_clause,[],[f4759,f4706,f2500,f27413]) ).
fof(f27413,plain,
( spl20_915
<=> ! [X13,X14,X16,X15] :
( sP0(X13,singleton(X14),X15)
| ~ empty(X15)
| sK6(X13,singleton(X14),X15) = X14
| ~ ordinal(X13)
| ordinal_subset(X16,X13)
| ~ ordinal(X16)
| ~ empty(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_915])]) ).
fof(f4759,plain,
( ! [X16,X14,X15,X13] :
( sP0(X13,singleton(X14),X15)
| ~ empty(X15)
| sK6(X13,singleton(X14),X15) = X14
| ~ ordinal(X13)
| ordinal_subset(X16,X13)
| ~ ordinal(X16)
| ~ empty(X16) )
| ~ spl20_234
| ~ spl20_325 ),
inference(resolution,[],[f4707,f2501]) ).
fof(f27411,plain,
( spl20_431
| ~ spl20_453 ),
inference(avatar_split_clause,[],[f12566,f12332,f10101]) ).
fof(f12332,plain,
( spl20_453
<=> ! [X0] :
( sK1 != X0
| sP0(singleton(sK2),sK2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_453])]) ).
fof(f12566,plain,
( sP0(singleton(sK2),sK2,sK1)
| ~ spl20_453 ),
inference(equality_resolution,[],[f12333]) ).
fof(f12333,plain,
( ! [X0] :
( sK1 != X0
| sP0(singleton(sK2),sK2,X0) )
| ~ spl20_453 ),
inference(avatar_component_clause,[],[f12332]) ).
fof(f27410,plain,
( spl20_914
| ~ spl20_223
| ~ spl20_322 ),
inference(avatar_split_clause,[],[f4684,f4415,f2310,f27408]) ).
fof(f27408,plain,
( spl20_914
<=> ! [X43,X44,X42] :
( subset(sK6(X42,X43,sK3(powerset(X44))),X43)
| ~ empty(X42)
| sP0(X42,X43,sK3(powerset(X44)))
| ~ epsilon_transitive(X43)
| ~ empty(X44)
| epsilon_transitive(powerset(X44)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_914])]) ).
fof(f4415,plain,
( spl20_322
<=> ! [X6,X4,X5] :
( in(sK6(X4,X5,X6),X6)
| sP0(X4,X5,X6)
| ~ empty(X4)
| subset(sK6(X4,X5,X6),X5)
| ~ epsilon_transitive(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_322])]) ).
fof(f4684,plain,
( ! [X44,X42,X43] :
( subset(sK6(X42,X43,sK3(powerset(X44))),X43)
| ~ empty(X42)
| sP0(X42,X43,sK3(powerset(X44)))
| ~ epsilon_transitive(X43)
| ~ empty(X44)
| epsilon_transitive(powerset(X44)) )
| ~ spl20_223
| ~ spl20_322 ),
inference(resolution,[],[f4416,f2311]) ).
fof(f4416,plain,
( ! [X6,X4,X5] :
( subset(sK6(X4,X5,X6),X5)
| in(sK6(X4,X5,X6),X6)
| ~ empty(X4)
| sP0(X4,X5,X6)
| ~ epsilon_transitive(X5) )
| ~ spl20_322 ),
inference(avatar_component_clause,[],[f4415]) ).
fof(f27406,plain,
( spl20_913
| ~ spl20_153
| ~ spl20_322 ),
inference(avatar_split_clause,[],[f4681,f4415,f1230,f27404]) ).
fof(f27404,plain,
( spl20_913
<=> ! [X34,X36,X35] :
( subset(sK6(X34,X35,singleton(X36)),X35)
| ~ empty(X34)
| sP0(X34,X35,singleton(X36))
| ~ epsilon_transitive(X35)
| sK6(X34,X35,singleton(X36)) = X36 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_913])]) ).
fof(f4681,plain,
( ! [X36,X34,X35] :
( subset(sK6(X34,X35,singleton(X36)),X35)
| ~ empty(X34)
| sP0(X34,X35,singleton(X36))
| ~ epsilon_transitive(X35)
| sK6(X34,X35,singleton(X36)) = X36 )
| ~ spl20_153
| ~ spl20_322 ),
inference(resolution,[],[f4416,f1231]) ).
fof(f27402,plain,
( spl20_912
| ~ spl20_234
| ~ spl20_322 ),
inference(avatar_split_clause,[],[f4675,f4415,f2500,f27400]) ).
fof(f27400,plain,
( spl20_912
<=> ! [X17,X14,X16,X15] :
( subset(sK6(X14,X15,X16),X15)
| ~ empty(X14)
| sP0(X14,X15,X16)
| ~ epsilon_transitive(X15)
| ~ ordinal(X16)
| ordinal_subset(X17,X16)
| ~ ordinal(X17)
| ~ empty(X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_912])]) ).
fof(f4675,plain,
( ! [X16,X14,X17,X15] :
( subset(sK6(X14,X15,X16),X15)
| ~ empty(X14)
| sP0(X14,X15,X16)
| ~ epsilon_transitive(X15)
| ~ ordinal(X16)
| ordinal_subset(X17,X16)
| ~ ordinal(X17)
| ~ empty(X17) )
| ~ spl20_234
| ~ spl20_322 ),
inference(resolution,[],[f4416,f2501]) ).
fof(f27398,plain,
( spl20_911
| ~ spl20_160
| ~ spl20_322 ),
inference(avatar_split_clause,[],[f4666,f4415,f1291,f27396]) ).
fof(f27396,plain,
( spl20_911
<=> ! [X0,X3,X2,X1] :
( in(sK6(X0,X1,X2),X2)
| ~ empty(X0)
| sP0(X0,X1,X2)
| ~ epsilon_transitive(X1)
| ~ in(X3,sK6(X0,X1,X2))
| element(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_911])]) ).
fof(f4666,plain,
( ! [X2,X3,X0,X1] :
( in(sK6(X0,X1,X2),X2)
| ~ empty(X0)
| sP0(X0,X1,X2)
| ~ epsilon_transitive(X1)
| ~ in(X3,sK6(X0,X1,X2))
| element(X3,X1) )
| ~ spl20_160
| ~ spl20_322 ),
inference(resolution,[],[f4416,f1292]) ).
fof(f27394,plain,
( spl20_910
| ~ spl20_223
| ~ spl20_321 ),
inference(avatar_split_clause,[],[f4656,f4411,f2310,f27392]) ).
fof(f27392,plain,
( spl20_910
<=> ! [X41,X43,X42] :
( subset(sK6(X41,sK3(powerset(X42)),X43),X43)
| ~ empty(X41)
| sP0(X41,sK3(powerset(X42)),X43)
| ~ epsilon_transitive(X43)
| ~ empty(X42)
| epsilon_transitive(powerset(X42)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_910])]) ).
fof(f4411,plain,
( spl20_321
<=> ! [X6,X7,X8] :
( in(sK6(X6,X7,X8),X7)
| sP0(X6,X7,X8)
| ~ empty(X6)
| subset(sK6(X6,X7,X8),X8)
| ~ epsilon_transitive(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_321])]) ).
fof(f4656,plain,
( ! [X41,X42,X43] :
( subset(sK6(X41,sK3(powerset(X42)),X43),X43)
| ~ empty(X41)
| sP0(X41,sK3(powerset(X42)),X43)
| ~ epsilon_transitive(X43)
| ~ empty(X42)
| epsilon_transitive(powerset(X42)) )
| ~ spl20_223
| ~ spl20_321 ),
inference(resolution,[],[f4412,f2311]) ).
fof(f4412,plain,
( ! [X8,X6,X7] :
( subset(sK6(X6,X7,X8),X8)
| in(sK6(X6,X7,X8),X7)
| ~ empty(X6)
| sP0(X6,X7,X8)
| ~ epsilon_transitive(X8) )
| ~ spl20_321 ),
inference(avatar_component_clause,[],[f4411]) ).
fof(f27390,plain,
( spl20_909
| ~ spl20_153
| ~ spl20_321 ),
inference(avatar_split_clause,[],[f4653,f4411,f1230,f27388]) ).
fof(f27388,plain,
( spl20_909
<=> ! [X34,X35,X33] :
( subset(sK6(X33,singleton(X34),X35),X35)
| ~ empty(X33)
| sP0(X33,singleton(X34),X35)
| ~ epsilon_transitive(X35)
| sK6(X33,singleton(X34),X35) = X34 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_909])]) ).
fof(f4653,plain,
( ! [X34,X35,X33] :
( subset(sK6(X33,singleton(X34),X35),X35)
| ~ empty(X33)
| sP0(X33,singleton(X34),X35)
| ~ epsilon_transitive(X35)
| sK6(X33,singleton(X34),X35) = X34 )
| ~ spl20_153
| ~ spl20_321 ),
inference(resolution,[],[f4412,f1231]) ).
fof(f27386,plain,
( spl20_908
| ~ spl20_234
| ~ spl20_321 ),
inference(avatar_split_clause,[],[f4647,f4411,f2500,f27384]) ).
fof(f27384,plain,
( spl20_908
<=> ! [X13,X14,X16,X15] :
( subset(sK6(X13,X14,X15),X15)
| ~ empty(X13)
| sP0(X13,X14,X15)
| ~ epsilon_transitive(X15)
| ~ ordinal(X14)
| ordinal_subset(X16,X14)
| ~ ordinal(X16)
| ~ empty(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_908])]) ).
fof(f4647,plain,
( ! [X16,X14,X15,X13] :
( subset(sK6(X13,X14,X15),X15)
| ~ empty(X13)
| sP0(X13,X14,X15)
| ~ epsilon_transitive(X15)
| ~ ordinal(X14)
| ordinal_subset(X16,X14)
| ~ ordinal(X16)
| ~ empty(X16) )
| ~ spl20_234
| ~ spl20_321 ),
inference(resolution,[],[f4412,f2501]) ).
fof(f27382,plain,
( spl20_907
| ~ spl20_160
| ~ spl20_321 ),
inference(avatar_split_clause,[],[f4638,f4411,f1291,f27380]) ).
fof(f27380,plain,
( spl20_907
<=> ! [X0,X3,X2,X1] :
( in(sK6(X0,X1,X2),X1)
| ~ empty(X0)
| sP0(X0,X1,X2)
| ~ epsilon_transitive(X2)
| ~ in(X3,sK6(X0,X1,X2))
| element(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_907])]) ).
fof(f4638,plain,
( ! [X2,X3,X0,X1] :
( in(sK6(X0,X1,X2),X1)
| ~ empty(X0)
| sP0(X0,X1,X2)
| ~ epsilon_transitive(X2)
| ~ in(X3,sK6(X0,X1,X2))
| element(X3,X2) )
| ~ spl20_160
| ~ spl20_321 ),
inference(resolution,[],[f4412,f1292]) ).
fof(f27378,plain,
( spl20_906
| ~ spl20_223
| ~ spl20_320 ),
inference(avatar_split_clause,[],[f4628,f4407,f2310,f27376]) ).
fof(f27376,plain,
( spl20_906
<=> ! [X44,X43,X42] :
( subset(sK6(X42,X43,sK3(powerset(X44))),X42)
| ~ empty(X43)
| sP0(X42,X43,sK3(powerset(X44)))
| ~ epsilon_transitive(X42)
| ~ empty(X44)
| epsilon_transitive(powerset(X44)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_906])]) ).
fof(f4407,plain,
( spl20_320
<=> ! [X6,X4,X5] :
( in(sK6(X4,X5,X6),X6)
| sP0(X4,X5,X6)
| ~ empty(X5)
| subset(sK6(X4,X5,X6),X4)
| ~ epsilon_transitive(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_320])]) ).
fof(f4628,plain,
( ! [X44,X42,X43] :
( subset(sK6(X42,X43,sK3(powerset(X44))),X42)
| ~ empty(X43)
| sP0(X42,X43,sK3(powerset(X44)))
| ~ epsilon_transitive(X42)
| ~ empty(X44)
| epsilon_transitive(powerset(X44)) )
| ~ spl20_223
| ~ spl20_320 ),
inference(resolution,[],[f4408,f2311]) ).
fof(f4408,plain,
( ! [X6,X4,X5] :
( subset(sK6(X4,X5,X6),X4)
| in(sK6(X4,X5,X6),X6)
| ~ empty(X5)
| sP0(X4,X5,X6)
| ~ epsilon_transitive(X4) )
| ~ spl20_320 ),
inference(avatar_component_clause,[],[f4407]) ).
fof(f27369,plain,
( spl20_197
| ~ spl20_79
| ~ spl20_861 ),
inference(avatar_split_clause,[],[f27289,f24211,f685,f2040]) ).
fof(f2040,plain,
( spl20_197
<=> sK1 = succ(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_197])]) ).
fof(f685,plain,
( spl20_79
<=> ! [X0] : succ(X0) = set_union2(X0,singleton(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_79])]) ).
fof(f24211,plain,
( spl20_861
<=> sK1 = set_union2(sK2,singleton(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_861])]) ).
fof(f27289,plain,
( sK1 = succ(sK2)
| ~ spl20_79
| ~ spl20_861 ),
inference(superposition,[],[f24213,f686]) ).
fof(f686,plain,
( ! [X0] : succ(X0) = set_union2(X0,singleton(X0))
| ~ spl20_79 ),
inference(avatar_component_clause,[],[f685]) ).
fof(f24213,plain,
( sK1 = set_union2(sK2,singleton(sK2))
| ~ spl20_861 ),
inference(avatar_component_clause,[],[f24211]) ).
fof(f27368,plain,
( spl20_905
| ~ spl20_153
| ~ spl20_320 ),
inference(avatar_split_clause,[],[f4625,f4407,f1230,f27366]) ).
fof(f27366,plain,
( spl20_905
<=> ! [X34,X36,X35] :
( subset(sK6(X34,X35,singleton(X36)),X34)
| ~ empty(X35)
| sP0(X34,X35,singleton(X36))
| ~ epsilon_transitive(X34)
| sK6(X34,X35,singleton(X36)) = X36 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_905])]) ).
fof(f4625,plain,
( ! [X36,X34,X35] :
( subset(sK6(X34,X35,singleton(X36)),X34)
| ~ empty(X35)
| sP0(X34,X35,singleton(X36))
| ~ epsilon_transitive(X34)
| sK6(X34,X35,singleton(X36)) = X36 )
| ~ spl20_153
| ~ spl20_320 ),
inference(resolution,[],[f4408,f1231]) ).
fof(f27364,plain,
( spl20_904
| ~ spl20_234
| ~ spl20_320 ),
inference(avatar_split_clause,[],[f4619,f4407,f2500,f27362]) ).
fof(f27362,plain,
( spl20_904
<=> ! [X17,X14,X16,X15] :
( subset(sK6(X14,X15,X16),X14)
| ~ empty(X15)
| sP0(X14,X15,X16)
| ~ epsilon_transitive(X14)
| ~ ordinal(X16)
| ordinal_subset(X17,X16)
| ~ ordinal(X17)
| ~ empty(X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_904])]) ).
fof(f4619,plain,
( ! [X16,X14,X17,X15] :
( subset(sK6(X14,X15,X16),X14)
| ~ empty(X15)
| sP0(X14,X15,X16)
| ~ epsilon_transitive(X14)
| ~ ordinal(X16)
| ordinal_subset(X17,X16)
| ~ ordinal(X17)
| ~ empty(X17) )
| ~ spl20_234
| ~ spl20_320 ),
inference(resolution,[],[f4408,f2501]) ).
fof(f27360,plain,
( spl20_903
| ~ spl20_160
| ~ spl20_320 ),
inference(avatar_split_clause,[],[f4610,f4407,f1291,f27358]) ).
fof(f27358,plain,
( spl20_903
<=> ! [X0,X3,X2,X1] :
( in(sK6(X0,X1,X2),X2)
| ~ empty(X1)
| sP0(X0,X1,X2)
| ~ epsilon_transitive(X0)
| ~ in(X3,sK6(X0,X1,X2))
| element(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_903])]) ).
fof(f4610,plain,
( ! [X2,X3,X0,X1] :
( in(sK6(X0,X1,X2),X2)
| ~ empty(X1)
| sP0(X0,X1,X2)
| ~ epsilon_transitive(X0)
| ~ in(X3,sK6(X0,X1,X2))
| element(X3,X0) )
| ~ spl20_160
| ~ spl20_320 ),
inference(resolution,[],[f4408,f1292]) ).
fof(f27356,plain,
( spl20_902
| ~ spl20_223
| ~ spl20_319 ),
inference(avatar_split_clause,[],[f4600,f4403,f2310,f27354]) ).
fof(f27354,plain,
( spl20_902
<=> ! [X41,X43,X42] :
( subset(sK6(sK3(powerset(X41)),X42,X43),X43)
| ~ empty(X42)
| sP0(sK3(powerset(X41)),X42,X43)
| ~ epsilon_transitive(X43)
| ~ empty(X41)
| epsilon_transitive(powerset(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_902])]) ).
fof(f4403,plain,
( spl20_319
<=> ! [X6,X8,X7] :
( in(sK6(X6,X7,X8),X6)
| sP0(X6,X7,X8)
| ~ empty(X7)
| subset(sK6(X6,X7,X8),X8)
| ~ epsilon_transitive(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_319])]) ).
fof(f4600,plain,
( ! [X41,X42,X43] :
( subset(sK6(sK3(powerset(X41)),X42,X43),X43)
| ~ empty(X42)
| sP0(sK3(powerset(X41)),X42,X43)
| ~ epsilon_transitive(X43)
| ~ empty(X41)
| epsilon_transitive(powerset(X41)) )
| ~ spl20_223
| ~ spl20_319 ),
inference(resolution,[],[f4404,f2311]) ).
fof(f4404,plain,
( ! [X8,X6,X7] :
( subset(sK6(X6,X7,X8),X8)
| in(sK6(X6,X7,X8),X6)
| ~ empty(X7)
| sP0(X6,X7,X8)
| ~ epsilon_transitive(X8) )
| ~ spl20_319 ),
inference(avatar_component_clause,[],[f4403]) ).
fof(f27352,plain,
( spl20_901
| ~ spl20_153
| ~ spl20_319 ),
inference(avatar_split_clause,[],[f4597,f4403,f1230,f27350]) ).
fof(f27350,plain,
( spl20_901
<=> ! [X34,X35,X33] :
( subset(sK6(singleton(X33),X34,X35),X35)
| ~ empty(X34)
| sP0(singleton(X33),X34,X35)
| ~ epsilon_transitive(X35)
| sK6(singleton(X33),X34,X35) = X33 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_901])]) ).
fof(f4597,plain,
( ! [X34,X35,X33] :
( subset(sK6(singleton(X33),X34,X35),X35)
| ~ empty(X34)
| sP0(singleton(X33),X34,X35)
| ~ epsilon_transitive(X35)
| sK6(singleton(X33),X34,X35) = X33 )
| ~ spl20_153
| ~ spl20_319 ),
inference(resolution,[],[f4404,f1231]) ).
fof(f27348,plain,
( spl20_900
| ~ spl20_234
| ~ spl20_319 ),
inference(avatar_split_clause,[],[f4591,f4403,f2500,f27346]) ).
fof(f27346,plain,
( spl20_900
<=> ! [X13,X14,X16,X15] :
( subset(sK6(X13,X14,X15),X15)
| ~ empty(X14)
| sP0(X13,X14,X15)
| ~ epsilon_transitive(X15)
| ~ ordinal(X13)
| ordinal_subset(X16,X13)
| ~ ordinal(X16)
| ~ empty(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_900])]) ).
fof(f4591,plain,
( ! [X16,X14,X15,X13] :
( subset(sK6(X13,X14,X15),X15)
| ~ empty(X14)
| sP0(X13,X14,X15)
| ~ epsilon_transitive(X15)
| ~ ordinal(X13)
| ordinal_subset(X16,X13)
| ~ ordinal(X16)
| ~ empty(X16) )
| ~ spl20_234
| ~ spl20_319 ),
inference(resolution,[],[f4404,f2501]) ).
fof(f27344,plain,
( spl20_899
| ~ spl20_160
| ~ spl20_319 ),
inference(avatar_split_clause,[],[f4582,f4403,f1291,f27342]) ).
fof(f27342,plain,
( spl20_899
<=> ! [X0,X3,X2,X1] :
( in(sK6(X0,X1,X2),X0)
| ~ empty(X1)
| sP0(X0,X1,X2)
| ~ epsilon_transitive(X2)
| ~ in(X3,sK6(X0,X1,X2))
| element(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_899])]) ).
fof(f4582,plain,
( ! [X2,X3,X0,X1] :
( in(sK6(X0,X1,X2),X0)
| ~ empty(X1)
| sP0(X0,X1,X2)
| ~ epsilon_transitive(X2)
| ~ in(X3,sK6(X0,X1,X2))
| element(X3,X2) )
| ~ spl20_160
| ~ spl20_319 ),
inference(resolution,[],[f4404,f1292]) ).
fof(f27340,plain,
( spl20_898
| ~ spl20_223
| ~ spl20_318 ),
inference(avatar_split_clause,[],[f4572,f4399,f2310,f27338]) ).
fof(f27338,plain,
( spl20_898
<=> ! [X41,X43,X42] :
( subset(sK6(X41,sK3(powerset(X42)),X43),X41)
| ~ empty(X43)
| sP0(X41,sK3(powerset(X42)),X43)
| ~ epsilon_transitive(X41)
| ~ empty(X42)
| epsilon_transitive(powerset(X42)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_898])]) ).
fof(f4399,plain,
( spl20_318
<=> ! [X6,X4,X5] :
( in(sK6(X4,X5,X6),X5)
| sP0(X4,X5,X6)
| ~ empty(X6)
| subset(sK6(X4,X5,X6),X4)
| ~ epsilon_transitive(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_318])]) ).
fof(f4572,plain,
( ! [X41,X42,X43] :
( subset(sK6(X41,sK3(powerset(X42)),X43),X41)
| ~ empty(X43)
| sP0(X41,sK3(powerset(X42)),X43)
| ~ epsilon_transitive(X41)
| ~ empty(X42)
| epsilon_transitive(powerset(X42)) )
| ~ spl20_223
| ~ spl20_318 ),
inference(resolution,[],[f4400,f2311]) ).
fof(f4400,plain,
( ! [X6,X4,X5] :
( subset(sK6(X4,X5,X6),X4)
| in(sK6(X4,X5,X6),X5)
| ~ empty(X6)
| sP0(X4,X5,X6)
| ~ epsilon_transitive(X4) )
| ~ spl20_318 ),
inference(avatar_component_clause,[],[f4399]) ).
fof(f27336,plain,
( spl20_897
| ~ spl20_153
| ~ spl20_318 ),
inference(avatar_split_clause,[],[f4569,f4399,f1230,f27334]) ).
fof(f27334,plain,
( spl20_897
<=> ! [X34,X35,X33] :
( subset(sK6(X33,singleton(X34),X35),X33)
| ~ empty(X35)
| sP0(X33,singleton(X34),X35)
| ~ epsilon_transitive(X33)
| sK6(X33,singleton(X34),X35) = X34 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_897])]) ).
fof(f4569,plain,
( ! [X34,X35,X33] :
( subset(sK6(X33,singleton(X34),X35),X33)
| ~ empty(X35)
| sP0(X33,singleton(X34),X35)
| ~ epsilon_transitive(X33)
| sK6(X33,singleton(X34),X35) = X34 )
| ~ spl20_153
| ~ spl20_318 ),
inference(resolution,[],[f4400,f1231]) ).
fof(f27332,plain,
( spl20_896
| ~ spl20_234
| ~ spl20_318 ),
inference(avatar_split_clause,[],[f4563,f4399,f2500,f27330]) ).
fof(f27330,plain,
( spl20_896
<=> ! [X13,X14,X16,X15] :
( subset(sK6(X13,X14,X15),X13)
| ~ empty(X15)
| sP0(X13,X14,X15)
| ~ epsilon_transitive(X13)
| ~ ordinal(X14)
| ordinal_subset(X16,X14)
| ~ ordinal(X16)
| ~ empty(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_896])]) ).
fof(f4563,plain,
( ! [X16,X14,X15,X13] :
( subset(sK6(X13,X14,X15),X13)
| ~ empty(X15)
| sP0(X13,X14,X15)
| ~ epsilon_transitive(X13)
| ~ ordinal(X14)
| ordinal_subset(X16,X14)
| ~ ordinal(X16)
| ~ empty(X16) )
| ~ spl20_234
| ~ spl20_318 ),
inference(resolution,[],[f4400,f2501]) ).
fof(f27288,plain,
( spl20_895
| ~ spl20_160
| ~ spl20_318 ),
inference(avatar_split_clause,[],[f4554,f4399,f1291,f27286]) ).
fof(f27286,plain,
( spl20_895
<=> ! [X0,X3,X2,X1] :
( in(sK6(X0,X1,X2),X1)
| ~ empty(X2)
| sP0(X0,X1,X2)
| ~ epsilon_transitive(X0)
| ~ in(X3,sK6(X0,X1,X2))
| element(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_895])]) ).
fof(f4554,plain,
( ! [X2,X3,X0,X1] :
( in(sK6(X0,X1,X2),X1)
| ~ empty(X2)
| sP0(X0,X1,X2)
| ~ epsilon_transitive(X0)
| ~ in(X3,sK6(X0,X1,X2))
| element(X3,X0) )
| ~ spl20_160
| ~ spl20_318 ),
inference(resolution,[],[f4400,f1292]) ).
fof(f27284,plain,
( spl20_894
| ~ spl20_223
| ~ spl20_317 ),
inference(avatar_split_clause,[],[f4544,f4395,f2310,f27282]) ).
fof(f27282,plain,
( spl20_894
<=> ! [X41,X43,X42] :
( subset(sK6(sK3(powerset(X41)),X42,X43),X42)
| ~ empty(X43)
| sP0(sK3(powerset(X41)),X42,X43)
| ~ epsilon_transitive(X42)
| ~ empty(X41)
| epsilon_transitive(powerset(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_894])]) ).
fof(f4395,plain,
( spl20_317
<=> ! [X6,X4,X5] :
( in(sK6(X4,X5,X6),X4)
| sP0(X4,X5,X6)
| ~ empty(X6)
| subset(sK6(X4,X5,X6),X5)
| ~ epsilon_transitive(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_317])]) ).
fof(f4544,plain,
( ! [X41,X42,X43] :
( subset(sK6(sK3(powerset(X41)),X42,X43),X42)
| ~ empty(X43)
| sP0(sK3(powerset(X41)),X42,X43)
| ~ epsilon_transitive(X42)
| ~ empty(X41)
| epsilon_transitive(powerset(X41)) )
| ~ spl20_223
| ~ spl20_317 ),
inference(resolution,[],[f4396,f2311]) ).
fof(f4396,plain,
( ! [X6,X4,X5] :
( subset(sK6(X4,X5,X6),X5)
| in(sK6(X4,X5,X6),X4)
| ~ empty(X6)
| sP0(X4,X5,X6)
| ~ epsilon_transitive(X5) )
| ~ spl20_317 ),
inference(avatar_component_clause,[],[f4395]) ).
fof(f27280,plain,
( spl20_893
| ~ spl20_153
| ~ spl20_317 ),
inference(avatar_split_clause,[],[f4541,f4395,f1230,f27278]) ).
fof(f27278,plain,
( spl20_893
<=> ! [X34,X35,X33] :
( subset(sK6(singleton(X33),X34,X35),X34)
| ~ empty(X35)
| sP0(singleton(X33),X34,X35)
| ~ epsilon_transitive(X34)
| sK6(singleton(X33),X34,X35) = X33 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_893])]) ).
fof(f4541,plain,
( ! [X34,X35,X33] :
( subset(sK6(singleton(X33),X34,X35),X34)
| ~ empty(X35)
| sP0(singleton(X33),X34,X35)
| ~ epsilon_transitive(X34)
| sK6(singleton(X33),X34,X35) = X33 )
| ~ spl20_153
| ~ spl20_317 ),
inference(resolution,[],[f4396,f1231]) ).
fof(f27276,plain,
( spl20_892
| ~ spl20_234
| ~ spl20_317 ),
inference(avatar_split_clause,[],[f4535,f4395,f2500,f27274]) ).
fof(f27274,plain,
( spl20_892
<=> ! [X13,X14,X16,X15] :
( subset(sK6(X13,X14,X15),X14)
| ~ empty(X15)
| sP0(X13,X14,X15)
| ~ epsilon_transitive(X14)
| ~ ordinal(X13)
| ordinal_subset(X16,X13)
| ~ ordinal(X16)
| ~ empty(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_892])]) ).
fof(f4535,plain,
( ! [X16,X14,X15,X13] :
( subset(sK6(X13,X14,X15),X14)
| ~ empty(X15)
| sP0(X13,X14,X15)
| ~ epsilon_transitive(X14)
| ~ ordinal(X13)
| ordinal_subset(X16,X13)
| ~ ordinal(X16)
| ~ empty(X16) )
| ~ spl20_234
| ~ spl20_317 ),
inference(resolution,[],[f4396,f2501]) ).
fof(f27272,plain,
( spl20_891
| ~ spl20_160
| ~ spl20_317 ),
inference(avatar_split_clause,[],[f4526,f4395,f1291,f27270]) ).
fof(f27270,plain,
( spl20_891
<=> ! [X0,X3,X2,X1] :
( in(sK6(X0,X1,X2),X0)
| ~ empty(X2)
| sP0(X0,X1,X2)
| ~ epsilon_transitive(X1)
| ~ in(X3,sK6(X0,X1,X2))
| element(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_891])]) ).
fof(f4526,plain,
( ! [X2,X3,X0,X1] :
( in(sK6(X0,X1,X2),X0)
| ~ empty(X2)
| sP0(X0,X1,X2)
| ~ epsilon_transitive(X1)
| ~ in(X3,sK6(X0,X1,X2))
| element(X3,X1) )
| ~ spl20_160
| ~ spl20_317 ),
inference(resolution,[],[f4396,f1292]) ).
fof(f27268,plain,
( spl20_890
| ~ spl20_146
| ~ spl20_314 ),
inference(avatar_split_clause,[],[f4429,f4376,f1180,f27266]) ).
fof(f27266,plain,
( spl20_890
<=> ! [X20,X21] :
( sK5(X20,powerset(X21)) = X20
| element(sK4(sK5(X20,powerset(X21))),X21)
| powerset(X21) = singleton(X20)
| empty(sK5(X20,powerset(X21))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_890])]) ).
fof(f4376,plain,
( spl20_314
<=> ! [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_314])]) ).
fof(f4429,plain,
( ! [X21,X20] :
( sK5(X20,powerset(X21)) = X20
| element(sK4(sK5(X20,powerset(X21))),X21)
| powerset(X21) = singleton(X20)
| empty(sK5(X20,powerset(X21))) )
| ~ spl20_146
| ~ spl20_314 ),
inference(resolution,[],[f4377,f1181]) ).
fof(f4377,plain,
( ! [X2,X0,X1] :
( ~ in(X2,sK5(X0,powerset(X1)))
| sK5(X0,powerset(X1)) = X0
| element(X2,X1)
| singleton(X0) = powerset(X1) )
| ~ spl20_314 ),
inference(avatar_component_clause,[],[f4376]) ).
fof(f27264,plain,
( spl20_889
| ~ spl20_71
| ~ spl20_314 ),
inference(avatar_split_clause,[],[f4428,f4376,f637,f27262]) ).
fof(f27262,plain,
( spl20_889
<=> ! [X18,X19] :
( sK5(X18,powerset(X19)) = X18
| element(sK3(sK5(X18,powerset(X19))),X19)
| powerset(X19) = singleton(X18)
| epsilon_transitive(sK5(X18,powerset(X19))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_889])]) ).
fof(f637,plain,
( spl20_71
<=> ! [X0] :
( epsilon_transitive(X0)
| in(sK3(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_71])]) ).
fof(f4428,plain,
( ! [X18,X19] :
( sK5(X18,powerset(X19)) = X18
| element(sK3(sK5(X18,powerset(X19))),X19)
| powerset(X19) = singleton(X18)
| epsilon_transitive(sK5(X18,powerset(X19))) )
| ~ spl20_71
| ~ spl20_314 ),
inference(resolution,[],[f4377,f638]) ).
fof(f638,plain,
( ! [X0] :
( in(sK3(X0),X0)
| epsilon_transitive(X0) )
| ~ spl20_71 ),
inference(avatar_component_clause,[],[f637]) ).
fof(f27260,plain,
( spl20_888
| ~ spl20_84
| ~ spl20_313 ),
inference(avatar_split_clause,[],[f4420,f4372,f732,f27258]) ).
fof(f27258,plain,
( spl20_888
<=> ! [X6,X7] :
( sK5(X6,sK4(powerset(powerset(X7)))) = X6
| singleton(X6) = sK4(powerset(powerset(X7)))
| subset(sK5(X6,sK4(powerset(powerset(X7)))),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_888])]) ).
fof(f4420,plain,
( ! [X6,X7] :
( sK5(X6,sK4(powerset(powerset(X7)))) = X6
| singleton(X6) = sK4(powerset(powerset(X7)))
| subset(sK5(X6,sK4(powerset(powerset(X7)))),X7) )
| ~ spl20_84
| ~ spl20_313 ),
inference(resolution,[],[f4373,f733]) ).
fof(f27256,plain,
( spl20_887
| ~ spl20_94
| ~ spl20_301 ),
inference(avatar_split_clause,[],[f4044,f3629,f823,f27254]) ).
fof(f27254,plain,
( spl20_887
<=> ! [X6,X4,X5,X7] :
( in(sK6(X4,powerset(X5),X6),X6)
| ~ empty(X4)
| sP0(X4,powerset(X5),X6)
| ~ empty(X5)
| ~ in(X7,sK6(X4,powerset(X5),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_887])]) ).
fof(f4044,plain,
( ! [X6,X7,X4,X5] :
( in(sK6(X4,powerset(X5),X6),X6)
| ~ empty(X4)
| sP0(X4,powerset(X5),X6)
| ~ empty(X5)
| ~ in(X7,sK6(X4,powerset(X5),X6)) )
| ~ spl20_94
| ~ spl20_301 ),
inference(resolution,[],[f3630,f824]) ).
fof(f27252,plain,
( spl20_886
| ~ spl20_94
| ~ spl20_298 ),
inference(avatar_split_clause,[],[f3991,f3617,f823,f27250]) ).
fof(f27250,plain,
( spl20_886
<=> ! [X6,X4,X5,X7] :
( in(sK6(X4,X5,powerset(X6)),X5)
| ~ empty(X4)
| sP0(X4,X5,powerset(X6))
| ~ empty(X6)
| ~ in(X7,sK6(X4,X5,powerset(X6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_886])]) ).
fof(f3991,plain,
( ! [X6,X7,X4,X5] :
( in(sK6(X4,X5,powerset(X6)),X5)
| ~ empty(X4)
| sP0(X4,X5,powerset(X6))
| ~ empty(X6)
| ~ in(X7,sK6(X4,X5,powerset(X6))) )
| ~ spl20_94
| ~ spl20_298 ),
inference(resolution,[],[f3618,f824]) ).
fof(f27241,plain,
( spl20_885
| ~ spl20_94
| ~ spl20_294 ),
inference(avatar_split_clause,[],[f3938,f3578,f823,f27239]) ).
fof(f27239,plain,
( spl20_885
<=> ! [X6,X4,X5,X7] :
( in(sK6(powerset(X4),X5,X6),X6)
| ~ empty(X5)
| sP0(powerset(X4),X5,X6)
| ~ empty(X4)
| ~ in(X7,sK6(powerset(X4),X5,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_885])]) ).
fof(f3938,plain,
( ! [X6,X7,X4,X5] :
( in(sK6(powerset(X4),X5,X6),X6)
| ~ empty(X5)
| sP0(powerset(X4),X5,X6)
| ~ empty(X4)
| ~ in(X7,sK6(powerset(X4),X5,X6)) )
| ~ spl20_94
| ~ spl20_294 ),
inference(resolution,[],[f3579,f824]) ).
fof(f27237,plain,
( spl20_884
| ~ spl20_94
| ~ spl20_291 ),
inference(avatar_split_clause,[],[f3885,f3566,f823,f27235]) ).
fof(f27235,plain,
( spl20_884
<=> ! [X6,X4,X5,X7] :
( in(sK6(X4,X5,powerset(X6)),X4)
| ~ empty(X5)
| sP0(X4,X5,powerset(X6))
| ~ empty(X6)
| ~ in(X7,sK6(X4,X5,powerset(X6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_884])]) ).
fof(f3885,plain,
( ! [X6,X7,X4,X5] :
( in(sK6(X4,X5,powerset(X6)),X4)
| ~ empty(X5)
| sP0(X4,X5,powerset(X6))
| ~ empty(X6)
| ~ in(X7,sK6(X4,X5,powerset(X6))) )
| ~ spl20_94
| ~ spl20_291 ),
inference(resolution,[],[f3567,f824]) ).
fof(f27233,plain,
( spl20_883
| ~ spl20_94
| ~ spl20_288 ),
inference(avatar_split_clause,[],[f3832,f3554,f823,f27231]) ).
fof(f27231,plain,
( spl20_883
<=> ! [X6,X4,X5,X7] :
( in(sK6(powerset(X4),X5,X6),X5)
| ~ empty(X6)
| sP0(powerset(X4),X5,X6)
| ~ empty(X4)
| ~ in(X7,sK6(powerset(X4),X5,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_883])]) ).
fof(f3832,plain,
( ! [X6,X7,X4,X5] :
( in(sK6(powerset(X4),X5,X6),X5)
| ~ empty(X6)
| sP0(powerset(X4),X5,X6)
| ~ empty(X4)
| ~ in(X7,sK6(powerset(X4),X5,X6)) )
| ~ spl20_94
| ~ spl20_288 ),
inference(resolution,[],[f3555,f824]) ).
fof(f27229,plain,
( spl20_882
| ~ spl20_94
| ~ spl20_285 ),
inference(avatar_split_clause,[],[f3779,f3542,f823,f27227]) ).
fof(f27227,plain,
( spl20_882
<=> ! [X6,X4,X5,X7] :
( in(sK6(X4,powerset(X5),X6),X4)
| ~ empty(X6)
| sP0(X4,powerset(X5),X6)
| ~ empty(X5)
| ~ in(X7,sK6(X4,powerset(X5),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_882])]) ).
fof(f3779,plain,
( ! [X6,X7,X4,X5] :
( in(sK6(X4,powerset(X5),X6),X4)
| ~ empty(X6)
| sP0(X4,powerset(X5),X6)
| ~ empty(X5)
| ~ in(X7,sK6(X4,powerset(X5),X6)) )
| ~ spl20_94
| ~ spl20_285 ),
inference(resolution,[],[f3543,f824]) ).
fof(f27225,plain,
( spl20_881
| ~ spl20_245
| ~ spl20_278 ),
inference(avatar_split_clause,[],[f3664,f3514,f2725,f27223]) ).
fof(f27223,plain,
( spl20_881
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sK4(powerset(X0)) = X1
| ~ ordinal(sK4(powerset(X0)))
| ~ ordinal(X1)
| ordinal_subset(X2,X1)
| ~ ordinal(X2)
| element(sK4(powerset(X0)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_881])]) ).
fof(f3664,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sK4(powerset(X0)) = X1
| ~ ordinal(sK4(powerset(X0)))
| ~ ordinal(X1)
| ordinal_subset(X2,X1)
| ~ ordinal(X2)
| element(sK4(powerset(X0)),X2) )
| ~ spl20_245
| ~ spl20_278 ),
inference(duplicate_literal_removal,[],[f3640]) ).
fof(f3640,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sK4(powerset(X0)) = X1
| ~ ordinal(sK4(powerset(X0)))
| ~ ordinal(X1)
| ~ ordinal(X1)
| ordinal_subset(X2,X1)
| ~ ordinal(X2)
| element(sK4(powerset(X0)),X2) )
| ~ spl20_245
| ~ spl20_278 ),
inference(resolution,[],[f3515,f2726]) ).
fof(f27221,plain,
( spl20_880
| ~ spl20_91
| ~ spl20_275 ),
inference(avatar_split_clause,[],[f3475,f3444,f811,f27219]) ).
fof(f27219,plain,
( spl20_880
<=> ! [X9,X8] :
( sK5(X8,powerset(X9)) = X8
| singleton(X8) = powerset(X9)
| sK5(X8,powerset(X9)) = X9
| ~ subset(X9,sK5(X8,powerset(X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_880])]) ).
fof(f3475,plain,
( ! [X8,X9] :
( sK5(X8,powerset(X9)) = X8
| singleton(X8) = powerset(X9)
| sK5(X8,powerset(X9)) = X9
| ~ subset(X9,sK5(X8,powerset(X9))) )
| ~ spl20_91
| ~ spl20_275 ),
inference(resolution,[],[f3445,f812]) ).
fof(f27217,plain,
( spl20_879
| ~ spl20_245
| ~ spl20_272 ),
inference(avatar_split_clause,[],[f3416,f3020,f2725,f27215]) ).
fof(f27215,plain,
( spl20_879
<=> ! [X6,X7,X8] :
( element(sK6(X6,X6,X7),X6)
| sP0(X6,X6,X7)
| ~ ordinal(X7)
| ordinal_subset(X8,X7)
| ~ ordinal(X8)
| element(sK6(X6,X6,X7),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_879])]) ).
fof(f3416,plain,
( ! [X8,X6,X7] :
( element(sK6(X6,X6,X7),X6)
| sP0(X6,X6,X7)
| ~ ordinal(X7)
| ordinal_subset(X8,X7)
| ~ ordinal(X8)
| element(sK6(X6,X6,X7),X8) )
| ~ spl20_245
| ~ spl20_272 ),
inference(resolution,[],[f3021,f2726]) ).
fof(f27213,plain,
( spl20_878
| ~ spl20_245
| ~ spl20_271 ),
inference(avatar_split_clause,[],[f3391,f3016,f2725,f27211]) ).
fof(f27211,plain,
( spl20_878
<=> ! [X6,X7,X8] :
( sP0(X6,X6,sK4(powerset(X7)))
| ~ empty(X7)
| ~ ordinal(X6)
| ordinal_subset(X8,X6)
| ~ ordinal(X8)
| element(sK6(X6,X6,sK4(powerset(X7))),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_878])]) ).
fof(f3391,plain,
( ! [X8,X6,X7] :
( sP0(X6,X6,sK4(powerset(X7)))
| ~ empty(X7)
| ~ ordinal(X6)
| ordinal_subset(X8,X6)
| ~ ordinal(X8)
| element(sK6(X6,X6,sK4(powerset(X7))),X8) )
| ~ spl20_245
| ~ spl20_271 ),
inference(resolution,[],[f3017,f2726]) ).
fof(f27209,plain,
( spl20_877
| ~ spl20_223
| ~ spl20_269 ),
inference(avatar_split_clause,[],[f3374,f3008,f2310,f27207]) ).
fof(f27207,plain,
( spl20_877
<=> ! [X29,X28] :
( element(sK6(sK3(powerset(X28)),sK3(powerset(X28)),X29),X29)
| sP0(sK3(powerset(X28)),sK3(powerset(X28)),X29)
| ~ empty(X28)
| epsilon_transitive(powerset(X28)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_877])]) ).
fof(f3008,plain,
( spl20_269
<=> ! [X6,X7] :
( in(sK6(X6,X6,X7),X6)
| sP0(X6,X6,X7)
| element(sK6(X6,X6,X7),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_269])]) ).
fof(f3374,plain,
( ! [X28,X29] :
( element(sK6(sK3(powerset(X28)),sK3(powerset(X28)),X29),X29)
| sP0(sK3(powerset(X28)),sK3(powerset(X28)),X29)
| ~ empty(X28)
| epsilon_transitive(powerset(X28)) )
| ~ spl20_223
| ~ spl20_269 ),
inference(resolution,[],[f3009,f2311]) ).
fof(f3009,plain,
( ! [X6,X7] :
( element(sK6(X6,X6,X7),X7)
| in(sK6(X6,X6,X7),X6)
| sP0(X6,X6,X7) )
| ~ spl20_269 ),
inference(avatar_component_clause,[],[f3008]) ).
fof(f27205,plain,
( spl20_876
| ~ spl20_245
| ~ spl20_269 ),
inference(avatar_split_clause,[],[f3364,f3008,f2725,f27203]) ).
fof(f27203,plain,
( spl20_876
<=> ! [X6,X7,X8] :
( element(sK6(X6,X6,X7),X7)
| sP0(X6,X6,X7)
| ~ ordinal(X6)
| ordinal_subset(X8,X6)
| ~ ordinal(X8)
| element(sK6(X6,X6,X7),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_876])]) ).
fof(f3364,plain,
( ! [X8,X6,X7] :
( element(sK6(X6,X6,X7),X7)
| sP0(X6,X6,X7)
| ~ ordinal(X6)
| ordinal_subset(X8,X6)
| ~ ordinal(X8)
| element(sK6(X6,X6,X7),X8) )
| ~ spl20_245
| ~ spl20_269 ),
inference(resolution,[],[f3009,f2726]) ).
fof(f27201,plain,
( ~ spl20_875
| ~ spl20_75
| ~ spl20_867 ),
inference(avatar_split_clause,[],[f26940,f26456,f653,f27198]) ).
fof(f27198,plain,
( spl20_875
<=> in(sK1,sK4(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_875])]) ).
fof(f26940,plain,
( ~ in(sK1,sK4(sK1))
| ~ spl20_75
| ~ spl20_867 ),
inference(resolution,[],[f26458,f654]) ).
fof(f27196,plain,
( spl20_874
| ~ spl20_223
| ~ spl20_254 ),
inference(avatar_split_clause,[],[f3038,f2936,f2310,f27194]) ).
fof(f27194,plain,
( spl20_874
<=> ! [X24,X23] :
( sK3(powerset(X23)) = X24
| sK3(powerset(X23)) = singleton(X24)
| ~ ordinal(singleton(X24))
| ~ ordinal(sK3(powerset(X23)))
| ~ empty(X23)
| epsilon_transitive(powerset(X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_874])]) ).
fof(f3038,plain,
( ! [X24,X23] :
( sK3(powerset(X23)) = X24
| sK3(powerset(X23)) = singleton(X24)
| ~ ordinal(singleton(X24))
| ~ ordinal(sK3(powerset(X23)))
| ~ empty(X23)
| epsilon_transitive(powerset(X23)) )
| ~ spl20_223
| ~ spl20_254 ),
inference(resolution,[],[f2937,f2311]) ).
fof(f27192,plain,
( spl20_873
| ~ spl20_177
| ~ spl20_245 ),
inference(avatar_split_clause,[],[f2784,f2725,f1462,f27190]) ).
fof(f27190,plain,
( spl20_873
<=> ! [X155,X156,X154] :
( ~ ordinal(X154)
| ordinal_subset(X155,X154)
| ~ ordinal(X155)
| element(sK6(X154,X154,X156),X155)
| in(sK6(X154,X154,X156),X156)
| sP0(X154,X154,X156) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_873])]) ).
fof(f2784,plain,
( ! [X155,X156,X154] :
( ~ ordinal(X154)
| ordinal_subset(X155,X154)
| ~ ordinal(X155)
| element(sK6(X154,X154,X156),X155)
| in(sK6(X154,X154,X156),X156)
| sP0(X154,X154,X156) )
| ~ spl20_177
| ~ spl20_245 ),
inference(resolution,[],[f2726,f1463]) ).
fof(f27188,plain,
( spl20_872
| ~ spl20_177
| ~ spl20_245 ),
inference(avatar_split_clause,[],[f2782,f2725,f1462,f27186]) ).
fof(f27186,plain,
( spl20_872
<=> ! [X150,X149,X148] :
( ~ ordinal(X148)
| ordinal_subset(X149,X148)
| ~ ordinal(X149)
| element(sK6(X150,X150,X148),X149)
| in(sK6(X150,X150,X148),X150)
| sP0(X150,X150,X148) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_872])]) ).
fof(f2782,plain,
( ! [X150,X148,X149] :
( ~ ordinal(X148)
| ordinal_subset(X149,X148)
| ~ ordinal(X149)
| element(sK6(X150,X150,X148),X149)
| in(sK6(X150,X150,X148),X150)
| sP0(X150,X150,X148) )
| ~ spl20_177
| ~ spl20_245 ),
inference(resolution,[],[f2726,f1463]) ).
fof(f27184,plain,
( spl20_871
| ~ spl20_230
| ~ spl20_241 ),
inference(avatar_split_clause,[],[f2692,f2529,f2398,f27182]) ).
fof(f27182,plain,
( spl20_871
<=> ! [X24,X23] :
( sP0(sK3(powerset(X23)),sK3(powerset(X23)),X24)
| ~ empty(X24)
| element(sK6(sK3(powerset(X23)),sK3(powerset(X23)),X24),X23)
| epsilon_transitive(powerset(X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_871])]) ).
fof(f2692,plain,
( ! [X24,X23] :
( sP0(sK3(powerset(X23)),sK3(powerset(X23)),X24)
| ~ empty(X24)
| element(sK6(sK3(powerset(X23)),sK3(powerset(X23)),X24),X23)
| epsilon_transitive(powerset(X23)) )
| ~ spl20_230
| ~ spl20_241 ),
inference(resolution,[],[f2530,f2399]) ).
fof(f27180,plain,
( spl20_870
| ~ spl20_107
| ~ spl20_230 ),
inference(avatar_split_clause,[],[f2419,f2398,f915,f27178]) ).
fof(f27178,plain,
( spl20_870
<=> ! [X13,X12] :
( element(sK5(X12,sK3(powerset(X13))),X13)
| epsilon_transitive(powerset(X13))
| sK5(X12,sK3(powerset(X13))) = X12
| singleton(X12) = sK3(powerset(X13)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_870])]) ).
fof(f915,plain,
( spl20_107
<=> ! [X0,X1] :
( singleton(X0) = X1
| sK5(X0,X1) = X0
| in(sK5(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_107])]) ).
fof(f2419,plain,
( ! [X12,X13] :
( element(sK5(X12,sK3(powerset(X13))),X13)
| epsilon_transitive(powerset(X13))
| sK5(X12,sK3(powerset(X13))) = X12
| singleton(X12) = sK3(powerset(X13)) )
| ~ spl20_107
| ~ spl20_230 ),
inference(resolution,[],[f2399,f916]) ).
fof(f916,plain,
( ! [X0,X1] :
( in(sK5(X0,X1),X1)
| sK5(X0,X1) = X0
| singleton(X0) = X1 )
| ~ spl20_107 ),
inference(avatar_component_clause,[],[f915]) ).
fof(f27176,plain,
( spl20_869
| ~ spl20_177
| ~ spl20_223 ),
inference(avatar_split_clause,[],[f2370,f2310,f1462,f27174]) ).
fof(f27174,plain,
( spl20_869
<=> ! [X88,X87] :
( ~ empty(X87)
| epsilon_transitive(powerset(X87))
| in(sK6(sK3(powerset(X87)),sK3(powerset(X87)),X88),X88)
| sP0(sK3(powerset(X87)),sK3(powerset(X87)),X88) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_869])]) ).
fof(f2370,plain,
( ! [X88,X87] :
( ~ empty(X87)
| epsilon_transitive(powerset(X87))
| in(sK6(sK3(powerset(X87)),sK3(powerset(X87)),X88),X88)
| sP0(sK3(powerset(X87)),sK3(powerset(X87)),X88) )
| ~ spl20_177
| ~ spl20_223 ),
inference(resolution,[],[f2311,f1463]) ).
fof(f27172,plain,
( spl20_868
| ~ spl20_170
| ~ spl20_223 ),
inference(avatar_split_clause,[],[f2336,f2310,f1403,f27170]) ).
fof(f27170,plain,
( spl20_868
<=> ! [X0,X1] :
( ~ empty(X0)
| epsilon_transitive(powerset(X0))
| sK3(powerset(X0)) = X1
| ~ ordinal(sK3(powerset(X0)))
| ~ ordinal(X1)
| subset(sK3(powerset(X0)),X1)
| ~ epsilon_transitive(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_868])]) ).
fof(f2336,plain,
( ! [X0,X1] :
( ~ empty(X0)
| epsilon_transitive(powerset(X0))
| sK3(powerset(X0)) = X1
| ~ ordinal(sK3(powerset(X0)))
| ~ ordinal(X1)
| subset(sK3(powerset(X0)),X1)
| ~ epsilon_transitive(X1) )
| ~ spl20_170
| ~ spl20_223 ),
inference(resolution,[],[f2311,f1404]) ).
fof(f26459,plain,
( spl20_867
| ~ spl20_813
| ~ spl20_850 ),
inference(avatar_split_clause,[],[f25997,f24167,f23873,f26456]) ).
fof(f24167,plain,
( spl20_850
<=> ! [X2] :
( ~ in(X2,sK2)
| in(X2,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_850])]) ).
fof(f25997,plain,
( in(sK4(sK1),sK1)
| ~ spl20_813
| ~ spl20_850 ),
inference(resolution,[],[f24168,f23875]) ).
fof(f24168,plain,
( ! [X2] :
( ~ in(X2,sK2)
| in(X2,sK1) )
| ~ spl20_850 ),
inference(avatar_component_clause,[],[f24167]) ).
fof(f24841,plain,
( spl20_161
| spl20_866
| ~ spl20_146
| ~ spl20_455 ),
inference(avatar_split_clause,[],[f12350,f12340,f1180,f24838,f1308]) ).
fof(f12350,plain,
( element(sK4(sK2),sK1)
| empty(sK2)
| ~ spl20_146
| ~ spl20_455 ),
inference(resolution,[],[f12341,f1181]) ).
fof(f24230,plain,
( spl20_865
| ~ spl20_427 ),
inference(avatar_split_clause,[],[f10296,f9740,f24228]) ).
fof(f24228,plain,
( spl20_865
<=> ! [X0,X1] :
( element(sK6(X0,sK4(powerset(X0)),X1),X0)
| in(sK6(X0,sK4(powerset(X0)),X1),X1)
| sP0(X0,sK4(powerset(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_865])]) ).
fof(f9740,plain,
( spl20_427
<=> ! [X22,X21,X23] :
( element(sK6(X21,sK4(powerset(X22)),X23),X21)
| in(sK6(X21,sK4(powerset(X22)),X23),X23)
| sP0(X21,sK4(powerset(X22)),X23)
| element(sK6(X21,sK4(powerset(X22)),X23),X22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_427])]) ).
fof(f10296,plain,
( ! [X0,X1] :
( element(sK6(X0,sK4(powerset(X0)),X1),X0)
| in(sK6(X0,sK4(powerset(X0)),X1),X1)
| sP0(X0,sK4(powerset(X0)),X1) )
| ~ spl20_427 ),
inference(factoring,[],[f9741]) ).
fof(f9741,plain,
( ! [X21,X22,X23] :
( element(sK6(X21,sK4(powerset(X22)),X23),X22)
| element(sK6(X21,sK4(powerset(X22)),X23),X21)
| in(sK6(X21,sK4(powerset(X22)),X23),X23)
| sP0(X21,sK4(powerset(X22)),X23) )
| ~ spl20_427 ),
inference(avatar_component_clause,[],[f9740]) ).
fof(f24226,plain,
( spl20_864
| ~ spl20_426 ),
inference(avatar_split_clause,[],[f10246,f9736,f24224]) ).
fof(f24224,plain,
( spl20_864
<=> ! [X0,X1] :
( element(sK6(X0,X1,sK4(powerset(X0))),X0)
| in(sK6(X0,X1,sK4(powerset(X0))),X1)
| sP0(X0,X1,sK4(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_864])]) ).
fof(f9736,plain,
( spl20_426
<=> ! [X24,X25,X23] :
( element(sK6(X23,X24,sK4(powerset(X25))),X23)
| in(sK6(X23,X24,sK4(powerset(X25))),X24)
| sP0(X23,X24,sK4(powerset(X25)))
| element(sK6(X23,X24,sK4(powerset(X25))),X25) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_426])]) ).
fof(f10246,plain,
( ! [X0,X1] :
( element(sK6(X0,X1,sK4(powerset(X0))),X0)
| in(sK6(X0,X1,sK4(powerset(X0))),X1)
| sP0(X0,X1,sK4(powerset(X0))) )
| ~ spl20_426 ),
inference(factoring,[],[f9737]) ).
fof(f9737,plain,
( ! [X24,X25,X23] :
( element(sK6(X23,X24,sK4(powerset(X25))),X25)
| element(sK6(X23,X24,sK4(powerset(X25))),X23)
| in(sK6(X23,X24,sK4(powerset(X25))),X24)
| sP0(X23,X24,sK4(powerset(X25))) )
| ~ spl20_426 ),
inference(avatar_component_clause,[],[f9736]) ).
fof(f24222,plain,
( spl20_863
| ~ spl20_425 ),
inference(avatar_split_clause,[],[f10196,f9729,f24220]) ).
fof(f24220,plain,
( spl20_863
<=> ! [X0,X1] :
( element(sK6(sK4(powerset(X0)),X0,X1),X0)
| in(sK6(sK4(powerset(X0)),X0,X1),X1)
| sP0(sK4(powerset(X0)),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_863])]) ).
fof(f9729,plain,
( spl20_425
<=> ! [X22,X21,X23] :
( element(sK6(sK4(powerset(X21)),X22,X23),X22)
| in(sK6(sK4(powerset(X21)),X22,X23),X23)
| sP0(sK4(powerset(X21)),X22,X23)
| element(sK6(sK4(powerset(X21)),X22,X23),X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_425])]) ).
fof(f10196,plain,
( ! [X0,X1] :
( element(sK6(sK4(powerset(X0)),X0,X1),X0)
| in(sK6(sK4(powerset(X0)),X0,X1),X1)
| sP0(sK4(powerset(X0)),X0,X1) )
| ~ spl20_425 ),
inference(factoring,[],[f9730]) ).
fof(f9730,plain,
( ! [X21,X22,X23] :
( element(sK6(sK4(powerset(X21)),X22,X23),X22)
| element(sK6(sK4(powerset(X21)),X22,X23),X21)
| in(sK6(sK4(powerset(X21)),X22,X23),X23)
| sP0(sK4(powerset(X21)),X22,X23) )
| ~ spl20_425 ),
inference(avatar_component_clause,[],[f9729]) ).
fof(f24218,plain,
( spl20_862
| ~ spl20_424 ),
inference(avatar_split_clause,[],[f10146,f9725,f24216]) ).
fof(f24216,plain,
( spl20_862
<=> ! [X0,X1] :
( element(sK6(X0,X1,sK4(powerset(X1))),X1)
| in(sK6(X0,X1,sK4(powerset(X1))),X0)
| sP0(X0,X1,sK4(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_862])]) ).
fof(f9725,plain,
( spl20_424
<=> ! [X25,X24,X23] :
( element(sK6(X23,X24,sK4(powerset(X25))),X24)
| in(sK6(X23,X24,sK4(powerset(X25))),X23)
| sP0(X23,X24,sK4(powerset(X25)))
| element(sK6(X23,X24,sK4(powerset(X25))),X25) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_424])]) ).
fof(f10146,plain,
( ! [X0,X1] :
( element(sK6(X0,X1,sK4(powerset(X1))),X1)
| in(sK6(X0,X1,sK4(powerset(X1))),X0)
| sP0(X0,X1,sK4(powerset(X1))) )
| ~ spl20_424 ),
inference(factoring,[],[f9726]) ).
fof(f9726,plain,
( ! [X24,X25,X23] :
( element(sK6(X23,X24,sK4(powerset(X25))),X25)
| element(sK6(X23,X24,sK4(powerset(X25))),X24)
| in(sK6(X23,X24,sK4(powerset(X25))),X23)
| sP0(X23,X24,sK4(powerset(X25))) )
| ~ spl20_424 ),
inference(avatar_component_clause,[],[f9725]) ).
fof(f24214,plain,
( spl20_861
| ~ spl20_93
| ~ spl20_431 ),
inference(avatar_split_clause,[],[f12330,f10101,f819,f24211]) ).
fof(f12330,plain,
( sK1 = set_union2(sK2,singleton(sK2))
| ~ spl20_93
| ~ spl20_431 ),
inference(resolution,[],[f10103,f820]) ).
fof(f10103,plain,
( sP0(singleton(sK2),sK2,sK1)
| ~ spl20_431 ),
inference(avatar_component_clause,[],[f10101]) ).
fof(f24209,plain,
( spl20_860
| ~ spl20_423 ),
inference(avatar_split_clause,[],[f10091,f9721,f24207]) ).
fof(f24207,plain,
( spl20_860
<=> ! [X0,X1] :
( element(sK6(sK4(powerset(X0)),X1,X0),X0)
| in(sK6(sK4(powerset(X0)),X1,X0),X1)
| sP0(sK4(powerset(X0)),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_860])]) ).
fof(f9721,plain,
( spl20_423
<=> ! [X22,X21,X23] :
( element(sK6(sK4(powerset(X21)),X22,X23),X23)
| in(sK6(sK4(powerset(X21)),X22,X23),X22)
| sP0(sK4(powerset(X21)),X22,X23)
| element(sK6(sK4(powerset(X21)),X22,X23),X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_423])]) ).
fof(f10091,plain,
( ! [X0,X1] :
( element(sK6(sK4(powerset(X0)),X1,X0),X0)
| in(sK6(sK4(powerset(X0)),X1,X0),X1)
| sP0(sK4(powerset(X0)),X1,X0) )
| ~ spl20_423 ),
inference(factoring,[],[f9722]) ).
fof(f9722,plain,
( ! [X21,X22,X23] :
( element(sK6(sK4(powerset(X21)),X22,X23),X23)
| element(sK6(sK4(powerset(X21)),X22,X23),X21)
| in(sK6(sK4(powerset(X21)),X22,X23),X22)
| sP0(sK4(powerset(X21)),X22,X23) )
| ~ spl20_423 ),
inference(avatar_component_clause,[],[f9721]) ).
fof(f24205,plain,
( spl20_859
| ~ spl20_422 ),
inference(avatar_split_clause,[],[f10041,f9717,f24203]) ).
fof(f24203,plain,
( spl20_859
<=> ! [X0,X1] :
( element(sK6(X0,sK4(powerset(X1)),X1),X1)
| in(sK6(X0,sK4(powerset(X1)),X1),X0)
| sP0(X0,sK4(powerset(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_859])]) ).
fof(f9717,plain,
( spl20_422
<=> ! [X22,X21,X23] :
( element(sK6(X21,sK4(powerset(X22)),X23),X23)
| in(sK6(X21,sK4(powerset(X22)),X23),X21)
| sP0(X21,sK4(powerset(X22)),X23)
| element(sK6(X21,sK4(powerset(X22)),X23),X22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_422])]) ).
fof(f10041,plain,
( ! [X0,X1] :
( element(sK6(X0,sK4(powerset(X1)),X1),X1)
| in(sK6(X0,sK4(powerset(X1)),X1),X0)
| sP0(X0,sK4(powerset(X1)),X1) )
| ~ spl20_422 ),
inference(factoring,[],[f9718]) ).
fof(f9718,plain,
( ! [X21,X22,X23] :
( element(sK6(X21,sK4(powerset(X22)),X23),X23)
| element(sK6(X21,sK4(powerset(X22)),X23),X22)
| in(sK6(X21,sK4(powerset(X22)),X23),X21)
| sP0(X21,sK4(powerset(X22)),X23) )
| ~ spl20_422 ),
inference(avatar_component_clause,[],[f9717]) ).
fof(f24201,plain,
( spl20_858
| ~ spl20_151
| ~ spl20_367 ),
inference(avatar_split_clause,[],[f6079,f5363,f1221,f24199]) ).
fof(f24199,plain,
( spl20_858
<=> ! [X49,X48,X47] :
( element(sK6(X47,sK4(powerset(X48)),sK4(powerset(X49))),X47)
| sP0(X47,sK4(powerset(X48)),sK4(powerset(X49)))
| ~ empty(X49)
| ~ empty(X48) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_858])]) ).
fof(f6079,plain,
( ! [X48,X49,X47] :
( element(sK6(X47,sK4(powerset(X48)),sK4(powerset(X49))),X47)
| sP0(X47,sK4(powerset(X48)),sK4(powerset(X49)))
| ~ empty(X49)
| ~ empty(X48) )
| ~ spl20_151
| ~ spl20_367 ),
inference(resolution,[],[f5364,f1222]) ).
fof(f24197,plain,
( spl20_857
| ~ spl20_151
| ~ spl20_363 ),
inference(avatar_split_clause,[],[f5956,f5347,f1221,f24195]) ).
fof(f24195,plain,
( spl20_857
<=> ! [X48,X47,X49] :
( element(sK6(sK4(powerset(X47)),X48,sK4(powerset(X49))),X48)
| sP0(sK4(powerset(X47)),X48,sK4(powerset(X49)))
| ~ empty(X49)
| ~ empty(X47) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_857])]) ).
fof(f5956,plain,
( ! [X48,X49,X47] :
( element(sK6(sK4(powerset(X47)),X48,sK4(powerset(X49))),X48)
| sP0(sK4(powerset(X47)),X48,sK4(powerset(X49)))
| ~ empty(X49)
| ~ empty(X47) )
| ~ spl20_151
| ~ spl20_363 ),
inference(resolution,[],[f5348,f1222]) ).
fof(f24193,plain,
( spl20_856
| ~ spl20_151
| ~ spl20_358 ),
inference(avatar_split_clause,[],[f5834,f5319,f1221,f24191]) ).
fof(f24191,plain,
( spl20_856
<=> ! [X48,X47,X49] :
( element(sK6(sK4(powerset(X47)),sK4(powerset(X48)),X49),X49)
| sP0(sK4(powerset(X47)),sK4(powerset(X48)),X49)
| ~ empty(X48)
| ~ empty(X47) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_856])]) ).
fof(f5834,plain,
( ! [X48,X49,X47] :
( element(sK6(sK4(powerset(X47)),sK4(powerset(X48)),X49),X49)
| sP0(sK4(powerset(X47)),sK4(powerset(X48)),X49)
| ~ empty(X48)
| ~ empty(X47) )
| ~ spl20_151
| ~ spl20_358 ),
inference(resolution,[],[f5320,f1222]) ).
fof(f24189,plain,
( spl20_855
| ~ spl20_151
| ~ spl20_349 ),
inference(avatar_split_clause,[],[f5505,f5276,f1221,f24187]) ).
fof(f24187,plain,
( spl20_855
<=> ! [X48,X47,X49] :
( in(sK6(sK4(powerset(X47)),sK4(powerset(X48)),X49),X49)
| ~ empty(X48)
| sP0(sK4(powerset(X47)),sK4(powerset(X48)),X49)
| ~ empty(X47) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_855])]) ).
fof(f5505,plain,
( ! [X48,X49,X47] :
( in(sK6(sK4(powerset(X47)),sK4(powerset(X48)),X49),X49)
| ~ empty(X48)
| sP0(sK4(powerset(X47)),sK4(powerset(X48)),X49)
| ~ empty(X47) )
| ~ spl20_151
| ~ spl20_349 ),
inference(resolution,[],[f5277,f1222]) ).
fof(f24185,plain,
( spl20_854
| ~ spl20_151
| ~ spl20_348 ),
inference(avatar_split_clause,[],[f5452,f5272,f1221,f24183]) ).
fof(f24183,plain,
( spl20_854
<=> ! [X48,X47,X49] :
( in(sK6(sK4(powerset(X47)),X48,sK4(powerset(X49))),X48)
| ~ empty(X49)
| sP0(sK4(powerset(X47)),X48,sK4(powerset(X49)))
| ~ empty(X47) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_854])]) ).
fof(f5452,plain,
( ! [X48,X49,X47] :
( in(sK6(sK4(powerset(X47)),X48,sK4(powerset(X49))),X48)
| ~ empty(X49)
| sP0(sK4(powerset(X47)),X48,sK4(powerset(X49)))
| ~ empty(X47) )
| ~ spl20_151
| ~ spl20_348 ),
inference(resolution,[],[f5273,f1222]) ).
fof(f24181,plain,
( spl20_853
| ~ spl20_151
| ~ spl20_348 ),
inference(avatar_split_clause,[],[f5432,f5272,f1221,f24179]) ).
fof(f24179,plain,
( spl20_853
<=> ! [X49,X48,X47] :
( in(sK6(X47,sK4(powerset(X48)),sK4(powerset(X49))),X47)
| ~ empty(X49)
| sP0(X47,sK4(powerset(X48)),sK4(powerset(X49)))
| ~ empty(X48) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_853])]) ).
fof(f5432,plain,
( ! [X48,X49,X47] :
( in(sK6(X47,sK4(powerset(X48)),sK4(powerset(X49))),X47)
| ~ empty(X49)
| sP0(X47,sK4(powerset(X48)),sK4(powerset(X49)))
| ~ empty(X48) )
| ~ spl20_151
| ~ spl20_348 ),
inference(resolution,[],[f5273,f1222]) ).
fof(f24177,plain,
( spl20_852
| ~ spl20_75
| ~ spl20_344 ),
inference(avatar_split_clause,[],[f5230,f4952,f653,f24175]) ).
fof(f24175,plain,
( spl20_852
<=> ! [X25,X24,X26] :
( element(sK6(X24,X25,X26),X25)
| element(sK6(X24,X25,X26),X24)
| sP0(X24,X25,X26)
| ~ in(X26,sK6(X24,X25,X26)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_852])]) ).
fof(f5230,plain,
( ! [X26,X24,X25] :
( element(sK6(X24,X25,X26),X25)
| element(sK6(X24,X25,X26),X24)
| sP0(X24,X25,X26)
| ~ in(X26,sK6(X24,X25,X26)) )
| ~ spl20_75
| ~ spl20_344 ),
inference(resolution,[],[f4953,f654]) ).
fof(f24173,plain,
( spl20_851
| ~ spl20_75
| ~ spl20_341 ),
inference(avatar_split_clause,[],[f5177,f4940,f653,f24171]) ).
fof(f24171,plain,
( spl20_851
<=> ! [X25,X24,X23] :
( element(sK6(X23,X24,X25),X25)
| element(sK6(X23,X24,X25),X23)
| sP0(X23,X24,X25)
| ~ in(X24,sK6(X23,X24,X25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_851])]) ).
fof(f5177,plain,
( ! [X24,X25,X23] :
( element(sK6(X23,X24,X25),X25)
| element(sK6(X23,X24,X25),X23)
| sP0(X23,X24,X25)
| ~ in(X24,sK6(X23,X24,X25)) )
| ~ spl20_75
| ~ spl20_341 ),
inference(resolution,[],[f4941,f654]) ).
fof(f24169,plain,
( spl20_850
| ~ spl20_101
| ~ spl20_431 ),
inference(avatar_split_clause,[],[f12329,f10101,f862,f24167]) ).
fof(f862,plain,
( spl20_101
<=> ! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_101])]) ).
fof(f12329,plain,
( ! [X2] :
( ~ in(X2,sK2)
| in(X2,sK1) )
| ~ spl20_101
| ~ spl20_431 ),
inference(resolution,[],[f10103,f863]) ).
fof(f863,plain,
( ! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| ~ in(X4,X1)
| in(X4,X2) )
| ~ spl20_101 ),
inference(avatar_component_clause,[],[f862]) ).
fof(f24165,plain,
( spl20_849
| ~ spl20_75
| ~ spl20_339 ),
inference(avatar_split_clause,[],[f5136,f4932,f653,f24163]) ).
fof(f24163,plain,
( spl20_849
<=> ! [X25,X24,X23] :
( element(sK6(X23,X24,X25),X25)
| element(sK6(X23,X24,X25),X24)
| sP0(X23,X24,X25)
| ~ in(X23,sK6(X23,X24,X25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_849])]) ).
fof(f5136,plain,
( ! [X24,X25,X23] :
( element(sK6(X23,X24,X25),X25)
| element(sK6(X23,X24,X25),X24)
| sP0(X23,X24,X25)
| ~ in(X23,sK6(X23,X24,X25)) )
| ~ spl20_75
| ~ spl20_339 ),
inference(resolution,[],[f4933,f654]) ).
fof(f24161,plain,
( spl20_848
| ~ spl20_76
| ~ spl20_339 ),
inference(avatar_split_clause,[],[f5135,f4932,f657,f24159]) ).
fof(f24159,plain,
( spl20_848
<=> ! [X22,X20,X21] :
( element(sK6(X20,X21,X22),X22)
| element(sK6(X20,X21,X22),X21)
| sP0(X20,X21,X22)
| element(sK6(X20,X21,X22),X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_848])]) ).
fof(f657,plain,
( spl20_76
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_76])]) ).
fof(f5135,plain,
( ! [X21,X22,X20] :
( element(sK6(X20,X21,X22),X22)
| element(sK6(X20,X21,X22),X21)
| sP0(X20,X21,X22)
| element(sK6(X20,X21,X22),X20) )
| ~ spl20_76
| ~ spl20_339 ),
inference(resolution,[],[f4933,f658]) ).
fof(f658,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) )
| ~ spl20_76 ),
inference(avatar_component_clause,[],[f657]) ).
fof(f24157,plain,
( spl20_847
| ~ spl20_75
| ~ spl20_338 ),
inference(avatar_split_clause,[],[f5104,f4928,f653,f24155]) ).
fof(f24155,plain,
( spl20_847
<=> ! [X16,X17] :
( sP0(singleton(X16),singleton(X16),X17)
| sK6(singleton(X16),singleton(X16),X17) = X16
| ~ in(X17,sK6(singleton(X16),singleton(X16),X17)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_847])]) ).
fof(f5104,plain,
( ! [X16,X17] :
( sP0(singleton(X16),singleton(X16),X17)
| sK6(singleton(X16),singleton(X16),X17) = X16
| ~ in(X17,sK6(singleton(X16),singleton(X16),X17)) )
| ~ spl20_75
| ~ spl20_338 ),
inference(resolution,[],[f4929,f654]) ).
fof(f24153,plain,
( spl20_846
| ~ spl20_75
| ~ spl20_336 ),
inference(avatar_split_clause,[],[f5080,f4919,f653,f24151]) ).
fof(f24151,plain,
( spl20_846
<=> ! [X16,X17] :
( element(sK6(X16,X16,sK4(powerset(X17))),X17)
| sP0(X16,X16,sK4(powerset(X17)))
| ~ in(X16,sK6(X16,X16,sK4(powerset(X17)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_846])]) ).
fof(f5080,plain,
( ! [X16,X17] :
( element(sK6(X16,X16,sK4(powerset(X17))),X17)
| sP0(X16,X16,sK4(powerset(X17)))
| ~ in(X16,sK6(X16,X16,sK4(powerset(X17)))) )
| ~ spl20_75
| ~ spl20_336 ),
inference(resolution,[],[f4920,f654]) ).
fof(f24149,plain,
( spl20_845
| ~ spl20_88
| ~ spl20_321 ),
inference(avatar_split_clause,[],[f4648,f4411,f772,f24147]) ).
fof(f24147,plain,
( spl20_845
<=> ! [X18,X17,X19] :
( subset(sK6(X17,X18,X19),X19)
| ~ empty(X17)
| sP0(X17,X18,X19)
| ~ epsilon_transitive(X19)
| subset(sK6(X17,X18,X19),X18)
| ~ epsilon_transitive(X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_845])]) ).
fof(f4648,plain,
( ! [X18,X19,X17] :
( subset(sK6(X17,X18,X19),X19)
| ~ empty(X17)
| sP0(X17,X18,X19)
| ~ epsilon_transitive(X19)
| subset(sK6(X17,X18,X19),X18)
| ~ epsilon_transitive(X18) )
| ~ spl20_88
| ~ spl20_321 ),
inference(resolution,[],[f4412,f773]) ).
fof(f24145,plain,
( spl20_844
| ~ spl20_88
| ~ spl20_319 ),
inference(avatar_split_clause,[],[f4592,f4403,f772,f24143]) ).
fof(f24143,plain,
( spl20_844
<=> ! [X18,X17,X19] :
( subset(sK6(X17,X18,X19),X19)
| ~ empty(X18)
| sP0(X17,X18,X19)
| ~ epsilon_transitive(X19)
| subset(sK6(X17,X18,X19),X17)
| ~ epsilon_transitive(X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_844])]) ).
fof(f4592,plain,
( ! [X18,X19,X17] :
( subset(sK6(X17,X18,X19),X19)
| ~ empty(X18)
| sP0(X17,X18,X19)
| ~ epsilon_transitive(X19)
| subset(sK6(X17,X18,X19),X17)
| ~ epsilon_transitive(X17) )
| ~ spl20_88
| ~ spl20_319 ),
inference(resolution,[],[f4404,f773]) ).
fof(f24141,plain,
( spl20_843
| ~ spl20_88
| ~ spl20_317 ),
inference(avatar_split_clause,[],[f4536,f4395,f772,f24139]) ).
fof(f24139,plain,
( spl20_843
<=> ! [X18,X17,X19] :
( subset(sK6(X17,X18,X19),X18)
| ~ empty(X19)
| sP0(X17,X18,X19)
| ~ epsilon_transitive(X18)
| subset(sK6(X17,X18,X19),X17)
| ~ epsilon_transitive(X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_843])]) ).
fof(f4536,plain,
( ! [X18,X19,X17] :
( subset(sK6(X17,X18,X19),X18)
| ~ empty(X19)
| sP0(X17,X18,X19)
| ~ epsilon_transitive(X18)
| subset(sK6(X17,X18,X19),X17)
| ~ epsilon_transitive(X17) )
| ~ spl20_88
| ~ spl20_317 ),
inference(resolution,[],[f4396,f773]) ).
fof(f24137,plain,
( spl20_842
| ~ spl20_89
| ~ spl20_313 ),
inference(avatar_split_clause,[],[f4421,f4372,f776,f24135]) ).
fof(f24135,plain,
( spl20_842
<=> ! [X9,X8] :
( sK5(X8,sK4(powerset(X9))) = X8
| singleton(X8) = sK4(powerset(X9))
| empty(X9)
| in(sK5(X8,sK4(powerset(X9))),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_842])]) ).
fof(f4421,plain,
( ! [X8,X9] :
( sK5(X8,sK4(powerset(X9))) = X8
| singleton(X8) = sK4(powerset(X9))
| empty(X9)
| in(sK5(X8,sK4(powerset(X9))),X9) )
| ~ spl20_89
| ~ spl20_313 ),
inference(resolution,[],[f4373,f777]) ).
fof(f24133,plain,
( spl20_841
| ~ spl20_151
| ~ spl20_311 ),
inference(avatar_split_clause,[],[f4364,f4126,f1221,f24131]) ).
fof(f24131,plain,
( spl20_841
<=> ! [X32,X33] :
( sP0(sK4(powerset(X32)),sK4(powerset(X32)),singleton(X33))
| sK6(sK4(powerset(X32)),sK4(powerset(X32)),singleton(X33)) = X33
| ~ empty(X32) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_841])]) ).
fof(f4364,plain,
( ! [X32,X33] :
( sP0(sK4(powerset(X32)),sK4(powerset(X32)),singleton(X33))
| sK6(sK4(powerset(X32)),sK4(powerset(X32)),singleton(X33)) = X33
| ~ empty(X32) )
| ~ spl20_151
| ~ spl20_311 ),
inference(resolution,[],[f4127,f1222]) ).
fof(f24129,plain,
( spl20_840
| ~ spl20_242
| ~ spl20_307 ),
inference(avatar_split_clause,[],[f4221,f4110,f2533,f24127]) ).
fof(f24127,plain,
( spl20_840
<=> ! [X185,X183,X184] :
( sK5(X183,powerset(X184)) = X183
| ~ empty(X184)
| powerset(X184) = singleton(X183)
| sP0(X185,X185,sK5(X183,powerset(X184)))
| ~ empty(X185) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_840])]) ).
fof(f4221,plain,
( ! [X184,X185,X183] :
( sK5(X183,powerset(X184)) = X183
| ~ empty(X184)
| powerset(X184) = singleton(X183)
| sP0(X185,X185,sK5(X183,powerset(X184)))
| ~ empty(X185) )
| ~ spl20_242
| ~ spl20_307 ),
inference(resolution,[],[f4111,f2534]) ).
fof(f24118,plain,
( spl20_839
| ~ spl20_84
| ~ spl20_306 ),
inference(avatar_split_clause,[],[f4168,f4106,f732,f24116]) ).
fof(f24116,plain,
( spl20_839
<=> ! [X6,X7] :
( ~ ordinal(sK4(powerset(X6)))
| ~ ordinal(powerset(X7))
| sK4(powerset(X6)) = powerset(X7)
| element(powerset(X7),X6)
| subset(sK4(powerset(X6)),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_839])]) ).
fof(f4168,plain,
( ! [X6,X7] :
( ~ ordinal(sK4(powerset(X6)))
| ~ ordinal(powerset(X7))
| sK4(powerset(X6)) = powerset(X7)
| element(powerset(X7),X6)
| subset(sK4(powerset(X6)),X7) )
| ~ spl20_84
| ~ spl20_306 ),
inference(resolution,[],[f4107,f733]) ).
fof(f24114,plain,
( spl20_838
| ~ spl20_157
| ~ spl20_303 ),
inference(avatar_split_clause,[],[f4095,f3637,f1267,f24112]) ).
fof(f24112,plain,
( spl20_838
<=> ! [X45,X46,X47] :
( sP0(X45,sK4(powerset(X46)),sK4(powerset(X47)))
| ~ empty(X45)
| ~ empty(X46)
| element(sK6(X45,sK4(powerset(X46)),sK4(powerset(X47))),X47) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_838])]) ).
fof(f4095,plain,
( ! [X46,X47,X45] :
( sP0(X45,sK4(powerset(X46)),sK4(powerset(X47)))
| ~ empty(X45)
| ~ empty(X46)
| element(sK6(X45,sK4(powerset(X46)),sK4(powerset(X47))),X47) )
| ~ spl20_157
| ~ spl20_303 ),
inference(resolution,[],[f3638,f1268]) ).
fof(f24110,plain,
( spl20_837
| ~ spl20_157
| ~ spl20_300 ),
inference(avatar_split_clause,[],[f4037,f3625,f1267,f24108]) ).
fof(f24108,plain,
( spl20_837
<=> ! [X45,X44,X46] :
( sP0(X44,sK4(powerset(X45)),sK4(powerset(X46)))
| ~ empty(X44)
| ~ empty(X46)
| element(sK6(X44,sK4(powerset(X45)),sK4(powerset(X46))),X45) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_837])]) ).
fof(f4037,plain,
( ! [X46,X44,X45] :
( sP0(X44,sK4(powerset(X45)),sK4(powerset(X46)))
| ~ empty(X44)
| ~ empty(X46)
| element(sK6(X44,sK4(powerset(X45)),sK4(powerset(X46))),X45) )
| ~ spl20_157
| ~ spl20_300 ),
inference(resolution,[],[f3626,f1268]) ).
fof(f24106,plain,
( spl20_836
| ~ spl20_157
| ~ spl20_296 ),
inference(avatar_split_clause,[],[f3984,f3586,f1267,f24104]) ).
fof(f24104,plain,
( spl20_836
<=> ! [X45,X46,X47] :
( sP0(sK4(powerset(X45)),X46,sK4(powerset(X47)))
| ~ empty(X46)
| ~ empty(X45)
| element(sK6(sK4(powerset(X45)),X46,sK4(powerset(X47))),X47) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_836])]) ).
fof(f3984,plain,
( ! [X46,X47,X45] :
( sP0(sK4(powerset(X45)),X46,sK4(powerset(X47)))
| ~ empty(X46)
| ~ empty(X45)
| element(sK6(sK4(powerset(X45)),X46,sK4(powerset(X47))),X47) )
| ~ spl20_157
| ~ spl20_296 ),
inference(resolution,[],[f3587,f1268]) ).
fof(f24102,plain,
( spl20_835
| ~ spl20_157
| ~ spl20_293 ),
inference(avatar_split_clause,[],[f3931,f3574,f1267,f24100]) ).
fof(f24100,plain,
( spl20_835
<=> ! [X45,X44,X46] :
( sP0(sK4(powerset(X44)),X45,sK4(powerset(X46)))
| ~ empty(X45)
| ~ empty(X46)
| element(sK6(sK4(powerset(X44)),X45,sK4(powerset(X46))),X44) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_835])]) ).
fof(f3931,plain,
( ! [X46,X44,X45] :
( sP0(sK4(powerset(X44)),X45,sK4(powerset(X46)))
| ~ empty(X45)
| ~ empty(X46)
| element(sK6(sK4(powerset(X44)),X45,sK4(powerset(X46))),X44) )
| ~ spl20_157
| ~ spl20_293 ),
inference(resolution,[],[f3575,f1268]) ).
fof(f24098,plain,
( spl20_834
| ~ spl20_157
| ~ spl20_290 ),
inference(avatar_split_clause,[],[f3878,f3562,f1267,f24096]) ).
fof(f24096,plain,
( spl20_834
<=> ! [X45,X44,X46] :
( sP0(sK4(powerset(X44)),sK4(powerset(X45)),X46)
| ~ empty(X46)
| ~ empty(X44)
| element(sK6(sK4(powerset(X44)),sK4(powerset(X45)),X46),X45) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_834])]) ).
fof(f3878,plain,
( ! [X46,X44,X45] :
( sP0(sK4(powerset(X44)),sK4(powerset(X45)),X46)
| ~ empty(X46)
| ~ empty(X44)
| element(sK6(sK4(powerset(X44)),sK4(powerset(X45)),X46),X45) )
| ~ spl20_157
| ~ spl20_290 ),
inference(resolution,[],[f3563,f1268]) ).
fof(f24094,plain,
( spl20_833
| ~ spl20_157
| ~ spl20_287 ),
inference(avatar_split_clause,[],[f3825,f3550,f1267,f24092]) ).
fof(f24092,plain,
( spl20_833
<=> ! [X45,X44,X46] :
( sP0(sK4(powerset(X44)),sK4(powerset(X45)),X46)
| ~ empty(X46)
| ~ empty(X45)
| element(sK6(sK4(powerset(X44)),sK4(powerset(X45)),X46),X44) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_833])]) ).
fof(f3825,plain,
( ! [X46,X44,X45] :
( sP0(sK4(powerset(X44)),sK4(powerset(X45)),X46)
| ~ empty(X46)
| ~ empty(X45)
| element(sK6(sK4(powerset(X44)),sK4(powerset(X45)),X46),X44) )
| ~ spl20_157
| ~ spl20_287 ),
inference(resolution,[],[f3551,f1268]) ).
fof(f24090,plain,
( spl20_832
| ~ spl20_151
| ~ spl20_283 ),
inference(avatar_split_clause,[],[f3748,f3534,f1221,f24088]) ).
fof(f24088,plain,
( spl20_832
<=> ! [X32,X33] :
( subset(sK6(sK4(powerset(X32)),sK4(powerset(X32)),X33),X33)
| sP0(sK4(powerset(X32)),sK4(powerset(X32)),X33)
| ~ epsilon_transitive(X33)
| ~ empty(X32) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_832])]) ).
fof(f3748,plain,
( ! [X32,X33] :
( subset(sK6(sK4(powerset(X32)),sK4(powerset(X32)),X33),X33)
| sP0(sK4(powerset(X32)),sK4(powerset(X32)),X33)
| ~ epsilon_transitive(X33)
| ~ empty(X32) )
| ~ spl20_151
| ~ spl20_283 ),
inference(resolution,[],[f3535,f1222]) ).
fof(f24086,plain,
( spl20_831
| ~ spl20_157
| ~ spl20_278 ),
inference(avatar_split_clause,[],[f3652,f3514,f1267,f24084]) ).
fof(f24084,plain,
( spl20_831
<=> ! [X25,X26] :
( ~ empty(X25)
| sK4(powerset(X25)) = sK4(powerset(X26))
| ~ ordinal(sK4(powerset(X25)))
| ~ ordinal(sK4(powerset(X26)))
| element(sK4(powerset(X25)),X26) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_831])]) ).
fof(f3652,plain,
( ! [X26,X25] :
( ~ empty(X25)
| sK4(powerset(X25)) = sK4(powerset(X26))
| ~ ordinal(sK4(powerset(X25)))
| ~ ordinal(sK4(powerset(X26)))
| element(sK4(powerset(X25)),X26) )
| ~ spl20_157
| ~ spl20_278 ),
inference(resolution,[],[f3515,f1268]) ).
fof(f24082,plain,
( spl20_830
| ~ spl20_157
| ~ spl20_272 ),
inference(avatar_split_clause,[],[f3427,f3020,f1267,f24080]) ).
fof(f24080,plain,
( spl20_830
<=> ! [X30,X31] :
( element(sK6(X30,X30,sK4(powerset(X31))),X30)
| sP0(X30,X30,sK4(powerset(X31)))
| element(sK6(X30,X30,sK4(powerset(X31))),X31) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_830])]) ).
fof(f3427,plain,
( ! [X31,X30] :
( element(sK6(X30,X30,sK4(powerset(X31))),X30)
| sP0(X30,X30,sK4(powerset(X31)))
| element(sK6(X30,X30,sK4(powerset(X31))),X31) )
| ~ spl20_157
| ~ spl20_272 ),
inference(resolution,[],[f3021,f1268]) ).
fof(f24078,plain,
( ~ spl20_829
| ~ spl20_75
| ~ spl20_813 ),
inference(avatar_split_clause,[],[f24027,f23873,f653,f24075]) ).
fof(f24075,plain,
( spl20_829
<=> in(sK2,sK4(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_829])]) ).
fof(f24027,plain,
( ~ in(sK2,sK4(sK1))
| ~ spl20_75
| ~ spl20_813 ),
inference(resolution,[],[f23875,f654]) ).
fof(f24073,plain,
( spl20_828
| ~ spl20_84
| ~ spl20_272 ),
inference(avatar_split_clause,[],[f3410,f3020,f732,f24071]) ).
fof(f24071,plain,
( spl20_828
<=> ! [X6,X7] :
( in(sK6(powerset(X6),powerset(X6),X7),X7)
| sP0(powerset(X6),powerset(X6),X7)
| subset(sK6(powerset(X6),powerset(X6),X7),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_828])]) ).
fof(f3410,plain,
( ! [X6,X7] :
( in(sK6(powerset(X6),powerset(X6),X7),X7)
| sP0(powerset(X6),powerset(X6),X7)
| subset(sK6(powerset(X6),powerset(X6),X7),X6) )
| ~ spl20_84
| ~ spl20_272 ),
inference(resolution,[],[f3021,f733]) ).
fof(f24069,plain,
( spl20_827
| ~ spl20_153
| ~ spl20_269 ),
inference(avatar_split_clause,[],[f3371,f3008,f1230,f24067]) ).
fof(f24067,plain,
( spl20_827
<=> ! [X24,X23] :
( element(sK6(singleton(X23),singleton(X23),X24),X24)
| sP0(singleton(X23),singleton(X23),X24)
| sK6(singleton(X23),singleton(X23),X24) = X23 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_827])]) ).
fof(f3371,plain,
( ! [X24,X23] :
( element(sK6(singleton(X23),singleton(X23),X24),X24)
| sP0(singleton(X23),singleton(X23),X24)
| sK6(singleton(X23),singleton(X23),X24) = X23 )
| ~ spl20_153
| ~ spl20_269 ),
inference(resolution,[],[f3009,f1231]) ).
fof(f24065,plain,
( spl20_826
| ~ spl20_100
| ~ spl20_269 ),
inference(avatar_split_clause,[],[f3356,f3008,f858,f24063]) ).
fof(f24063,plain,
( spl20_826
<=> ! [X2,X0,X1] :
( in(sK6(X0,X0,powerset(X1)),X0)
| sP0(X0,X0,powerset(X1))
| element(X2,X1)
| ~ in(X2,sK6(X0,X0,powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_826])]) ).
fof(f3356,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X0,powerset(X1)),X0)
| sP0(X0,X0,powerset(X1))
| element(X2,X1)
| ~ in(X2,sK6(X0,X0,powerset(X1))) )
| ~ spl20_100
| ~ spl20_269 ),
inference(resolution,[],[f3009,f859]) ).
fof(f24061,plain,
( spl20_825
| ~ spl20_100
| ~ spl20_263 ),
inference(avatar_split_clause,[],[f3206,f2976,f858,f24059]) ).
fof(f24059,plain,
( spl20_825
<=> ! [X2,X0,X1] :
( in(sK6(X0,powerset(X1),X0),X0)
| sP0(X0,powerset(X1),X0)
| element(X2,X1)
| ~ in(X2,sK6(X0,powerset(X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_825])]) ).
fof(f2976,plain,
( spl20_263
<=> ! [X4,X5] :
( in(sK6(X4,X5,X4),X4)
| sP0(X4,X5,X4)
| element(sK6(X4,X5,X4),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_263])]) ).
fof(f3206,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,powerset(X1),X0),X0)
| sP0(X0,powerset(X1),X0)
| element(X2,X1)
| ~ in(X2,sK6(X0,powerset(X1),X0)) )
| ~ spl20_100
| ~ spl20_263 ),
inference(resolution,[],[f2977,f859]) ).
fof(f2977,plain,
( ! [X4,X5] :
( element(sK6(X4,X5,X4),X5)
| in(sK6(X4,X5,X4),X4)
| sP0(X4,X5,X4) )
| ~ spl20_263 ),
inference(avatar_component_clause,[],[f2976]) ).
fof(f24057,plain,
( spl20_824
| ~ spl20_100
| ~ spl20_259 ),
inference(avatar_split_clause,[],[f3088,f2960,f858,f24055]) ).
fof(f24055,plain,
( spl20_824
<=> ! [X2,X0,X1] :
( in(sK6(powerset(X0),X1,X1),X1)
| sP0(powerset(X0),X1,X1)
| element(X2,X0)
| ~ in(X2,sK6(powerset(X0),X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_824])]) ).
fof(f2960,plain,
( spl20_259
<=> ! [X4,X5] :
( in(sK6(X4,X5,X5),X5)
| sP0(X4,X5,X5)
| element(sK6(X4,X5,X5),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_259])]) ).
fof(f3088,plain,
( ! [X2,X0,X1] :
( in(sK6(powerset(X0),X1,X1),X1)
| sP0(powerset(X0),X1,X1)
| element(X2,X0)
| ~ in(X2,sK6(powerset(X0),X1,X1)) )
| ~ spl20_100
| ~ spl20_259 ),
inference(resolution,[],[f2961,f859]) ).
fof(f2961,plain,
( ! [X4,X5] :
( element(sK6(X4,X5,X5),X4)
| in(sK6(X4,X5,X5),X5)
| sP0(X4,X5,X5) )
| ~ spl20_259 ),
inference(avatar_component_clause,[],[f2960]) ).
fof(f24053,plain,
( spl20_823
| ~ spl20_100
| ~ spl20_256 ),
inference(avatar_split_clause,[],[f3048,f2944,f858,f24051]) ).
fof(f24051,plain,
( spl20_823
<=> ! [X2,X0,X1] :
( ~ ordinal(singleton(X0))
| ~ ordinal(powerset(X1))
| singleton(X0) = powerset(X1)
| powerset(X1) = X0
| element(X2,X1)
| ~ in(X2,singleton(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_823])]) ).
fof(f2944,plain,
( spl20_256
<=> ! [X9,X8] :
( singleton(X8) = X9
| ~ ordinal(singleton(X8))
| ~ ordinal(X9)
| element(singleton(X8),X9)
| X8 = X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_256])]) ).
fof(f3048,plain,
( ! [X2,X0,X1] :
( ~ ordinal(singleton(X0))
| ~ ordinal(powerset(X1))
| singleton(X0) = powerset(X1)
| powerset(X1) = X0
| element(X2,X1)
| ~ in(X2,singleton(X0)) )
| ~ spl20_100
| ~ spl20_256 ),
inference(resolution,[],[f2945,f859]) ).
fof(f2945,plain,
( ! [X8,X9] :
( element(singleton(X8),X9)
| ~ ordinal(singleton(X8))
| ~ ordinal(X9)
| singleton(X8) = X9
| X8 = X9 )
| ~ spl20_256 ),
inference(avatar_component_clause,[],[f2944]) ).
fof(f24049,plain,
( spl20_822
| ~ spl20_157
| ~ spl20_254 ),
inference(avatar_split_clause,[],[f3039,f2936,f1267,f24047]) ).
fof(f24047,plain,
( spl20_822
<=> ! [X25,X26] :
( sK4(powerset(X25)) = X26
| sK4(powerset(X25)) = singleton(X26)
| ~ ordinal(singleton(X26))
| ~ ordinal(sK4(powerset(X25)))
| element(singleton(X26),X25) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_822])]) ).
fof(f3039,plain,
( ! [X26,X25] :
( sK4(powerset(X25)) = X26
| sK4(powerset(X25)) = singleton(X26)
| ~ ordinal(singleton(X26))
| ~ ordinal(sK4(powerset(X25)))
| element(singleton(X26),X25) )
| ~ spl20_157
| ~ spl20_254 ),
inference(resolution,[],[f2937,f1268]) ).
fof(f24045,plain,
( spl20_821
| ~ spl20_104
| ~ spl20_231 ),
inference(avatar_split_clause,[],[f2452,f2402,f890,f24043]) ).
fof(f24043,plain,
( spl20_821
<=> ! [X16,X17,X15] :
( in(X15,X16)
| in(X15,X17)
| in(set_union2(X16,X17),X15)
| set_union2(X16,X17) = X15
| ~ ordinal(set_union2(X16,X17))
| ~ ordinal(X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_821])]) ).
fof(f890,plain,
( spl20_104
<=> ! [X0,X1] :
( in(X1,X0)
| X0 = X1
| in(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_104])]) ).
fof(f2452,plain,
( ! [X16,X17,X15] :
( in(X15,X16)
| in(X15,X17)
| in(set_union2(X16,X17),X15)
| set_union2(X16,X17) = X15
| ~ ordinal(set_union2(X16,X17))
| ~ ordinal(X15) )
| ~ spl20_104
| ~ spl20_231 ),
inference(resolution,[],[f2403,f891]) ).
fof(f891,plain,
( ! [X0,X1] :
( in(X1,X0)
| in(X0,X1)
| X0 = X1
| ~ ordinal(X1)
| ~ ordinal(X0) )
| ~ spl20_104 ),
inference(avatar_component_clause,[],[f890]) ).
fof(f24041,plain,
( spl20_820
| ~ spl20_167
| ~ spl20_231 ),
inference(avatar_split_clause,[],[f2450,f2402,f1371,f24039]) ).
fof(f24039,plain,
( spl20_820
<=> ! [X9,X11,X10] :
( in(X9,X10)
| in(X9,X11)
| set_union2(X10,X11) = X9
| ~ ordinal(set_union2(X10,X11))
| ~ ordinal(X9)
| element(set_union2(X10,X11),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_820])]) ).
fof(f1371,plain,
( spl20_167
<=> ! [X2,X3] :
( in(X3,X2)
| X2 = X3
| ~ ordinal(X2)
| ~ ordinal(X3)
| element(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_167])]) ).
fof(f2450,plain,
( ! [X10,X11,X9] :
( in(X9,X10)
| in(X9,X11)
| set_union2(X10,X11) = X9
| ~ ordinal(set_union2(X10,X11))
| ~ ordinal(X9)
| element(set_union2(X10,X11),X9) )
| ~ spl20_167
| ~ spl20_231 ),
inference(resolution,[],[f2403,f1372]) ).
fof(f1372,plain,
( ! [X2,X3] :
( in(X3,X2)
| X2 = X3
| ~ ordinal(X2)
| ~ ordinal(X3)
| element(X2,X3) )
| ~ spl20_167 ),
inference(avatar_component_clause,[],[f1371]) ).
fof(f24037,plain,
( spl20_819
| ~ spl20_104
| ~ spl20_230 ),
inference(avatar_split_clause,[],[f2415,f2398,f890,f24035]) ).
fof(f24035,plain,
( spl20_819
<=> ! [X6,X7] :
( element(X6,X7)
| epsilon_transitive(powerset(X7))
| in(sK3(powerset(X7)),X6)
| sK3(powerset(X7)) = X6
| ~ ordinal(sK3(powerset(X7)))
| ~ ordinal(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_819])]) ).
fof(f2415,plain,
( ! [X6,X7] :
( element(X6,X7)
| epsilon_transitive(powerset(X7))
| in(sK3(powerset(X7)),X6)
| sK3(powerset(X7)) = X6
| ~ ordinal(sK3(powerset(X7)))
| ~ ordinal(X6) )
| ~ spl20_104
| ~ spl20_230 ),
inference(resolution,[],[f2399,f891]) ).
fof(f24024,plain,
( spl20_818
| ~ spl20_167
| ~ spl20_230 ),
inference(avatar_split_clause,[],[f2413,f2398,f1371,f24022]) ).
fof(f24022,plain,
( spl20_818
<=> ! [X2,X3] :
( element(X2,X3)
| epsilon_transitive(powerset(X3))
| sK3(powerset(X3)) = X2
| ~ ordinal(sK3(powerset(X3)))
| ~ ordinal(X2)
| element(sK3(powerset(X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_818])]) ).
fof(f2413,plain,
( ! [X2,X3] :
( element(X2,X3)
| epsilon_transitive(powerset(X3))
| sK3(powerset(X3)) = X2
| ~ ordinal(sK3(powerset(X3)))
| ~ ordinal(X2)
| element(sK3(powerset(X3)),X2) )
| ~ spl20_167
| ~ spl20_230 ),
inference(resolution,[],[f2399,f1372]) ).
fof(f24020,plain,
( spl20_817
| ~ spl20_108
| ~ spl20_214 ),
inference(avatar_split_clause,[],[f2260,f2208,f923,f24018]) ).
fof(f24018,plain,
( spl20_817
<=> ! [X18,X19,X20,X21] :
( ~ in(sK6(X18,X19,set_union2(X20,X21)),X20)
| ~ in(sK6(X18,X19,set_union2(X20,X21)),X19)
| sP0(X18,X19,set_union2(X20,X21)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_817])]) ).
fof(f923,plain,
( spl20_108
<=> ! [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_108])]) ).
fof(f2208,plain,
( spl20_214
<=> ! [X6,X7,X8] :
( ~ in(X6,X7)
| in(X6,set_union2(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_214])]) ).
fof(f2260,plain,
( ! [X21,X18,X19,X20] :
( ~ in(sK6(X18,X19,set_union2(X20,X21)),X20)
| ~ in(sK6(X18,X19,set_union2(X20,X21)),X19)
| sP0(X18,X19,set_union2(X20,X21)) )
| ~ spl20_108
| ~ spl20_214 ),
inference(resolution,[],[f2209,f924]) ).
fof(f924,plain,
( ! [X2,X0,X1] :
( ~ in(sK6(X0,X1,X2),X2)
| ~ in(sK6(X0,X1,X2),X1)
| sP0(X0,X1,X2) )
| ~ spl20_108 ),
inference(avatar_component_clause,[],[f923]) ).
fof(f2209,plain,
( ! [X8,X6,X7] :
( in(X6,set_union2(X7,X8))
| ~ in(X6,X7) )
| ~ spl20_214 ),
inference(avatar_component_clause,[],[f2208]) ).
fof(f24016,plain,
( spl20_816
| ~ spl20_109
| ~ spl20_214 ),
inference(avatar_split_clause,[],[f2259,f2208,f927,f24014]) ).
fof(f24014,plain,
( spl20_816
<=> ! [X17,X14,X16,X15] :
( ~ in(sK6(X14,X15,set_union2(X16,X17)),X16)
| ~ in(sK6(X14,X15,set_union2(X16,X17)),X14)
| sP0(X14,X15,set_union2(X16,X17)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_816])]) ).
fof(f927,plain,
( spl20_109
<=> ! [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_109])]) ).
fof(f2259,plain,
( ! [X16,X14,X17,X15] :
( ~ in(sK6(X14,X15,set_union2(X16,X17)),X16)
| ~ in(sK6(X14,X15,set_union2(X16,X17)),X14)
| sP0(X14,X15,set_union2(X16,X17)) )
| ~ spl20_109
| ~ spl20_214 ),
inference(resolution,[],[f2209,f928]) ).
fof(f928,plain,
( ! [X2,X0,X1] :
( ~ in(sK6(X0,X1,X2),X2)
| ~ in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2) )
| ~ spl20_109 ),
inference(avatar_component_clause,[],[f927]) ).
fof(f24012,plain,
( spl20_815
| ~ spl20_108
| ~ spl20_213 ),
inference(avatar_split_clause,[],[f2243,f2204,f923,f24010]) ).
fof(f24010,plain,
( spl20_815
<=> ! [X18,X19,X20,X21] :
( ~ in(sK6(X18,X19,set_union2(X20,X21)),X21)
| ~ in(sK6(X18,X19,set_union2(X20,X21)),X19)
| sP0(X18,X19,set_union2(X20,X21)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_815])]) ).
fof(f2204,plain,
( spl20_213
<=> ! [X4,X5,X3] :
( ~ in(X3,X4)
| in(X3,set_union2(X5,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_213])]) ).
fof(f2243,plain,
( ! [X21,X18,X19,X20] :
( ~ in(sK6(X18,X19,set_union2(X20,X21)),X21)
| ~ in(sK6(X18,X19,set_union2(X20,X21)),X19)
| sP0(X18,X19,set_union2(X20,X21)) )
| ~ spl20_108
| ~ spl20_213 ),
inference(resolution,[],[f2205,f924]) ).
fof(f2205,plain,
( ! [X3,X4,X5] :
( in(X3,set_union2(X5,X4))
| ~ in(X3,X4) )
| ~ spl20_213 ),
inference(avatar_component_clause,[],[f2204]) ).
fof(f24008,plain,
( spl20_814
| ~ spl20_109
| ~ spl20_213 ),
inference(avatar_split_clause,[],[f2242,f2204,f927,f24006]) ).
fof(f24006,plain,
( spl20_814
<=> ! [X17,X14,X16,X15] :
( ~ in(sK6(X14,X15,set_union2(X16,X17)),X17)
| ~ in(sK6(X14,X15,set_union2(X16,X17)),X14)
| sP0(X14,X15,set_union2(X16,X17)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_814])]) ).
fof(f2242,plain,
( ! [X16,X14,X17,X15] :
( ~ in(sK6(X14,X15,set_union2(X16,X17)),X17)
| ~ in(sK6(X14,X15,set_union2(X16,X17)),X14)
| sP0(X14,X15,set_union2(X16,X17)) )
| ~ spl20_109
| ~ spl20_213 ),
inference(resolution,[],[f2205,f928]) ).
fof(f23876,plain,
( spl20_813
| spl20_161
| ~ spl20_89
| ~ spl20_182 ),
inference(avatar_split_clause,[],[f3355,f1644,f776,f1308,f23873]) ).
fof(f3355,plain,
( empty(sK2)
| in(sK4(sK1),sK2)
| ~ spl20_89
| ~ spl20_182 ),
inference(resolution,[],[f1646,f777]) ).
fof(f1646,plain,
( element(sK4(sK1),sK2)
| ~ spl20_182 ),
inference(avatar_component_clause,[],[f1644]) ).
fof(f23408,plain,
( ~ spl20_812
| ~ spl20_203
| spl20_680 ),
inference(avatar_split_clause,[],[f19505,f18263,f2084,f23405]) ).
fof(f23405,plain,
( spl20_812
<=> sK1 = singleton(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_812])]) ).
fof(f18263,plain,
( spl20_680
<=> sK1 = succ(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_680])]) ).
fof(f19505,plain,
( sK1 != singleton(sK8)
| ~ spl20_203
| spl20_680 ),
inference(superposition,[],[f18265,f2086]) ).
fof(f18265,plain,
( sK1 != succ(sK8)
| spl20_680 ),
inference(avatar_component_clause,[],[f18263]) ).
fof(f20384,plain,
( spl20_811
| ~ spl20_75
| ~ spl20_330 ),
inference(avatar_split_clause,[],[f4882,f4726,f653,f20382]) ).
fof(f20382,plain,
( spl20_811
<=> ! [X25,X24,X26] :
( sP0(X24,singleton(X25),X26)
| ~ empty(X24)
| sK6(X24,singleton(X25),X26) = X25
| ~ in(X26,sK6(X24,singleton(X25),X26)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_811])]) ).
fof(f4882,plain,
( ! [X26,X24,X25] :
( sP0(X24,singleton(X25),X26)
| ~ empty(X24)
| sK6(X24,singleton(X25),X26) = X25
| ~ in(X26,sK6(X24,singleton(X25),X26)) )
| ~ spl20_75
| ~ spl20_330 ),
inference(resolution,[],[f4727,f654]) ).
fof(f20380,plain,
( spl20_810
| ~ spl20_75
| ~ spl20_329 ),
inference(avatar_split_clause,[],[f4858,f4722,f653,f20378]) ).
fof(f20378,plain,
( spl20_810
<=> ! [X25,X24,X23] :
( sP0(X23,X24,singleton(X25))
| ~ empty(X23)
| sK6(X23,X24,singleton(X25)) = X25
| ~ in(X24,sK6(X23,X24,singleton(X25))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_810])]) ).
fof(f4858,plain,
( ! [X24,X25,X23] :
( sP0(X23,X24,singleton(X25))
| ~ empty(X23)
| sK6(X23,X24,singleton(X25)) = X25
| ~ in(X24,sK6(X23,X24,singleton(X25))) )
| ~ spl20_75
| ~ spl20_329 ),
inference(resolution,[],[f4723,f654]) ).
fof(f20376,plain,
( spl20_809
| ~ spl20_75
| ~ spl20_328 ),
inference(avatar_split_clause,[],[f4834,f4718,f653,f20374]) ).
fof(f20374,plain,
( spl20_809
<=> ! [X25,X24,X26] :
( sP0(singleton(X24),X25,X26)
| ~ empty(X25)
| sK6(singleton(X24),X25,X26) = X24
| ~ in(X26,sK6(singleton(X24),X25,X26)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_809])]) ).
fof(f4834,plain,
( ! [X26,X24,X25] :
( sP0(singleton(X24),X25,X26)
| ~ empty(X25)
| sK6(singleton(X24),X25,X26) = X24
| ~ in(X26,sK6(singleton(X24),X25,X26)) )
| ~ spl20_75
| ~ spl20_328 ),
inference(resolution,[],[f4719,f654]) ).
fof(f20361,plain,
( spl20_808
| ~ spl20_75
| ~ spl20_327 ),
inference(avatar_split_clause,[],[f4810,f4714,f653,f20359]) ).
fof(f20359,plain,
( spl20_808
<=> ! [X25,X24,X23] :
( sP0(X23,X24,singleton(X25))
| ~ empty(X24)
| sK6(X23,X24,singleton(X25)) = X25
| ~ in(X23,sK6(X23,X24,singleton(X25))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_808])]) ).
fof(f4810,plain,
( ! [X24,X25,X23] :
( sP0(X23,X24,singleton(X25))
| ~ empty(X24)
| sK6(X23,X24,singleton(X25)) = X25
| ~ in(X23,sK6(X23,X24,singleton(X25))) )
| ~ spl20_75
| ~ spl20_327 ),
inference(resolution,[],[f4715,f654]) ).
fof(f20357,plain,
( spl20_807
| ~ spl20_75
| ~ spl20_326 ),
inference(avatar_split_clause,[],[f4786,f4710,f653,f20355]) ).
fof(f20355,plain,
( spl20_807
<=> ! [X25,X24,X23] :
( sP0(singleton(X23),X24,X25)
| ~ empty(X25)
| sK6(singleton(X23),X24,X25) = X23
| ~ in(X24,sK6(singleton(X23),X24,X25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_807])]) ).
fof(f4786,plain,
( ! [X24,X25,X23] :
( sP0(singleton(X23),X24,X25)
| ~ empty(X25)
| sK6(singleton(X23),X24,X25) = X23
| ~ in(X24,sK6(singleton(X23),X24,X25)) )
| ~ spl20_75
| ~ spl20_326 ),
inference(resolution,[],[f4711,f654]) ).
fof(f20353,plain,
( spl20_806
| ~ spl20_75
| ~ spl20_325 ),
inference(avatar_split_clause,[],[f4762,f4706,f653,f20351]) ).
fof(f20351,plain,
( spl20_806
<=> ! [X25,X24,X23] :
( sP0(X23,singleton(X24),X25)
| ~ empty(X25)
| sK6(X23,singleton(X24),X25) = X24
| ~ in(X23,sK6(X23,singleton(X24),X25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_806])]) ).
fof(f4762,plain,
( ! [X24,X25,X23] :
( sP0(X23,singleton(X24),X25)
| ~ empty(X25)
| sK6(X23,singleton(X24),X25) = X24
| ~ in(X23,sK6(X23,singleton(X24),X25)) )
| ~ spl20_75
| ~ spl20_325 ),
inference(resolution,[],[f4707,f654]) ).
fof(f20349,plain,
( spl20_805
| ~ spl20_97
| ~ spl20_323 ),
inference(avatar_split_clause,[],[f4736,f4695,f846,f20347]) ).
fof(f20347,plain,
( spl20_805
<=> ! [X6,X7] :
( ~ ordinal(sK4(powerset(X6)))
| ~ ordinal(X7)
| sK4(powerset(X6)) = X7
| ~ epsilon_transitive(X7)
| element(X7,X6)
| ordinal_subset(sK4(powerset(X6)),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_805])]) ).
fof(f4736,plain,
( ! [X6,X7] :
( ~ ordinal(sK4(powerset(X6)))
| ~ ordinal(X7)
| sK4(powerset(X6)) = X7
| ~ epsilon_transitive(X7)
| element(X7,X6)
| ordinal_subset(sK4(powerset(X6)),X7) )
| ~ spl20_97
| ~ spl20_323 ),
inference(duplicate_literal_removal,[],[f4731]) ).
fof(f4731,plain,
( ! [X6,X7] :
( ~ ordinal(sK4(powerset(X6)))
| ~ ordinal(X7)
| sK4(powerset(X6)) = X7
| ~ epsilon_transitive(X7)
| element(X7,X6)
| ordinal_subset(sK4(powerset(X6)),X7)
| ~ ordinal(X7)
| ~ ordinal(sK4(powerset(X6))) )
| ~ spl20_97
| ~ spl20_323 ),
inference(resolution,[],[f4696,f847]) ).
fof(f20345,plain,
( spl20_804
| ~ spl20_91
| ~ spl20_323 ),
inference(avatar_split_clause,[],[f4735,f4695,f811,f20343]) ).
fof(f20343,plain,
( spl20_804
<=> ! [X9,X8] :
( ~ ordinal(sK4(powerset(X8)))
| ~ ordinal(X9)
| sK4(powerset(X8)) = X9
| ~ epsilon_transitive(X9)
| element(X9,X8)
| ~ subset(X9,sK4(powerset(X8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_804])]) ).
fof(f4735,plain,
( ! [X8,X9] :
( ~ ordinal(sK4(powerset(X8)))
| ~ ordinal(X9)
| sK4(powerset(X8)) = X9
| ~ epsilon_transitive(X9)
| element(X9,X8)
| ~ subset(X9,sK4(powerset(X8))) )
| ~ spl20_91
| ~ spl20_323 ),
inference(duplicate_literal_removal,[],[f4732]) ).
fof(f4732,plain,
( ! [X8,X9] :
( ~ ordinal(sK4(powerset(X8)))
| ~ ordinal(X9)
| sK4(powerset(X8)) = X9
| ~ epsilon_transitive(X9)
| element(X9,X8)
| sK4(powerset(X8)) = X9
| ~ subset(X9,sK4(powerset(X8))) )
| ~ spl20_91
| ~ spl20_323 ),
inference(resolution,[],[f4696,f812]) ).
fof(f20341,plain,
( spl20_803
| ~ spl20_234
| ~ spl20_311 ),
inference(avatar_split_clause,[],[f4353,f4126,f2500,f20339]) ).
fof(f20339,plain,
( spl20_803
<=> ! [X9,X11,X10] :
( sP0(X9,X9,singleton(X10))
| sK6(X9,X9,singleton(X10)) = X10
| ~ ordinal(X9)
| ordinal_subset(X11,X9)
| ~ ordinal(X11)
| ~ empty(X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_803])]) ).
fof(f4353,plain,
( ! [X10,X11,X9] :
( sP0(X9,X9,singleton(X10))
| sK6(X9,X9,singleton(X10)) = X10
| ~ ordinal(X9)
| ordinal_subset(X11,X9)
| ~ ordinal(X11)
| ~ empty(X11) )
| ~ spl20_234
| ~ spl20_311 ),
inference(resolution,[],[f4127,f2501]) ).
fof(f20337,plain,
( spl20_802
| ~ spl20_146
| ~ spl20_308 ),
inference(avatar_split_clause,[],[f4241,f4114,f1180,f20335]) ).
fof(f20335,plain,
( spl20_802
<=> ! [X20,X21] :
( sK5(X20,X21) = X20
| ~ epsilon_transitive(X21)
| singleton(X20) = X21
| element(sK4(sK5(X20,X21)),X21)
| empty(sK5(X20,X21)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_802])]) ).
fof(f4114,plain,
( spl20_308
<=> ! [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_308])]) ).
fof(f4241,plain,
( ! [X21,X20] :
( sK5(X20,X21) = X20
| ~ epsilon_transitive(X21)
| singleton(X20) = X21
| element(sK4(sK5(X20,X21)),X21)
| empty(sK5(X20,X21)) )
| ~ spl20_146
| ~ spl20_308 ),
inference(resolution,[],[f4115,f1181]) ).
fof(f4115,plain,
( ! [X2,X0,X1] :
( ~ in(X2,sK5(X0,X1))
| sK5(X0,X1) = X0
| ~ epsilon_transitive(X1)
| singleton(X0) = X1
| element(X2,X1) )
| ~ spl20_308 ),
inference(avatar_component_clause,[],[f4114]) ).
fof(f20333,plain,
( spl20_801
| ~ spl20_71
| ~ spl20_308 ),
inference(avatar_split_clause,[],[f4240,f4114,f637,f20331]) ).
fof(f20331,plain,
( spl20_801
<=> ! [X18,X19] :
( sK5(X18,X19) = X18
| ~ epsilon_transitive(X19)
| singleton(X18) = X19
| element(sK3(sK5(X18,X19)),X19)
| epsilon_transitive(sK5(X18,X19)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_801])]) ).
fof(f4240,plain,
( ! [X18,X19] :
( sK5(X18,X19) = X18
| ~ epsilon_transitive(X19)
| singleton(X18) = X19
| element(sK3(sK5(X18,X19)),X19)
| epsilon_transitive(sK5(X18,X19)) )
| ~ spl20_71
| ~ spl20_308 ),
inference(resolution,[],[f4115,f638]) ).
fof(f20329,plain,
( spl20_800
| ~ spl20_234
| ~ spl20_305 ),
inference(avatar_split_clause,[],[f4158,f4102,f2500,f20327]) ).
fof(f20327,plain,
( spl20_800
<=> ! [X4,X5,X3] :
( element(X3,X4)
| sK4(powerset(X4)) = X3
| ~ ordinal(sK4(powerset(X4)))
| ~ ordinal(X3)
| ordinal_subset(X5,X3)
| ~ ordinal(X5)
| ~ empty(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_800])]) ).
fof(f4158,plain,
( ! [X3,X4,X5] :
( element(X3,X4)
| sK4(powerset(X4)) = X3
| ~ ordinal(sK4(powerset(X4)))
| ~ ordinal(X3)
| ordinal_subset(X5,X3)
| ~ ordinal(X5)
| ~ empty(X5) )
| ~ spl20_234
| ~ spl20_305 ),
inference(duplicate_literal_removal,[],[f4130]) ).
fof(f4130,plain,
( ! [X3,X4,X5] :
( element(X3,X4)
| sK4(powerset(X4)) = X3
| ~ ordinal(sK4(powerset(X4)))
| ~ ordinal(X3)
| ~ ordinal(X3)
| ordinal_subset(X5,X3)
| ~ ordinal(X5)
| ~ empty(X5) )
| ~ spl20_234
| ~ spl20_305 ),
inference(resolution,[],[f4103,f2501]) ).
fof(f20325,plain,
( spl20_799
| ~ spl20_223
| ~ spl20_301 ),
inference(avatar_split_clause,[],[f4061,f3629,f2310,f20323]) ).
fof(f20323,plain,
( spl20_799
<=> ! [X43,X44,X42] :
( element(sK6(X42,X43,sK3(powerset(X44))),X43)
| ~ empty(X42)
| sP0(X42,X43,sK3(powerset(X44)))
| ~ empty(X44)
| epsilon_transitive(powerset(X44)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_799])]) ).
fof(f4061,plain,
( ! [X44,X42,X43] :
( element(sK6(X42,X43,sK3(powerset(X44))),X43)
| ~ empty(X42)
| sP0(X42,X43,sK3(powerset(X44)))
| ~ empty(X44)
| epsilon_transitive(powerset(X44)) )
| ~ spl20_223
| ~ spl20_301 ),
inference(resolution,[],[f3630,f2311]) ).
fof(f20320,plain,
( spl20_798
| ~ spl20_153
| ~ spl20_301 ),
inference(avatar_split_clause,[],[f4058,f3629,f1230,f20318]) ).
fof(f20318,plain,
( spl20_798
<=> ! [X34,X36,X35] :
( element(sK6(X34,X35,singleton(X36)),X35)
| ~ empty(X34)
| sP0(X34,X35,singleton(X36))
| sK6(X34,X35,singleton(X36)) = X36 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_798])]) ).
fof(f4058,plain,
( ! [X36,X34,X35] :
( element(sK6(X34,X35,singleton(X36)),X35)
| ~ empty(X34)
| sP0(X34,X35,singleton(X36))
| sK6(X34,X35,singleton(X36)) = X36 )
| ~ spl20_153
| ~ spl20_301 ),
inference(resolution,[],[f3630,f1231]) ).
fof(f20316,plain,
( spl20_797
| ~ spl20_234
| ~ spl20_301 ),
inference(avatar_split_clause,[],[f4052,f3629,f2500,f20314]) ).
fof(f20314,plain,
( spl20_797
<=> ! [X17,X14,X16,X15] :
( element(sK6(X14,X15,X16),X15)
| ~ empty(X14)
| sP0(X14,X15,X16)
| ~ ordinal(X16)
| ordinal_subset(X17,X16)
| ~ ordinal(X17)
| ~ empty(X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_797])]) ).
fof(f4052,plain,
( ! [X16,X14,X17,X15] :
( element(sK6(X14,X15,X16),X15)
| ~ empty(X14)
| sP0(X14,X15,X16)
| ~ ordinal(X16)
| ordinal_subset(X17,X16)
| ~ ordinal(X17)
| ~ empty(X17) )
| ~ spl20_234
| ~ spl20_301 ),
inference(resolution,[],[f3630,f2501]) ).
fof(f20312,plain,
( spl20_796
| ~ spl20_84
| ~ spl20_301 ),
inference(avatar_split_clause,[],[f4045,f3629,f732,f20310]) ).
fof(f20310,plain,
( spl20_796
<=> ! [X9,X8,X10] :
( in(sK6(X8,powerset(X9),X10),X10)
| ~ empty(X8)
| sP0(X8,powerset(X9),X10)
| subset(sK6(X8,powerset(X9),X10),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_796])]) ).
fof(f4045,plain,
( ! [X10,X8,X9] :
( in(sK6(X8,powerset(X9),X10),X10)
| ~ empty(X8)
| sP0(X8,powerset(X9),X10)
| subset(sK6(X8,powerset(X9),X10),X9) )
| ~ spl20_84
| ~ spl20_301 ),
inference(resolution,[],[f3630,f733]) ).
fof(f20308,plain,
( spl20_795
| ~ spl20_223
| ~ spl20_298 ),
inference(avatar_split_clause,[],[f4008,f3617,f2310,f20306]) ).
fof(f20306,plain,
( spl20_795
<=> ! [X41,X43,X42] :
( element(sK6(X41,sK3(powerset(X42)),X43),X43)
| ~ empty(X41)
| sP0(X41,sK3(powerset(X42)),X43)
| ~ empty(X42)
| epsilon_transitive(powerset(X42)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_795])]) ).
fof(f4008,plain,
( ! [X41,X42,X43] :
( element(sK6(X41,sK3(powerset(X42)),X43),X43)
| ~ empty(X41)
| sP0(X41,sK3(powerset(X42)),X43)
| ~ empty(X42)
| epsilon_transitive(powerset(X42)) )
| ~ spl20_223
| ~ spl20_298 ),
inference(resolution,[],[f3618,f2311]) ).
fof(f20304,plain,
( spl20_794
| ~ spl20_153
| ~ spl20_298 ),
inference(avatar_split_clause,[],[f4005,f3617,f1230,f20302]) ).
fof(f20302,plain,
( spl20_794
<=> ! [X34,X35,X33] :
( element(sK6(X33,singleton(X34),X35),X35)
| ~ empty(X33)
| sP0(X33,singleton(X34),X35)
| sK6(X33,singleton(X34),X35) = X34 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_794])]) ).
fof(f4005,plain,
( ! [X34,X35,X33] :
( element(sK6(X33,singleton(X34),X35),X35)
| ~ empty(X33)
| sP0(X33,singleton(X34),X35)
| sK6(X33,singleton(X34),X35) = X34 )
| ~ spl20_153
| ~ spl20_298 ),
inference(resolution,[],[f3618,f1231]) ).
fof(f20300,plain,
( spl20_793
| ~ spl20_234
| ~ spl20_298 ),
inference(avatar_split_clause,[],[f3999,f3617,f2500,f20298]) ).
fof(f20298,plain,
( spl20_793
<=> ! [X13,X14,X16,X15] :
( element(sK6(X13,X14,X15),X15)
| ~ empty(X13)
| sP0(X13,X14,X15)
| ~ ordinal(X14)
| ordinal_subset(X16,X14)
| ~ ordinal(X16)
| ~ empty(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_793])]) ).
fof(f3999,plain,
( ! [X16,X14,X15,X13] :
( element(sK6(X13,X14,X15),X15)
| ~ empty(X13)
| sP0(X13,X14,X15)
| ~ ordinal(X14)
| ordinal_subset(X16,X14)
| ~ ordinal(X16)
| ~ empty(X16) )
| ~ spl20_234
| ~ spl20_298 ),
inference(resolution,[],[f3618,f2501]) ).
fof(f20296,plain,
( spl20_792
| ~ spl20_84
| ~ spl20_298 ),
inference(avatar_split_clause,[],[f3992,f3617,f732,f20294]) ).
fof(f20294,plain,
( spl20_792
<=> ! [X9,X8,X10] :
( in(sK6(X8,X9,powerset(X10)),X9)
| ~ empty(X8)
| sP0(X8,X9,powerset(X10))
| subset(sK6(X8,X9,powerset(X10)),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_792])]) ).
fof(f3992,plain,
( ! [X10,X8,X9] :
( in(sK6(X8,X9,powerset(X10)),X9)
| ~ empty(X8)
| sP0(X8,X9,powerset(X10))
| subset(sK6(X8,X9,powerset(X10)),X10) )
| ~ spl20_84
| ~ spl20_298 ),
inference(resolution,[],[f3618,f733]) ).
fof(f20292,plain,
( spl20_791
| ~ spl20_223
| ~ spl20_294 ),
inference(avatar_split_clause,[],[f3955,f3578,f2310,f20290]) ).
fof(f20290,plain,
( spl20_791
<=> ! [X44,X43,X42] :
( element(sK6(X42,X43,sK3(powerset(X44))),X42)
| ~ empty(X43)
| sP0(X42,X43,sK3(powerset(X44)))
| ~ empty(X44)
| epsilon_transitive(powerset(X44)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_791])]) ).
fof(f3955,plain,
( ! [X44,X42,X43] :
( element(sK6(X42,X43,sK3(powerset(X44))),X42)
| ~ empty(X43)
| sP0(X42,X43,sK3(powerset(X44)))
| ~ empty(X44)
| epsilon_transitive(powerset(X44)) )
| ~ spl20_223
| ~ spl20_294 ),
inference(resolution,[],[f3579,f2311]) ).
fof(f20288,plain,
( spl20_790
| ~ spl20_153
| ~ spl20_294 ),
inference(avatar_split_clause,[],[f3952,f3578,f1230,f20286]) ).
fof(f20286,plain,
( spl20_790
<=> ! [X34,X36,X35] :
( element(sK6(X34,X35,singleton(X36)),X34)
| ~ empty(X35)
| sP0(X34,X35,singleton(X36))
| sK6(X34,X35,singleton(X36)) = X36 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_790])]) ).
fof(f3952,plain,
( ! [X36,X34,X35] :
( element(sK6(X34,X35,singleton(X36)),X34)
| ~ empty(X35)
| sP0(X34,X35,singleton(X36))
| sK6(X34,X35,singleton(X36)) = X36 )
| ~ spl20_153
| ~ spl20_294 ),
inference(resolution,[],[f3579,f1231]) ).
fof(f20284,plain,
( spl20_789
| ~ spl20_234
| ~ spl20_294 ),
inference(avatar_split_clause,[],[f3946,f3578,f2500,f20282]) ).
fof(f20282,plain,
( spl20_789
<=> ! [X17,X14,X16,X15] :
( element(sK6(X14,X15,X16),X14)
| ~ empty(X15)
| sP0(X14,X15,X16)
| ~ ordinal(X16)
| ordinal_subset(X17,X16)
| ~ ordinal(X17)
| ~ empty(X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_789])]) ).
fof(f3946,plain,
( ! [X16,X14,X17,X15] :
( element(sK6(X14,X15,X16),X14)
| ~ empty(X15)
| sP0(X14,X15,X16)
| ~ ordinal(X16)
| ordinal_subset(X17,X16)
| ~ ordinal(X17)
| ~ empty(X17) )
| ~ spl20_234
| ~ spl20_294 ),
inference(resolution,[],[f3579,f2501]) ).
fof(f20273,plain,
( spl20_788
| ~ spl20_84
| ~ spl20_294 ),
inference(avatar_split_clause,[],[f3939,f3578,f732,f20271]) ).
fof(f20271,plain,
( spl20_788
<=> ! [X9,X8,X10] :
( in(sK6(powerset(X8),X9,X10),X10)
| ~ empty(X9)
| sP0(powerset(X8),X9,X10)
| subset(sK6(powerset(X8),X9,X10),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_788])]) ).
fof(f3939,plain,
( ! [X10,X8,X9] :
( in(sK6(powerset(X8),X9,X10),X10)
| ~ empty(X9)
| sP0(powerset(X8),X9,X10)
| subset(sK6(powerset(X8),X9,X10),X8) )
| ~ spl20_84
| ~ spl20_294 ),
inference(resolution,[],[f3579,f733]) ).
fof(f20269,plain,
( spl20_787
| ~ spl20_223
| ~ spl20_291 ),
inference(avatar_split_clause,[],[f3902,f3566,f2310,f20267]) ).
fof(f20267,plain,
( spl20_787
<=> ! [X41,X43,X42] :
( element(sK6(sK3(powerset(X41)),X42,X43),X43)
| ~ empty(X42)
| sP0(sK3(powerset(X41)),X42,X43)
| ~ empty(X41)
| epsilon_transitive(powerset(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_787])]) ).
fof(f3902,plain,
( ! [X41,X42,X43] :
( element(sK6(sK3(powerset(X41)),X42,X43),X43)
| ~ empty(X42)
| sP0(sK3(powerset(X41)),X42,X43)
| ~ empty(X41)
| epsilon_transitive(powerset(X41)) )
| ~ spl20_223
| ~ spl20_291 ),
inference(resolution,[],[f3567,f2311]) ).
fof(f20265,plain,
( spl20_786
| ~ spl20_153
| ~ spl20_291 ),
inference(avatar_split_clause,[],[f3899,f3566,f1230,f20263]) ).
fof(f20263,plain,
( spl20_786
<=> ! [X34,X35,X33] :
( element(sK6(singleton(X33),X34,X35),X35)
| ~ empty(X34)
| sP0(singleton(X33),X34,X35)
| sK6(singleton(X33),X34,X35) = X33 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_786])]) ).
fof(f3899,plain,
( ! [X34,X35,X33] :
( element(sK6(singleton(X33),X34,X35),X35)
| ~ empty(X34)
| sP0(singleton(X33),X34,X35)
| sK6(singleton(X33),X34,X35) = X33 )
| ~ spl20_153
| ~ spl20_291 ),
inference(resolution,[],[f3567,f1231]) ).
fof(f20261,plain,
( spl20_785
| ~ spl20_234
| ~ spl20_291 ),
inference(avatar_split_clause,[],[f3893,f3566,f2500,f20259]) ).
fof(f20259,plain,
( spl20_785
<=> ! [X13,X14,X16,X15] :
( element(sK6(X13,X14,X15),X15)
| ~ empty(X14)
| sP0(X13,X14,X15)
| ~ ordinal(X13)
| ordinal_subset(X16,X13)
| ~ ordinal(X16)
| ~ empty(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_785])]) ).
fof(f3893,plain,
( ! [X16,X14,X15,X13] :
( element(sK6(X13,X14,X15),X15)
| ~ empty(X14)
| sP0(X13,X14,X15)
| ~ ordinal(X13)
| ordinal_subset(X16,X13)
| ~ ordinal(X16)
| ~ empty(X16) )
| ~ spl20_234
| ~ spl20_291 ),
inference(resolution,[],[f3567,f2501]) ).
fof(f20257,plain,
( spl20_784
| ~ spl20_84
| ~ spl20_291 ),
inference(avatar_split_clause,[],[f3886,f3566,f732,f20255]) ).
fof(f20255,plain,
( spl20_784
<=> ! [X9,X8,X10] :
( in(sK6(X8,X9,powerset(X10)),X8)
| ~ empty(X9)
| sP0(X8,X9,powerset(X10))
| subset(sK6(X8,X9,powerset(X10)),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_784])]) ).
fof(f3886,plain,
( ! [X10,X8,X9] :
( in(sK6(X8,X9,powerset(X10)),X8)
| ~ empty(X9)
| sP0(X8,X9,powerset(X10))
| subset(sK6(X8,X9,powerset(X10)),X10) )
| ~ spl20_84
| ~ spl20_291 ),
inference(resolution,[],[f3567,f733]) ).
fof(f20253,plain,
( spl20_783
| ~ spl20_223
| ~ spl20_288 ),
inference(avatar_split_clause,[],[f3849,f3554,f2310,f20251]) ).
fof(f20251,plain,
( spl20_783
<=> ! [X41,X43,X42] :
( element(sK6(X41,sK3(powerset(X42)),X43),X41)
| ~ empty(X43)
| sP0(X41,sK3(powerset(X42)),X43)
| ~ empty(X42)
| epsilon_transitive(powerset(X42)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_783])]) ).
fof(f3849,plain,
( ! [X41,X42,X43] :
( element(sK6(X41,sK3(powerset(X42)),X43),X41)
| ~ empty(X43)
| sP0(X41,sK3(powerset(X42)),X43)
| ~ empty(X42)
| epsilon_transitive(powerset(X42)) )
| ~ spl20_223
| ~ spl20_288 ),
inference(resolution,[],[f3555,f2311]) ).
fof(f20249,plain,
( spl20_782
| ~ spl20_153
| ~ spl20_288 ),
inference(avatar_split_clause,[],[f3846,f3554,f1230,f20247]) ).
fof(f20247,plain,
( spl20_782
<=> ! [X34,X35,X33] :
( element(sK6(X33,singleton(X34),X35),X33)
| ~ empty(X35)
| sP0(X33,singleton(X34),X35)
| sK6(X33,singleton(X34),X35) = X34 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_782])]) ).
fof(f3846,plain,
( ! [X34,X35,X33] :
( element(sK6(X33,singleton(X34),X35),X33)
| ~ empty(X35)
| sP0(X33,singleton(X34),X35)
| sK6(X33,singleton(X34),X35) = X34 )
| ~ spl20_153
| ~ spl20_288 ),
inference(resolution,[],[f3555,f1231]) ).
fof(f20245,plain,
( spl20_781
| ~ spl20_234
| ~ spl20_288 ),
inference(avatar_split_clause,[],[f3840,f3554,f2500,f20243]) ).
fof(f20243,plain,
( spl20_781
<=> ! [X13,X14,X16,X15] :
( element(sK6(X13,X14,X15),X13)
| ~ empty(X15)
| sP0(X13,X14,X15)
| ~ ordinal(X14)
| ordinal_subset(X16,X14)
| ~ ordinal(X16)
| ~ empty(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_781])]) ).
fof(f3840,plain,
( ! [X16,X14,X15,X13] :
( element(sK6(X13,X14,X15),X13)
| ~ empty(X15)
| sP0(X13,X14,X15)
| ~ ordinal(X14)
| ordinal_subset(X16,X14)
| ~ ordinal(X16)
| ~ empty(X16) )
| ~ spl20_234
| ~ spl20_288 ),
inference(resolution,[],[f3555,f2501]) ).
fof(f20241,plain,
( spl20_780
| ~ spl20_84
| ~ spl20_288 ),
inference(avatar_split_clause,[],[f3833,f3554,f732,f20239]) ).
fof(f20239,plain,
( spl20_780
<=> ! [X9,X8,X10] :
( in(sK6(powerset(X8),X9,X10),X9)
| ~ empty(X10)
| sP0(powerset(X8),X9,X10)
| subset(sK6(powerset(X8),X9,X10),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_780])]) ).
fof(f3833,plain,
( ! [X10,X8,X9] :
( in(sK6(powerset(X8),X9,X10),X9)
| ~ empty(X10)
| sP0(powerset(X8),X9,X10)
| subset(sK6(powerset(X8),X9,X10),X8) )
| ~ spl20_84
| ~ spl20_288 ),
inference(resolution,[],[f3555,f733]) ).
fof(f20237,plain,
( spl20_779
| ~ spl20_223
| ~ spl20_285 ),
inference(avatar_split_clause,[],[f3796,f3542,f2310,f20235]) ).
fof(f20235,plain,
( spl20_779
<=> ! [X41,X43,X42] :
( element(sK6(sK3(powerset(X41)),X42,X43),X42)
| ~ empty(X43)
| sP0(sK3(powerset(X41)),X42,X43)
| ~ empty(X41)
| epsilon_transitive(powerset(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_779])]) ).
fof(f3796,plain,
( ! [X41,X42,X43] :
( element(sK6(sK3(powerset(X41)),X42,X43),X42)
| ~ empty(X43)
| sP0(sK3(powerset(X41)),X42,X43)
| ~ empty(X41)
| epsilon_transitive(powerset(X41)) )
| ~ spl20_223
| ~ spl20_285 ),
inference(resolution,[],[f3543,f2311]) ).
fof(f20232,plain,
( spl20_778
| ~ spl20_153
| ~ spl20_285 ),
inference(avatar_split_clause,[],[f3793,f3542,f1230,f20230]) ).
fof(f20230,plain,
( spl20_778
<=> ! [X34,X35,X33] :
( element(sK6(singleton(X33),X34,X35),X34)
| ~ empty(X35)
| sP0(singleton(X33),X34,X35)
| sK6(singleton(X33),X34,X35) = X33 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_778])]) ).
fof(f3793,plain,
( ! [X34,X35,X33] :
( element(sK6(singleton(X33),X34,X35),X34)
| ~ empty(X35)
| sP0(singleton(X33),X34,X35)
| sK6(singleton(X33),X34,X35) = X33 )
| ~ spl20_153
| ~ spl20_285 ),
inference(resolution,[],[f3543,f1231]) ).
fof(f20228,plain,
( spl20_777
| ~ spl20_234
| ~ spl20_285 ),
inference(avatar_split_clause,[],[f3787,f3542,f2500,f20226]) ).
fof(f20226,plain,
( spl20_777
<=> ! [X13,X14,X16,X15] :
( element(sK6(X13,X14,X15),X14)
| ~ empty(X15)
| sP0(X13,X14,X15)
| ~ ordinal(X13)
| ordinal_subset(X16,X13)
| ~ ordinal(X16)
| ~ empty(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_777])]) ).
fof(f3787,plain,
( ! [X16,X14,X15,X13] :
( element(sK6(X13,X14,X15),X14)
| ~ empty(X15)
| sP0(X13,X14,X15)
| ~ ordinal(X13)
| ordinal_subset(X16,X13)
| ~ ordinal(X16)
| ~ empty(X16) )
| ~ spl20_234
| ~ spl20_285 ),
inference(resolution,[],[f3543,f2501]) ).
fof(f20224,plain,
( spl20_776
| ~ spl20_84
| ~ spl20_285 ),
inference(avatar_split_clause,[],[f3780,f3542,f732,f20222]) ).
fof(f20222,plain,
( spl20_776
<=> ! [X9,X8,X10] :
( in(sK6(X8,powerset(X9),X10),X8)
| ~ empty(X10)
| sP0(X8,powerset(X9),X10)
| subset(sK6(X8,powerset(X9),X10),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_776])]) ).
fof(f3780,plain,
( ! [X10,X8,X9] :
( in(sK6(X8,powerset(X9),X10),X8)
| ~ empty(X10)
| sP0(X8,powerset(X9),X10)
| subset(sK6(X8,powerset(X9),X10),X9) )
| ~ spl20_84
| ~ spl20_285 ),
inference(resolution,[],[f3543,f733]) ).
fof(f20220,plain,
( spl20_775
| ~ spl20_223
| ~ spl20_284 ),
inference(avatar_split_clause,[],[f3771,f3538,f2310,f20218]) ).
fof(f20218,plain,
( spl20_775
<=> ! [X29,X28] :
( subset(sK6(X28,X28,sK3(powerset(X29))),X28)
| sP0(X28,X28,sK3(powerset(X29)))
| ~ epsilon_transitive(X28)
| ~ empty(X29)
| epsilon_transitive(powerset(X29)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_775])]) ).
fof(f3771,plain,
( ! [X28,X29] :
( subset(sK6(X28,X28,sK3(powerset(X29))),X28)
| sP0(X28,X28,sK3(powerset(X29)))
| ~ epsilon_transitive(X28)
| ~ empty(X29)
| epsilon_transitive(powerset(X29)) )
| ~ spl20_223
| ~ spl20_284 ),
inference(resolution,[],[f3539,f2311]) ).
fof(f20216,plain,
( spl20_774
| ~ spl20_153
| ~ spl20_284 ),
inference(avatar_split_clause,[],[f3768,f3538,f1230,f20214]) ).
fof(f20214,plain,
( spl20_774
<=> ! [X24,X23] :
( subset(sK6(X23,X23,singleton(X24)),X23)
| sP0(X23,X23,singleton(X24))
| ~ epsilon_transitive(X23)
| sK6(X23,X23,singleton(X24)) = X24 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_774])]) ).
fof(f3768,plain,
( ! [X24,X23] :
( subset(sK6(X23,X23,singleton(X24)),X23)
| sP0(X23,X23,singleton(X24))
| ~ epsilon_transitive(X23)
| sK6(X23,X23,singleton(X24)) = X24 )
| ~ spl20_153
| ~ spl20_284 ),
inference(resolution,[],[f3539,f1231]) ).
fof(f20212,plain,
( spl20_773
| ~ spl20_234
| ~ spl20_284 ),
inference(avatar_split_clause,[],[f3762,f3538,f2500,f20210]) ).
fof(f20210,plain,
( spl20_773
<=> ! [X9,X11,X10] :
( subset(sK6(X9,X9,X10),X9)
| sP0(X9,X9,X10)
| ~ epsilon_transitive(X9)
| ~ ordinal(X10)
| ordinal_subset(X11,X10)
| ~ ordinal(X11)
| ~ empty(X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_773])]) ).
fof(f3762,plain,
( ! [X10,X11,X9] :
( subset(sK6(X9,X9,X10),X9)
| sP0(X9,X9,X10)
| ~ epsilon_transitive(X9)
| ~ ordinal(X10)
| ordinal_subset(X11,X10)
| ~ ordinal(X11)
| ~ empty(X11) )
| ~ spl20_234
| ~ spl20_284 ),
inference(resolution,[],[f3539,f2501]) ).
fof(f20208,plain,
( spl20_772
| ~ spl20_160
| ~ spl20_284 ),
inference(avatar_split_clause,[],[f3753,f3538,f1291,f20206]) ).
fof(f20206,plain,
( spl20_772
<=> ! [X2,X0,X1] :
( in(sK6(X0,X0,X1),X1)
| sP0(X0,X0,X1)
| ~ epsilon_transitive(X0)
| ~ in(X2,sK6(X0,X0,X1))
| element(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_772])]) ).
fof(f3753,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X0,X1),X1)
| sP0(X0,X0,X1)
| ~ epsilon_transitive(X0)
| ~ in(X2,sK6(X0,X0,X1))
| element(X2,X0) )
| ~ spl20_160
| ~ spl20_284 ),
inference(resolution,[],[f3539,f1292]) ).
fof(f20204,plain,
( spl20_771
| ~ spl20_234
| ~ spl20_283 ),
inference(avatar_split_clause,[],[f3737,f3534,f2500,f20202]) ).
fof(f20202,plain,
( spl20_771
<=> ! [X9,X11,X10] :
( subset(sK6(X9,X9,X10),X10)
| sP0(X9,X9,X10)
| ~ epsilon_transitive(X10)
| ~ ordinal(X9)
| ordinal_subset(X11,X9)
| ~ ordinal(X11)
| ~ empty(X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_771])]) ).
fof(f3737,plain,
( ! [X10,X11,X9] :
( subset(sK6(X9,X9,X10),X10)
| sP0(X9,X9,X10)
| ~ epsilon_transitive(X10)
| ~ ordinal(X9)
| ordinal_subset(X11,X9)
| ~ ordinal(X11)
| ~ empty(X11) )
| ~ spl20_234
| ~ spl20_283 ),
inference(resolution,[],[f3535,f2501]) ).
fof(f20200,plain,
( spl20_770
| ~ spl20_160
| ~ spl20_283 ),
inference(avatar_split_clause,[],[f3728,f3534,f1291,f20198]) ).
fof(f20198,plain,
( spl20_770
<=> ! [X2,X0,X1] :
( in(sK6(X0,X0,X1),X0)
| sP0(X0,X0,X1)
| ~ epsilon_transitive(X1)
| ~ in(X2,sK6(X0,X0,X1))
| element(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_770])]) ).
fof(f3728,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X0,X1),X0)
| sP0(X0,X0,X1)
| ~ epsilon_transitive(X1)
| ~ in(X2,sK6(X0,X0,X1))
| element(X2,X1) )
| ~ spl20_160
| ~ spl20_283 ),
inference(resolution,[],[f3535,f1292]) ).
fof(f20196,plain,
( spl20_769
| ~ spl20_160
| ~ spl20_282 ),
inference(avatar_split_clause,[],[f3703,f3530,f1291,f20194]) ).
fof(f20194,plain,
( spl20_769
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,X0),X0)
| sP0(X0,X1,X0)
| ~ epsilon_transitive(X1)
| ~ in(X2,sK6(X0,X1,X0))
| element(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_769])]) ).
fof(f3703,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X0),X0)
| sP0(X0,X1,X0)
| ~ epsilon_transitive(X1)
| ~ in(X2,sK6(X0,X1,X0))
| element(X2,X1) )
| ~ spl20_160
| ~ spl20_282 ),
inference(resolution,[],[f3531,f1292]) ).
fof(f20175,plain,
( spl20_768
| ~ spl20_160
| ~ spl20_281 ),
inference(avatar_split_clause,[],[f3678,f3526,f1291,f20173]) ).
fof(f20173,plain,
( spl20_768
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,X1),X1)
| sP0(X0,X1,X1)
| ~ epsilon_transitive(X0)
| ~ in(X2,sK6(X0,X1,X1))
| element(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_768])]) ).
fof(f3678,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X1),X1)
| sP0(X0,X1,X1)
| ~ epsilon_transitive(X0)
| ~ in(X2,sK6(X0,X1,X1))
| element(X2,X0) )
| ~ spl20_160
| ~ spl20_281 ),
inference(resolution,[],[f3527,f1292]) ).
fof(f20171,plain,
( spl20_767
| ~ spl20_160
| ~ spl20_280 ),
inference(avatar_split_clause,[],[f3669,f3522,f1291,f20169]) ).
fof(f20169,plain,
( spl20_767
<=> ! [X2,X0,X1] :
( ~ ordinal(singleton(X0))
| ~ ordinal(X1)
| singleton(X0) = X1
| ~ epsilon_transitive(X1)
| X0 = X1
| ~ in(X2,singleton(X0))
| element(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_767])]) ).
fof(f3522,plain,
( spl20_280
<=> ! [X9,X8] :
( singleton(X8) = X9
| ~ ordinal(singleton(X8))
| ~ ordinal(X9)
| subset(singleton(X8),X9)
| ~ epsilon_transitive(X9)
| X8 = X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_280])]) ).
fof(f3669,plain,
( ! [X2,X0,X1] :
( ~ ordinal(singleton(X0))
| ~ ordinal(X1)
| singleton(X0) = X1
| ~ epsilon_transitive(X1)
| X0 = X1
| ~ in(X2,singleton(X0))
| element(X2,X1) )
| ~ spl20_160
| ~ spl20_280 ),
inference(resolution,[],[f3523,f1292]) ).
fof(f3523,plain,
( ! [X8,X9] :
( subset(singleton(X8),X9)
| ~ ordinal(singleton(X8))
| ~ ordinal(X9)
| singleton(X8) = X9
| ~ epsilon_transitive(X9)
| X8 = X9 )
| ~ spl20_280 ),
inference(avatar_component_clause,[],[f3522]) ).
fof(f20167,plain,
( spl20_766
| ~ spl20_94
| ~ spl20_269 ),
inference(avatar_split_clause,[],[f3357,f3008,f823,f20165]) ).
fof(f20165,plain,
( spl20_766
<=> ! [X4,X5,X3] :
( in(sK6(X3,X3,powerset(X4)),X3)
| sP0(X3,X3,powerset(X4))
| ~ empty(X4)
| ~ in(X5,sK6(X3,X3,powerset(X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_766])]) ).
fof(f3357,plain,
( ! [X3,X4,X5] :
( in(sK6(X3,X3,powerset(X4)),X3)
| sP0(X3,X3,powerset(X4))
| ~ empty(X4)
| ~ in(X5,sK6(X3,X3,powerset(X4))) )
| ~ spl20_94
| ~ spl20_269 ),
inference(resolution,[],[f3009,f824]) ).
fof(f20163,plain,
( spl20_765
| ~ spl20_94
| ~ spl20_263 ),
inference(avatar_split_clause,[],[f3207,f2976,f823,f20161]) ).
fof(f20161,plain,
( spl20_765
<=> ! [X4,X5,X3] :
( in(sK6(X3,powerset(X4),X3),X3)
| sP0(X3,powerset(X4),X3)
| ~ empty(X4)
| ~ in(X5,sK6(X3,powerset(X4),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_765])]) ).
fof(f3207,plain,
( ! [X3,X4,X5] :
( in(sK6(X3,powerset(X4),X3),X3)
| sP0(X3,powerset(X4),X3)
| ~ empty(X4)
| ~ in(X5,sK6(X3,powerset(X4),X3)) )
| ~ spl20_94
| ~ spl20_263 ),
inference(resolution,[],[f2977,f824]) ).
fof(f20159,plain,
( spl20_764
| ~ spl20_94
| ~ spl20_259 ),
inference(avatar_split_clause,[],[f3089,f2960,f823,f20157]) ).
fof(f20157,plain,
( spl20_764
<=> ! [X4,X5,X3] :
( in(sK6(powerset(X3),X4,X4),X4)
| sP0(powerset(X3),X4,X4)
| ~ empty(X3)
| ~ in(X5,sK6(powerset(X3),X4,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_764])]) ).
fof(f3089,plain,
( ! [X3,X4,X5] :
( in(sK6(powerset(X3),X4,X4),X4)
| sP0(powerset(X3),X4,X4)
| ~ empty(X3)
| ~ in(X5,sK6(powerset(X3),X4,X4)) )
| ~ spl20_94
| ~ spl20_259 ),
inference(resolution,[],[f2961,f824]) ).
fof(f20155,plain,
( spl20_763
| ~ spl20_94
| ~ spl20_256 ),
inference(avatar_split_clause,[],[f3049,f2944,f823,f20153]) ).
fof(f20153,plain,
( spl20_763
<=> ! [X4,X5,X3] :
( ~ ordinal(singleton(X3))
| ~ ordinal(powerset(X4))
| powerset(X4) = singleton(X3)
| powerset(X4) = X3
| ~ empty(X4)
| ~ in(X5,singleton(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_763])]) ).
fof(f3049,plain,
( ! [X3,X4,X5] :
( ~ ordinal(singleton(X3))
| ~ ordinal(powerset(X4))
| powerset(X4) = singleton(X3)
| powerset(X4) = X3
| ~ empty(X4)
| ~ in(X5,singleton(X3)) )
| ~ spl20_94
| ~ spl20_256 ),
inference(resolution,[],[f2945,f824]) ).
fof(f20151,plain,
( spl20_762
| ~ spl20_245
| ~ spl20_254 ),
inference(avatar_split_clause,[],[f3047,f2936,f2725,f20149]) ).
fof(f20149,plain,
( spl20_762
<=> ! [X2,X0,X1] :
( X0 = X1
| singleton(X1) = X0
| ~ ordinal(singleton(X1))
| ~ ordinal(X0)
| ordinal_subset(X2,X0)
| ~ ordinal(X2)
| element(singleton(X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_762])]) ).
fof(f3047,plain,
( ! [X2,X0,X1] :
( X0 = X1
| singleton(X1) = X0
| ~ ordinal(singleton(X1))
| ~ ordinal(X0)
| ordinal_subset(X2,X0)
| ~ ordinal(X2)
| element(singleton(X1),X2) )
| ~ spl20_245
| ~ spl20_254 ),
inference(duplicate_literal_removal,[],[f3027]) ).
fof(f3027,plain,
( ! [X2,X0,X1] :
( X0 = X1
| singleton(X1) = X0
| ~ ordinal(singleton(X1))
| ~ ordinal(X0)
| ~ ordinal(X0)
| ordinal_subset(X2,X0)
| ~ ordinal(X2)
| element(singleton(X1),X2) )
| ~ spl20_245
| ~ spl20_254 ),
inference(resolution,[],[f2937,f2726]) ).
fof(f20147,plain,
( spl20_761
| ~ spl20_218
| ~ spl20_253 ),
inference(avatar_split_clause,[],[f2927,f2904,f2226,f20145]) ).
fof(f20145,plain,
( spl20_761
<=> ! [X11] :
( ~ ordinal(X11)
| ~ ordinal(succ(powerset(X11)))
| element(X11,succ(powerset(X11)))
| succ(powerset(X11)) = X11
| ~ epsilon_transitive(X11)
| empty(powerset(X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_761])]) ).
fof(f2226,plain,
( spl20_218
<=> ! [X8] :
( empty(powerset(X8))
| ~ subset(succ(powerset(X8)),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_218])]) ).
fof(f2904,plain,
( spl20_253
<=> ! [X0,X1] :
( X0 = X1
| ~ ordinal(X0)
| ~ ordinal(X1)
| element(X0,X1)
| subset(X1,X0)
| ~ epsilon_transitive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_253])]) ).
fof(f2927,plain,
( ! [X11] :
( ~ ordinal(X11)
| ~ ordinal(succ(powerset(X11)))
| element(X11,succ(powerset(X11)))
| succ(powerset(X11)) = X11
| ~ epsilon_transitive(X11)
| empty(powerset(X11)) )
| ~ spl20_218
| ~ spl20_253 ),
inference(resolution,[],[f2905,f2227]) ).
fof(f2227,plain,
( ! [X8] :
( ~ subset(succ(powerset(X8)),X8)
| empty(powerset(X8)) )
| ~ spl20_218 ),
inference(avatar_component_clause,[],[f2226]) ).
fof(f2905,plain,
( ! [X0,X1] :
( subset(X1,X0)
| ~ ordinal(X0)
| ~ ordinal(X1)
| element(X0,X1)
| X0 = X1
| ~ epsilon_transitive(X0) )
| ~ spl20_253 ),
inference(avatar_component_clause,[],[f2904]) ).
fof(f20143,plain,
( spl20_760
| ~ spl20_230
| ~ spl20_251 ),
inference(avatar_split_clause,[],[f2891,f2820,f2398,f20141]) ).
fof(f20141,plain,
( spl20_760
<=> ! [X41,X40,X39] :
( sP0(X39,X40,sK3(powerset(X41)))
| ~ empty(X40)
| ~ empty(X39)
| element(sK6(X39,X40,sK3(powerset(X41))),X41)
| epsilon_transitive(powerset(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_760])]) ).
fof(f2891,plain,
( ! [X40,X41,X39] :
( sP0(X39,X40,sK3(powerset(X41)))
| ~ empty(X40)
| ~ empty(X39)
| element(sK6(X39,X40,sK3(powerset(X41))),X41)
| epsilon_transitive(powerset(X41)) )
| ~ spl20_230
| ~ spl20_251 ),
inference(resolution,[],[f2821,f2399]) ).
fof(f20139,plain,
( spl20_759
| ~ spl20_245
| ~ spl20_251 ),
inference(avatar_split_clause,[],[f2882,f2820,f2725,f20137]) ).
fof(f20137,plain,
( spl20_759
<=> ! [X10,X11,X13,X12] :
( sP0(X10,X11,X12)
| ~ empty(X11)
| ~ empty(X10)
| ~ ordinal(X12)
| ordinal_subset(X13,X12)
| ~ ordinal(X13)
| element(sK6(X10,X11,X12),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_759])]) ).
fof(f2882,plain,
( ! [X10,X11,X12,X13] :
( sP0(X10,X11,X12)
| ~ empty(X11)
| ~ empty(X10)
| ~ ordinal(X12)
| ordinal_subset(X13,X12)
| ~ ordinal(X13)
| element(sK6(X10,X11,X12),X13) )
| ~ spl20_245
| ~ spl20_251 ),
inference(resolution,[],[f2821,f2726]) ).
fof(f20135,plain,
( spl20_758
| ~ spl20_230
| ~ spl20_250 ),
inference(avatar_split_clause,[],[f2870,f2816,f2398,f20133]) ).
fof(f20133,plain,
( spl20_758
<=> ! [X38,X39,X40] :
( sP0(X38,sK3(powerset(X39)),X40)
| ~ empty(X40)
| ~ empty(X38)
| element(sK6(X38,sK3(powerset(X39)),X40),X39)
| epsilon_transitive(powerset(X39)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_758])]) ).
fof(f2870,plain,
( ! [X40,X38,X39] :
( sP0(X38,sK3(powerset(X39)),X40)
| ~ empty(X40)
| ~ empty(X38)
| element(sK6(X38,sK3(powerset(X39)),X40),X39)
| epsilon_transitive(powerset(X39)) )
| ~ spl20_230
| ~ spl20_250 ),
inference(resolution,[],[f2817,f2399]) ).
fof(f20131,plain,
( spl20_757
| ~ spl20_245
| ~ spl20_250 ),
inference(avatar_split_clause,[],[f2861,f2816,f2725,f20129]) ).
fof(f20129,plain,
( spl20_757
<=> ! [X10,X11,X12,X9] :
( sP0(X9,X10,X11)
| ~ empty(X11)
| ~ empty(X9)
| ~ ordinal(X10)
| ordinal_subset(X12,X10)
| ~ ordinal(X12)
| element(sK6(X9,X10,X11),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_757])]) ).
fof(f2861,plain,
( ! [X10,X11,X9,X12] :
( sP0(X9,X10,X11)
| ~ empty(X11)
| ~ empty(X9)
| ~ ordinal(X10)
| ordinal_subset(X12,X10)
| ~ ordinal(X12)
| element(sK6(X9,X10,X11),X12) )
| ~ spl20_245
| ~ spl20_250 ),
inference(resolution,[],[f2817,f2726]) ).
fof(f20127,plain,
( spl20_756
| ~ spl20_230
| ~ spl20_249 ),
inference(avatar_split_clause,[],[f2849,f2812,f2398,f20125]) ).
fof(f20125,plain,
( spl20_756
<=> ! [X38,X39,X40] :
( sP0(sK3(powerset(X38)),X39,X40)
| ~ empty(X40)
| ~ empty(X39)
| element(sK6(sK3(powerset(X38)),X39,X40),X38)
| epsilon_transitive(powerset(X38)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_756])]) ).
fof(f2849,plain,
( ! [X40,X38,X39] :
( sP0(sK3(powerset(X38)),X39,X40)
| ~ empty(X40)
| ~ empty(X39)
| element(sK6(sK3(powerset(X38)),X39,X40),X38)
| epsilon_transitive(powerset(X38)) )
| ~ spl20_230
| ~ spl20_249 ),
inference(resolution,[],[f2813,f2399]) ).
fof(f20123,plain,
( spl20_755
| ~ spl20_245
| ~ spl20_249 ),
inference(avatar_split_clause,[],[f2840,f2812,f2725,f20121]) ).
fof(f20121,plain,
( spl20_755
<=> ! [X10,X11,X12,X9] :
( sP0(X9,X10,X11)
| ~ empty(X11)
| ~ empty(X10)
| ~ ordinal(X9)
| ordinal_subset(X12,X9)
| ~ ordinal(X12)
| element(sK6(X9,X10,X11),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_755])]) ).
fof(f2840,plain,
( ! [X10,X11,X9,X12] :
( sP0(X9,X10,X11)
| ~ empty(X11)
| ~ empty(X10)
| ~ ordinal(X9)
| ordinal_subset(X12,X9)
| ~ ordinal(X12)
| element(sK6(X9,X10,X11),X12) )
| ~ spl20_245
| ~ spl20_249 ),
inference(resolution,[],[f2813,f2726]) ).
fof(f20119,plain,
( spl20_754
| ~ spl20_107
| ~ spl20_245 ),
inference(avatar_split_clause,[],[f2751,f2725,f915,f20117]) ).
fof(f20117,plain,
( spl20_754
<=> ! [X34,X36,X35] :
( ~ ordinal(X34)
| ordinal_subset(X35,X34)
| ~ ordinal(X35)
| element(sK5(X36,X34),X35)
| sK5(X36,X34) = X36
| singleton(X36) = X34 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_754])]) ).
fof(f2751,plain,
( ! [X36,X34,X35] :
( ~ ordinal(X34)
| ordinal_subset(X35,X34)
| ~ ordinal(X35)
| element(sK5(X36,X34),X35)
| sK5(X36,X34) = X36
| singleton(X36) = X34 )
| ~ spl20_107
| ~ spl20_245 ),
inference(resolution,[],[f2726,f916]) ).
fof(f20115,plain,
( spl20_753
| ~ spl20_179
| ~ spl20_234 ),
inference(avatar_split_clause,[],[f2569,f2500,f1561,f20113]) ).
fof(f20113,plain,
( spl20_753
<=> ! [X102,X104,X103,X101] :
( ~ ordinal(X101)
| ordinal_subset(X102,X101)
| ~ ordinal(X102)
| ~ empty(X102)
| in(sK6(X101,X103,X104),X104)
| sP0(X101,X103,X104)
| ~ empty(X103) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_753])]) ).
fof(f2569,plain,
( ! [X101,X104,X102,X103] :
( ~ ordinal(X101)
| ordinal_subset(X102,X101)
| ~ ordinal(X102)
| ~ empty(X102)
| in(sK6(X101,X103,X104),X104)
| sP0(X101,X103,X104)
| ~ empty(X103) )
| ~ spl20_179
| ~ spl20_234 ),
inference(resolution,[],[f2501,f1562]) ).
fof(f20109,plain,
( ~ spl20_14
| spl20_181
| ~ spl20_297 ),
inference(avatar_split_clause,[],[f20014,f3590,f1640,f324]) ).
fof(f20014,plain,
( ~ empty(sK8)
| spl20_181
| ~ spl20_297 ),
inference(superposition,[],[f1641,f3592]) ).
fof(f1641,plain,
( ~ empty(sK1)
| spl20_181 ),
inference(avatar_component_clause,[],[f1640]) ).
fof(f20108,plain,
( spl20_752
| ~ spl20_178
| ~ spl20_234 ),
inference(avatar_split_clause,[],[f2568,f2500,f1557,f20106]) ).
fof(f20106,plain,
( spl20_752
<=> ! [X99,X98,X100,X97] :
( ~ ordinal(X97)
| ordinal_subset(X98,X97)
| ~ ordinal(X98)
| ~ empty(X98)
| in(sK6(X97,X99,X100),X99)
| sP0(X97,X99,X100)
| ~ empty(X100) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_752])]) ).
fof(f2568,plain,
( ! [X98,X99,X97,X100] :
( ~ ordinal(X97)
| ordinal_subset(X98,X97)
| ~ ordinal(X98)
| ~ empty(X98)
| in(sK6(X97,X99,X100),X99)
| sP0(X97,X99,X100)
| ~ empty(X100) )
| ~ spl20_178
| ~ spl20_234 ),
inference(resolution,[],[f2501,f1558]) ).
fof(f20104,plain,
( spl20_751
| ~ spl20_180
| ~ spl20_234 ),
inference(avatar_split_clause,[],[f2562,f2500,f1565,f20102]) ).
fof(f20102,plain,
( spl20_751
<=> ! [X74,X75,X76,X73] :
( ~ ordinal(X73)
| ordinal_subset(X74,X73)
| ~ ordinal(X74)
| ~ empty(X74)
| in(sK6(X75,X73,X76),X76)
| sP0(X75,X73,X76)
| ~ empty(X75) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_751])]) ).
fof(f2562,plain,
( ! [X73,X76,X74,X75] :
( ~ ordinal(X73)
| ordinal_subset(X74,X73)
| ~ ordinal(X74)
| ~ empty(X74)
| in(sK6(X75,X73,X76),X76)
| sP0(X75,X73,X76)
| ~ empty(X75) )
| ~ spl20_180
| ~ spl20_234 ),
inference(resolution,[],[f2501,f1566]) ).
fof(f20100,plain,
( spl20_750
| ~ spl20_178
| ~ spl20_234 ),
inference(avatar_split_clause,[],[f2561,f2500,f1557,f20098]) ).
fof(f20098,plain,
( spl20_750
<=> ! [X69,X71,X70,X72] :
( ~ ordinal(X69)
| ordinal_subset(X70,X69)
| ~ ordinal(X70)
| ~ empty(X70)
| in(sK6(X71,X69,X72),X71)
| sP0(X71,X69,X72)
| ~ empty(X72) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_750])]) ).
fof(f2561,plain,
( ! [X72,X70,X71,X69] :
( ~ ordinal(X69)
| ordinal_subset(X70,X69)
| ~ ordinal(X70)
| ~ empty(X70)
| in(sK6(X71,X69,X72),X71)
| sP0(X71,X69,X72)
| ~ empty(X72) )
| ~ spl20_178
| ~ spl20_234 ),
inference(resolution,[],[f2501,f1558]) ).
fof(f20096,plain,
( spl20_749
| ~ spl20_180
| ~ spl20_234 ),
inference(avatar_split_clause,[],[f2555,f2500,f1565,f20094]) ).
fof(f20094,plain,
( spl20_749
<=> ! [X48,X47,X46,X45] :
( ~ ordinal(X45)
| ordinal_subset(X46,X45)
| ~ ordinal(X46)
| ~ empty(X46)
| in(sK6(X47,X48,X45),X48)
| sP0(X47,X48,X45)
| ~ empty(X47) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_749])]) ).
fof(f2555,plain,
( ! [X48,X46,X47,X45] :
( ~ ordinal(X45)
| ordinal_subset(X46,X45)
| ~ ordinal(X46)
| ~ empty(X46)
| in(sK6(X47,X48,X45),X48)
| sP0(X47,X48,X45)
| ~ empty(X47) )
| ~ spl20_180
| ~ spl20_234 ),
inference(resolution,[],[f2501,f1566]) ).
fof(f20092,plain,
( spl20_748
| ~ spl20_179
| ~ spl20_234 ),
inference(avatar_split_clause,[],[f2554,f2500,f1561,f20090]) ).
fof(f20090,plain,
( spl20_748
<=> ! [X41,X42,X44,X43] :
( ~ ordinal(X41)
| ordinal_subset(X42,X41)
| ~ ordinal(X42)
| ~ empty(X42)
| in(sK6(X43,X44,X41),X43)
| sP0(X43,X44,X41)
| ~ empty(X44) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_748])]) ).
fof(f2554,plain,
( ! [X41,X44,X42,X43] :
( ~ ordinal(X41)
| ordinal_subset(X42,X41)
| ~ ordinal(X42)
| ~ empty(X42)
| in(sK6(X43,X44,X41),X43)
| sP0(X43,X44,X41)
| ~ empty(X44) )
| ~ spl20_179
| ~ spl20_234 ),
inference(resolution,[],[f2501,f1562]) ).
fof(f20088,plain,
( spl20_747
| ~ spl20_179
| ~ spl20_223 ),
inference(avatar_split_clause,[],[f2360,f2310,f1561,f20086]) ).
fof(f20086,plain,
( spl20_747
<=> ! [X64,X62,X63] :
( ~ empty(X62)
| epsilon_transitive(powerset(X62))
| in(sK6(sK3(powerset(X62)),X63,X64),X64)
| sP0(sK3(powerset(X62)),X63,X64)
| ~ empty(X63) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_747])]) ).
fof(f2360,plain,
( ! [X62,X63,X64] :
( ~ empty(X62)
| epsilon_transitive(powerset(X62))
| in(sK6(sK3(powerset(X62)),X63,X64),X64)
| sP0(sK3(powerset(X62)),X63,X64)
| ~ empty(X63) )
| ~ spl20_179
| ~ spl20_223 ),
inference(resolution,[],[f2311,f1562]) ).
fof(f20084,plain,
( spl20_746
| ~ spl20_178
| ~ spl20_223 ),
inference(avatar_split_clause,[],[f2359,f2310,f1557,f20082]) ).
fof(f20082,plain,
( spl20_746
<=> ! [X60,X59,X61] :
( ~ empty(X59)
| epsilon_transitive(powerset(X59))
| in(sK6(sK3(powerset(X59)),X60,X61),X60)
| sP0(sK3(powerset(X59)),X60,X61)
| ~ empty(X61) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_746])]) ).
fof(f2359,plain,
( ! [X59,X60,X61] :
( ~ empty(X59)
| epsilon_transitive(powerset(X59))
| in(sK6(sK3(powerset(X59)),X60,X61),X60)
| sP0(sK3(powerset(X59)),X60,X61)
| ~ empty(X61) )
| ~ spl20_178
| ~ spl20_223 ),
inference(resolution,[],[f2311,f1558]) ).
fof(f20080,plain,
( spl20_745
| ~ spl20_180
| ~ spl20_223 ),
inference(avatar_split_clause,[],[f2353,f2310,f1565,f20078]) ).
fof(f20078,plain,
( spl20_745
<=> ! [X41,X43,X42] :
( ~ empty(X41)
| epsilon_transitive(powerset(X41))
| in(sK6(X42,sK3(powerset(X41)),X43),X43)
| sP0(X42,sK3(powerset(X41)),X43)
| ~ empty(X42) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_745])]) ).
fof(f2353,plain,
( ! [X41,X42,X43] :
( ~ empty(X41)
| epsilon_transitive(powerset(X41))
| in(sK6(X42,sK3(powerset(X41)),X43),X43)
| sP0(X42,sK3(powerset(X41)),X43)
| ~ empty(X42) )
| ~ spl20_180
| ~ spl20_223 ),
inference(resolution,[],[f2311,f1566]) ).
fof(f20076,plain,
( spl20_744
| ~ spl20_178
| ~ spl20_223 ),
inference(avatar_split_clause,[],[f2352,f2310,f1557,f20074]) ).
fof(f20074,plain,
( spl20_744
<=> ! [X38,X40,X39] :
( ~ empty(X38)
| epsilon_transitive(powerset(X38))
| in(sK6(X39,sK3(powerset(X38)),X40),X39)
| sP0(X39,sK3(powerset(X38)),X40)
| ~ empty(X40) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_744])]) ).
fof(f2352,plain,
( ! [X40,X38,X39] :
( ~ empty(X38)
| epsilon_transitive(powerset(X38))
| in(sK6(X39,sK3(powerset(X38)),X40),X39)
| sP0(X39,sK3(powerset(X38)),X40)
| ~ empty(X40) )
| ~ spl20_178
| ~ spl20_223 ),
inference(resolution,[],[f2311,f1558]) ).
fof(f20072,plain,
( spl20_743
| ~ spl20_180
| ~ spl20_223 ),
inference(avatar_split_clause,[],[f2346,f2310,f1565,f20070]) ).
fof(f20070,plain,
( spl20_743
<=> ! [X22,X20,X21] :
( ~ empty(X20)
| epsilon_transitive(powerset(X20))
| in(sK6(X21,X22,sK3(powerset(X20))),X22)
| sP0(X21,X22,sK3(powerset(X20)))
| ~ empty(X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_743])]) ).
fof(f2346,plain,
( ! [X21,X22,X20] :
( ~ empty(X20)
| epsilon_transitive(powerset(X20))
| in(sK6(X21,X22,sK3(powerset(X20))),X22)
| sP0(X21,X22,sK3(powerset(X20)))
| ~ empty(X21) )
| ~ spl20_180
| ~ spl20_223 ),
inference(resolution,[],[f2311,f1566]) ).
fof(f20005,plain,
( spl20_742
| ~ spl20_179
| ~ spl20_223 ),
inference(avatar_split_clause,[],[f2345,f2310,f1561,f20003]) ).
fof(f20003,plain,
( spl20_742
<=> ! [X18,X17,X19] :
( ~ empty(X17)
| epsilon_transitive(powerset(X17))
| in(sK6(X18,X19,sK3(powerset(X17))),X18)
| sP0(X18,X19,sK3(powerset(X17)))
| ~ empty(X19) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_742])]) ).
fof(f2345,plain,
( ! [X18,X19,X17] :
( ~ empty(X17)
| epsilon_transitive(powerset(X17))
| in(sK6(X18,X19,sK3(powerset(X17))),X18)
| sP0(X18,X19,sK3(powerset(X17)))
| ~ empty(X19) )
| ~ spl20_179
| ~ spl20_223 ),
inference(resolution,[],[f2311,f1562]) ).
fof(f20001,plain,
( spl20_741
| ~ spl20_104
| ~ spl20_223 ),
inference(avatar_split_clause,[],[f2339,f2310,f890,f19999]) ).
fof(f19999,plain,
( spl20_741
<=> ! [X6,X7] :
( ~ empty(X6)
| epsilon_transitive(powerset(X6))
| in(sK3(powerset(X6)),X7)
| sK3(powerset(X6)) = X7
| ~ ordinal(sK3(powerset(X6)))
| ~ ordinal(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_741])]) ).
fof(f2339,plain,
( ! [X6,X7] :
( ~ empty(X6)
| epsilon_transitive(powerset(X6))
| in(sK3(powerset(X6)),X7)
| sK3(powerset(X6)) = X7
| ~ ordinal(sK3(powerset(X6)))
| ~ ordinal(X7) )
| ~ spl20_104
| ~ spl20_223 ),
inference(resolution,[],[f2311,f891]) ).
fof(f19997,plain,
( spl20_740
| ~ spl20_167
| ~ spl20_223 ),
inference(avatar_split_clause,[],[f2337,f2310,f1371,f19995]) ).
fof(f19995,plain,
( spl20_740
<=> ! [X2,X3] :
( ~ empty(X2)
| epsilon_transitive(powerset(X2))
| sK3(powerset(X2)) = X3
| ~ ordinal(sK3(powerset(X2)))
| ~ ordinal(X3)
| element(sK3(powerset(X2)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_740])]) ).
fof(f2337,plain,
( ! [X2,X3] :
( ~ empty(X2)
| epsilon_transitive(powerset(X2))
| sK3(powerset(X2)) = X3
| ~ ordinal(sK3(powerset(X2)))
| ~ ordinal(X3)
| element(sK3(powerset(X2)),X3) )
| ~ spl20_167
| ~ spl20_223 ),
inference(resolution,[],[f2311,f1372]) ).
fof(f19819,plain,
( spl20_297
| ~ spl20_153
| ~ spl20_691 ),
inference(avatar_split_clause,[],[f19626,f18308,f1230,f3590]) ).
fof(f18308,plain,
( spl20_691
<=> in(sK1,singleton(sK8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_691])]) ).
fof(f19626,plain,
( sK1 = sK8
| ~ spl20_153
| ~ spl20_691 ),
inference(resolution,[],[f18310,f1231]) ).
fof(f18310,plain,
( in(sK1,singleton(sK8))
| ~ spl20_691 ),
inference(avatar_component_clause,[],[f18308]) ).
fof(f19161,plain,
( spl20_739
| ~ spl20_75
| ~ spl20_322 ),
inference(avatar_split_clause,[],[f4678,f4415,f653,f19159]) ).
fof(f19159,plain,
( spl20_739
<=> ! [X25,X24,X26] :
( subset(sK6(X24,X25,X26),X25)
| ~ empty(X24)
| sP0(X24,X25,X26)
| ~ epsilon_transitive(X25)
| ~ in(X26,sK6(X24,X25,X26)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_739])]) ).
fof(f4678,plain,
( ! [X26,X24,X25] :
( subset(sK6(X24,X25,X26),X25)
| ~ empty(X24)
| sP0(X24,X25,X26)
| ~ epsilon_transitive(X25)
| ~ in(X26,sK6(X24,X25,X26)) )
| ~ spl20_75
| ~ spl20_322 ),
inference(resolution,[],[f4416,f654]) ).
fof(f19156,plain,
( spl20_738
| ~ spl20_75
| ~ spl20_321 ),
inference(avatar_split_clause,[],[f4650,f4411,f653,f19154]) ).
fof(f19154,plain,
( spl20_738
<=> ! [X25,X24,X23] :
( subset(sK6(X23,X24,X25),X25)
| ~ empty(X23)
| sP0(X23,X24,X25)
| ~ epsilon_transitive(X25)
| ~ in(X24,sK6(X23,X24,X25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_738])]) ).
fof(f4650,plain,
( ! [X24,X25,X23] :
( subset(sK6(X23,X24,X25),X25)
| ~ empty(X23)
| sP0(X23,X24,X25)
| ~ epsilon_transitive(X25)
| ~ in(X24,sK6(X23,X24,X25)) )
| ~ spl20_75
| ~ spl20_321 ),
inference(resolution,[],[f4412,f654]) ).
fof(f19152,plain,
( spl20_737
| ~ spl20_75
| ~ spl20_320 ),
inference(avatar_split_clause,[],[f4622,f4407,f653,f19150]) ).
fof(f19150,plain,
( spl20_737
<=> ! [X25,X24,X26] :
( subset(sK6(X24,X25,X26),X24)
| ~ empty(X25)
| sP0(X24,X25,X26)
| ~ epsilon_transitive(X24)
| ~ in(X26,sK6(X24,X25,X26)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_737])]) ).
fof(f4622,plain,
( ! [X26,X24,X25] :
( subset(sK6(X24,X25,X26),X24)
| ~ empty(X25)
| sP0(X24,X25,X26)
| ~ epsilon_transitive(X24)
| ~ in(X26,sK6(X24,X25,X26)) )
| ~ spl20_75
| ~ spl20_320 ),
inference(resolution,[],[f4408,f654]) ).
fof(f19148,plain,
( spl20_736
| ~ spl20_75
| ~ spl20_319 ),
inference(avatar_split_clause,[],[f4594,f4403,f653,f19146]) ).
fof(f19146,plain,
( spl20_736
<=> ! [X25,X24,X23] :
( subset(sK6(X23,X24,X25),X25)
| ~ empty(X24)
| sP0(X23,X24,X25)
| ~ epsilon_transitive(X25)
| ~ in(X23,sK6(X23,X24,X25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_736])]) ).
fof(f4594,plain,
( ! [X24,X25,X23] :
( subset(sK6(X23,X24,X25),X25)
| ~ empty(X24)
| sP0(X23,X24,X25)
| ~ epsilon_transitive(X25)
| ~ in(X23,sK6(X23,X24,X25)) )
| ~ spl20_75
| ~ spl20_319 ),
inference(resolution,[],[f4404,f654]) ).
fof(f19144,plain,
( spl20_735
| ~ spl20_75
| ~ spl20_318 ),
inference(avatar_split_clause,[],[f4566,f4399,f653,f19142]) ).
fof(f19142,plain,
( spl20_735
<=> ! [X24,X25,X23] :
( subset(sK6(X23,X24,X25),X23)
| ~ empty(X25)
| sP0(X23,X24,X25)
| ~ epsilon_transitive(X23)
| ~ in(X24,sK6(X23,X24,X25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_735])]) ).
fof(f4566,plain,
( ! [X24,X25,X23] :
( subset(sK6(X23,X24,X25),X23)
| ~ empty(X25)
| sP0(X23,X24,X25)
| ~ epsilon_transitive(X23)
| ~ in(X24,sK6(X23,X24,X25)) )
| ~ spl20_75
| ~ spl20_318 ),
inference(resolution,[],[f4400,f654]) ).
fof(f19140,plain,
( spl20_734
| ~ spl20_75
| ~ spl20_317 ),
inference(avatar_split_clause,[],[f4538,f4395,f653,f19138]) ).
fof(f19138,plain,
( spl20_734
<=> ! [X25,X24,X23] :
( subset(sK6(X23,X24,X25),X24)
| ~ empty(X25)
| sP0(X23,X24,X25)
| ~ epsilon_transitive(X24)
| ~ in(X23,sK6(X23,X24,X25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_734])]) ).
fof(f4538,plain,
( ! [X24,X25,X23] :
( subset(sK6(X23,X24,X25),X24)
| ~ empty(X25)
| sP0(X23,X24,X25)
| ~ epsilon_transitive(X24)
| ~ in(X23,sK6(X23,X24,X25)) )
| ~ spl20_75
| ~ spl20_317 ),
inference(resolution,[],[f4396,f654]) ).
fof(f19136,plain,
( spl20_733
| ~ spl20_75
| ~ spl20_316 ),
inference(avatar_split_clause,[],[f4510,f4391,f653,f19134]) ).
fof(f19134,plain,
( spl20_733
<=> ! [X16,X17] :
( sP0(sK4(powerset(X16)),sK4(powerset(X16)),X17)
| ~ empty(X16)
| ~ in(X17,sK6(sK4(powerset(X16)),sK4(powerset(X16)),X17)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_733])]) ).
fof(f4510,plain,
( ! [X16,X17] :
( sP0(sK4(powerset(X16)),sK4(powerset(X16)),X17)
| ~ empty(X16)
| ~ in(X17,sK6(sK4(powerset(X16)),sK4(powerset(X16)),X17)) )
| ~ spl20_75
| ~ spl20_316 ),
inference(resolution,[],[f4392,f654]) ).
fof(f19132,plain,
( spl20_732
| ~ spl20_97
| ~ spl20_315 ),
inference(avatar_split_clause,[],[f4501,f4387,f846,f19130]) ).
fof(f19130,plain,
( spl20_732
<=> ! [X6,X7] :
( ~ ordinal(sK4(powerset(X6)))
| ~ ordinal(X7)
| sK4(powerset(X6)) = X7
| ~ epsilon_transitive(X7)
| ~ empty(X6)
| ordinal_subset(sK4(powerset(X6)),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_732])]) ).
fof(f4387,plain,
( spl20_315
<=> ! [X13,X14] :
( sK4(powerset(X13)) = X14
| ~ ordinal(sK4(powerset(X13)))
| ~ ordinal(X14)
| subset(sK4(powerset(X13)),X14)
| ~ epsilon_transitive(X14)
| ~ empty(X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_315])]) ).
fof(f4501,plain,
( ! [X6,X7] :
( ~ ordinal(sK4(powerset(X6)))
| ~ ordinal(X7)
| sK4(powerset(X6)) = X7
| ~ epsilon_transitive(X7)
| ~ empty(X6)
| ordinal_subset(sK4(powerset(X6)),X7) )
| ~ spl20_97
| ~ spl20_315 ),
inference(duplicate_literal_removal,[],[f4496]) ).
fof(f4496,plain,
( ! [X6,X7] :
( ~ ordinal(sK4(powerset(X6)))
| ~ ordinal(X7)
| sK4(powerset(X6)) = X7
| ~ epsilon_transitive(X7)
| ~ empty(X6)
| ordinal_subset(sK4(powerset(X6)),X7)
| ~ ordinal(X7)
| ~ ordinal(sK4(powerset(X6))) )
| ~ spl20_97
| ~ spl20_315 ),
inference(resolution,[],[f4388,f847]) ).
fof(f4388,plain,
( ! [X14,X13] :
( subset(sK4(powerset(X13)),X14)
| ~ ordinal(sK4(powerset(X13)))
| ~ ordinal(X14)
| sK4(powerset(X13)) = X14
| ~ epsilon_transitive(X14)
| ~ empty(X13) )
| ~ spl20_315 ),
inference(avatar_component_clause,[],[f4387]) ).
fof(f19128,plain,
( spl20_731
| ~ spl20_91
| ~ spl20_315 ),
inference(avatar_split_clause,[],[f4500,f4387,f811,f19126]) ).
fof(f19126,plain,
( spl20_731
<=> ! [X9,X8] :
( ~ ordinal(sK4(powerset(X8)))
| ~ ordinal(X9)
| sK4(powerset(X8)) = X9
| ~ epsilon_transitive(X9)
| ~ empty(X8)
| ~ subset(X9,sK4(powerset(X8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_731])]) ).
fof(f4500,plain,
( ! [X8,X9] :
( ~ ordinal(sK4(powerset(X8)))
| ~ ordinal(X9)
| sK4(powerset(X8)) = X9
| ~ epsilon_transitive(X9)
| ~ empty(X8)
| ~ subset(X9,sK4(powerset(X8))) )
| ~ spl20_91
| ~ spl20_315 ),
inference(duplicate_literal_removal,[],[f4497]) ).
fof(f4497,plain,
( ! [X8,X9] :
( ~ ordinal(sK4(powerset(X8)))
| ~ ordinal(X9)
| sK4(powerset(X8)) = X9
| ~ epsilon_transitive(X9)
| ~ empty(X8)
| sK4(powerset(X8)) = X9
| ~ subset(X9,sK4(powerset(X8))) )
| ~ spl20_91
| ~ spl20_315 ),
inference(resolution,[],[f4388,f812]) ).
fof(f19124,plain,
( spl20_730
| ~ spl20_153
| ~ spl20_303 ),
inference(avatar_split_clause,[],[f4091,f3637,f1230,f19122]) ).
fof(f19122,plain,
( spl20_730
<=> ! [X34,X36,X35] :
( sP0(X34,sK4(powerset(X35)),singleton(X36))
| ~ empty(X34)
| ~ empty(X35)
| sK6(X34,sK4(powerset(X35)),singleton(X36)) = X36 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_730])]) ).
fof(f4091,plain,
( ! [X36,X34,X35] :
( sP0(X34,sK4(powerset(X35)),singleton(X36))
| ~ empty(X34)
| ~ empty(X35)
| sK6(X34,sK4(powerset(X35)),singleton(X36)) = X36 )
| ~ spl20_153
| ~ spl20_303 ),
inference(resolution,[],[f3638,f1231]) ).
fof(f19120,plain,
( spl20_729
| ~ spl20_88
| ~ spl20_303 ),
inference(avatar_split_clause,[],[f4086,f3637,f772,f19118]) ).
fof(f19118,plain,
( spl20_729
<=> ! [X20,X18,X19] :
( sP0(X18,sK4(powerset(X19)),X20)
| ~ empty(X18)
| ~ empty(X19)
| subset(sK6(X18,sK4(powerset(X19)),X20),X20)
| ~ epsilon_transitive(X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_729])]) ).
fof(f4086,plain,
( ! [X18,X19,X20] :
( sP0(X18,sK4(powerset(X19)),X20)
| ~ empty(X18)
| ~ empty(X19)
| subset(sK6(X18,sK4(powerset(X19)),X20),X20)
| ~ epsilon_transitive(X20) )
| ~ spl20_88
| ~ spl20_303 ),
inference(resolution,[],[f3638,f773]) ).
fof(f19116,plain,
( spl20_728
| ~ spl20_203
| ~ spl20_460
| ~ spl20_533 ),
inference(avatar_split_clause,[],[f14584,f14532,f12625,f2084,f19113]) ).
fof(f19113,plain,
( spl20_728
<=> ordinal_subset(sK1,singleton(sK8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_728])]) ).
fof(f14584,plain,
( ordinal_subset(sK1,singleton(sK8))
| ~ spl20_203
| ~ spl20_460
| ~ spl20_533 ),
inference(forward_demodulation,[],[f14567,f2086]) ).
fof(f14567,plain,
( ordinal_subset(sK1,succ(sK8))
| ~ spl20_460
| ~ spl20_533 ),
inference(superposition,[],[f12627,f14534]) ).
fof(f19111,plain,
( spl20_727
| ~ spl20_88
| ~ spl20_301 ),
inference(avatar_split_clause,[],[f4053,f3629,f772,f19109]) ).
fof(f19109,plain,
( spl20_727
<=> ! [X20,X18,X19] :
( element(sK6(X18,X19,X20),X19)
| ~ empty(X18)
| sP0(X18,X19,X20)
| subset(sK6(X18,X19,X20),X20)
| ~ epsilon_transitive(X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_727])]) ).
fof(f4053,plain,
( ! [X18,X19,X20] :
( element(sK6(X18,X19,X20),X19)
| ~ empty(X18)
| sP0(X18,X19,X20)
| subset(sK6(X18,X19,X20),X20)
| ~ epsilon_transitive(X20) )
| ~ spl20_88
| ~ spl20_301 ),
inference(resolution,[],[f3630,f773]) ).
fof(f19107,plain,
( spl20_726
| ~ spl20_153
| ~ spl20_300 ),
inference(avatar_split_clause,[],[f4033,f3625,f1230,f19105]) ).
fof(f19105,plain,
( spl20_726
<=> ! [X34,X35,X33] :
( sP0(X33,singleton(X34),sK4(powerset(X35)))
| ~ empty(X33)
| ~ empty(X35)
| sK6(X33,singleton(X34),sK4(powerset(X35))) = X34 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_726])]) ).
fof(f4033,plain,
( ! [X34,X35,X33] :
( sP0(X33,singleton(X34),sK4(powerset(X35)))
| ~ empty(X33)
| ~ empty(X35)
| sK6(X33,singleton(X34),sK4(powerset(X35))) = X34 )
| ~ spl20_153
| ~ spl20_300 ),
inference(resolution,[],[f3626,f1231]) ).
fof(f19103,plain,
( spl20_725
| ~ spl20_88
| ~ spl20_300 ),
inference(avatar_split_clause,[],[f4028,f3625,f772,f19101]) ).
fof(f19101,plain,
( spl20_725
<=> ! [X18,X17,X19] :
( sP0(X17,X18,sK4(powerset(X19)))
| ~ empty(X17)
| ~ empty(X19)
| subset(sK6(X17,X18,sK4(powerset(X19))),X18)
| ~ epsilon_transitive(X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_725])]) ).
fof(f4028,plain,
( ! [X18,X19,X17] :
( sP0(X17,X18,sK4(powerset(X19)))
| ~ empty(X17)
| ~ empty(X19)
| subset(sK6(X17,X18,sK4(powerset(X19))),X18)
| ~ epsilon_transitive(X18) )
| ~ spl20_88
| ~ spl20_300 ),
inference(resolution,[],[f3626,f773]) ).
fof(f19099,plain,
( spl20_724
| ~ spl20_88
| ~ spl20_298 ),
inference(avatar_split_clause,[],[f4000,f3617,f772,f19097]) ).
fof(f19097,plain,
( spl20_724
<=> ! [X18,X17,X19] :
( element(sK6(X17,X18,X19),X19)
| ~ empty(X17)
| sP0(X17,X18,X19)
| subset(sK6(X17,X18,X19),X18)
| ~ epsilon_transitive(X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_724])]) ).
fof(f4000,plain,
( ! [X18,X19,X17] :
( element(sK6(X17,X18,X19),X19)
| ~ empty(X17)
| sP0(X17,X18,X19)
| subset(sK6(X17,X18,X19),X18)
| ~ epsilon_transitive(X18) )
| ~ spl20_88
| ~ spl20_298 ),
inference(resolution,[],[f3618,f773]) ).
fof(f19095,plain,
( spl20_723
| ~ spl20_153
| ~ spl20_296 ),
inference(avatar_split_clause,[],[f3980,f3586,f1230,f19093]) ).
fof(f19093,plain,
( spl20_723
<=> ! [X34,X36,X35] :
( sP0(sK4(powerset(X34)),X35,singleton(X36))
| ~ empty(X35)
| ~ empty(X34)
| sK6(sK4(powerset(X34)),X35,singleton(X36)) = X36 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_723])]) ).
fof(f3980,plain,
( ! [X36,X34,X35] :
( sP0(sK4(powerset(X34)),X35,singleton(X36))
| ~ empty(X35)
| ~ empty(X34)
| sK6(sK4(powerset(X34)),X35,singleton(X36)) = X36 )
| ~ spl20_153
| ~ spl20_296 ),
inference(resolution,[],[f3587,f1231]) ).
fof(f19091,plain,
( spl20_722
| ~ spl20_88
| ~ spl20_296 ),
inference(avatar_split_clause,[],[f3975,f3586,f772,f19089]) ).
fof(f19089,plain,
( spl20_722
<=> ! [X20,X18,X19] :
( sP0(sK4(powerset(X18)),X19,X20)
| ~ empty(X19)
| ~ empty(X18)
| subset(sK6(sK4(powerset(X18)),X19,X20),X20)
| ~ epsilon_transitive(X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_722])]) ).
fof(f3975,plain,
( ! [X18,X19,X20] :
( sP0(sK4(powerset(X18)),X19,X20)
| ~ empty(X19)
| ~ empty(X18)
| subset(sK6(sK4(powerset(X18)),X19,X20),X20)
| ~ epsilon_transitive(X20) )
| ~ spl20_88
| ~ spl20_296 ),
inference(resolution,[],[f3587,f773]) ).
fof(f19087,plain,
( spl20_721
| ~ spl20_88
| ~ spl20_294 ),
inference(avatar_split_clause,[],[f3947,f3578,f772,f19085]) ).
fof(f19085,plain,
( spl20_721
<=> ! [X20,X18,X19] :
( element(sK6(X18,X19,X20),X18)
| ~ empty(X19)
| sP0(X18,X19,X20)
| subset(sK6(X18,X19,X20),X20)
| ~ epsilon_transitive(X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_721])]) ).
fof(f3947,plain,
( ! [X18,X19,X20] :
( element(sK6(X18,X19,X20),X18)
| ~ empty(X19)
| sP0(X18,X19,X20)
| subset(sK6(X18,X19,X20),X20)
| ~ epsilon_transitive(X20) )
| ~ spl20_88
| ~ spl20_294 ),
inference(resolution,[],[f3579,f773]) ).
fof(f19083,plain,
( spl20_720
| ~ spl20_153
| ~ spl20_293 ),
inference(avatar_split_clause,[],[f3927,f3574,f1230,f19081]) ).
fof(f19081,plain,
( spl20_720
<=> ! [X34,X35,X33] :
( sP0(singleton(X33),X34,sK4(powerset(X35)))
| ~ empty(X34)
| ~ empty(X35)
| sK6(singleton(X33),X34,sK4(powerset(X35))) = X33 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_720])]) ).
fof(f3927,plain,
( ! [X34,X35,X33] :
( sP0(singleton(X33),X34,sK4(powerset(X35)))
| ~ empty(X34)
| ~ empty(X35)
| sK6(singleton(X33),X34,sK4(powerset(X35))) = X33 )
| ~ spl20_153
| ~ spl20_293 ),
inference(resolution,[],[f3575,f1231]) ).
fof(f19079,plain,
( spl20_719
| ~ spl20_88
| ~ spl20_293 ),
inference(avatar_split_clause,[],[f3922,f3574,f772,f19077]) ).
fof(f19077,plain,
( spl20_719
<=> ! [X18,X17,X19] :
( sP0(X17,X18,sK4(powerset(X19)))
| ~ empty(X18)
| ~ empty(X19)
| subset(sK6(X17,X18,sK4(powerset(X19))),X17)
| ~ epsilon_transitive(X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_719])]) ).
fof(f3922,plain,
( ! [X18,X19,X17] :
( sP0(X17,X18,sK4(powerset(X19)))
| ~ empty(X18)
| ~ empty(X19)
| subset(sK6(X17,X18,sK4(powerset(X19))),X17)
| ~ epsilon_transitive(X17) )
| ~ spl20_88
| ~ spl20_293 ),
inference(resolution,[],[f3575,f773]) ).
fof(f19075,plain,
( spl20_718
| ~ spl20_88
| ~ spl20_291 ),
inference(avatar_split_clause,[],[f3894,f3566,f772,f19073]) ).
fof(f19073,plain,
( spl20_718
<=> ! [X18,X17,X19] :
( element(sK6(X17,X18,X19),X19)
| ~ empty(X18)
| sP0(X17,X18,X19)
| subset(sK6(X17,X18,X19),X17)
| ~ epsilon_transitive(X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_718])]) ).
fof(f3894,plain,
( ! [X18,X19,X17] :
( element(sK6(X17,X18,X19),X19)
| ~ empty(X18)
| sP0(X17,X18,X19)
| subset(sK6(X17,X18,X19),X17)
| ~ epsilon_transitive(X17) )
| ~ spl20_88
| ~ spl20_291 ),
inference(resolution,[],[f3567,f773]) ).
fof(f19071,plain,
( spl20_717
| ~ spl20_203
| ~ spl20_458
| ~ spl20_533 ),
inference(avatar_split_clause,[],[f14582,f14532,f12591,f2084,f19068]) ).
fof(f19068,plain,
( spl20_717
<=> subset(sK1,singleton(sK8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_717])]) ).
fof(f14582,plain,
( subset(sK1,singleton(sK8))
| ~ spl20_203
| ~ spl20_458
| ~ spl20_533 ),
inference(forward_demodulation,[],[f14565,f2086]) ).
fof(f14565,plain,
( subset(sK1,succ(sK8))
| ~ spl20_458
| ~ spl20_533 ),
inference(superposition,[],[f12593,f14534]) ).
fof(f19066,plain,
( spl20_716
| ~ spl20_153
| ~ spl20_290 ),
inference(avatar_split_clause,[],[f3874,f3562,f1230,f19064]) ).
fof(f19064,plain,
( spl20_716
<=> ! [X34,X35,X33] :
( sP0(sK4(powerset(X33)),singleton(X34),X35)
| ~ empty(X35)
| ~ empty(X33)
| sK6(sK4(powerset(X33)),singleton(X34),X35) = X34 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_716])]) ).
fof(f3874,plain,
( ! [X34,X35,X33] :
( sP0(sK4(powerset(X33)),singleton(X34),X35)
| ~ empty(X35)
| ~ empty(X33)
| sK6(sK4(powerset(X33)),singleton(X34),X35) = X34 )
| ~ spl20_153
| ~ spl20_290 ),
inference(resolution,[],[f3563,f1231]) ).
fof(f19062,plain,
( spl20_715
| ~ spl20_88
| ~ spl20_290 ),
inference(avatar_split_clause,[],[f3869,f3562,f772,f19060]) ).
fof(f19060,plain,
( spl20_715
<=> ! [X18,X17,X19] :
( sP0(sK4(powerset(X17)),X18,X19)
| ~ empty(X19)
| ~ empty(X17)
| subset(sK6(sK4(powerset(X17)),X18,X19),X18)
| ~ epsilon_transitive(X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_715])]) ).
fof(f3869,plain,
( ! [X18,X19,X17] :
( sP0(sK4(powerset(X17)),X18,X19)
| ~ empty(X19)
| ~ empty(X17)
| subset(sK6(sK4(powerset(X17)),X18,X19),X18)
| ~ epsilon_transitive(X18) )
| ~ spl20_88
| ~ spl20_290 ),
inference(resolution,[],[f3563,f773]) ).
fof(f19058,plain,
( spl20_714
| ~ spl20_88
| ~ spl20_288 ),
inference(avatar_split_clause,[],[f3841,f3554,f772,f19056]) ).
fof(f19056,plain,
( spl20_714
<=> ! [X18,X17,X19] :
( element(sK6(X17,X18,X19),X17)
| ~ empty(X19)
| sP0(X17,X18,X19)
| subset(sK6(X17,X18,X19),X18)
| ~ epsilon_transitive(X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_714])]) ).
fof(f3841,plain,
( ! [X18,X19,X17] :
( element(sK6(X17,X18,X19),X17)
| ~ empty(X19)
| sP0(X17,X18,X19)
| subset(sK6(X17,X18,X19),X18)
| ~ epsilon_transitive(X18) )
| ~ spl20_88
| ~ spl20_288 ),
inference(resolution,[],[f3555,f773]) ).
fof(f19054,plain,
( spl20_713
| ~ spl20_153
| ~ spl20_287 ),
inference(avatar_split_clause,[],[f3821,f3550,f1230,f19052]) ).
fof(f19052,plain,
( spl20_713
<=> ! [X34,X35,X33] :
( sP0(singleton(X33),sK4(powerset(X34)),X35)
| ~ empty(X35)
| ~ empty(X34)
| sK6(singleton(X33),sK4(powerset(X34)),X35) = X33 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_713])]) ).
fof(f3821,plain,
( ! [X34,X35,X33] :
( sP0(singleton(X33),sK4(powerset(X34)),X35)
| ~ empty(X35)
| ~ empty(X34)
| sK6(singleton(X33),sK4(powerset(X34)),X35) = X33 )
| ~ spl20_153
| ~ spl20_287 ),
inference(resolution,[],[f3551,f1231]) ).
fof(f19050,plain,
( spl20_712
| ~ spl20_88
| ~ spl20_287 ),
inference(avatar_split_clause,[],[f3816,f3550,f772,f19048]) ).
fof(f19048,plain,
( spl20_712
<=> ! [X18,X17,X19] :
( sP0(X17,sK4(powerset(X18)),X19)
| ~ empty(X19)
| ~ empty(X18)
| subset(sK6(X17,sK4(powerset(X18)),X19),X17)
| ~ epsilon_transitive(X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_712])]) ).
fof(f3816,plain,
( ! [X18,X19,X17] :
( sP0(X17,sK4(powerset(X18)),X19)
| ~ empty(X19)
| ~ empty(X18)
| subset(sK6(X17,sK4(powerset(X18)),X19),X17)
| ~ epsilon_transitive(X17) )
| ~ spl20_88
| ~ spl20_287 ),
inference(resolution,[],[f3551,f773]) ).
fof(f19046,plain,
( spl20_711
| ~ spl20_88
| ~ spl20_285 ),
inference(avatar_split_clause,[],[f3788,f3542,f772,f19044]) ).
fof(f19044,plain,
( spl20_711
<=> ! [X18,X17,X19] :
( element(sK6(X17,X18,X19),X18)
| ~ empty(X19)
| sP0(X17,X18,X19)
| subset(sK6(X17,X18,X19),X17)
| ~ epsilon_transitive(X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_711])]) ).
fof(f3788,plain,
( ! [X18,X19,X17] :
( element(sK6(X17,X18,X19),X18)
| ~ empty(X19)
| sP0(X17,X18,X19)
| subset(sK6(X17,X18,X19),X17)
| ~ epsilon_transitive(X17) )
| ~ spl20_88
| ~ spl20_285 ),
inference(resolution,[],[f3543,f773]) ).
fof(f19042,plain,
( spl20_710
| ~ spl20_88
| ~ spl20_283 ),
inference(avatar_split_clause,[],[f3738,f3534,f772,f19040]) ).
fof(f19040,plain,
( spl20_710
<=> ! [X13,X12] :
( subset(sK6(X12,X12,X13),X13)
| sP0(X12,X12,X13)
| ~ epsilon_transitive(X13)
| subset(sK6(X12,X12,X13),X12)
| ~ epsilon_transitive(X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_710])]) ).
fof(f3738,plain,
( ! [X12,X13] :
( subset(sK6(X12,X12,X13),X13)
| sP0(X12,X12,X13)
| ~ epsilon_transitive(X13)
| subset(sK6(X12,X12,X13),X12)
| ~ epsilon_transitive(X12) )
| ~ spl20_88
| ~ spl20_283 ),
inference(resolution,[],[f3535,f773]) ).
fof(f19038,plain,
( spl20_709
| ~ spl20_84
| ~ spl20_279 ),
inference(avatar_split_clause,[],[f3667,f3518,f732,f19036]) ).
fof(f19036,plain,
( spl20_709
<=> ! [X6,X7] :
( ~ ordinal(sK4(powerset(X6)))
| ~ ordinal(powerset(X7))
| sK4(powerset(X6)) = powerset(X7)
| ~ empty(X6)
| subset(sK4(powerset(X6)),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_709])]) ).
fof(f3518,plain,
( spl20_279
<=> ! [X13,X14] :
( sK4(powerset(X13)) = X14
| ~ ordinal(sK4(powerset(X13)))
| ~ ordinal(X14)
| element(sK4(powerset(X13)),X14)
| ~ empty(X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_279])]) ).
fof(f3667,plain,
( ! [X6,X7] :
( ~ ordinal(sK4(powerset(X6)))
| ~ ordinal(powerset(X7))
| sK4(powerset(X6)) = powerset(X7)
| ~ empty(X6)
| subset(sK4(powerset(X6)),X7) )
| ~ spl20_84
| ~ spl20_279 ),
inference(resolution,[],[f3519,f733]) ).
fof(f3519,plain,
( ! [X14,X13] :
( element(sK4(powerset(X13)),X14)
| ~ ordinal(sK4(powerset(X13)))
| ~ ordinal(X14)
| sK4(powerset(X13)) = X14
| ~ empty(X13) )
| ~ spl20_279 ),
inference(avatar_component_clause,[],[f3518]) ).
fof(f19034,plain,
( spl20_708
| ~ spl20_160
| ~ spl20_276 ),
inference(avatar_split_clause,[],[f3487,f3448,f1291,f19032]) ).
fof(f19032,plain,
( spl20_708
<=> ! [X2,X0,X1] :
( subset(X1,X0)
| ~ ordinal(X0)
| ~ ordinal(X1)
| ~ epsilon_transitive(X0)
| X0 = X1
| ~ epsilon_transitive(X1)
| ~ in(X2,X0)
| element(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_708])]) ).
fof(f3448,plain,
( spl20_276
<=> ! [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_276])]) ).
fof(f3487,plain,
( ! [X2,X0,X1] :
( subset(X1,X0)
| ~ ordinal(X0)
| ~ ordinal(X1)
| ~ epsilon_transitive(X0)
| X0 = X1
| ~ epsilon_transitive(X1)
| ~ in(X2,X0)
| element(X2,X1) )
| ~ spl20_160
| ~ spl20_276 ),
inference(resolution,[],[f3449,f1292]) ).
fof(f3449,plain,
( ! [X0,X1] :
( subset(X1,X0)
| subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0)
| ~ epsilon_transitive(X1)
| X0 = X1
| ~ epsilon_transitive(X0) )
| ~ spl20_276 ),
inference(avatar_component_clause,[],[f3448]) ).
fof(f19030,plain,
( spl20_707
| ~ spl20_153
| ~ spl20_271 ),
inference(avatar_split_clause,[],[f3398,f3016,f1230,f19028]) ).
fof(f19028,plain,
( spl20_707
<=> ! [X24,X23] :
( sP0(singleton(X23),singleton(X23),sK4(powerset(X24)))
| ~ empty(X24)
| sK6(singleton(X23),singleton(X23),sK4(powerset(X24))) = X23 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_707])]) ).
fof(f3398,plain,
( ! [X24,X23] :
( sP0(singleton(X23),singleton(X23),sK4(powerset(X24)))
| ~ empty(X24)
| sK6(singleton(X23),singleton(X23),sK4(powerset(X24))) = X23 )
| ~ spl20_153
| ~ spl20_271 ),
inference(resolution,[],[f3017,f1231]) ).
fof(f19026,plain,
( ~ spl20_706
| ~ spl20_203
| spl20_277
| ~ spl20_533 ),
inference(avatar_split_clause,[],[f14580,f14532,f3477,f2084,f19023]) ).
fof(f19023,plain,
( spl20_706
<=> in(singleton(sK8),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_706])]) ).
fof(f14580,plain,
( ~ in(singleton(sK8),sK1)
| ~ spl20_203
| spl20_277
| ~ spl20_533 ),
inference(forward_demodulation,[],[f14554,f2086]) ).
fof(f14554,plain,
( ~ in(succ(sK8),sK1)
| spl20_277
| ~ spl20_533 ),
inference(superposition,[],[f3478,f14534]) ).
fof(f3478,plain,
( ~ in(succ(sK2),sK1)
| spl20_277 ),
inference(avatar_component_clause,[],[f3477]) ).
fof(f19021,plain,
( spl20_705
| ~ spl20_151
| ~ spl20_269 ),
inference(avatar_split_clause,[],[f3376,f3008,f1221,f19019]) ).
fof(f19019,plain,
( spl20_705
<=> ! [X32,X33] :
( element(sK6(sK4(powerset(X32)),sK4(powerset(X32)),X33),X33)
| sP0(sK4(powerset(X32)),sK4(powerset(X32)),X33)
| ~ empty(X32) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_705])]) ).
fof(f3376,plain,
( ! [X32,X33] :
( element(sK6(sK4(powerset(X32)),sK4(powerset(X32)),X33),X33)
| sP0(sK4(powerset(X32)),sK4(powerset(X32)),X33)
| ~ empty(X32) )
| ~ spl20_151
| ~ spl20_269 ),
inference(resolution,[],[f3009,f1222]) ).
fof(f19017,plain,
( spl20_704
| ~ spl20_151
| ~ spl20_254 ),
inference(avatar_split_clause,[],[f3040,f2936,f1221,f19015]) ).
fof(f19015,plain,
( spl20_704
<=> ! [X27,X28] :
( sK4(powerset(X27)) = X28
| sK4(powerset(X27)) = singleton(X28)
| ~ ordinal(singleton(X28))
| ~ ordinal(sK4(powerset(X27)))
| ~ empty(X27) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_704])]) ).
fof(f3040,plain,
( ! [X28,X27] :
( sK4(powerset(X27)) = X28
| sK4(powerset(X27)) = singleton(X28)
| ~ ordinal(singleton(X28))
| ~ ordinal(sK4(powerset(X27)))
| ~ empty(X27) )
| ~ spl20_151
| ~ spl20_254 ),
inference(resolution,[],[f2937,f1222]) ).
fof(f19013,plain,
( spl20_703
| ~ spl20_222
| ~ spl20_253 ),
inference(avatar_split_clause,[],[f2932,f2904,f2306,f19011]) ).
fof(f19011,plain,
( spl20_703
<=> ! [X10] :
( ~ ordinal(sK4(powerset(X10)))
| ~ ordinal(X10)
| element(sK4(powerset(X10)),X10)
| sK4(powerset(X10)) = X10
| ~ epsilon_transitive(sK4(powerset(X10))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_703])]) ).
fof(f2306,plain,
( spl20_222
<=> ! [X1] :
( sK4(powerset(X1)) = X1
| ~ subset(X1,sK4(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_222])]) ).
fof(f2932,plain,
( ! [X10] :
( ~ ordinal(sK4(powerset(X10)))
| ~ ordinal(X10)
| element(sK4(powerset(X10)),X10)
| sK4(powerset(X10)) = X10
| ~ epsilon_transitive(sK4(powerset(X10))) )
| ~ spl20_222
| ~ spl20_253 ),
inference(duplicate_literal_removal,[],[f2926]) ).
fof(f2926,plain,
( ! [X10] :
( ~ ordinal(sK4(powerset(X10)))
| ~ ordinal(X10)
| element(sK4(powerset(X10)),X10)
| sK4(powerset(X10)) = X10
| ~ epsilon_transitive(sK4(powerset(X10)))
| sK4(powerset(X10)) = X10 )
| ~ spl20_222
| ~ spl20_253 ),
inference(resolution,[],[f2905,f2307]) ).
fof(f2307,plain,
( ! [X1] :
( ~ subset(X1,sK4(powerset(X1)))
| sK4(powerset(X1)) = X1 )
| ~ spl20_222 ),
inference(avatar_component_clause,[],[f2306]) ).
fof(f19009,plain,
( spl20_702
| ~ spl20_170
| ~ spl20_245 ),
inference(avatar_split_clause,[],[f2789,f2725,f1403,f19007]) ).
fof(f19007,plain,
( spl20_702
<=> ! [X2,X0,X1] :
( ~ ordinal(X0)
| ordinal_subset(X1,X0)
| ~ ordinal(X1)
| element(X2,X1)
| X0 = X2
| ~ ordinal(X2)
| subset(X0,X2)
| ~ epsilon_transitive(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_702])]) ).
fof(f2789,plain,
( ! [X2,X0,X1] :
( ~ ordinal(X0)
| ordinal_subset(X1,X0)
| ~ ordinal(X1)
| element(X2,X1)
| X0 = X2
| ~ ordinal(X2)
| subset(X0,X2)
| ~ epsilon_transitive(X2) )
| ~ spl20_170
| ~ spl20_245 ),
inference(duplicate_literal_removal,[],[f2739]) ).
fof(f2739,plain,
( ! [X2,X0,X1] :
( ~ ordinal(X0)
| ordinal_subset(X1,X0)
| ~ ordinal(X1)
| element(X2,X1)
| X0 = X2
| ~ ordinal(X0)
| ~ ordinal(X2)
| subset(X0,X2)
| ~ epsilon_transitive(X2) )
| ~ spl20_170
| ~ spl20_245 ),
inference(resolution,[],[f2726,f1404]) ).
fof(f19005,plain,
( spl20_701
| ~ spl20_157
| ~ spl20_241 ),
inference(avatar_split_clause,[],[f2694,f2529,f1267,f19003]) ).
fof(f19003,plain,
( spl20_701
<=> ! [X27,X28] :
( sP0(sK4(powerset(X27)),sK4(powerset(X27)),X28)
| ~ empty(X28)
| element(sK6(sK4(powerset(X27)),sK4(powerset(X27)),X28),X27) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_701])]) ).
fof(f2694,plain,
( ! [X28,X27] :
( sP0(sK4(powerset(X27)),sK4(powerset(X27)),X28)
| ~ empty(X28)
| element(sK6(sK4(powerset(X27)),sK4(powerset(X27)),X28),X27) )
| ~ spl20_157
| ~ spl20_241 ),
inference(resolution,[],[f2530,f1268]) ).
fof(f18943,plain,
( ~ spl20_700
| ~ spl20_203
| spl20_205
| ~ spl20_533 ),
inference(avatar_split_clause,[],[f14577,f14532,f2118,f2084,f18940]) ).
fof(f18940,plain,
( spl20_700
<=> subset(singleton(sK8),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_700])]) ).
fof(f14577,plain,
( ~ subset(singleton(sK8),sK1)
| ~ spl20_203
| spl20_205
| ~ spl20_533 ),
inference(forward_demodulation,[],[f14550,f2086]) ).
fof(f14550,plain,
( ~ subset(succ(sK8),sK1)
| spl20_205
| ~ spl20_533 ),
inference(superposition,[],[f2119,f14534]) ).
fof(f18670,plain,
( ~ spl20_699
| spl20_195
| ~ spl20_203
| ~ spl20_533 ),
inference(avatar_split_clause,[],[f14575,f14532,f2084,f2032,f18667]) ).
fof(f18667,plain,
( spl20_699
<=> element(singleton(sK8),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_699])]) ).
fof(f14575,plain,
( ~ element(singleton(sK8),sK1)
| spl20_195
| ~ spl20_203
| ~ spl20_533 ),
inference(forward_demodulation,[],[f14547,f2086]) ).
fof(f14547,plain,
( ~ element(succ(sK8),sK1)
| spl20_195
| ~ spl20_533 ),
inference(superposition,[],[f2033,f14534]) ).
fof(f18468,plain,
( spl20_698
| ~ spl20_176
| ~ spl20_203
| ~ spl20_533 ),
inference(avatar_split_clause,[],[f14574,f14532,f2084,f1447,f18465]) ).
fof(f14574,plain,
( element(sK1,singleton(sK8))
| ~ spl20_176
| ~ spl20_203
| ~ spl20_533 ),
inference(forward_demodulation,[],[f14545,f2086]) ).
fof(f14545,plain,
( element(sK1,succ(sK8))
| ~ spl20_176
| ~ spl20_533 ),
inference(superposition,[],[f1449,f14534]) ).
fof(f18335,plain,
( spl20_697
| ~ spl20_234
| ~ spl20_316 ),
inference(avatar_split_clause,[],[f4507,f4391,f2500,f18333]) ).
fof(f18333,plain,
( spl20_697
<=> ! [X9,X11,X10] :
( sP0(sK4(powerset(X9)),sK4(powerset(X9)),X10)
| ~ empty(X9)
| ~ ordinal(X10)
| ordinal_subset(X11,X10)
| ~ ordinal(X11)
| ~ empty(X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_697])]) ).
fof(f4507,plain,
( ! [X10,X11,X9] :
( sP0(sK4(powerset(X9)),sK4(powerset(X9)),X10)
| ~ empty(X9)
| ~ ordinal(X10)
| ordinal_subset(X11,X10)
| ~ ordinal(X11)
| ~ empty(X11) )
| ~ spl20_234
| ~ spl20_316 ),
inference(resolution,[],[f4392,f2501]) ).
fof(f18331,plain,
( spl20_696
| ~ spl20_75
| ~ spl20_311 ),
inference(avatar_split_clause,[],[f4356,f4126,f653,f18329]) ).
fof(f18329,plain,
( spl20_696
<=> ! [X16,X17] :
( sP0(X16,X16,singleton(X17))
| sK6(X16,X16,singleton(X17)) = X17
| ~ in(X16,sK6(X16,X16,singleton(X17))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_696])]) ).
fof(f4356,plain,
( ! [X16,X17] :
( sP0(X16,X16,singleton(X17))
| sK6(X16,X16,singleton(X17)) = X17
| ~ in(X16,sK6(X16,X16,singleton(X17))) )
| ~ spl20_75
| ~ spl20_311 ),
inference(resolution,[],[f4127,f654]) ).
fof(f18327,plain,
( spl20_695
| ~ spl20_234
| ~ spl20_303 ),
inference(avatar_split_clause,[],[f4085,f3637,f2500,f18325]) ).
fof(f18325,plain,
( spl20_695
<=> ! [X17,X14,X16,X15] :
( sP0(X14,sK4(powerset(X15)),X16)
| ~ empty(X14)
| ~ empty(X15)
| ~ ordinal(X16)
| ordinal_subset(X17,X16)
| ~ ordinal(X17)
| ~ empty(X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_695])]) ).
fof(f4085,plain,
( ! [X16,X14,X17,X15] :
( sP0(X14,sK4(powerset(X15)),X16)
| ~ empty(X14)
| ~ empty(X15)
| ~ ordinal(X16)
| ordinal_subset(X17,X16)
| ~ ordinal(X17)
| ~ empty(X17) )
| ~ spl20_234
| ~ spl20_303 ),
inference(resolution,[],[f3638,f2501]) ).
fof(f18323,plain,
( spl20_694
| ~ spl20_234
| ~ spl20_300 ),
inference(avatar_split_clause,[],[f4027,f3625,f2500,f18321]) ).
fof(f18321,plain,
( spl20_694
<=> ! [X13,X14,X16,X15] :
( sP0(X13,X14,sK4(powerset(X15)))
| ~ empty(X13)
| ~ empty(X15)
| ~ ordinal(X14)
| ordinal_subset(X16,X14)
| ~ ordinal(X16)
| ~ empty(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_694])]) ).
fof(f4027,plain,
( ! [X16,X14,X15,X13] :
( sP0(X13,X14,sK4(powerset(X15)))
| ~ empty(X13)
| ~ empty(X15)
| ~ ordinal(X14)
| ordinal_subset(X16,X14)
| ~ ordinal(X16)
| ~ empty(X16) )
| ~ spl20_234
| ~ spl20_300 ),
inference(resolution,[],[f3626,f2501]) ).
fof(f18319,plain,
( spl20_693
| ~ spl20_234
| ~ spl20_296 ),
inference(avatar_split_clause,[],[f3974,f3586,f2500,f18317]) ).
fof(f18317,plain,
( spl20_693
<=> ! [X17,X14,X16,X15] :
( sP0(sK4(powerset(X14)),X15,X16)
| ~ empty(X15)
| ~ empty(X14)
| ~ ordinal(X16)
| ordinal_subset(X17,X16)
| ~ ordinal(X17)
| ~ empty(X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_693])]) ).
fof(f3974,plain,
( ! [X16,X14,X17,X15] :
( sP0(sK4(powerset(X14)),X15,X16)
| ~ empty(X15)
| ~ empty(X14)
| ~ ordinal(X16)
| ordinal_subset(X17,X16)
| ~ ordinal(X17)
| ~ empty(X17) )
| ~ spl20_234
| ~ spl20_296 ),
inference(resolution,[],[f3587,f2501]) ).
fof(f18315,plain,
( spl20_692
| ~ spl20_234
| ~ spl20_293 ),
inference(avatar_split_clause,[],[f3921,f3574,f2500,f18313]) ).
fof(f18313,plain,
( spl20_692
<=> ! [X13,X14,X16,X15] :
( sP0(X13,X14,sK4(powerset(X15)))
| ~ empty(X14)
| ~ empty(X15)
| ~ ordinal(X13)
| ordinal_subset(X16,X13)
| ~ ordinal(X16)
| ~ empty(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_692])]) ).
fof(f3921,plain,
( ! [X16,X14,X15,X13] :
( sP0(X13,X14,sK4(powerset(X15)))
| ~ empty(X14)
| ~ empty(X15)
| ~ ordinal(X13)
| ordinal_subset(X16,X13)
| ~ ordinal(X16)
| ~ empty(X16) )
| ~ spl20_234
| ~ spl20_293 ),
inference(resolution,[],[f3575,f2501]) ).
fof(f18311,plain,
( spl20_691
| ~ spl20_3
| ~ spl20_203
| ~ spl20_533 ),
inference(avatar_split_clause,[],[f14573,f14532,f2084,f270,f18308]) ).
fof(f14573,plain,
( in(sK1,singleton(sK8))
| ~ spl20_3
| ~ spl20_203
| ~ spl20_533 ),
inference(forward_demodulation,[],[f14537,f2086]) ).
fof(f14537,plain,
( in(sK1,succ(sK8))
| ~ spl20_3
| ~ spl20_533 ),
inference(superposition,[],[f272,f14534]) ).
fof(f18306,plain,
( spl20_690
| ~ spl20_234
| ~ spl20_290 ),
inference(avatar_split_clause,[],[f3868,f3562,f2500,f18304]) ).
fof(f18304,plain,
( spl20_690
<=> ! [X13,X14,X16,X15] :
( sP0(sK4(powerset(X13)),X14,X15)
| ~ empty(X15)
| ~ empty(X13)
| ~ ordinal(X14)
| ordinal_subset(X16,X14)
| ~ ordinal(X16)
| ~ empty(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_690])]) ).
fof(f3868,plain,
( ! [X16,X14,X15,X13] :
( sP0(sK4(powerset(X13)),X14,X15)
| ~ empty(X15)
| ~ empty(X13)
| ~ ordinal(X14)
| ordinal_subset(X16,X14)
| ~ ordinal(X16)
| ~ empty(X16) )
| ~ spl20_234
| ~ spl20_290 ),
inference(resolution,[],[f3563,f2501]) ).
fof(f18302,plain,
( spl20_689
| ~ spl20_234
| ~ spl20_287 ),
inference(avatar_split_clause,[],[f3815,f3550,f2500,f18300]) ).
fof(f18300,plain,
( spl20_689
<=> ! [X13,X14,X16,X15] :
( sP0(X13,sK4(powerset(X14)),X15)
| ~ empty(X15)
| ~ empty(X14)
| ~ ordinal(X13)
| ordinal_subset(X16,X13)
| ~ ordinal(X16)
| ~ empty(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_689])]) ).
fof(f3815,plain,
( ! [X16,X14,X15,X13] :
( sP0(X13,sK4(powerset(X14)),X15)
| ~ empty(X15)
| ~ empty(X14)
| ~ ordinal(X13)
| ordinal_subset(X16,X13)
| ~ ordinal(X16)
| ~ empty(X16) )
| ~ spl20_234
| ~ spl20_287 ),
inference(resolution,[],[f3551,f2501]) ).
fof(f18298,plain,
( spl20_688
| ~ spl20_223
| ~ spl20_272 ),
inference(avatar_split_clause,[],[f3426,f3020,f2310,f18296]) ).
fof(f18296,plain,
( spl20_688
<=> ! [X29,X28] :
( element(sK6(X28,X28,sK3(powerset(X29))),X28)
| sP0(X28,X28,sK3(powerset(X29)))
| ~ empty(X29)
| epsilon_transitive(powerset(X29)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_688])]) ).
fof(f3426,plain,
( ! [X28,X29] :
( element(sK6(X28,X28,sK3(powerset(X29))),X28)
| sP0(X28,X28,sK3(powerset(X29)))
| ~ empty(X29)
| epsilon_transitive(powerset(X29)) )
| ~ spl20_223
| ~ spl20_272 ),
inference(resolution,[],[f3021,f2311]) ).
fof(f18294,plain,
( spl20_687
| ~ spl20_153
| ~ spl20_272 ),
inference(avatar_split_clause,[],[f3423,f3020,f1230,f18292]) ).
fof(f18292,plain,
( spl20_687
<=> ! [X24,X23] :
( element(sK6(X23,X23,singleton(X24)),X23)
| sP0(X23,X23,singleton(X24))
| sK6(X23,X23,singleton(X24)) = X24 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_687])]) ).
fof(f3423,plain,
( ! [X24,X23] :
( element(sK6(X23,X23,singleton(X24)),X23)
| sP0(X23,X23,singleton(X24))
| sK6(X23,X23,singleton(X24)) = X24 )
| ~ spl20_153
| ~ spl20_272 ),
inference(resolution,[],[f3021,f1231]) ).
fof(f18290,plain,
( spl20_686
| ~ spl20_234
| ~ spl20_272 ),
inference(avatar_split_clause,[],[f3417,f3020,f2500,f18288]) ).
fof(f18288,plain,
( spl20_686
<=> ! [X9,X11,X10] :
( element(sK6(X9,X9,X10),X9)
| sP0(X9,X9,X10)
| ~ ordinal(X10)
| ordinal_subset(X11,X10)
| ~ ordinal(X11)
| ~ empty(X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_686])]) ).
fof(f3417,plain,
( ! [X10,X11,X9] :
( element(sK6(X9,X9,X10),X9)
| sP0(X9,X9,X10)
| ~ ordinal(X10)
| ordinal_subset(X11,X10)
| ~ ordinal(X11)
| ~ empty(X11) )
| ~ spl20_234
| ~ spl20_272 ),
inference(resolution,[],[f3021,f2501]) ).
fof(f18286,plain,
( spl20_685
| ~ spl20_234
| ~ spl20_269 ),
inference(avatar_split_clause,[],[f3365,f3008,f2500,f18284]) ).
fof(f18284,plain,
( spl20_685
<=> ! [X9,X11,X10] :
( element(sK6(X9,X9,X10),X10)
| sP0(X9,X9,X10)
| ~ ordinal(X9)
| ordinal_subset(X11,X9)
| ~ ordinal(X11)
| ~ empty(X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_685])]) ).
fof(f3365,plain,
( ! [X10,X11,X9] :
( element(sK6(X9,X9,X10),X10)
| sP0(X9,X9,X10)
| ~ ordinal(X9)
| ordinal_subset(X11,X9)
| ~ ordinal(X11)
| ~ empty(X11) )
| ~ spl20_234
| ~ spl20_269 ),
inference(resolution,[],[f3009,f2501]) ).
fof(f18282,plain,
( spl20_684
| ~ spl20_84
| ~ spl20_269 ),
inference(avatar_split_clause,[],[f3358,f3008,f732,f18280]) ).
fof(f18280,plain,
( spl20_684
<=> ! [X6,X7] :
( in(sK6(X6,X6,powerset(X7)),X6)
| sP0(X6,X6,powerset(X7))
| subset(sK6(X6,X6,powerset(X7)),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_684])]) ).
fof(f3358,plain,
( ! [X6,X7] :
( in(sK6(X6,X6,powerset(X7)),X6)
| sP0(X6,X6,powerset(X7))
| subset(sK6(X6,X6,powerset(X7)),X7) )
| ~ spl20_84
| ~ spl20_269 ),
inference(resolution,[],[f3009,f733]) ).
fof(f18278,plain,
( spl20_683
| ~ spl20_84
| ~ spl20_263 ),
inference(avatar_split_clause,[],[f3208,f2976,f732,f18276]) ).
fof(f18276,plain,
( spl20_683
<=> ! [X6,X7] :
( in(sK6(X6,powerset(X7),X6),X6)
| sP0(X6,powerset(X7),X6)
| subset(sK6(X6,powerset(X7),X6),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_683])]) ).
fof(f3208,plain,
( ! [X6,X7] :
( in(sK6(X6,powerset(X7),X6),X6)
| sP0(X6,powerset(X7),X6)
| subset(sK6(X6,powerset(X7),X6),X7) )
| ~ spl20_84
| ~ spl20_263 ),
inference(resolution,[],[f2977,f733]) ).
fof(f18274,plain,
( spl20_682
| ~ spl20_84
| ~ spl20_259 ),
inference(avatar_split_clause,[],[f3090,f2960,f732,f18272]) ).
fof(f18272,plain,
( spl20_682
<=> ! [X6,X7] :
( in(sK6(powerset(X6),X7,X7),X7)
| sP0(powerset(X6),X7,X7)
| subset(sK6(powerset(X6),X7,X7),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_682])]) ).
fof(f3090,plain,
( ! [X6,X7] :
( in(sK6(powerset(X6),X7,X7),X7)
| sP0(powerset(X6),X7,X7)
| subset(sK6(powerset(X6),X7,X7),X6) )
| ~ spl20_84
| ~ spl20_259 ),
inference(resolution,[],[f2961,f733]) ).
fof(f18270,plain,
( spl20_681
| ~ spl20_84
| ~ spl20_256 ),
inference(avatar_split_clause,[],[f3050,f2944,f732,f18268]) ).
fof(f18268,plain,
( spl20_681
<=> ! [X6,X7] :
( ~ ordinal(singleton(X6))
| ~ ordinal(powerset(X7))
| singleton(X6) = powerset(X7)
| powerset(X7) = X6
| subset(singleton(X6),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_681])]) ).
fof(f3050,plain,
( ! [X6,X7] :
( ~ ordinal(singleton(X6))
| ~ ordinal(powerset(X7))
| singleton(X6) = powerset(X7)
| powerset(X7) = X6
| subset(singleton(X6),X7) )
| ~ spl20_84
| ~ spl20_256 ),
inference(resolution,[],[f2945,f733]) ).
fof(f18266,plain,
( ~ spl20_680
| spl20_197
| ~ spl20_533 ),
inference(avatar_split_clause,[],[f14549,f14532,f2040,f18263]) ).
fof(f14549,plain,
( sK1 != succ(sK8)
| spl20_197
| ~ spl20_533 ),
inference(superposition,[],[f2041,f14534]) ).
fof(f2041,plain,
( sK1 != succ(sK2)
| spl20_197 ),
inference(avatar_component_clause,[],[f2040]) ).
fof(f18261,plain,
( spl20_679
| ~ spl20_234
| ~ spl20_254 ),
inference(avatar_split_clause,[],[f3046,f2936,f2500,f18259]) ).
fof(f18259,plain,
( spl20_679
<=> ! [X4,X5,X3] :
( X3 = X4
| singleton(X4) = X3
| ~ ordinal(singleton(X4))
| ~ ordinal(X3)
| ordinal_subset(X5,X3)
| ~ ordinal(X5)
| ~ empty(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_679])]) ).
fof(f3046,plain,
( ! [X3,X4,X5] :
( X3 = X4
| singleton(X4) = X3
| ~ ordinal(singleton(X4))
| ~ ordinal(X3)
| ordinal_subset(X5,X3)
| ~ ordinal(X5)
| ~ empty(X5) )
| ~ spl20_234
| ~ spl20_254 ),
inference(duplicate_literal_removal,[],[f3028]) ).
fof(f3028,plain,
( ! [X3,X4,X5] :
( X3 = X4
| singleton(X4) = X3
| ~ ordinal(singleton(X4))
| ~ ordinal(X3)
| ~ ordinal(X3)
| ordinal_subset(X5,X3)
| ~ ordinal(X5)
| ~ empty(X5) )
| ~ spl20_234
| ~ spl20_254 ),
inference(resolution,[],[f2937,f2501]) ).
fof(f18257,plain,
( spl20_678
| ~ spl20_153
| ~ spl20_254 ),
inference(avatar_split_clause,[],[f3034,f2936,f1230,f18255]) ).
fof(f18255,plain,
( spl20_678
<=> ! [X18,X17] :
( singleton(X17) = X18
| singleton(X17) = singleton(X18)
| ~ ordinal(singleton(X18))
| ~ ordinal(singleton(X17))
| singleton(X18) = X17 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_678])]) ).
fof(f3034,plain,
( ! [X18,X17] :
( singleton(X17) = X18
| singleton(X17) = singleton(X18)
| ~ ordinal(singleton(X18))
| ~ ordinal(singleton(X17))
| singleton(X18) = X17 )
| ~ spl20_153
| ~ spl20_254 ),
inference(resolution,[],[f2937,f1231]) ).
fof(f18253,plain,
( spl20_677
| ~ spl20_209
| ~ spl20_252 ),
inference(avatar_split_clause,[],[f2909,f2900,f2154,f18251]) ).
fof(f18251,plain,
( spl20_677
<=> ! [X4,X3] :
( sK5(X3,sK4(powerset(sK4(powerset(X4))))) = X3
| singleton(X3) = sK4(powerset(sK4(powerset(X4))))
| ~ empty(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_677])]) ).
fof(f2154,plain,
( spl20_209
<=> ! [X5] :
( ~ empty(X5)
| empty(sK4(powerset(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_209])]) ).
fof(f2900,plain,
( spl20_252
<=> ! [X6,X7] :
( ~ empty(X6)
| sK5(X7,sK4(powerset(X6))) = X7
| sK4(powerset(X6)) = singleton(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_252])]) ).
fof(f2909,plain,
( ! [X3,X4] :
( sK5(X3,sK4(powerset(sK4(powerset(X4))))) = X3
| singleton(X3) = sK4(powerset(sK4(powerset(X4))))
| ~ empty(X4) )
| ~ spl20_209
| ~ spl20_252 ),
inference(resolution,[],[f2901,f2155]) ).
fof(f2155,plain,
( ! [X5] :
( empty(sK4(powerset(X5)))
| ~ empty(X5) )
| ~ spl20_209 ),
inference(avatar_component_clause,[],[f2154]) ).
fof(f2901,plain,
( ! [X6,X7] :
( ~ empty(X6)
| sK5(X7,sK4(powerset(X6))) = X7
| sK4(powerset(X6)) = singleton(X7) )
| ~ spl20_252 ),
inference(avatar_component_clause,[],[f2900]) ).
fof(f18249,plain,
( spl20_676
| ~ spl20_100
| ~ spl20_246 ),
inference(avatar_split_clause,[],[f2791,f2729,f858,f18247]) ).
fof(f18247,plain,
( spl20_676
<=> ! [X2,X0,X1] :
( element(powerset(X1),X0)
| ~ ordinal(X0)
| ~ ordinal(powerset(X1))
| powerset(X1) = X0
| element(X2,X1)
| ~ in(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_676])]) ).
fof(f2729,plain,
( spl20_246
<=> ! [X2,X3] :
( X2 = X3
| ~ ordinal(X2)
| ~ ordinal(X3)
| element(X2,X3)
| element(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_246])]) ).
fof(f2791,plain,
( ! [X2,X0,X1] :
( element(powerset(X1),X0)
| ~ ordinal(X0)
| ~ ordinal(powerset(X1))
| powerset(X1) = X0
| element(X2,X1)
| ~ in(X2,X0) )
| ~ spl20_100
| ~ spl20_246 ),
inference(resolution,[],[f2730,f859]) ).
fof(f2730,plain,
( ! [X2,X3] :
( element(X3,X2)
| element(X2,X3)
| ~ ordinal(X3)
| ~ ordinal(X2)
| X2 = X3 )
| ~ spl20_246 ),
inference(avatar_component_clause,[],[f2729]) ).
fof(f18245,plain,
( spl20_675
| ~ spl20_241
| ~ spl20_245 ),
inference(avatar_split_clause,[],[f2783,f2725,f2529,f18243]) ).
fof(f18243,plain,
( spl20_675
<=> ! [X153,X152,X151] :
( ~ ordinal(X151)
| ordinal_subset(X152,X151)
| ~ ordinal(X152)
| element(sK6(X151,X151,X153),X152)
| sP0(X151,X151,X153)
| ~ empty(X153) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_675])]) ).
fof(f2783,plain,
( ! [X152,X153,X151] :
( ~ ordinal(X151)
| ordinal_subset(X152,X151)
| ~ ordinal(X152)
| element(sK6(X151,X151,X153),X152)
| sP0(X151,X151,X153)
| ~ empty(X153) )
| ~ spl20_241
| ~ spl20_245 ),
inference(resolution,[],[f2726,f2530]) ).
fof(f18241,plain,
( spl20_674
| ~ spl20_242
| ~ spl20_245 ),
inference(avatar_split_clause,[],[f2781,f2725,f2533,f18239]) ).
fof(f18239,plain,
( spl20_674
<=> ! [X146,X145,X147] :
( ~ ordinal(X145)
| ordinal_subset(X146,X145)
| ~ ordinal(X146)
| element(sK6(X147,X147,X145),X146)
| sP0(X147,X147,X145)
| ~ empty(X147) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_674])]) ).
fof(f2781,plain,
( ! [X145,X146,X147] :
( ~ ordinal(X145)
| ordinal_subset(X146,X145)
| ~ ordinal(X146)
| element(sK6(X147,X147,X145),X146)
| sP0(X147,X147,X145)
| ~ empty(X147) )
| ~ spl20_242
| ~ spl20_245 ),
inference(resolution,[],[f2726,f2534]) ).
fof(f18237,plain,
( spl20_673
| ~ spl20_230
| ~ spl20_242 ),
inference(avatar_split_clause,[],[f2712,f2533,f2398,f18235]) ).
fof(f18235,plain,
( spl20_673
<=> ! [X24,X23] :
( sP0(X23,X23,sK3(powerset(X24)))
| ~ empty(X23)
| element(sK6(X23,X23,sK3(powerset(X24))),X24)
| epsilon_transitive(powerset(X24)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_673])]) ).
fof(f2712,plain,
( ! [X24,X23] :
( sP0(X23,X23,sK3(powerset(X24)))
| ~ empty(X23)
| element(sK6(X23,X23,sK3(powerset(X24))),X24)
| epsilon_transitive(powerset(X24)) )
| ~ spl20_230
| ~ spl20_242 ),
inference(resolution,[],[f2534,f2399]) ).
fof(f18233,plain,
( spl20_672
| ~ spl20_170
| ~ spl20_234 ),
inference(avatar_split_clause,[],[f2584,f2500,f1403,f18231]) ).
fof(f18231,plain,
( spl20_672
<=> ! [X2,X0,X1] :
( ~ ordinal(X0)
| ordinal_subset(X1,X0)
| ~ ordinal(X1)
| ~ empty(X1)
| X0 = X2
| ~ ordinal(X2)
| subset(X0,X2)
| ~ epsilon_transitive(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_672])]) ).
fof(f2584,plain,
( ! [X2,X0,X1] :
( ~ ordinal(X0)
| ordinal_subset(X1,X0)
| ~ ordinal(X1)
| ~ empty(X1)
| X0 = X2
| ~ ordinal(X2)
| subset(X0,X2)
| ~ epsilon_transitive(X2) )
| ~ spl20_170
| ~ spl20_234 ),
inference(duplicate_literal_removal,[],[f2540]) ).
fof(f2540,plain,
( ! [X2,X0,X1] :
( ~ ordinal(X0)
| ordinal_subset(X1,X0)
| ~ ordinal(X1)
| ~ empty(X1)
| X0 = X2
| ~ ordinal(X0)
| ~ ordinal(X2)
| subset(X0,X2)
| ~ epsilon_transitive(X2) )
| ~ spl20_170
| ~ spl20_234 ),
inference(resolution,[],[f2501,f1404]) ).
fof(f18229,plain,
( spl20_671
| ~ spl20_177
| ~ spl20_234 ),
inference(avatar_split_clause,[],[f2579,f2500,f1462,f18227]) ).
fof(f18227,plain,
( spl20_671
<=> ! [X137,X136,X138] :
( ~ ordinal(X136)
| ordinal_subset(X137,X136)
| ~ ordinal(X137)
| ~ empty(X137)
| in(sK6(X136,X136,X138),X138)
| sP0(X136,X136,X138) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_671])]) ).
fof(f2579,plain,
( ! [X138,X136,X137] :
( ~ ordinal(X136)
| ordinal_subset(X137,X136)
| ~ ordinal(X137)
| ~ empty(X137)
| in(sK6(X136,X136,X138),X138)
| sP0(X136,X136,X138) )
| ~ spl20_177
| ~ spl20_234 ),
inference(resolution,[],[f2501,f1463]) ).
fof(f18225,plain,
( spl20_670
| ~ spl20_177
| ~ spl20_234 ),
inference(avatar_split_clause,[],[f2578,f2500,f1462,f18223]) ).
fof(f18223,plain,
( spl20_670
<=> ! [X134,X133,X135] :
( ~ ordinal(X133)
| ordinal_subset(X134,X133)
| ~ ordinal(X134)
| ~ empty(X134)
| in(sK6(X135,X135,X133),X135)
| sP0(X135,X135,X133) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_670])]) ).
fof(f2578,plain,
( ! [X133,X134,X135] :
( ~ ordinal(X133)
| ordinal_subset(X134,X133)
| ~ ordinal(X134)
| ~ empty(X134)
| in(sK6(X135,X135,X133),X135)
| sP0(X135,X135,X133) )
| ~ spl20_177
| ~ spl20_234 ),
inference(resolution,[],[f2501,f1463]) ).
fof(f18221,plain,
( spl20_669
| ~ spl20_182
| ~ spl20_533 ),
inference(avatar_split_clause,[],[f14546,f14532,f1644,f18218]) ).
fof(f18218,plain,
( spl20_669
<=> element(sK4(sK1),sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_669])]) ).
fof(f14546,plain,
( element(sK4(sK1),sK8)
| ~ spl20_182
| ~ spl20_533 ),
inference(superposition,[],[f1646,f14534]) ).
fof(f18216,plain,
( spl20_668
| ~ spl20_166
| ~ spl20_231 ),
inference(avatar_split_clause,[],[f2451,f2402,f1355,f18214]) ).
fof(f18214,plain,
( spl20_668
<=> ! [X13,X12,X14] :
( in(X12,X13)
| in(X12,X14)
| set_union2(X13,X14) = X12
| ~ ordinal(set_union2(X13,X14))
| ~ ordinal(X12)
| ~ empty(X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_668])]) ).
fof(f2451,plain,
( ! [X14,X12,X13] :
( in(X12,X13)
| in(X12,X14)
| set_union2(X13,X14) = X12
| ~ ordinal(set_union2(X13,X14))
| ~ ordinal(X12)
| ~ empty(X12) )
| ~ spl20_166
| ~ spl20_231 ),
inference(resolution,[],[f2403,f1356]) ).
fof(f18212,plain,
( spl20_667
| ~ spl20_166
| ~ spl20_230 ),
inference(avatar_split_clause,[],[f2414,f2398,f1355,f18210]) ).
fof(f18210,plain,
( spl20_667
<=> ! [X4,X5] :
( element(X4,X5)
| epsilon_transitive(powerset(X5))
| sK3(powerset(X5)) = X4
| ~ ordinal(sK3(powerset(X5)))
| ~ ordinal(X4)
| ~ empty(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_667])]) ).
fof(f2414,plain,
( ! [X4,X5] :
( element(X4,X5)
| epsilon_transitive(powerset(X5))
| sK3(powerset(X5)) = X4
| ~ ordinal(sK3(powerset(X5)))
| ~ ordinal(X4)
| ~ empty(X4) )
| ~ spl20_166
| ~ spl20_230 ),
inference(resolution,[],[f2399,f1356]) ).
fof(f18208,plain,
( spl20_666
| ~ spl20_177
| ~ spl20_223 ),
inference(avatar_split_clause,[],[f2369,f2310,f1462,f18206]) ).
fof(f18206,plain,
( spl20_666
<=> ! [X86,X85] :
( ~ empty(X85)
| epsilon_transitive(powerset(X85))
| in(sK6(X86,X86,sK3(powerset(X85))),X86)
| sP0(X86,X86,sK3(powerset(X85))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_666])]) ).
fof(f2369,plain,
( ! [X86,X85] :
( ~ empty(X85)
| epsilon_transitive(powerset(X85))
| in(sK6(X86,X86,sK3(powerset(X85))),X86)
| sP0(X86,X86,sK3(powerset(X85))) )
| ~ spl20_177
| ~ spl20_223 ),
inference(resolution,[],[f2311,f1463]) ).
fof(f17267,plain,
( ~ spl20_122
| ~ spl20_82
| spl20_627 ),
inference(avatar_split_clause,[],[f17136,f17002,f696,f1023]) ).
fof(f17002,plain,
( spl20_627
<=> ordinal_subset(sK8,sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_627])]) ).
fof(f17136,plain,
( ~ ordinal(sK8)
| ~ spl20_82
| spl20_627 ),
inference(resolution,[],[f17004,f697]) ).
fof(f17004,plain,
( ~ ordinal_subset(sK8,sK8)
| spl20_627 ),
inference(avatar_component_clause,[],[f17002]) ).
fof(f17175,plain,
( spl20_665
| ~ spl20_146
| ~ spl20_307 ),
inference(avatar_split_clause,[],[f4177,f4110,f1180,f17173]) ).
fof(f17173,plain,
( spl20_665
<=> ! [X20,X21] :
( sK5(X20,powerset(X21)) = X20
| ~ empty(X21)
| powerset(X21) = singleton(X20)
| empty(sK5(X20,powerset(X21))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_665])]) ).
fof(f4177,plain,
( ! [X21,X20] :
( sK5(X20,powerset(X21)) = X20
| ~ empty(X21)
| powerset(X21) = singleton(X20)
| empty(sK5(X20,powerset(X21))) )
| ~ spl20_146
| ~ spl20_307 ),
inference(resolution,[],[f4111,f1181]) ).
fof(f17171,plain,
( spl20_664
| ~ spl20_71
| ~ spl20_307 ),
inference(avatar_split_clause,[],[f4176,f4110,f637,f17169]) ).
fof(f17169,plain,
( spl20_664
<=> ! [X18,X19] :
( sK5(X18,powerset(X19)) = X18
| ~ empty(X19)
| powerset(X19) = singleton(X18)
| epsilon_transitive(sK5(X18,powerset(X19))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_664])]) ).
fof(f4176,plain,
( ! [X18,X19] :
( sK5(X18,powerset(X19)) = X18
| ~ empty(X19)
| powerset(X19) = singleton(X18)
| epsilon_transitive(sK5(X18,powerset(X19))) )
| ~ spl20_71
| ~ spl20_307 ),
inference(resolution,[],[f4111,f638]) ).
fof(f17167,plain,
( spl20_663
| ~ spl20_75
| ~ spl20_303 ),
inference(avatar_split_clause,[],[f4088,f3637,f653,f17165]) ).
fof(f17165,plain,
( spl20_663
<=> ! [X25,X24,X26] :
( sP0(X24,sK4(powerset(X25)),X26)
| ~ empty(X24)
| ~ empty(X25)
| ~ in(X26,sK6(X24,sK4(powerset(X25)),X26)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_663])]) ).
fof(f4088,plain,
( ! [X26,X24,X25] :
( sP0(X24,sK4(powerset(X25)),X26)
| ~ empty(X24)
| ~ empty(X25)
| ~ in(X26,sK6(X24,sK4(powerset(X25)),X26)) )
| ~ spl20_75
| ~ spl20_303 ),
inference(resolution,[],[f3638,f654]) ).
fof(f17163,plain,
( spl20_662
| ~ spl20_75
| ~ spl20_301 ),
inference(avatar_split_clause,[],[f4055,f3629,f653,f17161]) ).
fof(f17161,plain,
( spl20_662
<=> ! [X25,X24,X26] :
( element(sK6(X24,X25,X26),X25)
| ~ empty(X24)
| sP0(X24,X25,X26)
| ~ in(X26,sK6(X24,X25,X26)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_662])]) ).
fof(f4055,plain,
( ! [X26,X24,X25] :
( element(sK6(X24,X25,X26),X25)
| ~ empty(X24)
| sP0(X24,X25,X26)
| ~ in(X26,sK6(X24,X25,X26)) )
| ~ spl20_75
| ~ spl20_301 ),
inference(resolution,[],[f3630,f654]) ).
fof(f17159,plain,
( spl20_661
| ~ spl20_75
| ~ spl20_300 ),
inference(avatar_split_clause,[],[f4030,f3625,f653,f17157]) ).
fof(f17157,plain,
( spl20_661
<=> ! [X25,X24,X23] :
( sP0(X23,X24,sK4(powerset(X25)))
| ~ empty(X23)
| ~ empty(X25)
| ~ in(X24,sK6(X23,X24,sK4(powerset(X25)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_661])]) ).
fof(f4030,plain,
( ! [X24,X25,X23] :
( sP0(X23,X24,sK4(powerset(X25)))
| ~ empty(X23)
| ~ empty(X25)
| ~ in(X24,sK6(X23,X24,sK4(powerset(X25)))) )
| ~ spl20_75
| ~ spl20_300 ),
inference(resolution,[],[f3626,f654]) ).
fof(f17155,plain,
( spl20_660
| ~ spl20_76
| ~ spl20_300 ),
inference(avatar_split_clause,[],[f4029,f3625,f657,f17153]) ).
fof(f17153,plain,
( spl20_660
<=> ! [X22,X20,X21] :
( sP0(X20,X21,sK4(powerset(X22)))
| ~ empty(X20)
| ~ empty(X22)
| element(sK6(X20,X21,sK4(powerset(X22))),X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_660])]) ).
fof(f4029,plain,
( ! [X21,X22,X20] :
( sP0(X20,X21,sK4(powerset(X22)))
| ~ empty(X20)
| ~ empty(X22)
| element(sK6(X20,X21,sK4(powerset(X22))),X21) )
| ~ spl20_76
| ~ spl20_300 ),
inference(resolution,[],[f3626,f658]) ).
fof(f17135,plain,
( spl20_659
| ~ spl20_151
| ~ spl20_298 ),
inference(avatar_split_clause,[],[f4010,f3617,f1221,f17133]) ).
fof(f17133,plain,
( spl20_659
<=> ! [X48,X47,X49] :
( element(sK6(X47,sK4(powerset(X48)),X49),X49)
| ~ empty(X47)
| sP0(X47,sK4(powerset(X48)),X49)
| ~ empty(X48) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_659])]) ).
fof(f4010,plain,
( ! [X48,X49,X47] :
( element(sK6(X47,sK4(powerset(X48)),X49),X49)
| ~ empty(X47)
| sP0(X47,sK4(powerset(X48)),X49)
| ~ empty(X48) )
| ~ spl20_151
| ~ spl20_298 ),
inference(resolution,[],[f3618,f1222]) ).
fof(f17131,plain,
( spl20_658
| ~ spl20_75
| ~ spl20_298 ),
inference(avatar_split_clause,[],[f4002,f3617,f653,f17129]) ).
fof(f17129,plain,
( spl20_658
<=> ! [X25,X24,X23] :
( element(sK6(X23,X24,X25),X25)
| ~ empty(X23)
| sP0(X23,X24,X25)
| ~ in(X24,sK6(X23,X24,X25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_658])]) ).
fof(f4002,plain,
( ! [X24,X25,X23] :
( element(sK6(X23,X24,X25),X25)
| ~ empty(X23)
| sP0(X23,X24,X25)
| ~ in(X24,sK6(X23,X24,X25)) )
| ~ spl20_75
| ~ spl20_298 ),
inference(resolution,[],[f3618,f654]) ).
fof(f17127,plain,
( spl20_657
| ~ spl20_76
| ~ spl20_298 ),
inference(avatar_split_clause,[],[f4001,f3617,f657,f17125]) ).
fof(f17125,plain,
( spl20_657
<=> ! [X22,X20,X21] :
( element(sK6(X20,X21,X22),X22)
| ~ empty(X20)
| sP0(X20,X21,X22)
| element(sK6(X20,X21,X22),X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_657])]) ).
fof(f4001,plain,
( ! [X21,X22,X20] :
( element(sK6(X20,X21,X22),X22)
| ~ empty(X20)
| sP0(X20,X21,X22)
| element(sK6(X20,X21,X22),X21) )
| ~ spl20_76
| ~ spl20_298 ),
inference(resolution,[],[f3618,f658]) ).
fof(f17123,plain,
( spl20_656
| ~ spl20_75
| ~ spl20_296 ),
inference(avatar_split_clause,[],[f3977,f3586,f653,f17121]) ).
fof(f17121,plain,
( spl20_656
<=> ! [X25,X24,X26] :
( sP0(sK4(powerset(X24)),X25,X26)
| ~ empty(X25)
| ~ empty(X24)
| ~ in(X26,sK6(sK4(powerset(X24)),X25,X26)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_656])]) ).
fof(f3977,plain,
( ! [X26,X24,X25] :
( sP0(sK4(powerset(X24)),X25,X26)
| ~ empty(X25)
| ~ empty(X24)
| ~ in(X26,sK6(sK4(powerset(X24)),X25,X26)) )
| ~ spl20_75
| ~ spl20_296 ),
inference(resolution,[],[f3587,f654]) ).
fof(f17119,plain,
( spl20_655
| ~ spl20_75
| ~ spl20_294 ),
inference(avatar_split_clause,[],[f3949,f3578,f653,f17117]) ).
fof(f17117,plain,
( spl20_655
<=> ! [X25,X24,X26] :
( element(sK6(X24,X25,X26),X24)
| ~ empty(X25)
| sP0(X24,X25,X26)
| ~ in(X26,sK6(X24,X25,X26)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_655])]) ).
fof(f3949,plain,
( ! [X26,X24,X25] :
( element(sK6(X24,X25,X26),X24)
| ~ empty(X25)
| sP0(X24,X25,X26)
| ~ in(X26,sK6(X24,X25,X26)) )
| ~ spl20_75
| ~ spl20_294 ),
inference(resolution,[],[f3579,f654]) ).
fof(f17115,plain,
( spl20_654
| ~ spl20_75
| ~ spl20_293 ),
inference(avatar_split_clause,[],[f3924,f3574,f653,f17113]) ).
fof(f17113,plain,
( spl20_654
<=> ! [X25,X24,X23] :
( sP0(X23,X24,sK4(powerset(X25)))
| ~ empty(X24)
| ~ empty(X25)
| ~ in(X23,sK6(X23,X24,sK4(powerset(X25)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_654])]) ).
fof(f3924,plain,
( ! [X24,X25,X23] :
( sP0(X23,X24,sK4(powerset(X25)))
| ~ empty(X24)
| ~ empty(X25)
| ~ in(X23,sK6(X23,X24,sK4(powerset(X25)))) )
| ~ spl20_75
| ~ spl20_293 ),
inference(resolution,[],[f3575,f654]) ).
fof(f17111,plain,
( spl20_653
| ~ spl20_76
| ~ spl20_293 ),
inference(avatar_split_clause,[],[f3923,f3574,f657,f17109]) ).
fof(f17109,plain,
( spl20_653
<=> ! [X22,X20,X21] :
( sP0(X20,X21,sK4(powerset(X22)))
| ~ empty(X21)
| ~ empty(X22)
| element(sK6(X20,X21,sK4(powerset(X22))),X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_653])]) ).
fof(f3923,plain,
( ! [X21,X22,X20] :
( sP0(X20,X21,sK4(powerset(X22)))
| ~ empty(X21)
| ~ empty(X22)
| element(sK6(X20,X21,sK4(powerset(X22))),X20) )
| ~ spl20_76
| ~ spl20_293 ),
inference(resolution,[],[f3575,f658]) ).
fof(f17107,plain,
( spl20_652
| ~ spl20_151
| ~ spl20_291 ),
inference(avatar_split_clause,[],[f3904,f3566,f1221,f17105]) ).
fof(f17105,plain,
( spl20_652
<=> ! [X48,X47,X49] :
( element(sK6(sK4(powerset(X47)),X48,X49),X49)
| ~ empty(X48)
| sP0(sK4(powerset(X47)),X48,X49)
| ~ empty(X47) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_652])]) ).
fof(f3904,plain,
( ! [X48,X49,X47] :
( element(sK6(sK4(powerset(X47)),X48,X49),X49)
| ~ empty(X48)
| sP0(sK4(powerset(X47)),X48,X49)
| ~ empty(X47) )
| ~ spl20_151
| ~ spl20_291 ),
inference(resolution,[],[f3567,f1222]) ).
fof(f17103,plain,
( spl20_651
| ~ spl20_75
| ~ spl20_291 ),
inference(avatar_split_clause,[],[f3896,f3566,f653,f17101]) ).
fof(f17101,plain,
( spl20_651
<=> ! [X25,X24,X23] :
( element(sK6(X23,X24,X25),X25)
| ~ empty(X24)
| sP0(X23,X24,X25)
| ~ in(X23,sK6(X23,X24,X25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_651])]) ).
fof(f3896,plain,
( ! [X24,X25,X23] :
( element(sK6(X23,X24,X25),X25)
| ~ empty(X24)
| sP0(X23,X24,X25)
| ~ in(X23,sK6(X23,X24,X25)) )
| ~ spl20_75
| ~ spl20_291 ),
inference(resolution,[],[f3567,f654]) ).
fof(f17099,plain,
( spl20_650
| ~ spl20_76
| ~ spl20_291 ),
inference(avatar_split_clause,[],[f3895,f3566,f657,f17097]) ).
fof(f17097,plain,
( spl20_650
<=> ! [X22,X20,X21] :
( element(sK6(X20,X21,X22),X22)
| ~ empty(X21)
| sP0(X20,X21,X22)
| element(sK6(X20,X21,X22),X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_650])]) ).
fof(f3895,plain,
( ! [X21,X22,X20] :
( element(sK6(X20,X21,X22),X22)
| ~ empty(X21)
| sP0(X20,X21,X22)
| element(sK6(X20,X21,X22),X20) )
| ~ spl20_76
| ~ spl20_291 ),
inference(resolution,[],[f3567,f658]) ).
fof(f17095,plain,
( ~ spl20_649
| spl20_518
| ~ spl20_533 ),
inference(avatar_split_clause,[],[f16699,f14532,f14297,f17092]) ).
fof(f17092,plain,
( spl20_649
<=> in(sK8,sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_649])]) ).
fof(f14297,plain,
( spl20_518
<=> in(sK2,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_518])]) ).
fof(f16699,plain,
( ~ in(sK8,sK8)
| spl20_518
| ~ spl20_533 ),
inference(superposition,[],[f14298,f14534]) ).
fof(f14298,plain,
( ~ in(sK2,sK2)
| spl20_518 ),
inference(avatar_component_clause,[],[f14297]) ).
fof(f17090,plain,
( spl20_648
| ~ spl20_75
| ~ spl20_290 ),
inference(avatar_split_clause,[],[f3871,f3562,f653,f17088]) ).
fof(f17088,plain,
( spl20_648
<=> ! [X25,X24,X23] :
( sP0(sK4(powerset(X23)),X24,X25)
| ~ empty(X25)
| ~ empty(X23)
| ~ in(X24,sK6(sK4(powerset(X23)),X24,X25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_648])]) ).
fof(f3871,plain,
( ! [X24,X25,X23] :
( sP0(sK4(powerset(X23)),X24,X25)
| ~ empty(X25)
| ~ empty(X23)
| ~ in(X24,sK6(sK4(powerset(X23)),X24,X25)) )
| ~ spl20_75
| ~ spl20_290 ),
inference(resolution,[],[f3563,f654]) ).
fof(f17086,plain,
( spl20_647
| ~ spl20_75
| ~ spl20_288 ),
inference(avatar_split_clause,[],[f3843,f3554,f653,f17084]) ).
fof(f17084,plain,
( spl20_647
<=> ! [X24,X25,X23] :
( element(sK6(X23,X24,X25),X23)
| ~ empty(X25)
| sP0(X23,X24,X25)
| ~ in(X24,sK6(X23,X24,X25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_647])]) ).
fof(f3843,plain,
( ! [X24,X25,X23] :
( element(sK6(X23,X24,X25),X23)
| ~ empty(X25)
| sP0(X23,X24,X25)
| ~ in(X24,sK6(X23,X24,X25)) )
| ~ spl20_75
| ~ spl20_288 ),
inference(resolution,[],[f3555,f654]) ).
fof(f17082,plain,
( spl20_646
| ~ spl20_75
| ~ spl20_287 ),
inference(avatar_split_clause,[],[f3818,f3550,f653,f17080]) ).
fof(f17080,plain,
( spl20_646
<=> ! [X25,X24,X23] :
( sP0(X23,sK4(powerset(X24)),X25)
| ~ empty(X25)
| ~ empty(X24)
| ~ in(X23,sK6(X23,sK4(powerset(X24)),X25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_646])]) ).
fof(f3818,plain,
( ! [X24,X25,X23] :
( sP0(X23,sK4(powerset(X24)),X25)
| ~ empty(X25)
| ~ empty(X24)
| ~ in(X23,sK6(X23,sK4(powerset(X24)),X25)) )
| ~ spl20_75
| ~ spl20_287 ),
inference(resolution,[],[f3551,f654]) ).
fof(f17078,plain,
( spl20_645
| ~ spl20_76
| ~ spl20_287 ),
inference(avatar_split_clause,[],[f3817,f3550,f657,f17076]) ).
fof(f17076,plain,
( spl20_645
<=> ! [X22,X20,X21] :
( sP0(X20,sK4(powerset(X21)),X22)
| ~ empty(X22)
| ~ empty(X21)
| element(sK6(X20,sK4(powerset(X21)),X22),X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_645])]) ).
fof(f3817,plain,
( ! [X21,X22,X20] :
( sP0(X20,sK4(powerset(X21)),X22)
| ~ empty(X22)
| ~ empty(X21)
| element(sK6(X20,sK4(powerset(X21)),X22),X20) )
| ~ spl20_76
| ~ spl20_287 ),
inference(resolution,[],[f3551,f658]) ).
fof(f17074,plain,
( spl20_644
| ~ spl20_151
| ~ spl20_285 ),
inference(avatar_split_clause,[],[f3798,f3542,f1221,f17072]) ).
fof(f17072,plain,
( spl20_644
<=> ! [X48,X47,X49] :
( element(sK6(sK4(powerset(X47)),X48,X49),X48)
| ~ empty(X49)
| sP0(sK4(powerset(X47)),X48,X49)
| ~ empty(X47) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_644])]) ).
fof(f3798,plain,
( ! [X48,X49,X47] :
( element(sK6(sK4(powerset(X47)),X48,X49),X48)
| ~ empty(X49)
| sP0(sK4(powerset(X47)),X48,X49)
| ~ empty(X47) )
| ~ spl20_151
| ~ spl20_285 ),
inference(resolution,[],[f3543,f1222]) ).
fof(f17070,plain,
( spl20_643
| ~ spl20_75
| ~ spl20_285 ),
inference(avatar_split_clause,[],[f3790,f3542,f653,f17068]) ).
fof(f17068,plain,
( spl20_643
<=> ! [X25,X24,X23] :
( element(sK6(X23,X24,X25),X24)
| ~ empty(X25)
| sP0(X23,X24,X25)
| ~ in(X23,sK6(X23,X24,X25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_643])]) ).
fof(f3790,plain,
( ! [X24,X25,X23] :
( element(sK6(X23,X24,X25),X24)
| ~ empty(X25)
| sP0(X23,X24,X25)
| ~ in(X23,sK6(X23,X24,X25)) )
| ~ spl20_75
| ~ spl20_285 ),
inference(resolution,[],[f3543,f654]) ).
fof(f17066,plain,
( spl20_642
| ~ spl20_76
| ~ spl20_285 ),
inference(avatar_split_clause,[],[f3789,f3542,f657,f17064]) ).
fof(f17064,plain,
( spl20_642
<=> ! [X22,X20,X21] :
( element(sK6(X20,X21,X22),X21)
| ~ empty(X22)
| sP0(X20,X21,X22)
| element(sK6(X20,X21,X22),X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_642])]) ).
fof(f3789,plain,
( ! [X21,X22,X20] :
( element(sK6(X20,X21,X22),X21)
| ~ empty(X22)
| sP0(X20,X21,X22)
| element(sK6(X20,X21,X22),X20) )
| ~ spl20_76
| ~ spl20_285 ),
inference(resolution,[],[f3543,f658]) ).
fof(f17062,plain,
( spl20_641
| ~ spl20_75
| ~ spl20_284 ),
inference(avatar_split_clause,[],[f3765,f3538,f653,f17060]) ).
fof(f17060,plain,
( spl20_641
<=> ! [X16,X17] :
( subset(sK6(X16,X16,X17),X16)
| sP0(X16,X16,X17)
| ~ epsilon_transitive(X16)
| ~ in(X17,sK6(X16,X16,X17)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_641])]) ).
fof(f3765,plain,
( ! [X16,X17] :
( subset(sK6(X16,X16,X17),X16)
| sP0(X16,X16,X17)
| ~ epsilon_transitive(X16)
| ~ in(X17,sK6(X16,X16,X17)) )
| ~ spl20_75
| ~ spl20_284 ),
inference(resolution,[],[f3539,f654]) ).
fof(f17058,plain,
( spl20_640
| ~ spl20_75
| ~ spl20_283 ),
inference(avatar_split_clause,[],[f3740,f3534,f653,f17056]) ).
fof(f17056,plain,
( spl20_640
<=> ! [X16,X17] :
( subset(sK6(X16,X16,X17),X17)
| sP0(X16,X16,X17)
| ~ epsilon_transitive(X17)
| ~ in(X16,sK6(X16,X16,X17)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_640])]) ).
fof(f3740,plain,
( ! [X16,X17] :
( subset(sK6(X16,X16,X17),X17)
| sP0(X16,X16,X17)
| ~ epsilon_transitive(X17)
| ~ in(X16,sK6(X16,X16,X17)) )
| ~ spl20_75
| ~ spl20_283 ),
inference(resolution,[],[f3535,f654]) ).
fof(f17054,plain,
( spl20_639
| ~ spl20_97
| ~ spl20_280 ),
inference(avatar_split_clause,[],[f3676,f3522,f846,f17052]) ).
fof(f17052,plain,
( spl20_639
<=> ! [X6,X7] :
( ~ ordinal(singleton(X6))
| ~ ordinal(X7)
| singleton(X6) = X7
| ~ epsilon_transitive(X7)
| X6 = X7
| ordinal_subset(singleton(X6),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_639])]) ).
fof(f3676,plain,
( ! [X6,X7] :
( ~ ordinal(singleton(X6))
| ~ ordinal(X7)
| singleton(X6) = X7
| ~ epsilon_transitive(X7)
| X6 = X7
| ordinal_subset(singleton(X6),X7) )
| ~ spl20_97
| ~ spl20_280 ),
inference(duplicate_literal_removal,[],[f3671]) ).
fof(f3671,plain,
( ! [X6,X7] :
( ~ ordinal(singleton(X6))
| ~ ordinal(X7)
| singleton(X6) = X7
| ~ epsilon_transitive(X7)
| X6 = X7
| ordinal_subset(singleton(X6),X7)
| ~ ordinal(X7)
| ~ ordinal(singleton(X6)) )
| ~ spl20_97
| ~ spl20_280 ),
inference(resolution,[],[f3523,f847]) ).
fof(f17050,plain,
( ~ spl20_638
| spl20_418
| ~ spl20_533 ),
inference(avatar_split_clause,[],[f14560,f14532,f9265,f17047]) ).
fof(f17047,plain,
( spl20_638
<=> element(sK1,sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_638])]) ).
fof(f9265,plain,
( spl20_418
<=> element(sK1,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_418])]) ).
fof(f14560,plain,
( ~ element(sK1,sK8)
| spl20_418
| ~ spl20_533 ),
inference(superposition,[],[f9267,f14534]) ).
fof(f9267,plain,
( ~ element(sK1,sK2)
| spl20_418 ),
inference(avatar_component_clause,[],[f9265]) ).
fof(f17045,plain,
( spl20_637
| ~ spl20_91
| ~ spl20_280 ),
inference(avatar_split_clause,[],[f3675,f3522,f811,f17043]) ).
fof(f17043,plain,
( spl20_637
<=> ! [X9,X8] :
( ~ ordinal(singleton(X8))
| ~ ordinal(X9)
| singleton(X8) = X9
| ~ epsilon_transitive(X9)
| X8 = X9
| ~ subset(X9,singleton(X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_637])]) ).
fof(f3675,plain,
( ! [X8,X9] :
( ~ ordinal(singleton(X8))
| ~ ordinal(X9)
| singleton(X8) = X9
| ~ epsilon_transitive(X9)
| X8 = X9
| ~ subset(X9,singleton(X8)) )
| ~ spl20_91
| ~ spl20_280 ),
inference(duplicate_literal_removal,[],[f3672]) ).
fof(f3672,plain,
( ! [X8,X9] :
( ~ ordinal(singleton(X8))
| ~ ordinal(X9)
| singleton(X8) = X9
| ~ epsilon_transitive(X9)
| X8 = X9
| singleton(X8) = X9
| ~ subset(X9,singleton(X8)) )
| ~ spl20_91
| ~ spl20_280 ),
inference(resolution,[],[f3523,f812]) ).
fof(f17041,plain,
( spl20_636
| ~ spl20_88
| ~ spl20_272 ),
inference(avatar_split_clause,[],[f3418,f3020,f772,f17039]) ).
fof(f17039,plain,
( spl20_636
<=> ! [X13,X12] :
( element(sK6(X12,X12,X13),X12)
| sP0(X12,X12,X13)
| subset(sK6(X12,X12,X13),X13)
| ~ epsilon_transitive(X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_636])]) ).
fof(f3418,plain,
( ! [X12,X13] :
( element(sK6(X12,X12,X13),X12)
| sP0(X12,X12,X13)
| subset(sK6(X12,X12,X13),X13)
| ~ epsilon_transitive(X13) )
| ~ spl20_88
| ~ spl20_272 ),
inference(resolution,[],[f3021,f773]) ).
fof(f17037,plain,
( spl20_635
| ~ spl20_88
| ~ spl20_271 ),
inference(avatar_split_clause,[],[f3393,f3016,f772,f17035]) ).
fof(f17035,plain,
( spl20_635
<=> ! [X13,X12] :
( sP0(X12,X12,sK4(powerset(X13)))
| ~ empty(X13)
| subset(sK6(X12,X12,sK4(powerset(X13))),X12)
| ~ epsilon_transitive(X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_635])]) ).
fof(f3393,plain,
( ! [X12,X13] :
( sP0(X12,X12,sK4(powerset(X13)))
| ~ empty(X13)
| subset(sK6(X12,X12,sK4(powerset(X13))),X12)
| ~ epsilon_transitive(X12) )
| ~ spl20_88
| ~ spl20_271 ),
inference(resolution,[],[f3017,f773]) ).
fof(f17033,plain,
( spl20_634
| ~ spl20_88
| ~ spl20_269 ),
inference(avatar_split_clause,[],[f3366,f3008,f772,f17031]) ).
fof(f17031,plain,
( spl20_634
<=> ! [X13,X12] :
( element(sK6(X12,X12,X13),X13)
| sP0(X12,X12,X13)
| subset(sK6(X12,X12,X13),X12)
| ~ epsilon_transitive(X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_634])]) ).
fof(f3366,plain,
( ! [X12,X13] :
( element(sK6(X12,X12,X13),X13)
| sP0(X12,X12,X13)
| subset(sK6(X12,X12,X13),X12)
| ~ epsilon_transitive(X12) )
| ~ spl20_88
| ~ spl20_269 ),
inference(resolution,[],[f3009,f773]) ).
fof(f17029,plain,
( spl20_633
| ~ spl20_160
| ~ spl20_253 ),
inference(avatar_split_clause,[],[f2922,f2904,f1291,f17027]) ).
fof(f17027,plain,
( spl20_633
<=> ! [X2,X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| element(X0,X1)
| X0 = X1
| ~ epsilon_transitive(X0)
| ~ in(X2,X1)
| element(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_633])]) ).
fof(f2922,plain,
( ! [X2,X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| element(X0,X1)
| X0 = X1
| ~ epsilon_transitive(X0)
| ~ in(X2,X1)
| element(X2,X0) )
| ~ spl20_160
| ~ spl20_253 ),
inference(resolution,[],[f2905,f1292]) ).
fof(f17025,plain,
( spl20_632
| ~ spl20_157
| ~ spl20_251 ),
inference(avatar_split_clause,[],[f2893,f2820,f1267,f17023]) ).
fof(f17023,plain,
( spl20_632
<=> ! [X45,X46,X47] :
( sP0(X45,X46,sK4(powerset(X47)))
| ~ empty(X46)
| ~ empty(X45)
| element(sK6(X45,X46,sK4(powerset(X47))),X47) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_632])]) ).
fof(f2893,plain,
( ! [X46,X47,X45] :
( sP0(X45,X46,sK4(powerset(X47)))
| ~ empty(X46)
| ~ empty(X45)
| element(sK6(X45,X46,sK4(powerset(X47))),X47) )
| ~ spl20_157
| ~ spl20_251 ),
inference(resolution,[],[f2821,f1268]) ).
fof(f17021,plain,
( spl20_631
| ~ spl20_157
| ~ spl20_250 ),
inference(avatar_split_clause,[],[f2872,f2816,f1267,f17019]) ).
fof(f17019,plain,
( spl20_631
<=> ! [X45,X44,X46] :
( sP0(X44,sK4(powerset(X45)),X46)
| ~ empty(X46)
| ~ empty(X44)
| element(sK6(X44,sK4(powerset(X45)),X46),X45) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_631])]) ).
fof(f2872,plain,
( ! [X46,X44,X45] :
( sP0(X44,sK4(powerset(X45)),X46)
| ~ empty(X46)
| ~ empty(X44)
| element(sK6(X44,sK4(powerset(X45)),X46),X45) )
| ~ spl20_157
| ~ spl20_250 ),
inference(resolution,[],[f2817,f1268]) ).
fof(f17017,plain,
( spl20_630
| ~ spl20_157
| ~ spl20_249 ),
inference(avatar_split_clause,[],[f2851,f2812,f1267,f17015]) ).
fof(f17015,plain,
( spl20_630
<=> ! [X45,X44,X46] :
( sP0(sK4(powerset(X44)),X45,X46)
| ~ empty(X46)
| ~ empty(X45)
| element(sK6(sK4(powerset(X44)),X45,X46),X44) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_630])]) ).
fof(f2851,plain,
( ! [X46,X44,X45] :
( sP0(sK4(powerset(X44)),X45,X46)
| ~ empty(X46)
| ~ empty(X45)
| element(sK6(sK4(powerset(X44)),X45,X46),X44) )
| ~ spl20_157
| ~ spl20_249 ),
inference(resolution,[],[f2813,f1268]) ).
fof(f17013,plain,
( spl20_629
| ~ spl20_94
| ~ spl20_246 ),
inference(avatar_split_clause,[],[f2792,f2729,f823,f17011]) ).
fof(f17011,plain,
( spl20_629
<=> ! [X4,X5,X3] :
( element(powerset(X4),X3)
| ~ ordinal(X3)
| ~ ordinal(powerset(X4))
| powerset(X4) = X3
| ~ empty(X4)
| ~ in(X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_629])]) ).
fof(f2792,plain,
( ! [X3,X4,X5] :
( element(powerset(X4),X3)
| ~ ordinal(X3)
| ~ ordinal(powerset(X4))
| powerset(X4) = X3
| ~ empty(X4)
| ~ in(X5,X3) )
| ~ spl20_94
| ~ spl20_246 ),
inference(resolution,[],[f2730,f824]) ).
fof(f17009,plain,
( spl20_628
| ~ spl20_167
| ~ spl20_245 ),
inference(avatar_split_clause,[],[f2788,f2725,f1371,f17007]) ).
fof(f17007,plain,
( spl20_628
<=> ! [X4,X5,X3] :
( ~ ordinal(X3)
| ordinal_subset(X4,X3)
| ~ ordinal(X4)
| element(X5,X4)
| X3 = X5
| ~ ordinal(X5)
| element(X3,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_628])]) ).
fof(f2788,plain,
( ! [X3,X4,X5] :
( ~ ordinal(X3)
| ordinal_subset(X4,X3)
| ~ ordinal(X4)
| element(X5,X4)
| X3 = X5
| ~ ordinal(X5)
| element(X3,X5) )
| ~ spl20_167
| ~ spl20_245 ),
inference(duplicate_literal_removal,[],[f2740]) ).
fof(f2740,plain,
( ! [X3,X4,X5] :
( ~ ordinal(X3)
| ordinal_subset(X4,X3)
| ~ ordinal(X4)
| element(X5,X4)
| X3 = X5
| ~ ordinal(X3)
| ~ ordinal(X5)
| element(X3,X5) )
| ~ spl20_167
| ~ spl20_245 ),
inference(resolution,[],[f2726,f1372]) ).
fof(f17005,plain,
( ~ spl20_627
| spl20_376
| ~ spl20_533 ),
inference(avatar_split_clause,[],[f14559,f14532,f5698,f17002]) ).
fof(f5698,plain,
( spl20_376
<=> ordinal_subset(sK8,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_376])]) ).
fof(f14559,plain,
( ~ ordinal_subset(sK8,sK8)
| spl20_376
| ~ spl20_533 ),
inference(superposition,[],[f5699,f14534]) ).
fof(f5699,plain,
( ~ ordinal_subset(sK8,sK2)
| spl20_376 ),
inference(avatar_component_clause,[],[f5698]) ).
fof(f17000,plain,
( spl20_626
| ~ spl20_104
| ~ spl20_245 ),
inference(avatar_split_clause,[],[f2786,f2725,f890,f16998]) ).
fof(f16998,plain,
( spl20_626
<=> ! [X9,X11,X10] :
( ~ ordinal(X9)
| ordinal_subset(X10,X9)
| ~ ordinal(X10)
| element(X11,X10)
| in(X9,X11)
| X9 = X11
| ~ ordinal(X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_626])]) ).
fof(f2786,plain,
( ! [X10,X11,X9] :
( ~ ordinal(X9)
| ordinal_subset(X10,X9)
| ~ ordinal(X10)
| element(X11,X10)
| in(X9,X11)
| X9 = X11
| ~ ordinal(X11) )
| ~ spl20_104
| ~ spl20_245 ),
inference(duplicate_literal_removal,[],[f2742]) ).
fof(f2742,plain,
( ! [X10,X11,X9] :
( ~ ordinal(X9)
| ordinal_subset(X10,X9)
| ~ ordinal(X10)
| element(X11,X10)
| in(X9,X11)
| X9 = X11
| ~ ordinal(X9)
| ~ ordinal(X11) )
| ~ spl20_104
| ~ spl20_245 ),
inference(resolution,[],[f2726,f891]) ).
fof(f16996,plain,
( spl20_625
| ~ spl20_163
| ~ spl20_245 ),
inference(avatar_split_clause,[],[f2748,f2725,f1316,f16994]) ).
fof(f16994,plain,
( spl20_625
<=> ! [X29,X27,X28] :
( ~ ordinal(powerset(X27))
| ordinal_subset(X28,powerset(X27))
| ~ ordinal(X28)
| element(X29,X28)
| empty(powerset(X27))
| ~ subset(X29,X27) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_625])]) ).
fof(f1316,plain,
( spl20_163
<=> ! [X2,X1] :
( empty(powerset(X1))
| in(X2,powerset(X1))
| ~ subset(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_163])]) ).
fof(f2748,plain,
( ! [X28,X29,X27] :
( ~ ordinal(powerset(X27))
| ordinal_subset(X28,powerset(X27))
| ~ ordinal(X28)
| element(X29,X28)
| empty(powerset(X27))
| ~ subset(X29,X27) )
| ~ spl20_163
| ~ spl20_245 ),
inference(resolution,[],[f2726,f1317]) ).
fof(f1317,plain,
( ! [X2,X1] :
( in(X2,powerset(X1))
| empty(powerset(X1))
| ~ subset(X2,X1) )
| ~ spl20_163 ),
inference(avatar_component_clause,[],[f1316]) ).
fof(f16992,plain,
( spl20_624
| ~ spl20_97
| ~ spl20_244 ),
inference(avatar_split_clause,[],[f2734,f2721,f846,f16990]) ).
fof(f16990,plain,
( spl20_624
<=> ! [X6,X7] :
( ~ subset(X6,X7)
| empty(powerset(X7))
| ~ epsilon_transitive(powerset(X7))
| ordinal_subset(X6,powerset(X7))
| ~ ordinal(powerset(X7))
| ~ ordinal(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_624])]) ).
fof(f2721,plain,
( spl20_244
<=> ! [X0,X1] :
( empty(powerset(X0))
| ~ subset(X1,X0)
| subset(X1,powerset(X0))
| ~ epsilon_transitive(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_244])]) ).
fof(f2734,plain,
( ! [X6,X7] :
( ~ subset(X6,X7)
| empty(powerset(X7))
| ~ epsilon_transitive(powerset(X7))
| ordinal_subset(X6,powerset(X7))
| ~ ordinal(powerset(X7))
| ~ ordinal(X6) )
| ~ spl20_97
| ~ spl20_244 ),
inference(resolution,[],[f2722,f847]) ).
fof(f2722,plain,
( ! [X0,X1] :
( subset(X1,powerset(X0))
| ~ subset(X1,X0)
| empty(powerset(X0))
| ~ epsilon_transitive(powerset(X0)) )
| ~ spl20_244 ),
inference(avatar_component_clause,[],[f2721]) ).
fof(f16988,plain,
( spl20_623
| ~ spl20_107
| ~ spl20_234 ),
inference(avatar_split_clause,[],[f2552,f2500,f915,f16986]) ).
fof(f16986,plain,
( spl20_623
<=> ! [X34,X36,X35] :
( ~ ordinal(X34)
| ordinal_subset(X35,X34)
| ~ ordinal(X35)
| ~ empty(X35)
| sK5(X36,X34) = X36
| singleton(X36) = X34 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_623])]) ).
fof(f2552,plain,
( ! [X36,X34,X35] :
( ~ ordinal(X34)
| ordinal_subset(X35,X34)
| ~ ordinal(X35)
| ~ empty(X35)
| sK5(X36,X34) = X36
| singleton(X36) = X34 )
| ~ spl20_107
| ~ spl20_234 ),
inference(resolution,[],[f2501,f916]) ).
fof(f16984,plain,
( spl20_622
| ~ spl20_107
| ~ spl20_223 ),
inference(avatar_split_clause,[],[f2343,f2310,f915,f16982]) ).
fof(f16982,plain,
( spl20_622
<=> ! [X13,X12] :
( ~ empty(X12)
| epsilon_transitive(powerset(X12))
| sK5(X13,sK3(powerset(X12))) = X13
| singleton(X13) = sK3(powerset(X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_622])]) ).
fof(f2343,plain,
( ! [X12,X13] :
( ~ empty(X12)
| epsilon_transitive(powerset(X12))
| sK5(X13,sK3(powerset(X12))) = X13
| singleton(X13) = sK3(powerset(X12)) )
| ~ spl20_107
| ~ spl20_223 ),
inference(resolution,[],[f2311,f916]) ).
fof(f16882,plain,
( spl20_621
| ~ spl20_337
| ~ spl20_533 ),
inference(avatar_split_clause,[],[f14557,f14532,f4923,f16879]) ).
fof(f16879,plain,
( spl20_621
<=> element(sK8,sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_621])]) ).
fof(f4923,plain,
( spl20_337
<=> element(sK2,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_337])]) ).
fof(f14557,plain,
( element(sK8,sK8)
| ~ spl20_337
| ~ spl20_533 ),
inference(superposition,[],[f4925,f14534]) ).
fof(f4925,plain,
( element(sK2,sK2)
| ~ spl20_337 ),
inference(avatar_component_clause,[],[f4923]) ).
fof(f16726,plain,
( spl20_620
| ~ spl20_223
| ~ spl20_316 ),
inference(avatar_split_clause,[],[f4516,f4391,f2310,f16724]) ).
fof(f16724,plain,
( spl20_620
<=> ! [X29,X28] :
( sP0(sK4(powerset(X28)),sK4(powerset(X28)),sK3(powerset(X29)))
| ~ empty(X28)
| ~ empty(X29)
| epsilon_transitive(powerset(X29)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_620])]) ).
fof(f4516,plain,
( ! [X28,X29] :
( sP0(sK4(powerset(X28)),sK4(powerset(X28)),sK3(powerset(X29)))
| ~ empty(X28)
| ~ empty(X29)
| epsilon_transitive(powerset(X29)) )
| ~ spl20_223
| ~ spl20_316 ),
inference(resolution,[],[f4392,f2311]) ).
fof(f16722,plain,
( spl20_619
| ~ spl20_223
| ~ spl20_303 ),
inference(avatar_split_clause,[],[f4094,f3637,f2310,f16720]) ).
fof(f16720,plain,
( spl20_619
<=> ! [X44,X43,X42] :
( sP0(X42,sK4(powerset(X43)),sK3(powerset(X44)))
| ~ empty(X42)
| ~ empty(X43)
| ~ empty(X44)
| epsilon_transitive(powerset(X44)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_619])]) ).
fof(f4094,plain,
( ! [X44,X42,X43] :
( sP0(X42,sK4(powerset(X43)),sK3(powerset(X44)))
| ~ empty(X42)
| ~ empty(X43)
| ~ empty(X44)
| epsilon_transitive(powerset(X44)) )
| ~ spl20_223
| ~ spl20_303 ),
inference(resolution,[],[f3638,f2311]) ).
fof(f16718,plain,
( spl20_618
| ~ spl20_223
| ~ spl20_300 ),
inference(avatar_split_clause,[],[f4036,f3625,f2310,f16716]) ).
fof(f16716,plain,
( spl20_618
<=> ! [X41,X43,X42] :
( sP0(X41,sK3(powerset(X42)),sK4(powerset(X43)))
| ~ empty(X41)
| ~ empty(X43)
| ~ empty(X42)
| epsilon_transitive(powerset(X42)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_618])]) ).
fof(f4036,plain,
( ! [X41,X42,X43] :
( sP0(X41,sK3(powerset(X42)),sK4(powerset(X43)))
| ~ empty(X41)
| ~ empty(X43)
| ~ empty(X42)
| epsilon_transitive(powerset(X42)) )
| ~ spl20_223
| ~ spl20_300 ),
inference(resolution,[],[f3626,f2311]) ).
fof(f16714,plain,
( spl20_617
| ~ spl20_223
| ~ spl20_296 ),
inference(avatar_split_clause,[],[f3983,f3586,f2310,f16712]) ).
fof(f16712,plain,
( spl20_617
<=> ! [X44,X43,X42] :
( sP0(sK4(powerset(X42)),X43,sK3(powerset(X44)))
| ~ empty(X43)
| ~ empty(X42)
| ~ empty(X44)
| epsilon_transitive(powerset(X44)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_617])]) ).
fof(f3983,plain,
( ! [X44,X42,X43] :
( sP0(sK4(powerset(X42)),X43,sK3(powerset(X44)))
| ~ empty(X43)
| ~ empty(X42)
| ~ empty(X44)
| epsilon_transitive(powerset(X44)) )
| ~ spl20_223
| ~ spl20_296 ),
inference(resolution,[],[f3587,f2311]) ).
fof(f16710,plain,
( spl20_616
| ~ spl20_223
| ~ spl20_293 ),
inference(avatar_split_clause,[],[f3930,f3574,f2310,f16708]) ).
fof(f16708,plain,
( spl20_616
<=> ! [X41,X43,X42] :
( sP0(sK3(powerset(X41)),X42,sK4(powerset(X43)))
| ~ empty(X42)
| ~ empty(X43)
| ~ empty(X41)
| epsilon_transitive(powerset(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_616])]) ).
fof(f3930,plain,
( ! [X41,X42,X43] :
( sP0(sK3(powerset(X41)),X42,sK4(powerset(X43)))
| ~ empty(X42)
| ~ empty(X43)
| ~ empty(X41)
| epsilon_transitive(powerset(X41)) )
| ~ spl20_223
| ~ spl20_293 ),
inference(resolution,[],[f3575,f2311]) ).
fof(f16706,plain,
( spl20_615
| ~ spl20_223
| ~ spl20_290 ),
inference(avatar_split_clause,[],[f3877,f3562,f2310,f16704]) ).
fof(f16704,plain,
( spl20_615
<=> ! [X41,X43,X42] :
( sP0(sK4(powerset(X41)),sK3(powerset(X42)),X43)
| ~ empty(X43)
| ~ empty(X41)
| ~ empty(X42)
| epsilon_transitive(powerset(X42)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_615])]) ).
fof(f3877,plain,
( ! [X41,X42,X43] :
( sP0(sK4(powerset(X41)),sK3(powerset(X42)),X43)
| ~ empty(X43)
| ~ empty(X41)
| ~ empty(X42)
| epsilon_transitive(powerset(X42)) )
| ~ spl20_223
| ~ spl20_290 ),
inference(resolution,[],[f3563,f2311]) ).
fof(f16693,plain,
( spl20_614
| ~ spl20_223
| ~ spl20_287 ),
inference(avatar_split_clause,[],[f3824,f3550,f2310,f16691]) ).
fof(f16691,plain,
( spl20_614
<=> ! [X41,X43,X42] :
( sP0(sK3(powerset(X41)),sK4(powerset(X42)),X43)
| ~ empty(X43)
| ~ empty(X42)
| ~ empty(X41)
| epsilon_transitive(powerset(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_614])]) ).
fof(f3824,plain,
( ! [X41,X42,X43] :
( sP0(sK3(powerset(X41)),sK4(powerset(X42)),X43)
| ~ empty(X43)
| ~ empty(X42)
| ~ empty(X41)
| epsilon_transitive(powerset(X41)) )
| ~ spl20_223
| ~ spl20_287 ),
inference(resolution,[],[f3551,f2311]) ).
fof(f16689,plain,
( spl20_613
| ~ spl20_223
| ~ spl20_271 ),
inference(avatar_split_clause,[],[f3401,f3016,f2310,f16687]) ).
fof(f16687,plain,
( spl20_613
<=> ! [X29,X28] :
( sP0(sK3(powerset(X28)),sK3(powerset(X28)),sK4(powerset(X29)))
| ~ empty(X29)
| ~ empty(X28)
| epsilon_transitive(powerset(X28)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_613])]) ).
fof(f3401,plain,
( ! [X28,X29] :
( sP0(sK3(powerset(X28)),sK3(powerset(X28)),sK4(powerset(X29)))
| ~ empty(X29)
| ~ empty(X28)
| epsilon_transitive(powerset(X28)) )
| ~ spl20_223
| ~ spl20_271 ),
inference(resolution,[],[f3017,f2311]) ).
fof(f16685,plain,
( spl20_612
| ~ spl20_234
| ~ spl20_271 ),
inference(avatar_split_clause,[],[f3392,f3016,f2500,f16683]) ).
fof(f16683,plain,
( spl20_612
<=> ! [X9,X11,X10] :
( sP0(X9,X9,sK4(powerset(X10)))
| ~ empty(X10)
| ~ ordinal(X9)
| ordinal_subset(X11,X9)
| ~ ordinal(X11)
| ~ empty(X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_612])]) ).
fof(f3392,plain,
( ! [X10,X11,X9] :
( sP0(X9,X9,sK4(powerset(X10)))
| ~ empty(X10)
| ~ ordinal(X9)
| ordinal_subset(X11,X9)
| ~ ordinal(X11)
| ~ empty(X11) )
| ~ spl20_234
| ~ spl20_271 ),
inference(resolution,[],[f3017,f2501]) ).
fof(f16681,plain,
( spl20_611
| ~ spl20_234
| ~ spl20_251 ),
inference(avatar_split_clause,[],[f2883,f2820,f2500,f16679]) ).
fof(f16679,plain,
( spl20_611
<=> ! [X17,X14,X16,X15] :
( sP0(X14,X15,X16)
| ~ empty(X15)
| ~ empty(X14)
| ~ ordinal(X16)
| ordinal_subset(X17,X16)
| ~ ordinal(X17)
| ~ empty(X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_611])]) ).
fof(f2883,plain,
( ! [X16,X14,X17,X15] :
( sP0(X14,X15,X16)
| ~ empty(X15)
| ~ empty(X14)
| ~ ordinal(X16)
| ordinal_subset(X17,X16)
| ~ ordinal(X17)
| ~ empty(X17) )
| ~ spl20_234
| ~ spl20_251 ),
inference(resolution,[],[f2821,f2501]) ).
fof(f16677,plain,
( spl20_610
| ~ spl20_234
| ~ spl20_250 ),
inference(avatar_split_clause,[],[f2862,f2816,f2500,f16675]) ).
fof(f16675,plain,
( spl20_610
<=> ! [X13,X14,X16,X15] :
( sP0(X13,X14,X15)
| ~ empty(X15)
| ~ empty(X13)
| ~ ordinal(X14)
| ordinal_subset(X16,X14)
| ~ ordinal(X16)
| ~ empty(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_610])]) ).
fof(f2862,plain,
( ! [X16,X14,X15,X13] :
( sP0(X13,X14,X15)
| ~ empty(X15)
| ~ empty(X13)
| ~ ordinal(X14)
| ordinal_subset(X16,X14)
| ~ ordinal(X16)
| ~ empty(X16) )
| ~ spl20_234
| ~ spl20_250 ),
inference(resolution,[],[f2817,f2501]) ).
fof(f16673,plain,
( spl20_609
| ~ spl20_234
| ~ spl20_249 ),
inference(avatar_split_clause,[],[f2841,f2812,f2500,f16671]) ).
fof(f16671,plain,
( spl20_609
<=> ! [X13,X14,X16,X15] :
( sP0(X13,X14,X15)
| ~ empty(X15)
| ~ empty(X14)
| ~ ordinal(X13)
| ordinal_subset(X16,X13)
| ~ ordinal(X16)
| ~ empty(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_609])]) ).
fof(f2841,plain,
( ! [X16,X14,X15,X13] :
( sP0(X13,X14,X15)
| ~ empty(X15)
| ~ empty(X14)
| ~ ordinal(X13)
| ordinal_subset(X16,X13)
| ~ ordinal(X16)
| ~ empty(X16) )
| ~ spl20_234
| ~ spl20_249 ),
inference(resolution,[],[f2813,f2501]) ).
fof(f16669,plain,
( spl20_608
| ~ spl20_222
| ~ spl20_247 ),
inference(avatar_split_clause,[],[f2833,f2804,f2306,f16667]) ).
fof(f16667,plain,
( spl20_608
<=> ! [X10] :
( ~ ordinal(sK4(powerset(X10)))
| ~ ordinal(X10)
| ~ empty(X10)
| sK4(powerset(X10)) = X10
| ~ epsilon_transitive(sK4(powerset(X10))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_608])]) ).
fof(f2804,plain,
( spl20_247
<=> ! [X0,X1] :
( X0 = X1
| ~ ordinal(X0)
| ~ ordinal(X1)
| ~ empty(X1)
| subset(X1,X0)
| ~ epsilon_transitive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_247])]) ).
fof(f2833,plain,
( ! [X10] :
( ~ ordinal(sK4(powerset(X10)))
| ~ ordinal(X10)
| ~ empty(X10)
| sK4(powerset(X10)) = X10
| ~ epsilon_transitive(sK4(powerset(X10))) )
| ~ spl20_222
| ~ spl20_247 ),
inference(duplicate_literal_removal,[],[f2827]) ).
fof(f2827,plain,
( ! [X10] :
( ~ ordinal(sK4(powerset(X10)))
| ~ ordinal(X10)
| ~ empty(X10)
| sK4(powerset(X10)) = X10
| ~ epsilon_transitive(sK4(powerset(X10)))
| sK4(powerset(X10)) = X10 )
| ~ spl20_222
| ~ spl20_247 ),
inference(resolution,[],[f2805,f2307]) ).
fof(f2805,plain,
( ! [X0,X1] :
( subset(X1,X0)
| ~ ordinal(X0)
| ~ ordinal(X1)
| ~ empty(X1)
| X0 = X1
| ~ epsilon_transitive(X0) )
| ~ spl20_247 ),
inference(avatar_component_clause,[],[f2804]) ).
fof(f16665,plain,
( spl20_607
| ~ spl20_166
| ~ spl20_245 ),
inference(avatar_split_clause,[],[f2787,f2725,f1355,f16663]) ).
fof(f16663,plain,
( spl20_607
<=> ! [X6,X7,X8] :
( ~ ordinal(X6)
| ordinal_subset(X7,X6)
| ~ ordinal(X7)
| element(X8,X7)
| X6 = X8
| ~ ordinal(X8)
| ~ empty(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_607])]) ).
fof(f2787,plain,
( ! [X8,X6,X7] :
( ~ ordinal(X6)
| ordinal_subset(X7,X6)
| ~ ordinal(X7)
| element(X8,X7)
| X6 = X8
| ~ ordinal(X8)
| ~ empty(X8) )
| ~ spl20_166
| ~ spl20_245 ),
inference(duplicate_literal_removal,[],[f2741]) ).
fof(f2741,plain,
( ! [X8,X6,X7] :
( ~ ordinal(X6)
| ordinal_subset(X7,X6)
| ~ ordinal(X7)
| element(X8,X7)
| X6 = X8
| ~ ordinal(X6)
| ~ ordinal(X8)
| ~ empty(X8) )
| ~ spl20_166
| ~ spl20_245 ),
inference(resolution,[],[f2726,f1356]) ).
fof(f16661,plain,
( spl20_606
| ~ spl20_213
| ~ spl20_245 ),
inference(avatar_split_clause,[],[f2745,f2725,f2204,f16659]) ).
fof(f16659,plain,
( spl20_606
<=> ! [X19,X20,X21,X22] :
( ~ ordinal(set_union2(X19,X20))
| ordinal_subset(X21,set_union2(X19,X20))
| ~ ordinal(X21)
| element(X22,X21)
| ~ in(X22,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_606])]) ).
fof(f2745,plain,
( ! [X21,X19,X22,X20] :
( ~ ordinal(set_union2(X19,X20))
| ordinal_subset(X21,set_union2(X19,X20))
| ~ ordinal(X21)
| element(X22,X21)
| ~ in(X22,X20) )
| ~ spl20_213
| ~ spl20_245 ),
inference(resolution,[],[f2726,f2205]) ).
fof(f16657,plain,
( spl20_605
| ~ spl20_214
| ~ spl20_245 ),
inference(avatar_split_clause,[],[f2744,f2725,f2208,f16655]) ).
fof(f16655,plain,
( spl20_605
<=> ! [X18,X17,X16,X15] :
( ~ ordinal(set_union2(X15,X16))
| ordinal_subset(X17,set_union2(X15,X16))
| ~ ordinal(X17)
| element(X18,X17)
| ~ in(X18,X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_605])]) ).
fof(f2744,plain,
( ! [X18,X16,X17,X15] :
( ~ ordinal(set_union2(X15,X16))
| ordinal_subset(X17,set_union2(X15,X16))
| ~ ordinal(X17)
| element(X18,X17)
| ~ in(X18,X15) )
| ~ spl20_214
| ~ spl20_245 ),
inference(resolution,[],[f2726,f2209]) ).
fof(f16652,plain,
( spl20_604
| ~ spl20_91
| ~ spl20_244 ),
inference(avatar_split_clause,[],[f2735,f2721,f811,f16650]) ).
fof(f16650,plain,
( spl20_604
<=> ! [X9,X8] :
( ~ subset(X8,X9)
| empty(powerset(X9))
| ~ epsilon_transitive(powerset(X9))
| powerset(X9) = X8
| ~ subset(powerset(X9),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_604])]) ).
fof(f2735,plain,
( ! [X8,X9] :
( ~ subset(X8,X9)
| empty(powerset(X9))
| ~ epsilon_transitive(powerset(X9))
| powerset(X9) = X8
| ~ subset(powerset(X9),X8) )
| ~ spl20_91
| ~ spl20_244 ),
inference(resolution,[],[f2722,f812]) ).
fof(f16648,plain,
( spl20_603
| ~ spl20_167
| ~ spl20_234 ),
inference(avatar_split_clause,[],[f2583,f2500,f1371,f16646]) ).
fof(f16646,plain,
( spl20_603
<=> ! [X4,X5,X3] :
( ~ ordinal(X3)
| ordinal_subset(X4,X3)
| ~ ordinal(X4)
| ~ empty(X4)
| X3 = X5
| ~ ordinal(X5)
| element(X3,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_603])]) ).
fof(f2583,plain,
( ! [X3,X4,X5] :
( ~ ordinal(X3)
| ordinal_subset(X4,X3)
| ~ ordinal(X4)
| ~ empty(X4)
| X3 = X5
| ~ ordinal(X5)
| element(X3,X5) )
| ~ spl20_167
| ~ spl20_234 ),
inference(duplicate_literal_removal,[],[f2541]) ).
fof(f2541,plain,
( ! [X3,X4,X5] :
( ~ ordinal(X3)
| ordinal_subset(X4,X3)
| ~ ordinal(X4)
| ~ empty(X4)
| X3 = X5
| ~ ordinal(X3)
| ~ ordinal(X5)
| element(X3,X5) )
| ~ spl20_167
| ~ spl20_234 ),
inference(resolution,[],[f2501,f1372]) ).
fof(f16644,plain,
( spl20_602
| ~ spl20_104
| ~ spl20_234 ),
inference(avatar_split_clause,[],[f2581,f2500,f890,f16642]) ).
fof(f16642,plain,
( spl20_602
<=> ! [X9,X11,X10] :
( ~ ordinal(X9)
| ordinal_subset(X10,X9)
| ~ ordinal(X10)
| ~ empty(X10)
| in(X9,X11)
| X9 = X11
| ~ ordinal(X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_602])]) ).
fof(f2581,plain,
( ! [X10,X11,X9] :
( ~ ordinal(X9)
| ordinal_subset(X10,X9)
| ~ ordinal(X10)
| ~ empty(X10)
| in(X9,X11)
| X9 = X11
| ~ ordinal(X11) )
| ~ spl20_104
| ~ spl20_234 ),
inference(duplicate_literal_removal,[],[f2543]) ).
fof(f2543,plain,
( ! [X10,X11,X9] :
( ~ ordinal(X9)
| ordinal_subset(X10,X9)
| ~ ordinal(X10)
| ~ empty(X10)
| in(X9,X11)
| X9 = X11
| ~ ordinal(X9)
| ~ ordinal(X11) )
| ~ spl20_104
| ~ spl20_234 ),
inference(resolution,[],[f2501,f891]) ).
fof(f16180,plain,
( spl20_601
| ~ spl20_75
| ~ spl20_272 ),
inference(avatar_split_clause,[],[f3420,f3020,f653,f16178]) ).
fof(f16178,plain,
( spl20_601
<=> ! [X16,X17] :
( element(sK6(X16,X16,X17),X16)
| sP0(X16,X16,X17)
| ~ in(X17,sK6(X16,X16,X17)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_601])]) ).
fof(f3420,plain,
( ! [X16,X17] :
( element(sK6(X16,X16,X17),X16)
| sP0(X16,X16,X17)
| ~ in(X17,sK6(X16,X16,X17)) )
| ~ spl20_75
| ~ spl20_272 ),
inference(resolution,[],[f3021,f654]) ).
fof(f16176,plain,
( spl20_600
| ~ spl20_75
| ~ spl20_271 ),
inference(avatar_split_clause,[],[f3395,f3016,f653,f16174]) ).
fof(f16174,plain,
( spl20_600
<=> ! [X16,X17] :
( sP0(X16,X16,sK4(powerset(X17)))
| ~ empty(X17)
| ~ in(X16,sK6(X16,X16,sK4(powerset(X17)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_600])]) ).
fof(f3395,plain,
( ! [X16,X17] :
( sP0(X16,X16,sK4(powerset(X17)))
| ~ empty(X17)
| ~ in(X16,sK6(X16,X16,sK4(powerset(X17)))) )
| ~ spl20_75
| ~ spl20_271 ),
inference(resolution,[],[f3017,f654]) ).
fof(f16172,plain,
( spl20_599
| ~ spl20_76
| ~ spl20_271 ),
inference(avatar_split_clause,[],[f3394,f3016,f657,f16170]) ).
fof(f16170,plain,
( spl20_599
<=> ! [X14,X15] :
( sP0(X14,X14,sK4(powerset(X15)))
| ~ empty(X15)
| element(sK6(X14,X14,sK4(powerset(X15))),X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_599])]) ).
fof(f3394,plain,
( ! [X14,X15] :
( sP0(X14,X14,sK4(powerset(X15)))
| ~ empty(X15)
| element(sK6(X14,X14,sK4(powerset(X15))),X14) )
| ~ spl20_76
| ~ spl20_271 ),
inference(resolution,[],[f3017,f658]) ).
fof(f16168,plain,
( spl20_598
| ~ spl20_75
| ~ spl20_269 ),
inference(avatar_split_clause,[],[f3368,f3008,f653,f16166]) ).
fof(f16166,plain,
( spl20_598
<=> ! [X16,X17] :
( element(sK6(X16,X16,X17),X17)
| sP0(X16,X16,X17)
| ~ in(X16,sK6(X16,X16,X17)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_598])]) ).
fof(f3368,plain,
( ! [X16,X17] :
( element(sK6(X16,X16,X17),X17)
| sP0(X16,X16,X17)
| ~ in(X16,sK6(X16,X16,X17)) )
| ~ spl20_75
| ~ spl20_269 ),
inference(resolution,[],[f3009,f654]) ).
fof(f16164,plain,
( spl20_597
| ~ spl20_76
| ~ spl20_269 ),
inference(avatar_split_clause,[],[f3367,f3008,f657,f16162]) ).
fof(f16162,plain,
( spl20_597
<=> ! [X14,X15] :
( element(sK6(X14,X14,X15),X15)
| sP0(X14,X14,X15)
| element(sK6(X14,X14,X15),X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_597])]) ).
fof(f3367,plain,
( ! [X14,X15] :
( element(sK6(X14,X14,X15),X15)
| sP0(X14,X14,X15)
| element(sK6(X14,X14,X15),X14) )
| ~ spl20_76
| ~ spl20_269 ),
inference(resolution,[],[f3009,f658]) ).
fof(f16160,plain,
( spl20_596
| ~ spl20_153
| ~ spl20_251 ),
inference(avatar_split_clause,[],[f2889,f2820,f1230,f16158]) ).
fof(f16158,plain,
( spl20_596
<=> ! [X34,X36,X35] :
( sP0(X34,X35,singleton(X36))
| ~ empty(X35)
| ~ empty(X34)
| sK6(X34,X35,singleton(X36)) = X36 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_596])]) ).
fof(f2889,plain,
( ! [X36,X34,X35] :
( sP0(X34,X35,singleton(X36))
| ~ empty(X35)
| ~ empty(X34)
| sK6(X34,X35,singleton(X36)) = X36 )
| ~ spl20_153
| ~ spl20_251 ),
inference(resolution,[],[f2821,f1231]) ).
fof(f16156,plain,
( spl20_595
| ~ spl20_88
| ~ spl20_251 ),
inference(avatar_split_clause,[],[f2884,f2820,f772,f16154]) ).
fof(f16154,plain,
( spl20_595
<=> ! [X20,X18,X19] :
( sP0(X18,X19,X20)
| ~ empty(X19)
| ~ empty(X18)
| subset(sK6(X18,X19,X20),X20)
| ~ epsilon_transitive(X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_595])]) ).
fof(f2884,plain,
( ! [X18,X19,X20] :
( sP0(X18,X19,X20)
| ~ empty(X19)
| ~ empty(X18)
| subset(sK6(X18,X19,X20),X20)
| ~ epsilon_transitive(X20) )
| ~ spl20_88
| ~ spl20_251 ),
inference(resolution,[],[f2821,f773]) ).
fof(f16146,plain,
( spl20_594
| ~ spl20_153
| ~ spl20_250 ),
inference(avatar_split_clause,[],[f2868,f2816,f1230,f16144]) ).
fof(f16144,plain,
( spl20_594
<=> ! [X34,X35,X33] :
( sP0(X33,singleton(X34),X35)
| ~ empty(X35)
| ~ empty(X33)
| sK6(X33,singleton(X34),X35) = X34 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_594])]) ).
fof(f2868,plain,
( ! [X34,X35,X33] :
( sP0(X33,singleton(X34),X35)
| ~ empty(X35)
| ~ empty(X33)
| sK6(X33,singleton(X34),X35) = X34 )
| ~ spl20_153
| ~ spl20_250 ),
inference(resolution,[],[f2817,f1231]) ).
fof(f16142,plain,
( spl20_593
| ~ spl20_88
| ~ spl20_250 ),
inference(avatar_split_clause,[],[f2863,f2816,f772,f16140]) ).
fof(f16140,plain,
( spl20_593
<=> ! [X18,X17,X19] :
( sP0(X17,X18,X19)
| ~ empty(X19)
| ~ empty(X17)
| subset(sK6(X17,X18,X19),X18)
| ~ epsilon_transitive(X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_593])]) ).
fof(f2863,plain,
( ! [X18,X19,X17] :
( sP0(X17,X18,X19)
| ~ empty(X19)
| ~ empty(X17)
| subset(sK6(X17,X18,X19),X18)
| ~ epsilon_transitive(X18) )
| ~ spl20_88
| ~ spl20_250 ),
inference(resolution,[],[f2817,f773]) ).
fof(f16138,plain,
( spl20_592
| ~ spl20_153
| ~ spl20_249 ),
inference(avatar_split_clause,[],[f2847,f2812,f1230,f16136]) ).
fof(f16136,plain,
( spl20_592
<=> ! [X34,X35,X33] :
( sP0(singleton(X33),X34,X35)
| ~ empty(X35)
| ~ empty(X34)
| sK6(singleton(X33),X34,X35) = X33 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_592])]) ).
fof(f2847,plain,
( ! [X34,X35,X33] :
( sP0(singleton(X33),X34,X35)
| ~ empty(X35)
| ~ empty(X34)
| sK6(singleton(X33),X34,X35) = X33 )
| ~ spl20_153
| ~ spl20_249 ),
inference(resolution,[],[f2813,f1231]) ).
fof(f16134,plain,
( spl20_591
| ~ spl20_88
| ~ spl20_249 ),
inference(avatar_split_clause,[],[f2842,f2812,f772,f16132]) ).
fof(f16132,plain,
( spl20_591
<=> ! [X18,X17,X19] :
( sP0(X17,X18,X19)
| ~ empty(X19)
| ~ empty(X18)
| subset(sK6(X17,X18,X19),X17)
| ~ epsilon_transitive(X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_591])]) ).
fof(f2842,plain,
( ! [X18,X19,X17] :
( sP0(X17,X18,X19)
| ~ empty(X19)
| ~ empty(X18)
| subset(sK6(X17,X18,X19),X17)
| ~ epsilon_transitive(X17) )
| ~ spl20_88
| ~ spl20_249 ),
inference(resolution,[],[f2813,f773]) ).
fof(f16130,plain,
( spl20_590
| ~ spl20_84
| ~ spl20_246 ),
inference(avatar_split_clause,[],[f2793,f2729,f732,f16128]) ).
fof(f16128,plain,
( spl20_590
<=> ! [X6,X7] :
( element(powerset(X7),X6)
| ~ ordinal(X6)
| ~ ordinal(powerset(X7))
| powerset(X7) = X6
| subset(X6,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_590])]) ).
fof(f2793,plain,
( ! [X6,X7] :
( element(powerset(X7),X6)
| ~ ordinal(X6)
| ~ ordinal(powerset(X7))
| powerset(X7) = X6
| subset(X6,X7) )
| ~ spl20_84
| ~ spl20_246 ),
inference(resolution,[],[f2730,f733]) ).
fof(f16126,plain,
( spl20_589
| ~ spl20_218
| ~ spl20_244 ),
inference(avatar_split_clause,[],[f2736,f2721,f2226,f16124]) ).
fof(f16124,plain,
( spl20_589
<=> ! [X10] :
( ~ subset(succ(powerset(powerset(X10))),X10)
| empty(powerset(X10))
| ~ epsilon_transitive(powerset(X10))
| empty(powerset(powerset(X10))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_589])]) ).
fof(f2736,plain,
( ! [X10] :
( ~ subset(succ(powerset(powerset(X10))),X10)
| empty(powerset(X10))
| ~ epsilon_transitive(powerset(X10))
| empty(powerset(powerset(X10))) )
| ~ spl20_218
| ~ spl20_244 ),
inference(resolution,[],[f2722,f2227]) ).
fof(f16122,plain,
( spl20_588
| ~ spl20_160
| ~ spl20_244 ),
inference(avatar_split_clause,[],[f2732,f2721,f1291,f16120]) ).
fof(f16120,plain,
( spl20_588
<=> ! [X2,X0,X1] :
( ~ subset(X0,X1)
| empty(powerset(X1))
| ~ epsilon_transitive(powerset(X1))
| ~ in(X2,X0)
| element(X2,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_588])]) ).
fof(f2732,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,X1)
| empty(powerset(X1))
| ~ epsilon_transitive(powerset(X1))
| ~ in(X2,X0)
| element(X2,powerset(X1)) )
| ~ spl20_160
| ~ spl20_244 ),
inference(resolution,[],[f2722,f1292]) ).
fof(f16118,plain,
( spl20_587
| ~ spl20_157
| ~ spl20_242 ),
inference(avatar_split_clause,[],[f2714,f2533,f1267,f16116]) ).
fof(f16116,plain,
( spl20_587
<=> ! [X27,X28] :
( sP0(X27,X27,sK4(powerset(X28)))
| ~ empty(X27)
| element(sK6(X27,X27,sK4(powerset(X28))),X28) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_587])]) ).
fof(f2714,plain,
( ! [X28,X27] :
( sP0(X27,X27,sK4(powerset(X28)))
| ~ empty(X27)
| element(sK6(X27,X27,sK4(powerset(X28))),X28) )
| ~ spl20_157
| ~ spl20_242 ),
inference(resolution,[],[f2534,f1268]) ).
fof(f16114,plain,
( spl20_586
| ~ spl20_153
| ~ spl20_241 ),
inference(avatar_split_clause,[],[f2690,f2529,f1230,f16112]) ).
fof(f16112,plain,
( spl20_586
<=> ! [X20,X21] :
( sP0(singleton(X20),singleton(X20),X21)
| ~ empty(X21)
| sK6(singleton(X20),singleton(X20),X21) = X20 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_586])]) ).
fof(f2690,plain,
( ! [X21,X20] :
( sP0(singleton(X20),singleton(X20),X21)
| ~ empty(X21)
| sK6(singleton(X20),singleton(X20),X21) = X20 )
| ~ spl20_153
| ~ spl20_241 ),
inference(resolution,[],[f2530,f1231]) ).
fof(f16110,plain,
( spl20_585
| ~ spl20_213
| ~ spl20_234 ),
inference(avatar_split_clause,[],[f2546,f2500,f2204,f16108]) ).
fof(f16108,plain,
( spl20_585
<=> ! [X22,X20,X21,X19] :
( ~ ordinal(set_union2(X19,X20))
| ordinal_subset(X21,set_union2(X19,X20))
| ~ ordinal(X21)
| ~ empty(X21)
| ~ in(X22,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_585])]) ).
fof(f2546,plain,
( ! [X21,X19,X22,X20] :
( ~ ordinal(set_union2(X19,X20))
| ordinal_subset(X21,set_union2(X19,X20))
| ~ ordinal(X21)
| ~ empty(X21)
| ~ in(X22,X20) )
| ~ spl20_213
| ~ spl20_234 ),
inference(resolution,[],[f2501,f2205]) ).
fof(f16100,plain,
( spl20_584
| ~ spl20_214
| ~ spl20_234 ),
inference(avatar_split_clause,[],[f2545,f2500,f2208,f16098]) ).
fof(f16098,plain,
( spl20_584
<=> ! [X18,X16,X17,X15] :
( ~ ordinal(set_union2(X15,X16))
| ordinal_subset(X17,set_union2(X15,X16))
| ~ ordinal(X17)
| ~ empty(X17)
| ~ in(X18,X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_584])]) ).
fof(f2545,plain,
( ! [X18,X16,X17,X15] :
( ~ ordinal(set_union2(X15,X16))
| ordinal_subset(X17,set_union2(X15,X16))
| ~ ordinal(X17)
| ~ empty(X17)
| ~ in(X18,X15) )
| ~ spl20_214
| ~ spl20_234 ),
inference(resolution,[],[f2501,f2209]) ).
fof(f16096,plain,
( spl20_583
| ~ spl20_146
| ~ spl20_231 ),
inference(avatar_split_clause,[],[f2455,f2402,f1180,f16094]) ).
fof(f16094,plain,
( spl20_583
<=> ! [X24,X23] :
( in(sK4(set_union2(X23,X24)),X23)
| in(sK4(set_union2(X23,X24)),X24)
| empty(set_union2(X23,X24)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_583])]) ).
fof(f2455,plain,
( ! [X24,X23] :
( in(sK4(set_union2(X23,X24)),X23)
| in(sK4(set_union2(X23,X24)),X24)
| empty(set_union2(X23,X24)) )
| ~ spl20_146
| ~ spl20_231 ),
inference(resolution,[],[f2403,f1181]) ).
fof(f16092,plain,
( spl20_582
| ~ spl20_71
| ~ spl20_231 ),
inference(avatar_split_clause,[],[f2454,f2402,f637,f16090]) ).
fof(f16090,plain,
( spl20_582
<=> ! [X22,X21] :
( in(sK3(set_union2(X21,X22)),X21)
| in(sK3(set_union2(X21,X22)),X22)
| epsilon_transitive(set_union2(X21,X22)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_582])]) ).
fof(f2454,plain,
( ! [X21,X22] :
( in(sK3(set_union2(X21,X22)),X21)
| in(sK3(set_union2(X21,X22)),X22)
| epsilon_transitive(set_union2(X21,X22)) )
| ~ spl20_71
| ~ spl20_231 ),
inference(resolution,[],[f2403,f638]) ).
fof(f15469,plain,
( spl20_581
| ~ spl20_103
| ~ spl20_274 ),
inference(avatar_split_clause,[],[f3466,f3440,f886,f15467]) ).
fof(f15467,plain,
( spl20_581
<=> ! [X9,X8] :
( singleton(X8) = singleton(X9)
| ~ in(X8,singleton(X9))
| sK5(X8,singleton(X9)) = X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_581])]) ).
fof(f886,plain,
( spl20_103
<=> ! [X0,X1] :
( singleton(X0) = X1
| sK5(X0,X1) != X0
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_103])]) ).
fof(f3440,plain,
( spl20_274
<=> ! [X6,X7] :
( sK5(X6,singleton(X7)) = X7
| sK5(X6,singleton(X7)) = X6
| singleton(X6) = singleton(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_274])]) ).
fof(f3466,plain,
( ! [X8,X9] :
( singleton(X8) = singleton(X9)
| ~ in(X8,singleton(X9))
| sK5(X8,singleton(X9)) = X9 )
| ~ spl20_103
| ~ spl20_274 ),
inference(trivial_inequality_removal,[],[f3465]) ).
fof(f3465,plain,
( ! [X8,X9] :
( X8 != X8
| singleton(X8) = singleton(X9)
| ~ in(X8,singleton(X9))
| sK5(X8,singleton(X9)) = X9 )
| ~ spl20_103
| ~ spl20_274 ),
inference(duplicate_literal_removal,[],[f3462]) ).
fof(f3462,plain,
( ! [X8,X9] :
( X8 != X8
| singleton(X8) = singleton(X9)
| ~ in(X8,singleton(X9))
| sK5(X8,singleton(X9)) = X9
| singleton(X8) = singleton(X9) )
| ~ spl20_103
| ~ spl20_274 ),
inference(superposition,[],[f887,f3441]) ).
fof(f3441,plain,
( ! [X6,X7] :
( sK5(X6,singleton(X7)) = X7
| sK5(X6,singleton(X7)) = X6
| singleton(X6) = singleton(X7) )
| ~ spl20_274 ),
inference(avatar_component_clause,[],[f3440]) ).
fof(f887,plain,
( ! [X0,X1] :
( sK5(X0,X1) != X0
| singleton(X0) = X1
| ~ in(X0,X1) )
| ~ spl20_103 ),
inference(avatar_component_clause,[],[f886]) ).
fof(f15465,plain,
( spl20_580
| ~ spl20_97
| ~ spl20_253 ),
inference(avatar_split_clause,[],[f2934,f2904,f846,f15463]) ).
fof(f15463,plain,
( spl20_580
<=> ! [X6,X7] :
( ~ ordinal(X6)
| ~ ordinal(X7)
| element(X6,X7)
| X6 = X7
| ~ epsilon_transitive(X6)
| ordinal_subset(X7,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_580])]) ).
fof(f2934,plain,
( ! [X6,X7] :
( ~ ordinal(X6)
| ~ ordinal(X7)
| element(X6,X7)
| X6 = X7
| ~ epsilon_transitive(X6)
| ordinal_subset(X7,X6) )
| ~ spl20_97
| ~ spl20_253 ),
inference(duplicate_literal_removal,[],[f2924]) ).
fof(f2924,plain,
( ! [X6,X7] :
( ~ ordinal(X6)
| ~ ordinal(X7)
| element(X6,X7)
| X6 = X7
| ~ epsilon_transitive(X6)
| ordinal_subset(X7,X6)
| ~ ordinal(X6)
| ~ ordinal(X7) )
| ~ spl20_97
| ~ spl20_253 ),
inference(resolution,[],[f2905,f847]) ).
fof(f15461,plain,
( spl20_579
| ~ spl20_91
| ~ spl20_253 ),
inference(avatar_split_clause,[],[f2933,f2904,f811,f15459]) ).
fof(f15459,plain,
( spl20_579
<=> ! [X9,X8] :
( ~ ordinal(X8)
| ~ ordinal(X9)
| element(X8,X9)
| X8 = X9
| ~ epsilon_transitive(X8)
| ~ subset(X8,X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_579])]) ).
fof(f2933,plain,
( ! [X8,X9] :
( ~ ordinal(X8)
| ~ ordinal(X9)
| element(X8,X9)
| X8 = X9
| ~ epsilon_transitive(X8)
| ~ subset(X8,X9) )
| ~ spl20_91
| ~ spl20_253 ),
inference(duplicate_literal_removal,[],[f2925]) ).
fof(f2925,plain,
( ! [X8,X9] :
( ~ ordinal(X8)
| ~ ordinal(X9)
| element(X8,X9)
| X8 = X9
| ~ epsilon_transitive(X8)
| X8 = X9
| ~ subset(X8,X9) )
| ~ spl20_91
| ~ spl20_253 ),
inference(resolution,[],[f2905,f812]) ).
fof(f15457,plain,
( spl20_578
| ~ spl20_223
| ~ spl20_251 ),
inference(avatar_split_clause,[],[f2892,f2820,f2310,f15455]) ).
fof(f15455,plain,
( spl20_578
<=> ! [X44,X43,X42] :
( sP0(X42,X43,sK3(powerset(X44)))
| ~ empty(X43)
| ~ empty(X42)
| ~ empty(X44)
| epsilon_transitive(powerset(X44)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_578])]) ).
fof(f2892,plain,
( ! [X44,X42,X43] :
( sP0(X42,X43,sK3(powerset(X44)))
| ~ empty(X43)
| ~ empty(X42)
| ~ empty(X44)
| epsilon_transitive(powerset(X44)) )
| ~ spl20_223
| ~ spl20_251 ),
inference(resolution,[],[f2821,f2311]) ).
fof(f15453,plain,
( spl20_577
| ~ spl20_223
| ~ spl20_250 ),
inference(avatar_split_clause,[],[f2871,f2816,f2310,f15451]) ).
fof(f15451,plain,
( spl20_577
<=> ! [X41,X43,X42] :
( sP0(X41,sK3(powerset(X42)),X43)
| ~ empty(X43)
| ~ empty(X41)
| ~ empty(X42)
| epsilon_transitive(powerset(X42)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_577])]) ).
fof(f2871,plain,
( ! [X41,X42,X43] :
( sP0(X41,sK3(powerset(X42)),X43)
| ~ empty(X43)
| ~ empty(X41)
| ~ empty(X42)
| epsilon_transitive(powerset(X42)) )
| ~ spl20_223
| ~ spl20_250 ),
inference(resolution,[],[f2817,f2311]) ).
fof(f15449,plain,
( spl20_576
| ~ spl20_223
| ~ spl20_249 ),
inference(avatar_split_clause,[],[f2850,f2812,f2310,f15447]) ).
fof(f15447,plain,
( spl20_576
<=> ! [X41,X43,X42] :
( sP0(sK3(powerset(X41)),X42,X43)
| ~ empty(X43)
| ~ empty(X42)
| ~ empty(X41)
| epsilon_transitive(powerset(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_576])]) ).
fof(f2850,plain,
( ! [X41,X42,X43] :
( sP0(sK3(powerset(X41)),X42,X43)
| ~ empty(X43)
| ~ empty(X42)
| ~ empty(X41)
| epsilon_transitive(powerset(X41)) )
| ~ spl20_223
| ~ spl20_249 ),
inference(resolution,[],[f2813,f2311]) ).
fof(f15441,plain,
( spl20_575
| ~ spl20_234
| ~ spl20_242 ),
inference(avatar_split_clause,[],[f2704,f2533,f2500,f15439]) ).
fof(f15439,plain,
( spl20_575
<=> ! [X6,X7,X8] :
( sP0(X6,X6,X7)
| ~ empty(X6)
| ~ ordinal(X7)
| ordinal_subset(X8,X7)
| ~ ordinal(X8)
| ~ empty(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_575])]) ).
fof(f2704,plain,
( ! [X8,X6,X7] :
( sP0(X6,X6,X7)
| ~ empty(X6)
| ~ ordinal(X7)
| ordinal_subset(X8,X7)
| ~ ordinal(X8)
| ~ empty(X8) )
| ~ spl20_234
| ~ spl20_242 ),
inference(resolution,[],[f2534,f2501]) ).
fof(f15437,plain,
( spl20_574
| ~ spl20_223
| ~ spl20_241 ),
inference(avatar_split_clause,[],[f2693,f2529,f2310,f15435]) ).
fof(f15435,plain,
( spl20_574
<=> ! [X25,X26] :
( sP0(sK3(powerset(X25)),sK3(powerset(X25)),X26)
| ~ empty(X26)
| ~ empty(X25)
| epsilon_transitive(powerset(X25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_574])]) ).
fof(f2693,plain,
( ! [X26,X25] :
( sP0(sK3(powerset(X25)),sK3(powerset(X25)),X26)
| ~ empty(X26)
| ~ empty(X25)
| epsilon_transitive(powerset(X25)) )
| ~ spl20_223
| ~ spl20_241 ),
inference(resolution,[],[f2530,f2311]) ).
fof(f15433,plain,
( spl20_573
| ~ spl20_234
| ~ spl20_241 ),
inference(avatar_split_clause,[],[f2684,f2529,f2500,f15431]) ).
fof(f15431,plain,
( spl20_573
<=> ! [X6,X7,X8] :
( sP0(X6,X6,X7)
| ~ empty(X7)
| ~ ordinal(X6)
| ordinal_subset(X8,X6)
| ~ ordinal(X8)
| ~ empty(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_573])]) ).
fof(f2684,plain,
( ! [X8,X6,X7] :
( sP0(X6,X6,X7)
| ~ empty(X7)
| ~ ordinal(X6)
| ordinal_subset(X8,X6)
| ~ ordinal(X8)
| ~ empty(X8) )
| ~ spl20_234
| ~ spl20_241 ),
inference(resolution,[],[f2530,f2501]) ).
fof(f15429,plain,
( spl20_572
| ~ spl20_100
| ~ spl20_225 ),
inference(avatar_split_clause,[],[f2375,f2318,f858,f15427]) ).
fof(f15427,plain,
( spl20_572
<=> ! [X0,X1] :
( empty(sK4(powerset(powerset(X0))))
| element(X1,X0)
| ~ in(X1,sK4(sK4(powerset(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_572])]) ).
fof(f2318,plain,
( spl20_225
<=> ! [X5] :
( element(sK4(sK4(powerset(X5))),X5)
| empty(sK4(powerset(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_225])]) ).
fof(f2375,plain,
( ! [X0,X1] :
( empty(sK4(powerset(powerset(X0))))
| element(X1,X0)
| ~ in(X1,sK4(sK4(powerset(powerset(X0))))) )
| ~ spl20_100
| ~ spl20_225 ),
inference(resolution,[],[f2319,f859]) ).
fof(f2319,plain,
( ! [X5] :
( element(sK4(sK4(powerset(X5))),X5)
| empty(sK4(powerset(X5))) )
| ~ spl20_225 ),
inference(avatar_component_clause,[],[f2318]) ).
fof(f15425,plain,
( spl20_571
| ~ spl20_100
| ~ spl20_224 ),
inference(avatar_split_clause,[],[f2371,f2314,f858,f15423]) ).
fof(f15423,plain,
( spl20_571
<=> ! [X0,X1] :
( epsilon_transitive(sK4(powerset(powerset(X0))))
| element(X1,X0)
| ~ in(X1,sK3(sK4(powerset(powerset(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_571])]) ).
fof(f2314,plain,
( spl20_224
<=> ! [X4] :
( element(sK3(sK4(powerset(X4))),X4)
| epsilon_transitive(sK4(powerset(X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_224])]) ).
fof(f2371,plain,
( ! [X0,X1] :
( epsilon_transitive(sK4(powerset(powerset(X0))))
| element(X1,X0)
| ~ in(X1,sK3(sK4(powerset(powerset(X0))))) )
| ~ spl20_100
| ~ spl20_224 ),
inference(resolution,[],[f2315,f859]) ).
fof(f2315,plain,
( ! [X4] :
( element(sK3(sK4(powerset(X4))),X4)
| epsilon_transitive(sK4(powerset(X4))) )
| ~ spl20_224 ),
inference(avatar_component_clause,[],[f2314]) ).
fof(f15407,plain,
( spl20_570
| ~ spl20_456
| ~ spl20_533 ),
inference(avatar_split_clause,[],[f14563,f14532,f12556,f15404]) ).
fof(f15404,plain,
( spl20_570
<=> ordinal_subset(sK8,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_570])]) ).
fof(f14563,plain,
( ordinal_subset(sK8,sK1)
| ~ spl20_456
| ~ spl20_533 ),
inference(superposition,[],[f12558,f14534]) ).
fof(f15224,plain,
( spl20_569
| ~ spl20_312
| ~ spl20_533 ),
inference(avatar_split_clause,[],[f14556,f14532,f4161,f15221]) ).
fof(f15221,plain,
( spl20_569
<=> element(sK8,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_569])]) ).
fof(f14556,plain,
( element(sK8,sK1)
| ~ spl20_312
| ~ spl20_533 ),
inference(superposition,[],[f4163,f14534]) ).
fof(f14864,plain,
( spl20_568
| ~ spl20_151
| ~ spl20_300 ),
inference(avatar_split_clause,[],[f4038,f3625,f1221,f14862]) ).
fof(f14862,plain,
( spl20_568
<=> ! [X48,X47,X49] :
( sP0(X47,sK4(powerset(X48)),sK4(powerset(X49)))
| ~ empty(X47)
| ~ empty(X49)
| ~ empty(X48) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_568])]) ).
fof(f4038,plain,
( ! [X48,X49,X47] :
( sP0(X47,sK4(powerset(X48)),sK4(powerset(X49)))
| ~ empty(X47)
| ~ empty(X49)
| ~ empty(X48) )
| ~ spl20_151
| ~ spl20_300 ),
inference(resolution,[],[f3626,f1222]) ).
fof(f14860,plain,
( spl20_567
| ~ spl20_151
| ~ spl20_293 ),
inference(avatar_split_clause,[],[f3932,f3574,f1221,f14858]) ).
fof(f14858,plain,
( spl20_567
<=> ! [X48,X47,X49] :
( sP0(sK4(powerset(X47)),X48,sK4(powerset(X49)))
| ~ empty(X48)
| ~ empty(X49)
| ~ empty(X47) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_567])]) ).
fof(f3932,plain,
( ! [X48,X49,X47] :
( sP0(sK4(powerset(X47)),X48,sK4(powerset(X49)))
| ~ empty(X48)
| ~ empty(X49)
| ~ empty(X47) )
| ~ spl20_151
| ~ spl20_293 ),
inference(resolution,[],[f3575,f1222]) ).
fof(f14856,plain,
( ~ spl20_566
| spl20_304
| ~ spl20_533 ),
inference(avatar_split_clause,[],[f14555,f14532,f4069,f14853]) ).
fof(f14853,plain,
( spl20_566
<=> in(sK1,sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_566])]) ).
fof(f14555,plain,
( ~ in(sK1,sK8)
| spl20_304
| ~ spl20_533 ),
inference(superposition,[],[f4071,f14534]) ).
fof(f4071,plain,
( ~ in(sK1,sK2)
| spl20_304 ),
inference(avatar_component_clause,[],[f4069]) ).
fof(f14851,plain,
( spl20_565
| ~ spl20_151
| ~ spl20_287 ),
inference(avatar_split_clause,[],[f3826,f3550,f1221,f14849]) ).
fof(f14849,plain,
( spl20_565
<=> ! [X48,X47,X49] :
( sP0(sK4(powerset(X47)),sK4(powerset(X48)),X49)
| ~ empty(X49)
| ~ empty(X48)
| ~ empty(X47) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_565])]) ).
fof(f3826,plain,
( ! [X48,X49,X47] :
( sP0(sK4(powerset(X47)),sK4(powerset(X48)),X49)
| ~ empty(X49)
| ~ empty(X48)
| ~ empty(X47) )
| ~ spl20_151
| ~ spl20_287 ),
inference(resolution,[],[f3551,f1222]) ).
fof(f14847,plain,
( spl20_564
| ~ spl20_274 ),
inference(avatar_split_clause,[],[f3464,f3440,f14845]) ).
fof(f14845,plain,
( spl20_564
<=> ! [X0,X1] :
( X0 != X1
| sK5(X0,singleton(X1)) = X1
| singleton(X0) = singleton(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_564])]) ).
fof(f3464,plain,
( ! [X0,X1] :
( X0 != X1
| sK5(X0,singleton(X1)) = X1
| singleton(X0) = singleton(X1) )
| ~ spl20_274 ),
inference(equality_factoring,[],[f3441]) ).
fof(f14843,plain,
( spl20_563
| ~ spl20_274 ),
inference(avatar_split_clause,[],[f3463,f3440,f14841]) ).
fof(f14841,plain,
( spl20_563
<=> ! [X0,X1] :
( X0 != X1
| sK5(X0,singleton(X1)) = X0
| singleton(X0) = singleton(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_563])]) ).
fof(f3463,plain,
( ! [X0,X1] :
( X0 != X1
| sK5(X0,singleton(X1)) = X0
| singleton(X0) = singleton(X1) )
| ~ spl20_274 ),
inference(equality_factoring,[],[f3441]) ).
fof(f14839,plain,
( spl20_562
| ~ spl20_151
| ~ spl20_271 ),
inference(avatar_split_clause,[],[f3403,f3016,f1221,f14837]) ).
fof(f14837,plain,
( spl20_562
<=> ! [X32,X33] :
( sP0(sK4(powerset(X32)),sK4(powerset(X32)),sK4(powerset(X33)))
| ~ empty(X33)
| ~ empty(X32) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_562])]) ).
fof(f3403,plain,
( ! [X32,X33] :
( sP0(sK4(powerset(X32)),sK4(powerset(X32)),sK4(powerset(X33)))
| ~ empty(X33)
| ~ empty(X32) )
| ~ spl20_151
| ~ spl20_271 ),
inference(resolution,[],[f3017,f1222]) ).
fof(f14835,plain,
( spl20_561
| ~ spl20_75
| ~ spl20_251 ),
inference(avatar_split_clause,[],[f2886,f2820,f653,f14833]) ).
fof(f14833,plain,
( spl20_561
<=> ! [X25,X24,X26] :
( sP0(X24,X25,X26)
| ~ empty(X25)
| ~ empty(X24)
| ~ in(X26,sK6(X24,X25,X26)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_561])]) ).
fof(f2886,plain,
( ! [X26,X24,X25] :
( sP0(X24,X25,X26)
| ~ empty(X25)
| ~ empty(X24)
| ~ in(X26,sK6(X24,X25,X26)) )
| ~ spl20_75
| ~ spl20_251 ),
inference(resolution,[],[f2821,f654]) ).
fof(f14831,plain,
( spl20_560
| ~ spl20_76
| ~ spl20_251 ),
inference(avatar_split_clause,[],[f2885,f2820,f657,f14829]) ).
fof(f14829,plain,
( spl20_560
<=> ! [X22,X21,X23] :
( sP0(X21,X22,X23)
| ~ empty(X22)
| ~ empty(X21)
| element(sK6(X21,X22,X23),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_560])]) ).
fof(f2885,plain,
( ! [X21,X22,X23] :
( sP0(X21,X22,X23)
| ~ empty(X22)
| ~ empty(X21)
| element(sK6(X21,X22,X23),X23) )
| ~ spl20_76
| ~ spl20_251 ),
inference(resolution,[],[f2821,f658]) ).
fof(f14827,plain,
( spl20_559
| ~ spl20_75
| ~ spl20_250 ),
inference(avatar_split_clause,[],[f2865,f2816,f653,f14825]) ).
fof(f14825,plain,
( spl20_559
<=> ! [X25,X24,X23] :
( sP0(X23,X24,X25)
| ~ empty(X25)
| ~ empty(X23)
| ~ in(X24,sK6(X23,X24,X25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_559])]) ).
fof(f2865,plain,
( ! [X24,X25,X23] :
( sP0(X23,X24,X25)
| ~ empty(X25)
| ~ empty(X23)
| ~ in(X24,sK6(X23,X24,X25)) )
| ~ spl20_75
| ~ spl20_250 ),
inference(resolution,[],[f2817,f654]) ).
fof(f14823,plain,
( spl20_558
| ~ spl20_76
| ~ spl20_250 ),
inference(avatar_split_clause,[],[f2864,f2816,f657,f14821]) ).
fof(f14821,plain,
( spl20_558
<=> ! [X22,X20,X21] :
( sP0(X20,X21,X22)
| ~ empty(X22)
| ~ empty(X20)
| element(sK6(X20,X21,X22),X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_558])]) ).
fof(f2864,plain,
( ! [X21,X22,X20] :
( sP0(X20,X21,X22)
| ~ empty(X22)
| ~ empty(X20)
| element(sK6(X20,X21,X22),X21) )
| ~ spl20_76
| ~ spl20_250 ),
inference(resolution,[],[f2817,f658]) ).
fof(f14819,plain,
( spl20_557
| ~ spl20_75
| ~ spl20_249 ),
inference(avatar_split_clause,[],[f2844,f2812,f653,f14817]) ).
fof(f14817,plain,
( spl20_557
<=> ! [X25,X24,X23] :
( sP0(X23,X24,X25)
| ~ empty(X25)
| ~ empty(X24)
| ~ in(X23,sK6(X23,X24,X25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_557])]) ).
fof(f2844,plain,
( ! [X24,X25,X23] :
( sP0(X23,X24,X25)
| ~ empty(X25)
| ~ empty(X24)
| ~ in(X23,sK6(X23,X24,X25)) )
| ~ spl20_75
| ~ spl20_249 ),
inference(resolution,[],[f2813,f654]) ).
fof(f14815,plain,
( spl20_556
| ~ spl20_76
| ~ spl20_249 ),
inference(avatar_split_clause,[],[f2843,f2812,f657,f14813]) ).
fof(f14813,plain,
( spl20_556
<=> ! [X22,X20,X21] :
( sP0(X20,X21,X22)
| ~ empty(X22)
| ~ empty(X21)
| element(sK6(X20,X21,X22),X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_556])]) ).
fof(f2843,plain,
( ! [X21,X22,X20] :
( sP0(X20,X21,X22)
| ~ empty(X22)
| ~ empty(X21)
| element(sK6(X20,X21,X22),X20) )
| ~ spl20_76
| ~ spl20_249 ),
inference(resolution,[],[f2813,f658]) ).
fof(f14811,plain,
( spl20_555
| ~ spl20_243
| ~ spl20_533 ),
inference(avatar_split_clause,[],[f14553,f14532,f2671,f14808]) ).
fof(f14553,plain,
( in(sK8,sK1)
| ~ spl20_243
| ~ spl20_533 ),
inference(superposition,[],[f2673,f14534]) ).
fof(f14806,plain,
( spl20_554
| ~ spl20_97
| ~ spl20_247 ),
inference(avatar_split_clause,[],[f2835,f2804,f846,f14804]) ).
fof(f14804,plain,
( spl20_554
<=> ! [X6,X7] :
( ~ ordinal(X6)
| ~ ordinal(X7)
| ~ empty(X7)
| X6 = X7
| ~ epsilon_transitive(X6)
| ordinal_subset(X7,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_554])]) ).
fof(f2835,plain,
( ! [X6,X7] :
( ~ ordinal(X6)
| ~ ordinal(X7)
| ~ empty(X7)
| X6 = X7
| ~ epsilon_transitive(X6)
| ordinal_subset(X7,X6) )
| ~ spl20_97
| ~ spl20_247 ),
inference(duplicate_literal_removal,[],[f2825]) ).
fof(f2825,plain,
( ! [X6,X7] :
( ~ ordinal(X6)
| ~ ordinal(X7)
| ~ empty(X7)
| X6 = X7
| ~ epsilon_transitive(X6)
| ordinal_subset(X7,X6)
| ~ ordinal(X6)
| ~ ordinal(X7) )
| ~ spl20_97
| ~ spl20_247 ),
inference(resolution,[],[f2805,f847]) ).
fof(f14802,plain,
( spl20_553
| ~ spl20_91
| ~ spl20_247 ),
inference(avatar_split_clause,[],[f2834,f2804,f811,f14800]) ).
fof(f14800,plain,
( spl20_553
<=> ! [X9,X8] :
( ~ ordinal(X8)
| ~ ordinal(X9)
| ~ empty(X9)
| X8 = X9
| ~ epsilon_transitive(X8)
| ~ subset(X8,X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_553])]) ).
fof(f2834,plain,
( ! [X8,X9] :
( ~ ordinal(X8)
| ~ ordinal(X9)
| ~ empty(X9)
| X8 = X9
| ~ epsilon_transitive(X8)
| ~ subset(X8,X9) )
| ~ spl20_91
| ~ spl20_247 ),
inference(duplicate_literal_removal,[],[f2826]) ).
fof(f2826,plain,
( ! [X8,X9] :
( ~ ordinal(X8)
| ~ ordinal(X9)
| ~ empty(X9)
| X8 = X9
| ~ epsilon_transitive(X8)
| X8 = X9
| ~ subset(X8,X9) )
| ~ spl20_91
| ~ spl20_247 ),
inference(resolution,[],[f2805,f812]) ).
fof(f14798,plain,
( spl20_552
| ~ spl20_153
| ~ spl20_242 ),
inference(avatar_split_clause,[],[f2710,f2533,f1230,f14796]) ).
fof(f14796,plain,
( spl20_552
<=> ! [X20,X21] :
( sP0(X20,X20,singleton(X21))
| ~ empty(X20)
| sK6(X20,X20,singleton(X21)) = X21 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_552])]) ).
fof(f2710,plain,
( ! [X21,X20] :
( sP0(X20,X20,singleton(X21))
| ~ empty(X20)
| sK6(X20,X20,singleton(X21)) = X21 )
| ~ spl20_153
| ~ spl20_242 ),
inference(resolution,[],[f2534,f1231]) ).
fof(f14794,plain,
( spl20_551
| ~ spl20_88
| ~ spl20_242 ),
inference(avatar_split_clause,[],[f2705,f2533,f772,f14792]) ).
fof(f14792,plain,
( spl20_551
<=> ! [X9,X10] :
( sP0(X9,X9,X10)
| ~ empty(X9)
| subset(sK6(X9,X9,X10),X10)
| ~ epsilon_transitive(X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_551])]) ).
fof(f2705,plain,
( ! [X10,X9] :
( sP0(X9,X9,X10)
| ~ empty(X9)
| subset(sK6(X9,X9,X10),X10)
| ~ epsilon_transitive(X10) )
| ~ spl20_88
| ~ spl20_242 ),
inference(resolution,[],[f2534,f773]) ).
fof(f14790,plain,
( spl20_550
| ~ spl20_88
| ~ spl20_241 ),
inference(avatar_split_clause,[],[f2685,f2529,f772,f14788]) ).
fof(f14788,plain,
( spl20_550
<=> ! [X9,X10] :
( sP0(X9,X9,X10)
| ~ empty(X10)
| subset(sK6(X9,X9,X10),X9)
| ~ epsilon_transitive(X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_550])]) ).
fof(f2685,plain,
( ! [X10,X9] :
( sP0(X9,X9,X10)
| ~ empty(X10)
| subset(sK6(X9,X9,X10),X9)
| ~ epsilon_transitive(X9) )
| ~ spl20_88
| ~ spl20_241 ),
inference(resolution,[],[f2530,f773]) ).
fof(f14786,plain,
( spl20_549
| ~ spl20_84
| ~ spl20_235 ),
inference(avatar_split_clause,[],[f2587,f2504,f732,f14784]) ).
fof(f14784,plain,
( spl20_549
<=> ! [X6,X7] :
( ~ ordinal(powerset(X6))
| ~ ordinal(X7)
| ~ empty(X7)
| powerset(X6) = X7
| subset(X7,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_549])]) ).
fof(f2504,plain,
( spl20_235
<=> ! [X2,X3] :
( X2 = X3
| ~ ordinal(X2)
| ~ ordinal(X3)
| ~ empty(X3)
| element(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_235])]) ).
fof(f2587,plain,
( ! [X6,X7] :
( ~ ordinal(powerset(X6))
| ~ ordinal(X7)
| ~ empty(X7)
| powerset(X6) = X7
| subset(X7,X6) )
| ~ spl20_84
| ~ spl20_235 ),
inference(resolution,[],[f2505,f733]) ).
fof(f2505,plain,
( ! [X2,X3] :
( element(X3,X2)
| ~ ordinal(X2)
| ~ ordinal(X3)
| ~ empty(X3)
| X2 = X3 )
| ~ spl20_235 ),
inference(avatar_component_clause,[],[f2504]) ).
fof(f14782,plain,
( spl20_548
| ~ spl20_163
| ~ spl20_227 ),
inference(avatar_split_clause,[],[f2392,f2326,f1316,f14780]) ).
fof(f14780,plain,
( spl20_548
<=> ! [X18,X19] :
( ~ subset(powerset(X18),X19)
| empty(powerset(X19))
| empty(powerset(X18))
| ~ subset(powerset(X19),X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_548])]) ).
fof(f2326,plain,
( spl20_227
<=> ! [X4,X5] :
( empty(powerset(X4))
| ~ subset(X5,X4)
| ~ in(powerset(X4),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_227])]) ).
fof(f2392,plain,
( ! [X18,X19] :
( ~ subset(powerset(X18),X19)
| empty(powerset(X19))
| empty(powerset(X18))
| ~ subset(powerset(X19),X18) )
| ~ spl20_163
| ~ spl20_227 ),
inference(resolution,[],[f2327,f1317]) ).
fof(f2327,plain,
( ! [X4,X5] :
( ~ in(powerset(X4),X5)
| ~ subset(X5,X4)
| empty(powerset(X4)) )
| ~ spl20_227 ),
inference(avatar_component_clause,[],[f2326]) ).
fof(f14778,plain,
( spl20_547
| ~ spl20_94
| ~ spl20_225 ),
inference(avatar_split_clause,[],[f2376,f2318,f823,f14776]) ).
fof(f14776,plain,
( spl20_547
<=> ! [X2,X3] :
( empty(sK4(powerset(powerset(X2))))
| ~ empty(X2)
| ~ in(X3,sK4(sK4(powerset(powerset(X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_547])]) ).
fof(f2376,plain,
( ! [X2,X3] :
( empty(sK4(powerset(powerset(X2))))
| ~ empty(X2)
| ~ in(X3,sK4(sK4(powerset(powerset(X2))))) )
| ~ spl20_94
| ~ spl20_225 ),
inference(resolution,[],[f2319,f824]) ).
fof(f14774,plain,
( spl20_546
| ~ spl20_94
| ~ spl20_224 ),
inference(avatar_split_clause,[],[f2372,f2314,f823,f14772]) ).
fof(f14772,plain,
( spl20_546
<=> ! [X2,X3] :
( epsilon_transitive(sK4(powerset(powerset(X2))))
| ~ empty(X2)
| ~ in(X3,sK3(sK4(powerset(powerset(X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_546])]) ).
fof(f2372,plain,
( ! [X2,X3] :
( epsilon_transitive(sK4(powerset(powerset(X2))))
| ~ empty(X2)
| ~ in(X3,sK3(sK4(powerset(powerset(X2))))) )
| ~ spl20_94
| ~ spl20_224 ),
inference(resolution,[],[f2315,f824]) ).
fof(f14770,plain,
( spl20_545
| ~ spl20_164
| ~ spl20_218 ),
inference(avatar_split_clause,[],[f2280,f2226,f1320,f14768]) ).
fof(f14768,plain,
( spl20_545
<=> ! [X0] :
( empty(powerset(X0))
| ~ ordinal(X0)
| ~ ordinal(succ(powerset(X0)))
| ordinal_subset(X0,succ(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_545])]) ).
fof(f2280,plain,
( ! [X0] :
( empty(powerset(X0))
| ~ ordinal(X0)
| ~ ordinal(succ(powerset(X0)))
| ordinal_subset(X0,succ(powerset(X0))) )
| ~ spl20_164
| ~ spl20_218 ),
inference(resolution,[],[f2227,f1321]) ).
fof(f14766,plain,
( spl20_544
| ~ spl20_120
| ~ spl20_533 ),
inference(avatar_split_clause,[],[f14542,f14532,f1014,f14763]) ).
fof(f14763,plain,
( spl20_544
<=> subset(sK8,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_544])]) ).
fof(f14542,plain,
( subset(sK8,sK1)
| ~ spl20_120
| ~ spl20_533 ),
inference(superposition,[],[f1015,f14534]) ).
fof(f14761,plain,
( spl20_543
| ~ spl20_97
| ~ spl20_211 ),
inference(avatar_split_clause,[],[f2231,f2196,f846,f14759]) ).
fof(f14759,plain,
( spl20_543
<=> ! [X4] :
( epsilon_transitive(powerset(X4))
| ordinal_subset(sK3(powerset(X4)),X4)
| ~ ordinal(X4)
| ~ ordinal(sK3(powerset(X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_543])]) ).
fof(f2196,plain,
( spl20_211
<=> ! [X4] :
( epsilon_transitive(powerset(X4))
| subset(sK3(powerset(X4)),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_211])]) ).
fof(f2231,plain,
( ! [X4] :
( epsilon_transitive(powerset(X4))
| ordinal_subset(sK3(powerset(X4)),X4)
| ~ ordinal(X4)
| ~ ordinal(sK3(powerset(X4))) )
| ~ spl20_97
| ~ spl20_211 ),
inference(resolution,[],[f2197,f847]) ).
fof(f2197,plain,
( ! [X4] :
( subset(sK3(powerset(X4)),X4)
| epsilon_transitive(powerset(X4)) )
| ~ spl20_211 ),
inference(avatar_component_clause,[],[f2196]) ).
fof(f14722,plain,
( spl20_542
| ~ spl20_5
| ~ spl20_125
| ~ spl20_252 ),
inference(avatar_split_clause,[],[f2915,f2900,f1044,f279,f14720]) ).
fof(f14720,plain,
( spl20_542
<=> ! [X2] :
( singleton(X2) = sK4(powerset(sK8))
| sK5(X2,sK4(powerset(sK8))) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_542])]) ).
fof(f279,plain,
( spl20_5
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_5])]) ).
fof(f1044,plain,
( spl20_125
<=> empty_set = sK8 ),
introduced(avatar_definition,[new_symbols(naming,[spl20_125])]) ).
fof(f2915,plain,
( ! [X2] :
( singleton(X2) = sK4(powerset(sK8))
| sK5(X2,sK4(powerset(sK8))) = X2 )
| ~ spl20_5
| ~ spl20_125
| ~ spl20_252 ),
inference(forward_demodulation,[],[f2914,f1046]) ).
fof(f1046,plain,
( empty_set = sK8
| ~ spl20_125 ),
inference(avatar_component_clause,[],[f1044]) ).
fof(f2914,plain,
( ! [X2] :
( sK5(X2,sK4(powerset(sK8))) = X2
| singleton(X2) = sK4(powerset(empty_set)) )
| ~ spl20_5
| ~ spl20_125
| ~ spl20_252 ),
inference(forward_demodulation,[],[f2908,f1046]) ).
fof(f2908,plain,
( ! [X2] :
( sK5(X2,sK4(powerset(empty_set))) = X2
| singleton(X2) = sK4(powerset(empty_set)) )
| ~ spl20_5
| ~ spl20_252 ),
inference(resolution,[],[f2901,f281]) ).
fof(f281,plain,
( empty(empty_set)
| ~ spl20_5 ),
inference(avatar_component_clause,[],[f279]) ).
fof(f14718,plain,
( spl20_541
| ~ spl20_146
| ~ spl20_245 ),
inference(avatar_split_clause,[],[f2750,f2725,f1180,f14716]) ).
fof(f14716,plain,
( spl20_541
<=> ! [X32,X33] :
( ~ ordinal(X32)
| ordinal_subset(X33,X32)
| ~ ordinal(X33)
| element(sK4(X32),X33)
| empty(X32) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_541])]) ).
fof(f2750,plain,
( ! [X32,X33] :
( ~ ordinal(X32)
| ordinal_subset(X33,X32)
| ~ ordinal(X33)
| element(sK4(X32),X33)
| empty(X32) )
| ~ spl20_146
| ~ spl20_245 ),
inference(resolution,[],[f2726,f1181]) ).
fof(f14714,plain,
( spl20_540
| ~ spl20_223
| ~ spl20_242 ),
inference(avatar_split_clause,[],[f2713,f2533,f2310,f14712]) ).
fof(f14712,plain,
( spl20_540
<=> ! [X25,X26] :
( sP0(X25,X25,sK3(powerset(X26)))
| ~ empty(X25)
| ~ empty(X26)
| epsilon_transitive(powerset(X26)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_540])]) ).
fof(f2713,plain,
( ! [X26,X25] :
( sP0(X25,X25,sK3(powerset(X26)))
| ~ empty(X25)
| ~ empty(X26)
| epsilon_transitive(powerset(X26)) )
| ~ spl20_223
| ~ spl20_242 ),
inference(resolution,[],[f2534,f2311]) ).
fof(f14710,plain,
( ~ spl20_539
| spl20_105
| ~ spl20_533 ),
inference(avatar_split_clause,[],[f14541,f14532,f894,f14707]) ).
fof(f14707,plain,
( spl20_539
<=> subset(sK1,sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_539])]) ).
fof(f14541,plain,
( ~ subset(sK1,sK8)
| spl20_105
| ~ spl20_533 ),
inference(superposition,[],[f895,f14534]) ).
fof(f14705,plain,
( spl20_538
| ~ spl20_146
| ~ spl20_230 ),
inference(avatar_split_clause,[],[f2418,f2398,f1180,f14703]) ).
fof(f14703,plain,
( spl20_538
<=> ! [X11] :
( element(sK4(sK3(powerset(X11))),X11)
| epsilon_transitive(powerset(X11))
| empty(sK3(powerset(X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_538])]) ).
fof(f2418,plain,
( ! [X11] :
( element(sK4(sK3(powerset(X11))),X11)
| epsilon_transitive(powerset(X11))
| empty(sK3(powerset(X11))) )
| ~ spl20_146
| ~ spl20_230 ),
inference(resolution,[],[f2399,f1181]) ).
fof(f14701,plain,
( spl20_537
| ~ spl20_71
| ~ spl20_230 ),
inference(avatar_split_clause,[],[f2417,f2398,f637,f14699]) ).
fof(f14699,plain,
( spl20_537
<=> ! [X10] :
( element(sK3(sK3(powerset(X10))),X10)
| epsilon_transitive(powerset(X10))
| epsilon_transitive(sK3(powerset(X10))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_537])]) ).
fof(f2417,plain,
( ! [X10] :
( element(sK3(sK3(powerset(X10))),X10)
| epsilon_transitive(powerset(X10))
| epsilon_transitive(sK3(powerset(X10))) )
| ~ spl20_71
| ~ spl20_230 ),
inference(resolution,[],[f2399,f638]) ).
fof(f14697,plain,
( spl20_536
| ~ spl20_97
| ~ spl20_212 ),
inference(avatar_split_clause,[],[f2235,f2200,f846,f14695]) ).
fof(f14695,plain,
( spl20_536
<=> ! [X4] :
( empty(X4)
| ~ epsilon_transitive(X4)
| ordinal_subset(sK4(X4),X4)
| ~ ordinal(X4)
| ~ ordinal(sK4(X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_536])]) ).
fof(f2200,plain,
( spl20_212
<=> ! [X0] :
( empty(X0)
| subset(sK4(X0),X0)
| ~ epsilon_transitive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_212])]) ).
fof(f2235,plain,
( ! [X4] :
( empty(X4)
| ~ epsilon_transitive(X4)
| ordinal_subset(sK4(X4),X4)
| ~ ordinal(X4)
| ~ ordinal(sK4(X4)) )
| ~ spl20_97
| ~ spl20_212 ),
inference(resolution,[],[f2201,f847]) ).
fof(f2201,plain,
( ! [X0] :
( subset(sK4(X0),X0)
| empty(X0)
| ~ epsilon_transitive(X0) )
| ~ spl20_212 ),
inference(avatar_component_clause,[],[f2200]) ).
fof(f14693,plain,
( spl20_535
| ~ spl20_91
| ~ spl20_211 ),
inference(avatar_split_clause,[],[f2232,f2196,f811,f14691]) ).
fof(f14691,plain,
( spl20_535
<=> ! [X5] :
( epsilon_transitive(powerset(X5))
| sK3(powerset(X5)) = X5
| ~ subset(X5,sK3(powerset(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_535])]) ).
fof(f2232,plain,
( ! [X5] :
( epsilon_transitive(powerset(X5))
| sK3(powerset(X5)) = X5
| ~ subset(X5,sK3(powerset(X5))) )
| ~ spl20_91
| ~ spl20_211 ),
inference(resolution,[],[f2197,f812]) ).
fof(f14650,plain,
( ~ spl20_534
| spl20_4
| ~ spl20_533 ),
inference(avatar_split_clause,[],[f14538,f14532,f274,f14647]) ).
fof(f14647,plain,
( spl20_534
<=> ordinal_subset(sK1,sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_534])]) ).
fof(f14538,plain,
( ~ ordinal_subset(sK1,sK8)
| spl20_4
| ~ spl20_533 ),
inference(superposition,[],[f275,f14534]) ).
fof(f14535,plain,
( spl20_533
| ~ spl20_66
| ~ spl20_125
| ~ spl20_161 ),
inference(avatar_split_clause,[],[f14509,f1308,f1044,f605,f14532]) ).
fof(f605,plain,
( spl20_66
<=> ! [X0] :
( empty_set = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_66])]) ).
fof(f14509,plain,
( sK2 = sK8
| ~ spl20_66
| ~ spl20_125
| ~ spl20_161 ),
inference(forward_demodulation,[],[f14502,f1046]) ).
fof(f14502,plain,
( empty_set = sK2
| ~ spl20_66
| ~ spl20_161 ),
inference(resolution,[],[f1309,f606]) ).
fof(f606,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = X0 )
| ~ spl20_66 ),
inference(avatar_component_clause,[],[f605]) ).
fof(f1309,plain,
( empty(sK2)
| ~ spl20_161 ),
inference(avatar_component_clause,[],[f1308]) ).
fof(f14529,plain,
( spl20_532
| ~ spl20_56
| ~ spl20_161 ),
inference(avatar_split_clause,[],[f14498,f1308,f527,f14526]) ).
fof(f527,plain,
( spl20_56
<=> ! [X0] :
( relation(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_56])]) ).
fof(f14498,plain,
( relation(sK2)
| ~ spl20_56
| ~ spl20_161 ),
inference(resolution,[],[f1309,f528]) ).
fof(f528,plain,
( ! [X0] :
( ~ empty(X0)
| relation(X0) )
| ~ spl20_56 ),
inference(avatar_component_clause,[],[f527]) ).
fof(f14523,plain,
( spl20_531
| ~ spl20_55
| ~ spl20_161 ),
inference(avatar_split_clause,[],[f14497,f1308,f523,f14520]) ).
fof(f14520,plain,
( spl20_531
<=> function(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_531])]) ).
fof(f523,plain,
( spl20_55
<=> ! [X0] :
( function(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_55])]) ).
fof(f14497,plain,
( function(sK2)
| ~ spl20_55
| ~ spl20_161 ),
inference(resolution,[],[f1309,f524]) ).
fof(f524,plain,
( ! [X0] :
( ~ empty(X0)
| function(X0) )
| ~ spl20_55 ),
inference(avatar_component_clause,[],[f523]) ).
fof(f14496,plain,
( ~ spl20_518
| ~ spl20_75
| ~ spl20_518 ),
inference(avatar_split_clause,[],[f14346,f14297,f653,f14297]) ).
fof(f14346,plain,
( ~ in(sK2,sK2)
| ~ spl20_75
| ~ spl20_518 ),
inference(resolution,[],[f14299,f654]) ).
fof(f14299,plain,
( in(sK2,sK2)
| ~ spl20_518 ),
inference(avatar_component_clause,[],[f14297]) ).
fof(f14355,plain,
( spl20_530
| ~ spl20_151
| ~ spl20_251 ),
inference(avatar_split_clause,[],[f2894,f2820,f1221,f14353]) ).
fof(f14353,plain,
( spl20_530
<=> ! [X50,X48,X49] :
( sP0(X48,X49,sK4(powerset(X50)))
| ~ empty(X49)
| ~ empty(X48)
| ~ empty(X50) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_530])]) ).
fof(f2894,plain,
( ! [X50,X48,X49] :
( sP0(X48,X49,sK4(powerset(X50)))
| ~ empty(X49)
| ~ empty(X48)
| ~ empty(X50) )
| ~ spl20_151
| ~ spl20_251 ),
inference(resolution,[],[f2821,f1222]) ).
fof(f14351,plain,
( spl20_529
| ~ spl20_151
| ~ spl20_250 ),
inference(avatar_split_clause,[],[f2873,f2816,f1221,f14349]) ).
fof(f14349,plain,
( spl20_529
<=> ! [X48,X47,X49] :
( sP0(X47,sK4(powerset(X48)),X49)
| ~ empty(X49)
| ~ empty(X47)
| ~ empty(X48) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_529])]) ).
fof(f2873,plain,
( ! [X48,X49,X47] :
( sP0(X47,sK4(powerset(X48)),X49)
| ~ empty(X49)
| ~ empty(X47)
| ~ empty(X48) )
| ~ spl20_151
| ~ spl20_250 ),
inference(resolution,[],[f2817,f1222]) ).
fof(f14340,plain,
( spl20_528
| ~ spl20_151
| ~ spl20_249 ),
inference(avatar_split_clause,[],[f2852,f2812,f1221,f14338]) ).
fof(f14338,plain,
( spl20_528
<=> ! [X48,X47,X49] :
( sP0(sK4(powerset(X47)),X48,X49)
| ~ empty(X49)
| ~ empty(X48)
| ~ empty(X47) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_528])]) ).
fof(f2852,plain,
( ! [X48,X49,X47] :
( sP0(sK4(powerset(X47)),X48,X49)
| ~ empty(X49)
| ~ empty(X48)
| ~ empty(X47) )
| ~ spl20_151
| ~ spl20_249 ),
inference(resolution,[],[f2813,f1222]) ).
fof(f14336,plain,
( spl20_527
| ~ spl20_201
| ~ spl20_245 ),
inference(avatar_split_clause,[],[f2747,f2725,f2058,f14334]) ).
fof(f14334,plain,
( spl20_527
<=> ! [X25,X26] :
( ~ ordinal(singleton(X25))
| ordinal_subset(X26,singleton(X25))
| ~ ordinal(X26)
| element(X25,X26) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_527])]) ).
fof(f2058,plain,
( spl20_201
<=> ! [X0] : in(X0,singleton(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_201])]) ).
fof(f2747,plain,
( ! [X26,X25] :
( ~ ordinal(singleton(X25))
| ordinal_subset(X26,singleton(X25))
| ~ ordinal(X26)
| element(X25,X26) )
| ~ spl20_201
| ~ spl20_245 ),
inference(resolution,[],[f2726,f2059]) ).
fof(f2059,plain,
( ! [X0] : in(X0,singleton(X0))
| ~ spl20_201 ),
inference(avatar_component_clause,[],[f2058]) ).
fof(f14332,plain,
( spl20_526
| ~ spl20_52
| ~ spl20_245 ),
inference(avatar_split_clause,[],[f2746,f2725,f511,f14330]) ).
fof(f14330,plain,
( spl20_526
<=> ! [X24,X23] :
( ~ ordinal(succ(X23))
| ordinal_subset(X24,succ(X23))
| ~ ordinal(X24)
| element(X23,X24) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_526])]) ).
fof(f2746,plain,
( ! [X24,X23] :
( ~ ordinal(succ(X23))
| ordinal_subset(X24,succ(X23))
| ~ ordinal(X24)
| element(X23,X24) )
| ~ spl20_52
| ~ spl20_245 ),
inference(resolution,[],[f2726,f512]) ).
fof(f14328,plain,
( spl20_525
| ~ spl20_75
| ~ spl20_242 ),
inference(avatar_split_clause,[],[f2707,f2533,f653,f14326]) ).
fof(f14326,plain,
( spl20_525
<=> ! [X13,X14] :
( sP0(X13,X13,X14)
| ~ empty(X13)
| ~ in(X14,sK6(X13,X13,X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_525])]) ).
fof(f2707,plain,
( ! [X14,X13] :
( sP0(X13,X13,X14)
| ~ empty(X13)
| ~ in(X14,sK6(X13,X13,X14)) )
| ~ spl20_75
| ~ spl20_242 ),
inference(resolution,[],[f2534,f654]) ).
fof(f14324,plain,
( spl20_524
| ~ spl20_76
| ~ spl20_242 ),
inference(avatar_split_clause,[],[f2706,f2533,f657,f14322]) ).
fof(f14322,plain,
( spl20_524
<=> ! [X11,X12] :
( sP0(X11,X11,X12)
| ~ empty(X11)
| element(sK6(X11,X11,X12),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_524])]) ).
fof(f2706,plain,
( ! [X11,X12] :
( sP0(X11,X11,X12)
| ~ empty(X11)
| element(sK6(X11,X11,X12),X12) )
| ~ spl20_76
| ~ spl20_242 ),
inference(resolution,[],[f2534,f658]) ).
fof(f14320,plain,
( spl20_523
| ~ spl20_151
| ~ spl20_241 ),
inference(avatar_split_clause,[],[f2695,f2529,f1221,f14318]) ).
fof(f14318,plain,
( spl20_523
<=> ! [X29,X30] :
( sP0(sK4(powerset(X29)),sK4(powerset(X29)),X30)
| ~ empty(X30)
| ~ empty(X29) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_523])]) ).
fof(f2695,plain,
( ! [X29,X30] :
( sP0(sK4(powerset(X29)),sK4(powerset(X29)),X30)
| ~ empty(X30)
| ~ empty(X29) )
| ~ spl20_151
| ~ spl20_241 ),
inference(resolution,[],[f2530,f1222]) ).
fof(f14316,plain,
( spl20_522
| ~ spl20_75
| ~ spl20_241 ),
inference(avatar_split_clause,[],[f2687,f2529,f653,f14314]) ).
fof(f14314,plain,
( spl20_522
<=> ! [X13,X14] :
( sP0(X13,X13,X14)
| ~ empty(X14)
| ~ in(X13,sK6(X13,X13,X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_522])]) ).
fof(f2687,plain,
( ! [X14,X13] :
( sP0(X13,X13,X14)
| ~ empty(X14)
| ~ in(X13,sK6(X13,X13,X14)) )
| ~ spl20_75
| ~ spl20_241 ),
inference(resolution,[],[f2530,f654]) ).
fof(f14312,plain,
( spl20_521
| ~ spl20_76
| ~ spl20_241 ),
inference(avatar_split_clause,[],[f2686,f2529,f657,f14310]) ).
fof(f14310,plain,
( spl20_521
<=> ! [X11,X12] :
( sP0(X11,X11,X12)
| ~ empty(X12)
| element(sK6(X11,X11,X12),X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_521])]) ).
fof(f2686,plain,
( ! [X11,X12] :
( sP0(X11,X11,X12)
| ~ empty(X12)
| element(sK6(X11,X11,X12),X11) )
| ~ spl20_76
| ~ spl20_241 ),
inference(resolution,[],[f2530,f658]) ).
fof(f14308,plain,
( spl20_520
| ~ spl20_213
| ~ spl20_227 ),
inference(avatar_split_clause,[],[f2389,f2326,f2204,f14306]) ).
fof(f14306,plain,
( spl20_520
<=> ! [X13,X14,X15] :
( ~ subset(set_union2(X13,X14),X15)
| empty(powerset(X15))
| ~ in(powerset(X15),X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_520])]) ).
fof(f2389,plain,
( ! [X14,X15,X13] :
( ~ subset(set_union2(X13,X14),X15)
| empty(powerset(X15))
| ~ in(powerset(X15),X14) )
| ~ spl20_213
| ~ spl20_227 ),
inference(resolution,[],[f2327,f2205]) ).
fof(f14304,plain,
( spl20_519
| ~ spl20_214
| ~ spl20_227 ),
inference(avatar_split_clause,[],[f2388,f2326,f2208,f14302]) ).
fof(f14302,plain,
( spl20_519
<=> ! [X11,X12,X10] :
( ~ subset(set_union2(X10,X11),X12)
| empty(powerset(X12))
| ~ in(powerset(X12),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_519])]) ).
fof(f2388,plain,
( ! [X10,X11,X12] :
( ~ subset(set_union2(X10,X11),X12)
| empty(powerset(X12))
| ~ in(powerset(X12),X10) )
| ~ spl20_214
| ~ spl20_227 ),
inference(resolution,[],[f2327,f2209]) ).
fof(f14300,plain,
( spl20_518
| spl20_161
| ~ spl20_89
| ~ spl20_337 ),
inference(avatar_split_clause,[],[f6949,f4923,f776,f1308,f14297]) ).
fof(f6949,plain,
( empty(sK2)
| in(sK2,sK2)
| ~ spl20_89
| ~ spl20_337 ),
inference(resolution,[],[f4925,f777]) ).
fof(f14295,plain,
( spl20_517
| ~ spl20_89
| ~ spl20_225 ),
inference(avatar_split_clause,[],[f2378,f2318,f776,f14293]) ).
fof(f14293,plain,
( spl20_517
<=> ! [X5] :
( empty(sK4(powerset(X5)))
| empty(X5)
| in(sK4(sK4(powerset(X5))),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_517])]) ).
fof(f2378,plain,
( ! [X5] :
( empty(sK4(powerset(X5)))
| empty(X5)
| in(sK4(sK4(powerset(X5))),X5) )
| ~ spl20_89
| ~ spl20_225 ),
inference(resolution,[],[f2319,f777]) ).
fof(f14291,plain,
( spl20_516
| ~ spl20_84
| ~ spl20_225 ),
inference(avatar_split_clause,[],[f2377,f2318,f732,f14289]) ).
fof(f14289,plain,
( spl20_516
<=> ! [X4] :
( empty(sK4(powerset(powerset(X4))))
| subset(sK4(sK4(powerset(powerset(X4)))),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_516])]) ).
fof(f2377,plain,
( ! [X4] :
( empty(sK4(powerset(powerset(X4))))
| subset(sK4(sK4(powerset(powerset(X4)))),X4) )
| ~ spl20_84
| ~ spl20_225 ),
inference(resolution,[],[f2319,f733]) ).
fof(f14287,plain,
( spl20_515
| ~ spl20_89
| ~ spl20_224 ),
inference(avatar_split_clause,[],[f2374,f2314,f776,f14285]) ).
fof(f14285,plain,
( spl20_515
<=> ! [X5] :
( epsilon_transitive(sK4(powerset(X5)))
| empty(X5)
| in(sK3(sK4(powerset(X5))),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_515])]) ).
fof(f2374,plain,
( ! [X5] :
( epsilon_transitive(sK4(powerset(X5)))
| empty(X5)
| in(sK3(sK4(powerset(X5))),X5) )
| ~ spl20_89
| ~ spl20_224 ),
inference(resolution,[],[f2315,f777]) ).
fof(f14283,plain,
( spl20_514
| ~ spl20_84
| ~ spl20_224 ),
inference(avatar_split_clause,[],[f2373,f2314,f732,f14281]) ).
fof(f14281,plain,
( spl20_514
<=> ! [X4] :
( epsilon_transitive(sK4(powerset(powerset(X4))))
| subset(sK3(sK4(powerset(powerset(X4)))),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_514])]) ).
fof(f2373,plain,
( ! [X4] :
( epsilon_transitive(sK4(powerset(powerset(X4))))
| subset(sK3(sK4(powerset(powerset(X4)))),X4) )
| ~ spl20_84
| ~ spl20_224 ),
inference(resolution,[],[f2315,f733]) ).
fof(f14279,plain,
( spl20_513
| ~ spl20_88
| ~ spl20_214 ),
inference(avatar_split_clause,[],[f2254,f2208,f772,f14277]) ).
fof(f14277,plain,
( spl20_513
<=> ! [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_513])]) ).
fof(f2254,plain,
( ! [X2,X0,X1] :
( ~ in(X0,X1)
| subset(X0,set_union2(X1,X2))
| ~ epsilon_transitive(set_union2(X1,X2)) )
| ~ spl20_88
| ~ spl20_214 ),
inference(resolution,[],[f2209,f773]) ).
fof(f14275,plain,
( spl20_512
| ~ spl20_88
| ~ spl20_213 ),
inference(avatar_split_clause,[],[f2237,f2204,f772,f14273]) ).
fof(f14273,plain,
( spl20_512
<=> ! [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_512])]) ).
fof(f2237,plain,
( ! [X2,X0,X1] :
( ~ in(X0,X1)
| subset(X0,set_union2(X2,X1))
| ~ epsilon_transitive(set_union2(X2,X1)) )
| ~ spl20_88
| ~ spl20_213 ),
inference(resolution,[],[f2205,f773]) ).
fof(f14271,plain,
( spl20_511
| ~ spl20_91
| ~ spl20_212 ),
inference(avatar_split_clause,[],[f2236,f2200,f811,f14269]) ).
fof(f14269,plain,
( spl20_511
<=> ! [X5] :
( empty(X5)
| ~ epsilon_transitive(X5)
| sK4(X5) = X5
| ~ subset(X5,sK4(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_511])]) ).
fof(f2236,plain,
( ! [X5] :
( empty(X5)
| ~ epsilon_transitive(X5)
| sK4(X5) = X5
| ~ subset(X5,sK4(X5)) )
| ~ spl20_91
| ~ spl20_212 ),
inference(resolution,[],[f2201,f812]) ).
fof(f13929,plain,
( spl20_510
| ~ spl20_146
| ~ spl20_234 ),
inference(avatar_split_clause,[],[f2551,f2500,f1180,f13927]) ).
fof(f13927,plain,
( spl20_510
<=> ! [X32,X33] :
( ~ ordinal(X32)
| ordinal_subset(X33,X32)
| ~ ordinal(X33)
| ~ empty(X33)
| empty(X32) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_510])]) ).
fof(f2551,plain,
( ! [X32,X33] :
( ~ ordinal(X32)
| ordinal_subset(X33,X32)
| ~ ordinal(X33)
| ~ empty(X33)
| empty(X32) )
| ~ spl20_146
| ~ spl20_234 ),
inference(resolution,[],[f2501,f1181]) ).
fof(f13925,plain,
( spl20_509
| ~ spl20_201
| ~ spl20_234 ),
inference(avatar_split_clause,[],[f2548,f2500,f2058,f13923]) ).
fof(f13923,plain,
( spl20_509
<=> ! [X25,X26] :
( ~ ordinal(singleton(X25))
| ordinal_subset(X26,singleton(X25))
| ~ ordinal(X26)
| ~ empty(X26) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_509])]) ).
fof(f2548,plain,
( ! [X26,X25] :
( ~ ordinal(singleton(X25))
| ordinal_subset(X26,singleton(X25))
| ~ ordinal(X26)
| ~ empty(X26) )
| ~ spl20_201
| ~ spl20_234 ),
inference(resolution,[],[f2501,f2059]) ).
fof(f13921,plain,
( spl20_508
| ~ spl20_52
| ~ spl20_234 ),
inference(avatar_split_clause,[],[f2547,f2500,f511,f13919]) ).
fof(f13919,plain,
( spl20_508
<=> ! [X24,X23] :
( ~ ordinal(succ(X23))
| ordinal_subset(X24,succ(X23))
| ~ ordinal(X24)
| ~ empty(X24) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_508])]) ).
fof(f2547,plain,
( ! [X24,X23] :
( ~ ordinal(succ(X23))
| ordinal_subset(X24,succ(X23))
| ~ ordinal(X24)
| ~ empty(X24) )
| ~ spl20_52
| ~ spl20_234 ),
inference(resolution,[],[f2501,f512]) ).
fof(f13917,plain,
( spl20_507
| ~ spl20_160
| ~ spl20_212 ),
inference(avatar_split_clause,[],[f2233,f2200,f1291,f13915]) ).
fof(f13915,plain,
( spl20_507
<=> ! [X0,X1] :
( empty(X0)
| ~ epsilon_transitive(X0)
| ~ in(X1,sK4(X0))
| element(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_507])]) ).
fof(f2233,plain,
( ! [X0,X1] :
( empty(X0)
| ~ epsilon_transitive(X0)
| ~ in(X1,sK4(X0))
| element(X1,X0) )
| ~ spl20_160
| ~ spl20_212 ),
inference(resolution,[],[f2201,f1292]) ).
fof(f13913,plain,
( spl20_506
| ~ spl20_106
| ~ spl20_207 ),
inference(avatar_split_clause,[],[f2174,f2146,f899,f13911]) ).
fof(f899,plain,
( spl20_106
<=> ! [X2,X4,X0,X1] :
( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_106])]) ).
fof(f2146,plain,
( spl20_207
<=> ! [X5] : sP0(singleton(X5),X5,succ(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_207])]) ).
fof(f2174,plain,
( ! [X0,X1] :
( in(X0,X1)
| ~ in(X0,succ(X1))
| in(X0,singleton(X1)) )
| ~ spl20_106
| ~ spl20_207 ),
inference(resolution,[],[f2147,f900]) ).
fof(f900,plain,
( ! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| in(X4,X1)
| ~ in(X4,X2)
| in(X4,X0) )
| ~ spl20_106 ),
inference(avatar_component_clause,[],[f899]) ).
fof(f2147,plain,
( ! [X5] : sP0(singleton(X5),X5,succ(X5))
| ~ spl20_207 ),
inference(avatar_component_clause,[],[f2146]) ).
fof(f13790,plain,
( spl20_505
| ~ spl20_174
| ~ spl20_268 ),
inference(avatar_split_clause,[],[f3339,f2996,f1432,f13788]) ).
fof(f13788,plain,
( spl20_505
<=> ! [X50,X49] :
( sP0(X49,X50,X49)
| in(sK6(X49,X50,X49),X50) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_505])]) ).
fof(f1432,plain,
( spl20_174
<=> ! [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_174])]) ).
fof(f2996,plain,
( spl20_268
<=> ! [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_268])]) ).
fof(f3339,plain,
( ! [X50,X49] :
( sP0(X49,X50,X49)
| in(sK6(X49,X50,X49),X50) )
| ~ spl20_174
| ~ spl20_268 ),
inference(duplicate_literal_removal,[],[f3320]) ).
fof(f3320,plain,
( ! [X50,X49] :
( sP0(X49,X50,X49)
| in(sK6(X49,X50,X49),X50)
| in(sK6(X49,X50,X49),X50)
| sP0(X49,X50,X49) )
| ~ spl20_174
| ~ spl20_268 ),
inference(resolution,[],[f2997,f1433]) ).
fof(f1433,plain,
( ! [X2,X3] :
( in(sK6(X2,X3,X2),X3)
| in(sK6(X2,X3,X2),X2)
| sP0(X2,X3,X2) )
| ~ spl20_174 ),
inference(avatar_component_clause,[],[f1432]) ).
fof(f2997,plain,
( ! [X0,X1] :
( ~ in(sK6(X0,X1,X0),X0)
| sP0(X0,X1,X0)
| in(sK6(X0,X1,X0),X1) )
| ~ spl20_268 ),
inference(avatar_component_clause,[],[f2996]) ).
fof(f13786,plain,
( spl20_504
| ~ spl20_173
| ~ spl20_262 ),
inference(avatar_split_clause,[],[f3194,f2972,f1428,f13784]) ).
fof(f13784,plain,
( spl20_504
<=> ! [X45,X44] :
( sP0(X44,X45,X45)
| in(sK6(X44,X45,X45),X44) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_504])]) ).
fof(f1428,plain,
( spl20_173
<=> ! [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_173])]) ).
fof(f2972,plain,
( spl20_262
<=> ! [X2,X3] :
( in(sK6(X2,X3,X3),X2)
| sP0(X2,X3,X3)
| ~ in(sK6(X2,X3,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_262])]) ).
fof(f3194,plain,
( ! [X44,X45] :
( sP0(X44,X45,X45)
| in(sK6(X44,X45,X45),X44) )
| ~ spl20_173
| ~ spl20_262 ),
inference(duplicate_literal_removal,[],[f3166]) ).
fof(f3166,plain,
( ! [X44,X45] :
( sP0(X44,X45,X45)
| in(sK6(X44,X45,X45),X44)
| in(sK6(X44,X45,X45),X44)
| sP0(X44,X45,X45) )
| ~ spl20_173
| ~ spl20_262 ),
inference(resolution,[],[f2973,f1429]) ).
fof(f1429,plain,
( ! [X0,X1] :
( in(sK6(X0,X1,X1),X1)
| in(sK6(X0,X1,X1),X0)
| sP0(X0,X1,X1) )
| ~ spl20_173 ),
inference(avatar_component_clause,[],[f1428]) ).
fof(f2973,plain,
( ! [X2,X3] :
( ~ in(sK6(X2,X3,X3),X3)
| sP0(X2,X3,X3)
| in(sK6(X2,X3,X3),X2) )
| ~ spl20_262 ),
inference(avatar_component_clause,[],[f2972]) ).
fof(f13782,plain,
( spl20_503
| ~ spl20_68
| ~ spl20_249 ),
inference(avatar_split_clause,[],[f2845,f2812,f613,f13780]) ).
fof(f13780,plain,
( spl20_503
<=> ! [X27,X28,X26] :
( sP0(X26,X27,X28)
| ~ empty(X28)
| ~ empty(X27)
| ~ empty(X26) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_503])]) ).
fof(f2845,plain,
( ! [X28,X26,X27] :
( sP0(X26,X27,X28)
| ~ empty(X28)
| ~ empty(X27)
| ~ empty(X26) )
| ~ spl20_68
| ~ spl20_249 ),
inference(resolution,[],[f2813,f614]) ).
fof(f13778,plain,
( spl20_502
| ~ spl20_151
| ~ spl20_242 ),
inference(avatar_split_clause,[],[f2715,f2533,f1221,f13776]) ).
fof(f13776,plain,
( spl20_502
<=> ! [X29,X30] :
( sP0(X29,X29,sK4(powerset(X30)))
| ~ empty(X29)
| ~ empty(X30) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_502])]) ).
fof(f2715,plain,
( ! [X29,X30] :
( sP0(X29,X29,sK4(powerset(X30)))
| ~ empty(X29)
| ~ empty(X30) )
| ~ spl20_151
| ~ spl20_242 ),
inference(resolution,[],[f2534,f1222]) ).
fof(f13774,plain,
( spl20_501
| ~ spl20_151
| ~ spl20_240 ),
inference(avatar_split_clause,[],[f2665,f2525,f1221,f13772]) ).
fof(f13772,plain,
( spl20_501
<=> ! [X29,X28] :
( sP0(X28,sK4(powerset(X29)),X28)
| ~ empty(X28)
| ~ empty(X29) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_501])]) ).
fof(f2525,plain,
( spl20_240
<=> ! [X11,X10] :
( in(sK6(X10,X11,X10),X11)
| sP0(X10,X11,X10)
| ~ empty(X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_240])]) ).
fof(f2665,plain,
( ! [X28,X29] :
( sP0(X28,sK4(powerset(X29)),X28)
| ~ empty(X28)
| ~ empty(X29) )
| ~ spl20_151
| ~ spl20_240 ),
inference(resolution,[],[f2526,f1222]) ).
fof(f2526,plain,
( ! [X10,X11] :
( in(sK6(X10,X11,X10),X11)
| sP0(X10,X11,X10)
| ~ empty(X10) )
| ~ spl20_240 ),
inference(avatar_component_clause,[],[f2525]) ).
fof(f13770,plain,
( spl20_500
| ~ spl20_151
| ~ spl20_236 ),
inference(avatar_split_clause,[],[f2605,f2508,f1221,f13768]) ).
fof(f13768,plain,
( spl20_500
<=> ! [X29,X28] :
( sP0(sK4(powerset(X28)),X29,X29)
| ~ empty(X29)
| ~ empty(X28) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_500])]) ).
fof(f2508,plain,
( spl20_236
<=> ! [X11,X10] :
( in(sK6(X10,X11,X11),X10)
| sP0(X10,X11,X11)
| ~ empty(X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_236])]) ).
fof(f2605,plain,
( ! [X28,X29] :
( sP0(sK4(powerset(X28)),X29,X29)
| ~ empty(X29)
| ~ empty(X28) )
| ~ spl20_151
| ~ spl20_236 ),
inference(resolution,[],[f2509,f1222]) ).
fof(f2509,plain,
( ! [X10,X11] :
( in(sK6(X10,X11,X11),X10)
| sP0(X10,X11,X11)
| ~ empty(X11) )
| ~ spl20_236 ),
inference(avatar_component_clause,[],[f2508]) ).
fof(f13739,plain,
( spl20_499
| ~ spl20_146
| ~ spl20_223 ),
inference(avatar_split_clause,[],[f2342,f2310,f1180,f13737]) ).
fof(f13737,plain,
( spl20_499
<=> ! [X11] :
( ~ empty(X11)
| epsilon_transitive(powerset(X11))
| empty(sK3(powerset(X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_499])]) ).
fof(f2342,plain,
( ! [X11] :
( ~ empty(X11)
| epsilon_transitive(powerset(X11))
| empty(sK3(powerset(X11))) )
| ~ spl20_146
| ~ spl20_223 ),
inference(resolution,[],[f2311,f1181]) ).
fof(f13735,plain,
( spl20_498
| ~ spl20_71
| ~ spl20_223 ),
inference(avatar_split_clause,[],[f2341,f2310,f637,f13733]) ).
fof(f13733,plain,
( spl20_498
<=> ! [X10] :
( ~ empty(X10)
| epsilon_transitive(powerset(X10))
| epsilon_transitive(sK3(powerset(X10))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_498])]) ).
fof(f2341,plain,
( ! [X10] :
( ~ empty(X10)
| epsilon_transitive(powerset(X10))
| epsilon_transitive(sK3(powerset(X10))) )
| ~ spl20_71
| ~ spl20_223 ),
inference(resolution,[],[f2311,f638]) ).
fof(f13731,plain,
( spl20_497
| ~ spl20_86
| ~ spl20_209 ),
inference(avatar_split_clause,[],[f2186,f2154,f740,f13729]) ).
fof(f13729,plain,
( spl20_497
<=> ! [X6,X7] :
( ~ empty(X6)
| sK4(powerset(X6)) = X7
| ~ empty(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_497])]) ).
fof(f740,plain,
( spl20_86
<=> ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_86])]) ).
fof(f2186,plain,
( ! [X6,X7] :
( ~ empty(X6)
| sK4(powerset(X6)) = X7
| ~ empty(X7) )
| ~ spl20_86
| ~ spl20_209 ),
inference(resolution,[],[f2155,f741]) ).
fof(f741,plain,
( ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) )
| ~ spl20_86 ),
inference(avatar_component_clause,[],[f740]) ).
fof(f13679,plain,
( ~ spl20_496
| ~ spl20_462
| ~ spl20_466 ),
inference(avatar_split_clause,[],[f12885,f12868,f12811,f13676]) ).
fof(f13676,plain,
( spl20_496
<=> in(singleton(succ(sK2)),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_496])]) ).
fof(f12868,plain,
( spl20_466
<=> ! [X3] : ~ in(singleton(X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_466])]) ).
fof(f12885,plain,
( ~ in(singleton(succ(sK2)),sK1)
| ~ spl20_462
| ~ spl20_466 ),
inference(resolution,[],[f12869,f12812]) ).
fof(f12869,plain,
( ! [X3] : ~ in(singleton(X3),X3)
| ~ spl20_466 ),
inference(avatar_component_clause,[],[f12868]) ).
fof(f13458,plain,
( spl20_495
| ~ spl20_68
| ~ spl20_241 ),
inference(avatar_split_clause,[],[f2688,f2529,f613,f13456]) ).
fof(f13456,plain,
( spl20_495
<=> ! [X16,X15] :
( sP0(X15,X15,X16)
| ~ empty(X16)
| ~ empty(X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_495])]) ).
fof(f2688,plain,
( ! [X16,X15] :
( sP0(X15,X15,X16)
| ~ empty(X16)
| ~ empty(X15) )
| ~ spl20_68
| ~ spl20_241 ),
inference(resolution,[],[f2530,f614]) ).
fof(f13454,plain,
( spl20_494
| ~ spl20_68
| ~ spl20_238 ),
inference(avatar_split_clause,[],[f2638,f2516,f613,f13452]) ).
fof(f13452,plain,
( spl20_494
<=> ! [X16,X17] :
( sP0(X16,X17,X16)
| ~ empty(X17)
| ~ empty(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_494])]) ).
fof(f2516,plain,
( spl20_238
<=> ! [X9,X8] :
( in(sK6(X8,X9,X8),X8)
| sP0(X8,X9,X8)
| ~ empty(X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_238])]) ).
fof(f2638,plain,
( ! [X16,X17] :
( sP0(X16,X17,X16)
| ~ empty(X17)
| ~ empty(X16) )
| ~ spl20_68
| ~ spl20_238 ),
inference(resolution,[],[f2517,f614]) ).
fof(f2517,plain,
( ! [X8,X9] :
( in(sK6(X8,X9,X8),X8)
| sP0(X8,X9,X8)
| ~ empty(X9) )
| ~ spl20_238 ),
inference(avatar_component_clause,[],[f2516]) ).
fof(f13450,plain,
( spl20_493
| ~ spl20_68
| ~ spl20_236 ),
inference(avatar_split_clause,[],[f2598,f2508,f613,f13448]) ).
fof(f13448,plain,
( spl20_493
<=> ! [X14,X15] :
( sP0(X14,X15,X15)
| ~ empty(X15)
| ~ empty(X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_493])]) ).
fof(f2598,plain,
( ! [X14,X15] :
( sP0(X14,X15,X15)
| ~ empty(X15)
| ~ empty(X14) )
| ~ spl20_68
| ~ spl20_236 ),
inference(resolution,[],[f2509,f614]) ).
fof(f13446,plain,
( spl20_492
| ~ spl20_201
| ~ spl20_227 ),
inference(avatar_split_clause,[],[f2391,f2326,f2058,f13444]) ).
fof(f13444,plain,
( spl20_492
<=> ! [X17] :
( ~ subset(singleton(powerset(X17)),X17)
| empty(powerset(X17)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_492])]) ).
fof(f2391,plain,
( ! [X17] :
( ~ subset(singleton(powerset(X17)),X17)
| empty(powerset(X17)) )
| ~ spl20_201
| ~ spl20_227 ),
inference(resolution,[],[f2327,f2059]) ).
fof(f13442,plain,
( spl20_491
| ~ spl20_75
| ~ spl20_214 ),
inference(avatar_split_clause,[],[f2256,f2208,f653,f13440]) ).
fof(f13440,plain,
( spl20_491
<=> ! [X6,X7,X8] :
( ~ in(X6,X7)
| ~ in(set_union2(X7,X8),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_491])]) ).
fof(f2256,plain,
( ! [X8,X6,X7] :
( ~ in(X6,X7)
| ~ in(set_union2(X7,X8),X6) )
| ~ spl20_75
| ~ spl20_214 ),
inference(resolution,[],[f2209,f654]) ).
fof(f13438,plain,
( spl20_490
| ~ spl20_76
| ~ spl20_214 ),
inference(avatar_split_clause,[],[f2255,f2208,f657,f13436]) ).
fof(f13436,plain,
( spl20_490
<=> ! [X4,X5,X3] :
( ~ in(X3,X4)
| element(X3,set_union2(X4,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_490])]) ).
fof(f2255,plain,
( ! [X3,X4,X5] :
( ~ in(X3,X4)
| element(X3,set_union2(X4,X5)) )
| ~ spl20_76
| ~ spl20_214 ),
inference(resolution,[],[f2209,f658]) ).
fof(f13434,plain,
( ~ spl20_489
| ~ spl20_129
| ~ spl20_462 ),
inference(avatar_split_clause,[],[f12840,f12811,f1085,f13431]) ).
fof(f13431,plain,
( spl20_489
<=> in(succ(succ(sK2)),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_489])]) ).
fof(f12840,plain,
( ~ in(succ(succ(sK2)),sK1)
| ~ spl20_129
| ~ spl20_462 ),
inference(resolution,[],[f12812,f1086]) ).
fof(f13429,plain,
( spl20_488
| ~ spl20_75
| ~ spl20_213 ),
inference(avatar_split_clause,[],[f2239,f2204,f653,f13427]) ).
fof(f13427,plain,
( spl20_488
<=> ! [X6,X7,X8] :
( ~ in(X6,X7)
| ~ in(set_union2(X8,X7),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_488])]) ).
fof(f2239,plain,
( ! [X8,X6,X7] :
( ~ in(X6,X7)
| ~ in(set_union2(X8,X7),X6) )
| ~ spl20_75
| ~ spl20_213 ),
inference(resolution,[],[f2205,f654]) ).
fof(f13425,plain,
( spl20_487
| ~ spl20_76
| ~ spl20_213 ),
inference(avatar_split_clause,[],[f2238,f2204,f657,f13423]) ).
fof(f13423,plain,
( spl20_487
<=> ! [X4,X5,X3] :
( ~ in(X3,X4)
| element(X3,set_union2(X5,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_487])]) ).
fof(f2238,plain,
( ! [X3,X4,X5] :
( ~ in(X3,X4)
| element(X3,set_union2(X5,X4)) )
| ~ spl20_76
| ~ spl20_213 ),
inference(resolution,[],[f2205,f658]) ).
fof(f13421,plain,
( spl20_486
| ~ spl20_102
| ~ spl20_207 ),
inference(avatar_split_clause,[],[f2175,f2146,f866,f13419]) ).
fof(f13419,plain,
( spl20_486
<=> ! [X2,X3] :
( ~ in(X2,singleton(X3))
| in(X2,succ(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_486])]) ).
fof(f866,plain,
( spl20_102
<=> ! [X4,X0,X2,X1] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_102])]) ).
fof(f2175,plain,
( ! [X2,X3] :
( ~ in(X2,singleton(X3))
| in(X2,succ(X3)) )
| ~ spl20_102
| ~ spl20_207 ),
inference(resolution,[],[f2147,f867]) ).
fof(f867,plain,
( ! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| ~ in(X4,X0)
| in(X4,X2) )
| ~ spl20_102 ),
inference(avatar_component_clause,[],[f866]) ).
fof(f13197,plain,
( spl20_485
| ~ spl20_103
| ~ spl20_221 ),
inference(avatar_split_clause,[],[f2304,f2292,f886,f13195]) ).
fof(f13195,plain,
( spl20_485
<=> ! [X4] :
( sK8 = singleton(X4)
| ~ in(X4,sK8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_485])]) ).
fof(f2292,plain,
( spl20_221
<=> ! [X0] :
( sK5(X0,sK8) = X0
| singleton(X0) = sK8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_221])]) ).
fof(f2304,plain,
( ! [X4] :
( sK8 = singleton(X4)
| ~ in(X4,sK8) )
| ~ spl20_103
| ~ spl20_221 ),
inference(trivial_inequality_removal,[],[f2303]) ).
fof(f2303,plain,
( ! [X4] :
( X4 != X4
| sK8 = singleton(X4)
| ~ in(X4,sK8) )
| ~ spl20_103
| ~ spl20_221 ),
inference(duplicate_literal_removal,[],[f2302]) ).
fof(f2302,plain,
( ! [X4] :
( X4 != X4
| sK8 = singleton(X4)
| ~ in(X4,sK8)
| sK8 = singleton(X4) )
| ~ spl20_103
| ~ spl20_221 ),
inference(superposition,[],[f887,f2293]) ).
fof(f2293,plain,
( ! [X0] :
( sK5(X0,sK8) = X0
| singleton(X0) = sK8 )
| ~ spl20_221 ),
inference(avatar_component_clause,[],[f2292]) ).
fof(f13193,plain,
( spl20_484
| ~ spl20_454 ),
inference(avatar_split_clause,[],[f12567,f12336,f13190]) ).
fof(f12336,plain,
( spl20_454
<=> ! [X1] :
( sK1 != X1
| sP0(sK2,singleton(sK2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_454])]) ).
fof(f12567,plain,
( sP0(sK2,singleton(sK2),sK1)
| ~ spl20_454 ),
inference(equality_resolution,[],[f12337]) ).
fof(f12337,plain,
( ! [X1] :
( sK1 != X1
| sP0(sK2,singleton(sK2),X1) )
| ~ spl20_454 ),
inference(avatar_component_clause,[],[f12336]) ).
fof(f13188,plain,
( spl20_483
| ~ spl20_68
| ~ spl20_214 ),
inference(avatar_split_clause,[],[f2257,f2208,f613,f13186]) ).
fof(f13186,plain,
( spl20_483
<=> ! [X9,X11,X10] :
( ~ in(X9,X10)
| ~ empty(set_union2(X10,X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_483])]) ).
fof(f2257,plain,
( ! [X10,X11,X9] :
( ~ in(X9,X10)
| ~ empty(set_union2(X10,X11)) )
| ~ spl20_68
| ~ spl20_214 ),
inference(resolution,[],[f2209,f614]) ).
fof(f13184,plain,
( spl20_482
| ~ spl20_68
| ~ spl20_213 ),
inference(avatar_split_clause,[],[f2240,f2204,f613,f13182]) ).
fof(f13182,plain,
( spl20_482
<=> ! [X9,X11,X10] :
( ~ in(X9,X10)
| ~ empty(set_union2(X11,X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_482])]) ).
fof(f2240,plain,
( ! [X10,X11,X9] :
( ~ in(X9,X10)
| ~ empty(set_union2(X11,X10)) )
| ~ spl20_68
| ~ spl20_213 ),
inference(resolution,[],[f2205,f614]) ).
fof(f13180,plain,
( spl20_481
| ~ spl20_66
| ~ spl20_125
| ~ spl20_209 ),
inference(avatar_split_clause,[],[f2189,f2154,f1044,f605,f13178]) ).
fof(f13178,plain,
( spl20_481
<=> ! [X5] :
( sK8 = sK4(powerset(X5))
| ~ empty(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_481])]) ).
fof(f2189,plain,
( ! [X5] :
( sK8 = sK4(powerset(X5))
| ~ empty(X5) )
| ~ spl20_66
| ~ spl20_125
| ~ spl20_209 ),
inference(forward_demodulation,[],[f2185,f1046]) ).
fof(f2185,plain,
( ! [X5] :
( ~ empty(X5)
| empty_set = sK4(powerset(X5)) )
| ~ spl20_66
| ~ spl20_209 ),
inference(resolution,[],[f2155,f606]) ).
fof(f13176,plain,
( spl20_480
| ~ spl20_101
| ~ spl20_207 ),
inference(avatar_split_clause,[],[f2176,f2146,f862,f13174]) ).
fof(f13174,plain,
( spl20_480
<=> ! [X4,X5] :
( ~ in(X4,X5)
| in(X4,succ(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_480])]) ).
fof(f2176,plain,
( ! [X4,X5] :
( ~ in(X4,X5)
| in(X4,succ(X5)) )
| ~ spl20_101
| ~ spl20_207 ),
inference(resolution,[],[f2147,f863]) ).
fof(f13172,plain,
( spl20_479
| ~ spl20_88
| ~ spl20_201 ),
inference(avatar_split_clause,[],[f2075,f2058,f772,f13170]) ).
fof(f13170,plain,
( spl20_479
<=> ! [X1] :
( subset(X1,singleton(X1))
| ~ epsilon_transitive(singleton(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_479])]) ).
fof(f2075,plain,
( ! [X1] :
( subset(X1,singleton(X1))
| ~ epsilon_transitive(singleton(X1)) )
| ~ spl20_88
| ~ spl20_201 ),
inference(resolution,[],[f2059,f773]) ).
fof(f13130,plain,
( spl20_228
| ~ spl20_3
| ~ spl20_451 ),
inference(avatar_split_clause,[],[f12642,f12274,f270,f2330]) ).
fof(f12274,plain,
( spl20_451
<=> ! [X0] :
( ~ in(X0,succ(sK2))
| element(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_451])]) ).
fof(f12642,plain,
( element(sK1,sK1)
| ~ spl20_3
| ~ spl20_451 ),
inference(resolution,[],[f12275,f272]) ).
fof(f12275,plain,
( ! [X0] :
( ~ in(X0,succ(sK2))
| element(X0,sK1) )
| ~ spl20_451 ),
inference(avatar_component_clause,[],[f12274]) ).
fof(f12955,plain,
( spl20_478
| ~ spl20_129
| ~ spl20_214 ),
inference(avatar_split_clause,[],[f2258,f2208,f1085,f12953]) ).
fof(f2258,plain,
( ! [X12,X13] : ~ in(succ(set_union2(X12,X13)),X12)
| ~ spl20_129
| ~ spl20_214 ),
inference(resolution,[],[f2209,f1086]) ).
fof(f12951,plain,
( spl20_477
| ~ spl20_129
| ~ spl20_213 ),
inference(avatar_split_clause,[],[f2241,f2204,f1085,f12949]) ).
fof(f2241,plain,
( ! [X12,X13] : ~ in(succ(set_union2(X12,X13)),X13)
| ~ spl20_129
| ~ spl20_213 ),
inference(resolution,[],[f2205,f1086]) ).
fof(f12947,plain,
( spl20_476
| ~ spl20_59
| ~ spl20_209 ),
inference(avatar_split_clause,[],[f2184,f2154,f539,f12945]) ).
fof(f12945,plain,
( spl20_476
<=> ! [X4] :
( ~ empty(X4)
| ordinal(sK4(powerset(X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_476])]) ).
fof(f539,plain,
( spl20_59
<=> ! [X0] :
( ordinal(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_59])]) ).
fof(f2184,plain,
( ! [X4] :
( ~ empty(X4)
| ordinal(sK4(powerset(X4))) )
| ~ spl20_59
| ~ spl20_209 ),
inference(resolution,[],[f2155,f540]) ).
fof(f540,plain,
( ! [X0] :
( ~ empty(X0)
| ordinal(X0) )
| ~ spl20_59 ),
inference(avatar_component_clause,[],[f539]) ).
fof(f12943,plain,
( spl20_475
| ~ spl20_58
| ~ spl20_209 ),
inference(avatar_split_clause,[],[f2183,f2154,f535,f12941]) ).
fof(f12941,plain,
( spl20_475
<=> ! [X3] :
( ~ empty(X3)
| epsilon_connected(sK4(powerset(X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_475])]) ).
fof(f535,plain,
( spl20_58
<=> ! [X0] :
( epsilon_connected(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_58])]) ).
fof(f2183,plain,
( ! [X3] :
( ~ empty(X3)
| epsilon_connected(sK4(powerset(X3))) )
| ~ spl20_58
| ~ spl20_209 ),
inference(resolution,[],[f2155,f536]) ).
fof(f536,plain,
( ! [X0] :
( ~ empty(X0)
| epsilon_connected(X0) )
| ~ spl20_58 ),
inference(avatar_component_clause,[],[f535]) ).
fof(f12939,plain,
( spl20_474
| ~ spl20_56
| ~ spl20_209 ),
inference(avatar_split_clause,[],[f2181,f2154,f527,f12937]) ).
fof(f12937,plain,
( spl20_474
<=> ! [X1] :
( ~ empty(X1)
| relation(sK4(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_474])]) ).
fof(f2181,plain,
( ! [X1] :
( ~ empty(X1)
| relation(sK4(powerset(X1))) )
| ~ spl20_56
| ~ spl20_209 ),
inference(resolution,[],[f2155,f528]) ).
fof(f12935,plain,
( spl20_473
| ~ spl20_55
| ~ spl20_209 ),
inference(avatar_split_clause,[],[f2180,f2154,f523,f12933]) ).
fof(f12933,plain,
( spl20_473
<=> ! [X0] :
( ~ empty(X0)
| function(sK4(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_473])]) ).
fof(f2180,plain,
( ! [X0] :
( ~ empty(X0)
| function(sK4(powerset(X0))) )
| ~ spl20_55
| ~ spl20_209 ),
inference(resolution,[],[f2155,f524]) ).
fof(f12926,plain,
( spl20_239
| spl20_181
| ~ spl20_89
| ~ spl20_228 ),
inference(avatar_split_clause,[],[f12312,f2330,f776,f1640,f2520]) ).
fof(f2520,plain,
( spl20_239
<=> in(sK1,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_239])]) ).
fof(f12312,plain,
( empty(sK1)
| in(sK1,sK1)
| ~ spl20_89
| ~ spl20_228 ),
inference(resolution,[],[f2332,f777]) ).
fof(f2332,plain,
( element(sK1,sK1)
| ~ spl20_228 ),
inference(avatar_component_clause,[],[f2330]) ).
fof(f12925,plain,
( spl20_472
| ~ spl20_79
| ~ spl20_206 ),
inference(avatar_split_clause,[],[f2169,f2142,f685,f12923]) ).
fof(f12923,plain,
( spl20_472
<=> ! [X5] : sP0(X5,singleton(X5),succ(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_472])]) ).
fof(f2169,plain,
( ! [X5] : sP0(X5,singleton(X5),succ(X5))
| ~ spl20_79
| ~ spl20_206 ),
inference(superposition,[],[f2143,f686]) ).
fof(f12921,plain,
( spl20_471
| ~ spl20_101
| ~ spl20_199 ),
inference(avatar_split_clause,[],[f2068,f2050,f862,f12919]) ).
fof(f12919,plain,
( spl20_471
<=> ! [X4,X5] :
( ~ in(X4,sK8)
| in(X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_471])]) ).
fof(f2050,plain,
( spl20_199
<=> ! [X7] : sP0(X7,sK8,X7) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_199])]) ).
fof(f2068,plain,
( ! [X4,X5] :
( ~ in(X4,sK8)
| in(X4,X5) )
| ~ spl20_101
| ~ spl20_199 ),
inference(resolution,[],[f2051,f863]) ).
fof(f2051,plain,
( ! [X7] : sP0(X7,sK8,X7)
| ~ spl20_199 ),
inference(avatar_component_clause,[],[f2050]) ).
fof(f12914,plain,
( ~ spl20_122
| spl20_470
| ~ spl20_65
| ~ spl20_203 ),
inference(avatar_split_clause,[],[f2104,f2084,f601,f12911,f1023]) ).
fof(f12911,plain,
( spl20_470
<=> ordinal(singleton(sK8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_470])]) ).
fof(f601,plain,
( spl20_65
<=> ! [X0] :
( ordinal(succ(X0))
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_65])]) ).
fof(f2104,plain,
( ordinal(singleton(sK8))
| ~ ordinal(sK8)
| ~ spl20_65
| ~ spl20_203 ),
inference(superposition,[],[f602,f2086]) ).
fof(f602,plain,
( ! [X0] :
( ordinal(succ(X0))
| ~ ordinal(X0) )
| ~ spl20_65 ),
inference(avatar_component_clause,[],[f601]) ).
fof(f12908,plain,
( ~ spl20_122
| spl20_469
| ~ spl20_63
| ~ spl20_203 ),
inference(avatar_split_clause,[],[f2103,f2084,f592,f12905,f1023]) ).
fof(f12905,plain,
( spl20_469
<=> epsilon_connected(singleton(sK8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_469])]) ).
fof(f592,plain,
( spl20_63
<=> ! [X0] :
( epsilon_connected(succ(X0))
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_63])]) ).
fof(f2103,plain,
( epsilon_connected(singleton(sK8))
| ~ ordinal(sK8)
| ~ spl20_63
| ~ spl20_203 ),
inference(superposition,[],[f593,f2086]) ).
fof(f593,plain,
( ! [X0] :
( epsilon_connected(succ(X0))
| ~ ordinal(X0) )
| ~ spl20_63 ),
inference(avatar_component_clause,[],[f592]) ).
fof(f12903,plain,
( ~ spl20_122
| spl20_468
| ~ spl20_62
| ~ spl20_203 ),
inference(avatar_split_clause,[],[f2102,f2084,f588,f12900,f1023]) ).
fof(f12900,plain,
( spl20_468
<=> epsilon_transitive(singleton(sK8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_468])]) ).
fof(f588,plain,
( spl20_62
<=> ! [X0] :
( epsilon_transitive(succ(X0))
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_62])]) ).
fof(f2102,plain,
( epsilon_transitive(singleton(sK8))
| ~ ordinal(sK8)
| ~ spl20_62
| ~ spl20_203 ),
inference(superposition,[],[f589,f2086]) ).
fof(f589,plain,
( ! [X0] :
( epsilon_transitive(succ(X0))
| ~ ordinal(X0) )
| ~ spl20_62 ),
inference(avatar_component_clause,[],[f588]) ).
fof(f12887,plain,
( ~ spl20_239
| ~ spl20_75
| ~ spl20_239 ),
inference(avatar_split_clause,[],[f12611,f2520,f653,f2520]) ).
fof(f12611,plain,
( ~ in(sK1,sK1)
| ~ spl20_75
| ~ spl20_239 ),
inference(resolution,[],[f2521,f654]) ).
fof(f2521,plain,
( in(sK1,sK1)
| ~ spl20_239 ),
inference(avatar_component_clause,[],[f2520]) ).
fof(f12875,plain,
( ~ spl20_467
| ~ spl20_51
| ~ spl20_203 ),
inference(avatar_split_clause,[],[f2100,f2084,f507,f12872]) ).
fof(f12872,plain,
( spl20_467
<=> sK8 = singleton(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_467])]) ).
fof(f507,plain,
( spl20_51
<=> ! [X0] : succ(X0) != X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl20_51])]) ).
fof(f2100,plain,
( sK8 != singleton(sK8)
| ~ spl20_51
| ~ spl20_203 ),
inference(superposition,[],[f508,f2086]) ).
fof(f508,plain,
( ! [X0] : succ(X0) != X0
| ~ spl20_51 ),
inference(avatar_component_clause,[],[f507]) ).
fof(f12870,plain,
( spl20_466
| ~ spl20_75
| ~ spl20_201 ),
inference(avatar_split_clause,[],[f2077,f2058,f653,f12868]) ).
fof(f2077,plain,
( ! [X3] : ~ in(singleton(X3),X3)
| ~ spl20_75
| ~ spl20_201 ),
inference(resolution,[],[f2059,f654]) ).
fof(f12866,plain,
( spl20_465
| ~ spl20_76
| ~ spl20_201 ),
inference(avatar_split_clause,[],[f2076,f2058,f657,f12864]) ).
fof(f12864,plain,
( spl20_465
<=> ! [X2] : element(X2,singleton(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_465])]) ).
fof(f2076,plain,
( ! [X2] : element(X2,singleton(X2))
| ~ spl20_76
| ~ spl20_201 ),
inference(resolution,[],[f2059,f658]) ).
fof(f12861,plain,
( spl20_464
| ~ spl20_68
| ~ spl20_201 ),
inference(avatar_split_clause,[],[f2078,f2058,f613,f12859]) ).
fof(f12859,plain,
( spl20_464
<=> ! [X4] : ~ empty(singleton(X4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_464])]) ).
fof(f2078,plain,
( ! [X4] : ~ empty(singleton(X4))
| ~ spl20_68
| ~ spl20_201 ),
inference(resolution,[],[f2059,f614]) ).
fof(f12855,plain,
( spl20_463
| ~ spl20_196
| ~ spl20_3
| ~ spl20_245 ),
inference(avatar_split_clause,[],[f12582,f2725,f270,f2036,f12853]) ).
fof(f12853,plain,
( spl20_463
<=> ! [X0] :
( ordinal_subset(X0,succ(sK2))
| element(sK1,X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_463])]) ).
fof(f12582,plain,
( ! [X0] :
( ~ ordinal(succ(sK2))
| ordinal_subset(X0,succ(sK2))
| ~ ordinal(X0)
| element(sK1,X0) )
| ~ spl20_3
| ~ spl20_245 ),
inference(resolution,[],[f272,f2726]) ).
fof(f12832,plain,
( spl20_418
| ~ spl20_175
| ~ spl20_239 ),
inference(avatar_split_clause,[],[f12606,f2520,f1436,f9265]) ).
fof(f12606,plain,
( element(sK1,sK2)
| ~ spl20_175
| ~ spl20_239 ),
inference(resolution,[],[f2521,f1437]) ).
fof(f1437,plain,
( ! [X4] :
( ~ in(X4,sK1)
| element(X4,sK2) )
| ~ spl20_175 ),
inference(avatar_component_clause,[],[f1436]) ).
fof(f12825,plain,
( ~ spl20_49
| ~ spl20_461 ),
inference(avatar_contradiction_clause,[],[f12814]) ).
fof(f12814,plain,
( $false
| ~ spl20_49
| ~ spl20_461 ),
inference(resolution,[],[f12809,f500]) ).
fof(f12809,plain,
( empty(succ(sK2))
| ~ spl20_461 ),
inference(avatar_component_clause,[],[f12807]) ).
fof(f12813,plain,
( spl20_461
| spl20_462
| ~ spl20_89
| ~ spl20_459 ),
inference(avatar_split_clause,[],[f12617,f12614,f776,f12811,f12807]) ).
fof(f12614,plain,
( spl20_459
<=> ! [X0] :
( ~ in(X0,sK1)
| element(X0,succ(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_459])]) ).
fof(f12617,plain,
( ! [X0] :
( ~ in(X0,sK1)
| empty(succ(sK2))
| in(X0,succ(sK2)) )
| ~ spl20_89
| ~ spl20_459 ),
inference(resolution,[],[f12615,f777]) ).
fof(f12615,plain,
( ! [X0] :
( element(X0,succ(sK2))
| ~ in(X0,sK1) )
| ~ spl20_459 ),
inference(avatar_component_clause,[],[f12614]) ).
fof(f12628,plain,
( ~ spl20_1
| ~ spl20_196
| spl20_460
| ~ spl20_97
| ~ spl20_458 ),
inference(avatar_split_clause,[],[f12597,f12591,f846,f12625,f2036,f260]) ).
fof(f12597,plain,
( ordinal_subset(sK1,succ(sK2))
| ~ ordinal(succ(sK2))
| ~ ordinal(sK1)
| ~ spl20_97
| ~ spl20_458 ),
inference(resolution,[],[f12593,f847]) ).
fof(f12618,plain,
( ~ spl20_205
| spl20_197
| ~ spl20_91
| ~ spl20_458 ),
inference(avatar_split_clause,[],[f12598,f12591,f811,f2040,f2118]) ).
fof(f12598,plain,
( sK1 = succ(sK2)
| ~ subset(succ(sK2),sK1)
| ~ spl20_91
| ~ spl20_458 ),
inference(resolution,[],[f12593,f812]) ).
fof(f12616,plain,
( spl20_459
| ~ spl20_160
| ~ spl20_458 ),
inference(avatar_split_clause,[],[f12595,f12591,f1291,f12614]) ).
fof(f12595,plain,
( ! [X0] :
( ~ in(X0,sK1)
| element(X0,succ(sK2)) )
| ~ spl20_160
| ~ spl20_458 ),
inference(resolution,[],[f12593,f1292]) ).
fof(f12594,plain,
( ~ spl20_219
| spl20_458
| ~ spl20_3
| ~ spl20_88 ),
inference(avatar_split_clause,[],[f1441,f772,f270,f12591,f2282]) ).
fof(f1441,plain,
( subset(sK1,succ(sK2))
| ~ epsilon_transitive(succ(sK2))
| ~ spl20_3
| ~ spl20_88 ),
inference(resolution,[],[f272,f773]) ).
fof(f12588,plain,
( spl20_176
| ~ spl20_3
| ~ spl20_76 ),
inference(avatar_split_clause,[],[f1442,f657,f270,f1447]) ).
fof(f1442,plain,
( element(sK1,succ(sK2))
| ~ spl20_3
| ~ spl20_76 ),
inference(resolution,[],[f272,f658]) ).
fof(f12581,plain,
( spl20_239
| ~ spl20_3
| ~ spl20_197 ),
inference(avatar_split_clause,[],[f12547,f2040,f270,f2520]) ).
fof(f12547,plain,
( in(sK1,sK1)
| ~ spl20_3
| ~ spl20_197 ),
inference(forward_demodulation,[],[f272,f2042]) ).
fof(f2042,plain,
( sK1 = succ(sK2)
| ~ spl20_197 ),
inference(avatar_component_clause,[],[f2040]) ).
fof(f12575,plain,
( ~ spl20_239
| ~ spl20_3
| ~ spl20_75
| ~ spl20_197 ),
inference(avatar_split_clause,[],[f12544,f2040,f653,f270,f2520]) ).
fof(f12544,plain,
( ~ in(sK1,sK1)
| ~ spl20_3
| ~ spl20_75
| ~ spl20_197 ),
inference(forward_demodulation,[],[f1443,f2042]) ).
fof(f1443,plain,
( ~ in(succ(sK2),sK1)
| ~ spl20_3
| ~ spl20_75 ),
inference(resolution,[],[f272,f654]) ).
fof(f12574,plain,
( spl20_239
| ~ spl20_197
| ~ spl20_277 ),
inference(avatar_split_clause,[],[f12284,f3477,f2040,f2520]) ).
fof(f12284,plain,
( in(sK1,sK1)
| ~ spl20_197
| ~ spl20_277 ),
inference(superposition,[],[f3479,f2042]) ).
fof(f12571,plain,
( ~ spl20_1
| spl20_457
| ~ spl20_166
| ~ spl20_175 ),
inference(avatar_split_clause,[],[f1474,f1436,f1355,f12569,f260]) ).
fof(f12569,plain,
( spl20_457
<=> ! [X2] :
( element(X2,sK2)
| ~ empty(X2)
| ~ ordinal(X2)
| sK1 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_457])]) ).
fof(f1474,plain,
( ! [X2] :
( element(X2,sK2)
| sK1 = X2
| ~ ordinal(sK1)
| ~ ordinal(X2)
| ~ empty(X2) )
| ~ spl20_166
| ~ spl20_175 ),
inference(resolution,[],[f1437,f1356]) ).
fof(f12561,plain,
( spl20_4
| ~ spl20_2
| ~ spl20_1
| spl20_120
| ~ spl20_164 ),
inference(avatar_split_clause,[],[f1335,f1320,f1014,f260,f265,f274]) ).
fof(f265,plain,
( spl20_2
<=> ordinal(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_2])]) ).
fof(f1335,plain,
( ~ ordinal(sK1)
| ~ ordinal(sK2)
| ordinal_subset(sK1,sK2)
| spl20_120
| ~ spl20_164 ),
inference(resolution,[],[f1321,f1016]) ).
fof(f1016,plain,
( ~ subset(sK2,sK1)
| spl20_120 ),
inference(avatar_component_clause,[],[f1014]) ).
fof(f12559,plain,
( spl20_456
| ~ spl20_1
| ~ spl20_2
| spl20_105
| ~ spl20_164 ),
inference(avatar_split_clause,[],[f1445,f1320,f894,f265,f260,f12556]) ).
fof(f1445,plain,
( ~ ordinal(sK2)
| ~ ordinal(sK1)
| ordinal_subset(sK2,sK1)
| spl20_105
| ~ spl20_164 ),
inference(resolution,[],[f895,f1321]) ).
fof(f12540,plain,
( ~ spl20_121
| ~ spl20_51
| ~ spl20_197 ),
inference(avatar_split_clause,[],[f12287,f2040,f507,f1018]) ).
fof(f12287,plain,
( sK1 != sK2
| ~ spl20_51
| ~ spl20_197 ),
inference(superposition,[],[f508,f2042]) ).
fof(f12512,plain,
( ~ spl20_64
| spl20_121
| ~ spl20_105
| ~ spl20_197
| ~ spl20_232 ),
inference(avatar_split_clause,[],[f2494,f2406,f2040,f894,f1018,f596]) ).
fof(f2406,plain,
( spl20_232
<=> ! [X1] :
( ~ epsilon_transitive(succ(X1))
| succ(X1) = X1
| ~ subset(succ(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_232])]) ).
fof(f2494,plain,
( ~ subset(sK1,sK2)
| sK1 = sK2
| ~ epsilon_transitive(sK1)
| ~ spl20_197
| ~ spl20_232 ),
inference(superposition,[],[f2407,f2042]) ).
fof(f2407,plain,
( ! [X1] :
( ~ subset(succ(X1),X1)
| succ(X1) = X1
| ~ epsilon_transitive(succ(X1)) )
| ~ spl20_232 ),
inference(avatar_component_clause,[],[f2406]) ).
fof(f12342,plain,
( ~ spl20_64
| spl20_455
| ~ spl20_197
| ~ spl20_226 ),
inference(avatar_split_clause,[],[f2382,f2322,f2040,f12340,f596]) ).
fof(f2322,plain,
( spl20_226
<=> ! [X2,X3] :
( ~ in(X2,X3)
| element(X2,succ(X3))
| ~ epsilon_transitive(succ(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_226])]) ).
fof(f2382,plain,
( ! [X1] :
( element(X1,sK1)
| ~ in(X1,sK2)
| ~ epsilon_transitive(sK1) )
| ~ spl20_197
| ~ spl20_226 ),
inference(superposition,[],[f2323,f2042]) ).
fof(f2323,plain,
( ! [X2,X3] :
( element(X2,succ(X3))
| ~ in(X2,X3)
| ~ epsilon_transitive(succ(X3)) )
| ~ spl20_226 ),
inference(avatar_component_clause,[],[f2322]) ).
fof(f12338,plain,
( spl20_454
| ~ spl20_197
| ~ spl20_220 ),
inference(avatar_split_clause,[],[f2296,f2288,f2040,f12336]) ).
fof(f2288,plain,
( spl20_220
<=> ! [X9,X8] :
( succ(X8) != X9
| sP0(X8,singleton(X8),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_220])]) ).
fof(f2296,plain,
( ! [X1] :
( sK1 != X1
| sP0(sK2,singleton(sK2),X1) )
| ~ spl20_197
| ~ spl20_220 ),
inference(superposition,[],[f2289,f2042]) ).
fof(f2289,plain,
( ! [X8,X9] :
( succ(X8) != X9
| sP0(X8,singleton(X8),X9) )
| ~ spl20_220 ),
inference(avatar_component_clause,[],[f2288]) ).
fof(f12334,plain,
( spl20_453
| ~ spl20_159
| ~ spl20_197 ),
inference(avatar_split_clause,[],[f2135,f2040,f1287,f12332]) ).
fof(f1287,plain,
( spl20_159
<=> ! [X9,X8] :
( succ(X8) != X9
| sP0(singleton(X8),X8,X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_159])]) ).
fof(f2135,plain,
( ! [X0] :
( sK1 != X0
| sP0(singleton(sK2),sK2,X0) )
| ~ spl20_159
| ~ spl20_197 ),
inference(superposition,[],[f1288,f2042]) ).
fof(f1288,plain,
( ! [X8,X9] :
( succ(X8) != X9
| sP0(singleton(X8),X8,X9) )
| ~ spl20_159 ),
inference(avatar_component_clause,[],[f1287]) ).
fof(f12322,plain,
( ~ spl20_50
| spl20_452 ),
inference(avatar_contradiction_clause,[],[f12313]) ).
fof(f12313,plain,
( $false
| ~ spl20_50
| spl20_452 ),
inference(resolution,[],[f12310,f504]) ).
fof(f504,plain,
( ! [X0] : subset(X0,X0)
| ~ spl20_50 ),
inference(avatar_component_clause,[],[f503]) ).
fof(f503,plain,
( spl20_50
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_50])]) ).
fof(f12310,plain,
( ~ subset(sK1,sK1)
| spl20_452 ),
inference(avatar_component_clause,[],[f12308]) ).
fof(f12311,plain,
( ~ spl20_452
| ~ spl20_197
| spl20_205 ),
inference(avatar_split_clause,[],[f2137,f2118,f2040,f12308]) ).
fof(f2137,plain,
( ~ subset(sK1,sK1)
| ~ spl20_197
| spl20_205 ),
inference(superposition,[],[f2119,f2042]) ).
fof(f12276,plain,
( spl20_451
| ~ spl20_160
| ~ spl20_205 ),
inference(avatar_split_clause,[],[f2676,f2118,f1291,f12274]) ).
fof(f2676,plain,
( ! [X0] :
( ~ in(X0,succ(sK2))
| element(X0,sK1) )
| ~ spl20_160
| ~ spl20_205 ),
inference(resolution,[],[f2120,f1292]) ).
fof(f2120,plain,
( subset(succ(sK2),sK1)
| ~ spl20_205 ),
inference(avatar_component_clause,[],[f2118]) ).
fof(f12094,plain,
( spl20_450
| ~ spl20_170
| ~ spl20_193 ),
inference(avatar_split_clause,[],[f2014,f1915,f1403,f12092]) ).
fof(f12092,plain,
( spl20_450
<=> ! [X58,X60,X59] :
( sP0(X58,X59,X60)
| in(X60,sK6(X58,X59,X60))
| sK6(X58,X59,X60) = X60
| ~ ordinal(X60)
| ~ ordinal(sK6(X58,X59,X60))
| sK6(X58,X59,X60) = X58
| ~ ordinal(X58)
| subset(X58,sK6(X58,X59,X60))
| ~ epsilon_transitive(sK6(X58,X59,X60)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_450])]) ).
fof(f1915,plain,
( spl20_193
<=> ! [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_193])]) ).
fof(f2014,plain,
( ! [X58,X59,X60] :
( sP0(X58,X59,X60)
| in(X60,sK6(X58,X59,X60))
| sK6(X58,X59,X60) = X60
| ~ ordinal(X60)
| ~ ordinal(sK6(X58,X59,X60))
| sK6(X58,X59,X60) = X58
| ~ ordinal(X58)
| subset(X58,sK6(X58,X59,X60))
| ~ epsilon_transitive(sK6(X58,X59,X60)) )
| ~ spl20_170
| ~ spl20_193 ),
inference(duplicate_literal_removal,[],[f2004]) ).
fof(f2004,plain,
( ! [X58,X59,X60] :
( sP0(X58,X59,X60)
| in(X60,sK6(X58,X59,X60))
| sK6(X58,X59,X60) = X60
| ~ ordinal(X60)
| ~ ordinal(sK6(X58,X59,X60))
| sK6(X58,X59,X60) = X58
| ~ ordinal(X58)
| ~ ordinal(sK6(X58,X59,X60))
| subset(X58,sK6(X58,X59,X60))
| ~ epsilon_transitive(sK6(X58,X59,X60)) )
| ~ spl20_170
| ~ spl20_193 ),
inference(resolution,[],[f1916,f1404]) ).
fof(f1916,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_193 ),
inference(avatar_component_clause,[],[f1915]) ).
fof(f12090,plain,
( spl20_449
| ~ spl20_170
| ~ spl20_192 ),
inference(avatar_split_clause,[],[f1960,f1911,f1403,f12088]) ).
fof(f12088,plain,
( spl20_449
<=> ! [X58,X60,X59] :
( sP0(X58,X59,X60)
| in(X60,sK6(X58,X59,X60))
| sK6(X58,X59,X60) = X60
| ~ ordinal(X60)
| ~ ordinal(sK6(X58,X59,X60))
| sK6(X58,X59,X60) = X59
| ~ ordinal(X59)
| subset(X59,sK6(X58,X59,X60))
| ~ epsilon_transitive(sK6(X58,X59,X60)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_449])]) ).
fof(f1911,plain,
( spl20_192
<=> ! [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_192])]) ).
fof(f1960,plain,
( ! [X58,X59,X60] :
( sP0(X58,X59,X60)
| in(X60,sK6(X58,X59,X60))
| sK6(X58,X59,X60) = X60
| ~ ordinal(X60)
| ~ ordinal(sK6(X58,X59,X60))
| sK6(X58,X59,X60) = X59
| ~ ordinal(X59)
| subset(X59,sK6(X58,X59,X60))
| ~ epsilon_transitive(sK6(X58,X59,X60)) )
| ~ spl20_170
| ~ spl20_192 ),
inference(duplicate_literal_removal,[],[f1950]) ).
fof(f1950,plain,
( ! [X58,X59,X60] :
( sP0(X58,X59,X60)
| in(X60,sK6(X58,X59,X60))
| sK6(X58,X59,X60) = X60
| ~ ordinal(X60)
| ~ ordinal(sK6(X58,X59,X60))
| sK6(X58,X59,X60) = X59
| ~ ordinal(X59)
| ~ ordinal(sK6(X58,X59,X60))
| subset(X59,sK6(X58,X59,X60))
| ~ epsilon_transitive(sK6(X58,X59,X60)) )
| ~ spl20_170
| ~ spl20_192 ),
inference(resolution,[],[f1912,f1404]) ).
fof(f1912,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_192 ),
inference(avatar_component_clause,[],[f1911]) ).
fof(f11578,plain,
( spl20_448
| ~ spl20_167
| ~ spl20_193 ),
inference(avatar_split_clause,[],[f2013,f1915,f1371,f11576]) ).
fof(f11576,plain,
( spl20_448
<=> ! [X61,X62,X63] :
( sP0(X61,X62,X63)
| in(X63,sK6(X61,X62,X63))
| sK6(X61,X62,X63) = X63
| ~ ordinal(X63)
| ~ ordinal(sK6(X61,X62,X63))
| sK6(X61,X62,X63) = X61
| ~ ordinal(X61)
| element(X61,sK6(X61,X62,X63)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_448])]) ).
fof(f2013,plain,
( ! [X62,X63,X61] :
( sP0(X61,X62,X63)
| in(X63,sK6(X61,X62,X63))
| sK6(X61,X62,X63) = X63
| ~ ordinal(X63)
| ~ ordinal(sK6(X61,X62,X63))
| sK6(X61,X62,X63) = X61
| ~ ordinal(X61)
| element(X61,sK6(X61,X62,X63)) )
| ~ spl20_167
| ~ spl20_193 ),
inference(duplicate_literal_removal,[],[f2005]) ).
fof(f2005,plain,
( ! [X62,X63,X61] :
( sP0(X61,X62,X63)
| in(X63,sK6(X61,X62,X63))
| sK6(X61,X62,X63) = X63
| ~ ordinal(X63)
| ~ ordinal(sK6(X61,X62,X63))
| sK6(X61,X62,X63) = X61
| ~ ordinal(X61)
| ~ ordinal(sK6(X61,X62,X63))
| element(X61,sK6(X61,X62,X63)) )
| ~ spl20_167
| ~ spl20_193 ),
inference(resolution,[],[f1916,f1372]) ).
fof(f11574,plain,
( spl20_447
| ~ spl20_104
| ~ spl20_193 ),
inference(avatar_split_clause,[],[f2011,f1915,f890,f11572]) ).
fof(f2011,plain,
( ! [X68,X69,X67] :
( sP0(X67,X68,X69)
| in(X69,sK6(X67,X68,X69))
| sK6(X67,X68,X69) = X69
| ~ ordinal(X69)
| ~ ordinal(sK6(X67,X68,X69))
| in(X67,sK6(X67,X68,X69))
| sK6(X67,X68,X69) = X67
| ~ ordinal(X67) )
| ~ spl20_104
| ~ spl20_193 ),
inference(duplicate_literal_removal,[],[f2007]) ).
fof(f2007,plain,
( ! [X68,X69,X67] :
( sP0(X67,X68,X69)
| in(X69,sK6(X67,X68,X69))
| sK6(X67,X68,X69) = X69
| ~ ordinal(X69)
| ~ ordinal(sK6(X67,X68,X69))
| in(X67,sK6(X67,X68,X69))
| sK6(X67,X68,X69) = X67
| ~ ordinal(X67)
| ~ ordinal(sK6(X67,X68,X69)) )
| ~ spl20_104
| ~ spl20_193 ),
inference(resolution,[],[f1916,f891]) ).
fof(f11570,plain,
( spl20_446
| ~ spl20_163
| ~ spl20_193 ),
inference(avatar_split_clause,[],[f2009,f1915,f1316,f11568]) ).
fof(f11568,plain,
( spl20_446
<=> ! [X73,X75,X74] :
( sP0(powerset(X73),X74,X75)
| in(X75,sK6(powerset(X73),X74,X75))
| sK6(powerset(X73),X74,X75) = X75
| ~ ordinal(X75)
| ~ ordinal(sK6(powerset(X73),X74,X75))
| empty(powerset(X73))
| ~ subset(sK6(powerset(X73),X74,X75),X73) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_446])]) ).
fof(f2009,plain,
( ! [X73,X74,X75] :
( sP0(powerset(X73),X74,X75)
| in(X75,sK6(powerset(X73),X74,X75))
| sK6(powerset(X73),X74,X75) = X75
| ~ ordinal(X75)
| ~ ordinal(sK6(powerset(X73),X74,X75))
| empty(powerset(X73))
| ~ subset(sK6(powerset(X73),X74,X75),X73) )
| ~ spl20_163
| ~ spl20_193 ),
inference(resolution,[],[f1916,f1317]) ).
fof(f11566,plain,
( spl20_445
| ~ spl20_167
| ~ spl20_192 ),
inference(avatar_split_clause,[],[f1959,f1911,f1371,f11564]) ).
fof(f11564,plain,
( spl20_445
<=> ! [X61,X62,X63] :
( sP0(X61,X62,X63)
| in(X63,sK6(X61,X62,X63))
| sK6(X61,X62,X63) = X63
| ~ ordinal(X63)
| ~ ordinal(sK6(X61,X62,X63))
| sK6(X61,X62,X63) = X62
| ~ ordinal(X62)
| element(X62,sK6(X61,X62,X63)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_445])]) ).
fof(f1959,plain,
( ! [X62,X63,X61] :
( sP0(X61,X62,X63)
| in(X63,sK6(X61,X62,X63))
| sK6(X61,X62,X63) = X63
| ~ ordinal(X63)
| ~ ordinal(sK6(X61,X62,X63))
| sK6(X61,X62,X63) = X62
| ~ ordinal(X62)
| element(X62,sK6(X61,X62,X63)) )
| ~ spl20_167
| ~ spl20_192 ),
inference(duplicate_literal_removal,[],[f1951]) ).
fof(f1951,plain,
( ! [X62,X63,X61] :
( sP0(X61,X62,X63)
| in(X63,sK6(X61,X62,X63))
| sK6(X61,X62,X63) = X63
| ~ ordinal(X63)
| ~ ordinal(sK6(X61,X62,X63))
| sK6(X61,X62,X63) = X62
| ~ ordinal(X62)
| ~ ordinal(sK6(X61,X62,X63))
| element(X62,sK6(X61,X62,X63)) )
| ~ spl20_167
| ~ spl20_192 ),
inference(resolution,[],[f1912,f1372]) ).
fof(f11562,plain,
( spl20_444
| ~ spl20_104
| ~ spl20_192 ),
inference(avatar_split_clause,[],[f1957,f1911,f890,f11560]) ).
fof(f1957,plain,
( ! [X68,X69,X67] :
( sP0(X67,X68,X69)
| in(X69,sK6(X67,X68,X69))
| sK6(X67,X68,X69) = X69
| ~ ordinal(X69)
| ~ ordinal(sK6(X67,X68,X69))
| in(X68,sK6(X67,X68,X69))
| sK6(X67,X68,X69) = X68
| ~ ordinal(X68) )
| ~ spl20_104
| ~ spl20_192 ),
inference(duplicate_literal_removal,[],[f1953]) ).
fof(f1953,plain,
( ! [X68,X69,X67] :
( sP0(X67,X68,X69)
| in(X69,sK6(X67,X68,X69))
| sK6(X67,X68,X69) = X69
| ~ ordinal(X69)
| ~ ordinal(sK6(X67,X68,X69))
| in(X68,sK6(X67,X68,X69))
| sK6(X67,X68,X69) = X68
| ~ ordinal(X68)
| ~ ordinal(sK6(X67,X68,X69)) )
| ~ spl20_104
| ~ spl20_192 ),
inference(resolution,[],[f1912,f891]) ).
fof(f11558,plain,
( spl20_443
| ~ spl20_163
| ~ spl20_192 ),
inference(avatar_split_clause,[],[f1955,f1911,f1316,f11556]) ).
fof(f11556,plain,
( spl20_443
<=> ! [X73,X75,X74] :
( sP0(X73,powerset(X74),X75)
| in(X75,sK6(X73,powerset(X74),X75))
| sK6(X73,powerset(X74),X75) = X75
| ~ ordinal(X75)
| ~ ordinal(sK6(X73,powerset(X74),X75))
| empty(powerset(X74))
| ~ subset(sK6(X73,powerset(X74),X75),X74) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_443])]) ).
fof(f1955,plain,
( ! [X73,X74,X75] :
( sP0(X73,powerset(X74),X75)
| in(X75,sK6(X73,powerset(X74),X75))
| sK6(X73,powerset(X74),X75) = X75
| ~ ordinal(X75)
| ~ ordinal(sK6(X73,powerset(X74),X75))
| empty(powerset(X74))
| ~ subset(sK6(X73,powerset(X74),X75),X74) )
| ~ spl20_163
| ~ spl20_192 ),
inference(resolution,[],[f1912,f1317]) ).
fof(f10933,plain,
( spl20_442
| ~ spl20_108
| ~ spl20_170 ),
inference(avatar_split_clause,[],[f1418,f1403,f923,f10931]) ).
fof(f10931,plain,
( spl20_442
<=> ! [X22,X21,X23] :
( sK6(X22,X23,X21) = X21
| ~ ordinal(X21)
| ~ ordinal(sK6(X22,X23,X21))
| subset(X21,sK6(X22,X23,X21))
| ~ epsilon_transitive(sK6(X22,X23,X21))
| ~ in(sK6(X22,X23,X21),X23)
| sP0(X22,X23,X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_442])]) ).
fof(f1418,plain,
( ! [X21,X22,X23] :
( sK6(X22,X23,X21) = X21
| ~ ordinal(X21)
| ~ ordinal(sK6(X22,X23,X21))
| subset(X21,sK6(X22,X23,X21))
| ~ epsilon_transitive(sK6(X22,X23,X21))
| ~ in(sK6(X22,X23,X21),X23)
| sP0(X22,X23,X21) )
| ~ spl20_108
| ~ spl20_170 ),
inference(resolution,[],[f1404,f924]) ).
fof(f10929,plain,
( spl20_441
| ~ spl20_109
| ~ spl20_170 ),
inference(avatar_split_clause,[],[f1417,f1403,f927,f10927]) ).
fof(f10927,plain,
( spl20_441
<=> ! [X20,X18,X19] :
( sK6(X19,X20,X18) = X18
| ~ ordinal(X18)
| ~ ordinal(sK6(X19,X20,X18))
| subset(X18,sK6(X19,X20,X18))
| ~ epsilon_transitive(sK6(X19,X20,X18))
| ~ in(sK6(X19,X20,X18),X19)
| sP0(X19,X20,X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_441])]) ).
fof(f1417,plain,
( ! [X18,X19,X20] :
( sK6(X19,X20,X18) = X18
| ~ ordinal(X18)
| ~ ordinal(sK6(X19,X20,X18))
| subset(X18,sK6(X19,X20,X18))
| ~ epsilon_transitive(sK6(X19,X20,X18))
| ~ in(sK6(X19,X20,X18),X19)
| sP0(X19,X20,X18) )
| ~ spl20_109
| ~ spl20_170 ),
inference(resolution,[],[f1404,f928]) ).
fof(f10626,plain,
( spl20_195
| ~ spl20_76
| ~ spl20_277 ),
inference(avatar_split_clause,[],[f5291,f3477,f657,f2032]) ).
fof(f5291,plain,
( element(succ(sK2),sK1)
| ~ spl20_76
| ~ spl20_277 ),
inference(resolution,[],[f3479,f658]) ).
fof(f10625,plain,
( spl20_440
| ~ spl20_157
| ~ spl20_191 ),
inference(avatar_split_clause,[],[f1897,f1800,f1267,f10623]) ).
fof(f10623,plain,
( spl20_440
<=> ! [X22,X21,X23] :
( subset(sK6(X21,sK4(powerset(X22)),X23),X21)
| in(sK6(X21,sK4(powerset(X22)),X23),X23)
| sP0(X21,sK4(powerset(X22)),X23)
| ~ epsilon_transitive(X21)
| element(sK6(X21,sK4(powerset(X22)),X23),X22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_440])]) ).
fof(f1800,plain,
( spl20_191
<=> ! [X6,X4,X5] :
( in(sK6(X4,X5,X6),X6)
| in(sK6(X4,X5,X6),X5)
| sP0(X4,X5,X6)
| subset(sK6(X4,X5,X6),X4)
| ~ epsilon_transitive(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_191])]) ).
fof(f1897,plain,
( ! [X21,X22,X23] :
( subset(sK6(X21,sK4(powerset(X22)),X23),X21)
| in(sK6(X21,sK4(powerset(X22)),X23),X23)
| sP0(X21,sK4(powerset(X22)),X23)
| ~ epsilon_transitive(X21)
| element(sK6(X21,sK4(powerset(X22)),X23),X22) )
| ~ spl20_157
| ~ spl20_191 ),
inference(resolution,[],[f1801,f1268]) ).
fof(f1801,plain,
( ! [X6,X4,X5] :
( subset(sK6(X4,X5,X6),X4)
| in(sK6(X4,X5,X6),X6)
| in(sK6(X4,X5,X6),X5)
| sP0(X4,X5,X6)
| ~ epsilon_transitive(X4) )
| ~ spl20_191 ),
inference(avatar_component_clause,[],[f1800]) ).
fof(f10621,plain,
( spl20_439
| ~ spl20_157
| ~ spl20_191 ),
inference(avatar_split_clause,[],[f1887,f1800,f1267,f10619]) ).
fof(f10619,plain,
( spl20_439
<=> ! [X24,X25,X23] :
( subset(sK6(X23,X24,sK4(powerset(X25))),X23)
| in(sK6(X23,X24,sK4(powerset(X25))),X24)
| sP0(X23,X24,sK4(powerset(X25)))
| ~ epsilon_transitive(X23)
| element(sK6(X23,X24,sK4(powerset(X25))),X25) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_439])]) ).
fof(f1887,plain,
( ! [X24,X25,X23] :
( subset(sK6(X23,X24,sK4(powerset(X25))),X23)
| in(sK6(X23,X24,sK4(powerset(X25))),X24)
| sP0(X23,X24,sK4(powerset(X25)))
| ~ epsilon_transitive(X23)
| element(sK6(X23,X24,sK4(powerset(X25))),X25) )
| ~ spl20_157
| ~ spl20_191 ),
inference(resolution,[],[f1801,f1268]) ).
fof(f10617,plain,
( spl20_438
| ~ spl20_157
| ~ spl20_190 ),
inference(avatar_split_clause,[],[f1862,f1796,f1267,f10615]) ).
fof(f10615,plain,
( spl20_438
<=> ! [X22,X21,X23] :
( subset(sK6(sK4(powerset(X21)),X22,X23),X22)
| in(sK6(sK4(powerset(X21)),X22,X23),X23)
| sP0(sK4(powerset(X21)),X22,X23)
| ~ epsilon_transitive(X22)
| element(sK6(sK4(powerset(X21)),X22,X23),X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_438])]) ).
fof(f1796,plain,
( spl20_190
<=> ! [X6,X4,X5] :
( in(sK6(X4,X5,X6),X6)
| in(sK6(X4,X5,X6),X4)
| sP0(X4,X5,X6)
| subset(sK6(X4,X5,X6),X5)
| ~ epsilon_transitive(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_190])]) ).
fof(f1862,plain,
( ! [X21,X22,X23] :
( subset(sK6(sK4(powerset(X21)),X22,X23),X22)
| in(sK6(sK4(powerset(X21)),X22,X23),X23)
| sP0(sK4(powerset(X21)),X22,X23)
| ~ epsilon_transitive(X22)
| element(sK6(sK4(powerset(X21)),X22,X23),X21) )
| ~ spl20_157
| ~ spl20_190 ),
inference(resolution,[],[f1797,f1268]) ).
fof(f1797,plain,
( ! [X6,X4,X5] :
( subset(sK6(X4,X5,X6),X5)
| in(sK6(X4,X5,X6),X6)
| in(sK6(X4,X5,X6),X4)
| sP0(X4,X5,X6)
| ~ epsilon_transitive(X5) )
| ~ spl20_190 ),
inference(avatar_component_clause,[],[f1796]) ).
fof(f10613,plain,
( spl20_437
| ~ spl20_157
| ~ spl20_190 ),
inference(avatar_split_clause,[],[f1852,f1796,f1267,f10611]) ).
fof(f10611,plain,
( spl20_437
<=> ! [X25,X24,X23] :
( subset(sK6(X23,X24,sK4(powerset(X25))),X24)
| in(sK6(X23,X24,sK4(powerset(X25))),X23)
| sP0(X23,X24,sK4(powerset(X25)))
| ~ epsilon_transitive(X24)
| element(sK6(X23,X24,sK4(powerset(X25))),X25) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_437])]) ).
fof(f1852,plain,
( ! [X24,X25,X23] :
( subset(sK6(X23,X24,sK4(powerset(X25))),X24)
| in(sK6(X23,X24,sK4(powerset(X25))),X23)
| sP0(X23,X24,sK4(powerset(X25)))
| ~ epsilon_transitive(X24)
| element(sK6(X23,X24,sK4(powerset(X25))),X25) )
| ~ spl20_157
| ~ spl20_190 ),
inference(resolution,[],[f1797,f1268]) ).
fof(f10609,plain,
( spl20_436
| ~ spl20_157
| ~ spl20_189 ),
inference(avatar_split_clause,[],[f1825,f1792,f1267,f10607]) ).
fof(f10607,plain,
( spl20_436
<=> ! [X22,X21,X23] :
( subset(sK6(sK4(powerset(X21)),X22,X23),X23)
| in(sK6(sK4(powerset(X21)),X22,X23),X22)
| sP0(sK4(powerset(X21)),X22,X23)
| ~ epsilon_transitive(X23)
| element(sK6(sK4(powerset(X21)),X22,X23),X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_436])]) ).
fof(f1792,plain,
( spl20_189
<=> ! [X6,X7,X8] :
( in(sK6(X6,X7,X8),X7)
| in(sK6(X6,X7,X8),X6)
| sP0(X6,X7,X8)
| subset(sK6(X6,X7,X8),X8)
| ~ epsilon_transitive(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_189])]) ).
fof(f1825,plain,
( ! [X21,X22,X23] :
( subset(sK6(sK4(powerset(X21)),X22,X23),X23)
| in(sK6(sK4(powerset(X21)),X22,X23),X22)
| sP0(sK4(powerset(X21)),X22,X23)
| ~ epsilon_transitive(X23)
| element(sK6(sK4(powerset(X21)),X22,X23),X21) )
| ~ spl20_157
| ~ spl20_189 ),
inference(resolution,[],[f1793,f1268]) ).
fof(f1793,plain,
( ! [X8,X6,X7] :
( subset(sK6(X6,X7,X8),X8)
| in(sK6(X6,X7,X8),X7)
| in(sK6(X6,X7,X8),X6)
| sP0(X6,X7,X8)
| ~ epsilon_transitive(X8) )
| ~ spl20_189 ),
inference(avatar_component_clause,[],[f1792]) ).
fof(f10605,plain,
( spl20_435
| ~ spl20_157
| ~ spl20_189 ),
inference(avatar_split_clause,[],[f1815,f1792,f1267,f10603]) ).
fof(f10603,plain,
( spl20_435
<=> ! [X22,X21,X23] :
( subset(sK6(X21,sK4(powerset(X22)),X23),X23)
| in(sK6(X21,sK4(powerset(X22)),X23),X21)
| sP0(X21,sK4(powerset(X22)),X23)
| ~ epsilon_transitive(X23)
| element(sK6(X21,sK4(powerset(X22)),X23),X22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_435])]) ).
fof(f1815,plain,
( ! [X21,X22,X23] :
( subset(sK6(X21,sK4(powerset(X22)),X23),X23)
| in(sK6(X21,sK4(powerset(X22)),X23),X21)
| sP0(X21,sK4(powerset(X22)),X23)
| ~ epsilon_transitive(X23)
| element(sK6(X21,sK4(powerset(X22)),X23),X22) )
| ~ spl20_157
| ~ spl20_189 ),
inference(resolution,[],[f1793,f1268]) ).
fof(f10362,plain,
( spl20_434
| ~ spl20_97
| ~ spl20_191 ),
inference(avatar_split_clause,[],[f1877,f1800,f846,f10360]) ).
fof(f10360,plain,
( spl20_434
<=> ! [X9,X8,X10] :
( in(sK6(X8,X9,X10),X10)
| in(sK6(X8,X9,X10),X9)
| sP0(X8,X9,X10)
| ~ epsilon_transitive(X8)
| ordinal_subset(sK6(X8,X9,X10),X8)
| ~ ordinal(X8)
| ~ ordinal(sK6(X8,X9,X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_434])]) ).
fof(f1877,plain,
( ! [X10,X8,X9] :
( in(sK6(X8,X9,X10),X10)
| in(sK6(X8,X9,X10),X9)
| sP0(X8,X9,X10)
| ~ epsilon_transitive(X8)
| ordinal_subset(sK6(X8,X9,X10),X8)
| ~ ordinal(X8)
| ~ ordinal(sK6(X8,X9,X10)) )
| ~ spl20_97
| ~ spl20_191 ),
inference(resolution,[],[f1801,f847]) ).
fof(f10351,plain,
( spl20_433
| ~ spl20_97
| ~ spl20_190 ),
inference(avatar_split_clause,[],[f1842,f1796,f846,f10349]) ).
fof(f10349,plain,
( spl20_433
<=> ! [X9,X8,X10] :
( in(sK6(X8,X9,X10),X10)
| in(sK6(X8,X9,X10),X8)
| sP0(X8,X9,X10)
| ~ epsilon_transitive(X9)
| ordinal_subset(sK6(X8,X9,X10),X9)
| ~ ordinal(X9)
| ~ ordinal(sK6(X8,X9,X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_433])]) ).
fof(f1842,plain,
( ! [X10,X8,X9] :
( in(sK6(X8,X9,X10),X10)
| in(sK6(X8,X9,X10),X8)
| sP0(X8,X9,X10)
| ~ epsilon_transitive(X9)
| ordinal_subset(sK6(X8,X9,X10),X9)
| ~ ordinal(X9)
| ~ ordinal(sK6(X8,X9,X10)) )
| ~ spl20_97
| ~ spl20_190 ),
inference(resolution,[],[f1797,f847]) ).
fof(f10347,plain,
( spl20_432
| ~ spl20_97
| ~ spl20_189 ),
inference(avatar_split_clause,[],[f1805,f1792,f846,f10345]) ).
fof(f10345,plain,
( spl20_432
<=> ! [X9,X8,X10] :
( in(sK6(X8,X9,X10),X9)
| in(sK6(X8,X9,X10),X8)
| sP0(X8,X9,X10)
| ~ epsilon_transitive(X10)
| ordinal_subset(sK6(X8,X9,X10),X10)
| ~ ordinal(X10)
| ~ ordinal(sK6(X8,X9,X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_432])]) ).
fof(f1805,plain,
( ! [X10,X8,X9] :
( in(sK6(X8,X9,X10),X9)
| in(sK6(X8,X9,X10),X8)
| sP0(X8,X9,X10)
| ~ epsilon_transitive(X10)
| ordinal_subset(sK6(X8,X9,X10),X10)
| ~ ordinal(X10)
| ~ ordinal(sK6(X8,X9,X10)) )
| ~ spl20_97
| ~ spl20_189 ),
inference(resolution,[],[f1793,f847]) ).
fof(f10104,plain,
( spl20_431
| ~ spl20_197
| ~ spl20_207 ),
inference(avatar_split_clause,[],[f2179,f2146,f2040,f10101]) ).
fof(f2179,plain,
( sP0(singleton(sK2),sK2,sK1)
| ~ spl20_197
| ~ spl20_207 ),
inference(superposition,[],[f2147,f2042]) ).
fof(f9754,plain,
( spl20_430
| ~ spl20_91
| ~ spl20_191 ),
inference(avatar_split_clause,[],[f1878,f1800,f811,f9752]) ).
fof(f9752,plain,
( spl20_430
<=> ! [X13,X12,X11] :
( in(sK6(X11,X12,X13),X13)
| in(sK6(X11,X12,X13),X12)
| sP0(X11,X12,X13)
| ~ epsilon_transitive(X11)
| sK6(X11,X12,X13) = X11
| ~ subset(X11,sK6(X11,X12,X13)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_430])]) ).
fof(f1878,plain,
( ! [X11,X12,X13] :
( in(sK6(X11,X12,X13),X13)
| in(sK6(X11,X12,X13),X12)
| sP0(X11,X12,X13)
| ~ epsilon_transitive(X11)
| sK6(X11,X12,X13) = X11
| ~ subset(X11,sK6(X11,X12,X13)) )
| ~ spl20_91
| ~ spl20_191 ),
inference(resolution,[],[f1801,f812]) ).
fof(f9750,plain,
( spl20_429
| ~ spl20_91
| ~ spl20_190 ),
inference(avatar_split_clause,[],[f1843,f1796,f811,f9748]) ).
fof(f9748,plain,
( spl20_429
<=> ! [X13,X12,X11] :
( in(sK6(X11,X12,X13),X13)
| in(sK6(X11,X12,X13),X11)
| sP0(X11,X12,X13)
| ~ epsilon_transitive(X12)
| sK6(X11,X12,X13) = X12
| ~ subset(X12,sK6(X11,X12,X13)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_429])]) ).
fof(f1843,plain,
( ! [X11,X12,X13] :
( in(sK6(X11,X12,X13),X13)
| in(sK6(X11,X12,X13),X11)
| sP0(X11,X12,X13)
| ~ epsilon_transitive(X12)
| sK6(X11,X12,X13) = X12
| ~ subset(X12,sK6(X11,X12,X13)) )
| ~ spl20_91
| ~ spl20_190 ),
inference(resolution,[],[f1797,f812]) ).
fof(f9746,plain,
( spl20_428
| ~ spl20_91
| ~ spl20_189 ),
inference(avatar_split_clause,[],[f1806,f1792,f811,f9744]) ).
fof(f9744,plain,
( spl20_428
<=> ! [X13,X12,X11] :
( in(sK6(X11,X12,X13),X12)
| in(sK6(X11,X12,X13),X11)
| sP0(X11,X12,X13)
| ~ epsilon_transitive(X13)
| sK6(X11,X12,X13) = X13
| ~ subset(X13,sK6(X11,X12,X13)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_428])]) ).
fof(f1806,plain,
( ! [X11,X12,X13] :
( in(sK6(X11,X12,X13),X12)
| in(sK6(X11,X12,X13),X11)
| sP0(X11,X12,X13)
| ~ epsilon_transitive(X13)
| sK6(X11,X12,X13) = X13
| ~ subset(X13,sK6(X11,X12,X13)) )
| ~ spl20_91
| ~ spl20_189 ),
inference(resolution,[],[f1793,f812]) ).
fof(f9742,plain,
( spl20_427
| ~ spl20_157
| ~ spl20_187 ),
inference(avatar_split_clause,[],[f1773,f1665,f1267,f9740]) ).
fof(f1773,plain,
( ! [X21,X22,X23] :
( element(sK6(X21,sK4(powerset(X22)),X23),X21)
| in(sK6(X21,sK4(powerset(X22)),X23),X23)
| sP0(X21,sK4(powerset(X22)),X23)
| element(sK6(X21,sK4(powerset(X22)),X23),X22) )
| ~ spl20_157
| ~ spl20_187 ),
inference(resolution,[],[f1666,f1268]) ).
fof(f9738,plain,
( spl20_426
| ~ spl20_157
| ~ spl20_187 ),
inference(avatar_split_clause,[],[f1763,f1665,f1267,f9736]) ).
fof(f1763,plain,
( ! [X24,X25,X23] :
( element(sK6(X23,X24,sK4(powerset(X25))),X23)
| in(sK6(X23,X24,sK4(powerset(X25))),X24)
| sP0(X23,X24,sK4(powerset(X25)))
| element(sK6(X23,X24,sK4(powerset(X25))),X25) )
| ~ spl20_157
| ~ spl20_187 ),
inference(resolution,[],[f1666,f1268]) ).
fof(f9731,plain,
( spl20_425
| ~ spl20_157
| ~ spl20_185 ),
inference(avatar_split_clause,[],[f1728,f1657,f1267,f9729]) ).
fof(f1728,plain,
( ! [X21,X22,X23] :
( element(sK6(sK4(powerset(X21)),X22,X23),X22)
| in(sK6(sK4(powerset(X21)),X22,X23),X23)
| sP0(sK4(powerset(X21)),X22,X23)
| element(sK6(sK4(powerset(X21)),X22,X23),X21) )
| ~ spl20_157
| ~ spl20_185 ),
inference(resolution,[],[f1658,f1268]) ).
fof(f9727,plain,
( spl20_424
| ~ spl20_157
| ~ spl20_185 ),
inference(avatar_split_clause,[],[f1718,f1657,f1267,f9725]) ).
fof(f1718,plain,
( ! [X24,X25,X23] :
( element(sK6(X23,X24,sK4(powerset(X25))),X24)
| in(sK6(X23,X24,sK4(powerset(X25))),X23)
| sP0(X23,X24,sK4(powerset(X25)))
| element(sK6(X23,X24,sK4(powerset(X25))),X25) )
| ~ spl20_157
| ~ spl20_185 ),
inference(resolution,[],[f1658,f1268]) ).
fof(f9723,plain,
( spl20_423
| ~ spl20_157
| ~ spl20_183 ),
inference(avatar_split_clause,[],[f1694,f1649,f1267,f9721]) ).
fof(f1694,plain,
( ! [X21,X22,X23] :
( element(sK6(sK4(powerset(X21)),X22,X23),X23)
| in(sK6(sK4(powerset(X21)),X22,X23),X22)
| sP0(sK4(powerset(X21)),X22,X23)
| element(sK6(sK4(powerset(X21)),X22,X23),X21) )
| ~ spl20_157
| ~ spl20_183 ),
inference(resolution,[],[f1650,f1268]) ).
fof(f9719,plain,
( spl20_422
| ~ spl20_157
| ~ spl20_183 ),
inference(avatar_split_clause,[],[f1684,f1649,f1267,f9717]) ).
fof(f1684,plain,
( ! [X21,X22,X23] :
( element(sK6(X21,sK4(powerset(X22)),X23),X23)
| in(sK6(X21,sK4(powerset(X22)),X23),X21)
| sP0(X21,sK4(powerset(X22)),X23)
| element(sK6(X21,sK4(powerset(X22)),X23),X22) )
| ~ spl20_157
| ~ spl20_183 ),
inference(resolution,[],[f1650,f1268]) ).
fof(f9715,plain,
( spl20_421
| ~ spl20_110
| ~ spl20_157 ),
inference(avatar_split_clause,[],[f1281,f1267,f935,f9713]) ).
fof(f9713,plain,
( spl20_421
<=> ! [X16,X14,X15] :
( element(sK6(sK4(powerset(X14)),X15,X16),X14)
| in(sK6(sK4(powerset(X14)),X15,X16),X16)
| in(sK6(sK4(powerset(X14)),X15,X16),X15)
| sP0(sK4(powerset(X14)),X15,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_421])]) ).
fof(f1281,plain,
( ! [X16,X14,X15] :
( element(sK6(sK4(powerset(X14)),X15,X16),X14)
| in(sK6(sK4(powerset(X14)),X15,X16),X16)
| in(sK6(sK4(powerset(X14)),X15,X16),X15)
| sP0(sK4(powerset(X14)),X15,X16) )
| ~ spl20_110
| ~ spl20_157 ),
inference(resolution,[],[f1268,f936]) ).
fof(f9711,plain,
( spl20_420
| ~ spl20_110
| ~ spl20_157 ),
inference(avatar_split_clause,[],[f1280,f1267,f935,f9709]) ).
fof(f9709,plain,
( spl20_420
<=> ! [X13,X12,X11] :
( element(sK6(X11,sK4(powerset(X12)),X13),X12)
| in(sK6(X11,sK4(powerset(X12)),X13),X13)
| in(sK6(X11,sK4(powerset(X12)),X13),X11)
| sP0(X11,sK4(powerset(X12)),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_420])]) ).
fof(f1280,plain,
( ! [X11,X12,X13] :
( element(sK6(X11,sK4(powerset(X12)),X13),X12)
| in(sK6(X11,sK4(powerset(X12)),X13),X13)
| in(sK6(X11,sK4(powerset(X12)),X13),X11)
| sP0(X11,sK4(powerset(X12)),X13) )
| ~ spl20_110
| ~ spl20_157 ),
inference(resolution,[],[f1268,f936]) ).
fof(f9707,plain,
( spl20_419
| ~ spl20_110
| ~ spl20_157 ),
inference(avatar_split_clause,[],[f1279,f1267,f935,f9705]) ).
fof(f9705,plain,
( spl20_419
<=> ! [X9,X8,X10] :
( element(sK6(X8,X9,sK4(powerset(X10))),X10)
| in(sK6(X8,X9,sK4(powerset(X10))),X9)
| in(sK6(X8,X9,sK4(powerset(X10))),X8)
| sP0(X8,X9,sK4(powerset(X10))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_419])]) ).
fof(f1279,plain,
( ! [X10,X8,X9] :
( element(sK6(X8,X9,sK4(powerset(X10))),X10)
| in(sK6(X8,X9,sK4(powerset(X10))),X9)
| in(sK6(X8,X9,sK4(powerset(X10))),X8)
| sP0(X8,X9,sK4(powerset(X10))) )
| ~ spl20_110
| ~ spl20_157 ),
inference(resolution,[],[f1268,f936]) ).
fof(f9268,plain,
( ~ spl20_418
| ~ spl20_197
| spl20_362 ),
inference(avatar_split_clause,[],[f8593,f5335,f2040,f9265]) ).
fof(f8593,plain,
( ~ element(sK1,sK2)
| ~ spl20_197
| spl20_362 ),
inference(superposition,[],[f5336,f2042]) ).
fof(f5336,plain,
( ~ element(succ(sK2),sK2)
| spl20_362 ),
inference(avatar_component_clause,[],[f5335]) ).
fof(f8731,plain,
( spl20_417
| ~ spl20_100
| ~ spl20_187 ),
inference(avatar_split_clause,[],[f1751,f1665,f858,f8729]) ).
fof(f8729,plain,
( spl20_417
<=> ! [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_417])]) ).
fof(f1751,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_100
| ~ spl20_187 ),
inference(resolution,[],[f1666,f859]) ).
fof(f8727,plain,
( spl20_416
| ~ spl20_100
| ~ spl20_185 ),
inference(avatar_split_clause,[],[f1706,f1657,f858,f8725]) ).
fof(f8725,plain,
( spl20_416
<=> ! [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_416])]) ).
fof(f1706,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_100
| ~ spl20_185 ),
inference(resolution,[],[f1658,f859]) ).
fof(f8723,plain,
( spl20_415
| ~ spl20_100
| ~ spl20_183 ),
inference(avatar_split_clause,[],[f1672,f1649,f858,f8721]) ).
fof(f8721,plain,
( spl20_415
<=> ! [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_415])]) ).
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_100
| ~ spl20_183 ),
inference(resolution,[],[f1650,f859]) ).
fof(f8719,plain,
( spl20_414
| ~ spl20_108
| ~ spl20_167 ),
inference(avatar_split_clause,[],[f1385,f1371,f923,f8717]) ).
fof(f8717,plain,
( spl20_414
<=> ! [X20,X21,X19] :
( sK6(X20,X21,X19) = X19
| ~ ordinal(X19)
| ~ ordinal(sK6(X20,X21,X19))
| element(X19,sK6(X20,X21,X19))
| ~ in(sK6(X20,X21,X19),X21)
| sP0(X20,X21,X19) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_414])]) ).
fof(f1385,plain,
( ! [X21,X19,X20] :
( sK6(X20,X21,X19) = X19
| ~ ordinal(X19)
| ~ ordinal(sK6(X20,X21,X19))
| element(X19,sK6(X20,X21,X19))
| ~ in(sK6(X20,X21,X19),X21)
| sP0(X20,X21,X19) )
| ~ spl20_108
| ~ spl20_167 ),
inference(resolution,[],[f1372,f924]) ).
fof(f8715,plain,
( spl20_413
| ~ spl20_109
| ~ spl20_167 ),
inference(avatar_split_clause,[],[f1384,f1371,f927,f8713]) ).
fof(f8713,plain,
( spl20_413
<=> ! [X18,X16,X17] :
( sK6(X17,X18,X16) = X16
| ~ ordinal(X16)
| ~ ordinal(sK6(X17,X18,X16))
| element(X16,sK6(X17,X18,X16))
| ~ in(sK6(X17,X18,X16),X17)
| sP0(X17,X18,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_413])]) ).
fof(f1384,plain,
( ! [X18,X16,X17] :
( sK6(X17,X18,X16) = X16
| ~ ordinal(X16)
| ~ ordinal(sK6(X17,X18,X16))
| element(X16,sK6(X17,X18,X16))
| ~ in(sK6(X17,X18,X16),X17)
| sP0(X17,X18,X16) )
| ~ spl20_109
| ~ spl20_167 ),
inference(resolution,[],[f1372,f928]) ).
fof(f7519,plain,
( spl20_412
| ~ spl20_153
| ~ spl20_191 ),
inference(avatar_split_clause,[],[f1895,f1800,f1230,f7517]) ).
fof(f7517,plain,
( spl20_412
<=> ! [X18,X16,X17] :
( subset(sK6(X16,singleton(X17),X18),X16)
| in(sK6(X16,singleton(X17),X18),X18)
| sP0(X16,singleton(X17),X18)
| ~ epsilon_transitive(X16)
| sK6(X16,singleton(X17),X18) = X17 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_412])]) ).
fof(f1895,plain,
( ! [X18,X16,X17] :
( subset(sK6(X16,singleton(X17),X18),X16)
| in(sK6(X16,singleton(X17),X18),X18)
| sP0(X16,singleton(X17),X18)
| ~ epsilon_transitive(X16)
| sK6(X16,singleton(X17),X18) = X17 )
| ~ spl20_153
| ~ spl20_191 ),
inference(resolution,[],[f1801,f1231]) ).
fof(f7509,plain,
( spl20_411
| ~ spl20_153
| ~ spl20_191 ),
inference(avatar_split_clause,[],[f1885,f1800,f1230,f7507]) ).
fof(f7507,plain,
( spl20_411
<=> ! [X20,X18,X19] :
( subset(sK6(X18,X19,singleton(X20)),X18)
| in(sK6(X18,X19,singleton(X20)),X19)
| sP0(X18,X19,singleton(X20))
| ~ epsilon_transitive(X18)
| sK6(X18,X19,singleton(X20)) = X20 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_411])]) ).
fof(f1885,plain,
( ! [X18,X19,X20] :
( subset(sK6(X18,X19,singleton(X20)),X18)
| in(sK6(X18,X19,singleton(X20)),X19)
| sP0(X18,X19,singleton(X20))
| ~ epsilon_transitive(X18)
| sK6(X18,X19,singleton(X20)) = X20 )
| ~ spl20_153
| ~ spl20_191 ),
inference(resolution,[],[f1801,f1231]) ).
fof(f7505,plain,
( spl20_410
| ~ spl20_153
| ~ spl20_190 ),
inference(avatar_split_clause,[],[f1860,f1796,f1230,f7503]) ).
fof(f7503,plain,
( spl20_410
<=> ! [X18,X16,X17] :
( subset(sK6(singleton(X16),X17,X18),X17)
| in(sK6(singleton(X16),X17,X18),X18)
| sP0(singleton(X16),X17,X18)
| ~ epsilon_transitive(X17)
| sK6(singleton(X16),X17,X18) = X16 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_410])]) ).
fof(f1860,plain,
( ! [X18,X16,X17] :
( subset(sK6(singleton(X16),X17,X18),X17)
| in(sK6(singleton(X16),X17,X18),X18)
| sP0(singleton(X16),X17,X18)
| ~ epsilon_transitive(X17)
| sK6(singleton(X16),X17,X18) = X16 )
| ~ spl20_153
| ~ spl20_190 ),
inference(resolution,[],[f1797,f1231]) ).
fof(f7501,plain,
( spl20_409
| ~ spl20_153
| ~ spl20_190 ),
inference(avatar_split_clause,[],[f1850,f1796,f1230,f7499]) ).
fof(f7499,plain,
( spl20_409
<=> ! [X20,X18,X19] :
( subset(sK6(X18,X19,singleton(X20)),X19)
| in(sK6(X18,X19,singleton(X20)),X18)
| sP0(X18,X19,singleton(X20))
| ~ epsilon_transitive(X19)
| sK6(X18,X19,singleton(X20)) = X20 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_409])]) ).
fof(f1850,plain,
( ! [X18,X19,X20] :
( subset(sK6(X18,X19,singleton(X20)),X19)
| in(sK6(X18,X19,singleton(X20)),X18)
| sP0(X18,X19,singleton(X20))
| ~ epsilon_transitive(X19)
| sK6(X18,X19,singleton(X20)) = X20 )
| ~ spl20_153
| ~ spl20_190 ),
inference(resolution,[],[f1797,f1231]) ).
fof(f7497,plain,
( spl20_408
| ~ spl20_153
| ~ spl20_189 ),
inference(avatar_split_clause,[],[f1823,f1792,f1230,f7495]) ).
fof(f7495,plain,
( spl20_408
<=> ! [X18,X16,X17] :
( subset(sK6(singleton(X16),X17,X18),X18)
| in(sK6(singleton(X16),X17,X18),X17)
| sP0(singleton(X16),X17,X18)
| ~ epsilon_transitive(X18)
| sK6(singleton(X16),X17,X18) = X16 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_408])]) ).
fof(f1823,plain,
( ! [X18,X16,X17] :
( subset(sK6(singleton(X16),X17,X18),X18)
| in(sK6(singleton(X16),X17,X18),X17)
| sP0(singleton(X16),X17,X18)
| ~ epsilon_transitive(X18)
| sK6(singleton(X16),X17,X18) = X16 )
| ~ spl20_153
| ~ spl20_189 ),
inference(resolution,[],[f1793,f1231]) ).
fof(f7493,plain,
( spl20_407
| ~ spl20_153
| ~ spl20_189 ),
inference(avatar_split_clause,[],[f1813,f1792,f1230,f7491]) ).
fof(f7491,plain,
( spl20_407
<=> ! [X18,X16,X17] :
( subset(sK6(X16,singleton(X17),X18),X18)
| in(sK6(X16,singleton(X17),X18),X16)
| sP0(X16,singleton(X17),X18)
| ~ epsilon_transitive(X18)
| sK6(X16,singleton(X17),X18) = X17 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_407])]) ).
fof(f1813,plain,
( ! [X18,X16,X17] :
( subset(sK6(X16,singleton(X17),X18),X18)
| in(sK6(X16,singleton(X17),X18),X16)
| sP0(X16,singleton(X17),X18)
| ~ epsilon_transitive(X18)
| sK6(X16,singleton(X17),X18) = X17 )
| ~ spl20_153
| ~ spl20_189 ),
inference(resolution,[],[f1793,f1231]) ).
fof(f7489,plain,
( spl20_406
| ~ spl20_94
| ~ spl20_187 ),
inference(avatar_split_clause,[],[f1752,f1665,f823,f7487]) ).
fof(f7487,plain,
( spl20_406
<=> ! [X6,X4,X5,X7] :
( in(sK6(powerset(X4),X5,X6),X6)
| in(sK6(powerset(X4),X5,X6),X5)
| sP0(powerset(X4),X5,X6)
| ~ empty(X4)
| ~ in(X7,sK6(powerset(X4),X5,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_406])]) ).
fof(f1752,plain,
( ! [X6,X7,X4,X5] :
( in(sK6(powerset(X4),X5,X6),X6)
| in(sK6(powerset(X4),X5,X6),X5)
| sP0(powerset(X4),X5,X6)
| ~ empty(X4)
| ~ in(X7,sK6(powerset(X4),X5,X6)) )
| ~ spl20_94
| ~ spl20_187 ),
inference(resolution,[],[f1666,f824]) ).
fof(f7485,plain,
( spl20_405
| ~ spl20_94
| ~ spl20_185 ),
inference(avatar_split_clause,[],[f1707,f1657,f823,f7483]) ).
fof(f7483,plain,
( spl20_405
<=> ! [X6,X4,X5,X7] :
( in(sK6(X4,powerset(X5),X6),X6)
| in(sK6(X4,powerset(X5),X6),X4)
| sP0(X4,powerset(X5),X6)
| ~ empty(X5)
| ~ in(X7,sK6(X4,powerset(X5),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_405])]) ).
fof(f1707,plain,
( ! [X6,X7,X4,X5] :
( in(sK6(X4,powerset(X5),X6),X6)
| in(sK6(X4,powerset(X5),X6),X4)
| sP0(X4,powerset(X5),X6)
| ~ empty(X5)
| ~ in(X7,sK6(X4,powerset(X5),X6)) )
| ~ spl20_94
| ~ spl20_185 ),
inference(resolution,[],[f1658,f824]) ).
fof(f7481,plain,
( spl20_404
| ~ spl20_94
| ~ spl20_183 ),
inference(avatar_split_clause,[],[f1673,f1649,f823,f7479]) ).
fof(f7479,plain,
( spl20_404
<=> ! [X6,X4,X5,X7] :
( in(sK6(X4,X5,powerset(X6)),X5)
| in(sK6(X4,X5,powerset(X6)),X4)
| sP0(X4,X5,powerset(X6))
| ~ empty(X6)
| ~ in(X7,sK6(X4,X5,powerset(X6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_404])]) ).
fof(f1673,plain,
( ! [X6,X7,X4,X5] :
( in(sK6(X4,X5,powerset(X6)),X5)
| in(sK6(X4,X5,powerset(X6)),X4)
| sP0(X4,X5,powerset(X6))
| ~ empty(X6)
| ~ in(X7,sK6(X4,X5,powerset(X6))) )
| ~ spl20_94
| ~ spl20_183 ),
inference(resolution,[],[f1650,f824]) ).
fof(f7477,plain,
( spl20_403
| ~ spl20_157
| ~ spl20_177 ),
inference(avatar_split_clause,[],[f1551,f1462,f1267,f7475]) ).
fof(f7475,plain,
( spl20_403
<=> ! [X13,X14] :
( in(sK6(sK4(powerset(X13)),sK4(powerset(X13)),X14),X14)
| sP0(sK4(powerset(X13)),sK4(powerset(X13)),X14)
| element(sK6(sK4(powerset(X13)),sK4(powerset(X13)),X14),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_403])]) ).
fof(f1551,plain,
( ! [X14,X13] :
( in(sK6(sK4(powerset(X13)),sK4(powerset(X13)),X14),X14)
| sP0(sK4(powerset(X13)),sK4(powerset(X13)),X14)
| element(sK6(sK4(powerset(X13)),sK4(powerset(X13)),X14),X13) )
| ~ spl20_157
| ~ spl20_177 ),
inference(resolution,[],[f1463,f1268]) ).
fof(f7473,plain,
( spl20_402
| ~ spl20_108
| ~ spl20_166 ),
inference(avatar_split_clause,[],[f1369,f1355,f923,f7471]) ).
fof(f7471,plain,
( spl20_402
<=> ! [X20,X21,X19] :
( sK6(X20,X21,X19) = X19
| ~ ordinal(X19)
| ~ ordinal(sK6(X20,X21,X19))
| ~ empty(sK6(X20,X21,X19))
| ~ in(sK6(X20,X21,X19),X21)
| sP0(X20,X21,X19) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_402])]) ).
fof(f1369,plain,
( ! [X21,X19,X20] :
( sK6(X20,X21,X19) = X19
| ~ ordinal(X19)
| ~ ordinal(sK6(X20,X21,X19))
| ~ empty(sK6(X20,X21,X19))
| ~ in(sK6(X20,X21,X19),X21)
| sP0(X20,X21,X19) )
| ~ spl20_108
| ~ spl20_166 ),
inference(resolution,[],[f1356,f924]) ).
fof(f7467,plain,
( spl20_401
| ~ spl20_109
| ~ spl20_166 ),
inference(avatar_split_clause,[],[f1368,f1355,f927,f7465]) ).
fof(f7465,plain,
( spl20_401
<=> ! [X18,X16,X17] :
( sK6(X17,X18,X16) = X16
| ~ ordinal(X16)
| ~ ordinal(sK6(X17,X18,X16))
| ~ empty(sK6(X17,X18,X16))
| ~ in(sK6(X17,X18,X16),X17)
| sP0(X17,X18,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_401])]) ).
fof(f1368,plain,
( ! [X18,X16,X17] :
( sK6(X17,X18,X16) = X16
| ~ ordinal(X16)
| ~ ordinal(sK6(X17,X18,X16))
| ~ empty(sK6(X17,X18,X16))
| ~ in(sK6(X17,X18,X16),X17)
| sP0(X17,X18,X16) )
| ~ spl20_109
| ~ spl20_166 ),
inference(resolution,[],[f1356,f928]) ).
fof(f7049,plain,
( spl20_400
| ~ spl20_160
| ~ spl20_191 ),
inference(avatar_split_clause,[],[f1875,f1800,f1291,f7047]) ).
fof(f7047,plain,
( spl20_400
<=> ! [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_400])]) ).
fof(f1875,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_160
| ~ spl20_191 ),
inference(resolution,[],[f1801,f1292]) ).
fof(f7045,plain,
( spl20_399
| ~ spl20_160
| ~ spl20_190 ),
inference(avatar_split_clause,[],[f1840,f1796,f1291,f7043]) ).
fof(f7043,plain,
( spl20_399
<=> ! [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_399])]) ).
fof(f1840,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_160
| ~ spl20_190 ),
inference(resolution,[],[f1797,f1292]) ).
fof(f7041,plain,
( spl20_398
| ~ spl20_160
| ~ spl20_189 ),
inference(avatar_split_clause,[],[f1803,f1792,f1291,f7039]) ).
fof(f7039,plain,
( spl20_398
<=> ! [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_398])]) ).
fof(f1803,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_160
| ~ spl20_189 ),
inference(resolution,[],[f1793,f1292]) ).
fof(f6288,plain,
( spl20_397
| ~ spl20_151
| ~ spl20_191 ),
inference(avatar_split_clause,[],[f1898,f1800,f1221,f6286]) ).
fof(f6286,plain,
( spl20_397
<=> ! [X25,X24,X26] :
( subset(sK6(X24,sK4(powerset(X25)),X26),X24)
| in(sK6(X24,sK4(powerset(X25)),X26),X26)
| sP0(X24,sK4(powerset(X25)),X26)
| ~ epsilon_transitive(X24)
| ~ empty(X25) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_397])]) ).
fof(f1898,plain,
( ! [X26,X24,X25] :
( subset(sK6(X24,sK4(powerset(X25)),X26),X24)
| in(sK6(X24,sK4(powerset(X25)),X26),X26)
| sP0(X24,sK4(powerset(X25)),X26)
| ~ epsilon_transitive(X24)
| ~ empty(X25) )
| ~ spl20_151
| ~ spl20_191 ),
inference(resolution,[],[f1801,f1222]) ).
fof(f6284,plain,
( spl20_396
| ~ spl20_151
| ~ spl20_191 ),
inference(avatar_split_clause,[],[f1888,f1800,f1221,f6282]) ).
fof(f1888,plain,
( ! [X28,X26,X27] :
( subset(sK6(X26,X27,sK4(powerset(X28))),X26)
| in(sK6(X26,X27,sK4(powerset(X28))),X27)
| sP0(X26,X27,sK4(powerset(X28)))
| ~ epsilon_transitive(X26)
| ~ empty(X28) )
| ~ spl20_151
| ~ spl20_191 ),
inference(resolution,[],[f1801,f1222]) ).
fof(f6279,plain,
( spl20_395
| ~ spl20_151
| ~ spl20_190 ),
inference(avatar_split_clause,[],[f1863,f1796,f1221,f6277]) ).
fof(f6277,plain,
( spl20_395
<=> ! [X25,X24,X26] :
( subset(sK6(sK4(powerset(X24)),X25,X26),X25)
| in(sK6(sK4(powerset(X24)),X25,X26),X26)
| sP0(sK4(powerset(X24)),X25,X26)
| ~ epsilon_transitive(X25)
| ~ empty(X24) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_395])]) ).
fof(f1863,plain,
( ! [X26,X24,X25] :
( subset(sK6(sK4(powerset(X24)),X25,X26),X25)
| in(sK6(sK4(powerset(X24)),X25,X26),X26)
| sP0(sK4(powerset(X24)),X25,X26)
| ~ epsilon_transitive(X25)
| ~ empty(X24) )
| ~ spl20_151
| ~ spl20_190 ),
inference(resolution,[],[f1797,f1222]) ).
fof(f6275,plain,
( spl20_394
| ~ spl20_88
| ~ spl20_190 ),
inference(avatar_split_clause,[],[f1856,f1796,f772,f6273]) ).
fof(f6273,plain,
( spl20_394
<=> ! [X6,X4,X5] :
( subset(sK6(X4,X5,X6),X5)
| in(sK6(X4,X5,X6),X6)
| sP0(X4,X5,X6)
| ~ epsilon_transitive(X5)
| subset(sK6(X4,X5,X6),X4)
| ~ epsilon_transitive(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_394])]) ).
fof(f1856,plain,
( ! [X6,X4,X5] :
( subset(sK6(X4,X5,X6),X5)
| in(sK6(X4,X5,X6),X6)
| sP0(X4,X5,X6)
| ~ epsilon_transitive(X5)
| subset(sK6(X4,X5,X6),X4)
| ~ epsilon_transitive(X4) )
| ~ spl20_88
| ~ spl20_190 ),
inference(resolution,[],[f1797,f773]) ).
fof(f6271,plain,
( spl20_393
| ~ spl20_151
| ~ spl20_190 ),
inference(avatar_split_clause,[],[f1853,f1796,f1221,f6269]) ).
fof(f1853,plain,
( ! [X28,X26,X27] :
( subset(sK6(X26,X27,sK4(powerset(X28))),X27)
| in(sK6(X26,X27,sK4(powerset(X28))),X26)
| sP0(X26,X27,sK4(powerset(X28)))
| ~ epsilon_transitive(X27)
| ~ empty(X28) )
| ~ spl20_151
| ~ spl20_190 ),
inference(resolution,[],[f1797,f1222]) ).
fof(f6267,plain,
( spl20_392
| ~ spl20_151
| ~ spl20_189 ),
inference(avatar_split_clause,[],[f1826,f1792,f1221,f6265]) ).
fof(f6265,plain,
( spl20_392
<=> ! [X25,X24,X26] :
( subset(sK6(sK4(powerset(X24)),X25,X26),X26)
| in(sK6(sK4(powerset(X24)),X25,X26),X25)
| sP0(sK4(powerset(X24)),X25,X26)
| ~ epsilon_transitive(X26)
| ~ empty(X24) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_392])]) ).
fof(f1826,plain,
( ! [X26,X24,X25] :
( subset(sK6(sK4(powerset(X24)),X25,X26),X26)
| in(sK6(sK4(powerset(X24)),X25,X26),X25)
| sP0(sK4(powerset(X24)),X25,X26)
| ~ epsilon_transitive(X26)
| ~ empty(X24) )
| ~ spl20_151
| ~ spl20_189 ),
inference(resolution,[],[f1793,f1222]) ).
fof(f6263,plain,
( spl20_391
| ~ spl20_88
| ~ spl20_189 ),
inference(avatar_split_clause,[],[f1819,f1792,f772,f6261]) ).
fof(f6261,plain,
( spl20_391
<=> ! [X6,X4,X5] :
( subset(sK6(X4,X5,X6),X6)
| in(sK6(X4,X5,X6),X5)
| sP0(X4,X5,X6)
| ~ epsilon_transitive(X6)
| subset(sK6(X4,X5,X6),X4)
| ~ epsilon_transitive(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_391])]) ).
fof(f1819,plain,
( ! [X6,X4,X5] :
( subset(sK6(X4,X5,X6),X6)
| in(sK6(X4,X5,X6),X5)
| sP0(X4,X5,X6)
| ~ epsilon_transitive(X6)
| subset(sK6(X4,X5,X6),X4)
| ~ epsilon_transitive(X4) )
| ~ spl20_88
| ~ spl20_189 ),
inference(resolution,[],[f1793,f773]) ).
fof(f6259,plain,
( spl20_390
| ~ spl20_151
| ~ spl20_189 ),
inference(avatar_split_clause,[],[f1816,f1792,f1221,f6257]) ).
fof(f1816,plain,
( ! [X26,X24,X25] :
( subset(sK6(X24,sK4(powerset(X25)),X26),X26)
| in(sK6(X24,sK4(powerset(X25)),X26),X24)
| sP0(X24,sK4(powerset(X25)),X26)
| ~ epsilon_transitive(X26)
| ~ empty(X25) )
| ~ spl20_151
| ~ spl20_189 ),
inference(resolution,[],[f1793,f1222]) ).
fof(f6255,plain,
( spl20_389
| ~ spl20_88
| ~ spl20_189 ),
inference(avatar_split_clause,[],[f1809,f1792,f772,f6253]) ).
fof(f6253,plain,
( spl20_389
<=> ! [X6,X4,X5] :
( subset(sK6(X4,X5,X6),X6)
| in(sK6(X4,X5,X6),X4)
| sP0(X4,X5,X6)
| ~ epsilon_transitive(X6)
| subset(sK6(X4,X5,X6),X5)
| ~ epsilon_transitive(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_389])]) ).
fof(f1809,plain,
( ! [X6,X4,X5] :
( subset(sK6(X4,X5,X6),X6)
| in(sK6(X4,X5,X6),X4)
| sP0(X4,X5,X6)
| ~ epsilon_transitive(X6)
| subset(sK6(X4,X5,X6),X5)
| ~ epsilon_transitive(X5) )
| ~ spl20_88
| ~ spl20_189 ),
inference(resolution,[],[f1793,f773]) ).
fof(f6251,plain,
( spl20_388
| ~ spl20_153
| ~ spl20_187 ),
inference(avatar_split_clause,[],[f1771,f1665,f1230,f6249]) ).
fof(f6249,plain,
( spl20_388
<=> ! [X18,X16,X17] :
( element(sK6(X16,singleton(X17),X18),X16)
| in(sK6(X16,singleton(X17),X18),X18)
| sP0(X16,singleton(X17),X18)
| sK6(X16,singleton(X17),X18) = X17 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_388])]) ).
fof(f1771,plain,
( ! [X18,X16,X17] :
( element(sK6(X16,singleton(X17),X18),X16)
| in(sK6(X16,singleton(X17),X18),X18)
| sP0(X16,singleton(X17),X18)
| sK6(X16,singleton(X17),X18) = X17 )
| ~ spl20_153
| ~ spl20_187 ),
inference(resolution,[],[f1666,f1231]) ).
fof(f6247,plain,
( spl20_387
| ~ spl20_153
| ~ spl20_187 ),
inference(avatar_split_clause,[],[f1761,f1665,f1230,f6245]) ).
fof(f6245,plain,
( spl20_387
<=> ! [X20,X18,X19] :
( element(sK6(X18,X19,singleton(X20)),X18)
| in(sK6(X18,X19,singleton(X20)),X19)
| sP0(X18,X19,singleton(X20))
| sK6(X18,X19,singleton(X20)) = X20 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_387])]) ).
fof(f1761,plain,
( ! [X18,X19,X20] :
( element(sK6(X18,X19,singleton(X20)),X18)
| in(sK6(X18,X19,singleton(X20)),X19)
| sP0(X18,X19,singleton(X20))
| sK6(X18,X19,singleton(X20)) = X20 )
| ~ spl20_153
| ~ spl20_187 ),
inference(resolution,[],[f1666,f1231]) ).
fof(f6243,plain,
( spl20_386
| ~ spl20_84
| ~ spl20_187 ),
inference(avatar_split_clause,[],[f1753,f1665,f732,f6241]) ).
fof(f6241,plain,
( spl20_386
<=> ! [X9,X8,X10] :
( in(sK6(powerset(X8),X9,X10),X10)
| in(sK6(powerset(X8),X9,X10),X9)
| sP0(powerset(X8),X9,X10)
| subset(sK6(powerset(X8),X9,X10),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_386])]) ).
fof(f1753,plain,
( ! [X10,X8,X9] :
( in(sK6(powerset(X8),X9,X10),X10)
| in(sK6(powerset(X8),X9,X10),X9)
| sP0(powerset(X8),X9,X10)
| subset(sK6(powerset(X8),X9,X10),X8) )
| ~ spl20_84
| ~ spl20_187 ),
inference(resolution,[],[f1666,f733]) ).
fof(f6232,plain,
( spl20_385
| ~ spl20_153
| ~ spl20_185 ),
inference(avatar_split_clause,[],[f1726,f1657,f1230,f6230]) ).
fof(f6230,plain,
( spl20_385
<=> ! [X18,X16,X17] :
( element(sK6(singleton(X16),X17,X18),X17)
| in(sK6(singleton(X16),X17,X18),X18)
| sP0(singleton(X16),X17,X18)
| sK6(singleton(X16),X17,X18) = X16 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_385])]) ).
fof(f1726,plain,
( ! [X18,X16,X17] :
( element(sK6(singleton(X16),X17,X18),X17)
| in(sK6(singleton(X16),X17,X18),X18)
| sP0(singleton(X16),X17,X18)
| sK6(singleton(X16),X17,X18) = X16 )
| ~ spl20_153
| ~ spl20_185 ),
inference(resolution,[],[f1658,f1231]) ).
fof(f6228,plain,
( spl20_384
| ~ spl20_153
| ~ spl20_185 ),
inference(avatar_split_clause,[],[f1716,f1657,f1230,f6226]) ).
fof(f6226,plain,
( spl20_384
<=> ! [X20,X18,X19] :
( element(sK6(X18,X19,singleton(X20)),X19)
| in(sK6(X18,X19,singleton(X20)),X18)
| sP0(X18,X19,singleton(X20))
| sK6(X18,X19,singleton(X20)) = X20 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_384])]) ).
fof(f1716,plain,
( ! [X18,X19,X20] :
( element(sK6(X18,X19,singleton(X20)),X19)
| in(sK6(X18,X19,singleton(X20)),X18)
| sP0(X18,X19,singleton(X20))
| sK6(X18,X19,singleton(X20)) = X20 )
| ~ spl20_153
| ~ spl20_185 ),
inference(resolution,[],[f1658,f1231]) ).
fof(f6224,plain,
( spl20_383
| ~ spl20_84
| ~ spl20_185 ),
inference(avatar_split_clause,[],[f1708,f1657,f732,f6222]) ).
fof(f6222,plain,
( spl20_383
<=> ! [X9,X8,X10] :
( in(sK6(X8,powerset(X9),X10),X10)
| in(sK6(X8,powerset(X9),X10),X8)
| sP0(X8,powerset(X9),X10)
| subset(sK6(X8,powerset(X9),X10),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_383])]) ).
fof(f1708,plain,
( ! [X10,X8,X9] :
( in(sK6(X8,powerset(X9),X10),X10)
| in(sK6(X8,powerset(X9),X10),X8)
| sP0(X8,powerset(X9),X10)
| subset(sK6(X8,powerset(X9),X10),X9) )
| ~ spl20_84
| ~ spl20_185 ),
inference(resolution,[],[f1658,f733]) ).
fof(f6220,plain,
( spl20_382
| ~ spl20_153
| ~ spl20_183 ),
inference(avatar_split_clause,[],[f1692,f1649,f1230,f6218]) ).
fof(f6218,plain,
( spl20_382
<=> ! [X18,X16,X17] :
( element(sK6(singleton(X16),X17,X18),X18)
| in(sK6(singleton(X16),X17,X18),X17)
| sP0(singleton(X16),X17,X18)
| sK6(singleton(X16),X17,X18) = X16 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_382])]) ).
fof(f1692,plain,
( ! [X18,X16,X17] :
( element(sK6(singleton(X16),X17,X18),X18)
| in(sK6(singleton(X16),X17,X18),X17)
| sP0(singleton(X16),X17,X18)
| sK6(singleton(X16),X17,X18) = X16 )
| ~ spl20_153
| ~ spl20_183 ),
inference(resolution,[],[f1650,f1231]) ).
fof(f6216,plain,
( spl20_381
| ~ spl20_153
| ~ spl20_183 ),
inference(avatar_split_clause,[],[f1682,f1649,f1230,f6214]) ).
fof(f6214,plain,
( spl20_381
<=> ! [X18,X16,X17] :
( element(sK6(X16,singleton(X17),X18),X18)
| in(sK6(X16,singleton(X17),X18),X16)
| sP0(X16,singleton(X17),X18)
| sK6(X16,singleton(X17),X18) = X17 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_381])]) ).
fof(f1682,plain,
( ! [X18,X16,X17] :
( element(sK6(X16,singleton(X17),X18),X18)
| in(sK6(X16,singleton(X17),X18),X16)
| sP0(X16,singleton(X17),X18)
| sK6(X16,singleton(X17),X18) = X17 )
| ~ spl20_153
| ~ spl20_183 ),
inference(resolution,[],[f1650,f1231]) ).
fof(f6212,plain,
( spl20_380
| ~ spl20_84
| ~ spl20_183 ),
inference(avatar_split_clause,[],[f1674,f1649,f732,f6210]) ).
fof(f6210,plain,
( spl20_380
<=> ! [X9,X8,X10] :
( in(sK6(X8,X9,powerset(X10)),X9)
| in(sK6(X8,X9,powerset(X10)),X8)
| sP0(X8,X9,powerset(X10))
| subset(sK6(X8,X9,powerset(X10)),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_380])]) ).
fof(f1674,plain,
( ! [X10,X8,X9] :
( in(sK6(X8,X9,powerset(X10)),X9)
| in(sK6(X8,X9,powerset(X10)),X8)
| sP0(X8,X9,powerset(X10))
| subset(sK6(X8,X9,powerset(X10)),X10) )
| ~ spl20_84
| ~ spl20_183 ),
inference(resolution,[],[f1650,f733]) ).
fof(f6208,plain,
( spl20_379
| ~ spl20_110
| ~ spl20_153 ),
inference(avatar_split_clause,[],[f1256,f1230,f935,f6206]) ).
fof(f6206,plain,
( spl20_379
<=> ! [X16,X14,X15] :
( sK6(singleton(X14),X15,X16) = X14
| in(sK6(singleton(X14),X15,X16),X16)
| in(sK6(singleton(X14),X15,X16),X15)
| sP0(singleton(X14),X15,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_379])]) ).
fof(f1256,plain,
( ! [X16,X14,X15] :
( sK6(singleton(X14),X15,X16) = X14
| in(sK6(singleton(X14),X15,X16),X16)
| in(sK6(singleton(X14),X15,X16),X15)
| sP0(singleton(X14),X15,X16) )
| ~ spl20_110
| ~ spl20_153 ),
inference(resolution,[],[f1231,f936]) ).
fof(f6204,plain,
( spl20_378
| ~ spl20_110
| ~ spl20_153 ),
inference(avatar_split_clause,[],[f1255,f1230,f935,f6202]) ).
fof(f6202,plain,
( spl20_378
<=> ! [X13,X12,X11] :
( sK6(X11,singleton(X12),X13) = X12
| in(sK6(X11,singleton(X12),X13),X13)
| in(sK6(X11,singleton(X12),X13),X11)
| sP0(X11,singleton(X12),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_378])]) ).
fof(f1255,plain,
( ! [X11,X12,X13] :
( sK6(X11,singleton(X12),X13) = X12
| in(sK6(X11,singleton(X12),X13),X13)
| in(sK6(X11,singleton(X12),X13),X11)
| sP0(X11,singleton(X12),X13) )
| ~ spl20_110
| ~ spl20_153 ),
inference(resolution,[],[f1231,f936]) ).
fof(f6200,plain,
( spl20_377
| ~ spl20_110
| ~ spl20_153 ),
inference(avatar_split_clause,[],[f1254,f1230,f935,f6198]) ).
fof(f6198,plain,
( spl20_377
<=> ! [X9,X8,X10] :
( sK6(X8,X9,singleton(X10)) = X10
| in(sK6(X8,X9,singleton(X10)),X9)
| in(sK6(X8,X9,singleton(X10)),X8)
| sP0(X8,X9,singleton(X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_377])]) ).
fof(f1254,plain,
( ! [X10,X8,X9] :
( sK6(X8,X9,singleton(X10)) = X10
| in(sK6(X8,X9,singleton(X10)),X9)
| in(sK6(X8,X9,singleton(X10)),X8)
| sP0(X8,X9,singleton(X10)) )
| ~ spl20_110
| ~ spl20_153 ),
inference(resolution,[],[f1231,f936]) ).
fof(f5998,plain,
( ~ spl20_181
| ~ spl20_68
| ~ spl20_243 ),
inference(avatar_split_clause,[],[f4385,f2671,f613,f1640]) ).
fof(f4385,plain,
( ~ empty(sK1)
| ~ spl20_68
| ~ spl20_243 ),
inference(resolution,[],[f2673,f614]) ).
fof(f5701,plain,
( spl20_376
| ~ spl20_4
| ~ spl20_297 ),
inference(avatar_split_clause,[],[f5388,f3590,f274,f5698]) ).
fof(f5388,plain,
( ordinal_subset(sK8,sK2)
| ~ spl20_4
| ~ spl20_297 ),
inference(superposition,[],[f276,f3592]) ).
fof(f276,plain,
( ordinal_subset(sK1,sK2)
| ~ spl20_4 ),
inference(avatar_component_clause,[],[f274]) ).
fof(f5415,plain,
( spl20_375
| ~ spl20_75
| ~ spl20_191 ),
inference(avatar_split_clause,[],[f1893,f1800,f653,f5413]) ).
fof(f5413,plain,
( spl20_375
<=> ! [X11,X12,X10] :
( subset(sK6(X10,X11,X12),X10)
| in(sK6(X10,X11,X12),X12)
| sP0(X10,X11,X12)
| ~ epsilon_transitive(X10)
| ~ in(X11,sK6(X10,X11,X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_375])]) ).
fof(f1893,plain,
( ! [X10,X11,X12] :
( subset(sK6(X10,X11,X12),X10)
| in(sK6(X10,X11,X12),X12)
| sP0(X10,X11,X12)
| ~ epsilon_transitive(X10)
| ~ in(X11,sK6(X10,X11,X12)) )
| ~ spl20_75
| ~ spl20_191 ),
inference(resolution,[],[f1801,f654]) ).
fof(f5411,plain,
( spl20_374
| ~ spl20_75
| ~ spl20_191 ),
inference(avatar_split_clause,[],[f1883,f1800,f653,f5409]) ).
fof(f5409,plain,
( spl20_374
<=> ! [X13,X12,X14] :
( subset(sK6(X12,X13,X14),X12)
| in(sK6(X12,X13,X14),X13)
| sP0(X12,X13,X14)
| ~ epsilon_transitive(X12)
| ~ in(X14,sK6(X12,X13,X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_374])]) ).
fof(f1883,plain,
( ! [X14,X12,X13] :
( subset(sK6(X12,X13,X14),X12)
| in(sK6(X12,X13,X14),X13)
| sP0(X12,X13,X14)
| ~ epsilon_transitive(X12)
| ~ in(X14,sK6(X12,X13,X14)) )
| ~ spl20_75
| ~ spl20_191 ),
inference(resolution,[],[f1801,f654]) ).
fof(f5407,plain,
( spl20_373
| ~ spl20_75
| ~ spl20_190 ),
inference(avatar_split_clause,[],[f1858,f1796,f653,f5405]) ).
fof(f5405,plain,
( spl20_373
<=> ! [X12,X11,X10] :
( subset(sK6(X10,X11,X12),X11)
| in(sK6(X10,X11,X12),X12)
| sP0(X10,X11,X12)
| ~ epsilon_transitive(X11)
| ~ in(X10,sK6(X10,X11,X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_373])]) ).
fof(f1858,plain,
( ! [X10,X11,X12] :
( subset(sK6(X10,X11,X12),X11)
| in(sK6(X10,X11,X12),X12)
| sP0(X10,X11,X12)
| ~ epsilon_transitive(X11)
| ~ in(X10,sK6(X10,X11,X12)) )
| ~ spl20_75
| ~ spl20_190 ),
inference(resolution,[],[f1797,f654]) ).
fof(f5385,plain,
( spl20_372
| ~ spl20_75
| ~ spl20_190 ),
inference(avatar_split_clause,[],[f1848,f1796,f653,f5383]) ).
fof(f5383,plain,
( spl20_372
<=> ! [X13,X12,X14] :
( subset(sK6(X12,X13,X14),X13)
| in(sK6(X12,X13,X14),X12)
| sP0(X12,X13,X14)
| ~ epsilon_transitive(X13)
| ~ in(X14,sK6(X12,X13,X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_372])]) ).
fof(f1848,plain,
( ! [X14,X12,X13] :
( subset(sK6(X12,X13,X14),X13)
| in(sK6(X12,X13,X14),X12)
| sP0(X12,X13,X14)
| ~ epsilon_transitive(X13)
| ~ in(X14,sK6(X12,X13,X14)) )
| ~ spl20_75
| ~ spl20_190 ),
inference(resolution,[],[f1797,f654]) ).
fof(f5381,plain,
( spl20_371
| ~ spl20_75
| ~ spl20_189 ),
inference(avatar_split_clause,[],[f1821,f1792,f653,f5379]) ).
fof(f5379,plain,
( spl20_371
<=> ! [X11,X12,X10] :
( subset(sK6(X10,X11,X12),X12)
| in(sK6(X10,X11,X12),X11)
| sP0(X10,X11,X12)
| ~ epsilon_transitive(X12)
| ~ in(X10,sK6(X10,X11,X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_371])]) ).
fof(f1821,plain,
( ! [X10,X11,X12] :
( subset(sK6(X10,X11,X12),X12)
| in(sK6(X10,X11,X12),X11)
| sP0(X10,X11,X12)
| ~ epsilon_transitive(X12)
| ~ in(X10,sK6(X10,X11,X12)) )
| ~ spl20_75
| ~ spl20_189 ),
inference(resolution,[],[f1793,f654]) ).
fof(f5377,plain,
( spl20_370
| ~ spl20_75
| ~ spl20_189 ),
inference(avatar_split_clause,[],[f1811,f1792,f653,f5375]) ).
fof(f5375,plain,
( spl20_370
<=> ! [X11,X12,X10] :
( subset(sK6(X10,X11,X12),X12)
| in(sK6(X10,X11,X12),X10)
| sP0(X10,X11,X12)
| ~ epsilon_transitive(X12)
| ~ in(X11,sK6(X10,X11,X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_370])]) ).
fof(f1811,plain,
( ! [X10,X11,X12] :
( subset(sK6(X10,X11,X12),X12)
| in(sK6(X10,X11,X12),X10)
| sP0(X10,X11,X12)
| ~ epsilon_transitive(X12)
| ~ in(X11,sK6(X10,X11,X12)) )
| ~ spl20_75
| ~ spl20_189 ),
inference(resolution,[],[f1793,f654]) ).
fof(f5373,plain,
( spl20_369
| ~ spl20_151
| ~ spl20_187 ),
inference(avatar_split_clause,[],[f1774,f1665,f1221,f5371]) ).
fof(f1774,plain,
( ! [X26,X24,X25] :
( element(sK6(X24,sK4(powerset(X25)),X26),X24)
| in(sK6(X24,sK4(powerset(X25)),X26),X26)
| sP0(X24,sK4(powerset(X25)),X26)
| ~ empty(X25) )
| ~ spl20_151
| ~ spl20_187 ),
inference(resolution,[],[f1666,f1222]) ).
fof(f5369,plain,
( spl20_368
| ~ spl20_88
| ~ spl20_187 ),
inference(avatar_split_clause,[],[f1767,f1665,f772,f5367]) ).
fof(f1767,plain,
( ! [X6,X4,X5] :
( element(sK6(X4,X5,X6),X4)
| in(sK6(X4,X5,X6),X6)
| sP0(X4,X5,X6)
| subset(sK6(X4,X5,X6),X5)
| ~ epsilon_transitive(X5) )
| ~ spl20_88
| ~ spl20_187 ),
inference(resolution,[],[f1666,f773]) ).
fof(f5365,plain,
( spl20_367
| ~ spl20_151
| ~ spl20_187 ),
inference(avatar_split_clause,[],[f1764,f1665,f1221,f5363]) ).
fof(f1764,plain,
( ! [X28,X26,X27] :
( element(sK6(X26,X27,sK4(powerset(X28))),X26)
| in(sK6(X26,X27,sK4(powerset(X28))),X27)
| sP0(X26,X27,sK4(powerset(X28)))
| ~ empty(X28) )
| ~ spl20_151
| ~ spl20_187 ),
inference(resolution,[],[f1666,f1222]) ).
fof(f5361,plain,
( spl20_366
| ~ spl20_88
| ~ spl20_187 ),
inference(avatar_split_clause,[],[f1757,f1665,f772,f5359]) ).
fof(f1757,plain,
( ! [X8,X6,X7] :
( element(sK6(X6,X7,X8),X6)
| in(sK6(X6,X7,X8),X7)
| sP0(X6,X7,X8)
| subset(sK6(X6,X7,X8),X8)
| ~ epsilon_transitive(X8) )
| ~ spl20_88
| ~ spl20_187 ),
inference(resolution,[],[f1666,f773]) ).
fof(f5357,plain,
( spl20_365
| ~ spl20_151
| ~ spl20_185 ),
inference(avatar_split_clause,[],[f1729,f1657,f1221,f5355]) ).
fof(f1729,plain,
( ! [X26,X24,X25] :
( element(sK6(sK4(powerset(X24)),X25,X26),X25)
| in(sK6(sK4(powerset(X24)),X25,X26),X26)
| sP0(sK4(powerset(X24)),X25,X26)
| ~ empty(X24) )
| ~ spl20_151
| ~ spl20_185 ),
inference(resolution,[],[f1658,f1222]) ).
fof(f5353,plain,
( spl20_364
| ~ spl20_88
| ~ spl20_185 ),
inference(avatar_split_clause,[],[f1722,f1657,f772,f5351]) ).
fof(f1722,plain,
( ! [X6,X4,X5] :
( element(sK6(X4,X5,X6),X5)
| in(sK6(X4,X5,X6),X6)
| sP0(X4,X5,X6)
| subset(sK6(X4,X5,X6),X4)
| ~ epsilon_transitive(X4) )
| ~ spl20_88
| ~ spl20_185 ),
inference(resolution,[],[f1658,f773]) ).
fof(f5349,plain,
( spl20_363
| ~ spl20_151
| ~ spl20_185 ),
inference(avatar_split_clause,[],[f1719,f1657,f1221,f5347]) ).
fof(f1719,plain,
( ! [X28,X26,X27] :
( element(sK6(X26,X27,sK4(powerset(X28))),X27)
| in(sK6(X26,X27,sK4(powerset(X28))),X26)
| sP0(X26,X27,sK4(powerset(X28)))
| ~ empty(X28) )
| ~ spl20_151
| ~ spl20_185 ),
inference(resolution,[],[f1658,f1222]) ).
fof(f5338,plain,
( spl20_362
| ~ spl20_175
| ~ spl20_277 ),
inference(avatar_split_clause,[],[f5287,f3477,f1436,f5335]) ).
fof(f5287,plain,
( element(succ(sK2),sK2)
| ~ spl20_175
| ~ spl20_277 ),
inference(resolution,[],[f3479,f1437]) ).
fof(f5333,plain,
( spl20_361
| ~ spl20_88
| ~ spl20_185 ),
inference(avatar_split_clause,[],[f1712,f1657,f772,f5331]) ).
fof(f1712,plain,
( ! [X8,X6,X7] :
( element(sK6(X6,X7,X8),X7)
| in(sK6(X6,X7,X8),X6)
| sP0(X6,X7,X8)
| subset(sK6(X6,X7,X8),X8)
| ~ epsilon_transitive(X8) )
| ~ spl20_88
| ~ spl20_185 ),
inference(resolution,[],[f1658,f773]) ).
fof(f5329,plain,
( spl20_360
| ~ spl20_151
| ~ spl20_183 ),
inference(avatar_split_clause,[],[f1695,f1649,f1221,f5327]) ).
fof(f1695,plain,
( ! [X26,X24,X25] :
( element(sK6(sK4(powerset(X24)),X25,X26),X26)
| in(sK6(sK4(powerset(X24)),X25,X26),X25)
| sP0(sK4(powerset(X24)),X25,X26)
| ~ empty(X24) )
| ~ spl20_151
| ~ spl20_183 ),
inference(resolution,[],[f1650,f1222]) ).
fof(f5325,plain,
( spl20_359
| ~ spl20_88
| ~ spl20_183 ),
inference(avatar_split_clause,[],[f1688,f1649,f772,f5323]) ).
fof(f1688,plain,
( ! [X6,X4,X5] :
( element(sK6(X4,X5,X6),X6)
| in(sK6(X4,X5,X6),X5)
| sP0(X4,X5,X6)
| subset(sK6(X4,X5,X6),X4)
| ~ epsilon_transitive(X4) )
| ~ spl20_88
| ~ spl20_183 ),
inference(resolution,[],[f1650,f773]) ).
fof(f5321,plain,
( spl20_358
| ~ spl20_151
| ~ spl20_183 ),
inference(avatar_split_clause,[],[f1685,f1649,f1221,f5319]) ).
fof(f1685,plain,
( ! [X26,X24,X25] :
( element(sK6(X24,sK4(powerset(X25)),X26),X26)
| in(sK6(X24,sK4(powerset(X25)),X26),X24)
| sP0(X24,sK4(powerset(X25)),X26)
| ~ empty(X25) )
| ~ spl20_151
| ~ spl20_183 ),
inference(resolution,[],[f1650,f1222]) ).
fof(f5317,plain,
( spl20_357
| ~ spl20_88
| ~ spl20_183 ),
inference(avatar_split_clause,[],[f1678,f1649,f772,f5315]) ).
fof(f1678,plain,
( ! [X6,X4,X5] :
( element(sK6(X4,X5,X6),X6)
| in(sK6(X4,X5,X6),X4)
| sP0(X4,X5,X6)
| subset(sK6(X4,X5,X6),X5)
| ~ epsilon_transitive(X5) )
| ~ spl20_88
| ~ spl20_183 ),
inference(resolution,[],[f1650,f773]) ).
fof(f5313,plain,
( spl20_356
| ~ spl20_157
| ~ spl20_180 ),
inference(avatar_split_clause,[],[f1634,f1565,f1267,f5311]) ).
fof(f1634,plain,
( ! [X21,X22,X23] :
( in(sK6(X21,sK4(powerset(X22)),X23),X23)
| sP0(X21,sK4(powerset(X22)),X23)
| ~ empty(X21)
| element(sK6(X21,sK4(powerset(X22)),X23),X22) )
| ~ spl20_157
| ~ spl20_180 ),
inference(resolution,[],[f1566,f1268]) ).
fof(f5309,plain,
( spl20_355
| ~ spl20_157
| ~ spl20_180 ),
inference(avatar_split_clause,[],[f1624,f1565,f1267,f5307]) ).
fof(f1624,plain,
( ! [X24,X25,X23] :
( in(sK6(X23,X24,sK4(powerset(X25))),X24)
| sP0(X23,X24,sK4(powerset(X25)))
| ~ empty(X23)
| element(sK6(X23,X24,sK4(powerset(X25))),X25) )
| ~ spl20_157
| ~ spl20_180 ),
inference(resolution,[],[f1566,f1268]) ).
fof(f5305,plain,
( spl20_354
| ~ spl20_157
| ~ spl20_179 ),
inference(avatar_split_clause,[],[f1611,f1561,f1267,f5303]) ).
fof(f1611,plain,
( ! [X21,X22,X23] :
( in(sK6(sK4(powerset(X21)),X22,X23),X23)
| sP0(sK4(powerset(X21)),X22,X23)
| ~ empty(X22)
| element(sK6(sK4(powerset(X21)),X22,X23),X21) )
| ~ spl20_157
| ~ spl20_179 ),
inference(resolution,[],[f1562,f1268]) ).
fof(f5301,plain,
( spl20_353
| ~ spl20_157
| ~ spl20_179 ),
inference(avatar_split_clause,[],[f1601,f1561,f1267,f5299]) ).
fof(f1601,plain,
( ! [X24,X25,X23] :
( in(sK6(X23,X24,sK4(powerset(X25))),X23)
| sP0(X23,X24,sK4(powerset(X25)))
| ~ empty(X24)
| element(sK6(X23,X24,sK4(powerset(X25))),X25) )
| ~ spl20_157
| ~ spl20_179 ),
inference(resolution,[],[f1562,f1268]) ).
fof(f5297,plain,
( spl20_352
| ~ spl20_157
| ~ spl20_178 ),
inference(avatar_split_clause,[],[f1586,f1557,f1267,f5295]) ).
fof(f1586,plain,
( ! [X21,X22,X23] :
( in(sK6(sK4(powerset(X21)),X22,X23),X22)
| sP0(sK4(powerset(X21)),X22,X23)
| ~ empty(X23)
| element(sK6(sK4(powerset(X21)),X22,X23),X21) )
| ~ spl20_157
| ~ spl20_178 ),
inference(resolution,[],[f1558,f1268]) ).
fof(f5286,plain,
( spl20_351
| ~ spl20_157
| ~ spl20_178 ),
inference(avatar_split_clause,[],[f1576,f1557,f1267,f5284]) ).
fof(f1576,plain,
( ! [X21,X22,X23] :
( in(sK6(X21,sK4(powerset(X22)),X23),X21)
| sP0(X21,sK4(powerset(X22)),X23)
| ~ empty(X23)
| element(sK6(X21,sK4(powerset(X22)),X23),X22) )
| ~ spl20_157
| ~ spl20_178 ),
inference(resolution,[],[f1558,f1268]) ).
fof(f5282,plain,
( spl20_350
| ~ spl20_110
| ~ spl20_151 ),
inference(avatar_split_clause,[],[f1248,f1221,f935,f5280]) ).
fof(f1248,plain,
( ! [X16,X14,X15] :
( ~ empty(X14)
| in(sK6(sK4(powerset(X14)),X15,X16),X16)
| in(sK6(sK4(powerset(X14)),X15,X16),X15)
| sP0(sK4(powerset(X14)),X15,X16) )
| ~ spl20_110
| ~ spl20_151 ),
inference(resolution,[],[f1222,f936]) ).
fof(f5278,plain,
( spl20_349
| ~ spl20_110
| ~ spl20_151 ),
inference(avatar_split_clause,[],[f1247,f1221,f935,f5276]) ).
fof(f1247,plain,
( ! [X11,X12,X13] :
( ~ empty(X11)
| in(sK6(X12,sK4(powerset(X11)),X13),X13)
| in(sK6(X12,sK4(powerset(X11)),X13),X12)
| sP0(X12,sK4(powerset(X11)),X13) )
| ~ spl20_110
| ~ spl20_151 ),
inference(resolution,[],[f1222,f936]) ).
fof(f5274,plain,
( spl20_348
| ~ spl20_110
| ~ spl20_151 ),
inference(avatar_split_clause,[],[f1246,f1221,f935,f5272]) ).
fof(f1246,plain,
( ! [X10,X8,X9] :
( ~ empty(X8)
| in(sK6(X9,X10,sK4(powerset(X8))),X10)
| in(sK6(X9,X10,sK4(powerset(X8))),X9)
| sP0(X9,X10,sK4(powerset(X8))) )
| ~ spl20_110
| ~ spl20_151 ),
inference(resolution,[],[f1222,f936]) ).
fof(f4966,plain,
( spl20_347
| ~ spl20_75
| ~ spl20_187 ),
inference(avatar_split_clause,[],[f1769,f1665,f653,f4964]) ).
fof(f4964,plain,
( spl20_347
<=> ! [X11,X12,X10] :
( element(sK6(X10,X11,X12),X10)
| in(sK6(X10,X11,X12),X12)
| sP0(X10,X11,X12)
| ~ in(X11,sK6(X10,X11,X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_347])]) ).
fof(f1769,plain,
( ! [X10,X11,X12] :
( element(sK6(X10,X11,X12),X10)
| in(sK6(X10,X11,X12),X12)
| sP0(X10,X11,X12)
| ~ in(X11,sK6(X10,X11,X12)) )
| ~ spl20_75
| ~ spl20_187 ),
inference(resolution,[],[f1666,f654]) ).
fof(f4962,plain,
( spl20_346
| ~ spl20_75
| ~ spl20_187 ),
inference(avatar_split_clause,[],[f1759,f1665,f653,f4960]) ).
fof(f4960,plain,
( spl20_346
<=> ! [X13,X12,X14] :
( element(sK6(X12,X13,X14),X12)
| in(sK6(X12,X13,X14),X13)
| sP0(X12,X13,X14)
| ~ in(X14,sK6(X12,X13,X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_346])]) ).
fof(f1759,plain,
( ! [X14,X12,X13] :
( element(sK6(X12,X13,X14),X12)
| in(sK6(X12,X13,X14),X13)
| sP0(X12,X13,X14)
| ~ in(X14,sK6(X12,X13,X14)) )
| ~ spl20_75
| ~ spl20_187 ),
inference(resolution,[],[f1666,f654]) ).
fof(f4958,plain,
( spl20_345
| ~ spl20_75
| ~ spl20_185 ),
inference(avatar_split_clause,[],[f1724,f1657,f653,f4956]) ).
fof(f4956,plain,
( spl20_345
<=> ! [X12,X11,X10] :
( element(sK6(X10,X11,X12),X11)
| in(sK6(X10,X11,X12),X12)
| sP0(X10,X11,X12)
| ~ in(X10,sK6(X10,X11,X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_345])]) ).
fof(f1724,plain,
( ! [X10,X11,X12] :
( element(sK6(X10,X11,X12),X11)
| in(sK6(X10,X11,X12),X12)
| sP0(X10,X11,X12)
| ~ in(X10,sK6(X10,X11,X12)) )
| ~ spl20_75
| ~ spl20_185 ),
inference(resolution,[],[f1658,f654]) ).
fof(f4954,plain,
( spl20_344
| ~ spl20_76
| ~ spl20_185 ),
inference(avatar_split_clause,[],[f1723,f1657,f657,f4952]) ).
fof(f1723,plain,
( ! [X8,X9,X7] :
( element(sK6(X7,X8,X9),X8)
| in(sK6(X7,X8,X9),X9)
| sP0(X7,X8,X9)
| element(sK6(X7,X8,X9),X7) )
| ~ spl20_76
| ~ spl20_185 ),
inference(resolution,[],[f1658,f658]) ).
fof(f4950,plain,
( spl20_343
| ~ spl20_75
| ~ spl20_185 ),
inference(avatar_split_clause,[],[f1714,f1657,f653,f4948]) ).
fof(f4948,plain,
( spl20_343
<=> ! [X13,X12,X14] :
( element(sK6(X12,X13,X14),X13)
| in(sK6(X12,X13,X14),X12)
| sP0(X12,X13,X14)
| ~ in(X14,sK6(X12,X13,X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_343])]) ).
fof(f1714,plain,
( ! [X14,X12,X13] :
( element(sK6(X12,X13,X14),X13)
| in(sK6(X12,X13,X14),X12)
| sP0(X12,X13,X14)
| ~ in(X14,sK6(X12,X13,X14)) )
| ~ spl20_75
| ~ spl20_185 ),
inference(resolution,[],[f1658,f654]) ).
fof(f4946,plain,
( spl20_342
| ~ spl20_75
| ~ spl20_183 ),
inference(avatar_split_clause,[],[f1690,f1649,f653,f4944]) ).
fof(f4944,plain,
( spl20_342
<=> ! [X11,X12,X10] :
( element(sK6(X10,X11,X12),X12)
| in(sK6(X10,X11,X12),X11)
| sP0(X10,X11,X12)
| ~ in(X10,sK6(X10,X11,X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_342])]) ).
fof(f1690,plain,
( ! [X10,X11,X12] :
( element(sK6(X10,X11,X12),X12)
| in(sK6(X10,X11,X12),X11)
| sP0(X10,X11,X12)
| ~ in(X10,sK6(X10,X11,X12)) )
| ~ spl20_75
| ~ spl20_183 ),
inference(resolution,[],[f1650,f654]) ).
fof(f4942,plain,
( spl20_341
| ~ spl20_76
| ~ spl20_183 ),
inference(avatar_split_clause,[],[f1689,f1649,f657,f4940]) ).
fof(f1689,plain,
( ! [X8,X9,X7] :
( element(sK6(X7,X8,X9),X9)
| in(sK6(X7,X8,X9),X8)
| sP0(X7,X8,X9)
| element(sK6(X7,X8,X9),X7) )
| ~ spl20_76
| ~ spl20_183 ),
inference(resolution,[],[f1650,f658]) ).
fof(f4938,plain,
( spl20_340
| ~ spl20_75
| ~ spl20_183 ),
inference(avatar_split_clause,[],[f1680,f1649,f653,f4936]) ).
fof(f4936,plain,
( spl20_340
<=> ! [X11,X12,X10] :
( element(sK6(X10,X11,X12),X12)
| in(sK6(X10,X11,X12),X10)
| sP0(X10,X11,X12)
| ~ in(X11,sK6(X10,X11,X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_340])]) ).
fof(f1680,plain,
( ! [X10,X11,X12] :
( element(sK6(X10,X11,X12),X12)
| in(sK6(X10,X11,X12),X10)
| sP0(X10,X11,X12)
| ~ in(X11,sK6(X10,X11,X12)) )
| ~ spl20_75
| ~ spl20_183 ),
inference(resolution,[],[f1650,f654]) ).
fof(f4934,plain,
( spl20_339
| ~ spl20_76
| ~ spl20_183 ),
inference(avatar_split_clause,[],[f1679,f1649,f657,f4932]) ).
fof(f1679,plain,
( ! [X8,X9,X7] :
( element(sK6(X7,X8,X9),X9)
| in(sK6(X7,X8,X9),X7)
| sP0(X7,X8,X9)
| element(sK6(X7,X8,X9),X8) )
| ~ spl20_76
| ~ spl20_183 ),
inference(resolution,[],[f1650,f658]) ).
fof(f4930,plain,
( spl20_338
| ~ spl20_153
| ~ spl20_177 ),
inference(avatar_split_clause,[],[f1549,f1462,f1230,f4928]) ).
fof(f1549,plain,
( ! [X10,X11] :
( in(sK6(singleton(X10),singleton(X10),X11),X11)
| sP0(singleton(X10),singleton(X10),X11)
| sK6(singleton(X10),singleton(X10),X11) = X10 )
| ~ spl20_153
| ~ spl20_177 ),
inference(resolution,[],[f1463,f1231]) ).
fof(f4926,plain,
( spl20_337
| ~ spl20_175
| ~ spl20_243 ),
inference(avatar_split_clause,[],[f4379,f2671,f1436,f4923]) ).
fof(f4379,plain,
( element(sK2,sK2)
| ~ spl20_175
| ~ spl20_243 ),
inference(resolution,[],[f2673,f1437]) ).
fof(f4921,plain,
( spl20_336
| ~ spl20_157
| ~ spl20_177 ),
inference(avatar_split_clause,[],[f1541,f1462,f1267,f4919]) ).
fof(f1541,plain,
( ! [X16,X15] :
( in(sK6(X15,X15,sK4(powerset(X16))),X15)
| sP0(X15,X15,sK4(powerset(X16)))
| element(sK6(X15,X15,sK4(powerset(X16))),X16) )
| ~ spl20_157
| ~ spl20_177 ),
inference(resolution,[],[f1463,f1268]) ).
fof(f4917,plain,
( spl20_335
| ~ spl20_157
| ~ spl20_174 ),
inference(avatar_split_clause,[],[f1518,f1432,f1267,f4915]) ).
fof(f1518,plain,
( ! [X14,X13] :
( in(sK6(X13,sK4(powerset(X14)),X13),X13)
| sP0(X13,sK4(powerset(X14)),X13)
| element(sK6(X13,sK4(powerset(X14)),X13),X14) )
| ~ spl20_157
| ~ spl20_174 ),
inference(resolution,[],[f1433,f1268]) ).
fof(f4913,plain,
( spl20_334
| ~ spl20_157
| ~ spl20_173 ),
inference(avatar_split_clause,[],[f1505,f1428,f1267,f4911]) ).
fof(f1505,plain,
( ! [X14,X13] :
( in(sK6(sK4(powerset(X13)),X14,X14),X14)
| sP0(sK4(powerset(X13)),X14,X14)
| element(sK6(sK4(powerset(X13)),X14,X14),X13) )
| ~ spl20_157
| ~ spl20_173 ),
inference(resolution,[],[f1429,f1268]) ).
fof(f4909,plain,
( spl20_333
| ~ spl20_97
| ~ spl20_172 ),
inference(avatar_split_clause,[],[f1485,f1424,f846,f4907]) ).
fof(f4907,plain,
( spl20_333
<=> ! [X6,X7] :
( singleton(X6) = X7
| sK5(X6,X7) = X6
| ~ epsilon_transitive(X7)
| ordinal_subset(sK5(X6,X7),X7)
| ~ ordinal(X7)
| ~ ordinal(sK5(X6,X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_333])]) ).
fof(f1424,plain,
( spl20_172
<=> ! [X0,X1] :
( sK5(X0,X1) = X0
| singleton(X0) = X1
| subset(sK5(X0,X1),X1)
| ~ epsilon_transitive(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_172])]) ).
fof(f1485,plain,
( ! [X6,X7] :
( singleton(X6) = X7
| sK5(X6,X7) = X6
| ~ epsilon_transitive(X7)
| ordinal_subset(sK5(X6,X7),X7)
| ~ ordinal(X7)
| ~ ordinal(sK5(X6,X7)) )
| ~ spl20_97
| ~ spl20_172 ),
inference(resolution,[],[f1425,f847]) ).
fof(f1425,plain,
( ! [X0,X1] :
( subset(sK5(X0,X1),X1)
| singleton(X0) = X1
| sK5(X0,X1) = X0
| ~ epsilon_transitive(X1) )
| ~ spl20_172 ),
inference(avatar_component_clause,[],[f1424]) ).
fof(f4905,plain,
( spl20_332
| ~ spl20_108
| ~ spl20_163 ),
inference(avatar_split_clause,[],[f1329,f1316,f923,f4903]) ).
fof(f4903,plain,
( spl20_332
<=> ! [X13,X12,X14] :
( empty(powerset(X12))
| ~ subset(sK6(X13,X14,powerset(X12)),X12)
| ~ in(sK6(X13,X14,powerset(X12)),X14)
| sP0(X13,X14,powerset(X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_332])]) ).
fof(f1329,plain,
( ! [X14,X12,X13] :
( empty(powerset(X12))
| ~ subset(sK6(X13,X14,powerset(X12)),X12)
| ~ in(sK6(X13,X14,powerset(X12)),X14)
| sP0(X13,X14,powerset(X12)) )
| ~ spl20_108
| ~ spl20_163 ),
inference(resolution,[],[f1317,f924]) ).
fof(f4901,plain,
( spl20_331
| ~ spl20_109
| ~ spl20_163 ),
inference(avatar_split_clause,[],[f1328,f1316,f927,f4899]) ).
fof(f4899,plain,
( spl20_331
<=> ! [X9,X11,X10] :
( empty(powerset(X9))
| ~ subset(sK6(X10,X11,powerset(X9)),X9)
| ~ in(sK6(X10,X11,powerset(X9)),X10)
| sP0(X10,X11,powerset(X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_331])]) ).
fof(f1328,plain,
( ! [X10,X11,X9] :
( empty(powerset(X9))
| ~ subset(sK6(X10,X11,powerset(X9)),X9)
| ~ in(sK6(X10,X11,powerset(X9)),X10)
| sP0(X10,X11,powerset(X9)) )
| ~ spl20_109
| ~ spl20_163 ),
inference(resolution,[],[f1317,f928]) ).
fof(f4728,plain,
( spl20_330
| ~ spl20_153
| ~ spl20_180 ),
inference(avatar_split_clause,[],[f1632,f1565,f1230,f4726]) ).
fof(f1632,plain,
( ! [X18,X16,X17] :
( in(sK6(X16,singleton(X17),X18),X18)
| sP0(X16,singleton(X17),X18)
| ~ empty(X16)
| sK6(X16,singleton(X17),X18) = X17 )
| ~ spl20_153
| ~ spl20_180 ),
inference(resolution,[],[f1566,f1231]) ).
fof(f4724,plain,
( spl20_329
| ~ spl20_153
| ~ spl20_180 ),
inference(avatar_split_clause,[],[f1622,f1565,f1230,f4722]) ).
fof(f1622,plain,
( ! [X18,X19,X20] :
( in(sK6(X18,X19,singleton(X20)),X19)
| sP0(X18,X19,singleton(X20))
| ~ empty(X18)
| sK6(X18,X19,singleton(X20)) = X20 )
| ~ spl20_153
| ~ spl20_180 ),
inference(resolution,[],[f1566,f1231]) ).
fof(f4720,plain,
( spl20_328
| ~ spl20_153
| ~ spl20_179 ),
inference(avatar_split_clause,[],[f1609,f1561,f1230,f4718]) ).
fof(f1609,plain,
( ! [X18,X16,X17] :
( in(sK6(singleton(X16),X17,X18),X18)
| sP0(singleton(X16),X17,X18)
| ~ empty(X17)
| sK6(singleton(X16),X17,X18) = X16 )
| ~ spl20_153
| ~ spl20_179 ),
inference(resolution,[],[f1562,f1231]) ).
fof(f4716,plain,
( spl20_327
| ~ spl20_153
| ~ spl20_179 ),
inference(avatar_split_clause,[],[f1599,f1561,f1230,f4714]) ).
fof(f1599,plain,
( ! [X18,X19,X20] :
( in(sK6(X18,X19,singleton(X20)),X18)
| sP0(X18,X19,singleton(X20))
| ~ empty(X19)
| sK6(X18,X19,singleton(X20)) = X20 )
| ~ spl20_153
| ~ spl20_179 ),
inference(resolution,[],[f1562,f1231]) ).
fof(f4712,plain,
( spl20_326
| ~ spl20_153
| ~ spl20_178 ),
inference(avatar_split_clause,[],[f1584,f1557,f1230,f4710]) ).
fof(f1584,plain,
( ! [X18,X16,X17] :
( in(sK6(singleton(X16),X17,X18),X17)
| sP0(singleton(X16),X17,X18)
| ~ empty(X18)
| sK6(singleton(X16),X17,X18) = X16 )
| ~ spl20_153
| ~ spl20_178 ),
inference(resolution,[],[f1558,f1231]) ).
fof(f4708,plain,
( spl20_325
| ~ spl20_153
| ~ spl20_178 ),
inference(avatar_split_clause,[],[f1574,f1557,f1230,f4706]) ).
fof(f1574,plain,
( ! [X18,X16,X17] :
( in(sK6(X16,singleton(X17),X18),X16)
| sP0(X16,singleton(X17),X18)
| ~ empty(X18)
| sK6(X16,singleton(X17),X18) = X17 )
| ~ spl20_153
| ~ spl20_178 ),
inference(resolution,[],[f1558,f1231]) ).
fof(f4701,plain,
( spl20_324
| ~ spl20_91
| ~ spl20_172 ),
inference(avatar_split_clause,[],[f1486,f1424,f811,f4699]) ).
fof(f4699,plain,
( spl20_324
<=> ! [X9,X8] :
( singleton(X8) = X9
| sK5(X8,X9) = X8
| ~ epsilon_transitive(X9)
| sK5(X8,X9) = X9
| ~ subset(X9,sK5(X8,X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_324])]) ).
fof(f1486,plain,
( ! [X8,X9] :
( singleton(X8) = X9
| sK5(X8,X9) = X8
| ~ epsilon_transitive(X9)
| sK5(X8,X9) = X9
| ~ subset(X9,sK5(X8,X9)) )
| ~ spl20_91
| ~ spl20_172 ),
inference(resolution,[],[f1425,f812]) ).
fof(f4697,plain,
( spl20_323
| ~ spl20_157
| ~ spl20_170 ),
inference(avatar_split_clause,[],[f1412,f1403,f1267,f4695]) ).
fof(f1412,plain,
( ! [X11,X12] :
( sK4(powerset(X11)) = X12
| ~ ordinal(sK4(powerset(X11)))
| ~ ordinal(X12)
| subset(sK4(powerset(X11)),X12)
| ~ epsilon_transitive(X12)
| element(X12,X11) )
| ~ spl20_157
| ~ spl20_170 ),
inference(resolution,[],[f1404,f1268]) ).
fof(f4417,plain,
( spl20_322
| ~ spl20_88
| ~ spl20_180 ),
inference(avatar_split_clause,[],[f1628,f1565,f772,f4415]) ).
fof(f1628,plain,
( ! [X6,X4,X5] :
( in(sK6(X4,X5,X6),X6)
| sP0(X4,X5,X6)
| ~ empty(X4)
| subset(sK6(X4,X5,X6),X5)
| ~ epsilon_transitive(X5) )
| ~ spl20_88
| ~ spl20_180 ),
inference(resolution,[],[f1566,f773]) ).
fof(f4413,plain,
( spl20_321
| ~ spl20_88
| ~ spl20_180 ),
inference(avatar_split_clause,[],[f1618,f1565,f772,f4411]) ).
fof(f1618,plain,
( ! [X8,X6,X7] :
( in(sK6(X6,X7,X8),X7)
| sP0(X6,X7,X8)
| ~ empty(X6)
| subset(sK6(X6,X7,X8),X8)
| ~ epsilon_transitive(X8) )
| ~ spl20_88
| ~ spl20_180 ),
inference(resolution,[],[f1566,f773]) ).
fof(f4409,plain,
( spl20_320
| ~ spl20_88
| ~ spl20_179 ),
inference(avatar_split_clause,[],[f1605,f1561,f772,f4407]) ).
fof(f1605,plain,
( ! [X6,X4,X5] :
( in(sK6(X4,X5,X6),X6)
| sP0(X4,X5,X6)
| ~ empty(X5)
| subset(sK6(X4,X5,X6),X4)
| ~ epsilon_transitive(X4) )
| ~ spl20_88
| ~ spl20_179 ),
inference(resolution,[],[f1562,f773]) ).
fof(f4405,plain,
( spl20_319
| ~ spl20_88
| ~ spl20_179 ),
inference(avatar_split_clause,[],[f1595,f1561,f772,f4403]) ).
fof(f1595,plain,
( ! [X8,X6,X7] :
( in(sK6(X6,X7,X8),X6)
| sP0(X6,X7,X8)
| ~ empty(X7)
| subset(sK6(X6,X7,X8),X8)
| ~ epsilon_transitive(X8) )
| ~ spl20_88
| ~ spl20_179 ),
inference(resolution,[],[f1562,f773]) ).
fof(f4401,plain,
( spl20_318
| ~ spl20_88
| ~ spl20_178 ),
inference(avatar_split_clause,[],[f1580,f1557,f772,f4399]) ).
fof(f1580,plain,
( ! [X6,X4,X5] :
( in(sK6(X4,X5,X6),X5)
| sP0(X4,X5,X6)
| ~ empty(X6)
| subset(sK6(X4,X5,X6),X4)
| ~ epsilon_transitive(X4) )
| ~ spl20_88
| ~ spl20_178 ),
inference(resolution,[],[f1558,f773]) ).
fof(f4397,plain,
( spl20_317
| ~ spl20_88
| ~ spl20_178 ),
inference(avatar_split_clause,[],[f1570,f1557,f772,f4395]) ).
fof(f1570,plain,
( ! [X6,X4,X5] :
( in(sK6(X4,X5,X6),X4)
| sP0(X4,X5,X6)
| ~ empty(X6)
| subset(sK6(X4,X5,X6),X5)
| ~ epsilon_transitive(X5) )
| ~ spl20_88
| ~ spl20_178 ),
inference(resolution,[],[f1558,f773]) ).
fof(f4393,plain,
( spl20_316
| ~ spl20_151
| ~ spl20_177 ),
inference(avatar_split_clause,[],[f1552,f1462,f1221,f4391]) ).
fof(f1552,plain,
( ! [X16,X15] :
( in(sK6(sK4(powerset(X15)),sK4(powerset(X15)),X16),X16)
| sP0(sK4(powerset(X15)),sK4(powerset(X15)),X16)
| ~ empty(X15) )
| ~ spl20_151
| ~ spl20_177 ),
inference(resolution,[],[f1463,f1222]) ).
fof(f4389,plain,
( spl20_315
| ~ spl20_151
| ~ spl20_170 ),
inference(avatar_split_clause,[],[f1413,f1403,f1221,f4387]) ).
fof(f1413,plain,
( ! [X14,X13] :
( sK4(powerset(X13)) = X14
| ~ ordinal(sK4(powerset(X13)))
| ~ ordinal(X14)
| subset(sK4(powerset(X13)),X14)
| ~ epsilon_transitive(X14)
| ~ empty(X13) )
| ~ spl20_151
| ~ spl20_170 ),
inference(resolution,[],[f1404,f1222]) ).
fof(f4378,plain,
( spl20_314
| ~ spl20_100
| ~ spl20_168 ),
inference(avatar_split_clause,[],[f1394,f1387,f858,f4376]) ).
fof(f1387,plain,
( spl20_168
<=> ! [X2,X3] :
( sK5(X2,X3) = X2
| singleton(X2) = X3
| element(sK5(X2,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_168])]) ).
fof(f1394,plain,
( ! [X2,X0,X1] :
( singleton(X0) = powerset(X1)
| sK5(X0,powerset(X1)) = X0
| element(X2,X1)
| ~ in(X2,sK5(X0,powerset(X1))) )
| ~ spl20_100
| ~ spl20_168 ),
inference(resolution,[],[f1388,f859]) ).
fof(f1388,plain,
( ! [X2,X3] :
( element(sK5(X2,X3),X3)
| singleton(X2) = X3
| sK5(X2,X3) = X2 )
| ~ spl20_168 ),
inference(avatar_component_clause,[],[f1387]) ).
fof(f4374,plain,
( spl20_313
| ~ spl20_107
| ~ spl20_157 ),
inference(avatar_split_clause,[],[f1278,f1267,f915,f4372]) ).
fof(f1278,plain,
( ! [X6,X7] :
( element(sK5(X6,sK4(powerset(X7))),X7)
| sK5(X6,sK4(powerset(X7))) = X6
| singleton(X6) = sK4(powerset(X7)) )
| ~ spl20_107
| ~ spl20_157 ),
inference(resolution,[],[f1268,f916]) ).
fof(f4164,plain,
( spl20_312
| ~ spl20_130
| ~ spl20_197 ),
inference(avatar_split_clause,[],[f2133,f2040,f1089,f4161]) ).
fof(f1089,plain,
( spl20_130
<=> ! [X0] : element(X0,succ(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_130])]) ).
fof(f2133,plain,
( element(sK2,sK1)
| ~ spl20_130
| ~ spl20_197 ),
inference(superposition,[],[f1090,f2042]) ).
fof(f1090,plain,
( ! [X0] : element(X0,succ(X0))
| ~ spl20_130 ),
inference(avatar_component_clause,[],[f1089]) ).
fof(f4128,plain,
( spl20_311
| ~ spl20_153
| ~ spl20_177 ),
inference(avatar_split_clause,[],[f1539,f1462,f1230,f4126]) ).
fof(f1539,plain,
( ! [X12,X13] :
( in(sK6(X12,X12,singleton(X13)),X12)
| sP0(X12,X12,singleton(X13))
| sK6(X12,X12,singleton(X13)) = X13 )
| ~ spl20_153
| ~ spl20_177 ),
inference(resolution,[],[f1463,f1231]) ).
fof(f4124,plain,
( spl20_310
| ~ spl20_153
| ~ spl20_174 ),
inference(avatar_split_clause,[],[f1516,f1432,f1230,f4122]) ).
fof(f4122,plain,
( spl20_310
<=> ! [X11,X10] :
( in(sK6(X10,singleton(X11),X10),X10)
| sP0(X10,singleton(X11),X10)
| sK6(X10,singleton(X11),X10) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_310])]) ).
fof(f1516,plain,
( ! [X10,X11] :
( in(sK6(X10,singleton(X11),X10),X10)
| sP0(X10,singleton(X11),X10)
| sK6(X10,singleton(X11),X10) = X11 )
| ~ spl20_153
| ~ spl20_174 ),
inference(resolution,[],[f1433,f1231]) ).
fof(f4120,plain,
( spl20_309
| ~ spl20_153
| ~ spl20_173 ),
inference(avatar_split_clause,[],[f1503,f1428,f1230,f4118]) ).
fof(f4118,plain,
( spl20_309
<=> ! [X11,X10] :
( in(sK6(singleton(X10),X11,X11),X11)
| sP0(singleton(X10),X11,X11)
| sK6(singleton(X10),X11,X11) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_309])]) ).
fof(f1503,plain,
( ! [X10,X11] :
( in(sK6(singleton(X10),X11,X11),X11)
| sP0(singleton(X10),X11,X11)
| sK6(singleton(X10),X11,X11) = X10 )
| ~ spl20_153
| ~ spl20_173 ),
inference(resolution,[],[f1429,f1231]) ).
fof(f4116,plain,
( spl20_308
| ~ spl20_160
| ~ spl20_172 ),
inference(avatar_split_clause,[],[f1483,f1424,f1291,f4114]) ).
fof(f1483,plain,
( ! [X2,X0,X1] :
( singleton(X0) = X1
| sK5(X0,X1) = X0
| ~ epsilon_transitive(X1)
| ~ in(X2,sK5(X0,X1))
| element(X2,X1) )
| ~ spl20_160
| ~ spl20_172 ),
inference(resolution,[],[f1425,f1292]) ).
fof(f4112,plain,
( spl20_307
| ~ spl20_94
| ~ spl20_168 ),
inference(avatar_split_clause,[],[f1395,f1387,f823,f4110]) ).
fof(f1395,plain,
( ! [X3,X4,X5] :
( powerset(X4) = singleton(X3)
| sK5(X3,powerset(X4)) = X3
| ~ empty(X4)
| ~ in(X5,sK5(X3,powerset(X4))) )
| ~ spl20_94
| ~ spl20_168 ),
inference(resolution,[],[f1388,f824]) ).
fof(f4108,plain,
( spl20_306
| ~ spl20_157
| ~ spl20_167 ),
inference(avatar_split_clause,[],[f1380,f1371,f1267,f4106]) ).
fof(f1380,plain,
( ! [X11,X12] :
( sK4(powerset(X11)) = X12
| ~ ordinal(sK4(powerset(X11)))
| ~ ordinal(X12)
| element(sK4(powerset(X11)),X12)
| element(X12,X11) )
| ~ spl20_157
| ~ spl20_167 ),
inference(resolution,[],[f1372,f1268]) ).
fof(f4104,plain,
( spl20_305
| ~ spl20_104
| ~ spl20_157 ),
inference(avatar_split_clause,[],[f1274,f1267,f890,f4102]) ).
fof(f1274,plain,
( ! [X0,X1] :
( element(X0,X1)
| in(sK4(powerset(X1)),X0)
| sK4(powerset(X1)) = X0
| ~ ordinal(sK4(powerset(X1)))
| ~ ordinal(X0) )
| ~ spl20_104
| ~ spl20_157 ),
inference(resolution,[],[f1268,f891]) ).
fof(f4072,plain,
( ~ spl20_304
| ~ spl20_129
| ~ spl20_197 ),
inference(avatar_split_clause,[],[f2132,f2040,f1085,f4069]) ).
fof(f2132,plain,
( ~ in(sK1,sK2)
| ~ spl20_129
| ~ spl20_197 ),
inference(superposition,[],[f1086,f2042]) ).
fof(f3677,plain,
( ~ spl20_181
| ~ spl20_49
| ~ spl20_197 ),
inference(avatar_split_clause,[],[f2126,f2040,f499,f1640]) ).
fof(f2126,plain,
( ~ empty(sK1)
| ~ spl20_49
| ~ spl20_197 ),
inference(superposition,[],[f500,f2042]) ).
fof(f3639,plain,
( spl20_303
| ~ spl20_151
| ~ spl20_180 ),
inference(avatar_split_clause,[],[f1635,f1565,f1221,f3637]) ).
fof(f1635,plain,
( ! [X26,X24,X25] :
( in(sK6(X24,sK4(powerset(X25)),X26),X26)
| sP0(X24,sK4(powerset(X25)),X26)
| ~ empty(X24)
| ~ empty(X25) )
| ~ spl20_151
| ~ spl20_180 ),
inference(resolution,[],[f1566,f1222]) ).
fof(f3635,plain,
( spl20_302
| ~ spl20_75
| ~ spl20_180 ),
inference(avatar_split_clause,[],[f1630,f1565,f653,f3633]) ).
fof(f3633,plain,
( spl20_302
<=> ! [X11,X12,X10] :
( in(sK6(X10,X11,X12),X12)
| sP0(X10,X11,X12)
| ~ empty(X10)
| ~ in(X11,sK6(X10,X11,X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_302])]) ).
fof(f1630,plain,
( ! [X10,X11,X12] :
( in(sK6(X10,X11,X12),X12)
| sP0(X10,X11,X12)
| ~ empty(X10)
| ~ in(X11,sK6(X10,X11,X12)) )
| ~ spl20_75
| ~ spl20_180 ),
inference(resolution,[],[f1566,f654]) ).
fof(f3631,plain,
( spl20_301
| ~ spl20_76
| ~ spl20_180 ),
inference(avatar_split_clause,[],[f1629,f1565,f657,f3629]) ).
fof(f1629,plain,
( ! [X8,X9,X7] :
( in(sK6(X7,X8,X9),X9)
| sP0(X7,X8,X9)
| ~ empty(X7)
| element(sK6(X7,X8,X9),X8) )
| ~ spl20_76
| ~ spl20_180 ),
inference(resolution,[],[f1566,f658]) ).
fof(f3627,plain,
( spl20_300
| ~ spl20_151
| ~ spl20_180 ),
inference(avatar_split_clause,[],[f1625,f1565,f1221,f3625]) ).
fof(f1625,plain,
( ! [X28,X26,X27] :
( in(sK6(X26,X27,sK4(powerset(X28))),X27)
| sP0(X26,X27,sK4(powerset(X28)))
| ~ empty(X26)
| ~ empty(X28) )
| ~ spl20_151
| ~ spl20_180 ),
inference(resolution,[],[f1566,f1222]) ).
fof(f3623,plain,
( spl20_299
| ~ spl20_75
| ~ spl20_180 ),
inference(avatar_split_clause,[],[f1620,f1565,f653,f3621]) ).
fof(f3621,plain,
( spl20_299
<=> ! [X13,X12,X14] :
( in(sK6(X12,X13,X14),X13)
| sP0(X12,X13,X14)
| ~ empty(X12)
| ~ in(X14,sK6(X12,X13,X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_299])]) ).
fof(f1620,plain,
( ! [X14,X12,X13] :
( in(sK6(X12,X13,X14),X13)
| sP0(X12,X13,X14)
| ~ empty(X12)
| ~ in(X14,sK6(X12,X13,X14)) )
| ~ spl20_75
| ~ spl20_180 ),
inference(resolution,[],[f1566,f654]) ).
fof(f3619,plain,
( spl20_298
| ~ spl20_76
| ~ spl20_180 ),
inference(avatar_split_clause,[],[f1619,f1565,f657,f3617]) ).
fof(f1619,plain,
( ! [X10,X11,X9] :
( in(sK6(X9,X10,X11),X10)
| sP0(X9,X10,X11)
| ~ empty(X9)
| element(sK6(X9,X10,X11),X11) )
| ~ spl20_76
| ~ spl20_180 ),
inference(resolution,[],[f1566,f658]) ).
fof(f3593,plain,
( spl20_297
| ~ spl20_66
| ~ spl20_125
| ~ spl20_181 ),
inference(avatar_split_clause,[],[f1747,f1640,f1044,f605,f3590]) ).
fof(f1747,plain,
( sK1 = sK8
| ~ spl20_66
| ~ spl20_125
| ~ spl20_181 ),
inference(forward_demodulation,[],[f1743,f1046]) ).
fof(f1743,plain,
( empty_set = sK1
| ~ spl20_66
| ~ spl20_181 ),
inference(resolution,[],[f1642,f606]) ).
fof(f1642,plain,
( empty(sK1)
| ~ spl20_181 ),
inference(avatar_component_clause,[],[f1640]) ).
fof(f3588,plain,
( spl20_296
| ~ spl20_151
| ~ spl20_179 ),
inference(avatar_split_clause,[],[f1612,f1561,f1221,f3586]) ).
fof(f1612,plain,
( ! [X26,X24,X25] :
( in(sK6(sK4(powerset(X24)),X25,X26),X26)
| sP0(sK4(powerset(X24)),X25,X26)
| ~ empty(X25)
| ~ empty(X24) )
| ~ spl20_151
| ~ spl20_179 ),
inference(resolution,[],[f1562,f1222]) ).
fof(f3584,plain,
( spl20_295
| ~ spl20_75
| ~ spl20_179 ),
inference(avatar_split_clause,[],[f1607,f1561,f653,f3582]) ).
fof(f3582,plain,
( spl20_295
<=> ! [X11,X12,X10] :
( in(sK6(X10,X11,X12),X12)
| sP0(X10,X11,X12)
| ~ empty(X11)
| ~ in(X10,sK6(X10,X11,X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_295])]) ).
fof(f1607,plain,
( ! [X10,X11,X12] :
( in(sK6(X10,X11,X12),X12)
| sP0(X10,X11,X12)
| ~ empty(X11)
| ~ in(X10,sK6(X10,X11,X12)) )
| ~ spl20_75
| ~ spl20_179 ),
inference(resolution,[],[f1562,f654]) ).
fof(f3580,plain,
( spl20_294
| ~ spl20_76
| ~ spl20_179 ),
inference(avatar_split_clause,[],[f1606,f1561,f657,f3578]) ).
fof(f1606,plain,
( ! [X8,X9,X7] :
( in(sK6(X7,X8,X9),X9)
| sP0(X7,X8,X9)
| ~ empty(X8)
| element(sK6(X7,X8,X9),X7) )
| ~ spl20_76
| ~ spl20_179 ),
inference(resolution,[],[f1562,f658]) ).
fof(f3576,plain,
( spl20_293
| ~ spl20_151
| ~ spl20_179 ),
inference(avatar_split_clause,[],[f1602,f1561,f1221,f3574]) ).
fof(f1602,plain,
( ! [X28,X26,X27] :
( in(sK6(X26,X27,sK4(powerset(X28))),X26)
| sP0(X26,X27,sK4(powerset(X28)))
| ~ empty(X27)
| ~ empty(X28) )
| ~ spl20_151
| ~ spl20_179 ),
inference(resolution,[],[f1562,f1222]) ).
fof(f3572,plain,
( spl20_292
| ~ spl20_75
| ~ spl20_179 ),
inference(avatar_split_clause,[],[f1597,f1561,f653,f3570]) ).
fof(f3570,plain,
( spl20_292
<=> ! [X13,X12,X14] :
( in(sK6(X12,X13,X14),X12)
| sP0(X12,X13,X14)
| ~ empty(X13)
| ~ in(X14,sK6(X12,X13,X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_292])]) ).
fof(f1597,plain,
( ! [X14,X12,X13] :
( in(sK6(X12,X13,X14),X12)
| sP0(X12,X13,X14)
| ~ empty(X13)
| ~ in(X14,sK6(X12,X13,X14)) )
| ~ spl20_75
| ~ spl20_179 ),
inference(resolution,[],[f1562,f654]) ).
fof(f3568,plain,
( spl20_291
| ~ spl20_76
| ~ spl20_179 ),
inference(avatar_split_clause,[],[f1596,f1561,f657,f3566]) ).
fof(f1596,plain,
( ! [X10,X11,X9] :
( in(sK6(X9,X10,X11),X9)
| sP0(X9,X10,X11)
| ~ empty(X10)
| element(sK6(X9,X10,X11),X11) )
| ~ spl20_76
| ~ spl20_179 ),
inference(resolution,[],[f1562,f658]) ).
fof(f3564,plain,
( spl20_290
| ~ spl20_151
| ~ spl20_178 ),
inference(avatar_split_clause,[],[f1587,f1557,f1221,f3562]) ).
fof(f1587,plain,
( ! [X26,X24,X25] :
( in(sK6(sK4(powerset(X24)),X25,X26),X25)
| sP0(sK4(powerset(X24)),X25,X26)
| ~ empty(X26)
| ~ empty(X24) )
| ~ spl20_151
| ~ spl20_178 ),
inference(resolution,[],[f1558,f1222]) ).
fof(f3560,plain,
( spl20_289
| ~ spl20_75
| ~ spl20_178 ),
inference(avatar_split_clause,[],[f1582,f1557,f653,f3558]) ).
fof(f3558,plain,
( spl20_289
<=> ! [X12,X11,X10] :
( in(sK6(X10,X11,X12),X11)
| sP0(X10,X11,X12)
| ~ empty(X12)
| ~ in(X10,sK6(X10,X11,X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_289])]) ).
fof(f1582,plain,
( ! [X10,X11,X12] :
( in(sK6(X10,X11,X12),X11)
| sP0(X10,X11,X12)
| ~ empty(X12)
| ~ in(X10,sK6(X10,X11,X12)) )
| ~ spl20_75
| ~ spl20_178 ),
inference(resolution,[],[f1558,f654]) ).
fof(f3556,plain,
( spl20_288
| ~ spl20_76
| ~ spl20_178 ),
inference(avatar_split_clause,[],[f1581,f1557,f657,f3554]) ).
fof(f1581,plain,
( ! [X8,X9,X7] :
( in(sK6(X7,X8,X9),X8)
| sP0(X7,X8,X9)
| ~ empty(X9)
| element(sK6(X7,X8,X9),X7) )
| ~ spl20_76
| ~ spl20_178 ),
inference(resolution,[],[f1558,f658]) ).
fof(f3552,plain,
( spl20_287
| ~ spl20_151
| ~ spl20_178 ),
inference(avatar_split_clause,[],[f1577,f1557,f1221,f3550]) ).
fof(f1577,plain,
( ! [X26,X24,X25] :
( in(sK6(X24,sK4(powerset(X25)),X26),X24)
| sP0(X24,sK4(powerset(X25)),X26)
| ~ empty(X26)
| ~ empty(X25) )
| ~ spl20_151
| ~ spl20_178 ),
inference(resolution,[],[f1558,f1222]) ).
fof(f3548,plain,
( spl20_286
| ~ spl20_75
| ~ spl20_178 ),
inference(avatar_split_clause,[],[f1572,f1557,f653,f3546]) ).
fof(f3546,plain,
( spl20_286
<=> ! [X11,X12,X10] :
( in(sK6(X10,X11,X12),X10)
| sP0(X10,X11,X12)
| ~ empty(X12)
| ~ in(X11,sK6(X10,X11,X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_286])]) ).
fof(f1572,plain,
( ! [X10,X11,X12] :
( in(sK6(X10,X11,X12),X10)
| sP0(X10,X11,X12)
| ~ empty(X12)
| ~ in(X11,sK6(X10,X11,X12)) )
| ~ spl20_75
| ~ spl20_178 ),
inference(resolution,[],[f1558,f654]) ).
fof(f3544,plain,
( spl20_285
| ~ spl20_76
| ~ spl20_178 ),
inference(avatar_split_clause,[],[f1571,f1557,f657,f3542]) ).
fof(f1571,plain,
( ! [X8,X9,X7] :
( in(sK6(X7,X8,X9),X7)
| sP0(X7,X8,X9)
| ~ empty(X9)
| element(sK6(X7,X8,X9),X8) )
| ~ spl20_76
| ~ spl20_178 ),
inference(resolution,[],[f1558,f658]) ).
fof(f3540,plain,
( spl20_284
| ~ spl20_88
| ~ spl20_177 ),
inference(avatar_split_clause,[],[f1545,f1462,f772,f3538]) ).
fof(f1545,plain,
( ! [X2,X3] :
( in(sK6(X2,X2,X3),X3)
| sP0(X2,X2,X3)
| subset(sK6(X2,X2,X3),X2)
| ~ epsilon_transitive(X2) )
| ~ spl20_88
| ~ spl20_177 ),
inference(resolution,[],[f1463,f773]) ).
fof(f3536,plain,
( spl20_283
| ~ spl20_88
| ~ spl20_177 ),
inference(avatar_split_clause,[],[f1535,f1462,f772,f3534]) ).
fof(f1535,plain,
( ! [X4,X5] :
( in(sK6(X4,X4,X5),X4)
| sP0(X4,X4,X5)
| subset(sK6(X4,X4,X5),X5)
| ~ epsilon_transitive(X5) )
| ~ spl20_88
| ~ spl20_177 ),
inference(resolution,[],[f1463,f773]) ).
fof(f3532,plain,
( spl20_282
| ~ spl20_88
| ~ spl20_174 ),
inference(avatar_split_clause,[],[f1512,f1432,f772,f3530]) ).
fof(f1512,plain,
( ! [X2,X3] :
( in(sK6(X2,X3,X2),X2)
| sP0(X2,X3,X2)
| subset(sK6(X2,X3,X2),X3)
| ~ epsilon_transitive(X3) )
| ~ spl20_88
| ~ spl20_174 ),
inference(resolution,[],[f1433,f773]) ).
fof(f3528,plain,
( spl20_281
| ~ spl20_88
| ~ spl20_173 ),
inference(avatar_split_clause,[],[f1499,f1428,f772,f3526]) ).
fof(f1499,plain,
( ! [X2,X3] :
( in(sK6(X2,X3,X3),X3)
| sP0(X2,X3,X3)
| subset(sK6(X2,X3,X3),X2)
| ~ epsilon_transitive(X2) )
| ~ spl20_88
| ~ spl20_173 ),
inference(resolution,[],[f1429,f773]) ).
fof(f3524,plain,
( spl20_280
| ~ spl20_153
| ~ spl20_170 ),
inference(avatar_split_clause,[],[f1410,f1403,f1230,f3522]) ).
fof(f1410,plain,
( ! [X8,X9] :
( singleton(X8) = X9
| ~ ordinal(singleton(X8))
| ~ ordinal(X9)
| subset(singleton(X8),X9)
| ~ epsilon_transitive(X9)
| X8 = X9 )
| ~ spl20_153
| ~ spl20_170 ),
inference(resolution,[],[f1404,f1231]) ).
fof(f3520,plain,
( spl20_279
| ~ spl20_151
| ~ spl20_167 ),
inference(avatar_split_clause,[],[f1381,f1371,f1221,f3518]) ).
fof(f1381,plain,
( ! [X14,X13] :
( sK4(powerset(X13)) = X14
| ~ ordinal(sK4(powerset(X13)))
| ~ ordinal(X14)
| element(sK4(powerset(X13)),X14)
| ~ empty(X13) )
| ~ spl20_151
| ~ spl20_167 ),
inference(resolution,[],[f1372,f1222]) ).
fof(f3516,plain,
( spl20_278
| ~ spl20_104
| ~ spl20_151 ),
inference(avatar_split_clause,[],[f1241,f1221,f890,f3514]) ).
fof(f1241,plain,
( ! [X0,X1] :
( ~ empty(X0)
| in(sK4(powerset(X0)),X1)
| sK4(powerset(X0)) = X1
| ~ ordinal(sK4(powerset(X0)))
| ~ ordinal(X1) )
| ~ spl20_104
| ~ spl20_151 ),
inference(resolution,[],[f1222,f891]) ).
fof(f3480,plain,
( spl20_277
| spl20_181
| ~ spl20_89
| ~ spl20_195 ),
inference(avatar_split_clause,[],[f2116,f2032,f776,f1640,f3477]) ).
fof(f2116,plain,
( empty(sK1)
| in(succ(sK2),sK1)
| ~ spl20_89
| ~ spl20_195 ),
inference(resolution,[],[f2034,f777]) ).
fof(f2034,plain,
( element(succ(sK2),sK1)
| ~ spl20_195 ),
inference(avatar_component_clause,[],[f2032]) ).
fof(f3450,plain,
( spl20_276
| ~ spl20_88
| ~ spl20_170 ),
inference(avatar_split_clause,[],[f1406,f1403,f772,f3448]) ).
fof(f1406,plain,
( ! [X0,X1] :
( X0 = X1
| ~ ordinal(X0)
| ~ ordinal(X1)
| subset(X0,X1)
| ~ epsilon_transitive(X1)
| subset(X1,X0)
| ~ epsilon_transitive(X0) )
| ~ spl20_88
| ~ spl20_170 ),
inference(resolution,[],[f1404,f773]) ).
fof(f3446,plain,
( spl20_275
| ~ spl20_84
| ~ spl20_168 ),
inference(avatar_split_clause,[],[f1396,f1387,f732,f3444]) ).
fof(f1396,plain,
( ! [X6,X7] :
( singleton(X6) = powerset(X7)
| sK5(X6,powerset(X7)) = X6
| subset(sK5(X6,powerset(X7)),X7) )
| ~ spl20_84
| ~ spl20_168 ),
inference(resolution,[],[f1388,f733]) ).
fof(f3442,plain,
( spl20_274
| ~ spl20_107
| ~ spl20_153 ),
inference(avatar_split_clause,[],[f1253,f1230,f915,f3440]) ).
fof(f1253,plain,
( ! [X6,X7] :
( sK5(X6,singleton(X7)) = X7
| sK5(X6,singleton(X7)) = X6
| singleton(X6) = singleton(X7) )
| ~ spl20_107
| ~ spl20_153 ),
inference(resolution,[],[f1231,f916]) ).
fof(f3026,plain,
( spl20_273
| ~ spl20_75
| ~ spl20_177 ),
inference(avatar_split_clause,[],[f1547,f1462,f653,f3024]) ).
fof(f3024,plain,
( spl20_273
<=> ! [X6,X7] :
( in(sK6(X6,X6,X7),X7)
| sP0(X6,X6,X7)
| ~ in(X6,sK6(X6,X6,X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_273])]) ).
fof(f1547,plain,
( ! [X6,X7] :
( in(sK6(X6,X6,X7),X7)
| sP0(X6,X6,X7)
| ~ in(X6,sK6(X6,X6,X7)) )
| ~ spl20_75
| ~ spl20_177 ),
inference(resolution,[],[f1463,f654]) ).
fof(f3022,plain,
( spl20_272
| ~ spl20_76
| ~ spl20_177 ),
inference(avatar_split_clause,[],[f1546,f1462,f657,f3020]) ).
fof(f1546,plain,
( ! [X4,X5] :
( in(sK6(X4,X4,X5),X5)
| sP0(X4,X4,X5)
| element(sK6(X4,X4,X5),X4) )
| ~ spl20_76
| ~ spl20_177 ),
inference(resolution,[],[f1463,f658]) ).
fof(f3018,plain,
( spl20_271
| ~ spl20_151
| ~ spl20_177 ),
inference(avatar_split_clause,[],[f1542,f1462,f1221,f3016]) ).
fof(f1542,plain,
( ! [X18,X17] :
( in(sK6(X17,X17,sK4(powerset(X18))),X17)
| sP0(X17,X17,sK4(powerset(X18)))
| ~ empty(X18) )
| ~ spl20_151
| ~ spl20_177 ),
inference(resolution,[],[f1463,f1222]) ).
fof(f3014,plain,
( spl20_270
| ~ spl20_75
| ~ spl20_177 ),
inference(avatar_split_clause,[],[f1537,f1462,f653,f3012]) ).
fof(f3012,plain,
( spl20_270
<=> ! [X9,X8] :
( in(sK6(X8,X8,X9),X8)
| sP0(X8,X8,X9)
| ~ in(X9,sK6(X8,X8,X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_270])]) ).
fof(f1537,plain,
( ! [X8,X9] :
( in(sK6(X8,X8,X9),X8)
| sP0(X8,X8,X9)
| ~ in(X9,sK6(X8,X8,X9)) )
| ~ spl20_75
| ~ spl20_177 ),
inference(resolution,[],[f1463,f654]) ).
fof(f3010,plain,
( spl20_269
| ~ spl20_76
| ~ spl20_177 ),
inference(avatar_split_clause,[],[f1536,f1462,f657,f3008]) ).
fof(f1536,plain,
( ! [X6,X7] :
( in(sK6(X6,X6,X7),X6)
| sP0(X6,X6,X7)
| element(sK6(X6,X6,X7),X7) )
| ~ spl20_76
| ~ spl20_177 ),
inference(resolution,[],[f1463,f658]) ).
fof(f2998,plain,
( spl20_268
| ~ spl20_109
| ~ spl20_174 ),
inference(avatar_split_clause,[],[f1532,f1432,f927,f2996]) ).
fof(f1532,plain,
( ! [X0,X1] :
( in(sK6(X0,X1,X0),X1)
| sP0(X0,X1,X0)
| ~ in(sK6(X0,X1,X0),X0) )
| ~ spl20_109
| ~ spl20_174 ),
inference(duplicate_literal_removal,[],[f1520]) ).
fof(f1520,plain,
( ! [X0,X1] :
( in(sK6(X0,X1,X0),X1)
| sP0(X0,X1,X0)
| ~ in(sK6(X0,X1,X0),X0)
| sP0(X0,X1,X0) )
| ~ spl20_109
| ~ spl20_174 ),
inference(resolution,[],[f1433,f928]) ).
fof(f2994,plain,
( spl20_267
| ~ spl20_75
| ~ spl20_174 ),
inference(avatar_split_clause,[],[f1524,f1432,f653,f2992]) ).
fof(f2992,plain,
( spl20_267
<=> ! [X9,X8] :
( in(sK6(X8,X9,X8),X9)
| sP0(X8,X9,X8)
| ~ in(X8,sK6(X8,X9,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_267])]) ).
fof(f1524,plain,
( ! [X8,X9] :
( in(sK6(X8,X9,X8),X9)
| sP0(X8,X9,X8)
| ~ in(X8,sK6(X8,X9,X8)) )
| ~ spl20_75
| ~ spl20_174 ),
inference(resolution,[],[f1433,f654]) ).
fof(f2990,plain,
( spl20_266
| ~ spl20_76
| ~ spl20_174 ),
inference(avatar_split_clause,[],[f1523,f1432,f657,f2988]) ).
fof(f2988,plain,
( spl20_266
<=> ! [X6,X7] :
( in(sK6(X6,X7,X6),X7)
| sP0(X6,X7,X6)
| element(sK6(X6,X7,X6),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_266])]) ).
fof(f1523,plain,
( ! [X6,X7] :
( in(sK6(X6,X7,X6),X7)
| sP0(X6,X7,X6)
| element(sK6(X6,X7,X6),X6) )
| ~ spl20_76
| ~ spl20_174 ),
inference(resolution,[],[f1433,f658]) ).
fof(f2986,plain,
( spl20_265
| ~ spl20_151
| ~ spl20_174 ),
inference(avatar_split_clause,[],[f1519,f1432,f1221,f2984]) ).
fof(f2984,plain,
( spl20_265
<=> ! [X16,X15] :
( in(sK6(X15,sK4(powerset(X16)),X15),X15)
| sP0(X15,sK4(powerset(X16)),X15)
| ~ empty(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_265])]) ).
fof(f1519,plain,
( ! [X16,X15] :
( in(sK6(X15,sK4(powerset(X16)),X15),X15)
| sP0(X15,sK4(powerset(X16)),X15)
| ~ empty(X16) )
| ~ spl20_151
| ~ spl20_174 ),
inference(resolution,[],[f1433,f1222]) ).
fof(f2982,plain,
( spl20_264
| ~ spl20_75
| ~ spl20_174 ),
inference(avatar_split_clause,[],[f1514,f1432,f653,f2980]) ).
fof(f2980,plain,
( spl20_264
<=> ! [X6,X7] :
( in(sK6(X6,X7,X6),X6)
| sP0(X6,X7,X6)
| ~ in(X7,sK6(X6,X7,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_264])]) ).
fof(f1514,plain,
( ! [X6,X7] :
( in(sK6(X6,X7,X6),X6)
| sP0(X6,X7,X6)
| ~ in(X7,sK6(X6,X7,X6)) )
| ~ spl20_75
| ~ spl20_174 ),
inference(resolution,[],[f1433,f654]) ).
fof(f2978,plain,
( spl20_263
| ~ spl20_76
| ~ spl20_174 ),
inference(avatar_split_clause,[],[f1513,f1432,f657,f2976]) ).
fof(f1513,plain,
( ! [X4,X5] :
( in(sK6(X4,X5,X4),X4)
| sP0(X4,X5,X4)
| element(sK6(X4,X5,X4),X5) )
| ~ spl20_76
| ~ spl20_174 ),
inference(resolution,[],[f1433,f658]) ).
fof(f2974,plain,
( spl20_262
| ~ spl20_108
| ~ spl20_173 ),
inference(avatar_split_clause,[],[f1508,f1428,f923,f2972]) ).
fof(f1508,plain,
( ! [X2,X3] :
( in(sK6(X2,X3,X3),X2)
| sP0(X2,X3,X3)
| ~ in(sK6(X2,X3,X3),X3) )
| ~ spl20_108
| ~ spl20_173 ),
inference(duplicate_literal_removal,[],[f1488]) ).
fof(f1488,plain,
( ! [X2,X3] :
( in(sK6(X2,X3,X3),X2)
| sP0(X2,X3,X3)
| ~ in(sK6(X2,X3,X3),X3)
| sP0(X2,X3,X3) )
| ~ spl20_108
| ~ spl20_173 ),
inference(resolution,[],[f1429,f924]) ).
fof(f2970,plain,
( spl20_261
| ~ spl20_151
| ~ spl20_173 ),
inference(avatar_split_clause,[],[f1506,f1428,f1221,f2968]) ).
fof(f2968,plain,
( spl20_261
<=> ! [X16,X15] :
( in(sK6(sK4(powerset(X15)),X16,X16),X16)
| sP0(sK4(powerset(X15)),X16,X16)
| ~ empty(X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_261])]) ).
fof(f1506,plain,
( ! [X16,X15] :
( in(sK6(sK4(powerset(X15)),X16,X16),X16)
| sP0(sK4(powerset(X15)),X16,X16)
| ~ empty(X15) )
| ~ spl20_151
| ~ spl20_173 ),
inference(resolution,[],[f1429,f1222]) ).
fof(f2966,plain,
( spl20_260
| ~ spl20_75
| ~ spl20_173 ),
inference(avatar_split_clause,[],[f1501,f1428,f653,f2964]) ).
fof(f2964,plain,
( spl20_260
<=> ! [X6,X7] :
( in(sK6(X6,X7,X7),X7)
| sP0(X6,X7,X7)
| ~ in(X6,sK6(X6,X7,X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_260])]) ).
fof(f1501,plain,
( ! [X6,X7] :
( in(sK6(X6,X7,X7),X7)
| sP0(X6,X7,X7)
| ~ in(X6,sK6(X6,X7,X7)) )
| ~ spl20_75
| ~ spl20_173 ),
inference(resolution,[],[f1429,f654]) ).
fof(f2962,plain,
( spl20_259
| ~ spl20_76
| ~ spl20_173 ),
inference(avatar_split_clause,[],[f1500,f1428,f657,f2960]) ).
fof(f1500,plain,
( ! [X4,X5] :
( in(sK6(X4,X5,X5),X5)
| sP0(X4,X5,X5)
| element(sK6(X4,X5,X5),X4) )
| ~ spl20_76
| ~ spl20_173 ),
inference(resolution,[],[f1429,f658]) ).
fof(f2954,plain,
( spl20_258
| ~ spl20_75
| ~ spl20_173 ),
inference(avatar_split_clause,[],[f1491,f1428,f653,f2952]) ).
fof(f2952,plain,
( spl20_258
<=> ! [X9,X8] :
( in(sK6(X8,X9,X9),X8)
| sP0(X8,X9,X9)
| ~ in(X9,sK6(X8,X9,X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_258])]) ).
fof(f1491,plain,
( ! [X8,X9] :
( in(sK6(X8,X9,X9),X8)
| sP0(X8,X9,X9)
| ~ in(X9,sK6(X8,X9,X9)) )
| ~ spl20_75
| ~ spl20_173 ),
inference(resolution,[],[f1429,f654]) ).
fof(f2950,plain,
( spl20_257
| ~ spl20_76
| ~ spl20_173 ),
inference(avatar_split_clause,[],[f1490,f1428,f657,f2948]) ).
fof(f2948,plain,
( spl20_257
<=> ! [X6,X7] :
( in(sK6(X6,X7,X7),X6)
| sP0(X6,X7,X7)
| element(sK6(X6,X7,X7),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_257])]) ).
fof(f1490,plain,
( ! [X6,X7] :
( in(sK6(X6,X7,X7),X6)
| sP0(X6,X7,X7)
| element(sK6(X6,X7,X7),X7) )
| ~ spl20_76
| ~ spl20_173 ),
inference(resolution,[],[f1429,f658]) ).
fof(f2946,plain,
( spl20_256
| ~ spl20_153
| ~ spl20_167 ),
inference(avatar_split_clause,[],[f1378,f1371,f1230,f2944]) ).
fof(f1378,plain,
( ! [X8,X9] :
( singleton(X8) = X9
| ~ ordinal(singleton(X8))
| ~ ordinal(X9)
| element(singleton(X8),X9)
| X8 = X9 )
| ~ spl20_153
| ~ spl20_167 ),
inference(resolution,[],[f1372,f1231]) ).
fof(f2942,plain,
( spl20_255
| ~ spl20_157
| ~ spl20_166 ),
inference(avatar_split_clause,[],[f1364,f1355,f1267,f2940]) ).
fof(f2940,plain,
( spl20_255
<=> ! [X11,X12] :
( sK4(powerset(X11)) = X12
| ~ ordinal(sK4(powerset(X11)))
| ~ ordinal(X12)
| ~ empty(X12)
| element(X12,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_255])]) ).
fof(f1364,plain,
( ! [X11,X12] :
( sK4(powerset(X11)) = X12
| ~ ordinal(sK4(powerset(X11)))
| ~ ordinal(X12)
| ~ empty(X12)
| element(X12,X11) )
| ~ spl20_157
| ~ spl20_166 ),
inference(resolution,[],[f1356,f1268]) ).
fof(f2938,plain,
( spl20_254
| ~ spl20_104
| ~ spl20_153 ),
inference(avatar_split_clause,[],[f1249,f1230,f890,f2936]) ).
fof(f1249,plain,
( ! [X0,X1] :
( X0 = X1
| in(singleton(X1),X0)
| singleton(X1) = X0
| ~ ordinal(singleton(X1))
| ~ ordinal(X0) )
| ~ spl20_104
| ~ spl20_153 ),
inference(resolution,[],[f1231,f891]) ).
fof(f2906,plain,
( spl20_253
| ~ spl20_88
| ~ spl20_167 ),
inference(avatar_split_clause,[],[f1374,f1371,f772,f2904]) ).
fof(f1374,plain,
( ! [X0,X1] :
( X0 = X1
| ~ ordinal(X0)
| ~ ordinal(X1)
| element(X0,X1)
| subset(X1,X0)
| ~ epsilon_transitive(X0) )
| ~ spl20_88
| ~ spl20_167 ),
inference(resolution,[],[f1372,f773]) ).
fof(f2902,plain,
( spl20_252
| ~ spl20_107
| ~ spl20_151 ),
inference(avatar_split_clause,[],[f1245,f1221,f915,f2900]) ).
fof(f1245,plain,
( ! [X6,X7] :
( ~ empty(X6)
| sK5(X7,sK4(powerset(X6))) = X7
| sK4(powerset(X6)) = singleton(X7) )
| ~ spl20_107
| ~ spl20_151 ),
inference(resolution,[],[f1222,f916]) ).
fof(f2822,plain,
( spl20_251
| ~ spl20_68
| ~ spl20_179 ),
inference(avatar_split_clause,[],[f1608,f1561,f613,f2820]) ).
fof(f1608,plain,
( ! [X14,X15,X13] :
( in(sK6(X13,X14,X15),X15)
| sP0(X13,X14,X15)
| ~ empty(X14)
| ~ empty(X13) )
| ~ spl20_68
| ~ spl20_179 ),
inference(resolution,[],[f1562,f614]) ).
fof(f2818,plain,
( spl20_250
| ~ spl20_68
| ~ spl20_178 ),
inference(avatar_split_clause,[],[f1583,f1557,f613,f2816]) ).
fof(f1583,plain,
( ! [X14,X15,X13] :
( in(sK6(X13,X14,X15),X14)
| sP0(X13,X14,X15)
| ~ empty(X15)
| ~ empty(X13) )
| ~ spl20_68
| ~ spl20_178 ),
inference(resolution,[],[f1558,f614]) ).
fof(f2814,plain,
( spl20_249
| ~ spl20_68
| ~ spl20_178 ),
inference(avatar_split_clause,[],[f1573,f1557,f613,f2812]) ).
fof(f1573,plain,
( ! [X14,X15,X13] :
( in(sK6(X13,X14,X15),X13)
| sP0(X13,X14,X15)
| ~ empty(X15)
| ~ empty(X14) )
| ~ spl20_68
| ~ spl20_178 ),
inference(resolution,[],[f1558,f614]) ).
fof(f2810,plain,
( spl20_248
| ~ spl20_153
| ~ spl20_166 ),
inference(avatar_split_clause,[],[f1362,f1355,f1230,f2808]) ).
fof(f2808,plain,
( spl20_248
<=> ! [X9,X8] :
( singleton(X8) = X9
| ~ ordinal(singleton(X8))
| ~ ordinal(X9)
| ~ empty(X9)
| X8 = X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_248])]) ).
fof(f1362,plain,
( ! [X8,X9] :
( singleton(X8) = X9
| ~ ordinal(singleton(X8))
| ~ ordinal(X9)
| ~ empty(X9)
| X8 = X9 )
| ~ spl20_153
| ~ spl20_166 ),
inference(resolution,[],[f1356,f1231]) ).
fof(f2806,plain,
( spl20_247
| ~ spl20_88
| ~ spl20_166 ),
inference(avatar_split_clause,[],[f1358,f1355,f772,f2804]) ).
fof(f1358,plain,
( ! [X0,X1] :
( X0 = X1
| ~ ordinal(X0)
| ~ ordinal(X1)
| ~ empty(X1)
| subset(X1,X0)
| ~ epsilon_transitive(X0) )
| ~ spl20_88
| ~ spl20_166 ),
inference(resolution,[],[f1356,f773]) ).
fof(f2731,plain,
( spl20_246
| ~ spl20_76
| ~ spl20_167 ),
inference(avatar_split_clause,[],[f1375,f1371,f657,f2729]) ).
fof(f1375,plain,
( ! [X2,X3] :
( X2 = X3
| ~ ordinal(X2)
| ~ ordinal(X3)
| element(X2,X3)
| element(X3,X2) )
| ~ spl20_76
| ~ spl20_167 ),
inference(resolution,[],[f1372,f658]) ).
fof(f2727,plain,
( spl20_245
| ~ spl20_160
| ~ spl20_164 ),
inference(avatar_split_clause,[],[f1331,f1320,f1291,f2725]) ).
fof(f1331,plain,
( ! [X2,X3,X1] :
( ~ ordinal(X1)
| ~ ordinal(X2)
| ordinal_subset(X1,X2)
| ~ in(X3,X2)
| element(X3,X1) )
| ~ spl20_160
| ~ spl20_164 ),
inference(resolution,[],[f1321,f1292]) ).
fof(f2723,plain,
( spl20_244
| ~ spl20_88
| ~ spl20_163 ),
inference(avatar_split_clause,[],[f1323,f1316,f772,f2721]) ).
fof(f1323,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| ~ subset(X1,X0)
| subset(X1,powerset(X0))
| ~ epsilon_transitive(powerset(X0)) )
| ~ spl20_88
| ~ spl20_163 ),
inference(resolution,[],[f1317,f773]) ).
fof(f2674,plain,
( spl20_243
| ~ spl20_52
| ~ spl20_197 ),
inference(avatar_split_clause,[],[f2128,f2040,f511,f2671]) ).
fof(f2128,plain,
( in(sK2,sK1)
| ~ spl20_52
| ~ spl20_197 ),
inference(superposition,[],[f512,f2042]) ).
fof(f2535,plain,
( spl20_242
| ~ spl20_68
| ~ spl20_177 ),
inference(avatar_split_clause,[],[f1548,f1462,f613,f2533]) ).
fof(f1548,plain,
( ! [X8,X9] :
( in(sK6(X8,X8,X9),X9)
| sP0(X8,X8,X9)
| ~ empty(X8) )
| ~ spl20_68
| ~ spl20_177 ),
inference(resolution,[],[f1463,f614]) ).
fof(f2531,plain,
( spl20_241
| ~ spl20_68
| ~ spl20_177 ),
inference(avatar_split_clause,[],[f1538,f1462,f613,f2529]) ).
fof(f1538,plain,
( ! [X10,X11] :
( in(sK6(X10,X10,X11),X10)
| sP0(X10,X10,X11)
| ~ empty(X11) )
| ~ spl20_68
| ~ spl20_177 ),
inference(resolution,[],[f1463,f614]) ).
fof(f2527,plain,
( spl20_240
| ~ spl20_68
| ~ spl20_174 ),
inference(avatar_split_clause,[],[f1525,f1432,f613,f2525]) ).
fof(f1525,plain,
( ! [X10,X11] :
( in(sK6(X10,X11,X10),X11)
| sP0(X10,X11,X10)
| ~ empty(X10) )
| ~ spl20_68
| ~ spl20_174 ),
inference(resolution,[],[f1433,f614]) ).
fof(f2523,plain,
( ~ spl20_239
| spl20_3
| ~ spl20_197 ),
inference(avatar_split_clause,[],[f2125,f2040,f270,f2520]) ).
fof(f2125,plain,
( ~ in(sK1,sK1)
| spl20_3
| ~ spl20_197 ),
inference(superposition,[],[f271,f2042]) ).
fof(f2518,plain,
( spl20_238
| ~ spl20_68
| ~ spl20_174 ),
inference(avatar_split_clause,[],[f1515,f1432,f613,f2516]) ).
fof(f1515,plain,
( ! [X8,X9] :
( in(sK6(X8,X9,X8),X8)
| sP0(X8,X9,X8)
| ~ empty(X9) )
| ~ spl20_68
| ~ spl20_174 ),
inference(resolution,[],[f1433,f614]) ).
fof(f2514,plain,
( spl20_237
| ~ spl20_68
| ~ spl20_173 ),
inference(avatar_split_clause,[],[f1502,f1428,f613,f2512]) ).
fof(f2512,plain,
( spl20_237
<=> ! [X9,X8] :
( in(sK6(X8,X9,X9),X9)
| sP0(X8,X9,X9)
| ~ empty(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_237])]) ).
fof(f1502,plain,
( ! [X8,X9] :
( in(sK6(X8,X9,X9),X9)
| sP0(X8,X9,X9)
| ~ empty(X8) )
| ~ spl20_68
| ~ spl20_173 ),
inference(resolution,[],[f1429,f614]) ).
fof(f2510,plain,
( spl20_236
| ~ spl20_68
| ~ spl20_173 ),
inference(avatar_split_clause,[],[f1492,f1428,f613,f2508]) ).
fof(f1492,plain,
( ! [X10,X11] :
( in(sK6(X10,X11,X11),X10)
| sP0(X10,X11,X11)
| ~ empty(X11) )
| ~ spl20_68
| ~ spl20_173 ),
inference(resolution,[],[f1429,f614]) ).
fof(f2506,plain,
( spl20_235
| ~ spl20_76
| ~ spl20_166 ),
inference(avatar_split_clause,[],[f1359,f1355,f657,f2504]) ).
fof(f1359,plain,
( ! [X2,X3] :
( X2 = X3
| ~ ordinal(X2)
| ~ ordinal(X3)
| ~ empty(X3)
| element(X3,X2) )
| ~ spl20_76
| ~ spl20_166 ),
inference(resolution,[],[f1356,f658]) ).
fof(f2502,plain,
( spl20_234
| ~ spl20_156
| ~ spl20_164 ),
inference(avatar_split_clause,[],[f1332,f1320,f1263,f2500]) ).
fof(f1332,plain,
( ! [X6,X4,X5] :
( ~ ordinal(X4)
| ~ ordinal(X5)
| ordinal_subset(X4,X5)
| ~ in(X6,X5)
| ~ empty(X4) )
| ~ spl20_156
| ~ spl20_164 ),
inference(resolution,[],[f1321,f1264]) ).
fof(f2498,plain,
( spl20_233
| ~ spl20_97
| ~ spl20_148 ),
inference(avatar_split_clause,[],[f1237,f1209,f846,f2496]) ).
fof(f2496,plain,
( spl20_233
<=> ! [X0] :
( ~ epsilon_transitive(succ(X0))
| ordinal_subset(X0,succ(X0))
| ~ ordinal(succ(X0))
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_233])]) ).
fof(f1209,plain,
( spl20_148
<=> ! [X0] :
( subset(X0,succ(X0))
| ~ epsilon_transitive(succ(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_148])]) ).
fof(f1237,plain,
( ! [X0] :
( ~ epsilon_transitive(succ(X0))
| ordinal_subset(X0,succ(X0))
| ~ ordinal(succ(X0))
| ~ ordinal(X0) )
| ~ spl20_97
| ~ spl20_148 ),
inference(resolution,[],[f1210,f847]) ).
fof(f1210,plain,
( ! [X0] :
( subset(X0,succ(X0))
| ~ epsilon_transitive(succ(X0)) )
| ~ spl20_148 ),
inference(avatar_component_clause,[],[f1209]) ).
fof(f2409,plain,
( ~ spl20_228
| spl20_176
| ~ spl20_197 ),
inference(avatar_split_clause,[],[f2124,f2040,f1447,f2330]) ).
fof(f2124,plain,
( ~ element(sK1,sK1)
| spl20_176
| ~ spl20_197 ),
inference(superposition,[],[f1448,f2042]) ).
fof(f2408,plain,
( spl20_232
| ~ spl20_91
| ~ spl20_148 ),
inference(avatar_split_clause,[],[f1238,f1209,f811,f2406]) ).
fof(f1238,plain,
( ! [X1] :
( ~ epsilon_transitive(succ(X1))
| succ(X1) = X1
| ~ subset(succ(X1),X1) )
| ~ spl20_91
| ~ spl20_148 ),
inference(resolution,[],[f1210,f812]) ).
fof(f2404,plain,
( spl20_231
| ~ spl20_106
| ~ spl20_147 ),
inference(avatar_split_clause,[],[f1197,f1184,f899,f2402]) ).
fof(f1184,plain,
( spl20_147
<=> ! [X0,X1] : sP0(X0,X1,set_union2(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_147])]) ).
fof(f1197,plain,
( ! [X2,X0,X1] :
( in(X0,X1)
| ~ in(X0,set_union2(X1,X2))
| in(X0,X2) )
| ~ spl20_106
| ~ spl20_147 ),
inference(resolution,[],[f1185,f900]) ).
fof(f1185,plain,
( ! [X0,X1] : sP0(X0,X1,set_union2(X1,X0))
| ~ spl20_147 ),
inference(avatar_component_clause,[],[f1184]) ).
fof(f2400,plain,
( spl20_230
| ~ spl20_100
| ~ spl20_135 ),
inference(avatar_split_clause,[],[f1189,f1131,f858,f2398]) ).
fof(f1131,plain,
( spl20_135
<=> ! [X1] :
( element(sK3(X1),X1)
| epsilon_transitive(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_135])]) ).
fof(f1189,plain,
( ! [X0,X1] :
( epsilon_transitive(powerset(X0))
| element(X1,X0)
| ~ in(X1,sK3(powerset(X0))) )
| ~ spl20_100
| ~ spl20_135 ),
inference(resolution,[],[f1132,f859]) ).
fof(f1132,plain,
( ! [X1] :
( element(sK3(X1),X1)
| epsilon_transitive(X1) )
| ~ spl20_135 ),
inference(avatar_component_clause,[],[f1131]) ).
fof(f2396,plain,
( spl20_229
| ~ spl20_97
| ~ spl20_132 ),
inference(avatar_split_clause,[],[f1119,f1100,f846,f2394]) ).
fof(f2394,plain,
( spl20_229
<=> ! [X0] :
( ordinal_subset(sK4(powerset(X0)),X0)
| ~ ordinal(X0)
| ~ ordinal(sK4(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_229])]) ).
fof(f1100,plain,
( spl20_132
<=> ! [X0] : subset(sK4(powerset(X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_132])]) ).
fof(f1119,plain,
( ! [X0] :
( ordinal_subset(sK4(powerset(X0)),X0)
| ~ ordinal(X0)
| ~ ordinal(sK4(powerset(X0))) )
| ~ spl20_97
| ~ spl20_132 ),
inference(resolution,[],[f1101,f847]) ).
fof(f1101,plain,
( ! [X0] : subset(sK4(powerset(X0)),X0)
| ~ spl20_132 ),
inference(avatar_component_clause,[],[f1100]) ).
fof(f2333,plain,
( spl20_228
| ~ spl20_195
| ~ spl20_197 ),
inference(avatar_split_clause,[],[f2122,f2040,f2032,f2330]) ).
fof(f2122,plain,
( element(sK1,sK1)
| ~ spl20_195
| ~ spl20_197 ),
inference(superposition,[],[f2034,f2042]) ).
fof(f2328,plain,
( spl20_227
| ~ spl20_75
| ~ spl20_163 ),
inference(avatar_split_clause,[],[f1325,f1316,f653,f2326]) ).
fof(f1325,plain,
( ! [X4,X5] :
( empty(powerset(X4))
| ~ subset(X5,X4)
| ~ in(powerset(X4),X5) )
| ~ spl20_75
| ~ spl20_163 ),
inference(resolution,[],[f1317,f654]) ).
fof(f2324,plain,
( spl20_226
| ~ spl20_148
| ~ spl20_160 ),
inference(avatar_split_clause,[],[f1304,f1291,f1209,f2322]) ).
fof(f1304,plain,
( ! [X2,X3] :
( ~ in(X2,X3)
| element(X2,succ(X3))
| ~ epsilon_transitive(succ(X3)) )
| ~ spl20_148
| ~ spl20_160 ),
inference(resolution,[],[f1292,f1210]) ).
fof(f2320,plain,
( spl20_225
| ~ spl20_146
| ~ spl20_157 ),
inference(avatar_split_clause,[],[f1277,f1267,f1180,f2318]) ).
fof(f1277,plain,
( ! [X5] :
( element(sK4(sK4(powerset(X5))),X5)
| empty(sK4(powerset(X5))) )
| ~ spl20_146
| ~ spl20_157 ),
inference(resolution,[],[f1268,f1181]) ).
fof(f2316,plain,
( spl20_224
| ~ spl20_71
| ~ spl20_157 ),
inference(avatar_split_clause,[],[f1276,f1267,f637,f2314]) ).
fof(f1276,plain,
( ! [X4] :
( element(sK3(sK4(powerset(X4))),X4)
| epsilon_transitive(sK4(powerset(X4))) )
| ~ spl20_71
| ~ spl20_157 ),
inference(resolution,[],[f1268,f638]) ).
fof(f2312,plain,
( spl20_223
| ~ spl20_94
| ~ spl20_135 ),
inference(avatar_split_clause,[],[f1190,f1131,f823,f2310]) ).
fof(f1190,plain,
( ! [X2,X3] :
( epsilon_transitive(powerset(X2))
| ~ empty(X2)
| ~ in(X3,sK3(powerset(X2))) )
| ~ spl20_94
| ~ spl20_135 ),
inference(resolution,[],[f1132,f824]) ).
fof(f2308,plain,
( spl20_222
| ~ spl20_91
| ~ spl20_132 ),
inference(avatar_split_clause,[],[f1120,f1100,f811,f2306]) ).
fof(f1120,plain,
( ! [X1] :
( sK4(powerset(X1)) = X1
| ~ subset(X1,sK4(powerset(X1))) )
| ~ spl20_91
| ~ spl20_132 ),
inference(resolution,[],[f1101,f812]) ).
fof(f2294,plain,
( spl20_221
| ~ spl20_5
| ~ spl20_125
| ~ spl20_165 ),
inference(avatar_split_clause,[],[f1347,f1338,f1044,f279,f2292]) ).
fof(f1338,plain,
( spl20_165
<=> ! [X6,X7] :
( sK5(X6,X7) = X6
| singleton(X6) = X7
| ~ empty(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_165])]) ).
fof(f1347,plain,
( ! [X0] :
( sK5(X0,sK8) = X0
| singleton(X0) = sK8 )
| ~ spl20_5
| ~ spl20_125
| ~ spl20_165 ),
inference(forward_demodulation,[],[f1346,f1046]) ).
fof(f1346,plain,
( ! [X0] :
( singleton(X0) = sK8
| sK5(X0,empty_set) = X0 )
| ~ spl20_5
| ~ spl20_125
| ~ spl20_165 ),
inference(forward_demodulation,[],[f1341,f1046]) ).
fof(f1341,plain,
( ! [X0] :
( singleton(X0) = empty_set
| sK5(X0,empty_set) = X0 )
| ~ spl20_5
| ~ spl20_165 ),
inference(resolution,[],[f1339,f281]) ).
fof(f1339,plain,
( ! [X6,X7] :
( ~ empty(X7)
| singleton(X6) = X7
| sK5(X6,X7) = X6 )
| ~ spl20_165 ),
inference(avatar_component_clause,[],[f1338]) ).
fof(f2290,plain,
( spl20_220
| ~ spl20_79
| ~ spl20_158 ),
inference(avatar_split_clause,[],[f1297,f1283,f685,f2288]) ).
fof(f1283,plain,
( spl20_158
<=> ! [X4,X2,X3] :
( set_union2(X3,X2) != X4
| sP0(X3,X2,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_158])]) ).
fof(f1297,plain,
( ! [X8,X9] :
( succ(X8) != X9
| sP0(X8,singleton(X8),X9) )
| ~ spl20_79
| ~ spl20_158 ),
inference(superposition,[],[f1284,f686]) ).
fof(f1284,plain,
( ! [X2,X3,X4] :
( set_union2(X3,X2) != X4
| sP0(X3,X2,X4) )
| ~ spl20_158 ),
inference(avatar_component_clause,[],[f1283]) ).
fof(f2285,plain,
( spl20_219
| ~ spl20_53
| ~ spl20_196 ),
inference(avatar_split_clause,[],[f2115,f2036,f515,f2282]) ).
fof(f515,plain,
( spl20_53
<=> ! [X0] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_53])]) ).
fof(f2115,plain,
( epsilon_transitive(succ(sK2))
| ~ spl20_53
| ~ spl20_196 ),
inference(resolution,[],[f2037,f516]) ).
fof(f516,plain,
( ! [X0] :
( ~ ordinal(X0)
| epsilon_transitive(X0) )
| ~ spl20_53 ),
inference(avatar_component_clause,[],[f515]) ).
fof(f2228,plain,
( spl20_218
| ~ spl20_129
| ~ spl20_163 ),
inference(avatar_split_clause,[],[f1327,f1316,f1085,f2226]) ).
fof(f1327,plain,
( ! [X8] :
( empty(powerset(X8))
| ~ subset(succ(powerset(X8)),X8) )
| ~ spl20_129
| ~ spl20_163 ),
inference(resolution,[],[f1317,f1086]) ).
fof(f2224,plain,
( spl20_217
| ~ spl20_146
| ~ spl20_153 ),
inference(avatar_split_clause,[],[f1252,f1230,f1180,f2222]) ).
fof(f2222,plain,
( spl20_217
<=> ! [X5] :
( sK4(singleton(X5)) = X5
| empty(singleton(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_217])]) ).
fof(f1252,plain,
( ! [X5] :
( sK4(singleton(X5)) = X5
| empty(singleton(X5)) )
| ~ spl20_146
| ~ spl20_153 ),
inference(resolution,[],[f1231,f1181]) ).
fof(f2220,plain,
( spl20_216
| ~ spl20_71
| ~ spl20_153 ),
inference(avatar_split_clause,[],[f1251,f1230,f637,f2218]) ).
fof(f2218,plain,
( spl20_216
<=> ! [X4] :
( sK3(singleton(X4)) = X4
| epsilon_transitive(singleton(X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_216])]) ).
fof(f1251,plain,
( ! [X4] :
( sK3(singleton(X4)) = X4
| epsilon_transitive(singleton(X4)) )
| ~ spl20_71
| ~ spl20_153 ),
inference(resolution,[],[f1231,f638]) ).
fof(f2215,plain,
( spl20_215
| ~ spl20_54
| ~ spl20_196 ),
inference(avatar_split_clause,[],[f2114,f2036,f519,f2212]) ).
fof(f519,plain,
( spl20_54
<=> ! [X0] :
( epsilon_connected(X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_54])]) ).
fof(f2114,plain,
( epsilon_connected(succ(sK2))
| ~ spl20_54
| ~ spl20_196 ),
inference(resolution,[],[f2037,f520]) ).
fof(f520,plain,
( ! [X0] :
( ~ ordinal(X0)
| epsilon_connected(X0) )
| ~ spl20_54 ),
inference(avatar_component_clause,[],[f519]) ).
fof(f2210,plain,
( spl20_214
| ~ spl20_101
| ~ spl20_147 ),
inference(avatar_split_clause,[],[f1199,f1184,f862,f2208]) ).
fof(f1199,plain,
( ! [X8,X6,X7] :
( ~ in(X6,X7)
| in(X6,set_union2(X7,X8)) )
| ~ spl20_101
| ~ spl20_147 ),
inference(resolution,[],[f1185,f863]) ).
fof(f2206,plain,
( spl20_213
| ~ spl20_102
| ~ spl20_147 ),
inference(avatar_split_clause,[],[f1198,f1184,f866,f2204]) ).
fof(f1198,plain,
( ! [X3,X4,X5] :
( ~ in(X3,X4)
| in(X3,set_union2(X5,X4)) )
| ~ spl20_102
| ~ spl20_147 ),
inference(resolution,[],[f1185,f867]) ).
fof(f2202,plain,
( spl20_212
| ~ spl20_88
| ~ spl20_146 ),
inference(avatar_split_clause,[],[f1193,f1180,f772,f2200]) ).
fof(f1193,plain,
( ! [X0] :
( empty(X0)
| subset(sK4(X0),X0)
| ~ epsilon_transitive(X0) )
| ~ spl20_88
| ~ spl20_146 ),
inference(resolution,[],[f1181,f773]) ).
fof(f2198,plain,
( spl20_211
| ~ spl20_84
| ~ spl20_135 ),
inference(avatar_split_clause,[],[f1191,f1131,f732,f2196]) ).
fof(f1191,plain,
( ! [X4] :
( epsilon_transitive(powerset(X4))
| subset(sK3(powerset(X4)),X4) )
| ~ spl20_84
| ~ spl20_135 ),
inference(resolution,[],[f1132,f733]) ).
fof(f2193,plain,
( spl20_210
| ~ spl20_92
| ~ spl20_131 ),
inference(avatar_split_clause,[],[f1111,f1096,f815,f2191]) ).
fof(f2191,plain,
( spl20_210
<=> ! [X0,X1] :
( X0 != X1
| sP0(X0,sK8,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_210])]) ).
fof(f815,plain,
( spl20_92
<=> ! [X2,X0,X1] :
( sP0(X1,X0,X2)
| set_union2(X0,X1) != X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_92])]) ).
fof(f1096,plain,
( spl20_131
<=> ! [X6] : set_union2(sK8,X6) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl20_131])]) ).
fof(f1111,plain,
( ! [X0,X1] :
( X0 != X1
| sP0(X0,sK8,X1) )
| ~ spl20_92
| ~ spl20_131 ),
inference(superposition,[],[f816,f1097]) ).
fof(f1097,plain,
( ! [X6] : set_union2(sK8,X6) = X6
| ~ spl20_131 ),
inference(avatar_component_clause,[],[f1096]) ).
fof(f816,plain,
( ! [X2,X0,X1] :
( set_union2(X0,X1) != X2
| sP0(X1,X0,X2) )
| ~ spl20_92 ),
inference(avatar_component_clause,[],[f815]) ).
fof(f2156,plain,
( spl20_209
| ~ spl20_146
| ~ spl20_151 ),
inference(avatar_split_clause,[],[f1244,f1221,f1180,f2154]) ).
fof(f1244,plain,
( ! [X5] :
( ~ empty(X5)
| empty(sK4(powerset(X5))) )
| ~ spl20_146
| ~ spl20_151 ),
inference(resolution,[],[f1222,f1181]) ).
fof(f2152,plain,
( spl20_208
| ~ spl20_71
| ~ spl20_151 ),
inference(avatar_split_clause,[],[f1243,f1221,f637,f2150]) ).
fof(f2150,plain,
( spl20_208
<=> ! [X4] :
( ~ empty(X4)
| epsilon_transitive(sK4(powerset(X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_208])]) ).
fof(f1243,plain,
( ! [X4] :
( ~ empty(X4)
| epsilon_transitive(sK4(powerset(X4))) )
| ~ spl20_71
| ~ spl20_151 ),
inference(resolution,[],[f1222,f638]) ).
fof(f2148,plain,
( spl20_207
| ~ spl20_79
| ~ spl20_147 ),
inference(avatar_split_clause,[],[f1204,f1184,f685,f2146]) ).
fof(f1204,plain,
( ! [X5] : sP0(singleton(X5),X5,succ(X5))
| ~ spl20_79
| ~ spl20_147 ),
inference(superposition,[],[f1185,f686]) ).
fof(f2144,plain,
( spl20_206
| ~ spl20_80
| ~ spl20_147 ),
inference(avatar_split_clause,[],[f1202,f1184,f689,f2142]) ).
fof(f689,plain,
( spl20_80
<=> ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_80])]) ).
fof(f1202,plain,
( ! [X2,X1] : sP0(X2,X1,set_union2(X2,X1))
| ~ spl20_80
| ~ spl20_147 ),
inference(superposition,[],[f1185,f690]) ).
fof(f690,plain,
( ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0)
| ~ spl20_80 ),
inference(avatar_component_clause,[],[f689]) ).
fof(f2121,plain,
( ~ spl20_64
| spl20_205
| ~ spl20_1
| ~ spl20_196
| spl20_197
| spl20_3
| ~ spl20_170 ),
inference(avatar_split_clause,[],[f1416,f1403,f270,f2040,f2036,f260,f2118,f596]) ).
fof(f1416,plain,
( sK1 = succ(sK2)
| ~ ordinal(succ(sK2))
| ~ ordinal(sK1)
| subset(succ(sK2),sK1)
| ~ epsilon_transitive(sK1)
| spl20_3
| ~ spl20_170 ),
inference(resolution,[],[f1404,f271]) ).
fof(f2113,plain,
( ~ spl20_2
| ~ spl20_65
| spl20_196 ),
inference(avatar_split_clause,[],[f2044,f2036,f601,f265]) ).
fof(f2044,plain,
( ~ ordinal(sK2)
| ~ spl20_65
| spl20_196 ),
inference(resolution,[],[f2038,f602]) ).
fof(f2038,plain,
( ~ ordinal(succ(sK2))
| spl20_196 ),
inference(avatar_component_clause,[],[f2036]) ).
fof(f2112,plain,
( spl20_204
| ~ spl20_75
| ~ spl20_146 ),
inference(avatar_split_clause,[],[f1195,f1180,f653,f2110]) ).
fof(f2110,plain,
( spl20_204
<=> ! [X2] :
( empty(X2)
| ~ in(X2,sK4(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_204])]) ).
fof(f1195,plain,
( ! [X2] :
( empty(X2)
| ~ in(X2,sK4(X2)) )
| ~ spl20_75
| ~ spl20_146 ),
inference(resolution,[],[f1181,f654]) ).
fof(f2087,plain,
( spl20_203
| ~ spl20_79
| ~ spl20_131 ),
inference(avatar_split_clause,[],[f1109,f1096,f685,f2084]) ).
fof(f1109,plain,
( singleton(sK8) = succ(sK8)
| ~ spl20_79
| ~ spl20_131 ),
inference(superposition,[],[f1097,f686]) ).
fof(f2082,plain,
( spl20_202
| ~ spl20_61
| ~ spl20_125 ),
inference(avatar_split_clause,[],[f1071,f1044,f584,f2080]) ).
fof(f2080,plain,
( spl20_202
<=> ! [X0] : set_union2(X0,sK8) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl20_202])]) ).
fof(f584,plain,
( spl20_61
<=> ! [X0] : set_union2(X0,empty_set) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl20_61])]) ).
fof(f1071,plain,
( ! [X0] : set_union2(X0,sK8) = X0
| ~ spl20_61
| ~ spl20_125 ),
inference(superposition,[],[f585,f1046]) ).
fof(f585,plain,
( ! [X0] : set_union2(X0,empty_set) = X0
| ~ spl20_61 ),
inference(avatar_component_clause,[],[f584]) ).
fof(f2060,plain,
( spl20_201
| ~ spl20_154 ),
inference(avatar_split_clause,[],[f1257,f1234,f2058]) ).
fof(f1234,plain,
( spl20_154
<=> ! [X0,X1] :
( X0 != X1
| in(X1,singleton(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_154])]) ).
fof(f1257,plain,
( ! [X0] : in(X0,singleton(X0))
| ~ spl20_154 ),
inference(equality_resolution,[],[f1235]) ).
fof(f1235,plain,
( ! [X0,X1] :
( X0 != X1
| in(X1,singleton(X0)) )
| ~ spl20_154 ),
inference(avatar_component_clause,[],[f1234]) ).
fof(f2056,plain,
( spl20_200
| ~ spl20_61
| ~ spl20_125
| ~ spl20_147 ),
inference(avatar_split_clause,[],[f1207,f1184,f1044,f584,f2054]) ).
fof(f2054,plain,
( spl20_200
<=> ! [X6] : sP0(sK8,X6,X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_200])]) ).
fof(f1207,plain,
( ! [X6] : sP0(sK8,X6,X6)
| ~ spl20_61
| ~ spl20_125
| ~ spl20_147 ),
inference(forward_demodulation,[],[f1205,f1046]) ).
fof(f1205,plain,
( ! [X6] : sP0(empty_set,X6,X6)
| ~ spl20_61
| ~ spl20_147 ),
inference(superposition,[],[f1185,f585]) ).
fof(f2052,plain,
( spl20_199
| ~ spl20_131
| ~ spl20_147 ),
inference(avatar_split_clause,[],[f1206,f1184,f1096,f2050]) ).
fof(f1206,plain,
( ! [X7] : sP0(X7,sK8,X7)
| ~ spl20_131
| ~ spl20_147 ),
inference(superposition,[],[f1185,f1097]) ).
fof(f2048,plain,
( spl20_198
| ~ spl20_67
| ~ spl20_147 ),
inference(avatar_split_clause,[],[f1201,f1184,f609,f2046]) ).
fof(f2046,plain,
( spl20_198
<=> ! [X0] : sP0(X0,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_198])]) ).
fof(f609,plain,
( spl20_67
<=> ! [X0] : set_union2(X0,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl20_67])]) ).
fof(f1201,plain,
( ! [X0] : sP0(X0,X0,X0)
| ~ spl20_67
| ~ spl20_147 ),
inference(superposition,[],[f1185,f610]) ).
fof(f610,plain,
( ! [X0] : set_union2(X0,X0) = X0
| ~ spl20_67 ),
inference(avatar_component_clause,[],[f609]) ).
fof(f2043,plain,
( spl20_195
| ~ spl20_1
| ~ spl20_196
| spl20_197
| spl20_3
| ~ spl20_167 ),
inference(avatar_split_clause,[],[f1383,f1371,f270,f2040,f2036,f260,f2032]) ).
fof(f1383,plain,
( sK1 = succ(sK2)
| ~ ordinal(succ(sK2))
| ~ ordinal(sK1)
| element(succ(sK2),sK1)
| spl20_3
| ~ spl20_167 ),
inference(resolution,[],[f1372,f271]) ).
fof(f1922,plain,
( spl20_194
| ~ spl20_55
| ~ spl20_181 ),
inference(avatar_split_clause,[],[f1738,f1640,f523,f1919]) ).
fof(f1919,plain,
( spl20_194
<=> function(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_194])]) ).
fof(f1738,plain,
( function(sK1)
| ~ spl20_55
| ~ spl20_181 ),
inference(resolution,[],[f1642,f524]) ).
fof(f1917,plain,
( spl20_193
| ~ spl20_104
| ~ spl20_109 ),
inference(avatar_split_clause,[],[f932,f927,f890,f1915]) ).
fof(f932,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_104
| ~ spl20_109 ),
inference(resolution,[],[f928,f891]) ).
fof(f1913,plain,
( spl20_192
| ~ spl20_104
| ~ spl20_108 ),
inference(avatar_split_clause,[],[f930,f923,f890,f1911]) ).
fof(f930,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_104
| ~ spl20_108 ),
inference(resolution,[],[f924,f891]) ).
fof(f1802,plain,
( spl20_191
| ~ spl20_88
| ~ spl20_110 ),
inference(avatar_split_clause,[],[f954,f935,f772,f1800]) ).
fof(f954,plain,
( ! [X6,X4,X5] :
( in(sK6(X4,X5,X6),X6)
| in(sK6(X4,X5,X6),X5)
| sP0(X4,X5,X6)
| subset(sK6(X4,X5,X6),X4)
| ~ epsilon_transitive(X4) )
| ~ spl20_88
| ~ spl20_110 ),
inference(resolution,[],[f936,f773]) ).
fof(f1798,plain,
( spl20_190
| ~ spl20_88
| ~ spl20_110 ),
inference(avatar_split_clause,[],[f948,f935,f772,f1796]) ).
fof(f948,plain,
( ! [X6,X4,X5] :
( in(sK6(X4,X5,X6),X6)
| in(sK6(X4,X5,X6),X4)
| sP0(X4,X5,X6)
| subset(sK6(X4,X5,X6),X5)
| ~ epsilon_transitive(X5) )
| ~ spl20_88
| ~ spl20_110 ),
inference(resolution,[],[f936,f773]) ).
fof(f1794,plain,
( spl20_189
| ~ spl20_88
| ~ spl20_110 ),
inference(avatar_split_clause,[],[f942,f935,f772,f1792]) ).
fof(f942,plain,
( ! [X8,X6,X7] :
( in(sK6(X6,X7,X8),X7)
| in(sK6(X6,X7,X8),X6)
| sP0(X6,X7,X8)
| subset(sK6(X6,X7,X8),X8)
| ~ epsilon_transitive(X8) )
| ~ spl20_88
| ~ spl20_110 ),
inference(resolution,[],[f936,f773]) ).
fof(f1671,plain,
( spl20_188
| ~ spl20_75
| ~ spl20_110 ),
inference(avatar_split_clause,[],[f956,f935,f653,f1669]) ).
fof(f1669,plain,
( spl20_188
<=> ! [X11,X12,X10] :
( in(sK6(X10,X11,X12),X12)
| in(sK6(X10,X11,X12),X11)
| sP0(X10,X11,X12)
| ~ in(X10,sK6(X10,X11,X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_188])]) ).
fof(f956,plain,
( ! [X10,X11,X12] :
( in(sK6(X10,X11,X12),X12)
| in(sK6(X10,X11,X12),X11)
| sP0(X10,X11,X12)
| ~ in(X10,sK6(X10,X11,X12)) )
| ~ spl20_75
| ~ spl20_110 ),
inference(resolution,[],[f936,f654]) ).
fof(f1667,plain,
( spl20_187
| ~ spl20_76
| ~ spl20_110 ),
inference(avatar_split_clause,[],[f955,f935,f657,f1665]) ).
fof(f955,plain,
( ! [X8,X9,X7] :
( in(sK6(X7,X8,X9),X9)
| in(sK6(X7,X8,X9),X8)
| sP0(X7,X8,X9)
| element(sK6(X7,X8,X9),X7) )
| ~ spl20_76
| ~ spl20_110 ),
inference(resolution,[],[f936,f658]) ).
fof(f1663,plain,
( spl20_186
| ~ spl20_75
| ~ spl20_110 ),
inference(avatar_split_clause,[],[f950,f935,f653,f1661]) ).
fof(f1661,plain,
( spl20_186
<=> ! [X11,X12,X10] :
( in(sK6(X10,X11,X12),X12)
| in(sK6(X10,X11,X12),X10)
| sP0(X10,X11,X12)
| ~ in(X11,sK6(X10,X11,X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_186])]) ).
fof(f950,plain,
( ! [X10,X11,X12] :
( in(sK6(X10,X11,X12),X12)
| in(sK6(X10,X11,X12),X10)
| sP0(X10,X11,X12)
| ~ in(X11,sK6(X10,X11,X12)) )
| ~ spl20_75
| ~ spl20_110 ),
inference(resolution,[],[f936,f654]) ).
fof(f1659,plain,
( spl20_185
| ~ spl20_76
| ~ spl20_110 ),
inference(avatar_split_clause,[],[f949,f935,f657,f1657]) ).
fof(f949,plain,
( ! [X8,X9,X7] :
( in(sK6(X7,X8,X9),X9)
| in(sK6(X7,X8,X9),X7)
| sP0(X7,X8,X9)
| element(sK6(X7,X8,X9),X8) )
| ~ spl20_76
| ~ spl20_110 ),
inference(resolution,[],[f936,f658]) ).
fof(f1655,plain,
( spl20_184
| ~ spl20_75
| ~ spl20_110 ),
inference(avatar_split_clause,[],[f944,f935,f653,f1653]) ).
fof(f1653,plain,
( spl20_184
<=> ! [X13,X12,X14] :
( in(sK6(X12,X13,X14),X13)
| in(sK6(X12,X13,X14),X12)
| sP0(X12,X13,X14)
| ~ in(X14,sK6(X12,X13,X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_184])]) ).
fof(f944,plain,
( ! [X14,X12,X13] :
( in(sK6(X12,X13,X14),X13)
| in(sK6(X12,X13,X14),X12)
| sP0(X12,X13,X14)
| ~ in(X14,sK6(X12,X13,X14)) )
| ~ spl20_75
| ~ spl20_110 ),
inference(resolution,[],[f936,f654]) ).
fof(f1651,plain,
( spl20_183
| ~ spl20_76
| ~ spl20_110 ),
inference(avatar_split_clause,[],[f943,f935,f657,f1649]) ).
fof(f943,plain,
( ! [X10,X11,X9] :
( in(sK6(X9,X10,X11),X10)
| in(sK6(X9,X10,X11),X9)
| sP0(X9,X10,X11)
| element(sK6(X9,X10,X11),X11) )
| ~ spl20_76
| ~ spl20_110 ),
inference(resolution,[],[f936,f658]) ).
fof(f1647,plain,
( spl20_181
| spl20_182
| ~ spl20_146
| ~ spl20_175 ),
inference(avatar_split_clause,[],[f1478,f1436,f1180,f1644,f1640]) ).
fof(f1478,plain,
( element(sK4(sK1),sK2)
| empty(sK1)
| ~ spl20_146
| ~ spl20_175 ),
inference(resolution,[],[f1437,f1181]) ).
fof(f1567,plain,
( spl20_180
| ~ spl20_68
| ~ spl20_110 ),
inference(avatar_split_clause,[],[f957,f935,f613,f1565]) ).
fof(f957,plain,
( ! [X14,X15,X13] :
( in(sK6(X13,X14,X15),X15)
| in(sK6(X13,X14,X15),X14)
| sP0(X13,X14,X15)
| ~ empty(X13) )
| ~ spl20_68
| ~ spl20_110 ),
inference(resolution,[],[f936,f614]) ).
fof(f1563,plain,
( spl20_179
| ~ spl20_68
| ~ spl20_110 ),
inference(avatar_split_clause,[],[f951,f935,f613,f1561]) ).
fof(f951,plain,
( ! [X14,X15,X13] :
( in(sK6(X13,X14,X15),X15)
| in(sK6(X13,X14,X15),X13)
| sP0(X13,X14,X15)
| ~ empty(X14) )
| ~ spl20_68
| ~ spl20_110 ),
inference(resolution,[],[f936,f614]) ).
fof(f1559,plain,
( spl20_178
| ~ spl20_68
| ~ spl20_110 ),
inference(avatar_split_clause,[],[f945,f935,f613,f1557]) ).
fof(f945,plain,
( ! [X16,X17,X15] :
( in(sK6(X15,X16,X17),X16)
| in(sK6(X15,X16,X17),X15)
| sP0(X15,X16,X17)
| ~ empty(X17) )
| ~ spl20_68
| ~ spl20_110 ),
inference(resolution,[],[f936,f614]) ).
fof(f1464,plain,
( spl20_177
| ~ spl20_110 ),
inference(avatar_split_clause,[],[f960,f935,f1462]) ).
fof(f960,plain,
( ! [X4,X5] :
( in(sK6(X4,X4,X5),X5)
| in(sK6(X4,X4,X5),X4)
| sP0(X4,X4,X5) )
| ~ spl20_110 ),
inference(factoring,[],[f936]) ).
fof(f1450,plain,
( spl20_176
| ~ spl20_3
| ~ spl20_76 ),
inference(avatar_split_clause,[],[f1442,f657,f270,f1447]) ).
fof(f1438,plain,
( spl20_175
| ~ spl20_105
| ~ spl20_160 ),
inference(avatar_split_clause,[],[f1305,f1291,f894,f1436]) ).
fof(f1434,plain,
( spl20_174
| ~ spl20_110 ),
inference(avatar_split_clause,[],[f959,f935,f1432]) ).
fof(f959,plain,
( ! [X2,X3] :
( in(sK6(X2,X3,X2),X2)
| in(sK6(X2,X3,X2),X3)
| sP0(X2,X3,X2) )
| ~ spl20_110 ),
inference(factoring,[],[f936]) ).
fof(f1430,plain,
( spl20_173
| ~ spl20_110 ),
inference(avatar_split_clause,[],[f958,f935,f1428]) ).
fof(f958,plain,
( ! [X0,X1] :
( in(sK6(X0,X1,X1),X1)
| in(sK6(X0,X1,X1),X0)
| sP0(X0,X1,X1) )
| ~ spl20_110 ),
inference(factoring,[],[f936]) ).
fof(f1426,plain,
( spl20_172
| ~ spl20_88
| ~ spl20_107 ),
inference(avatar_split_clause,[],[f918,f915,f772,f1424]) ).
fof(f918,plain,
( ! [X0,X1] :
( sK5(X0,X1) = X0
| singleton(X0) = X1
| subset(sK5(X0,X1),X1)
| ~ epsilon_transitive(X1) )
| ~ spl20_88
| ~ spl20_107 ),
inference(resolution,[],[f916,f773]) ).
fof(f1422,plain,
( spl20_171
| ~ spl20_87
| ~ spl20_90 ),
inference(avatar_split_clause,[],[f803,f780,f768,f1420]) ).
fof(f1420,plain,
( spl20_171
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ function(set_union2(X1,X0))
| ~ empty(set_union2(X1,X0))
| one_to_one(set_union2(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_171])]) ).
fof(f768,plain,
( spl20_87
<=> ! [X0] :
( one_to_one(X0)
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_87])]) ).
fof(f780,plain,
( spl20_90
<=> ! [X0,X1] :
( relation(set_union2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_90])]) ).
fof(f803,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ function(set_union2(X1,X0))
| ~ empty(set_union2(X1,X0))
| one_to_one(set_union2(X1,X0)) )
| ~ spl20_87
| ~ spl20_90 ),
inference(resolution,[],[f781,f769]) ).
fof(f769,plain,
( ! [X0] :
( ~ relation(X0)
| ~ function(X0)
| ~ empty(X0)
| one_to_one(X0) )
| ~ spl20_87 ),
inference(avatar_component_clause,[],[f768]) ).
fof(f781,plain,
( ! [X0,X1] :
( relation(set_union2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl20_90 ),
inference(avatar_component_clause,[],[f780]) ).
fof(f1405,plain,
( spl20_170
| ~ spl20_88
| ~ spl20_104 ),
inference(avatar_split_clause,[],[f903,f890,f772,f1403]) ).
fof(f903,plain,
( ! [X0,X1] :
( in(X1,X0)
| X0 = X1
| ~ ordinal(X0)
| ~ ordinal(X1)
| subset(X0,X1)
| ~ epsilon_transitive(X1) )
| ~ spl20_88
| ~ spl20_104 ),
inference(resolution,[],[f891,f773]) ).
fof(f1393,plain,
( spl20_169
| ~ spl20_75
| ~ spl20_107 ),
inference(avatar_split_clause,[],[f920,f915,f653,f1391]) ).
fof(f1391,plain,
( spl20_169
<=> ! [X4,X5] :
( sK5(X4,X5) = X4
| singleton(X4) = X5
| ~ in(X5,sK5(X4,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_169])]) ).
fof(f920,plain,
( ! [X4,X5] :
( sK5(X4,X5) = X4
| singleton(X4) = X5
| ~ in(X5,sK5(X4,X5)) )
| ~ spl20_75
| ~ spl20_107 ),
inference(resolution,[],[f916,f654]) ).
fof(f1389,plain,
( spl20_168
| ~ spl20_76
| ~ spl20_107 ),
inference(avatar_split_clause,[],[f919,f915,f657,f1387]) ).
fof(f919,plain,
( ! [X2,X3] :
( sK5(X2,X3) = X2
| singleton(X2) = X3
| element(sK5(X2,X3),X3) )
| ~ spl20_76
| ~ spl20_107 ),
inference(resolution,[],[f916,f658]) ).
fof(f1373,plain,
( spl20_167
| ~ spl20_76
| ~ spl20_104 ),
inference(avatar_split_clause,[],[f904,f890,f657,f1371]) ).
fof(f904,plain,
( ! [X2,X3] :
( in(X3,X2)
| X2 = X3
| ~ ordinal(X2)
| ~ ordinal(X3)
| element(X2,X3) )
| ~ spl20_76
| ~ spl20_104 ),
inference(resolution,[],[f891,f658]) ).
fof(f1357,plain,
( spl20_166
| ~ spl20_68
| ~ spl20_104 ),
inference(avatar_split_clause,[],[f906,f890,f613,f1355]) ).
fof(f906,plain,
( ! [X6,X7] :
( in(X7,X6)
| X6 = X7
| ~ ordinal(X6)
| ~ ordinal(X7)
| ~ empty(X7) )
| ~ spl20_68
| ~ spl20_104 ),
inference(resolution,[],[f891,f614]) ).
fof(f1340,plain,
( spl20_165
| ~ spl20_68
| ~ spl20_107 ),
inference(avatar_split_clause,[],[f921,f915,f613,f1338]) ).
fof(f921,plain,
( ! [X6,X7] :
( sK5(X6,X7) = X6
| singleton(X6) = X7
| ~ empty(X7) )
| ~ spl20_68
| ~ spl20_107 ),
inference(resolution,[],[f916,f614]) ).
fof(f1322,plain,
( spl20_164
| ~ spl20_95
| ~ spl20_96 ),
inference(avatar_split_clause,[],[f877,f842,f838,f1320]) ).
fof(f838,plain,
( spl20_95
<=> ! [X0,X1] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_95])]) ).
fof(f842,plain,
( spl20_96
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_96])]) ).
fof(f877,plain,
( ! [X2,X1] :
( subset(X1,X2)
| ~ ordinal(X2)
| ~ ordinal(X1)
| ordinal_subset(X2,X1) )
| ~ spl20_95
| ~ spl20_96 ),
inference(duplicate_literal_removal,[],[f874]) ).
fof(f874,plain,
( ! [X2,X1] :
( subset(X1,X2)
| ~ ordinal(X2)
| ~ ordinal(X1)
| ordinal_subset(X2,X1)
| ~ ordinal(X2)
| ~ ordinal(X1) )
| ~ spl20_95
| ~ spl20_96 ),
inference(resolution,[],[f843,f839]) ).
fof(f839,plain,
( ! [X0,X1] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) )
| ~ spl20_95 ),
inference(avatar_component_clause,[],[f838]) ).
fof(f843,plain,
( ! [X0,X1] :
( ~ ordinal_subset(X0,X1)
| subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) )
| ~ spl20_96 ),
inference(avatar_component_clause,[],[f842]) ).
fof(f1318,plain,
( spl20_163
| ~ spl20_85
| ~ spl20_89 ),
inference(avatar_split_clause,[],[f802,f776,f736,f1316]) ).
fof(f736,plain,
( spl20_85
<=> ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_85])]) ).
fof(f802,plain,
( ! [X2,X1] :
( empty(powerset(X1))
| in(X2,powerset(X1))
| ~ subset(X2,X1) )
| ~ spl20_85
| ~ spl20_89 ),
inference(resolution,[],[f777,f737]) ).
fof(f737,plain,
( ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) )
| ~ spl20_85 ),
inference(avatar_component_clause,[],[f736]) ).
fof(f1314,plain,
( ~ spl20_161
| spl20_162
| ~ spl20_105
| ~ spl20_156 ),
inference(avatar_split_clause,[],[f1272,f1263,f894,f1312,f1308]) ).
fof(f1272,plain,
( ! [X4] :
( ~ in(X4,sK1)
| ~ empty(sK2) )
| ~ spl20_105
| ~ spl20_156 ),
inference(resolution,[],[f1264,f896]) ).
fof(f1293,plain,
( spl20_160
| ~ spl20_85
| ~ spl20_100 ),
inference(avatar_split_clause,[],[f884,f858,f736,f1291]) ).
fof(f884,plain,
( ! [X2,X3,X4] :
( element(X2,X3)
| ~ in(X2,X4)
| ~ subset(X4,X3) )
| ~ spl20_85
| ~ spl20_100 ),
inference(resolution,[],[f859,f737]) ).
fof(f1289,plain,
( spl20_159
| ~ spl20_79
| ~ spl20_92 ),
inference(avatar_split_clause,[],[f830,f815,f685,f1287]) ).
fof(f830,plain,
( ! [X8,X9] :
( succ(X8) != X9
| sP0(singleton(X8),X8,X9) )
| ~ spl20_79
| ~ spl20_92 ),
inference(superposition,[],[f816,f686]) ).
fof(f1285,plain,
( spl20_158
| ~ spl20_80
| ~ spl20_92 ),
inference(avatar_split_clause,[],[f828,f815,f689,f1283]) ).
fof(f828,plain,
( ! [X2,X3,X4] :
( set_union2(X3,X2) != X4
| sP0(X3,X2,X4) )
| ~ spl20_80
| ~ spl20_92 ),
inference(superposition,[],[f816,f690]) ).
fof(f1269,plain,
( spl20_157
| ~ spl20_60
| ~ spl20_100 ),
inference(avatar_split_clause,[],[f883,f858,f543,f1267]) ).
fof(f543,plain,
( spl20_60
<=> ! [X0] : element(sK4(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_60])]) ).
fof(f883,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK4(powerset(X1))) )
| ~ spl20_60
| ~ spl20_100 ),
inference(resolution,[],[f859,f544]) ).
fof(f544,plain,
( ! [X0] : element(sK4(X0),X0)
| ~ spl20_60 ),
inference(avatar_component_clause,[],[f543]) ).
fof(f1265,plain,
( spl20_156
| ~ spl20_85
| ~ spl20_94 ),
inference(avatar_split_clause,[],[f836,f823,f736,f1263]) ).
fof(f836,plain,
( ! [X2,X3,X4] :
( ~ empty(X2)
| ~ in(X3,X4)
| ~ subset(X4,X2) )
| ~ spl20_85
| ~ spl20_94 ),
inference(resolution,[],[f824,f737]) ).
fof(f1261,plain,
( spl20_155
| ~ spl20_79
| ~ spl20_90 ),
inference(avatar_split_clause,[],[f807,f780,f685,f1259]) ).
fof(f1259,plain,
( spl20_155
<=> ! [X5] :
( relation(succ(X5))
| ~ relation(singleton(X5))
| ~ relation(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_155])]) ).
fof(f807,plain,
( ! [X5] :
( relation(succ(X5))
| ~ relation(singleton(X5))
| ~ relation(X5) )
| ~ spl20_79
| ~ spl20_90 ),
inference(superposition,[],[f781,f686]) ).
fof(f1236,plain,
( spl20_154
| ~ spl20_99 ),
inference(avatar_split_clause,[],[f882,f854,f1234]) ).
fof(f854,plain,
( spl20_99
<=> ! [X0,X1,X3] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_99])]) ).
fof(f882,plain,
( ! [X0,X1] :
( X0 != X1
| in(X1,singleton(X0)) )
| ~ spl20_99 ),
inference(equality_resolution,[],[f855]) ).
fof(f855,plain,
( ! [X3,X0,X1] :
( singleton(X0) != X1
| X0 != X3
| in(X3,X1) )
| ~ spl20_99 ),
inference(avatar_component_clause,[],[f854]) ).
fof(f1232,plain,
( spl20_153
| ~ spl20_98 ),
inference(avatar_split_clause,[],[f881,f850,f1230]) ).
fof(f850,plain,
( spl20_98
<=> ! [X0,X1,X3] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_98])]) ).
fof(f881,plain,
( ! [X0,X1] :
( ~ in(X0,singleton(X1))
| X0 = X1 )
| ~ spl20_98 ),
inference(equality_resolution,[],[f851]) ).
fof(f851,plain,
( ! [X3,X0,X1] :
( singleton(X0) != X1
| ~ in(X3,X1)
| X0 = X3 )
| ~ spl20_98 ),
inference(avatar_component_clause,[],[f850]) ).
fof(f1228,plain,
( spl20_152
| ~ spl20_9
| ~ spl20_125 ),
inference(avatar_split_clause,[],[f1067,f1044,f299,f1225]) ).
fof(f1225,plain,
( spl20_152
<=> one_to_one(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_152])]) ).
fof(f299,plain,
( spl20_9
<=> one_to_one(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_9])]) ).
fof(f1067,plain,
( one_to_one(sK8)
| ~ spl20_9
| ~ spl20_125 ),
inference(superposition,[],[f301,f1046]) ).
fof(f301,plain,
( one_to_one(empty_set)
| ~ spl20_9 ),
inference(avatar_component_clause,[],[f299]) ).
fof(f1223,plain,
( spl20_151
| ~ spl20_60
| ~ spl20_94 ),
inference(avatar_split_clause,[],[f835,f823,f543,f1221]) ).
fof(f835,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK4(powerset(X0))) )
| ~ spl20_60
| ~ spl20_94 ),
inference(resolution,[],[f824,f544]) ).
fof(f1219,plain,
( spl20_150
| ~ spl20_14
| ~ spl20_61
| ~ spl20_66
| ~ spl20_92 ),
inference(avatar_split_clause,[],[f833,f815,f605,f584,f324,f1217]) ).
fof(f1217,plain,
( spl20_150
<=> ! [X11,X10] :
( sP0(sK8,X10,X11)
| X10 != X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_150])]) ).
fof(f833,plain,
( ! [X10,X11] :
( sP0(sK8,X10,X11)
| X10 != X11 )
| ~ spl20_14
| ~ spl20_61
| ~ spl20_66
| ~ spl20_92 ),
inference(forward_demodulation,[],[f831,f619]) ).
fof(f619,plain,
( empty_set = sK8
| ~ spl20_14
| ~ spl20_66 ),
inference(resolution,[],[f606,f326]) ).
fof(f326,plain,
( empty(sK8)
| ~ spl20_14 ),
inference(avatar_component_clause,[],[f324]) ).
fof(f831,plain,
( ! [X10,X11] :
( X10 != X11
| sP0(empty_set,X10,X11) )
| ~ spl20_61
| ~ spl20_92 ),
inference(superposition,[],[f816,f585]) ).
fof(f1215,plain,
( spl20_149
| ~ spl20_67
| ~ spl20_92 ),
inference(avatar_split_clause,[],[f827,f815,f609,f1213]) ).
fof(f1213,plain,
( spl20_149
<=> ! [X0,X1] :
( X0 != X1
| sP0(X0,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_149])]) ).
fof(f827,plain,
( ! [X0,X1] :
( X0 != X1
| sP0(X0,X0,X1) )
| ~ spl20_67
| ~ spl20_92 ),
inference(superposition,[],[f816,f610]) ).
fof(f1211,plain,
( spl20_148
| ~ spl20_52
| ~ spl20_88 ),
inference(avatar_split_clause,[],[f799,f772,f511,f1209]) ).
fof(f799,plain,
( ! [X0] :
( subset(X0,succ(X0))
| ~ epsilon_transitive(succ(X0)) )
| ~ spl20_52
| ~ spl20_88 ),
inference(resolution,[],[f773,f512]) ).
fof(f1186,plain,
( spl20_147
| ~ spl20_92 ),
inference(avatar_split_clause,[],[f832,f815,f1184]) ).
fof(f832,plain,
( ! [X0,X1] : sP0(X0,X1,set_union2(X1,X0))
| ~ spl20_92 ),
inference(equality_resolution,[],[f816]) ).
fof(f1182,plain,
( spl20_146
| ~ spl20_60
| ~ spl20_89 ),
inference(avatar_split_clause,[],[f801,f776,f543,f1180]) ).
fof(f801,plain,
( ! [X0] :
( empty(X0)
| in(sK4(X0),X0) )
| ~ spl20_60
| ~ spl20_89 ),
inference(resolution,[],[f777,f544]) ).
fof(f1178,plain,
( spl20_145
| ~ spl20_7
| ~ spl20_125 ),
inference(avatar_split_clause,[],[f1065,f1044,f289,f1175]) ).
fof(f1175,plain,
( spl20_145
<=> relation_empty_yielding(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_145])]) ).
fof(f289,plain,
( spl20_7
<=> relation_empty_yielding(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_7])]) ).
fof(f1065,plain,
( relation_empty_yielding(sK8)
| ~ spl20_7
| ~ spl20_125 ),
inference(superposition,[],[f291,f1046]) ).
fof(f291,plain,
( relation_empty_yielding(empty_set)
| ~ spl20_7 ),
inference(avatar_component_clause,[],[f289]) ).
fof(f1173,plain,
( spl20_143
| ~ spl20_144
| ~ spl20_35
| ~ spl20_34
| ~ spl20_87 ),
inference(avatar_split_clause,[],[f789,f768,f424,f429,f1170,f1166]) ).
fof(f1166,plain,
( spl20_143
<=> one_to_one(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_143])]) ).
fof(f1170,plain,
( spl20_144
<=> empty(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_144])]) ).
fof(f429,plain,
( spl20_35
<=> function(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_35])]) ).
fof(f424,plain,
( spl20_34
<=> relation(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_34])]) ).
fof(f789,plain,
( ~ function(sK16)
| ~ empty(sK16)
| one_to_one(sK16)
| ~ spl20_34
| ~ spl20_87 ),
inference(resolution,[],[f769,f426]) ).
fof(f426,plain,
( relation(sK16)
| ~ spl20_34 ),
inference(avatar_component_clause,[],[f424]) ).
fof(f1164,plain,
( spl20_141
| ~ spl20_142
| ~ spl20_33
| ~ spl20_31
| ~ spl20_87 ),
inference(avatar_split_clause,[],[f788,f768,f409,f419,f1161,f1157]) ).
fof(f1157,plain,
( spl20_141
<=> one_to_one(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_141])]) ).
fof(f1161,plain,
( spl20_142
<=> empty(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_142])]) ).
fof(f419,plain,
( spl20_33
<=> function(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_33])]) ).
fof(f409,plain,
( spl20_31
<=> relation(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_31])]) ).
fof(f788,plain,
( ~ function(sK15)
| ~ empty(sK15)
| one_to_one(sK15)
| ~ spl20_31
| ~ spl20_87 ),
inference(resolution,[],[f769,f411]) ).
fof(f411,plain,
( relation(sK15)
| ~ spl20_31 ),
inference(avatar_component_clause,[],[f409]) ).
fof(f1155,plain,
( spl20_138
| ~ spl20_139
| ~ spl20_140
| ~ spl20_29
| ~ spl20_87 ),
inference(avatar_split_clause,[],[f787,f768,f399,f1152,f1148,f1144]) ).
fof(f1144,plain,
( spl20_138
<=> one_to_one(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_138])]) ).
fof(f1148,plain,
( spl20_139
<=> empty(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_139])]) ).
fof(f1152,plain,
( spl20_140
<=> function(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_140])]) ).
fof(f399,plain,
( spl20_29
<=> relation(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_29])]) ).
fof(f787,plain,
( ~ function(sK14)
| ~ empty(sK14)
| one_to_one(sK14)
| ~ spl20_29
| ~ spl20_87 ),
inference(resolution,[],[f769,f401]) ).
fof(f401,plain,
( relation(sK14)
| ~ spl20_29 ),
inference(avatar_component_clause,[],[f399]) ).
fof(f1142,plain,
( spl20_136
| ~ spl20_137
| ~ spl20_28
| ~ spl20_26
| ~ spl20_87 ),
inference(avatar_split_clause,[],[f786,f768,f384,f394,f1139,f1135]) ).
fof(f1135,plain,
( spl20_136
<=> one_to_one(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_136])]) ).
fof(f1139,plain,
( spl20_137
<=> empty(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_137])]) ).
fof(f394,plain,
( spl20_28
<=> function(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_28])]) ).
fof(f384,plain,
( spl20_26
<=> relation(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_26])]) ).
fof(f786,plain,
( ~ function(sK13)
| ~ empty(sK13)
| one_to_one(sK13)
| ~ spl20_26
| ~ spl20_87 ),
inference(resolution,[],[f769,f386]) ).
fof(f386,plain,
( relation(sK13)
| ~ spl20_26 ),
inference(avatar_component_clause,[],[f384]) ).
fof(f1133,plain,
( spl20_135
| ~ spl20_71
| ~ spl20_76 ),
inference(avatar_split_clause,[],[f682,f657,f637,f1131]) ).
fof(f682,plain,
( ! [X1] :
( element(sK3(X1),X1)
| epsilon_transitive(X1) )
| ~ spl20_71
| ~ spl20_76 ),
inference(resolution,[],[f658,f638]) ).
fof(f1129,plain,
( spl20_134
| ~ spl20_71
| ~ spl20_75 ),
inference(avatar_split_clause,[],[f680,f653,f637,f1127]) ).
fof(f1127,plain,
( spl20_134
<=> ! [X1] :
( ~ in(X1,sK3(X1))
| epsilon_transitive(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_134])]) ).
fof(f680,plain,
( ! [X1] :
( ~ in(X1,sK3(X1))
| epsilon_transitive(X1) )
| ~ spl20_71
| ~ spl20_75 ),
inference(resolution,[],[f654,f638]) ).
fof(f1106,plain,
( spl20_133
| ~ spl20_14
| ~ spl20_86 ),
inference(avatar_split_clause,[],[f760,f740,f324,f1104]) ).
fof(f1104,plain,
( spl20_133
<=> ! [X1] :
( sK8 = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_133])]) ).
fof(f760,plain,
( ! [X1] :
( sK8 = X1
| ~ empty(X1) )
| ~ spl20_14
| ~ spl20_86 ),
inference(resolution,[],[f741,f326]) ).
fof(f1102,plain,
( spl20_132
| ~ spl20_60
| ~ spl20_84 ),
inference(avatar_split_clause,[],[f757,f732,f543,f1100]) ).
fof(f757,plain,
( ! [X0] : subset(sK4(powerset(X0)),X0)
| ~ spl20_60
| ~ spl20_84 ),
inference(resolution,[],[f733,f544]) ).
fof(f1098,plain,
( spl20_131
| ~ spl20_14
| ~ spl20_61
| ~ spl20_66
| ~ spl20_80 ),
inference(avatar_split_clause,[],[f753,f689,f605,f584,f324,f1096]) ).
fof(f753,plain,
( ! [X6] : set_union2(sK8,X6) = X6
| ~ spl20_14
| ~ spl20_61
| ~ spl20_66
| ~ spl20_80 ),
inference(forward_demodulation,[],[f745,f619]) ).
fof(f745,plain,
( ! [X6] : set_union2(empty_set,X6) = X6
| ~ spl20_61
| ~ spl20_80 ),
inference(superposition,[],[f690,f585]) ).
fof(f1091,plain,
( spl20_130
| ~ spl20_52
| ~ spl20_76 ),
inference(avatar_split_clause,[],[f681,f657,f511,f1089]) ).
fof(f681,plain,
( ! [X0] : element(X0,succ(X0))
| ~ spl20_52
| ~ spl20_76 ),
inference(resolution,[],[f658,f512]) ).
fof(f1087,plain,
( spl20_129
| ~ spl20_52
| ~ spl20_75 ),
inference(avatar_split_clause,[],[f679,f653,f511,f1085]) ).
fof(f679,plain,
( ! [X0] : ~ in(succ(X0),X0)
| ~ spl20_52
| ~ spl20_75 ),
inference(resolution,[],[f654,f512]) ).
fof(f1062,plain,
( spl20_128
| ~ spl20_14
| ~ spl20_47
| ~ spl20_66 ),
inference(avatar_split_clause,[],[f625,f605,f489,f324,f1059]) ).
fof(f1059,plain,
( spl20_128
<=> sK8 = sK19 ),
introduced(avatar_definition,[new_symbols(naming,[spl20_128])]) ).
fof(f489,plain,
( spl20_47
<=> empty(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_47])]) ).
fof(f625,plain,
( sK8 = sK19
| ~ spl20_14
| ~ spl20_47
| ~ spl20_66 ),
inference(forward_demodulation,[],[f622,f619]) ).
fof(f622,plain,
( empty_set = sK19
| ~ spl20_47
| ~ spl20_66 ),
inference(resolution,[],[f606,f491]) ).
fof(f491,plain,
( empty(sK19)
| ~ spl20_47 ),
inference(avatar_component_clause,[],[f489]) ).
fof(f1057,plain,
( spl20_127
| ~ spl20_14
| ~ spl20_42
| ~ spl20_66 ),
inference(avatar_split_clause,[],[f624,f605,f464,f324,f1054]) ).
fof(f1054,plain,
( spl20_127
<=> sK8 = sK18 ),
introduced(avatar_definition,[new_symbols(naming,[spl20_127])]) ).
fof(f464,plain,
( spl20_42
<=> empty(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_42])]) ).
fof(f624,plain,
( sK8 = sK18
| ~ spl20_14
| ~ spl20_42
| ~ spl20_66 ),
inference(forward_demodulation,[],[f621,f619]) ).
fof(f621,plain,
( empty_set = sK18
| ~ spl20_42
| ~ spl20_66 ),
inference(resolution,[],[f606,f466]) ).
fof(f466,plain,
( empty(sK18)
| ~ spl20_42 ),
inference(avatar_component_clause,[],[f464]) ).
fof(f1052,plain,
( spl20_126
| ~ spl20_14
| ~ spl20_24
| ~ spl20_66 ),
inference(avatar_split_clause,[],[f623,f605,f374,f324,f1049]) ).
fof(f1049,plain,
( spl20_126
<=> sK8 = sK12 ),
introduced(avatar_definition,[new_symbols(naming,[spl20_126])]) ).
fof(f374,plain,
( spl20_24
<=> empty(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_24])]) ).
fof(f623,plain,
( sK8 = sK12
| ~ spl20_14
| ~ spl20_24
| ~ spl20_66 ),
inference(forward_demodulation,[],[f620,f619]) ).
fof(f620,plain,
( empty_set = sK12
| ~ spl20_24
| ~ spl20_66 ),
inference(resolution,[],[f606,f376]) ).
fof(f376,plain,
( empty(sK12)
| ~ spl20_24 ),
inference(avatar_component_clause,[],[f374]) ).
fof(f1047,plain,
( spl20_125
| ~ spl20_14
| ~ spl20_66 ),
inference(avatar_split_clause,[],[f619,f605,f324,f1044]) ).
fof(f1037,plain,
( spl20_124
| ~ spl20_47
| ~ spl20_59 ),
inference(avatar_split_clause,[],[f582,f539,f489,f1034]) ).
fof(f1034,plain,
( spl20_124
<=> ordinal(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_124])]) ).
fof(f582,plain,
( ordinal(sK19)
| ~ spl20_47
| ~ spl20_59 ),
inference(resolution,[],[f540,f491]) ).
fof(f1031,plain,
( spl20_123
| ~ spl20_24
| ~ spl20_59 ),
inference(avatar_split_clause,[],[f580,f539,f374,f1028]) ).
fof(f1028,plain,
( spl20_123
<=> ordinal(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_123])]) ).
fof(f580,plain,
( ordinal(sK12)
| ~ spl20_24
| ~ spl20_59 ),
inference(resolution,[],[f540,f376]) ).
fof(f1026,plain,
( spl20_122
| ~ spl20_14
| ~ spl20_59 ),
inference(avatar_split_clause,[],[f579,f539,f324,f1023]) ).
fof(f579,plain,
( ordinal(sK8)
| ~ spl20_14
| ~ spl20_59 ),
inference(resolution,[],[f540,f326]) ).
fof(f1021,plain,
( ~ spl20_120
| spl20_121
| ~ spl20_91
| ~ spl20_105 ),
inference(avatar_split_clause,[],[f939,f894,f811,f1018,f1014]) ).
fof(f1011,plain,
( spl20_119
| ~ spl20_47
| ~ spl20_58 ),
inference(avatar_split_clause,[],[f577,f535,f489,f1008]) ).
fof(f1008,plain,
( spl20_119
<=> epsilon_connected(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_119])]) ).
fof(f577,plain,
( epsilon_connected(sK19)
| ~ spl20_47
| ~ spl20_58 ),
inference(resolution,[],[f536,f491]) ).
fof(f1005,plain,
( spl20_118
| ~ spl20_24
| ~ spl20_58 ),
inference(avatar_split_clause,[],[f575,f535,f374,f1002]) ).
fof(f1002,plain,
( spl20_118
<=> epsilon_connected(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_118])]) ).
fof(f575,plain,
( epsilon_connected(sK12)
| ~ spl20_24
| ~ spl20_58 ),
inference(resolution,[],[f536,f376]) ).
fof(f1000,plain,
( spl20_117
| ~ spl20_14
| ~ spl20_58 ),
inference(avatar_split_clause,[],[f574,f535,f324,f997]) ).
fof(f997,plain,
( spl20_117
<=> epsilon_connected(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_117])]) ).
fof(f574,plain,
( epsilon_connected(sK8)
| ~ spl20_14
| ~ spl20_58 ),
inference(resolution,[],[f536,f326]) ).
fof(f994,plain,
( spl20_116
| ~ spl20_47
| ~ spl20_57 ),
inference(avatar_split_clause,[],[f572,f531,f489,f991]) ).
fof(f991,plain,
( spl20_116
<=> epsilon_transitive(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_116])]) ).
fof(f531,plain,
( spl20_57
<=> ! [X0] :
( epsilon_transitive(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_57])]) ).
fof(f572,plain,
( epsilon_transitive(sK19)
| ~ spl20_47
| ~ spl20_57 ),
inference(resolution,[],[f532,f491]) ).
fof(f532,plain,
( ! [X0] :
( ~ empty(X0)
| epsilon_transitive(X0) )
| ~ spl20_57 ),
inference(avatar_component_clause,[],[f531]) ).
fof(f988,plain,
( spl20_115
| ~ spl20_24
| ~ spl20_57 ),
inference(avatar_split_clause,[],[f570,f531,f374,f985]) ).
fof(f985,plain,
( spl20_115
<=> epsilon_transitive(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_115])]) ).
fof(f570,plain,
( epsilon_transitive(sK12)
| ~ spl20_24
| ~ spl20_57 ),
inference(resolution,[],[f532,f376]) ).
fof(f983,plain,
( spl20_114
| ~ spl20_14
| ~ spl20_57 ),
inference(avatar_split_clause,[],[f569,f531,f324,f980]) ).
fof(f980,plain,
( spl20_114
<=> epsilon_transitive(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_114])]) ).
fof(f569,plain,
( epsilon_transitive(sK8)
| ~ spl20_14
| ~ spl20_57 ),
inference(resolution,[],[f532,f326]) ).
fof(f978,plain,
( spl20_113
| ~ spl20_14
| ~ spl20_56 ),
inference(avatar_split_clause,[],[f564,f527,f324,f975]) ).
fof(f975,plain,
( spl20_113
<=> relation(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_113])]) ).
fof(f564,plain,
( relation(sK8)
| ~ spl20_14
| ~ spl20_56 ),
inference(resolution,[],[f528,f326]) ).
fof(f972,plain,
( spl20_112
| ~ spl20_24
| ~ spl20_55 ),
inference(avatar_split_clause,[],[f560,f523,f374,f969]) ).
fof(f969,plain,
( spl20_112
<=> function(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_112])]) ).
fof(f560,plain,
( function(sK12)
| ~ spl20_24
| ~ spl20_55 ),
inference(resolution,[],[f524,f376]) ).
fof(f967,plain,
( spl20_111
| ~ spl20_14
| ~ spl20_55 ),
inference(avatar_split_clause,[],[f559,f523,f324,f964]) ).
fof(f964,plain,
( spl20_111
<=> function(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_111])]) ).
fof(f559,plain,
( function(sK8)
| ~ spl20_14
| ~ spl20_55 ),
inference(resolution,[],[f524,f326]) ).
fof(f937,plain,
spl20_110,
inference(avatar_split_clause,[],[f216,f935]) ).
fof(f216,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,[],[f116]) ).
fof(f116,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])],[f114,f115]) ).
fof(f115,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(f114,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,[],[f113]) ).
fof(f113,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,[],[f112]) ).
fof(f112,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,[],[f91]) ).
fof(f91,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(f929,plain,
spl20_109,
inference(avatar_split_clause,[],[f218,f927]) ).
fof(f218,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ in(sK6(X0,X1,X2),X0)
| ~ in(sK6(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f116]) ).
fof(f925,plain,
spl20_108,
inference(avatar_split_clause,[],[f217,f923]) ).
fof(f217,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ in(sK6(X0,X1,X2),X1)
| ~ in(sK6(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f116]) ).
fof(f917,plain,
spl20_107,
inference(avatar_split_clause,[],[f206,f915]) ).
fof(f206,plain,
! [X0,X1] :
( singleton(X0) = X1
| sK5(X0,X1) = X0
| in(sK5(X0,X1),X1) ),
inference(cnf_transformation,[],[f110]) ).
fof(f110,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])],[f108,f109]) ).
fof(f109,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(f108,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,[],[f107]) ).
fof(f107,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/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',d1_tarski) ).
fof(f901,plain,
spl20_106,
inference(avatar_split_clause,[],[f213,f899]) ).
fof(f213,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f116]) ).
fof(f897,plain,
( ~ spl20_1
| ~ spl20_2
| spl20_105
| ~ spl20_4
| ~ spl20_96 ),
inference(avatar_split_clause,[],[f872,f842,f274,f894,f265,f260]) ).
fof(f872,plain,
( subset(sK1,sK2)
| ~ ordinal(sK2)
| ~ ordinal(sK1)
| ~ spl20_4
| ~ spl20_96 ),
inference(resolution,[],[f843,f276]) ).
fof(f892,plain,
spl20_104,
inference(avatar_split_clause,[],[f173,f890]) ).
fof(f173,plain,
! [X0,X1] :
( in(X1,X0)
| X0 = X1
| in(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0] :
( ! [X1] :
( in(X1,X0)
| X0 = X1
| in(X0,X1)
| ~ ordinal(X1) )
| ~ ordinal(X0) ),
inference(flattening,[],[f61]) ).
fof(f61,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/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',t24_ordinal1) ).
fof(f888,plain,
spl20_103,
inference(avatar_split_clause,[],[f258,f886]) ).
fof(f258,plain,
! [X0,X1] :
( singleton(X0) = X1
| sK5(X0,X1) != X0
| ~ in(X0,X1) ),
inference(inner_rewriting,[],[f207]) ).
fof(f207,plain,
! [X0,X1] :
( singleton(X0) = X1
| sK5(X0,X1) != X0
| ~ in(sK5(X0,X1),X1) ),
inference(cnf_transformation,[],[f110]) ).
fof(f868,plain,
spl20_102,
inference(avatar_split_clause,[],[f215,f866]) ).
fof(f215,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f116]) ).
fof(f864,plain,
spl20_101,
inference(avatar_split_clause,[],[f214,f862]) ).
fof(f214,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f116]) ).
fof(f860,plain,
spl20_100,
inference(avatar_split_clause,[],[f212,f858]) ).
fof(f212,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f88]) ).
fof(f88,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/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',t4_subset) ).
fof(f856,plain,
spl20_99,
inference(avatar_split_clause,[],[f205,f854]) ).
fof(f205,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f110]) ).
fof(f852,plain,
spl20_98,
inference(avatar_split_clause,[],[f204,f850]) ).
fof(f204,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f110]) ).
fof(f848,plain,
spl20_97,
inference(avatar_split_clause,[],[f199,f846]) ).
fof(f199,plain,
! [X0,X1] :
( ordinal_subset(X0,X1)
| ~ subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f104,plain,
! [X0,X1] :
( ( ( ordinal_subset(X0,X1)
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ ordinal_subset(X0,X1) ) )
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(nnf_transformation,[],[f83]) ).
fof(f83,plain,
! [X0,X1] :
( ( ordinal_subset(X0,X1)
<=> subset(X0,X1) )
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(flattening,[],[f82]) ).
fof(f82,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/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',redefinition_r1_ordinal1) ).
fof(f844,plain,
spl20_96,
inference(avatar_split_clause,[],[f198,f842]) ).
fof(f198,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f840,plain,
spl20_95,
inference(avatar_split_clause,[],[f197,f838]) ).
fof(f197,plain,
! [X0,X1] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0,X1] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(flattening,[],[f80]) ).
fof(f80,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/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',connectedness_r1_ordinal1) ).
fof(f825,plain,
spl20_94,
inference(avatar_split_clause,[],[f221,f823]) ).
fof(f221,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,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/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',t5_subset) ).
fof(f821,plain,
spl20_93,
inference(avatar_split_clause,[],[f220,f819]) ).
fof(f220,plain,
! [X2,X0,X1] :
( set_union2(X0,X1) = X2
| ~ sP0(X1,X0,X2) ),
inference(cnf_transformation,[],[f117]) ).
fof(f117,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,[],[f92]) ).
fof(f92,plain,
! [X0,X1,X2] :
( set_union2(X0,X1) = X2
<=> sP0(X1,X0,X2) ),
inference(definition_folding,[],[f14,f91]) ).
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/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',d2_xboole_0) ).
fof(f817,plain,
spl20_92,
inference(avatar_split_clause,[],[f219,f815]) ).
fof(f219,plain,
! [X2,X0,X1] :
( sP0(X1,X0,X2)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f117]) ).
fof(f813,plain,
spl20_91,
inference(avatar_split_clause,[],[f203,f811]) ).
fof(f203,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f106]) ).
fof(f106,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(flattening,[],[f105]) ).
fof(f105,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/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',d10_xboole_0) ).
fof(f782,plain,
spl20_90,
inference(avatar_split_clause,[],[f200,f780]) ).
fof(f200,plain,
! [X0,X1] :
( relation(set_union2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
! [X0,X1] :
( relation(set_union2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(flattening,[],[f84]) ).
fof(f84,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/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',fc2_relat_1) ).
fof(f778,plain,
spl20_89,
inference(avatar_split_clause,[],[f193,f776]) ).
fof(f193,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f74]) ).
fof(f74,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/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',t2_subset) ).
fof(f774,plain,
spl20_88,
inference(avatar_split_clause,[],[f184,f772]) ).
fof(f184,plain,
! [X2,X0] :
( subset(X2,X0)
| ~ in(X2,X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f101,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])],[f99,f100]) ).
fof(f100,plain,
! [X0] :
( ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) )
=> ( ~ subset(sK3(X0),X0)
& in(sK3(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f99,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(rectify,[],[f98]) ).
fof(f98,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,[],[f71]) ).
fof(f71,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/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',d2_ordinal1) ).
fof(f770,plain,
spl20_87,
inference(avatar_split_clause,[],[f183,f768]) ).
fof(f183,plain,
! [X0] :
( one_to_one(X0)
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0] :
( ( one_to_one(X0)
& function(X0)
& relation(X0) )
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ),
inference(flattening,[],[f69]) ).
fof(f69,plain,
! [X0] :
( ( one_to_one(X0)
& function(X0)
& relation(X0) )
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( ( function(X0)
& empty(X0)
& relation(X0) )
=> ( one_to_one(X0)
& function(X0)
& relation(X0) ) ),
file('/export/starexec/sandbox/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',cc2_funct_1) ).
fof(f742,plain,
spl20_86,
inference(avatar_split_clause,[],[f210,f740]) ).
fof(f210,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f86,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/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',t8_boole) ).
fof(f738,plain,
spl20_85,
inference(avatar_split_clause,[],[f209,f736]) ).
fof(f209,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f111]) ).
fof(f111,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/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',t3_subset) ).
fof(f734,plain,
spl20_84,
inference(avatar_split_clause,[],[f208,f732]) ).
fof(f208,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f111]) ).
fof(f715,plain,
( ~ spl20_12
| ~ spl20_81 ),
inference(avatar_contradiction_clause,[],[f704]) ).
fof(f704,plain,
( $false
| ~ spl20_12
| ~ spl20_81 ),
inference(resolution,[],[f694,f316]) ).
fof(f316,plain,
( ordinal(empty_set)
| ~ spl20_12 ),
inference(avatar_component_clause,[],[f314]) ).
fof(f314,plain,
( spl20_12
<=> ordinal(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_12])]) ).
fof(f694,plain,
( ! [X1] : ~ ordinal(X1)
| ~ spl20_81 ),
inference(avatar_component_clause,[],[f693]) ).
fof(f693,plain,
( spl20_81
<=> ! [X1] : ~ ordinal(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_81])]) ).
fof(f714,plain,
( ~ spl20_1
| ~ spl20_81 ),
inference(avatar_contradiction_clause,[],[f705]) ).
fof(f705,plain,
( $false
| ~ spl20_1
| ~ spl20_81 ),
inference(resolution,[],[f694,f262]) ).
fof(f262,plain,
( ordinal(sK1)
| ~ spl20_1 ),
inference(avatar_component_clause,[],[f260]) ).
fof(f713,plain,
( ~ spl20_2
| ~ spl20_81 ),
inference(avatar_contradiction_clause,[],[f706]) ).
fof(f706,plain,
( $false
| ~ spl20_2
| ~ spl20_81 ),
inference(resolution,[],[f694,f267]) ).
fof(f267,plain,
( ordinal(sK2)
| ~ spl20_2 ),
inference(avatar_component_clause,[],[f265]) ).
fof(f712,plain,
( ~ spl20_18
| ~ spl20_81 ),
inference(avatar_contradiction_clause,[],[f707]) ).
fof(f707,plain,
( $false
| ~ spl20_18
| ~ spl20_81 ),
inference(resolution,[],[f694,f346]) ).
fof(f346,plain,
( ordinal(sK9)
| ~ spl20_18 ),
inference(avatar_component_clause,[],[f344]) ).
fof(f344,plain,
( spl20_18
<=> ordinal(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_18])]) ).
fof(f711,plain,
( ~ spl20_23
| ~ spl20_81 ),
inference(avatar_contradiction_clause,[],[f708]) ).
fof(f708,plain,
( $false
| ~ spl20_23
| ~ spl20_81 ),
inference(resolution,[],[f694,f371]) ).
fof(f371,plain,
( ordinal(sK11)
| ~ spl20_23 ),
inference(avatar_component_clause,[],[f369]) ).
fof(f369,plain,
( spl20_23
<=> ordinal(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_23])]) ).
fof(f710,plain,
( ~ spl20_45
| ~ spl20_81 ),
inference(avatar_contradiction_clause,[],[f709]) ).
fof(f709,plain,
( $false
| ~ spl20_45
| ~ spl20_81 ),
inference(resolution,[],[f694,f481]) ).
fof(f481,plain,
( ordinal(sK18)
| ~ spl20_45 ),
inference(avatar_component_clause,[],[f479]) ).
fof(f479,plain,
( spl20_45
<=> ordinal(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_45])]) ).
fof(f703,plain,
( spl20_83
| ~ spl20_2
| ~ spl20_54 ),
inference(avatar_split_clause,[],[f554,f519,f265,f700]) ).
fof(f700,plain,
( spl20_83
<=> epsilon_connected(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_83])]) ).
fof(f554,plain,
( epsilon_connected(sK2)
| ~ spl20_2
| ~ spl20_54 ),
inference(resolution,[],[f520,f267]) ).
fof(f698,plain,
( spl20_81
| spl20_82 ),
inference(avatar_split_clause,[],[f196,f696,f693]) ).
fof(f196,plain,
! [X0,X1] :
( ordinal_subset(X0,X0)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0,X1] :
( ordinal_subset(X0,X0)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(flattening,[],[f78]) ).
fof(f78,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/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',reflexivity_r1_ordinal1) ).
fof(f691,plain,
spl20_80,
inference(avatar_split_clause,[],[f190,f689]) ).
fof(f190,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/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',commutativity_k2_xboole_0) ).
fof(f687,plain,
spl20_79,
inference(avatar_split_clause,[],[f166,f685]) ).
fof(f166,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/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',d1_ordinal1) ).
fof(f673,plain,
( spl20_78
| ~ spl20_1
| ~ spl20_54 ),
inference(avatar_split_clause,[],[f553,f519,f260,f670]) ).
fof(f670,plain,
( spl20_78
<=> epsilon_connected(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_78])]) ).
fof(f553,plain,
( epsilon_connected(sK1)
| ~ spl20_1
| ~ spl20_54 ),
inference(resolution,[],[f520,f262]) ).
fof(f663,plain,
spl20_77,
inference(avatar_split_clause,[],[f202,f661]) ).
fof(f661,plain,
( spl20_77
<=> ! [X0,X1] :
( subset(X1,X0)
| X0 != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_77])]) ).
fof(f202,plain,
! [X0,X1] :
( subset(X1,X0)
| X0 != X1 ),
inference(cnf_transformation,[],[f106]) ).
fof(f659,plain,
spl20_76,
inference(avatar_split_clause,[],[f195,f657]) ).
fof(f195,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f77,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/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',t1_subset) ).
fof(f655,plain,
spl20_75,
inference(avatar_split_clause,[],[f194,f653]) ).
fof(f194,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,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/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',antisymmetry_r2_hidden) ).
fof(f651,plain,
spl20_74,
inference(avatar_split_clause,[],[f192,f649]) ).
fof(f649,plain,
( spl20_74
<=> ! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_74])]) ).
fof(f192,plain,
! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f73,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/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',fc3_xboole_0) ).
fof(f647,plain,
spl20_73,
inference(avatar_split_clause,[],[f191,f645]) ).
fof(f645,plain,
( spl20_73
<=> ! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_73])]) ).
fof(f191,plain,
! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f72,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/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',fc2_xboole_0) ).
fof(f643,plain,
spl20_72,
inference(avatar_split_clause,[],[f186,f641]) ).
fof(f641,plain,
( spl20_72
<=> ! [X0] :
( epsilon_transitive(X0)
| ~ subset(sK3(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_72])]) ).
fof(f186,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ subset(sK3(X0),X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f639,plain,
spl20_71,
inference(avatar_split_clause,[],[f185,f637]) ).
fof(f185,plain,
! [X0] :
( epsilon_transitive(X0)
| in(sK3(X0),X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f635,plain,
spl20_70,
inference(avatar_split_clause,[],[f180,f633]) ).
fof(f633,plain,
( spl20_70
<=> ! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_70])]) ).
fof(f180,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(flattening,[],[f67]) ).
fof(f67,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/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',cc2_ordinal1) ).
fof(f630,plain,
( spl20_69
| ~ spl20_2
| ~ spl20_53 ),
inference(avatar_split_clause,[],[f548,f515,f265,f627]) ).
fof(f548,plain,
( epsilon_transitive(sK2)
| ~ spl20_2
| ~ spl20_53 ),
inference(resolution,[],[f516,f267]) ).
fof(f615,plain,
spl20_68,
inference(avatar_split_clause,[],[f211,f613]) ).
fof(f211,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f87]) ).
fof(f87,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/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',t7_boole) ).
fof(f611,plain,
spl20_67,
inference(avatar_split_clause,[],[f189,f609]) ).
fof(f189,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/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',idempotence_k2_xboole_0) ).
fof(f607,plain,
spl20_66,
inference(avatar_split_clause,[],[f176,f605]) ).
fof(f176,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f53]) ).
fof(f53,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',t6_boole) ).
fof(f603,plain,
spl20_65,
inference(avatar_split_clause,[],[f172,f601]) ).
fof(f172,plain,
! [X0] :
( ordinal(succ(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,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/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',fc3_ordinal1) ).
fof(f599,plain,
( spl20_64
| ~ spl20_1
| ~ spl20_53 ),
inference(avatar_split_clause,[],[f547,f515,f260,f596]) ).
fof(f547,plain,
( epsilon_transitive(sK1)
| ~ spl20_1
| ~ spl20_53 ),
inference(resolution,[],[f516,f262]) ).
fof(f594,plain,
spl20_63,
inference(avatar_split_clause,[],[f171,f592]) ).
fof(f171,plain,
! [X0] :
( epsilon_connected(succ(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f590,plain,
spl20_62,
inference(avatar_split_clause,[],[f170,f588]) ).
fof(f170,plain,
! [X0] :
( epsilon_transitive(succ(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f586,plain,
spl20_61,
inference(avatar_split_clause,[],[f165,f584]) ).
fof(f165,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/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',t1_boole) ).
fof(f545,plain,
spl20_60,
inference(avatar_split_clause,[],[f187,f543]) ).
fof(f187,plain,
! [X0] : element(sK4(X0),X0),
inference(cnf_transformation,[],[f103]) ).
fof(f103,plain,
! [X0] : element(sK4(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f15,f102]) ).
fof(f102,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/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',existence_m1_subset_1) ).
fof(f541,plain,
spl20_59,
inference(avatar_split_clause,[],[f179,f539]) ).
fof(f179,plain,
! [X0] :
( ordinal(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,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/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',cc3_ordinal1) ).
fof(f537,plain,
spl20_58,
inference(avatar_split_clause,[],[f178,f535]) ).
fof(f178,plain,
! [X0] :
( epsilon_connected(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f533,plain,
spl20_57,
inference(avatar_split_clause,[],[f177,f531]) ).
fof(f177,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f529,plain,
spl20_56,
inference(avatar_split_clause,[],[f175,f527]) ).
fof(f175,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( empty(X0)
=> relation(X0) ),
file('/export/starexec/sandbox/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',cc1_relat_1) ).
fof(f525,plain,
spl20_55,
inference(avatar_split_clause,[],[f174,f523]) ).
fof(f174,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( empty(X0)
=> function(X0) ),
file('/export/starexec/sandbox/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',cc1_funct_1) ).
fof(f521,plain,
spl20_54,
inference(avatar_split_clause,[],[f168,f519]) ).
fof(f168,plain,
! [X0] :
( epsilon_connected(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f59,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/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',cc1_ordinal1) ).
fof(f517,plain,
spl20_53,
inference(avatar_split_clause,[],[f167,f515]) ).
fof(f167,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f513,plain,
spl20_52,
inference(avatar_split_clause,[],[f164,f511]) ).
fof(f164,plain,
! [X0] : in(X0,succ(X0)),
inference(cnf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0] : in(X0,succ(X0)),
file('/export/starexec/sandbox/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',t10_ordinal1) ).
fof(f509,plain,
spl20_51,
inference(avatar_split_clause,[],[f163,f507]) ).
fof(f163,plain,
! [X0] : succ(X0) != X0,
inference(cnf_transformation,[],[f43]) ).
fof(f43,axiom,
! [X0] : succ(X0) != X0,
file('/export/starexec/sandbox/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',t14_ordinal1) ).
fof(f505,plain,
spl20_50,
inference(avatar_split_clause,[],[f188,f503]) ).
fof(f188,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/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',reflexivity_r1_tarski) ).
fof(f501,plain,
spl20_49,
inference(avatar_split_clause,[],[f162,f499]) ).
fof(f162,plain,
! [X0] : ~ empty(succ(X0)),
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0] : ~ empty(succ(X0)),
file('/export/starexec/sandbox/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',fc1_ordinal1) ).
fof(f497,plain,
spl20_48,
inference(avatar_split_clause,[],[f257,f494]) ).
fof(f494,plain,
( spl20_48
<=> function(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_48])]) ).
fof(f257,plain,
function(sK19),
inference(cnf_transformation,[],[f143]) ).
fof(f143,plain,
( function(sK19)
& empty(sK19)
& relation(sK19) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f30,f142]) ).
fof(f142,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/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',rc2_funct_1) ).
fof(f492,plain,
spl20_47,
inference(avatar_split_clause,[],[f256,f489]) ).
fof(f256,plain,
empty(sK19),
inference(cnf_transformation,[],[f143]) ).
fof(f487,plain,
spl20_46,
inference(avatar_split_clause,[],[f255,f484]) ).
fof(f484,plain,
( spl20_46
<=> relation(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_46])]) ).
fof(f255,plain,
relation(sK19),
inference(cnf_transformation,[],[f143]) ).
fof(f482,plain,
spl20_45,
inference(avatar_split_clause,[],[f254,f479]) ).
fof(f254,plain,
ordinal(sK18),
inference(cnf_transformation,[],[f141]) ).
fof(f141,plain,
( ordinal(sK18)
& epsilon_connected(sK18)
& epsilon_transitive(sK18)
& empty(sK18)
& one_to_one(sK18)
& function(sK18)
& relation(sK18) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f31,f140]) ).
fof(f140,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& one_to_one(X0)
& function(X0)
& relation(X0) )
=> ( ordinal(sK18)
& epsilon_connected(sK18)
& epsilon_transitive(sK18)
& empty(sK18)
& one_to_one(sK18)
& function(sK18)
& relation(sK18) ) ),
introduced(choice_axiom,[]) ).
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/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',rc2_ordinal1) ).
fof(f477,plain,
spl20_44,
inference(avatar_split_clause,[],[f253,f474]) ).
fof(f474,plain,
( spl20_44
<=> epsilon_connected(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_44])]) ).
fof(f253,plain,
epsilon_connected(sK18),
inference(cnf_transformation,[],[f141]) ).
fof(f472,plain,
spl20_43,
inference(avatar_split_clause,[],[f252,f469]) ).
fof(f469,plain,
( spl20_43
<=> epsilon_transitive(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_43])]) ).
fof(f252,plain,
epsilon_transitive(sK18),
inference(cnf_transformation,[],[f141]) ).
fof(f467,plain,
spl20_42,
inference(avatar_split_clause,[],[f251,f464]) ).
fof(f251,plain,
empty(sK18),
inference(cnf_transformation,[],[f141]) ).
fof(f462,plain,
spl20_41,
inference(avatar_split_clause,[],[f250,f459]) ).
fof(f459,plain,
( spl20_41
<=> one_to_one(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_41])]) ).
fof(f250,plain,
one_to_one(sK18),
inference(cnf_transformation,[],[f141]) ).
fof(f457,plain,
spl20_40,
inference(avatar_split_clause,[],[f249,f454]) ).
fof(f454,plain,
( spl20_40
<=> function(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_40])]) ).
fof(f249,plain,
function(sK18),
inference(cnf_transformation,[],[f141]) ).
fof(f452,plain,
spl20_39,
inference(avatar_split_clause,[],[f248,f449]) ).
fof(f449,plain,
( spl20_39
<=> relation(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_39])]) ).
fof(f248,plain,
relation(sK18),
inference(cnf_transformation,[],[f141]) ).
fof(f447,plain,
spl20_38,
inference(avatar_split_clause,[],[f247,f444]) ).
fof(f444,plain,
( spl20_38
<=> one_to_one(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_38])]) ).
fof(f247,plain,
one_to_one(sK17),
inference(cnf_transformation,[],[f139]) ).
fof(f139,plain,
( one_to_one(sK17)
& function(sK17)
& relation(sK17) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f34,f138]) ).
fof(f138,plain,
( ? [X0] :
( one_to_one(X0)
& function(X0)
& relation(X0) )
=> ( one_to_one(sK17)
& function(sK17)
& relation(sK17) ) ),
introduced(choice_axiom,[]) ).
fof(f34,axiom,
? [X0] :
( one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',rc3_funct_1) ).
fof(f442,plain,
spl20_37,
inference(avatar_split_clause,[],[f246,f439]) ).
fof(f439,plain,
( spl20_37
<=> function(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_37])]) ).
fof(f246,plain,
function(sK17),
inference(cnf_transformation,[],[f139]) ).
fof(f437,plain,
spl20_36,
inference(avatar_split_clause,[],[f245,f434]) ).
fof(f434,plain,
( spl20_36
<=> relation(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_36])]) ).
fof(f245,plain,
relation(sK17),
inference(cnf_transformation,[],[f139]) ).
fof(f432,plain,
spl20_35,
inference(avatar_split_clause,[],[f244,f429]) ).
fof(f244,plain,
function(sK16),
inference(cnf_transformation,[],[f137]) ).
fof(f137,plain,
( function(sK16)
& relation(sK16) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f26,f136]) ).
fof(f136,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/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',rc1_funct_1) ).
fof(f427,plain,
spl20_34,
inference(avatar_split_clause,[],[f243,f424]) ).
fof(f243,plain,
relation(sK16),
inference(cnf_transformation,[],[f137]) ).
fof(f422,plain,
spl20_33,
inference(avatar_split_clause,[],[f242,f419]) ).
fof(f242,plain,
function(sK15),
inference(cnf_transformation,[],[f135]) ).
fof(f135,plain,
( function(sK15)
& relation_empty_yielding(sK15)
& relation(sK15) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f37,f134]) ).
fof(f134,plain,
( ? [X0] :
( function(X0)
& relation_empty_yielding(X0)
& relation(X0) )
=> ( function(sK15)
& relation_empty_yielding(sK15)
& relation(sK15) ) ),
introduced(choice_axiom,[]) ).
fof(f37,axiom,
? [X0] :
( function(X0)
& relation_empty_yielding(X0)
& relation(X0) ),
file('/export/starexec/sandbox/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',rc4_funct_1) ).
fof(f417,plain,
spl20_32,
inference(avatar_split_clause,[],[f241,f414]) ).
fof(f414,plain,
( spl20_32
<=> relation_empty_yielding(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_32])]) ).
fof(f241,plain,
relation_empty_yielding(sK15),
inference(cnf_transformation,[],[f135]) ).
fof(f412,plain,
spl20_31,
inference(avatar_split_clause,[],[f240,f409]) ).
fof(f240,plain,
relation(sK15),
inference(cnf_transformation,[],[f135]) ).
fof(f407,plain,
spl20_30,
inference(avatar_split_clause,[],[f239,f404]) ).
fof(f404,plain,
( spl20_30
<=> relation_empty_yielding(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_30])]) ).
fof(f239,plain,
relation_empty_yielding(sK14),
inference(cnf_transformation,[],[f133]) ).
fof(f133,plain,
( relation_empty_yielding(sK14)
& relation(sK14) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f36,f132]) ).
fof(f132,plain,
( ? [X0] :
( relation_empty_yielding(X0)
& relation(X0) )
=> ( relation_empty_yielding(sK14)
& relation(sK14) ) ),
introduced(choice_axiom,[]) ).
fof(f36,axiom,
? [X0] :
( relation_empty_yielding(X0)
& relation(X0) ),
file('/export/starexec/sandbox/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',rc3_relat_1) ).
fof(f402,plain,
spl20_29,
inference(avatar_split_clause,[],[f238,f399]) ).
fof(f238,plain,
relation(sK14),
inference(cnf_transformation,[],[f133]) ).
fof(f397,plain,
spl20_28,
inference(avatar_split_clause,[],[f237,f394]) ).
fof(f237,plain,
function(sK13),
inference(cnf_transformation,[],[f131]) ).
fof(f131,plain,
( function(sK13)
& relation_non_empty(sK13)
& relation(sK13) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f38,f130]) ).
fof(f130,plain,
( ? [X0] :
( function(X0)
& relation_non_empty(X0)
& relation(X0) )
=> ( function(sK13)
& relation_non_empty(sK13)
& relation(sK13) ) ),
introduced(choice_axiom,[]) ).
fof(f38,axiom,
? [X0] :
( function(X0)
& relation_non_empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',rc5_funct_1) ).
fof(f392,plain,
spl20_27,
inference(avatar_split_clause,[],[f236,f389]) ).
fof(f389,plain,
( spl20_27
<=> relation_non_empty(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_27])]) ).
fof(f236,plain,
relation_non_empty(sK13),
inference(cnf_transformation,[],[f131]) ).
fof(f387,plain,
spl20_26,
inference(avatar_split_clause,[],[f235,f384]) ).
fof(f235,plain,
relation(sK13),
inference(cnf_transformation,[],[f131]) ).
fof(f382,plain,
spl20_25,
inference(avatar_split_clause,[],[f234,f379]) ).
fof(f379,plain,
( spl20_25
<=> relation(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_25])]) ).
fof(f234,plain,
relation(sK12),
inference(cnf_transformation,[],[f129]) ).
fof(f129,plain,
( relation(sK12)
& empty(sK12) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f28,f128]) ).
fof(f128,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/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',rc1_relat_1) ).
fof(f377,plain,
spl20_24,
inference(avatar_split_clause,[],[f233,f374]) ).
fof(f233,plain,
empty(sK12),
inference(cnf_transformation,[],[f129]) ).
fof(f372,plain,
spl20_23,
inference(avatar_split_clause,[],[f232,f369]) ).
fof(f232,plain,
ordinal(sK11),
inference(cnf_transformation,[],[f127]) ).
fof(f127,plain,
( ordinal(sK11)
& epsilon_connected(sK11)
& epsilon_transitive(sK11) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f27,f126]) ).
fof(f126,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/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',rc1_ordinal1) ).
fof(f367,plain,
spl20_22,
inference(avatar_split_clause,[],[f231,f364]) ).
fof(f364,plain,
( spl20_22
<=> epsilon_connected(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_22])]) ).
fof(f231,plain,
epsilon_connected(sK11),
inference(cnf_transformation,[],[f127]) ).
fof(f362,plain,
spl20_21,
inference(avatar_split_clause,[],[f230,f359]) ).
fof(f359,plain,
( spl20_21
<=> epsilon_transitive(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_21])]) ).
fof(f230,plain,
epsilon_transitive(sK11),
inference(cnf_transformation,[],[f127]) ).
fof(f357,plain,
spl20_20,
inference(avatar_split_clause,[],[f229,f354]) ).
fof(f354,plain,
( spl20_20
<=> relation(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_20])]) ).
fof(f229,plain,
relation(sK10),
inference(cnf_transformation,[],[f125]) ).
fof(f125,plain,
( relation(sK10)
& ~ empty(sK10) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f32,f124]) ).
fof(f124,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/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',rc2_relat_1) ).
fof(f352,plain,
~ spl20_19,
inference(avatar_split_clause,[],[f228,f349]) ).
fof(f349,plain,
( spl20_19
<=> empty(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_19])]) ).
fof(f228,plain,
~ empty(sK10),
inference(cnf_transformation,[],[f125]) ).
fof(f347,plain,
spl20_18,
inference(avatar_split_clause,[],[f227,f344]) ).
fof(f227,plain,
ordinal(sK9),
inference(cnf_transformation,[],[f123]) ).
fof(f123,plain,
( ordinal(sK9)
& epsilon_connected(sK9)
& epsilon_transitive(sK9)
& ~ empty(sK9) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f35,f122]) ).
fof(f122,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/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',rc3_ordinal1) ).
fof(f342,plain,
spl20_17,
inference(avatar_split_clause,[],[f226,f339]) ).
fof(f339,plain,
( spl20_17
<=> epsilon_connected(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_17])]) ).
fof(f226,plain,
epsilon_connected(sK9),
inference(cnf_transformation,[],[f123]) ).
fof(f337,plain,
spl20_16,
inference(avatar_split_clause,[],[f225,f334]) ).
fof(f334,plain,
( spl20_16
<=> epsilon_transitive(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_16])]) ).
fof(f225,plain,
epsilon_transitive(sK9),
inference(cnf_transformation,[],[f123]) ).
fof(f332,plain,
~ spl20_15,
inference(avatar_split_clause,[],[f224,f329]) ).
fof(f329,plain,
( spl20_15
<=> empty(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_15])]) ).
fof(f224,plain,
~ empty(sK9),
inference(cnf_transformation,[],[f123]) ).
fof(f327,plain,
spl20_14,
inference(avatar_split_clause,[],[f223,f324]) ).
fof(f223,plain,
empty(sK8),
inference(cnf_transformation,[],[f121]) ).
fof(f121,plain,
empty(sK8),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f29,f120]) ).
fof(f120,plain,
( ? [X0] : empty(X0)
=> empty(sK8) ),
introduced(choice_axiom,[]) ).
fof(f29,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',rc1_xboole_0) ).
fof(f322,plain,
~ spl20_13,
inference(avatar_split_clause,[],[f222,f319]) ).
fof(f319,plain,
( spl20_13
<=> empty(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_13])]) ).
fof(f222,plain,
~ empty(sK7),
inference(cnf_transformation,[],[f119]) ).
fof(f119,plain,
~ empty(sK7),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f33,f118]) ).
fof(f118,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK7) ),
introduced(choice_axiom,[]) ).
fof(f33,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',rc2_xboole_0) ).
fof(f317,plain,
spl20_12,
inference(avatar_split_clause,[],[f161,f314]) ).
fof(f161,plain,
ordinal(empty_set),
inference(cnf_transformation,[],[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/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',fc2_ordinal1) ).
fof(f312,plain,
spl20_11,
inference(avatar_split_clause,[],[f160,f309]) ).
fof(f309,plain,
( spl20_11
<=> epsilon_connected(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_11])]) ).
fof(f160,plain,
epsilon_connected(empty_set),
inference(cnf_transformation,[],[f19]) ).
fof(f307,plain,
spl20_10,
inference(avatar_split_clause,[],[f159,f304]) ).
fof(f304,plain,
( spl20_10
<=> epsilon_transitive(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_10])]) ).
fof(f159,plain,
epsilon_transitive(empty_set),
inference(cnf_transformation,[],[f19]) ).
fof(f302,plain,
spl20_9,
inference(avatar_split_clause,[],[f157,f299]) ).
fof(f157,plain,
one_to_one(empty_set),
inference(cnf_transformation,[],[f19]) ).
fof(f297,plain,
spl20_8,
inference(avatar_split_clause,[],[f156,f294]) ).
fof(f294,plain,
( spl20_8
<=> function(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_8])]) ).
fof(f156,plain,
function(empty_set),
inference(cnf_transformation,[],[f19]) ).
fof(f292,plain,
spl20_7,
inference(avatar_split_clause,[],[f153,f289]) ).
fof(f153,plain,
relation_empty_yielding(empty_set),
inference(cnf_transformation,[],[f16]) ).
fof(f16,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',fc12_relat_1) ).
fof(f287,plain,
spl20_6,
inference(avatar_split_clause,[],[f150,f284]) ).
fof(f284,plain,
( spl20_6
<=> relation(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_6])]) ).
fof(f150,plain,
relation(empty_set),
inference(cnf_transformation,[],[f24]) ).
fof(f24,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',fc4_relat_1) ).
fof(f282,plain,
spl20_5,
inference(avatar_split_clause,[],[f148,f279]) ).
fof(f148,plain,
empty(empty_set),
inference(cnf_transformation,[],[f18]) ).
fof(f18,axiom,
empty(empty_set),
file('/export/starexec/sandbox/tmp/tmp.nPWnCD0wMl/Vampire---4.8_15409',fc1_xboole_0) ).
fof(f277,plain,
( spl20_3
| spl20_4 ),
inference(avatar_split_clause,[],[f146,f274,f270]) ).
fof(f146,plain,
( ordinal_subset(sK1,sK2)
| in(sK1,succ(sK2)) ),
inference(cnf_transformation,[],[f97]) ).
fof(f268,plain,
spl20_2,
inference(avatar_split_clause,[],[f145,f265]) ).
fof(f145,plain,
ordinal(sK2),
inference(cnf_transformation,[],[f97]) ).
fof(f263,plain,
spl20_1,
inference(avatar_split_clause,[],[f144,f260]) ).
fof(f144,plain,
ordinal(sK1),
inference(cnf_transformation,[],[f97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM401+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.14 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.35 % Computer : n018.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 : Wed Aug 30 15:21:19 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.41 % (15650)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.42 % (15676)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.21/0.42 % (15677)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.21/0.42 % (15678)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 Vampire---4 for (569ds/0Mi)
% 0.21/0.42 % (15680)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 Vampire---4 for (531ds/0Mi)
% 0.21/0.42 % (15679)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.21/0.42 % (15681)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 Vampire---4 for (522ds/0Mi)
% 0.21/0.42 % (15683)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 Vampire---4 for (497ds/0Mi)
% 0.21/0.42 TRYING [1]
% 0.21/0.42 TRYING [2]
% 0.21/0.42 TRYING [3]
% 0.21/0.43 TRYING [1]
% 0.21/0.43 TRYING [2]
% 0.21/0.43 TRYING [4]
% 0.21/0.44 TRYING [5]
% 0.21/0.44 TRYING [3]
% 0.21/0.47 TRYING [6]
% 0.21/0.49 TRYING [4]
% 0.21/0.52 TRYING [7]
% 0.21/0.54 TRYING [1]
% 0.21/0.54 TRYING [2]
% 0.21/0.54 TRYING [3]
% 0.21/0.54 TRYING [4]
% 0.21/0.55 TRYING [5]
% 0.21/0.57 TRYING [6]
% 0.21/0.57 TRYING [5]
% 0.21/0.58 TRYING [8]
% 1.29/0.61 TRYING [7]
% 1.29/0.68 TRYING [8]
% 2.08/0.70 TRYING [9]
% 2.08/0.75 TRYING [6]
% 2.97/0.83 TRYING [9]
% 3.17/0.92 TRYING [10]
% 4.79/1.09 TRYING [10]
% 5.08/1.22 TRYING [7]
% 6.98/1.40 TRYING [11]
% 11.49/2.04 TRYING [11]
% 12.47/2.20 TRYING [8]
% 22.72/3.65 TRYING [12]
% 22.72/3.70 TRYING [12]
% 30.10/4.68 TRYING [9]
% 48.59/7.36 % (15680)First to succeed.
% 49.12/7.40 % (15680)Refutation found. Thanks to Tanya!
% 49.12/7.40 % SZS status Theorem for Vampire---4
% 49.12/7.40 % SZS output start Proof for Vampire---4
% See solution above
% 49.12/7.42 % (15680)------------------------------
% 49.12/7.42 % (15680)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 49.12/7.42 % (15680)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 49.12/7.42 % (15680)Termination reason: Refutation
% 49.12/7.42
% 49.12/7.42 % (15680)Memory used [KB]: 59231
% 49.12/7.42 % (15680)Time elapsed: 6.974 s
% 49.12/7.42 % (15680)------------------------------
% 49.12/7.42 % (15680)------------------------------
% 49.12/7.42 % (15650)Success in time 7.029 s
% 49.12/7.42 % Vampire---4.8 exiting
%------------------------------------------------------------------------------