TSTP Solution File: SET016+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET016+1 : TPTP v8.2.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 03:14:40 EDT 2024
% Result : Theorem 10.60s 1.94s
% Output : Refutation 11.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 815
% Syntax : Number of formulae : 2810 ( 133 unt; 0 def)
% Number of atoms : 9601 ( 998 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 12067 (5276 ~;5802 |; 167 &)
% ( 797 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 25 ( 2 avg)
% Number of predicates : 771 ( 769 usr; 765 prp; 0-2 aty)
% Number of functors : 36 ( 36 usr; 11 con; 0-3 aty)
% Number of variables : 3599 (3562 !; 37 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f28852,plain,
$false,
inference(avatar_sat_refutation,[],[f275,f280,f285,f290,f294,f298,f303,f307,f312,f317,f322,f326,f330,f334,f340,f344,f348,f352,f356,f360,f365,f369,f373,f377,f381,f385,f389,f393,f412,f416,f420,f424,f428,f432,f436,f440,f444,f448,f452,f456,f480,f488,f492,f496,f500,f504,f533,f548,f552,f556,f587,f591,f598,f602,f625,f629,f633,f637,f641,f645,f649,f653,f667,f671,f675,f679,f683,f700,f704,f708,f712,f726,f730,f734,f765,f769,f783,f787,f813,f822,f827,f837,f841,f847,f851,f855,f861,f865,f879,f889,f893,f897,f929,f933,f942,f948,f964,f966,f974,f986,f996,f998,f1006,f1019,f1029,f1033,f1043,f1047,f1051,f1058,f1065,f1069,f1073,f1137,f1146,f1161,f1165,f1193,f1197,f1201,f1205,f1209,f1214,f1223,f1232,f1236,f1240,f1244,f1248,f1253,f1257,f1261,f1265,f1269,f1447,f1451,f1455,f1459,f1463,f1467,f1471,f1475,f1479,f1483,f1487,f1491,f1495,f1500,f1504,f1508,f1512,f1516,f1708,f1726,f1730,f1734,f1738,f1742,f1746,f1750,f1754,f1758,f1765,f1769,f1773,f1777,f1905,f2093,f2097,f2101,f2119,f2123,f2127,f2131,f2234,f2250,f2254,f2258,f2262,f2341,f2360,f2364,f2498,f2502,f2506,f2510,f2514,f2550,f2554,f2558,f2723,f2727,f2731,f2739,f2748,f2776,f2780,f2798,f2802,f2806,f2988,f2992,f3011,f3015,f3019,f3023,f3027,f3031,f3035,f3039,f3047,f3051,f3538,f3542,f3546,f3550,f3554,f3558,f3562,f3631,f3860,f3865,f3869,f3922,f3926,f3997,f4001,f4105,f4109,f4113,f4122,f4136,f4141,f4146,f4151,f4156,f4162,f4166,f4244,f4610,f4620,f4624,f4636,f4640,f4644,f4802,f4811,f4815,f4927,f4966,f4970,f4975,f5033,f5075,f5087,f5102,f5141,f5145,f5215,f5219,f5360,f5364,f5424,f5509,f5522,f5535,f5548,f5552,f5556,f5636,f5640,f5644,f5662,f5671,f5677,f5681,f5813,f5818,f5823,f5828,f5833,f5838,f5842,f5846,f5855,f5860,f5865,f5881,f5887,f5891,f5895,f5899,f5978,f5982,f6015,f6071,f6076,f6191,f6196,f6200,f6211,f6278,f6283,f6288,f6293,f6310,f6479,f6722,f6728,f6856,f6860,f6864,f6868,f6987,f7048,f7135,f7139,f7143,f7147,f7159,f7163,f7168,f7305,f7310,f7314,f7318,f7629,f7816,f7820,f7824,f7828,f7832,f7837,f7994,f8084,f8089,f8247,f8252,f8256,f8616,f8683,f8768,f8777,f8783,f9022,f9220,f9270,f9273,f9466,f9470,f9474,f9478,f9482,f9486,f9609,f9613,f9619,f9715,f10283,f10386,f10519,f10594,f10600,f10604,f10609,f10618,f10623,f10799,f10804,f10878,f10950,f10954,f10958,f11052,f11056,f11064,f11081,f11085,f11089,f11188,f11192,f11196,f11200,f11204,f11208,f11213,f11218,f11223,f11228,f11233,f11242,f11404,f11489,f11493,f11497,f11511,f11644,f11649,f11734,f11740,f11744,f11748,f11752,f11756,f11761,f11766,f11770,f11774,f11778,f11779,f11783,f11787,f11791,f11795,f11800,f11805,f11809,f11844,f12496,f12500,f12504,f12513,f12627,f12638,f12642,f12646,f12650,f12654,f12660,f13010,f13059,f13157,f13162,f13242,f13572,f13577,f13583,f13588,f13645,f13649,f13656,f13657,f13719,f13720,f13721,f13722,f13723,f13724,f13725,f14518,f14522,f14527,f15541,f17109,f17113,f17117,f17121,f17289,f17293,f17297,f17366,f17467,f17489,f17548,f17603,f17662,f17666,f17840,f17844,f17934,f17955,f18082,f18086,f18168,f18172,f18176,f18180,f18184,f18188,f18322,f18327,f18332,f18337,f18341,f18345,f18490,f18558,f18563,f18567,f18571,f18575,f18587,f18591,f18596,f18605,f18614,f18623,f18631,f18636,f18777,f18785,f18793,f18797,f18802,f18810,f18815,f18819,f18823,f18827,f18831,f18835,f19070,f19077,f19081,f19088,f19108,f19116,f19128,f19133,f19143,f19147,f19173,f19201,f19206,f19212,f19216,f19349,f19353,f19368,f19374,f19381,f19392,f19396,f19400,f19404,f19408,f19413,f19417,f19421,f19425,f19429,f19433,f19437,f19441,f19446,f19451,f19455,f19459,f19463,f19467,f19471,f19475,f19479,f19485,f19489,f19609,f20467,f20471,f20500,f20506,f20512,f20516,f20521,f20525,f20529,f20533,f20537,f20541,f20545,f20549,f20553,f20557,f20561,f20565,f20569,f20573,f20577,f20581,f20585,f20589,f20593,f20597,f20601,f20605,f20609,f20613,f20617,f20622,f20627,f20632,f20637,f20641,f20645,f20649,f20653,f20657,f20661,f20665,f20669,f20673,f20677,f20681,f20685,f20689,f20744,f20989,f21098,f21442,f22893,f22897,f22903,f22909,f22915,f22921,f22925,f22938,f22943,f22947,f22951,f22955,f22959,f22963,f22967,f22971,f22975,f22979,f22983,f22988,f22992,f22996,f23000,f23004,f23008,f23012,f23016,f23020,f23024,f23028,f23033,f23037,f23041,f23045,f23053,f23057,f23063,f23067,f23081,f23085,f23091,f23095,f23099,f23103,f23107,f23112,f23117,f23126,f23130,f23134,f23139,f23144,f23149,f23153,f23157,f23165,f23174,f23178,f23182,f23190,f24293,f24577,f25724,f25729,f25734,f25739,f25745,f25749,f25753,f26188,f26192,f26196,f26200,f26204,f26208,f26212,f26217,f26221,f26225,f26229,f26233,f26237,f26241,f26245,f26249,f26253,f26257,f26262,f26266,f26270,f26274,f26278,f26282,f26286,f26290,f26294,f26298,f26302,f26330,f26334,f26338,f26342,f26346,f26350,f26354,f26358,f26362,f26366,f26367,f26585,f26664,f26743,f26748,f26894,f27025,f27098,f27103,f27108,f27113,f27114,f27115,f27119,f27125,f27135,f27137,f27142,f27151,f27214,f27218,f27219,f27226,f27235,f27438,f27439,f27490,f27500,f27511,f27737,f27742,f27748,f27907,f27909,f28732,f28848,f28851]) ).
fof(f28851,plain,
( ~ spl10_13
| spl10_764 ),
inference(avatar_contradiction_clause,[],[f28849]) ).
fof(f28849,plain,
( $false
| ~ spl10_13
| spl10_764 ),
inference(resolution,[],[f28847,f329]) ).
fof(f329,plain,
( ! [X0,X1] : member(unordered_pair(X0,X1),universal_class)
| ~ spl10_13 ),
inference(avatar_component_clause,[],[f328]) ).
fof(f328,plain,
( spl10_13
<=> ! [X0,X1] : member(unordered_pair(X0,X1),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_13])]) ).
fof(f28847,plain,
( ~ member(unordered_pair(sK2,sK2),universal_class)
| spl10_764 ),
inference(avatar_component_clause,[],[f28845]) ).
fof(f28845,plain,
( spl10_764
<=> member(unordered_pair(sK2,sK2),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_764])]) ).
fof(f28848,plain,
( ~ spl10_764
| spl10_314
| ~ spl10_41
| ~ spl10_108
| ~ spl10_363 ),
inference(avatar_split_clause,[],[f10633,f8780,f1004,f454,f6012,f28845]) ).
fof(f6012,plain,
( spl10_314
<=> unordered_pair(sK0,sK0) = unordered_pair(sK2,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_314])]) ).
fof(f454,plain,
( spl10_41
<=> ! [X2,X1] :
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_41])]) ).
fof(f1004,plain,
( spl10_108
<=> ! [X0] :
( ~ member(X0,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| unordered_pair(sK0,sK0) = X0
| unordered_pair(sK0,unordered_pair(sK1,sK1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_108])]) ).
fof(f8780,plain,
( spl10_363
<=> unordered_pair(sK0,sK0) = unordered_pair(sK0,unordered_pair(sK1,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_363])]) ).
fof(f10633,plain,
( unordered_pair(sK0,sK0) = unordered_pair(sK2,sK2)
| ~ member(unordered_pair(sK2,sK2),universal_class)
| ~ spl10_41
| ~ spl10_108
| ~ spl10_363 ),
inference(duplicate_literal_removal,[],[f10632]) ).
fof(f10632,plain,
( unordered_pair(sK0,sK0) = unordered_pair(sK2,sK2)
| unordered_pair(sK0,sK0) = unordered_pair(sK2,sK2)
| ~ member(unordered_pair(sK2,sK2),universal_class)
| ~ spl10_41
| ~ spl10_108
| ~ spl10_363 ),
inference(forward_demodulation,[],[f1008,f8782]) ).
fof(f8782,plain,
( unordered_pair(sK0,sK0) = unordered_pair(sK0,unordered_pair(sK1,sK1))
| ~ spl10_363 ),
inference(avatar_component_clause,[],[f8780]) ).
fof(f1008,plain,
( unordered_pair(sK0,sK0) = unordered_pair(sK2,sK2)
| unordered_pair(sK0,unordered_pair(sK1,sK1)) = unordered_pair(sK2,sK2)
| ~ member(unordered_pair(sK2,sK2),universal_class)
| ~ spl10_41
| ~ spl10_108 ),
inference(resolution,[],[f1005,f455]) ).
fof(f455,plain,
( ! [X2,X1] :
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) )
| ~ spl10_41 ),
inference(avatar_component_clause,[],[f454]) ).
fof(f1005,plain,
( ! [X0] :
( ~ member(X0,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| unordered_pair(sK0,sK0) = X0
| unordered_pair(sK0,unordered_pair(sK1,sK1)) = X0 )
| ~ spl10_108 ),
inference(avatar_component_clause,[],[f1004]) ).
fof(f28732,plain,
( ~ spl10_363
| ~ spl10_313
| spl10_530
| ~ spl10_534 ),
inference(avatar_split_clause,[],[f27019,f19085,f19063,f6008,f8780]) ).
fof(f6008,plain,
( spl10_313
<=> unordered_pair(sK0,sK0) = unordered_pair(sK2,unordered_pair(sK3,sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_313])]) ).
fof(f19063,plain,
( spl10_530
<=> unordered_pair(sK0,unordered_pair(sK1,sK1)) = sK4(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_530])]) ).
fof(f19085,plain,
( spl10_534
<=> unordered_pair(sK2,unordered_pair(sK3,sK3)) = sK4(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_534])]) ).
fof(f27019,plain,
( unordered_pair(sK0,sK0) != unordered_pair(sK0,unordered_pair(sK1,sK1))
| ~ spl10_313
| spl10_530
| ~ spl10_534 ),
inference(forward_demodulation,[],[f27018,f6010]) ).
fof(f6010,plain,
( unordered_pair(sK0,sK0) = unordered_pair(sK2,unordered_pair(sK3,sK3))
| ~ spl10_313 ),
inference(avatar_component_clause,[],[f6008]) ).
fof(f27018,plain,
( unordered_pair(sK0,unordered_pair(sK1,sK1)) != unordered_pair(sK2,unordered_pair(sK3,sK3))
| spl10_530
| ~ spl10_534 ),
inference(forward_demodulation,[],[f19064,f19087]) ).
fof(f19087,plain,
( unordered_pair(sK2,unordered_pair(sK3,sK3)) = sK4(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| ~ spl10_534 ),
inference(avatar_component_clause,[],[f19085]) ).
fof(f19064,plain,
( unordered_pair(sK0,unordered_pair(sK1,sK1)) != sK4(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| spl10_530 ),
inference(avatar_component_clause,[],[f19063]) ).
fof(f27909,plain,
( ~ spl10_1
| spl10_723
| ~ spl10_41
| ~ spl10_362 ),
inference(avatar_split_clause,[],[f9120,f8774,f454,f26259,f272]) ).
fof(f272,plain,
( spl10_1
<=> member(sK0,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_1])]) ).
fof(f26259,plain,
( spl10_723
<=> member(sK0,unordered_pair(sK2,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_723])]) ).
fof(f8774,plain,
( spl10_362
<=> unordered_pair(sK0,unordered_pair(sK1,sK1)) = unordered_pair(sK2,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_362])]) ).
fof(f9120,plain,
( member(sK0,unordered_pair(sK2,sK2))
| ~ member(sK0,universal_class)
| ~ spl10_41
| ~ spl10_362 ),
inference(superposition,[],[f455,f8776]) ).
fof(f8776,plain,
( unordered_pair(sK0,unordered_pair(sK1,sK1)) = unordered_pair(sK2,sK2)
| ~ spl10_362 ),
inference(avatar_component_clause,[],[f8774]) ).
fof(f27907,plain,
( spl10_763
| ~ spl10_362
| ~ spl10_444 ),
inference(avatar_split_clause,[],[f12703,f12625,f8774,f27905]) ).
fof(f27905,plain,
( spl10_763
<=> ! [X0,X1] :
( sK6(X0,X1) = unordered_pair(sK2,sK2)
| ~ subclass(X0,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| subclass(X0,X1)
| sK6(X0,X1) = unordered_pair(sK0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_763])]) ).
fof(f12625,plain,
( spl10_444
<=> ! [X0,X1] :
( ~ subclass(X0,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| subclass(X0,X1)
| sK6(X0,X1) = unordered_pair(sK0,sK0)
| sK6(X0,X1) = unordered_pair(sK0,unordered_pair(sK1,sK1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_444])]) ).
fof(f12703,plain,
( ! [X0,X1] :
( sK6(X0,X1) = unordered_pair(sK2,sK2)
| ~ subclass(X0,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| subclass(X0,X1)
| sK6(X0,X1) = unordered_pair(sK0,sK0) )
| ~ spl10_362
| ~ spl10_444 ),
inference(forward_demodulation,[],[f12626,f8776]) ).
fof(f12626,plain,
( ! [X0,X1] :
( ~ subclass(X0,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| subclass(X0,X1)
| sK6(X0,X1) = unordered_pair(sK0,sK0)
| sK6(X0,X1) = unordered_pair(sK0,unordered_pair(sK1,sK1)) )
| ~ spl10_444 ),
inference(avatar_component_clause,[],[f12625]) ).
fof(f27748,plain,
( spl10_762
| ~ spl10_745
| ~ spl10_761 ),
inference(avatar_split_clause,[],[f27744,f27740,f27022,f27746]) ).
fof(f27746,plain,
( spl10_762
<=> ! [X0,X1] :
( ~ member(null_class,X0)
| ~ member(null_class,X1)
| member(unordered_pair(sK2,sK2),sum_class(intersection(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_762])]) ).
fof(f27022,plain,
( spl10_745
<=> null_class = unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_745])]) ).
fof(f27740,plain,
( spl10_761
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0)),X1)
| member(unordered_pair(sK2,sK2),sum_class(intersection(X0,X1)))
| ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_761])]) ).
fof(f27744,plain,
( ! [X0,X1] :
( ~ member(null_class,X0)
| ~ member(null_class,X1)
| member(unordered_pair(sK2,sK2),sum_class(intersection(X0,X1))) )
| ~ spl10_745
| ~ spl10_761 ),
inference(forward_demodulation,[],[f27743,f27024]) ).
fof(f27024,plain,
( null_class = unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0))
| ~ spl10_745 ),
inference(avatar_component_clause,[],[f27022]) ).
fof(f27743,plain,
( ! [X0,X1] :
( ~ member(null_class,X1)
| member(unordered_pair(sK2,sK2),sum_class(intersection(X0,X1)))
| ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0)),X0) )
| ~ spl10_745
| ~ spl10_761 ),
inference(forward_demodulation,[],[f27741,f27024]) ).
fof(f27741,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0)),X1)
| member(unordered_pair(sK2,sK2),sum_class(intersection(X0,X1)))
| ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0)),X0) )
| ~ spl10_761 ),
inference(avatar_component_clause,[],[f27740]) ).
fof(f27742,plain,
( spl10_761
| ~ spl10_9
| ~ spl10_313
| ~ spl10_362
| ~ spl10_457 ),
inference(avatar_split_clause,[],[f26943,f13581,f8774,f6008,f309,f27740]) ).
fof(f309,plain,
( spl10_9
<=> unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK1,sK1))) = unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_9])]) ).
fof(f13581,plain,
( spl10_457
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X0)
| member(unordered_pair(sK0,unordered_pair(sK1,sK1)),sum_class(intersection(X0,X1)))
| ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_457])]) ).
fof(f26943,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0)),X1)
| member(unordered_pair(sK2,sK2),sum_class(intersection(X0,X1)))
| ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0)),X0) )
| ~ spl10_9
| ~ spl10_313
| ~ spl10_362
| ~ spl10_457 ),
inference(forward_demodulation,[],[f26942,f9142]) ).
fof(f9142,plain,
( unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0)) = unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK2,sK2))
| ~ spl10_9
| ~ spl10_313
| ~ spl10_362 ),
inference(forward_demodulation,[],[f9094,f6010]) ).
fof(f9094,plain,
( unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))) = unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK2,sK2))
| ~ spl10_9
| ~ spl10_362 ),
inference(superposition,[],[f311,f8776]) ).
fof(f311,plain,
( unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK1,sK1))) = unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))
| ~ spl10_9 ),
inference(avatar_component_clause,[],[f309]) ).
fof(f26942,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK2,sK2)),X1)
| member(unordered_pair(sK2,sK2),sum_class(intersection(X0,X1)))
| ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0)),X0) )
| ~ spl10_9
| ~ spl10_313
| ~ spl10_362
| ~ spl10_457 ),
inference(forward_demodulation,[],[f26941,f10667]) ).
fof(f10667,plain,
( unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))) = unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK2,sK2))
| ~ spl10_9
| ~ spl10_362 ),
inference(superposition,[],[f311,f8776]) ).
fof(f26941,plain,
( ! [X0,X1] :
( member(unordered_pair(sK2,sK2),sum_class(intersection(X0,X1)))
| ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0)),X0)
| ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X1) )
| ~ spl10_9
| ~ spl10_313
| ~ spl10_362
| ~ spl10_457 ),
inference(forward_demodulation,[],[f26940,f8776]) ).
fof(f26940,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0)),X0)
| member(unordered_pair(sK0,unordered_pair(sK1,sK1)),sum_class(intersection(X0,X1)))
| ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X1) )
| ~ spl10_9
| ~ spl10_313
| ~ spl10_362
| ~ spl10_457 ),
inference(forward_demodulation,[],[f26939,f9142]) ).
fof(f26939,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK2,sK2)),X0)
| member(unordered_pair(sK0,unordered_pair(sK1,sK1)),sum_class(intersection(X0,X1)))
| ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X1) )
| ~ spl10_9
| ~ spl10_362
| ~ spl10_457 ),
inference(forward_demodulation,[],[f13582,f10667]) ).
fof(f13582,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X0)
| member(unordered_pair(sK0,unordered_pair(sK1,sK1)),sum_class(intersection(X0,X1)))
| ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X1) )
| ~ spl10_457 ),
inference(avatar_component_clause,[],[f13581]) ).
fof(f27737,plain,
( spl10_760
| ~ spl10_362
| ~ spl10_420 ),
inference(avatar_split_clause,[],[f12709,f11732,f8774,f27735]) ).
fof(f27735,plain,
( spl10_760
<=> ! [X0] :
( sK4(X0) = unordered_pair(sK2,sK2)
| ~ subclass(X0,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| null_class = X0
| sK4(X0) = unordered_pair(sK0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_760])]) ).
fof(f11732,plain,
( spl10_420
<=> ! [X0] :
( ~ subclass(X0,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| null_class = X0
| sK4(X0) = unordered_pair(sK0,sK0)
| sK4(X0) = unordered_pair(sK0,unordered_pair(sK1,sK1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_420])]) ).
fof(f12709,plain,
( ! [X0] :
( sK4(X0) = unordered_pair(sK2,sK2)
| ~ subclass(X0,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| null_class = X0
| sK4(X0) = unordered_pair(sK0,sK0) )
| ~ spl10_362
| ~ spl10_420 ),
inference(forward_demodulation,[],[f11733,f8776]) ).
fof(f11733,plain,
( ! [X0] :
( ~ subclass(X0,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| null_class = X0
| sK4(X0) = unordered_pair(sK0,sK0)
| sK4(X0) = unordered_pair(sK0,unordered_pair(sK1,sK1)) )
| ~ spl10_420 ),
inference(avatar_component_clause,[],[f11732]) ).
fof(f27511,plain,
( spl10_387
| ~ spl10_1
| ~ spl10_239 ),
inference(avatar_split_clause,[],[f16340,f3995,f272,f10802]) ).
fof(f10802,plain,
( spl10_387
<=> ! [X0] :
( sK6(universal_class,X0) = second(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK6(universal_class,X0),sK6(universal_class,X0)))))
| subclass(universal_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_387])]) ).
fof(f3995,plain,
( spl10_239
<=> ! [X0,X1] :
( sK6(universal_class,X1) = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK6(universal_class,X1),sK6(universal_class,X1)))))
| ~ member(X0,universal_class)
| subclass(universal_class,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_239])]) ).
fof(f16340,plain,
( ! [X0] :
( sK6(universal_class,X0) = second(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK6(universal_class,X0),sK6(universal_class,X0)))))
| subclass(universal_class,X0) )
| ~ spl10_1
| ~ spl10_239 ),
inference(resolution,[],[f3996,f274]) ).
fof(f274,plain,
( member(sK0,universal_class)
| ~ spl10_1 ),
inference(avatar_component_clause,[],[f272]) ).
fof(f3996,plain,
( ! [X0,X1] :
( ~ member(X0,universal_class)
| sK6(universal_class,X1) = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK6(universal_class,X1),sK6(universal_class,X1)))))
| subclass(universal_class,X1) )
| ~ spl10_239 ),
inference(avatar_component_clause,[],[f3995]) ).
fof(f27500,plain,
( spl10_759
| ~ spl10_13
| ~ spl10_463 ),
inference(avatar_split_clause,[],[f14528,f14516,f328,f27498]) ).
fof(f27498,plain,
( spl10_759
<=> ! [X0,X1] : unordered_pair(X0,X1) = first(unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),unordered_pair(unordered_pair(X0,X1),unordered_pair(sK2,sK2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_759])]) ).
fof(f14516,plain,
( spl10_463
<=> ! [X0] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK2,sK2)))) = X0
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_463])]) ).
fof(f14528,plain,
( ! [X0,X1] : unordered_pair(X0,X1) = first(unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),unordered_pair(unordered_pair(X0,X1),unordered_pair(sK2,sK2))))
| ~ spl10_13
| ~ spl10_463 ),
inference(resolution,[],[f14517,f329]) ).
fof(f14517,plain,
( ! [X0] :
( ~ member(X0,universal_class)
| first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK2,sK2)))) = X0 )
| ~ spl10_463 ),
inference(avatar_component_clause,[],[f14516]) ).
fof(f27490,plain,
( spl10_758
| ~ spl10_9
| ~ spl10_313
| ~ spl10_362
| ~ spl10_455 ),
inference(avatar_split_clause,[],[f26938,f13570,f8774,f6008,f309,f27488]) ).
fof(f27488,plain,
( spl10_758
<=> ! [X0,X1] :
( sK6(X0,X1) = unordered_pair(sK2,sK2)
| ~ subclass(X0,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0)))
| subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_758])]) ).
fof(f13570,plain,
( spl10_455
<=> ! [X0,X1] :
( sK6(X0,X1) = unordered_pair(sK2,sK2)
| ~ subclass(X0,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| subclass(X0,X1)
| sK6(X0,X1) = unordered_pair(sK0,unordered_pair(sK1,sK1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_455])]) ).
fof(f26938,plain,
( ! [X0,X1] :
( sK6(X0,X1) = unordered_pair(sK2,sK2)
| ~ subclass(X0,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0)))
| subclass(X0,X1) )
| ~ spl10_9
| ~ spl10_313
| ~ spl10_362
| ~ spl10_455 ),
inference(duplicate_literal_removal,[],[f26937]) ).
fof(f26937,plain,
( ! [X0,X1] :
( sK6(X0,X1) = unordered_pair(sK2,sK2)
| ~ subclass(X0,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0)))
| sK6(X0,X1) = unordered_pair(sK2,sK2)
| subclass(X0,X1) )
| ~ spl10_9
| ~ spl10_313
| ~ spl10_362
| ~ spl10_455 ),
inference(forward_demodulation,[],[f26936,f8776]) ).
fof(f26936,plain,
( ! [X0,X1] :
( ~ subclass(X0,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0)))
| sK6(X0,X1) = unordered_pair(sK2,sK2)
| subclass(X0,X1)
| sK6(X0,X1) = unordered_pair(sK0,unordered_pair(sK1,sK1)) )
| ~ spl10_9
| ~ spl10_313
| ~ spl10_362
| ~ spl10_455 ),
inference(forward_demodulation,[],[f26935,f9142]) ).
fof(f26935,plain,
( ! [X0,X1] :
( ~ subclass(X0,unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK2,sK2)))
| sK6(X0,X1) = unordered_pair(sK2,sK2)
| subclass(X0,X1)
| sK6(X0,X1) = unordered_pair(sK0,unordered_pair(sK1,sK1)) )
| ~ spl10_9
| ~ spl10_362
| ~ spl10_455 ),
inference(forward_demodulation,[],[f13571,f10667]) ).
fof(f13571,plain,
( ! [X0,X1] :
( sK6(X0,X1) = unordered_pair(sK2,sK2)
| ~ subclass(X0,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| subclass(X0,X1)
| sK6(X0,X1) = unordered_pair(sK0,unordered_pair(sK1,sK1)) )
| ~ spl10_455 ),
inference(avatar_component_clause,[],[f13570]) ).
fof(f27439,plain,
( spl10_357
| ~ spl10_1
| ~ spl10_235 ),
inference(avatar_split_clause,[],[f16232,f3863,f272,f8254]) ).
fof(f8254,plain,
( spl10_357
<=> ! [X0] :
( sK0 = first(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK6(universal_class,X0),sK6(universal_class,X0)))))
| subclass(universal_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_357])]) ).
fof(f3863,plain,
( spl10_235
<=> ! [X0,X1] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK6(universal_class,X1),sK6(universal_class,X1))))) = X0
| ~ member(X0,universal_class)
| subclass(universal_class,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_235])]) ).
fof(f16232,plain,
( ! [X0] :
( sK0 = first(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK6(universal_class,X0),sK6(universal_class,X0)))))
| subclass(universal_class,X0) )
| ~ spl10_1
| ~ spl10_235 ),
inference(resolution,[],[f3864,f274]) ).
fof(f3864,plain,
( ! [X0,X1] :
( ~ member(X0,universal_class)
| first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK6(universal_class,X1),sK6(universal_class,X1))))) = X0
| subclass(universal_class,X1) )
| ~ spl10_235 ),
inference(avatar_component_clause,[],[f3863]) ).
fof(f27438,plain,
( spl10_757
| ~ spl10_15
| ~ spl10_463 ),
inference(avatar_split_clause,[],[f14534,f14516,f338,f27436]) ).
fof(f27436,plain,
( spl10_757
<=> ! [X0] :
( sK4(X0) = first(unordered_pair(unordered_pair(sK4(X0),sK4(X0)),unordered_pair(sK4(X0),unordered_pair(sK2,sK2))))
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_757])]) ).
fof(f338,plain,
( spl10_15
<=> ! [X0] :
( member(sK4(X0),universal_class)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_15])]) ).
fof(f14534,plain,
( ! [X0] :
( sK4(X0) = first(unordered_pair(unordered_pair(sK4(X0),sK4(X0)),unordered_pair(sK4(X0),unordered_pair(sK2,sK2))))
| null_class = X0 )
| ~ spl10_15
| ~ spl10_463 ),
inference(resolution,[],[f14517,f339]) ).
fof(f339,plain,
( ! [X0] :
( member(sK4(X0),universal_class)
| null_class = X0 )
| ~ spl10_15 ),
inference(avatar_component_clause,[],[f338]) ).
fof(f27235,plain,
( spl10_756
| ~ spl10_9
| ~ spl10_313
| ~ spl10_362
| ~ spl10_454 ),
inference(avatar_split_clause,[],[f26934,f13240,f8774,f6008,f309,f27233]) ).
fof(f27233,plain,
( spl10_756
<=> ! [X0] :
( sK4(X0) = unordered_pair(sK2,sK2)
| ~ subclass(X0,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0)))
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_756])]) ).
fof(f13240,plain,
( spl10_454
<=> ! [X0] :
( sK4(X0) = unordered_pair(sK2,sK2)
| ~ subclass(X0,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| null_class = X0
| sK4(X0) = unordered_pair(sK0,unordered_pair(sK1,sK1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_454])]) ).
fof(f26934,plain,
( ! [X0] :
( sK4(X0) = unordered_pair(sK2,sK2)
| ~ subclass(X0,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0)))
| null_class = X0 )
| ~ spl10_9
| ~ spl10_313
| ~ spl10_362
| ~ spl10_454 ),
inference(duplicate_literal_removal,[],[f26933]) ).
fof(f26933,plain,
( ! [X0] :
( sK4(X0) = unordered_pair(sK2,sK2)
| ~ subclass(X0,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0)))
| sK4(X0) = unordered_pair(sK2,sK2)
| null_class = X0 )
| ~ spl10_9
| ~ spl10_313
| ~ spl10_362
| ~ spl10_454 ),
inference(forward_demodulation,[],[f26932,f8776]) ).
fof(f26932,plain,
( ! [X0] :
( ~ subclass(X0,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0)))
| sK4(X0) = unordered_pair(sK2,sK2)
| null_class = X0
| sK4(X0) = unordered_pair(sK0,unordered_pair(sK1,sK1)) )
| ~ spl10_9
| ~ spl10_313
| ~ spl10_362
| ~ spl10_454 ),
inference(forward_demodulation,[],[f26931,f9142]) ).
fof(f26931,plain,
( ! [X0] :
( ~ subclass(X0,unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK2,sK2)))
| sK4(X0) = unordered_pair(sK2,sK2)
| null_class = X0
| sK4(X0) = unordered_pair(sK0,unordered_pair(sK1,sK1)) )
| ~ spl10_9
| ~ spl10_362
| ~ spl10_454 ),
inference(forward_demodulation,[],[f13241,f10667]) ).
fof(f13241,plain,
( ! [X0] :
( sK4(X0) = unordered_pair(sK2,sK2)
| ~ subclass(X0,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| null_class = X0
| sK4(X0) = unordered_pair(sK0,unordered_pair(sK1,sK1)) )
| ~ spl10_454 ),
inference(avatar_component_clause,[],[f13240]) ).
fof(f27226,plain,
( spl10_344
| ~ spl10_1
| ~ spl10_229 ),
inference(avatar_split_clause,[],[f16133,f3556,f272,f7316]) ).
fof(f7316,plain,
( spl10_344
<=> ! [X0] :
( sK4(X0) = second(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK4(X0),sK4(X0)))))
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_344])]) ).
fof(f3556,plain,
( spl10_229
<=> ! [X0,X1] :
( sK4(X1) = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK4(X1),sK4(X1)))))
| ~ member(X0,universal_class)
| null_class = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_229])]) ).
fof(f16133,plain,
( ! [X0] :
( sK4(X0) = second(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK4(X0),sK4(X0)))))
| null_class = X0 )
| ~ spl10_1
| ~ spl10_229 ),
inference(resolution,[],[f3557,f274]) ).
fof(f3557,plain,
( ! [X0,X1] :
( ~ member(X0,universal_class)
| sK4(X1) = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK4(X1),sK4(X1)))))
| null_class = X1 )
| ~ spl10_229 ),
inference(avatar_component_clause,[],[f3556]) ).
fof(f27219,plain,
( spl10_341
| ~ spl10_1
| ~ spl10_226 ),
inference(avatar_split_clause,[],[f15944,f3544,f272,f7303]) ).
fof(f7303,plain,
( spl10_341
<=> ! [X0,X1] : unordered_pair(X0,X1) = second(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_341])]) ).
fof(f3544,plain,
( spl10_226
<=> ! [X2,X0,X1] :
( unordered_pair(X1,X2) = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X2)))))
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_226])]) ).
fof(f15944,plain,
( ! [X0,X1] : unordered_pair(X0,X1) = second(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)))))
| ~ spl10_1
| ~ spl10_226 ),
inference(resolution,[],[f3545,f274]) ).
fof(f3545,plain,
( ! [X2,X0,X1] :
( ~ member(X0,universal_class)
| unordered_pair(X1,X2) = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X2))))) )
| ~ spl10_226 ),
inference(avatar_component_clause,[],[f3544]) ).
fof(f27218,plain,
( spl10_755
| ~ spl10_15
| ~ spl10_464 ),
inference(avatar_split_clause,[],[f14591,f14520,f338,f27216]) ).
fof(f27216,plain,
( spl10_755
<=> ! [X0] :
( sK0 = second(unordered_pair(unordered_pair(sK4(X0),sK4(X0)),unordered_pair(sK4(X0),unordered_pair(sK2,sK2))))
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_755])]) ).
fof(f14520,plain,
( spl10_464
<=> ! [X0] :
( sK0 = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK2,sK2))))
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_464])]) ).
fof(f14591,plain,
( ! [X0] :
( sK0 = second(unordered_pair(unordered_pair(sK4(X0),sK4(X0)),unordered_pair(sK4(X0),unordered_pair(sK2,sK2))))
| null_class = X0 )
| ~ spl10_15
| ~ spl10_464 ),
inference(resolution,[],[f14521,f339]) ).
fof(f14521,plain,
( ! [X0] :
( ~ member(X0,universal_class)
| sK0 = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK2,sK2)))) )
| ~ spl10_464 ),
inference(avatar_component_clause,[],[f14520]) ).
fof(f27214,plain,
( spl10_754
| ~ spl10_13
| ~ spl10_464 ),
inference(avatar_split_clause,[],[f14585,f14520,f328,f27212]) ).
fof(f27212,plain,
( spl10_754
<=> ! [X0,X1] : sK0 = second(unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),unordered_pair(unordered_pair(X0,X1),unordered_pair(sK2,sK2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_754])]) ).
fof(f14585,plain,
( ! [X0,X1] : sK0 = second(unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),unordered_pair(unordered_pair(X0,X1),unordered_pair(sK2,sK2))))
| ~ spl10_13
| ~ spl10_464 ),
inference(resolution,[],[f14521,f329]) ).
fof(f27151,plain,
( spl10_753
| ~ spl10_362
| ~ spl10_452 ),
inference(avatar_split_clause,[],[f26910,f13155,f8774,f27149]) ).
fof(f27149,plain,
( spl10_753
<=> ! [X0,X1] :
( ~ member(X0,unordered_pair(sK2,sK2))
| member(X0,sum_class(union(X1,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,sK2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_753])]) ).
fof(f13155,plain,
( spl10_452
<=> ! [X0,X1] :
( member(X0,sum_class(union(X1,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,sK2)))))
| ~ member(X0,unordered_pair(sK0,unordered_pair(sK1,sK1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_452])]) ).
fof(f26910,plain,
( ! [X0,X1] :
( ~ member(X0,unordered_pair(sK2,sK2))
| member(X0,sum_class(union(X1,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,sK2))))) )
| ~ spl10_362
| ~ spl10_452 ),
inference(forward_demodulation,[],[f13156,f8776]) ).
fof(f13156,plain,
( ! [X0,X1] :
( member(X0,sum_class(union(X1,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,sK2)))))
| ~ member(X0,unordered_pair(sK0,unordered_pair(sK1,sK1))) )
| ~ spl10_452 ),
inference(avatar_component_clause,[],[f13155]) ).
fof(f27142,plain,
( ~ spl10_752
| ~ spl10_313
| spl10_531
| ~ spl10_745 ),
inference(avatar_split_clause,[],[f27124,f27022,f19067,f6008,f27139]) ).
fof(f27139,plain,
( spl10_752
<=> unordered_pair(sK0,sK0) = sK4(null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_752])]) ).
fof(f19067,plain,
( spl10_531
<=> unordered_pair(sK0,sK0) = sK4(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_531])]) ).
fof(f27124,plain,
( unordered_pair(sK0,sK0) != sK4(null_class)
| ~ spl10_313
| spl10_531
| ~ spl10_745 ),
inference(forward_demodulation,[],[f27120,f27024]) ).
fof(f27120,plain,
( unordered_pair(sK0,sK0) != sK4(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0)))
| ~ spl10_313
| spl10_531 ),
inference(superposition,[],[f19068,f6010]) ).
fof(f19068,plain,
( unordered_pair(sK0,sK0) != sK4(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| spl10_531 ),
inference(avatar_component_clause,[],[f19067]) ).
fof(f27137,plain,
( spl10_332
| ~ spl10_1
| ~ spl10_219 ),
inference(avatar_split_clause,[],[f15808,f3033,f272,f6866]) ).
fof(f6866,plain,
( spl10_332
<=> ! [X0] :
( sK0 = first(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK4(X0),sK4(X0)))))
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_332])]) ).
fof(f3033,plain,
( spl10_219
<=> ! [X0,X1] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK4(X1),sK4(X1))))) = X0
| ~ member(X0,universal_class)
| null_class = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_219])]) ).
fof(f15808,plain,
( ! [X0] :
( sK0 = first(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK4(X0),sK4(X0)))))
| null_class = X0 )
| ~ spl10_1
| ~ spl10_219 ),
inference(resolution,[],[f3034,f274]) ).
fof(f3034,plain,
( ! [X0,X1] :
( ~ member(X0,universal_class)
| first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK4(X1),sK4(X1))))) = X0
| null_class = X1 )
| ~ spl10_219 ),
inference(avatar_component_clause,[],[f3033]) ).
fof(f27135,plain,
( spl10_751
| ~ spl10_9
| ~ spl10_362
| ~ spl10_374 ),
inference(avatar_split_clause,[],[f12717,f9611,f8774,f309,f27133]) ).
fof(f27133,plain,
( spl10_751
<=> ! [X0,X1] :
( member(X0,sum_class(union(X1,unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK2,sK2)))))
| ~ member(X0,unordered_pair(sK2,sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_751])]) ).
fof(f9611,plain,
( spl10_374
<=> ! [X0,X1] :
( ~ member(X0,unordered_pair(sK0,unordered_pair(sK1,sK1)))
| member(X0,sum_class(union(X1,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_374])]) ).
fof(f12717,plain,
( ! [X0,X1] :
( member(X0,sum_class(union(X1,unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK2,sK2)))))
| ~ member(X0,unordered_pair(sK2,sK2)) )
| ~ spl10_9
| ~ spl10_362
| ~ spl10_374 ),
inference(forward_demodulation,[],[f9614,f10667]) ).
fof(f9614,plain,
( ! [X0,X1] :
( ~ member(X0,unordered_pair(sK2,sK2))
| member(X0,sum_class(union(X1,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))))) )
| ~ spl10_362
| ~ spl10_374 ),
inference(forward_demodulation,[],[f9612,f8776]) ).
fof(f9612,plain,
( ! [X0,X1] :
( member(X0,sum_class(union(X1,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))))
| ~ member(X0,unordered_pair(sK0,unordered_pair(sK1,sK1))) )
| ~ spl10_374 ),
inference(avatar_component_clause,[],[f9611]) ).
fof(f27125,plain,
( spl10_319
| ~ spl10_1
| ~ spl10_210 ),
inference(avatar_split_clause,[],[f15547,f2804,f272,f6198]) ).
fof(f6198,plain,
( spl10_319
<=> ! [X0,X1] : sK0 = first(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_319])]) ).
fof(f2804,plain,
( spl10_210
<=> ! [X2,X0,X1] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X2))))) = X0
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_210])]) ).
fof(f15547,plain,
( ! [X0,X1] : sK0 = first(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)))))
| ~ spl10_1
| ~ spl10_210 ),
inference(resolution,[],[f2805,f274]) ).
fof(f2805,plain,
( ! [X2,X0,X1] :
( ~ member(X0,universal_class)
| first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X2))))) = X0 )
| ~ spl10_210 ),
inference(avatar_component_clause,[],[f2804]) ).
fof(f27119,plain,
( spl10_750
| ~ spl10_502
| ~ spl10_745 ),
inference(avatar_split_clause,[],[f27079,f27022,f18565,f27117]) ).
fof(f27117,plain,
( spl10_750
<=> ! [X0] :
( ~ member(null_class,X0)
| ~ subclass(universal_class,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_750])]) ).
fof(f18565,plain,
( spl10_502
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,complement(X0))
| ~ member(unordered_pair(X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_502])]) ).
fof(f27079,plain,
( ! [X0] :
( ~ member(null_class,X0)
| ~ subclass(universal_class,complement(X0)) )
| ~ spl10_502
| ~ spl10_745 ),
inference(superposition,[],[f18566,f27024]) ).
fof(f18566,plain,
( ! [X2,X0,X1] :
( ~ member(unordered_pair(X1,X2),X0)
| ~ subclass(universal_class,complement(X0)) )
| ~ spl10_502 ),
inference(avatar_component_clause,[],[f18565]) ).
fof(f27115,plain,
( spl10_305
| ~ spl10_1
| ~ spl10_191 ),
inference(avatar_split_clause,[],[f15443,f2362,f272,f5862]) ).
fof(f5862,plain,
( spl10_305
<=> sK0 = first(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK9,sK9)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_305])]) ).
fof(f2362,plain,
( spl10_191
<=> ! [X0] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK9,sK9)))) = X0
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_191])]) ).
fof(f15443,plain,
( sK0 = first(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK9,sK9))))
| ~ spl10_1
| ~ spl10_191 ),
inference(resolution,[],[f2363,f274]) ).
fof(f2363,plain,
( ! [X0] :
( ~ member(X0,universal_class)
| first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK9,sK9)))) = X0 )
| ~ spl10_191 ),
inference(avatar_component_clause,[],[f2362]) ).
fof(f27114,plain,
( spl10_304
| ~ spl10_1
| ~ spl10_190 ),
inference(avatar_split_clause,[],[f15381,f2358,f272,f5857]) ).
fof(f5857,plain,
( spl10_304
<=> sK9 = second(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK9,sK9)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_304])]) ).
fof(f2358,plain,
( spl10_190
<=> ! [X0] :
( sK9 = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK9,sK9))))
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_190])]) ).
fof(f15381,plain,
( sK9 = second(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK9,sK9))))
| ~ spl10_1
| ~ spl10_190 ),
inference(resolution,[],[f2359,f274]) ).
fof(f2359,plain,
( ! [X0] :
( ~ member(X0,universal_class)
| sK9 = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK9,sK9)))) )
| ~ spl10_190 ),
inference(avatar_component_clause,[],[f2358]) ).
fof(f27113,plain,
( spl10_749
| ~ spl10_7
| ~ spl10_464 ),
inference(avatar_split_clause,[],[f14593,f14520,f300,f27110]) ).
fof(f27110,plain,
( spl10_749
<=> sK0 = second(unordered_pair(unordered_pair(sK9,sK9),unordered_pair(sK9,unordered_pair(sK2,sK2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_749])]) ).
fof(f300,plain,
( spl10_7
<=> member(sK9,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_7])]) ).
fof(f14593,plain,
( sK0 = second(unordered_pair(unordered_pair(sK9,sK9),unordered_pair(sK9,unordered_pair(sK2,sK2))))
| ~ spl10_7
| ~ spl10_464 ),
inference(resolution,[],[f14521,f302]) ).
fof(f302,plain,
( member(sK9,universal_class)
| ~ spl10_7 ),
inference(avatar_component_clause,[],[f300]) ).
fof(f27108,plain,
( spl10_748
| ~ spl10_1
| ~ spl10_464 ),
inference(avatar_split_clause,[],[f14590,f14520,f272,f27105]) ).
fof(f27105,plain,
( spl10_748
<=> sK0 = second(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK2,sK2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_748])]) ).
fof(f14590,plain,
( sK0 = second(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK2,sK2))))
| ~ spl10_1
| ~ spl10_464 ),
inference(resolution,[],[f14521,f274]) ).
fof(f27103,plain,
( spl10_747
| ~ spl10_7
| ~ spl10_463 ),
inference(avatar_split_clause,[],[f14536,f14516,f300,f27100]) ).
fof(f27100,plain,
( spl10_747
<=> sK9 = first(unordered_pair(unordered_pair(sK9,sK9),unordered_pair(sK9,unordered_pair(sK2,sK2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_747])]) ).
fof(f14536,plain,
( sK9 = first(unordered_pair(unordered_pair(sK9,sK9),unordered_pair(sK9,unordered_pair(sK2,sK2))))
| ~ spl10_7
| ~ spl10_463 ),
inference(resolution,[],[f14517,f302]) ).
fof(f27098,plain,
( spl10_746
| ~ spl10_1
| ~ spl10_463 ),
inference(avatar_split_clause,[],[f14533,f14516,f272,f27095]) ).
fof(f27095,plain,
( spl10_746
<=> sK0 = first(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK2,sK2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_746])]) ).
fof(f14533,plain,
( sK0 = first(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK2,sK2))))
| ~ spl10_1
| ~ spl10_463 ),
inference(resolution,[],[f14517,f274]) ).
fof(f27025,plain,
( spl10_745
| ~ spl10_313
| ~ spl10_529 ),
inference(avatar_split_clause,[],[f27020,f19059,f6008,f27022]) ).
fof(f19059,plain,
( spl10_529
<=> null_class = unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_529])]) ).
fof(f27020,plain,
( null_class = unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0))
| ~ spl10_313
| ~ spl10_529 ),
inference(forward_demodulation,[],[f19061,f6010]) ).
fof(f19061,plain,
( null_class = unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))
| ~ spl10_529 ),
inference(avatar_component_clause,[],[f19059]) ).
fof(f26894,plain,
( spl10_361
| ~ spl10_530
| ~ spl10_534 ),
inference(avatar_split_clause,[],[f26510,f19085,f19063,f8770]) ).
fof(f8770,plain,
( spl10_361
<=> unordered_pair(sK0,unordered_pair(sK1,sK1)) = unordered_pair(sK2,unordered_pair(sK3,sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_361])]) ).
fof(f26510,plain,
( unordered_pair(sK0,unordered_pair(sK1,sK1)) = unordered_pair(sK2,unordered_pair(sK3,sK3))
| ~ spl10_530
| ~ spl10_534 ),
inference(forward_demodulation,[],[f19065,f19087]) ).
fof(f19065,plain,
( unordered_pair(sK0,unordered_pair(sK1,sK1)) = sK4(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| ~ spl10_530 ),
inference(avatar_component_clause,[],[f19063]) ).
fof(f26748,plain,
( ~ spl10_744
| ~ spl10_9
| ~ spl10_362
| spl10_382 ),
inference(avatar_split_clause,[],[f12723,f10606,f8774,f309,f26745]) ).
fof(f26745,plain,
( spl10_744
<=> inductive(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK2,sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_744])]) ).
fof(f10606,plain,
( spl10_382
<=> inductive(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_382])]) ).
fof(f12723,plain,
( ~ inductive(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK2,sK2)))
| ~ spl10_9
| ~ spl10_362
| spl10_382 ),
inference(forward_demodulation,[],[f10608,f10667]) ).
fof(f10608,plain,
( ~ inductive(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| spl10_382 ),
inference(avatar_component_clause,[],[f10606]) ).
fof(f26743,plain,
( ~ spl10_314
| ~ spl10_362
| spl10_363 ),
inference(avatar_split_clause,[],[f10935,f8780,f8774,f6012]) ).
fof(f10935,plain,
( unordered_pair(sK0,sK0) != unordered_pair(sK2,sK2)
| ~ spl10_362
| spl10_363 ),
inference(forward_demodulation,[],[f8781,f8776]) ).
fof(f8781,plain,
( unordered_pair(sK0,sK0) != unordered_pair(sK0,unordered_pair(sK1,sK1))
| spl10_363 ),
inference(avatar_component_clause,[],[f8780]) ).
fof(f26664,plain,
( spl10_96
| ~ spl10_1
| ~ spl10_75 ),
inference(avatar_split_clause,[],[f14409,f728,f272,f895]) ).
fof(f895,plain,
( spl10_96
<=> ! [X0] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK0,sK0)))) = X0
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_96])]) ).
fof(f728,plain,
( spl10_75
<=> ! [X0,X1] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))) = X0
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_75])]) ).
fof(f14409,plain,
( ! [X0] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK0,sK0)))) = X0
| ~ member(X0,universal_class) )
| ~ spl10_1
| ~ spl10_75 ),
inference(resolution,[],[f729,f274]) ).
fof(f729,plain,
( ! [X0,X1] :
( ~ member(X1,universal_class)
| first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))) = X0
| ~ member(X0,universal_class) )
| ~ spl10_75 ),
inference(avatar_component_clause,[],[f728]) ).
fof(f26585,plain,
( spl10_95
| ~ spl10_1
| ~ spl10_74 ),
inference(avatar_split_clause,[],[f14353,f724,f272,f891]) ).
fof(f891,plain,
( spl10_95
<=> ! [X0] :
( sK0 = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK0,sK0))))
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_95])]) ).
fof(f724,plain,
( spl10_74
<=> ! [X0,X1] :
( second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))) = X1
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_74])]) ).
fof(f14353,plain,
( ! [X0] :
( sK0 = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK0,sK0))))
| ~ member(X0,universal_class) )
| ~ spl10_1
| ~ spl10_74 ),
inference(resolution,[],[f725,f274]) ).
fof(f725,plain,
( ! [X0,X1] :
( ~ member(X1,universal_class)
| second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))) = X1
| ~ member(X0,universal_class) )
| ~ spl10_74 ),
inference(avatar_component_clause,[],[f724]) ).
fof(f26367,plain,
( spl10_2
| ~ spl10_54
| ~ spl10_723 ),
inference(avatar_split_clause,[],[f26316,f26259,f596,f277]) ).
fof(f277,plain,
( spl10_2
<=> sK0 = sK2 ),
introduced(avatar_definition,[new_symbols(naming,[spl10_2])]) ).
fof(f596,plain,
( spl10_54
<=> ! [X2,X0,X1] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_54])]) ).
fof(f26316,plain,
( sK0 = sK2
| ~ spl10_54
| ~ spl10_723 ),
inference(duplicate_literal_removal,[],[f26305]) ).
fof(f26305,plain,
( sK0 = sK2
| sK0 = sK2
| ~ spl10_54
| ~ spl10_723 ),
inference(resolution,[],[f26261,f597]) ).
fof(f597,plain,
( ! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 )
| ~ spl10_54 ),
inference(avatar_component_clause,[],[f596]) ).
fof(f26261,plain,
( member(sK0,unordered_pair(sK2,sK2))
| ~ spl10_723 ),
inference(avatar_component_clause,[],[f26259]) ).
fof(f26366,plain,
( spl10_743
| ~ spl10_119
| ~ spl10_173 ),
inference(avatar_split_clause,[],[f1992,f1771,f1071,f26364]) ).
fof(f26364,plain,
( spl10_743
<=> ! [X4,X0,X3,X2,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| member(X0,sum_class(union(X3,X4)))
| ~ subclass(universal_class,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_743])]) ).
fof(f1071,plain,
( spl10_119
<=> ! [X2,X0,X1] :
( member(unordered_pair(X0,X1),X2)
| ~ subclass(universal_class,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_119])]) ).
fof(f1771,plain,
( spl10_173
<=> ! [X0,X3,X2,X1] :
( member(X0,sum_class(union(X1,X2)))
| ~ member(X0,X3)
| ~ member(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_173])]) ).
fof(f1992,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ member(X0,unordered_pair(X1,X2))
| member(X0,sum_class(union(X3,X4)))
| ~ subclass(universal_class,X4) )
| ~ spl10_119
| ~ spl10_173 ),
inference(resolution,[],[f1772,f1072]) ).
fof(f1072,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(X0,X1),X2)
| ~ subclass(universal_class,X2) )
| ~ spl10_119 ),
inference(avatar_component_clause,[],[f1071]) ).
fof(f1772,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X3,X2)
| ~ member(X0,X3)
| member(X0,sum_class(union(X1,X2))) )
| ~ spl10_173 ),
inference(avatar_component_clause,[],[f1771]) ).
fof(f26362,plain,
( spl10_742
| ~ spl10_33
| ~ spl10_173 ),
inference(avatar_split_clause,[],[f1982,f1771,f422,f26360]) ).
fof(f26360,plain,
( spl10_742
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,sK6(X1,X2))
| member(X0,sum_class(union(X3,X1)))
| subclass(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_742])]) ).
fof(f422,plain,
( spl10_33
<=> ! [X0,X1] :
( subclass(X0,X1)
| member(sK6(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_33])]) ).
fof(f1982,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,sK6(X1,X2))
| member(X0,sum_class(union(X3,X1)))
| subclass(X1,X2) )
| ~ spl10_33
| ~ spl10_173 ),
inference(resolution,[],[f1772,f423]) ).
fof(f423,plain,
( ! [X0,X1] :
( member(sK6(X0,X1),X0)
| subclass(X0,X1) )
| ~ spl10_33 ),
inference(avatar_component_clause,[],[f422]) ).
fof(f26358,plain,
( spl10_741
| ~ spl10_119
| ~ spl10_170 ),
inference(avatar_split_clause,[],[f1953,f1756,f1071,f26356]) ).
fof(f26356,plain,
( spl10_741
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(X0,X1),sum_class(X2))
| subclass(X2,X3)
| ~ subclass(universal_class,sK6(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_741])]) ).
fof(f1756,plain,
( spl10_170
<=> ! [X2,X0,X1] :
( member(X0,sum_class(X1))
| ~ member(X0,sK6(X1,X2))
| subclass(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_170])]) ).
fof(f1953,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(X0,X1),sum_class(X2))
| subclass(X2,X3)
| ~ subclass(universal_class,sK6(X2,X3)) )
| ~ spl10_119
| ~ spl10_170 ),
inference(resolution,[],[f1757,f1072]) ).
fof(f1757,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sK6(X1,X2))
| member(X0,sum_class(X1))
| subclass(X1,X2) )
| ~ spl10_170 ),
inference(avatar_component_clause,[],[f1756]) ).
fof(f26354,plain,
( spl10_740
| ~ spl10_35
| ~ spl10_169 ),
inference(avatar_split_clause,[],[f1923,f1752,f430,f26352]) ).
fof(f26352,plain,
( spl10_740
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,sum_class(X1))
| ~ subclass(X1,intersection(X2,X3))
| member(sK7(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_740])]) ).
fof(f430,plain,
( spl10_35
<=> ! [X2,X0,X1] :
( member(X2,X0)
| ~ member(X2,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_35])]) ).
fof(f1752,plain,
( spl10_169
<=> ! [X2,X0,X1] :
( ~ member(X0,sum_class(X1))
| member(sK7(X0,X1),X2)
| ~ subclass(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_169])]) ).
fof(f1923,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,sum_class(X1))
| ~ subclass(X1,intersection(X2,X3))
| member(sK7(X0,X1),X2) )
| ~ spl10_35
| ~ spl10_169 ),
inference(resolution,[],[f1753,f431]) ).
fof(f431,plain,
( ! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X0) )
| ~ spl10_35 ),
inference(avatar_component_clause,[],[f430]) ).
fof(f1753,plain,
( ! [X2,X0,X1] :
( member(sK7(X0,X1),X2)
| ~ member(X0,sum_class(X1))
| ~ subclass(X1,X2) )
| ~ spl10_169 ),
inference(avatar_component_clause,[],[f1752]) ).
fof(f26350,plain,
( spl10_739
| ~ spl10_36
| ~ spl10_169 ),
inference(avatar_split_clause,[],[f1922,f1752,f434,f26348]) ).
fof(f26348,plain,
( spl10_739
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,sum_class(X1))
| ~ subclass(X1,intersection(X2,X3))
| member(sK7(X0,X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_739])]) ).
fof(f434,plain,
( spl10_36
<=> ! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_36])]) ).
fof(f1922,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,sum_class(X1))
| ~ subclass(X1,intersection(X2,X3))
| member(sK7(X0,X1),X3) )
| ~ spl10_36
| ~ spl10_169 ),
inference(resolution,[],[f1753,f435]) ).
fof(f435,plain,
( ! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X1) )
| ~ spl10_36 ),
inference(avatar_component_clause,[],[f434]) ).
fof(f26346,plain,
( spl10_738
| ~ spl10_114
| ~ spl10_165 ),
inference(avatar_split_clause,[],[f1872,f1736,f1049,f26344]) ).
fof(f26344,plain,
( spl10_738
<=> ! [X0,X1] :
( subclass(X0,union(X1,sum_class(universal_class)))
| ~ member(sK6(X0,union(X1,sum_class(universal_class))),sK9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_738])]) ).
fof(f1049,plain,
( spl10_114
<=> ! [X0] :
( member(X0,sum_class(universal_class))
| ~ member(X0,sK9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_114])]) ).
fof(f1736,plain,
( spl10_165
<=> ! [X2,X0,X1] :
( ~ member(sK6(X0,union(X1,X2)),X2)
| subclass(X0,union(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_165])]) ).
fof(f1872,plain,
( ! [X0,X1] :
( subclass(X0,union(X1,sum_class(universal_class)))
| ~ member(sK6(X0,union(X1,sum_class(universal_class))),sK9) )
| ~ spl10_114
| ~ spl10_165 ),
inference(resolution,[],[f1737,f1050]) ).
fof(f1050,plain,
( ! [X0] :
( member(X0,sum_class(universal_class))
| ~ member(X0,sK9) )
| ~ spl10_114 ),
inference(avatar_component_clause,[],[f1049]) ).
fof(f1737,plain,
( ! [X2,X0,X1] :
( ~ member(sK6(X0,union(X1,X2)),X2)
| subclass(X0,union(X1,X2)) )
| ~ spl10_165 ),
inference(avatar_component_clause,[],[f1736]) ).
fof(f26342,plain,
( spl10_737
| ~ spl10_114
| ~ spl10_164 ),
inference(avatar_split_clause,[],[f1850,f1732,f1049,f26340]) ).
fof(f26340,plain,
( spl10_737
<=> ! [X0,X1] :
( subclass(X0,union(sum_class(universal_class),X1))
| ~ member(sK6(X0,union(sum_class(universal_class),X1)),sK9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_737])]) ).
fof(f1732,plain,
( spl10_164
<=> ! [X2,X0,X1] :
( ~ member(sK6(X0,union(X1,X2)),X1)
| subclass(X0,union(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_164])]) ).
fof(f1850,plain,
( ! [X0,X1] :
( subclass(X0,union(sum_class(universal_class),X1))
| ~ member(sK6(X0,union(sum_class(universal_class),X1)),sK9) )
| ~ spl10_114
| ~ spl10_164 ),
inference(resolution,[],[f1733,f1050]) ).
fof(f1733,plain,
( ! [X2,X0,X1] :
( ~ member(sK6(X0,union(X1,X2)),X1)
| subclass(X0,union(X1,X2)) )
| ~ spl10_164 ),
inference(avatar_component_clause,[],[f1732]) ).
fof(f26338,plain,
( spl10_736
| ~ spl10_27
| ~ spl10_163 ),
inference(avatar_split_clause,[],[f1828,f1728,f387,f26336]) ).
fof(f26336,plain,
( spl10_736
<=> ! [X2,X0,X1] :
( subclass(intersection(X0,power_class(X1)),X2)
| subclass(sK6(intersection(X0,power_class(X1)),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_736])]) ).
fof(f387,plain,
( spl10_27
<=> ! [X0,X1] :
( subclass(X0,X1)
| ~ member(X0,power_class(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_27])]) ).
fof(f1728,plain,
( spl10_163
<=> ! [X2,X0,X1] :
( member(sK6(intersection(X0,X1),X2),X1)
| subclass(intersection(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_163])]) ).
fof(f1828,plain,
( ! [X2,X0,X1] :
( subclass(intersection(X0,power_class(X1)),X2)
| subclass(sK6(intersection(X0,power_class(X1)),X2),X1) )
| ~ spl10_27
| ~ spl10_163 ),
inference(resolution,[],[f1729,f388]) ).
fof(f388,plain,
( ! [X0,X1] :
( ~ member(X0,power_class(X1))
| subclass(X0,X1) )
| ~ spl10_27 ),
inference(avatar_component_clause,[],[f387]) ).
fof(f1729,plain,
( ! [X2,X0,X1] :
( member(sK6(intersection(X0,X1),X2),X1)
| subclass(intersection(X0,X1),X2) )
| ~ spl10_163 ),
inference(avatar_component_clause,[],[f1728]) ).
fof(f26334,plain,
( spl10_735
| ~ spl10_25
| ~ spl10_163 ),
inference(avatar_split_clause,[],[f1821,f1728,f379,f26332]) ).
fof(f26332,plain,
( spl10_735
<=> ! [X2,X0,X1] :
( subclass(intersection(X0,complement(X1)),X2)
| ~ member(sK6(intersection(X0,complement(X1)),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_735])]) ).
fof(f379,plain,
( spl10_25
<=> ! [X0,X1] :
( ~ member(X1,X0)
| ~ member(X1,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_25])]) ).
fof(f1821,plain,
( ! [X2,X0,X1] :
( subclass(intersection(X0,complement(X1)),X2)
| ~ member(sK6(intersection(X0,complement(X1)),X2),X1) )
| ~ spl10_25
| ~ spl10_163 ),
inference(resolution,[],[f1729,f380]) ).
fof(f380,plain,
( ! [X0,X1] :
( ~ member(X1,complement(X0))
| ~ member(X1,X0) )
| ~ spl10_25 ),
inference(avatar_component_clause,[],[f379]) ).
fof(f26330,plain,
( spl10_734
| ~ spl10_27
| ~ spl10_162 ),
inference(avatar_split_clause,[],[f1798,f1724,f387,f26328]) ).
fof(f26328,plain,
( spl10_734
<=> ! [X2,X0,X1] :
( subclass(intersection(power_class(X0),X1),X2)
| subclass(sK6(intersection(power_class(X0),X1),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_734])]) ).
fof(f1724,plain,
( spl10_162
<=> ! [X2,X0,X1] :
( member(sK6(intersection(X0,X1),X2),X0)
| subclass(intersection(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_162])]) ).
fof(f1798,plain,
( ! [X2,X0,X1] :
( subclass(intersection(power_class(X0),X1),X2)
| subclass(sK6(intersection(power_class(X0),X1),X2),X0) )
| ~ spl10_27
| ~ spl10_162 ),
inference(resolution,[],[f1725,f388]) ).
fof(f1725,plain,
( ! [X2,X0,X1] :
( member(sK6(intersection(X0,X1),X2),X0)
| subclass(intersection(X0,X1),X2) )
| ~ spl10_162 ),
inference(avatar_component_clause,[],[f1724]) ).
fof(f26302,plain,
( spl10_733
| ~ spl10_25
| ~ spl10_162 ),
inference(avatar_split_clause,[],[f1791,f1724,f379,f26300]) ).
fof(f26300,plain,
( spl10_733
<=> ! [X2,X0,X1] :
( subclass(intersection(complement(X0),X1),X2)
| ~ member(sK6(intersection(complement(X0),X1),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_733])]) ).
fof(f1791,plain,
( ! [X2,X0,X1] :
( subclass(intersection(complement(X0),X1),X2)
| ~ member(sK6(intersection(complement(X0),X1),X2),X0) )
| ~ spl10_25
| ~ spl10_162 ),
inference(resolution,[],[f1725,f380]) ).
fof(f26298,plain,
( spl10_732
| ~ spl10_33
| ~ spl10_160 ),
inference(avatar_split_clause,[],[f1713,f1514,f422,f26296]) ).
fof(f26296,plain,
( spl10_732
<=> ! [X0,X1] :
( member(sK6(sK5(X0),X1),sum_class(universal_class))
| ~ member(X0,identity_relation)
| subclass(sK5(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_732])]) ).
fof(f1514,plain,
( spl10_160
<=> ! [X0,X1] :
( member(X0,sum_class(universal_class))
| ~ member(X0,sK5(X1))
| ~ member(X1,identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_160])]) ).
fof(f1713,plain,
( ! [X0,X1] :
( member(sK6(sK5(X0),X1),sum_class(universal_class))
| ~ member(X0,identity_relation)
| subclass(sK5(X0),X1) )
| ~ spl10_33
| ~ spl10_160 ),
inference(resolution,[],[f1515,f423]) ).
fof(f1515,plain,
( ! [X0,X1] :
( ~ member(X0,sK5(X1))
| member(X0,sum_class(universal_class))
| ~ member(X1,identity_relation) )
| ~ spl10_160 ),
inference(avatar_component_clause,[],[f1514]) ).
fof(f26294,plain,
( spl10_731
| ~ spl10_33
| ~ spl10_159 ),
inference(avatar_split_clause,[],[f1694,f1510,f422,f26292]) ).
fof(f26292,plain,
( spl10_731
<=> ! [X0,X1] :
( member(sK6(sK4(X0),X1),sum_class(universal_class))
| null_class = X0
| subclass(sK4(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_731])]) ).
fof(f1510,plain,
( spl10_159
<=> ! [X0,X1] :
( member(X0,sum_class(universal_class))
| ~ member(X0,sK4(X1))
| null_class = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_159])]) ).
fof(f1694,plain,
( ! [X0,X1] :
( member(sK6(sK4(X0),X1),sum_class(universal_class))
| null_class = X0
| subclass(sK4(X0),X1) )
| ~ spl10_33
| ~ spl10_159 ),
inference(resolution,[],[f1511,f423]) ).
fof(f1511,plain,
( ! [X0,X1] :
( ~ member(X0,sK4(X1))
| member(X0,sum_class(universal_class))
| null_class = X1 )
| ~ spl10_159 ),
inference(avatar_component_clause,[],[f1510]) ).
fof(f26290,plain,
( spl10_730
| ~ spl10_33
| ~ spl10_158 ),
inference(avatar_split_clause,[],[f1680,f1506,f422,f26288]) ).
fof(f26288,plain,
( spl10_730
<=> ! [X0,X1] :
( member(sK6(power_class(X0),X1),sum_class(universal_class))
| ~ member(X0,universal_class)
| subclass(power_class(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_730])]) ).
fof(f1506,plain,
( spl10_158
<=> ! [X0,X1] :
( member(X0,sum_class(universal_class))
| ~ member(X0,power_class(X1))
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_158])]) ).
fof(f1680,plain,
( ! [X0,X1] :
( member(sK6(power_class(X0),X1),sum_class(universal_class))
| ~ member(X0,universal_class)
| subclass(power_class(X0),X1) )
| ~ spl10_33
| ~ spl10_158 ),
inference(resolution,[],[f1507,f423]) ).
fof(f1507,plain,
( ! [X0,X1] :
( ~ member(X0,power_class(X1))
| member(X0,sum_class(universal_class))
| ~ member(X1,universal_class) )
| ~ spl10_158 ),
inference(avatar_component_clause,[],[f1506]) ).
fof(f26286,plain,
( spl10_729
| ~ spl10_33
| ~ spl10_157 ),
inference(avatar_split_clause,[],[f1665,f1502,f422,f26284]) ).
fof(f26284,plain,
( spl10_729
<=> ! [X0,X1] :
( member(sK6(sum_class(X0),X1),sum_class(universal_class))
| ~ member(X0,universal_class)
| subclass(sum_class(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_729])]) ).
fof(f1502,plain,
( spl10_157
<=> ! [X0,X1] :
( member(X0,sum_class(universal_class))
| ~ member(X0,sum_class(X1))
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_157])]) ).
fof(f1665,plain,
( ! [X0,X1] :
( member(sK6(sum_class(X0),X1),sum_class(universal_class))
| ~ member(X0,universal_class)
| subclass(sum_class(X0),X1) )
| ~ spl10_33
| ~ spl10_157 ),
inference(resolution,[],[f1503,f423]) ).
fof(f1503,plain,
( ! [X0,X1] :
( ~ member(X0,sum_class(X1))
| member(X0,sum_class(universal_class))
| ~ member(X1,universal_class) )
| ~ spl10_157 ),
inference(avatar_component_clause,[],[f1502]) ).
fof(f26282,plain,
( spl10_728
| ~ spl10_33
| ~ spl10_155 ),
inference(avatar_split_clause,[],[f1648,f1493,f422,f26280]) ).
fof(f26280,plain,
( spl10_728
<=> ! [X0,X1] :
( member(sK6(sK4(X0),X1),sum_class(X0))
| null_class = X0
| subclass(sK4(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_728])]) ).
fof(f1493,plain,
( spl10_155
<=> ! [X0,X1] :
( member(X0,sum_class(X1))
| ~ member(X0,sK4(X1))
| null_class = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_155])]) ).
fof(f1648,plain,
( ! [X0,X1] :
( member(sK6(sK4(X0),X1),sum_class(X0))
| null_class = X0
| subclass(sK4(X0),X1) )
| ~ spl10_33
| ~ spl10_155 ),
inference(resolution,[],[f1494,f423]) ).
fof(f1494,plain,
( ! [X0,X1] :
( ~ member(X0,sK4(X1))
| member(X0,sum_class(X1))
| null_class = X1 )
| ~ spl10_155 ),
inference(avatar_component_clause,[],[f1493]) ).
fof(f26278,plain,
( spl10_727
| ~ spl10_45
| ~ spl10_154 ),
inference(avatar_split_clause,[],[f1643,f1489,f494,f26276]) ).
fof(f26276,plain,
( spl10_727
<=> ! [X2,X0,X1] :
( ~ member(X0,sum_class(power_class(X1)))
| member(sK7(X0,power_class(X1)),X2)
| ~ subclass(universal_class,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_727])]) ).
fof(f494,plain,
( spl10_45
<=> ! [X0,X1,X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_45])]) ).
fof(f1489,plain,
( spl10_154
<=> ! [X0,X1] :
( ~ member(X0,sum_class(power_class(X1)))
| member(sK7(X0,power_class(X1)),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_154])]) ).
fof(f1643,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum_class(power_class(X1)))
| member(sK7(X0,power_class(X1)),X2)
| ~ subclass(universal_class,X2) )
| ~ spl10_45
| ~ spl10_154 ),
inference(resolution,[],[f1490,f495]) ).
fof(f495,plain,
( ! [X3,X0,X1] :
( ~ member(X3,X0)
| member(X3,X1)
| ~ subclass(X0,X1) )
| ~ spl10_45 ),
inference(avatar_component_clause,[],[f494]) ).
fof(f1490,plain,
( ! [X0,X1] :
( member(sK7(X0,power_class(X1)),universal_class)
| ~ member(X0,sum_class(power_class(X1))) )
| ~ spl10_154 ),
inference(avatar_component_clause,[],[f1489]) ).
fof(f26274,plain,
( spl10_726
| ~ spl10_45
| ~ spl10_152 ),
inference(avatar_split_clause,[],[f1634,f1481,f494,f26272]) ).
fof(f26272,plain,
( spl10_726
<=> ! [X2,X0,X1] :
( ~ member(X0,sum_class(domain_of(X1)))
| member(sK7(X0,domain_of(X1)),X2)
| ~ subclass(universal_class,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_726])]) ).
fof(f1481,plain,
( spl10_152
<=> ! [X0,X1] :
( ~ member(X0,sum_class(domain_of(X1)))
| member(sK7(X0,domain_of(X1)),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_152])]) ).
fof(f1634,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum_class(domain_of(X1)))
| member(sK7(X0,domain_of(X1)),X2)
| ~ subclass(universal_class,X2) )
| ~ spl10_45
| ~ spl10_152 ),
inference(resolution,[],[f1482,f495]) ).
fof(f1482,plain,
( ! [X0,X1] :
( member(sK7(X0,domain_of(X1)),universal_class)
| ~ member(X0,sum_class(domain_of(X1))) )
| ~ spl10_152 ),
inference(avatar_component_clause,[],[f1481]) ).
fof(f26270,plain,
( spl10_725
| ~ spl10_45
| ~ spl10_151 ),
inference(avatar_split_clause,[],[f1626,f1477,f494,f26268]) ).
fof(f26268,plain,
( spl10_725
<=> ! [X2,X0,X1] :
( ~ member(X0,sum_class(complement(X1)))
| member(sK7(X0,complement(X1)),X2)
| ~ subclass(universal_class,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_725])]) ).
fof(f1477,plain,
( spl10_151
<=> ! [X0,X1] :
( ~ member(X0,sum_class(complement(X1)))
| member(sK7(X0,complement(X1)),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_151])]) ).
fof(f1626,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum_class(complement(X1)))
| member(sK7(X0,complement(X1)),X2)
| ~ subclass(universal_class,X2) )
| ~ spl10_45
| ~ spl10_151 ),
inference(resolution,[],[f1478,f495]) ).
fof(f1478,plain,
( ! [X0,X1] :
( member(sK7(X0,complement(X1)),universal_class)
| ~ member(X0,sum_class(complement(X1))) )
| ~ spl10_151 ),
inference(avatar_component_clause,[],[f1477]) ).
fof(f26266,plain,
( spl10_724
| ~ spl10_123
| ~ spl10_145 ),
inference(avatar_split_clause,[],[f1575,f1453,f1163,f26264]) ).
fof(f26264,plain,
( spl10_724
<=> ! [X0,X3,X2,X1] :
( ~ subclass(X0,unordered_pair(X1,X2))
| subclass(X0,X3)
| member(sK6(X0,X3),sum_class(universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_724])]) ).
fof(f1163,plain,
( spl10_123
<=> ! [X2,X0,X1] :
( member(X0,sum_class(universal_class))
| ~ member(X0,unordered_pair(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_123])]) ).
fof(f1453,plain,
( spl10_145
<=> ! [X2,X0,X1] :
( member(sK6(X0,X1),X2)
| ~ subclass(X0,X2)
| subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_145])]) ).
fof(f1575,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(X0,unordered_pair(X1,X2))
| subclass(X0,X3)
| member(sK6(X0,X3),sum_class(universal_class)) )
| ~ spl10_123
| ~ spl10_145 ),
inference(resolution,[],[f1454,f1164]) ).
fof(f1164,plain,
( ! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| member(X0,sum_class(universal_class)) )
| ~ spl10_123 ),
inference(avatar_component_clause,[],[f1163]) ).
fof(f1454,plain,
( ! [X2,X0,X1] :
( member(sK6(X0,X1),X2)
| ~ subclass(X0,X2)
| subclass(X0,X1) )
| ~ spl10_145 ),
inference(avatar_component_clause,[],[f1453]) ).
fof(f26262,plain,
( ~ spl10_1
| spl10_723
| ~ spl10_41
| ~ spl10_314 ),
inference(avatar_split_clause,[],[f12896,f6012,f454,f26259,f272]) ).
fof(f12896,plain,
( member(sK0,unordered_pair(sK2,sK2))
| ~ member(sK0,universal_class)
| ~ spl10_41
| ~ spl10_314 ),
inference(superposition,[],[f455,f6014]) ).
fof(f6014,plain,
( unordered_pair(sK0,sK0) = unordered_pair(sK2,sK2)
| ~ spl10_314 ),
inference(avatar_component_clause,[],[f6012]) ).
fof(f26257,plain,
( spl10_722
| ~ spl10_45
| ~ spl10_145 ),
inference(avatar_split_clause,[],[f1570,f1453,f494,f26255]) ).
fof(f26255,plain,
( spl10_722
<=> ! [X0,X3,X2,X1] :
( ~ subclass(X0,X1)
| subclass(X0,X2)
| member(sK6(X0,X2),X3)
| ~ subclass(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_722])]) ).
fof(f1570,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(X0,X1)
| subclass(X0,X2)
| member(sK6(X0,X2),X3)
| ~ subclass(X1,X3) )
| ~ spl10_45
| ~ spl10_145 ),
inference(resolution,[],[f1454,f495]) ).
fof(f26253,plain,
( spl10_721
| ~ spl10_45
| ~ spl10_144 ),
inference(avatar_split_clause,[],[f1543,f1449,f494,f26251]) ).
fof(f26251,plain,
( spl10_721
<=> ! [X2,X0,X1] :
( intersection(X0,X1) = null_class
| member(sK4(intersection(X0,X1)),X2)
| ~ subclass(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_721])]) ).
fof(f1449,plain,
( spl10_144
<=> ! [X0,X1] :
( member(sK4(intersection(X0,X1)),X1)
| intersection(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_144])]) ).
fof(f1543,plain,
( ! [X2,X0,X1] :
( intersection(X0,X1) = null_class
| member(sK4(intersection(X0,X1)),X2)
| ~ subclass(X1,X2) )
| ~ spl10_45
| ~ spl10_144 ),
inference(resolution,[],[f1450,f495]) ).
fof(f1450,plain,
( ! [X0,X1] :
( member(sK4(intersection(X0,X1)),X1)
| intersection(X0,X1) = null_class )
| ~ spl10_144 ),
inference(avatar_component_clause,[],[f1449]) ).
fof(f26249,plain,
( spl10_720
| ~ spl10_45
| ~ spl10_143 ),
inference(avatar_split_clause,[],[f1518,f1445,f494,f26247]) ).
fof(f26247,plain,
( spl10_720
<=> ! [X2,X0,X1] :
( intersection(X0,X1) = null_class
| member(sK4(intersection(X0,X1)),X2)
| ~ subclass(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_720])]) ).
fof(f1445,plain,
( spl10_143
<=> ! [X0,X1] :
( member(sK4(intersection(X0,X1)),X0)
| intersection(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_143])]) ).
fof(f1518,plain,
( ! [X2,X0,X1] :
( intersection(X0,X1) = null_class
| member(sK4(intersection(X0,X1)),X2)
| ~ subclass(X0,X2) )
| ~ spl10_45
| ~ spl10_143 ),
inference(resolution,[],[f1446,f495]) ).
fof(f1446,plain,
( ! [X0,X1] :
( member(sK4(intersection(X0,X1)),X0)
| intersection(X0,X1) = null_class )
| ~ spl10_143 ),
inference(avatar_component_clause,[],[f1445]) ).
fof(f26245,plain,
( spl10_719
| ~ spl10_51
| ~ spl10_140 ),
inference(avatar_split_clause,[],[f1418,f1259,f554,f26243]) ).
fof(f26243,plain,
( spl10_719
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| ~ member(X1,identity_relation)
| member(X2,sum_class(X0))
| ~ member(X2,sK5(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_719])]) ).
fof(f554,plain,
( spl10_51
<=> ! [X2,X0,X1] :
( member(X0,sum_class(X1))
| ~ member(X2,X1)
| ~ member(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_51])]) ).
fof(f1259,plain,
( spl10_140
<=> ! [X0,X1] :
( member(sK5(X0),X1)
| ~ subclass(universal_class,X1)
| ~ member(X0,identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_140])]) ).
fof(f1418,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| ~ member(X1,identity_relation)
| member(X2,sum_class(X0))
| ~ member(X2,sK5(X1)) )
| ~ spl10_51
| ~ spl10_140 ),
inference(resolution,[],[f1260,f555]) ).
fof(f555,plain,
( ! [X2,X0,X1] :
( ~ member(X2,X1)
| member(X0,sum_class(X1))
| ~ member(X0,X2) )
| ~ spl10_51 ),
inference(avatar_component_clause,[],[f554]) ).
fof(f1260,plain,
( ! [X0,X1] :
( member(sK5(X0),X1)
| ~ subclass(universal_class,X1)
| ~ member(X0,identity_relation) )
| ~ spl10_140 ),
inference(avatar_component_clause,[],[f1259]) ).
fof(f26241,plain,
( spl10_718
| ~ spl10_51
| ~ spl10_139 ),
inference(avatar_split_clause,[],[f1392,f1255,f554,f26239]) ).
fof(f26239,plain,
( spl10_718
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| null_class = X1
| member(X2,sum_class(X0))
| ~ member(X2,sK4(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_718])]) ).
fof(f1255,plain,
( spl10_139
<=> ! [X0,X1] :
( member(sK4(X0),X1)
| ~ subclass(universal_class,X1)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_139])]) ).
fof(f1392,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| null_class = X1
| member(X2,sum_class(X0))
| ~ member(X2,sK4(X1)) )
| ~ spl10_51
| ~ spl10_139 ),
inference(resolution,[],[f1256,f555]) ).
fof(f1256,plain,
( ! [X0,X1] :
( member(sK4(X0),X1)
| ~ subclass(universal_class,X1)
| null_class = X0 )
| ~ spl10_139 ),
inference(avatar_component_clause,[],[f1255]) ).
fof(f26237,plain,
( spl10_717
| ~ spl10_51
| ~ spl10_137 ),
inference(avatar_split_clause,[],[f1366,f1246,f554,f26235]) ).
fof(f26235,plain,
( spl10_717
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| ~ member(X1,universal_class)
| member(X2,sum_class(X0))
| ~ member(X2,power_class(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_717])]) ).
fof(f1246,plain,
( spl10_137
<=> ! [X0,X1] :
( member(power_class(X0),X1)
| ~ subclass(universal_class,X1)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_137])]) ).
fof(f1366,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| ~ member(X1,universal_class)
| member(X2,sum_class(X0))
| ~ member(X2,power_class(X1)) )
| ~ spl10_51
| ~ spl10_137 ),
inference(resolution,[],[f1247,f555]) ).
fof(f1247,plain,
( ! [X0,X1] :
( member(power_class(X0),X1)
| ~ subclass(universal_class,X1)
| ~ member(X0,universal_class) )
| ~ spl10_137 ),
inference(avatar_component_clause,[],[f1246]) ).
fof(f26233,plain,
( spl10_716
| ~ spl10_51
| ~ spl10_136 ),
inference(avatar_split_clause,[],[f1341,f1242,f554,f26231]) ).
fof(f26231,plain,
( spl10_716
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| ~ member(X1,universal_class)
| member(X2,sum_class(X0))
| ~ member(X2,sum_class(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_716])]) ).
fof(f1242,plain,
( spl10_136
<=> ! [X0,X1] :
( member(sum_class(X0),X1)
| ~ subclass(universal_class,X1)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_136])]) ).
fof(f1341,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| ~ member(X1,universal_class)
| member(X2,sum_class(X0))
| ~ member(X2,sum_class(X1)) )
| ~ spl10_51
| ~ spl10_136 ),
inference(resolution,[],[f1243,f555]) ).
fof(f1243,plain,
( ! [X0,X1] :
( member(sum_class(X0),X1)
| ~ subclass(universal_class,X1)
| ~ member(X0,universal_class) )
| ~ spl10_136 ),
inference(avatar_component_clause,[],[f1242]) ).
fof(f26229,plain,
( spl10_715
| ~ spl10_134
| ~ spl10_135 ),
inference(avatar_split_clause,[],[f1338,f1238,f1234,f26227]) ).
fof(f26227,plain,
( spl10_715
<=> ! [X0,X1] :
( ~ subclass(X0,sK4(X1))
| null_class = X0
| ~ member(sK4(X0),X1)
| null_class = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_715])]) ).
fof(f1234,plain,
( spl10_134
<=> ! [X0,X1] :
( ~ member(X0,sK4(X1))
| ~ member(X0,X1)
| null_class = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_134])]) ).
fof(f1238,plain,
( spl10_135
<=> ! [X0,X1] :
( member(sK4(X0),X1)
| ~ subclass(X0,X1)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_135])]) ).
fof(f1338,plain,
( ! [X0,X1] :
( ~ subclass(X0,sK4(X1))
| null_class = X0
| ~ member(sK4(X0),X1)
| null_class = X1 )
| ~ spl10_134
| ~ spl10_135 ),
inference(resolution,[],[f1239,f1235]) ).
fof(f1235,plain,
( ! [X0,X1] :
( ~ member(X0,sK4(X1))
| ~ member(X0,X1)
| null_class = X1 )
| ~ spl10_134 ),
inference(avatar_component_clause,[],[f1234]) ).
fof(f1239,plain,
( ! [X0,X1] :
( member(sK4(X0),X1)
| ~ subclass(X0,X1)
| null_class = X0 )
| ~ spl10_135 ),
inference(avatar_component_clause,[],[f1238]) ).
fof(f26225,plain,
( spl10_714
| ~ spl10_51
| ~ spl10_135 ),
inference(avatar_split_clause,[],[f1315,f1238,f554,f26223]) ).
fof(f26223,plain,
( spl10_714
<=> ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| null_class = X0
| member(X2,sum_class(X1))
| ~ member(X2,sK4(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_714])]) ).
fof(f1315,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| null_class = X0
| member(X2,sum_class(X1))
| ~ member(X2,sK4(X0)) )
| ~ spl10_51
| ~ spl10_135 ),
inference(resolution,[],[f1239,f555]) ).
fof(f26221,plain,
( spl10_713
| ~ spl10_47
| ~ spl10_134 ),
inference(avatar_split_clause,[],[f1312,f1234,f502,f26219]) ).
fof(f26219,plain,
( spl10_713
<=> ! [X0,X1] :
( ~ member(sK7(X0,sK4(X1)),X1)
| null_class = X1
| ~ member(X0,sum_class(sK4(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_713])]) ).
fof(f502,plain,
( spl10_47
<=> ! [X0,X1] :
( member(sK7(X0,X1),X1)
| ~ member(X0,sum_class(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_47])]) ).
fof(f1312,plain,
( ! [X0,X1] :
( ~ member(sK7(X0,sK4(X1)),X1)
| null_class = X1
| ~ member(X0,sum_class(sK4(X1))) )
| ~ spl10_47
| ~ spl10_134 ),
inference(resolution,[],[f1235,f503]) ).
fof(f503,plain,
( ! [X0,X1] :
( member(sK7(X0,X1),X1)
| ~ member(X0,sum_class(X1)) )
| ~ spl10_47 ),
inference(avatar_component_clause,[],[f502]) ).
fof(f26217,plain,
( ~ spl10_712
| ~ spl10_314
| spl10_379 ),
inference(avatar_split_clause,[],[f12891,f10591,f6012,f26214]) ).
fof(f26214,plain,
( spl10_712
<=> inductive(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_712])]) ).
fof(f10591,plain,
( spl10_379
<=> inductive(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_379])]) ).
fof(f12891,plain,
( ~ inductive(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,sK2)))
| ~ spl10_314
| spl10_379 ),
inference(superposition,[],[f10593,f6014]) ).
fof(f10593,plain,
( ~ inductive(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,sK0)))
| spl10_379 ),
inference(avatar_component_clause,[],[f10591]) ).
fof(f26212,plain,
( spl10_711
| ~ spl10_51
| ~ spl10_128 ),
inference(avatar_split_clause,[],[f1305,f1207,f554,f26210]) ).
fof(f26210,plain,
( spl10_711
<=> ! [X2,X0,X1] :
( subclass(power_class(X0),X1)
| member(X2,sum_class(universal_class))
| ~ member(X2,sK6(power_class(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_711])]) ).
fof(f1207,plain,
( spl10_128
<=> ! [X0,X1] :
( subclass(power_class(X0),X1)
| member(sK6(power_class(X0),X1),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_128])]) ).
fof(f1305,plain,
( ! [X2,X0,X1] :
( subclass(power_class(X0),X1)
| member(X2,sum_class(universal_class))
| ~ member(X2,sK6(power_class(X0),X1)) )
| ~ spl10_51
| ~ spl10_128 ),
inference(resolution,[],[f1208,f555]) ).
fof(f1208,plain,
( ! [X0,X1] :
( member(sK6(power_class(X0),X1),universal_class)
| subclass(power_class(X0),X1) )
| ~ spl10_128 ),
inference(avatar_component_clause,[],[f1207]) ).
fof(f26208,plain,
( spl10_710
| ~ spl10_51
| ~ spl10_126 ),
inference(avatar_split_clause,[],[f1294,f1199,f554,f26206]) ).
fof(f26206,plain,
( spl10_710
<=> ! [X2,X0,X1] :
( subclass(domain_of(X0),X1)
| member(X2,sum_class(universal_class))
| ~ member(X2,sK6(domain_of(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_710])]) ).
fof(f1199,plain,
( spl10_126
<=> ! [X0,X1] :
( subclass(domain_of(X0),X1)
| member(sK6(domain_of(X0),X1),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_126])]) ).
fof(f1294,plain,
( ! [X2,X0,X1] :
( subclass(domain_of(X0),X1)
| member(X2,sum_class(universal_class))
| ~ member(X2,sK6(domain_of(X0),X1)) )
| ~ spl10_51
| ~ spl10_126 ),
inference(resolution,[],[f1200,f555]) ).
fof(f1200,plain,
( ! [X0,X1] :
( member(sK6(domain_of(X0),X1),universal_class)
| subclass(domain_of(X0),X1) )
| ~ spl10_126 ),
inference(avatar_component_clause,[],[f1199]) ).
fof(f26204,plain,
( spl10_709
| ~ spl10_51
| ~ spl10_125 ),
inference(avatar_split_clause,[],[f1284,f1195,f554,f26202]) ).
fof(f26202,plain,
( spl10_709
<=> ! [X2,X0,X1] :
( subclass(complement(X0),X1)
| member(X2,sum_class(universal_class))
| ~ member(X2,sK6(complement(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_709])]) ).
fof(f1195,plain,
( spl10_125
<=> ! [X0,X1] :
( subclass(complement(X0),X1)
| member(sK6(complement(X0),X1),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_125])]) ).
fof(f1284,plain,
( ! [X2,X0,X1] :
( subclass(complement(X0),X1)
| member(X2,sum_class(universal_class))
| ~ member(X2,sK6(complement(X0),X1)) )
| ~ spl10_51
| ~ spl10_125 ),
inference(resolution,[],[f1196,f555]) ).
fof(f1196,plain,
( ! [X0,X1] :
( member(sK6(complement(X0),X1),universal_class)
| subclass(complement(X0),X1) )
| ~ spl10_125 ),
inference(avatar_component_clause,[],[f1195]) ).
fof(f26200,plain,
( spl10_708
| ~ spl10_37
| ~ spl10_124 ),
inference(avatar_split_clause,[],[f1274,f1191,f438,f26198]) ).
fof(f26198,plain,
( spl10_708
<=> ! [X2,X0,X1] :
( subclass(complement(union(X0,X1)),X2)
| ~ member(sK6(complement(union(X0,X1)),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_708])]) ).
fof(f438,plain,
( spl10_37
<=> ! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_37])]) ).
fof(f1191,plain,
( spl10_124
<=> ! [X0,X1] :
( subclass(complement(X0),X1)
| ~ member(sK6(complement(X0),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_124])]) ).
fof(f1274,plain,
( ! [X2,X0,X1] :
( subclass(complement(union(X0,X1)),X2)
| ~ member(sK6(complement(union(X0,X1)),X2),X0) )
| ~ spl10_37
| ~ spl10_124 ),
inference(resolution,[],[f1192,f439]) ).
fof(f439,plain,
( ! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X0) )
| ~ spl10_37 ),
inference(avatar_component_clause,[],[f438]) ).
fof(f1192,plain,
( ! [X0,X1] :
( ~ member(sK6(complement(X0),X1),X0)
| subclass(complement(X0),X1) )
| ~ spl10_124 ),
inference(avatar_component_clause,[],[f1191]) ).
fof(f26196,plain,
( spl10_707
| ~ spl10_38
| ~ spl10_124 ),
inference(avatar_split_clause,[],[f1273,f1191,f442,f26194]) ).
fof(f26194,plain,
( spl10_707
<=> ! [X2,X0,X1] :
( subclass(complement(union(X0,X1)),X2)
| ~ member(sK6(complement(union(X0,X1)),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_707])]) ).
fof(f442,plain,
( spl10_38
<=> ! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_38])]) ).
fof(f1273,plain,
( ! [X2,X0,X1] :
( subclass(complement(union(X0,X1)),X2)
| ~ member(sK6(complement(union(X0,X1)),X2),X1) )
| ~ spl10_38
| ~ spl10_124 ),
inference(resolution,[],[f1192,f443]) ).
fof(f443,plain,
( ! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X1) )
| ~ spl10_38 ),
inference(avatar_component_clause,[],[f442]) ).
fof(f26192,plain,
( spl10_706
| ~ spl10_47
| ~ spl10_123 ),
inference(avatar_split_clause,[],[f1187,f1163,f502,f26190]) ).
fof(f26190,plain,
( spl10_706
<=> ! [X2,X0,X1] :
( member(sK7(X0,unordered_pair(X1,X2)),sum_class(universal_class))
| ~ member(X0,sum_class(unordered_pair(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_706])]) ).
fof(f1187,plain,
( ! [X2,X0,X1] :
( member(sK7(X0,unordered_pair(X1,X2)),sum_class(universal_class))
| ~ member(X0,sum_class(unordered_pair(X1,X2))) )
| ~ spl10_47
| ~ spl10_123 ),
inference(resolution,[],[f1164,f503]) ).
fof(f26188,plain,
( spl10_705
| ~ spl10_43
| ~ spl10_122 ),
inference(avatar_split_clause,[],[f1177,f1159,f486,f26186]) ).
fof(f26186,plain,
( spl10_705
<=> ! [X0] :
( null_class = power_class(X0)
| sK4(power_class(X0)) = X0
| ~ subclass(X0,sK4(power_class(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_705])]) ).
fof(f486,plain,
( spl10_43
<=> ! [X0,X1] :
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_43])]) ).
fof(f1159,plain,
( spl10_122
<=> ! [X0] :
( subclass(sK4(power_class(X0)),X0)
| null_class = power_class(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_122])]) ).
fof(f1177,plain,
( ! [X0] :
( null_class = power_class(X0)
| sK4(power_class(X0)) = X0
| ~ subclass(X0,sK4(power_class(X0))) )
| ~ spl10_43
| ~ spl10_122 ),
inference(resolution,[],[f1160,f487]) ).
fof(f487,plain,
( ! [X0,X1] :
( ~ subclass(X1,X0)
| X0 = X1
| ~ subclass(X0,X1) )
| ~ spl10_43 ),
inference(avatar_component_clause,[],[f486]) ).
fof(f1160,plain,
( ! [X0] :
( subclass(sK4(power_class(X0)),X0)
| null_class = power_class(X0) )
| ~ spl10_122 ),
inference(avatar_component_clause,[],[f1159]) ).
fof(f25753,plain,
( spl10_704
| ~ spl10_314
| ~ spl10_700 ),
inference(avatar_split_clause,[],[f25735,f25732,f6012,f25751]) ).
fof(f25751,plain,
( spl10_704
<=> ! [X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(sK2,sK2))),unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(sK2,sK2)))),unordered_pair(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(sK2,sK2))),unordered_pair(X0,X0))),X1)
| ~ member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X0)
| ~ subclass(element_relation,flip(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_704])]) ).
fof(f25732,plain,
( spl10_700
<=> ! [X0,X1] :
( ~ member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X0)
| ~ subclass(element_relation,flip(X1))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(sK0,sK0))),unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(sK0,sK0)))),unordered_pair(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(sK0,sK0))),unordered_pair(X0,X0))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_700])]) ).
fof(f25735,plain,
( ! [X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(sK2,sK2))),unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(sK2,sK2)))),unordered_pair(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(sK2,sK2))),unordered_pair(X0,X0))),X1)
| ~ member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X0)
| ~ subclass(element_relation,flip(X1)) )
| ~ spl10_314
| ~ spl10_700 ),
inference(forward_demodulation,[],[f25733,f6014]) ).
fof(f25733,plain,
( ! [X0,X1] :
( ~ member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X0)
| ~ subclass(element_relation,flip(X1))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(sK0,sK0))),unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(sK0,sK0)))),unordered_pair(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(sK0,sK0))),unordered_pair(X0,X0))),X1) )
| ~ spl10_700 ),
inference(avatar_component_clause,[],[f25732]) ).
fof(f25749,plain,
( spl10_703
| ~ spl10_314
| ~ spl10_699 ),
inference(avatar_split_clause,[],[f25730,f25727,f6012,f25747]) ).
fof(f25747,plain,
( spl10_703
<=> ! [X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(X0,X0))),unordered_pair(sK2,sK2))),X1)
| ~ member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X0)
| ~ subclass(element_relation,rotate(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_703])]) ).
fof(f25727,plain,
( spl10_699
<=> ! [X0,X1] :
( ~ member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X0)
| ~ subclass(element_relation,rotate(X1))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(X0,X0))),unordered_pair(sK0,sK0))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_699])]) ).
fof(f25730,plain,
( ! [X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(X0,X0))),unordered_pair(sK2,sK2))),X1)
| ~ member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X0)
| ~ subclass(element_relation,rotate(X1)) )
| ~ spl10_314
| ~ spl10_699 ),
inference(forward_demodulation,[],[f25728,f6014]) ).
fof(f25728,plain,
( ! [X0,X1] :
( ~ member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X0)
| ~ subclass(element_relation,rotate(X1))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(X0,X0))),unordered_pair(sK0,sK0))),X1) )
| ~ spl10_699 ),
inference(avatar_component_clause,[],[f25727]) ).
fof(f25745,plain,
( spl10_702
| ~ spl10_72
| ~ spl10_463 ),
inference(avatar_split_clause,[],[f14530,f14516,f706,f25743]) ).
fof(f25743,plain,
( spl10_702
<=> ! [X0,X1] :
( domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(X1,universal_class)),universal_class)))) = first(unordered_pair(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(X1,universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(X1,universal_class)),universal_class))))),unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(X1,universal_class)),universal_class)))),unordered_pair(sK2,sK2))))
| ~ function(X0)
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_702])]) ).
fof(f706,plain,
( spl10_72
<=> ! [X0,X1] :
( member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class)))),universal_class)
| ~ function(X1)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_72])]) ).
fof(f14530,plain,
( ! [X0,X1] :
( domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(X1,universal_class)),universal_class)))) = first(unordered_pair(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(X1,universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(X1,universal_class)),universal_class))))),unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(X1,universal_class)),universal_class)))),unordered_pair(sK2,sK2))))
| ~ function(X0)
| ~ member(X1,universal_class) )
| ~ spl10_72
| ~ spl10_463 ),
inference(resolution,[],[f14517,f707]) ).
fof(f707,plain,
( ! [X0,X1] :
( member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class)))),universal_class)
| ~ function(X1)
| ~ member(X0,universal_class) )
| ~ spl10_72 ),
inference(avatar_component_clause,[],[f706]) ).
fof(f25739,plain,
( spl10_701
| ~ spl10_108
| ~ spl10_240 ),
inference(avatar_split_clause,[],[f4074,f3999,f1004,f25737]) ).
fof(f25737,plain,
( spl10_701
<=> ! [X0] :
( ~ member(X0,universal_class)
| null_class = X0
| ~ subclass(X0,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| unordered_pair(sK0,sK0) = sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))
| unordered_pair(sK0,unordered_pair(sK1,sK1)) = sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_701])]) ).
fof(f3999,plain,
( spl10_240
<=> ! [X0,X1] :
( null_class = X0
| ~ member(X0,universal_class)
| member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))),X1)
| ~ subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_240])]) ).
fof(f4074,plain,
( ! [X0] :
( ~ member(X0,universal_class)
| null_class = X0
| ~ subclass(X0,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| unordered_pair(sK0,sK0) = sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))
| unordered_pair(sK0,unordered_pair(sK1,sK1)) = sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))) )
| ~ spl10_108
| ~ spl10_240 ),
inference(resolution,[],[f4000,f1005]) ).
fof(f4000,plain,
( ! [X0,X1] :
( member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))),X1)
| ~ member(X0,universal_class)
| null_class = X0
| ~ subclass(X0,X1) )
| ~ spl10_240 ),
inference(avatar_component_clause,[],[f3999]) ).
fof(f25734,plain,
( spl10_700
| ~ spl10_202
| ~ spl10_216 ),
inference(avatar_split_clause,[],[f3281,f3021,f2729,f25732]) ).
fof(f2729,plain,
( spl10_202
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))),unordered_pair(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),unordered_pair(X0,X0))),flip(X1))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(sK0,sK0))),unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(sK0,sK0)))),unordered_pair(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(sK0,sK0))),unordered_pair(X0,X0))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_202])]) ).
fof(f3021,plain,
( spl10_216
<=> ! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(X1,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2)
| ~ subclass(element_relation,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_216])]) ).
fof(f3281,plain,
( ! [X0,X1] :
( ~ member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X0)
| ~ subclass(element_relation,flip(X1))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(sK0,sK0))),unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(sK0,sK0)))),unordered_pair(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(sK0,sK0))),unordered_pair(X0,X0))),X1) )
| ~ spl10_202
| ~ spl10_216 ),
inference(resolution,[],[f3022,f2730]) ).
fof(f2730,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))),unordered_pair(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),unordered_pair(X0,X0))),flip(X1))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(sK0,sK0))),unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(sK0,sK0)))),unordered_pair(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(sK0,sK0))),unordered_pair(X0,X0))),X1) )
| ~ spl10_202 ),
inference(avatar_component_clause,[],[f2729]) ).
fof(f3022,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2)
| ~ member(X1,universal_class)
| ~ member(X0,X1)
| ~ subclass(element_relation,X2) )
| ~ spl10_216 ),
inference(avatar_component_clause,[],[f3021]) ).
fof(f25729,plain,
( spl10_699
| ~ spl10_200
| ~ spl10_216 ),
inference(avatar_split_clause,[],[f3280,f3021,f2721,f25727]) ).
fof(f2721,plain,
( spl10_200
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))),unordered_pair(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),unordered_pair(X0,X0))),rotate(X1))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(X0,X0))),unordered_pair(sK0,sK0))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_200])]) ).
fof(f3280,plain,
( ! [X0,X1] :
( ~ member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X0)
| ~ subclass(element_relation,rotate(X1))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(X0,X0))),unordered_pair(sK0,sK0))),X1) )
| ~ spl10_200
| ~ spl10_216 ),
inference(resolution,[],[f3022,f2722]) ).
fof(f2722,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))),unordered_pair(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),unordered_pair(X0,X0))),rotate(X1))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(X0,X0))),unordered_pair(sK0,sK0))),X1) )
| ~ spl10_200 ),
inference(avatar_component_clause,[],[f2721]) ).
fof(f25724,plain,
( spl10_698
| ~ spl10_72
| ~ spl10_96 ),
inference(avatar_split_clause,[],[f914,f895,f706,f25722]) ).
fof(f25722,plain,
( spl10_698
<=> ! [X0,X1] :
( domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(X1,universal_class)),universal_class)))) = first(unordered_pair(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(X1,universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(X1,universal_class)),universal_class))))),unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(X1,universal_class)),universal_class)))),unordered_pair(sK0,sK0))))
| ~ function(X0)
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_698])]) ).
fof(f914,plain,
( ! [X0,X1] :
( domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(X1,universal_class)),universal_class)))) = first(unordered_pair(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(X1,universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(X1,universal_class)),universal_class))))),unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(X1,universal_class)),universal_class)))),unordered_pair(sK0,sK0))))
| ~ function(X0)
| ~ member(X1,universal_class) )
| ~ spl10_72
| ~ spl10_96 ),
inference(resolution,[],[f896,f707]) ).
fof(f896,plain,
( ! [X0] :
( ~ member(X0,universal_class)
| first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK0,sK0)))) = X0 )
| ~ spl10_96 ),
inference(avatar_component_clause,[],[f895]) ).
fof(f24577,plain,
( spl10_697
| ~ spl10_241
| ~ spl10_627 ),
inference(avatar_split_clause,[],[f22780,f20687,f4103,f24574]) ).
fof(f24574,plain,
( spl10_697
<=> subclass(union(sK0,sum_class(universal_class)),sum_class(universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_697])]) ).
fof(f4103,plain,
( spl10_241
<=> ! [X0] :
( ~ member(sK6(X0,sum_class(universal_class)),sK0)
| subclass(X0,sum_class(universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_241])]) ).
fof(f20687,plain,
( spl10_627
<=> ! [X0,X1] :
( member(sK6(union(X0,X1),X1),X0)
| subclass(union(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_627])]) ).
fof(f22780,plain,
( subclass(union(sK0,sum_class(universal_class)),sum_class(universal_class))
| ~ spl10_241
| ~ spl10_627 ),
inference(duplicate_literal_removal,[],[f22660]) ).
fof(f22660,plain,
( subclass(union(sK0,sum_class(universal_class)),sum_class(universal_class))
| subclass(union(sK0,sum_class(universal_class)),sum_class(universal_class))
| ~ spl10_241
| ~ spl10_627 ),
inference(resolution,[],[f20688,f4104]) ).
fof(f4104,plain,
( ! [X0] :
( ~ member(sK6(X0,sum_class(universal_class)),sK0)
| subclass(X0,sum_class(universal_class)) )
| ~ spl10_241 ),
inference(avatar_component_clause,[],[f4103]) ).
fof(f20688,plain,
( ! [X0,X1] :
( member(sK6(union(X0,X1),X1),X0)
| subclass(union(X0,X1),X1) )
| ~ spl10_627 ),
inference(avatar_component_clause,[],[f20687]) ).
fof(f24293,plain,
( spl10_696
| ~ spl10_241
| ~ spl10_626 ),
inference(avatar_split_clause,[],[f22541,f20683,f4103,f24290]) ).
fof(f24290,plain,
( spl10_696
<=> subclass(union(sum_class(universal_class),sK0),sum_class(universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_696])]) ).
fof(f20683,plain,
( spl10_626
<=> ! [X0,X1] :
( member(sK6(union(X0,X1),X0),X1)
| subclass(union(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_626])]) ).
fof(f22541,plain,
( subclass(union(sum_class(universal_class),sK0),sum_class(universal_class))
| ~ spl10_241
| ~ spl10_626 ),
inference(duplicate_literal_removal,[],[f22421]) ).
fof(f22421,plain,
( subclass(union(sum_class(universal_class),sK0),sum_class(universal_class))
| subclass(union(sum_class(universal_class),sK0),sum_class(universal_class))
| ~ spl10_241
| ~ spl10_626 ),
inference(resolution,[],[f20684,f4104]) ).
fof(f20684,plain,
( ! [X0,X1] :
( member(sK6(union(X0,X1),X0),X1)
| subclass(union(X0,X1),X0) )
| ~ spl10_626 ),
inference(avatar_component_clause,[],[f20683]) ).
fof(f23190,plain,
( ~ spl10_694
| spl10_695
| ~ spl10_5
| ~ spl10_262 ),
inference(avatar_split_clause,[],[f4901,f4813,f292,f23188,f23184]) ).
fof(f23184,plain,
( spl10_694
<=> subclass(successor_relation,null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_694])]) ).
fof(f23188,plain,
( spl10_695
<=> ! [X0] :
( ~ member(X0,universal_class)
| ~ member(union(X0,unordered_pair(X0,X0)),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_695])]) ).
fof(f292,plain,
( spl10_5
<=> ! [X0] : ~ member(X0,null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_5])]) ).
fof(f4813,plain,
( spl10_262
<=> ! [X0,X1] :
( ~ member(union(X0,unordered_pair(X0,X0)),universal_class)
| ~ member(X0,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(union(X0,unordered_pair(X0,X0)),union(X0,unordered_pair(X0,X0))))),X1)
| ~ subclass(successor_relation,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_262])]) ).
fof(f4901,plain,
( ! [X0] :
( ~ member(X0,universal_class)
| ~ member(union(X0,unordered_pair(X0,X0)),universal_class)
| ~ subclass(successor_relation,null_class) )
| ~ spl10_5
| ~ spl10_262 ),
inference(resolution,[],[f4814,f293]) ).
fof(f293,plain,
( ! [X0] : ~ member(X0,null_class)
| ~ spl10_5 ),
inference(avatar_component_clause,[],[f292]) ).
fof(f4814,plain,
( ! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(union(X0,unordered_pair(X0,X0)),union(X0,unordered_pair(X0,X0))))),X1)
| ~ member(X0,universal_class)
| ~ member(union(X0,unordered_pair(X0,X0)),universal_class)
| ~ subclass(successor_relation,X1) )
| ~ spl10_262 ),
inference(avatar_component_clause,[],[f4813]) ).
fof(f23182,plain,
( spl10_693
| ~ spl10_211 ),
inference(avatar_split_clause,[],[f3124,f2986,f23180]) ).
fof(f23180,plain,
( spl10_693
<=> ! [X0,X1] :
( member(sK7(X0,union(X1,X1)),X1)
| ~ member(X0,sum_class(union(X1,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_693])]) ).
fof(f2986,plain,
( spl10_211
<=> ! [X2,X0,X1] :
( member(sK7(X0,union(X1,X2)),X1)
| member(sK7(X0,union(X1,X2)),X2)
| ~ member(X0,sum_class(union(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_211])]) ).
fof(f3124,plain,
( ! [X0,X1] :
( member(sK7(X0,union(X1,X1)),X1)
| ~ member(X0,sum_class(union(X1,X1))) )
| ~ spl10_211 ),
inference(factoring,[],[f2987]) ).
fof(f2987,plain,
( ! [X2,X0,X1] :
( member(sK7(X0,union(X1,X2)),X2)
| member(sK7(X0,union(X1,X2)),X1)
| ~ member(X0,sum_class(union(X1,X2))) )
| ~ spl10_211 ),
inference(avatar_component_clause,[],[f2986]) ).
fof(f23178,plain,
( spl10_692
| ~ spl10_5
| ~ spl10_211 ),
inference(avatar_split_clause,[],[f3110,f2986,f292,f23176]) ).
fof(f23176,plain,
( spl10_692
<=> ! [X0,X1] :
( member(sK7(X0,union(null_class,X1)),X1)
| ~ member(X0,sum_class(union(null_class,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_692])]) ).
fof(f3110,plain,
( ! [X0,X1] :
( member(sK7(X0,union(null_class,X1)),X1)
| ~ member(X0,sum_class(union(null_class,X1))) )
| ~ spl10_5
| ~ spl10_211 ),
inference(resolution,[],[f2987,f293]) ).
fof(f23174,plain,
( spl10_691
| ~ spl10_5
| ~ spl10_211 ),
inference(avatar_split_clause,[],[f3074,f2986,f292,f23172]) ).
fof(f23172,plain,
( spl10_691
<=> ! [X0,X1] :
( member(sK7(X0,union(X1,null_class)),X1)
| ~ member(X0,sum_class(union(X1,null_class))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_691])]) ).
fof(f3074,plain,
( ! [X0,X1] :
( member(sK7(X0,union(X1,null_class)),X1)
| ~ member(X0,sum_class(union(X1,null_class))) )
| ~ spl10_5
| ~ spl10_211 ),
inference(resolution,[],[f2987,f293]) ).
fof(f23165,plain,
( ~ spl10_689
| spl10_690
| ~ spl10_76
| ~ spl10_199 ),
inference(avatar_split_clause,[],[f2674,f2556,f732,f23163,f23159]) ).
fof(f23159,plain,
( spl10_689
<=> subclass(identity_relation,successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_689])]) ).
fof(f23163,plain,
( spl10_690
<=> ! [X0] :
( ~ member(X0,universal_class)
| union(X0,unordered_pair(X0,X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_690])]) ).
fof(f732,plain,
( spl10_76
<=> ! [X0,X1] :
( union(X0,unordered_pair(X0,X0)) = X1
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_76])]) ).
fof(f2556,plain,
( spl10_199
<=> ! [X0,X1] :
( ~ member(X0,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0))),X1)
| ~ subclass(identity_relation,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_199])]) ).
fof(f2674,plain,
( ! [X0] :
( ~ member(X0,universal_class)
| ~ subclass(identity_relation,successor_relation)
| union(X0,unordered_pair(X0,X0)) = X0 )
| ~ spl10_76
| ~ spl10_199 ),
inference(resolution,[],[f2557,f733]) ).
fof(f733,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation)
| union(X0,unordered_pair(X0,X0)) = X1 )
| ~ spl10_76 ),
inference(avatar_component_clause,[],[f732]) ).
fof(f2557,plain,
( ! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0))),X1)
| ~ member(X0,universal_class)
| ~ subclass(identity_relation,X1) )
| ~ spl10_199 ),
inference(avatar_component_clause,[],[f2556]) ).
fof(f23157,plain,
( spl10_688
| ~ spl10_145
| ~ spl10_195 ),
inference(avatar_split_clause,[],[f2539,f2508,f1453,f23155]) ).
fof(f23155,plain,
( spl10_688
<=> ! [X0,X1] :
( ~ subclass(sK6(X0,power_class(X1)),X1)
| subclass(X0,power_class(X1))
| ~ subclass(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_688])]) ).
fof(f2508,plain,
( spl10_195
<=> ! [X0,X1] :
( ~ subclass(sK6(X0,power_class(X1)),X1)
| ~ member(sK6(X0,power_class(X1)),universal_class)
| subclass(X0,power_class(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_195])]) ).
fof(f2539,plain,
( ! [X0,X1] :
( ~ subclass(sK6(X0,power_class(X1)),X1)
| subclass(X0,power_class(X1))
| ~ subclass(X0,universal_class) )
| ~ spl10_145
| ~ spl10_195 ),
inference(duplicate_literal_removal,[],[f2538]) ).
fof(f2538,plain,
( ! [X0,X1] :
( ~ subclass(sK6(X0,power_class(X1)),X1)
| subclass(X0,power_class(X1))
| ~ subclass(X0,universal_class)
| subclass(X0,power_class(X1)) )
| ~ spl10_145
| ~ spl10_195 ),
inference(resolution,[],[f2509,f1454]) ).
fof(f2509,plain,
( ! [X0,X1] :
( ~ member(sK6(X0,power_class(X1)),universal_class)
| ~ subclass(sK6(X0,power_class(X1)),X1)
| subclass(X0,power_class(X1)) )
| ~ spl10_195 ),
inference(avatar_component_clause,[],[f2508]) ).
fof(f23153,plain,
( spl10_687
| ~ spl10_145
| ~ spl10_194 ),
inference(avatar_split_clause,[],[f2523,f2504,f1453,f23151]) ).
fof(f23151,plain,
( spl10_687
<=> ! [X0,X1] :
( member(sK6(X0,complement(X1)),X1)
| subclass(X0,complement(X1))
| ~ subclass(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_687])]) ).
fof(f2504,plain,
( spl10_194
<=> ! [X0,X1] :
( member(sK6(X0,complement(X1)),X1)
| ~ member(sK6(X0,complement(X1)),universal_class)
| subclass(X0,complement(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_194])]) ).
fof(f2523,plain,
( ! [X0,X1] :
( member(sK6(X0,complement(X1)),X1)
| subclass(X0,complement(X1))
| ~ subclass(X0,universal_class) )
| ~ spl10_145
| ~ spl10_194 ),
inference(duplicate_literal_removal,[],[f2522]) ).
fof(f2522,plain,
( ! [X0,X1] :
( member(sK6(X0,complement(X1)),X1)
| subclass(X0,complement(X1))
| ~ subclass(X0,universal_class)
| subclass(X0,complement(X1)) )
| ~ spl10_145
| ~ spl10_194 ),
inference(resolution,[],[f2505,f1454]) ).
fof(f2505,plain,
( ! [X0,X1] :
( ~ member(sK6(X0,complement(X1)),universal_class)
| member(sK6(X0,complement(X1)),X1)
| subclass(X0,complement(X1)) )
| ~ spl10_194 ),
inference(avatar_component_clause,[],[f2504]) ).
fof(f23149,plain,
( spl10_686
| ~ spl10_114
| ~ spl10_174 ),
inference(avatar_split_clause,[],[f2081,f1775,f1049,f23147]) ).
fof(f23147,plain,
( spl10_686
<=> ! [X2,X0,X1] :
( ~ member(X0,X1)
| member(X0,sum_class(union(sum_class(universal_class),X2)))
| ~ member(X1,sK9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_686])]) ).
fof(f1775,plain,
( spl10_174
<=> ! [X0,X3,X2,X1] :
( member(X0,sum_class(union(X1,X2)))
| ~ member(X0,X3)
| ~ member(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_174])]) ).
fof(f2081,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| member(X0,sum_class(union(sum_class(universal_class),X2)))
| ~ member(X1,sK9) )
| ~ spl10_114
| ~ spl10_174 ),
inference(resolution,[],[f1776,f1050]) ).
fof(f1776,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X3,X1)
| ~ member(X0,X3)
| member(X0,sum_class(union(X1,X2))) )
| ~ spl10_174 ),
inference(avatar_component_clause,[],[f1775]) ).
fof(f23144,plain,
( spl10_685
| ~ spl10_15
| ~ spl10_174 ),
inference(avatar_split_clause,[],[f2057,f1775,f338,f23142]) ).
fof(f23142,plain,
( spl10_685
<=> ! [X2,X0,X1] :
( ~ member(X0,sK4(X1))
| member(X0,sum_class(union(universal_class,X2)))
| null_class = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_685])]) ).
fof(f2057,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sK4(X1))
| member(X0,sum_class(union(universal_class,X2)))
| null_class = X1 )
| ~ spl10_15
| ~ spl10_174 ),
inference(resolution,[],[f1776,f339]) ).
fof(f23139,plain,
( spl10_684
| ~ spl10_18
| ~ spl10_174 ),
inference(avatar_split_clause,[],[f2055,f1775,f350,f23137]) ).
fof(f23137,plain,
( spl10_684
<=> ! [X2,X0,X1] :
( ~ member(X0,power_class(X1))
| member(X0,sum_class(union(universal_class,X2)))
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_684])]) ).
fof(f350,plain,
( spl10_18
<=> ! [X0] :
( member(power_class(X0),universal_class)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_18])]) ).
fof(f2055,plain,
( ! [X2,X0,X1] :
( ~ member(X0,power_class(X1))
| member(X0,sum_class(union(universal_class,X2)))
| ~ member(X1,universal_class) )
| ~ spl10_18
| ~ spl10_174 ),
inference(resolution,[],[f1776,f351]) ).
fof(f351,plain,
( ! [X0] :
( member(power_class(X0),universal_class)
| ~ member(X0,universal_class) )
| ~ spl10_18 ),
inference(avatar_component_clause,[],[f350]) ).
fof(f23134,plain,
( spl10_683
| ~ spl10_19
| ~ spl10_174 ),
inference(avatar_split_clause,[],[f2054,f1775,f354,f23132]) ).
fof(f23132,plain,
( spl10_683
<=> ! [X2,X0,X1] :
( ~ member(X0,sum_class(X1))
| member(X0,sum_class(union(universal_class,X2)))
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_683])]) ).
fof(f354,plain,
( spl10_19
<=> ! [X0] :
( member(sum_class(X0),universal_class)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_19])]) ).
fof(f2054,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum_class(X1))
| member(X0,sum_class(union(universal_class,X2)))
| ~ member(X1,universal_class) )
| ~ spl10_19
| ~ spl10_174 ),
inference(resolution,[],[f1776,f355]) ).
fof(f355,plain,
( ! [X0] :
( member(sum_class(X0),universal_class)
| ~ member(X0,universal_class) )
| ~ spl10_19 ),
inference(avatar_component_clause,[],[f354]) ).
fof(f23130,plain,
( spl10_682
| ~ spl10_16
| ~ spl10_174 ),
inference(avatar_split_clause,[],[f2036,f1775,f342,f23128]) ).
fof(f23128,plain,
( spl10_682
<=> ! [X2,X0,X1] :
( ~ member(X0,sK4(X1))
| member(X0,sum_class(union(X1,X2)))
| null_class = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_682])]) ).
fof(f342,plain,
( spl10_16
<=> ! [X0] :
( member(sK4(X0),X0)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_16])]) ).
fof(f2036,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sK4(X1))
| member(X0,sum_class(union(X1,X2)))
| null_class = X1 )
| ~ spl10_16
| ~ spl10_174 ),
inference(resolution,[],[f1776,f343]) ).
fof(f343,plain,
( ! [X0] :
( member(sK4(X0),X0)
| null_class = X0 )
| ~ spl10_16 ),
inference(avatar_component_clause,[],[f342]) ).
fof(f23126,plain,
( spl10_681
| ~ spl10_114
| ~ spl10_173 ),
inference(avatar_split_clause,[],[f2025,f1771,f1049,f23124]) ).
fof(f23124,plain,
( spl10_681
<=> ! [X2,X0,X1] :
( ~ member(X0,X1)
| member(X0,sum_class(union(X2,sum_class(universal_class))))
| ~ member(X1,sK9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_681])]) ).
fof(f2025,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| member(X0,sum_class(union(X2,sum_class(universal_class))))
| ~ member(X1,sK9) )
| ~ spl10_114
| ~ spl10_173 ),
inference(resolution,[],[f1772,f1050]) ).
fof(f23117,plain,
( spl10_680
| ~ spl10_15
| ~ spl10_173 ),
inference(avatar_split_clause,[],[f2001,f1771,f338,f23115]) ).
fof(f23115,plain,
( spl10_680
<=> ! [X2,X0,X1] :
( ~ member(X0,sK4(X1))
| member(X0,sum_class(union(X2,universal_class)))
| null_class = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_680])]) ).
fof(f2001,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sK4(X1))
| member(X0,sum_class(union(X2,universal_class)))
| null_class = X1 )
| ~ spl10_15
| ~ spl10_173 ),
inference(resolution,[],[f1772,f339]) ).
fof(f23112,plain,
( spl10_679
| ~ spl10_18
| ~ spl10_173 ),
inference(avatar_split_clause,[],[f1999,f1771,f350,f23110]) ).
fof(f23110,plain,
( spl10_679
<=> ! [X2,X0,X1] :
( ~ member(X0,power_class(X1))
| member(X0,sum_class(union(X2,universal_class)))
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_679])]) ).
fof(f1999,plain,
( ! [X2,X0,X1] :
( ~ member(X0,power_class(X1))
| member(X0,sum_class(union(X2,universal_class)))
| ~ member(X1,universal_class) )
| ~ spl10_18
| ~ spl10_173 ),
inference(resolution,[],[f1772,f351]) ).
fof(f23107,plain,
( spl10_678
| ~ spl10_19
| ~ spl10_173 ),
inference(avatar_split_clause,[],[f1998,f1771,f354,f23105]) ).
fof(f23105,plain,
( spl10_678
<=> ! [X2,X0,X1] :
( ~ member(X0,sum_class(X1))
| member(X0,sum_class(union(X2,universal_class)))
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_678])]) ).
fof(f1998,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum_class(X1))
| member(X0,sum_class(union(X2,universal_class)))
| ~ member(X1,universal_class) )
| ~ spl10_19
| ~ spl10_173 ),
inference(resolution,[],[f1772,f355]) ).
fof(f23103,plain,
( spl10_677
| ~ spl10_16
| ~ spl10_173 ),
inference(avatar_split_clause,[],[f1980,f1771,f342,f23101]) ).
fof(f23101,plain,
( spl10_677
<=> ! [X2,X0,X1] :
( ~ member(X0,sK4(X1))
| member(X0,sum_class(union(X2,X1)))
| null_class = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_677])]) ).
fof(f1980,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sK4(X1))
| member(X0,sum_class(union(X2,X1)))
| null_class = X1 )
| ~ spl10_16
| ~ spl10_173 ),
inference(resolution,[],[f1772,f343]) ).
fof(f23099,plain,
( spl10_676
| ~ spl10_27
| ~ spl10_169 ),
inference(avatar_split_clause,[],[f1931,f1752,f387,f23097]) ).
fof(f23097,plain,
( spl10_676
<=> ! [X2,X0,X1] :
( ~ member(X0,sum_class(X1))
| ~ subclass(X1,power_class(X2))
| subclass(sK7(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_676])]) ).
fof(f1931,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum_class(X1))
| ~ subclass(X1,power_class(X2))
| subclass(sK7(X0,X1),X2) )
| ~ spl10_27
| ~ spl10_169 ),
inference(resolution,[],[f1753,f388]) ).
fof(f23095,plain,
( spl10_675
| ~ spl10_25
| ~ spl10_169 ),
inference(avatar_split_clause,[],[f1924,f1752,f379,f23093]) ).
fof(f23093,plain,
( spl10_675
<=> ! [X2,X0,X1] :
( ~ member(X0,sum_class(X1))
| ~ subclass(X1,complement(X2))
| ~ member(sK7(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_675])]) ).
fof(f1924,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum_class(X1))
| ~ subclass(X1,complement(X2))
| ~ member(sK7(X0,X1),X2) )
| ~ spl10_25
| ~ spl10_169 ),
inference(resolution,[],[f1753,f380]) ).
fof(f23091,plain,
( spl10_674
| ~ spl10_20
| ~ spl10_168 ),
inference(avatar_split_clause,[],[f1909,f1748,f358,f23089]) ).
fof(f23089,plain,
( spl10_674
<=> ! [X0,X1] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,sum_class(X1))
| ~ function(sK7(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_674])]) ).
fof(f358,plain,
( spl10_20
<=> ! [X0] :
( subclass(X0,cross_product(universal_class,universal_class))
| ~ function(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_20])]) ).
fof(f1748,plain,
( spl10_168
<=> ! [X2,X0,X1] :
( ~ member(X0,sum_class(X1))
| member(X0,X2)
| ~ subclass(sK7(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_168])]) ).
fof(f1909,plain,
( ! [X0,X1] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,sum_class(X1))
| ~ function(sK7(X0,X1)) )
| ~ spl10_20
| ~ spl10_168 ),
inference(resolution,[],[f1749,f359]) ).
fof(f359,plain,
( ! [X0] :
( subclass(X0,cross_product(universal_class,universal_class))
| ~ function(X0) )
| ~ spl10_20 ),
inference(avatar_component_clause,[],[f358]) ).
fof(f1749,plain,
( ! [X2,X0,X1] :
( ~ subclass(sK7(X0,X1),X2)
| member(X0,X2)
| ~ member(X0,sum_class(X1)) )
| ~ spl10_168 ),
inference(avatar_component_clause,[],[f1748]) ).
fof(f23085,plain,
( spl10_673
| spl10_552
| ~ spl10_119
| ~ spl10_160 ),
inference(avatar_split_clause,[],[f1721,f1514,f1071,f19379,f23083]) ).
fof(f23083,plain,
( spl10_673
<=> ! [X2] :
( ~ member(X2,identity_relation)
| ~ subclass(universal_class,sK5(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_673])]) ).
fof(f19379,plain,
( spl10_552
<=> ! [X0,X1] : member(unordered_pair(X0,X1),sum_class(universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_552])]) ).
fof(f1721,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(X0,X1),sum_class(universal_class))
| ~ member(X2,identity_relation)
| ~ subclass(universal_class,sK5(X2)) )
| ~ spl10_119
| ~ spl10_160 ),
inference(resolution,[],[f1515,f1072]) ).
fof(f23081,plain,
( spl10_672
| ~ spl10_16
| ~ spl10_160 ),
inference(avatar_split_clause,[],[f1711,f1514,f342,f23079]) ).
fof(f23079,plain,
( spl10_672
<=> ! [X0] :
( member(sK4(sK5(X0)),sum_class(universal_class))
| ~ member(X0,identity_relation)
| null_class = sK5(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_672])]) ).
fof(f1711,plain,
( ! [X0] :
( member(sK4(sK5(X0)),sum_class(universal_class))
| ~ member(X0,identity_relation)
| null_class = sK5(X0) )
| ~ spl10_16
| ~ spl10_160 ),
inference(resolution,[],[f1515,f343]) ).
fof(f23067,plain,
( spl10_671
| spl10_552
| ~ spl10_119
| ~ spl10_159 ),
inference(avatar_split_clause,[],[f1702,f1510,f1071,f19379,f23065]) ).
fof(f23065,plain,
( spl10_671
<=> ! [X2] :
( null_class = X2
| ~ subclass(universal_class,sK4(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_671])]) ).
fof(f1702,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(X0,X1),sum_class(universal_class))
| null_class = X2
| ~ subclass(universal_class,sK4(X2)) )
| ~ spl10_119
| ~ spl10_159 ),
inference(resolution,[],[f1511,f1072]) ).
fof(f23063,plain,
( spl10_670
| ~ spl10_16
| ~ spl10_159 ),
inference(avatar_split_clause,[],[f1692,f1510,f342,f23061]) ).
fof(f23061,plain,
( spl10_670
<=> ! [X0] :
( member(sK4(sK4(X0)),sum_class(universal_class))
| null_class = X0
| null_class = sK4(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_670])]) ).
fof(f1692,plain,
( ! [X0] :
( member(sK4(sK4(X0)),sum_class(universal_class))
| null_class = X0
| null_class = sK4(X0) )
| ~ spl10_16
| ~ spl10_159 ),
inference(resolution,[],[f1511,f343]) ).
fof(f23057,plain,
( spl10_669
| spl10_552
| ~ spl10_119
| ~ spl10_158 ),
inference(avatar_split_clause,[],[f1688,f1506,f1071,f19379,f23055]) ).
fof(f23055,plain,
( spl10_669
<=> ! [X2] :
( ~ member(X2,universal_class)
| ~ subclass(universal_class,power_class(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_669])]) ).
fof(f1688,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(X0,X1),sum_class(universal_class))
| ~ member(X2,universal_class)
| ~ subclass(universal_class,power_class(X2)) )
| ~ spl10_119
| ~ spl10_158 ),
inference(resolution,[],[f1507,f1072]) ).
fof(f23053,plain,
( spl10_668
| ~ spl10_16
| ~ spl10_158 ),
inference(avatar_split_clause,[],[f1678,f1506,f342,f23051]) ).
fof(f23051,plain,
( spl10_668
<=> ! [X0] :
( member(sK4(power_class(X0)),sum_class(universal_class))
| ~ member(X0,universal_class)
| null_class = power_class(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_668])]) ).
fof(f1678,plain,
( ! [X0] :
( member(sK4(power_class(X0)),sum_class(universal_class))
| ~ member(X0,universal_class)
| null_class = power_class(X0) )
| ~ spl10_16
| ~ spl10_158 ),
inference(resolution,[],[f1507,f343]) ).
fof(f23045,plain,
( spl10_667
| spl10_552
| ~ spl10_119
| ~ spl10_157 ),
inference(avatar_split_clause,[],[f1673,f1502,f1071,f19379,f23043]) ).
fof(f23043,plain,
( spl10_667
<=> ! [X2] :
( ~ member(X2,universal_class)
| ~ subclass(universal_class,sum_class(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_667])]) ).
fof(f1673,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(X0,X1),sum_class(universal_class))
| ~ member(X2,universal_class)
| ~ subclass(universal_class,sum_class(X2)) )
| ~ spl10_119
| ~ spl10_157 ),
inference(resolution,[],[f1503,f1072]) ).
fof(f23041,plain,
( spl10_666
| ~ spl10_16
| ~ spl10_157 ),
inference(avatar_split_clause,[],[f1663,f1502,f342,f23039]) ).
fof(f23039,plain,
( spl10_666
<=> ! [X0] :
( member(sK4(sum_class(X0)),sum_class(universal_class))
| ~ member(X0,universal_class)
| null_class = sum_class(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_666])]) ).
fof(f1663,plain,
( ! [X0] :
( member(sK4(sum_class(X0)),sum_class(universal_class))
| ~ member(X0,universal_class)
| null_class = sum_class(X0) )
| ~ spl10_16
| ~ spl10_157 ),
inference(resolution,[],[f1503,f343]) ).
fof(f23037,plain,
( spl10_665
| ~ spl10_119
| ~ spl10_155 ),
inference(avatar_split_clause,[],[f1656,f1493,f1071,f23035]) ).
fof(f23035,plain,
( spl10_665
<=> ! [X2,X0,X1] :
( member(unordered_pair(X0,X1),sum_class(X2))
| null_class = X2
| ~ subclass(universal_class,sK4(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_665])]) ).
fof(f1656,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(X0,X1),sum_class(X2))
| null_class = X2
| ~ subclass(universal_class,sK4(X2)) )
| ~ spl10_119
| ~ spl10_155 ),
inference(resolution,[],[f1494,f1072]) ).
fof(f23033,plain,
( spl10_664
| ~ spl10_241
| ~ spl10_625 ),
inference(avatar_split_clause,[],[f22299,f20679,f4103,f23030]) ).
fof(f23030,plain,
( spl10_664
<=> subclass(union(sK0,sK0),sum_class(universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_664])]) ).
fof(f20679,plain,
( spl10_625
<=> ! [X0,X1] :
( member(sK6(union(X0,X0),X1),X0)
| subclass(union(X0,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_625])]) ).
fof(f22299,plain,
( subclass(union(sK0,sK0),sum_class(universal_class))
| ~ spl10_241
| ~ spl10_625 ),
inference(duplicate_literal_removal,[],[f22179]) ).
fof(f22179,plain,
( subclass(union(sK0,sK0),sum_class(universal_class))
| subclass(union(sK0,sK0),sum_class(universal_class))
| ~ spl10_241
| ~ spl10_625 ),
inference(resolution,[],[f20680,f4104]) ).
fof(f20680,plain,
( ! [X0,X1] :
( member(sK6(union(X0,X0),X1),X0)
| subclass(union(X0,X0),X1) )
| ~ spl10_625 ),
inference(avatar_component_clause,[],[f20679]) ).
fof(f23028,plain,
( spl10_663
| ~ spl10_16
| ~ spl10_155 ),
inference(avatar_split_clause,[],[f1646,f1493,f342,f23026]) ).
fof(f23026,plain,
( spl10_663
<=> ! [X0] :
( member(sK4(sK4(X0)),sum_class(X0))
| null_class = X0
| null_class = sK4(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_663])]) ).
fof(f1646,plain,
( ! [X0] :
( member(sK4(sK4(X0)),sum_class(X0))
| null_class = X0
| null_class = sK4(X0) )
| ~ spl10_16
| ~ spl10_155 ),
inference(resolution,[],[f1494,f343]) ).
fof(f23024,plain,
( spl10_662
| ~ spl10_118
| ~ spl10_153 ),
inference(avatar_split_clause,[],[f1635,f1485,f1067,f23022]) ).
fof(f23022,plain,
( spl10_662
<=> ! [X0,X1] :
( ~ member(X0,sum_class(power_class(X1)))
| member(null_class,X1)
| ~ inductive(sK7(X0,power_class(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_662])]) ).
fof(f1067,plain,
( spl10_118
<=> ! [X0,X1] :
( member(null_class,X0)
| ~ subclass(X1,X0)
| ~ inductive(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_118])]) ).
fof(f1485,plain,
( spl10_153
<=> ! [X0,X1] :
( ~ member(X0,sum_class(power_class(X1)))
| subclass(sK7(X0,power_class(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_153])]) ).
fof(f1635,plain,
( ! [X0,X1] :
( ~ member(X0,sum_class(power_class(X1)))
| member(null_class,X1)
| ~ inductive(sK7(X0,power_class(X1))) )
| ~ spl10_118
| ~ spl10_153 ),
inference(resolution,[],[f1486,f1068]) ).
fof(f1068,plain,
( ! [X0,X1] :
( ~ subclass(X1,X0)
| member(null_class,X0)
| ~ inductive(X1) )
| ~ spl10_118 ),
inference(avatar_component_clause,[],[f1067]) ).
fof(f1486,plain,
( ! [X0,X1] :
( subclass(sK7(X0,power_class(X1)),X1)
| ~ member(X0,sum_class(power_class(X1))) )
| ~ spl10_153 ),
inference(avatar_component_clause,[],[f1485]) ).
fof(f23020,plain,
( spl10_661
| ~ spl10_114
| ~ spl10_150 ),
inference(avatar_split_clause,[],[f1617,f1473,f1049,f23018]) ).
fof(f23018,plain,
( spl10_661
<=> ! [X0] :
( ~ member(X0,sum_class(complement(sum_class(universal_class))))
| ~ member(sK7(X0,complement(sum_class(universal_class))),sK9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_661])]) ).
fof(f1473,plain,
( spl10_150
<=> ! [X0,X1] :
( ~ member(X0,sum_class(complement(X1)))
| ~ member(sK7(X0,complement(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_150])]) ).
fof(f1617,plain,
( ! [X0] :
( ~ member(X0,sum_class(complement(sum_class(universal_class))))
| ~ member(sK7(X0,complement(sum_class(universal_class))),sK9) )
| ~ spl10_114
| ~ spl10_150 ),
inference(resolution,[],[f1474,f1050]) ).
fof(f1474,plain,
( ! [X0,X1] :
( ~ member(sK7(X0,complement(X1)),X1)
| ~ member(X0,sum_class(complement(X1))) )
| ~ spl10_150 ),
inference(avatar_component_clause,[],[f1473]) ).
fof(f23016,plain,
( spl10_660
| ~ spl10_35
| ~ spl10_145 ),
inference(avatar_split_clause,[],[f1581,f1453,f430,f23014]) ).
fof(f23014,plain,
( spl10_660
<=> ! [X0,X3,X2,X1] :
( ~ subclass(X0,intersection(X1,X2))
| subclass(X0,X3)
| member(sK6(X0,X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_660])]) ).
fof(f1581,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| subclass(X0,X3)
| member(sK6(X0,X3),X1) )
| ~ spl10_35
| ~ spl10_145 ),
inference(resolution,[],[f1454,f431]) ).
fof(f23012,plain,
( spl10_659
| ~ spl10_36
| ~ spl10_145 ),
inference(avatar_split_clause,[],[f1580,f1453,f434,f23010]) ).
fof(f23010,plain,
( spl10_659
<=> ! [X0,X3,X2,X1] :
( ~ subclass(X0,intersection(X1,X2))
| subclass(X0,X3)
| member(sK6(X0,X3),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_659])]) ).
fof(f1580,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| subclass(X0,X3)
| member(sK6(X0,X3),X2) )
| ~ spl10_36
| ~ spl10_145 ),
inference(resolution,[],[f1454,f435]) ).
fof(f23008,plain,
( spl10_658
| ~ spl10_27
| ~ spl10_144 ),
inference(avatar_split_clause,[],[f1562,f1449,f387,f23006]) ).
fof(f23006,plain,
( spl10_658
<=> ! [X0,X1] :
( null_class = intersection(X0,power_class(X1))
| subclass(sK4(intersection(X0,power_class(X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_658])]) ).
fof(f1562,plain,
( ! [X0,X1] :
( null_class = intersection(X0,power_class(X1))
| subclass(sK4(intersection(X0,power_class(X1))),X1) )
| ~ spl10_27
| ~ spl10_144 ),
inference(resolution,[],[f1450,f388]) ).
fof(f23004,plain,
( spl10_657
| ~ spl10_25
| ~ spl10_144 ),
inference(avatar_split_clause,[],[f1555,f1449,f379,f23002]) ).
fof(f23002,plain,
( spl10_657
<=> ! [X0,X1] :
( null_class = intersection(X0,complement(X1))
| ~ member(sK4(intersection(X0,complement(X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_657])]) ).
fof(f1555,plain,
( ! [X0,X1] :
( null_class = intersection(X0,complement(X1))
| ~ member(sK4(intersection(X0,complement(X1))),X1) )
| ~ spl10_25
| ~ spl10_144 ),
inference(resolution,[],[f1450,f380]) ).
fof(f23000,plain,
( spl10_656
| ~ spl10_27
| ~ spl10_143 ),
inference(avatar_split_clause,[],[f1537,f1445,f387,f22998]) ).
fof(f22998,plain,
( spl10_656
<=> ! [X0,X1] :
( null_class = intersection(power_class(X0),X1)
| subclass(sK4(intersection(power_class(X0),X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_656])]) ).
fof(f1537,plain,
( ! [X0,X1] :
( null_class = intersection(power_class(X0),X1)
| subclass(sK4(intersection(power_class(X0),X1)),X0) )
| ~ spl10_27
| ~ spl10_143 ),
inference(resolution,[],[f1446,f388]) ).
fof(f22996,plain,
( spl10_655
| ~ spl10_25
| ~ spl10_143 ),
inference(avatar_split_clause,[],[f1530,f1445,f379,f22994]) ).
fof(f22994,plain,
( spl10_655
<=> ! [X0,X1] :
( null_class = intersection(complement(X0),X1)
| ~ member(sK4(intersection(complement(X0),X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_655])]) ).
fof(f1530,plain,
( ! [X0,X1] :
( null_class = intersection(complement(X0),X1)
| ~ member(sK4(intersection(complement(X0),X1)),X0) )
| ~ spl10_25
| ~ spl10_143 ),
inference(resolution,[],[f1446,f380]) ).
fof(f22992,plain,
( spl10_654
| ~ spl10_45
| ~ spl10_140 ),
inference(avatar_split_clause,[],[f1419,f1259,f494,f22990]) ).
fof(f22990,plain,
( spl10_654
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| ~ member(X1,identity_relation)
| member(sK5(X1),X2)
| ~ subclass(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_654])]) ).
fof(f1419,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| ~ member(X1,identity_relation)
| member(sK5(X1),X2)
| ~ subclass(X0,X2) )
| ~ spl10_45
| ~ spl10_140 ),
inference(resolution,[],[f1260,f495]) ).
fof(f22988,plain,
( spl10_653
| ~ spl10_241
| ~ spl10_624 ),
inference(avatar_split_clause,[],[f22056,f20675,f4103,f22985]) ).
fof(f22985,plain,
( spl10_653
<=> subclass(union(null_class,sK0),sum_class(universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_653])]) ).
fof(f20675,plain,
( spl10_624
<=> ! [X0,X1] :
( member(sK6(union(null_class,X0),X1),X0)
| subclass(union(null_class,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_624])]) ).
fof(f22056,plain,
( subclass(union(null_class,sK0),sum_class(universal_class))
| ~ spl10_241
| ~ spl10_624 ),
inference(duplicate_literal_removal,[],[f21936]) ).
fof(f21936,plain,
( subclass(union(null_class,sK0),sum_class(universal_class))
| subclass(union(null_class,sK0),sum_class(universal_class))
| ~ spl10_241
| ~ spl10_624 ),
inference(resolution,[],[f20676,f4104]) ).
fof(f20676,plain,
( ! [X0,X1] :
( member(sK6(union(null_class,X0),X1),X0)
| subclass(union(null_class,X0),X1) )
| ~ spl10_624 ),
inference(avatar_component_clause,[],[f20675]) ).
fof(f22983,plain,
( spl10_652
| ~ spl10_45
| ~ spl10_139 ),
inference(avatar_split_clause,[],[f1393,f1255,f494,f22981]) ).
fof(f22981,plain,
( spl10_652
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| null_class = X1
| member(sK4(X1),X2)
| ~ subclass(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_652])]) ).
fof(f1393,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| null_class = X1
| member(sK4(X1),X2)
| ~ subclass(X0,X2) )
| ~ spl10_45
| ~ spl10_139 ),
inference(resolution,[],[f1256,f495]) ).
fof(f22979,plain,
( spl10_651
| ~ spl10_45
| ~ spl10_137 ),
inference(avatar_split_clause,[],[f1367,f1246,f494,f22977]) ).
fof(f22977,plain,
( spl10_651
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| ~ member(X1,universal_class)
| member(power_class(X1),X2)
| ~ subclass(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_651])]) ).
fof(f1367,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| ~ member(X1,universal_class)
| member(power_class(X1),X2)
| ~ subclass(X0,X2) )
| ~ spl10_45
| ~ spl10_137 ),
inference(resolution,[],[f1247,f495]) ).
fof(f22975,plain,
( spl10_650
| ~ spl10_45
| ~ spl10_136 ),
inference(avatar_split_clause,[],[f1342,f1242,f494,f22973]) ).
fof(f22973,plain,
( spl10_650
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| ~ member(X1,universal_class)
| member(sum_class(X1),X2)
| ~ subclass(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_650])]) ).
fof(f1342,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| ~ member(X1,universal_class)
| member(sum_class(X1),X2)
| ~ subclass(X0,X2) )
| ~ spl10_45
| ~ spl10_136 ),
inference(resolution,[],[f1243,f495]) ).
fof(f22971,plain,
( spl10_649
| ~ spl10_123
| ~ spl10_135 ),
inference(avatar_split_clause,[],[f1321,f1238,f1163,f22969]) ).
fof(f22969,plain,
( spl10_649
<=> ! [X2,X0,X1] :
( ~ subclass(X0,unordered_pair(X1,X2))
| null_class = X0
| member(sK4(X0),sum_class(universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_649])]) ).
fof(f1321,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,unordered_pair(X1,X2))
| null_class = X0
| member(sK4(X0),sum_class(universal_class)) )
| ~ spl10_123
| ~ spl10_135 ),
inference(resolution,[],[f1239,f1164]) ).
fof(f22967,plain,
( spl10_648
| ~ spl10_45
| ~ spl10_135 ),
inference(avatar_split_clause,[],[f1316,f1238,f494,f22965]) ).
fof(f22965,plain,
( spl10_648
<=> ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| null_class = X0
| member(sK4(X0),X2)
| ~ subclass(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_648])]) ).
fof(f1316,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| null_class = X0
| member(sK4(X0),X2)
| ~ subclass(X1,X2) )
| ~ spl10_45
| ~ spl10_135 ),
inference(resolution,[],[f1239,f495]) ).
fof(f22963,plain,
( spl10_647
| ~ spl10_33
| ~ spl10_134 ),
inference(avatar_split_clause,[],[f1311,f1234,f422,f22961]) ).
fof(f22961,plain,
( spl10_647
<=> ! [X0,X1] :
( ~ member(sK6(sK4(X0),X1),X0)
| null_class = X0
| subclass(sK4(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_647])]) ).
fof(f1311,plain,
( ! [X0,X1] :
( ~ member(sK6(sK4(X0),X1),X0)
| null_class = X0
| subclass(sK4(X0),X1) )
| ~ spl10_33
| ~ spl10_134 ),
inference(resolution,[],[f1235,f423]) ).
fof(f22959,plain,
( spl10_646
| ~ spl10_45
| ~ spl10_128 ),
inference(avatar_split_clause,[],[f1306,f1207,f494,f22957]) ).
fof(f22957,plain,
( spl10_646
<=> ! [X2,X0,X1] :
( subclass(power_class(X0),X1)
| member(sK6(power_class(X0),X1),X2)
| ~ subclass(universal_class,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_646])]) ).
fof(f1306,plain,
( ! [X2,X0,X1] :
( subclass(power_class(X0),X1)
| member(sK6(power_class(X0),X1),X2)
| ~ subclass(universal_class,X2) )
| ~ spl10_45
| ~ spl10_128 ),
inference(resolution,[],[f1208,f495]) ).
fof(f22955,plain,
( spl10_645
| ~ spl10_45
| ~ spl10_126 ),
inference(avatar_split_clause,[],[f1295,f1199,f494,f22953]) ).
fof(f22953,plain,
( spl10_645
<=> ! [X2,X0,X1] :
( subclass(domain_of(X0),X1)
| member(sK6(domain_of(X0),X1),X2)
| ~ subclass(universal_class,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_645])]) ).
fof(f1295,plain,
( ! [X2,X0,X1] :
( subclass(domain_of(X0),X1)
| member(sK6(domain_of(X0),X1),X2)
| ~ subclass(universal_class,X2) )
| ~ spl10_45
| ~ spl10_126 ),
inference(resolution,[],[f1200,f495]) ).
fof(f22951,plain,
( spl10_644
| ~ spl10_45
| ~ spl10_125 ),
inference(avatar_split_clause,[],[f1285,f1195,f494,f22949]) ).
fof(f22949,plain,
( spl10_644
<=> ! [X2,X0,X1] :
( subclass(complement(X0),X1)
| member(sK6(complement(X0),X1),X2)
| ~ subclass(universal_class,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_644])]) ).
fof(f1285,plain,
( ! [X2,X0,X1] :
( subclass(complement(X0),X1)
| member(sK6(complement(X0),X1),X2)
| ~ subclass(universal_class,X2) )
| ~ spl10_45
| ~ spl10_125 ),
inference(resolution,[],[f1196,f495]) ).
fof(f22947,plain,
( spl10_643
| ~ spl10_33
| ~ spl10_123 ),
inference(avatar_split_clause,[],[f1186,f1163,f422,f22945]) ).
fof(f22945,plain,
( spl10_643
<=> ! [X2,X0,X1] :
( member(sK6(unordered_pair(X0,X1),X2),sum_class(universal_class))
| subclass(unordered_pair(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_643])]) ).
fof(f1186,plain,
( ! [X2,X0,X1] :
( member(sK6(unordered_pair(X0,X1),X2),sum_class(universal_class))
| subclass(unordered_pair(X0,X1),X2) )
| ~ spl10_33
| ~ spl10_123 ),
inference(resolution,[],[f1164,f423]) ).
fof(f22943,plain,
( spl10_642
| ~ spl10_241
| ~ spl10_623 ),
inference(avatar_split_clause,[],[f21813,f20671,f4103,f22940]) ).
fof(f22940,plain,
( spl10_642
<=> subclass(union(sK0,null_class),sum_class(universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_642])]) ).
fof(f20671,plain,
( spl10_623
<=> ! [X0,X1] :
( member(sK6(union(X0,null_class),X1),X0)
| subclass(union(X0,null_class),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_623])]) ).
fof(f21813,plain,
( subclass(union(sK0,null_class),sum_class(universal_class))
| ~ spl10_241
| ~ spl10_623 ),
inference(duplicate_literal_removal,[],[f21693]) ).
fof(f21693,plain,
( subclass(union(sK0,null_class),sum_class(universal_class))
| subclass(union(sK0,null_class),sum_class(universal_class))
| ~ spl10_241
| ~ spl10_623 ),
inference(resolution,[],[f20672,f4104]) ).
fof(f20672,plain,
( ! [X0,X1] :
( member(sK6(union(X0,null_class),X1),X0)
| subclass(union(X0,null_class),X1) )
| ~ spl10_623 ),
inference(avatar_component_clause,[],[f20671]) ).
fof(f22938,plain,
( ~ spl10_639
| spl10_640
| spl10_641
| ~ spl10_117
| ~ spl10_122 ),
inference(avatar_split_clause,[],[f1178,f1159,f1063,f22935,f22931,f22927]) ).
fof(f22927,plain,
( spl10_639
<=> inductive(sK4(power_class(sK9))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_639])]) ).
fof(f22931,plain,
( spl10_640
<=> sK9 = sK4(power_class(sK9)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_640])]) ).
fof(f22935,plain,
( spl10_641
<=> null_class = power_class(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_641])]) ).
fof(f1063,plain,
( spl10_117
<=> ! [X0] :
( sK9 = X0
| ~ subclass(X0,sK9)
| ~ inductive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_117])]) ).
fof(f1178,plain,
( null_class = power_class(sK9)
| sK9 = sK4(power_class(sK9))
| ~ inductive(sK4(power_class(sK9)))
| ~ spl10_117
| ~ spl10_122 ),
inference(resolution,[],[f1160,f1064]) ).
fof(f1064,plain,
( ! [X0] :
( ~ subclass(X0,sK9)
| sK9 = X0
| ~ inductive(X0) )
| ~ spl10_117 ),
inference(avatar_component_clause,[],[f1063]) ).
fof(f22925,plain,
( spl10_638
| ~ spl10_37
| ~ spl10_121 ),
inference(avatar_split_clause,[],[f1171,f1144,f438,f22923]) ).
fof(f22923,plain,
( spl10_638
<=> ! [X0,X1] :
( null_class = complement(union(X0,X1))
| ~ member(sK4(complement(union(X0,X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_638])]) ).
fof(f1144,plain,
( spl10_121
<=> ! [X0] :
( ~ member(sK4(complement(X0)),X0)
| complement(X0) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_121])]) ).
fof(f1171,plain,
( ! [X0,X1] :
( null_class = complement(union(X0,X1))
| ~ member(sK4(complement(union(X0,X1))),X0) )
| ~ spl10_37
| ~ spl10_121 ),
inference(resolution,[],[f1145,f439]) ).
fof(f1145,plain,
( ! [X0] :
( ~ member(sK4(complement(X0)),X0)
| complement(X0) = null_class )
| ~ spl10_121 ),
inference(avatar_component_clause,[],[f1144]) ).
fof(f22921,plain,
( spl10_637
| ~ spl10_38
| ~ spl10_121 ),
inference(avatar_split_clause,[],[f1170,f1144,f442,f22919]) ).
fof(f22919,plain,
( spl10_637
<=> ! [X0,X1] :
( null_class = complement(union(X0,X1))
| ~ member(sK4(complement(union(X0,X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_637])]) ).
fof(f1170,plain,
( ! [X0,X1] :
( null_class = complement(union(X0,X1))
| ~ member(sK4(complement(union(X0,X1))),X1) )
| ~ spl10_38
| ~ spl10_121 ),
inference(resolution,[],[f1145,f443]) ).
fof(f22915,plain,
( spl10_636
| ~ spl10_108
| ~ spl10_179 ),
inference(avatar_split_clause,[],[f2182,f2099,f1004,f22913]) ).
fof(f22913,plain,
( spl10_636
<=> ! [X0,X1] :
( ~ member(X0,sum_class(intersection(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X1)))
| unordered_pair(sK0,sK0) = sK7(X0,intersection(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X1))
| unordered_pair(sK0,unordered_pair(sK1,sK1)) = sK7(X0,intersection(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_636])]) ).
fof(f2099,plain,
( spl10_179
<=> ! [X2,X0,X1] :
( ~ member(X0,sum_class(intersection(X1,X2)))
| member(sK7(X0,intersection(X1,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_179])]) ).
fof(f2182,plain,
( ! [X0,X1] :
( ~ member(X0,sum_class(intersection(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X1)))
| unordered_pair(sK0,sK0) = sK7(X0,intersection(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X1))
| unordered_pair(sK0,unordered_pair(sK1,sK1)) = sK7(X0,intersection(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X1)) )
| ~ spl10_108
| ~ spl10_179 ),
inference(resolution,[],[f2100,f1005]) ).
fof(f2100,plain,
( ! [X2,X0,X1] :
( member(sK7(X0,intersection(X1,X2)),X1)
| ~ member(X0,sum_class(intersection(X1,X2))) )
| ~ spl10_179 ),
inference(avatar_component_clause,[],[f2099]) ).
fof(f22909,plain,
( spl10_635
| ~ spl10_108
| ~ spl10_178 ),
inference(avatar_split_clause,[],[f2151,f2095,f1004,f22907]) ).
fof(f22907,plain,
( spl10_635
<=> ! [X0,X1] :
( ~ member(X0,sum_class(intersection(X1,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))))
| unordered_pair(sK0,sK0) = sK7(X0,intersection(X1,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))))
| unordered_pair(sK0,unordered_pair(sK1,sK1)) = sK7(X0,intersection(X1,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_635])]) ).
fof(f2095,plain,
( spl10_178
<=> ! [X2,X0,X1] :
( ~ member(X0,sum_class(intersection(X1,X2)))
| member(sK7(X0,intersection(X1,X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_178])]) ).
fof(f2151,plain,
( ! [X0,X1] :
( ~ member(X0,sum_class(intersection(X1,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))))
| unordered_pair(sK0,sK0) = sK7(X0,intersection(X1,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))))
| unordered_pair(sK0,unordered_pair(sK1,sK1)) = sK7(X0,intersection(X1,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))) )
| ~ spl10_108
| ~ spl10_178 ),
inference(resolution,[],[f2096,f1005]) ).
fof(f2096,plain,
( ! [X2,X0,X1] :
( member(sK7(X0,intersection(X1,X2)),X2)
| ~ member(X0,sum_class(intersection(X1,X2))) )
| ~ spl10_178 ),
inference(avatar_component_clause,[],[f2095]) ).
fof(f22903,plain,
( spl10_634
| ~ spl10_108
| ~ spl10_163 ),
inference(avatar_split_clause,[],[f1817,f1728,f1004,f22901]) ).
fof(f22901,plain,
( spl10_634
<=> ! [X0,X1] :
( subclass(intersection(X0,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))),X1)
| unordered_pair(sK0,sK0) = sK6(intersection(X0,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))),X1)
| unordered_pair(sK0,unordered_pair(sK1,sK1)) = sK6(intersection(X0,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_634])]) ).
fof(f1817,plain,
( ! [X0,X1] :
( subclass(intersection(X0,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))),X1)
| unordered_pair(sK0,sK0) = sK6(intersection(X0,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))),X1)
| unordered_pair(sK0,unordered_pair(sK1,sK1)) = sK6(intersection(X0,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))),X1) )
| ~ spl10_108
| ~ spl10_163 ),
inference(resolution,[],[f1729,f1005]) ).
fof(f22897,plain,
( spl10_633
| ~ spl10_108
| ~ spl10_162 ),
inference(avatar_split_clause,[],[f1787,f1724,f1004,f22895]) ).
fof(f22895,plain,
( spl10_633
<=> ! [X0,X1] :
( subclass(intersection(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X0),X1)
| unordered_pair(sK0,sK0) = sK6(intersection(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X0),X1)
| unordered_pair(sK0,unordered_pair(sK1,sK1)) = sK6(intersection(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_633])]) ).
fof(f1787,plain,
( ! [X0,X1] :
( subclass(intersection(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X0),X1)
| unordered_pair(sK0,sK0) = sK6(intersection(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X0),X1)
| unordered_pair(sK0,unordered_pair(sK1,sK1)) = sK6(intersection(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X0),X1) )
| ~ spl10_108
| ~ spl10_162 ),
inference(resolution,[],[f1725,f1005]) ).
fof(f22893,plain,
( spl10_632
| ~ spl10_300
| ~ spl10_617 ),
inference(avatar_split_clause,[],[f21568,f20647,f5840,f22890]) ).
fof(f22890,plain,
( spl10_632
<=> subclass(complement(sum_class(universal_class)),complement(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_632])]) ).
fof(f5840,plain,
( spl10_300
<=> ! [X0] :
( subclass(complement(sum_class(universal_class)),X0)
| ~ member(sK6(complement(sum_class(universal_class)),X0),sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_300])]) ).
fof(f20647,plain,
( spl10_617
<=> ! [X0,X1] :
( member(sK6(complement(X0),complement(X1)),X1)
| subclass(complement(X0),complement(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_617])]) ).
fof(f21568,plain,
( subclass(complement(sum_class(universal_class)),complement(sK0))
| ~ spl10_300
| ~ spl10_617 ),
inference(duplicate_literal_removal,[],[f21444]) ).
fof(f21444,plain,
( subclass(complement(sum_class(universal_class)),complement(sK0))
| subclass(complement(sum_class(universal_class)),complement(sK0))
| ~ spl10_300
| ~ spl10_617 ),
inference(resolution,[],[f20648,f5841]) ).
fof(f5841,plain,
( ! [X0] :
( ~ member(sK6(complement(sum_class(universal_class)),X0),sK0)
| subclass(complement(sum_class(universal_class)),X0) )
| ~ spl10_300 ),
inference(avatar_component_clause,[],[f5840]) ).
fof(f20648,plain,
( ! [X0,X1] :
( member(sK6(complement(X0),complement(X1)),X1)
| subclass(complement(X0),complement(X1)) )
| ~ spl10_617 ),
inference(avatar_component_clause,[],[f20647]) ).
fof(f21442,plain,
( spl10_631
| ~ spl10_54
| ~ spl10_314 ),
inference(avatar_split_clause,[],[f12697,f6012,f596,f21440]) ).
fof(f21440,plain,
( spl10_631
<=> ! [X0] :
( ~ member(X0,unordered_pair(sK2,sK2))
| sK0 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_631])]) ).
fof(f12697,plain,
( ! [X0] :
( ~ member(X0,unordered_pair(sK2,sK2))
| sK0 = X0 )
| ~ spl10_54
| ~ spl10_314 ),
inference(duplicate_literal_removal,[],[f10147]) ).
fof(f10147,plain,
( ! [X0] :
( ~ member(X0,unordered_pair(sK2,sK2))
| sK0 = X0
| sK0 = X0 )
| ~ spl10_54
| ~ spl10_314 ),
inference(superposition,[],[f597,f6014]) ).
fof(f21098,plain,
( spl10_630
| ~ spl10_161
| ~ spl10_361 ),
inference(avatar_split_clause,[],[f8948,f8770,f1705,f21095]) ).
fof(f21095,plain,
( spl10_630
<=> member(unordered_pair(sK2,unordered_pair(sK3,sK3)),sum_class(universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_630])]) ).
fof(f1705,plain,
( spl10_161
<=> member(unordered_pair(sK0,unordered_pair(sK1,sK1)),sum_class(universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_161])]) ).
fof(f8948,plain,
( member(unordered_pair(sK2,unordered_pair(sK3,sK3)),sum_class(universal_class))
| ~ spl10_161
| ~ spl10_361 ),
inference(superposition,[],[f1707,f8772]) ).
fof(f8772,plain,
( unordered_pair(sK0,unordered_pair(sK1,sK1)) = unordered_pair(sK2,unordered_pair(sK3,sK3))
| ~ spl10_361 ),
inference(avatar_component_clause,[],[f8770]) ).
fof(f1707,plain,
( member(unordered_pair(sK0,unordered_pair(sK1,sK1)),sum_class(universal_class))
| ~ spl10_161 ),
inference(avatar_component_clause,[],[f1705]) ).
fof(f20989,plain,
( spl10_629
| ~ spl10_162
| ~ spl10_312 ),
inference(avatar_split_clause,[],[f6005,f5980,f1724,f20987]) ).
fof(f20987,plain,
( spl10_629
<=> ! [X0,X1] : subclass(intersection(sK0,X0),union(X1,sum_class(universal_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_629])]) ).
fof(f5980,plain,
( spl10_312
<=> ! [X0,X1] :
( subclass(X0,union(X1,sum_class(universal_class)))
| ~ member(sK6(X0,union(X1,sum_class(universal_class))),sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_312])]) ).
fof(f6005,plain,
( ! [X0,X1] : subclass(intersection(sK0,X0),union(X1,sum_class(universal_class)))
| ~ spl10_162
| ~ spl10_312 ),
inference(duplicate_literal_removal,[],[f5996]) ).
fof(f5996,plain,
( ! [X0,X1] :
( subclass(intersection(sK0,X0),union(X1,sum_class(universal_class)))
| subclass(intersection(sK0,X0),union(X1,sum_class(universal_class))) )
| ~ spl10_162
| ~ spl10_312 ),
inference(resolution,[],[f5981,f1725]) ).
fof(f5981,plain,
( ! [X0,X1] :
( ~ member(sK6(X0,union(X1,sum_class(universal_class))),sK0)
| subclass(X0,union(X1,sum_class(universal_class))) )
| ~ spl10_312 ),
inference(avatar_component_clause,[],[f5980]) ).
fof(f20744,plain,
( spl10_628
| ~ spl10_163
| ~ spl10_312 ),
inference(avatar_split_clause,[],[f6003,f5980,f1728,f20742]) ).
fof(f20742,plain,
( spl10_628
<=> ! [X0,X1] : subclass(intersection(X0,sK0),union(X1,sum_class(universal_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_628])]) ).
fof(f6003,plain,
( ! [X0,X1] : subclass(intersection(X0,sK0),union(X1,sum_class(universal_class)))
| ~ spl10_163
| ~ spl10_312 ),
inference(duplicate_literal_removal,[],[f5998]) ).
fof(f5998,plain,
( ! [X0,X1] :
( subclass(intersection(X0,sK0),union(X1,sum_class(universal_class)))
| subclass(intersection(X0,sK0),union(X1,sum_class(universal_class))) )
| ~ spl10_163
| ~ spl10_312 ),
inference(resolution,[],[f5981,f1729]) ).
fof(f20689,plain,
( spl10_627
| ~ spl10_34
| ~ spl10_207 ),
inference(avatar_split_clause,[],[f2929,f2778,f426,f20687]) ).
fof(f426,plain,
( spl10_34
<=> ! [X0,X1] :
( subclass(X0,X1)
| ~ member(sK6(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_34])]) ).
fof(f2778,plain,
( spl10_207
<=> ! [X2,X0,X1] :
( member(sK6(union(X0,X1),X2),X0)
| member(sK6(union(X0,X1),X2),X1)
| subclass(union(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_207])]) ).
fof(f2929,plain,
( ! [X0,X1] :
( member(sK6(union(X0,X1),X1),X0)
| subclass(union(X0,X1),X1) )
| ~ spl10_34
| ~ spl10_207 ),
inference(duplicate_literal_removal,[],[f2835]) ).
fof(f2835,plain,
( ! [X0,X1] :
( member(sK6(union(X0,X1),X1),X0)
| subclass(union(X0,X1),X1)
| subclass(union(X0,X1),X1) )
| ~ spl10_34
| ~ spl10_207 ),
inference(resolution,[],[f2779,f427]) ).
fof(f427,plain,
( ! [X0,X1] :
( ~ member(sK6(X0,X1),X1)
| subclass(X0,X1) )
| ~ spl10_34 ),
inference(avatar_component_clause,[],[f426]) ).
fof(f2779,plain,
( ! [X2,X0,X1] :
( member(sK6(union(X0,X1),X2),X1)
| member(sK6(union(X0,X1),X2),X0)
| subclass(union(X0,X1),X2) )
| ~ spl10_207 ),
inference(avatar_component_clause,[],[f2778]) ).
fof(f20685,plain,
( spl10_626
| ~ spl10_34
| ~ spl10_207 ),
inference(avatar_split_clause,[],[f2923,f2778,f426,f20683]) ).
fof(f2923,plain,
( ! [X0,X1] :
( member(sK6(union(X0,X1),X0),X1)
| subclass(union(X0,X1),X0) )
| ~ spl10_34
| ~ spl10_207 ),
inference(duplicate_literal_removal,[],[f2876]) ).
fof(f2876,plain,
( ! [X0,X1] :
( member(sK6(union(X0,X1),X0),X1)
| subclass(union(X0,X1),X0)
| subclass(union(X0,X1),X0) )
| ~ spl10_34
| ~ spl10_207 ),
inference(resolution,[],[f2779,f427]) ).
fof(f20681,plain,
( spl10_625
| ~ spl10_207 ),
inference(avatar_split_clause,[],[f2917,f2778,f20679]) ).
fof(f2917,plain,
( ! [X0,X1] :
( member(sK6(union(X0,X0),X1),X0)
| subclass(union(X0,X0),X1) )
| ~ spl10_207 ),
inference(factoring,[],[f2779]) ).
fof(f20677,plain,
( spl10_624
| ~ spl10_5
| ~ spl10_207 ),
inference(avatar_split_clause,[],[f2903,f2778,f292,f20675]) ).
fof(f2903,plain,
( ! [X0,X1] :
( member(sK6(union(null_class,X0),X1),X0)
| subclass(union(null_class,X0),X1) )
| ~ spl10_5
| ~ spl10_207 ),
inference(resolution,[],[f2779,f293]) ).
fof(f20673,plain,
( spl10_623
| ~ spl10_5
| ~ spl10_207 ),
inference(avatar_split_clause,[],[f2862,f2778,f292,f20671]) ).
fof(f2862,plain,
( ! [X0,X1] :
( member(sK6(union(X0,null_class),X1),X0)
| subclass(union(X0,null_class),X1) )
| ~ spl10_5
| ~ spl10_207 ),
inference(resolution,[],[f2779,f293]) ).
fof(f20669,plain,
( spl10_622
| ~ spl10_33
| ~ spl10_206 ),
inference(avatar_split_clause,[],[f2834,f2774,f422,f20667]) ).
fof(f20667,plain,
( spl10_622
<=> ! [X0,X1] :
( ~ member(sK6(X0,intersection(X1,X0)),X1)
| subclass(X0,intersection(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_622])]) ).
fof(f2774,plain,
( spl10_206
<=> ! [X2,X0,X1] :
( ~ member(sK6(X0,intersection(X1,X2)),X2)
| ~ member(sK6(X0,intersection(X1,X2)),X1)
| subclass(X0,intersection(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_206])]) ).
fof(f2834,plain,
( ! [X0,X1] :
( ~ member(sK6(X0,intersection(X1,X0)),X1)
| subclass(X0,intersection(X1,X0)) )
| ~ spl10_33
| ~ spl10_206 ),
inference(duplicate_literal_removal,[],[f2807]) ).
fof(f2807,plain,
( ! [X0,X1] :
( ~ member(sK6(X0,intersection(X1,X0)),X1)
| subclass(X0,intersection(X1,X0))
| subclass(X0,intersection(X1,X0)) )
| ~ spl10_33
| ~ spl10_206 ),
inference(resolution,[],[f2775,f423]) ).
fof(f2775,plain,
( ! [X2,X0,X1] :
( ~ member(sK6(X0,intersection(X1,X2)),X2)
| ~ member(sK6(X0,intersection(X1,X2)),X1)
| subclass(X0,intersection(X1,X2)) )
| ~ spl10_206 ),
inference(avatar_component_clause,[],[f2774]) ).
fof(f20665,plain,
( spl10_621
| ~ spl10_125
| ~ spl10_195 ),
inference(avatar_split_clause,[],[f2546,f2508,f1195,f20663]) ).
fof(f20663,plain,
( spl10_621
<=> ! [X0,X1] :
( ~ subclass(sK6(complement(X0),power_class(X1)),X1)
| subclass(complement(X0),power_class(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_621])]) ).
fof(f2546,plain,
( ! [X0,X1] :
( ~ subclass(sK6(complement(X0),power_class(X1)),X1)
| subclass(complement(X0),power_class(X1)) )
| ~ spl10_125
| ~ spl10_195 ),
inference(duplicate_literal_removal,[],[f2531]) ).
fof(f2531,plain,
( ! [X0,X1] :
( ~ subclass(sK6(complement(X0),power_class(X1)),X1)
| subclass(complement(X0),power_class(X1))
| subclass(complement(X0),power_class(X1)) )
| ~ spl10_125
| ~ spl10_195 ),
inference(resolution,[],[f2509,f1196]) ).
fof(f20661,plain,
( spl10_620
| ~ spl10_126
| ~ spl10_195 ),
inference(avatar_split_clause,[],[f2545,f2508,f1199,f20659]) ).
fof(f20659,plain,
( spl10_620
<=> ! [X0,X1] :
( ~ subclass(sK6(domain_of(X0),power_class(X1)),X1)
| subclass(domain_of(X0),power_class(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_620])]) ).
fof(f2545,plain,
( ! [X0,X1] :
( ~ subclass(sK6(domain_of(X0),power_class(X1)),X1)
| subclass(domain_of(X0),power_class(X1)) )
| ~ spl10_126
| ~ spl10_195 ),
inference(duplicate_literal_removal,[],[f2532]) ).
fof(f2532,plain,
( ! [X0,X1] :
( ~ subclass(sK6(domain_of(X0),power_class(X1)),X1)
| subclass(domain_of(X0),power_class(X1))
| subclass(domain_of(X0),power_class(X1)) )
| ~ spl10_126
| ~ spl10_195 ),
inference(resolution,[],[f2509,f1200]) ).
fof(f20657,plain,
( spl10_619
| ~ spl10_128
| ~ spl10_195 ),
inference(avatar_split_clause,[],[f2544,f2508,f1207,f20655]) ).
fof(f20655,plain,
( spl10_619
<=> ! [X0,X1] :
( ~ subclass(sK6(power_class(X0),power_class(X1)),X1)
| subclass(power_class(X0),power_class(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_619])]) ).
fof(f2544,plain,
( ! [X0,X1] :
( ~ subclass(sK6(power_class(X0),power_class(X1)),X1)
| subclass(power_class(X0),power_class(X1)) )
| ~ spl10_128
| ~ spl10_195 ),
inference(duplicate_literal_removal,[],[f2533]) ).
fof(f2533,plain,
( ! [X0,X1] :
( ~ subclass(sK6(power_class(X0),power_class(X1)),X1)
| subclass(power_class(X0),power_class(X1))
| subclass(power_class(X0),power_class(X1)) )
| ~ spl10_128
| ~ spl10_195 ),
inference(resolution,[],[f2509,f1208]) ).
fof(f20653,plain,
( spl10_618
| ~ spl10_162
| ~ spl10_311 ),
inference(avatar_split_clause,[],[f5993,f5976,f1724,f20651]) ).
fof(f20651,plain,
( spl10_618
<=> ! [X0,X1] : subclass(intersection(sK0,X0),union(sum_class(universal_class),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_618])]) ).
fof(f5976,plain,
( spl10_311
<=> ! [X0,X1] :
( subclass(X0,union(sum_class(universal_class),X1))
| ~ member(sK6(X0,union(sum_class(universal_class),X1)),sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_311])]) ).
fof(f5993,plain,
( ! [X0,X1] : subclass(intersection(sK0,X0),union(sum_class(universal_class),X1))
| ~ spl10_162
| ~ spl10_311 ),
inference(duplicate_literal_removal,[],[f5984]) ).
fof(f5984,plain,
( ! [X0,X1] :
( subclass(intersection(sK0,X0),union(sum_class(universal_class),X1))
| subclass(intersection(sK0,X0),union(sum_class(universal_class),X1)) )
| ~ spl10_162
| ~ spl10_311 ),
inference(resolution,[],[f5977,f1725]) ).
fof(f5977,plain,
( ! [X0,X1] :
( ~ member(sK6(X0,union(sum_class(universal_class),X1)),sK0)
| subclass(X0,union(sum_class(universal_class),X1)) )
| ~ spl10_311 ),
inference(avatar_component_clause,[],[f5976]) ).
fof(f20649,plain,
( spl10_617
| ~ spl10_125
| ~ spl10_194 ),
inference(avatar_split_clause,[],[f2530,f2504,f1195,f20647]) ).
fof(f2530,plain,
( ! [X0,X1] :
( member(sK6(complement(X0),complement(X1)),X1)
| subclass(complement(X0),complement(X1)) )
| ~ spl10_125
| ~ spl10_194 ),
inference(duplicate_literal_removal,[],[f2515]) ).
fof(f2515,plain,
( ! [X0,X1] :
( member(sK6(complement(X0),complement(X1)),X1)
| subclass(complement(X0),complement(X1))
| subclass(complement(X0),complement(X1)) )
| ~ spl10_125
| ~ spl10_194 ),
inference(resolution,[],[f2505,f1196]) ).
fof(f20645,plain,
( spl10_616
| ~ spl10_126
| ~ spl10_194 ),
inference(avatar_split_clause,[],[f2529,f2504,f1199,f20643]) ).
fof(f20643,plain,
( spl10_616
<=> ! [X0,X1] :
( member(sK6(domain_of(X0),complement(X1)),X1)
| subclass(domain_of(X0),complement(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_616])]) ).
fof(f2529,plain,
( ! [X0,X1] :
( member(sK6(domain_of(X0),complement(X1)),X1)
| subclass(domain_of(X0),complement(X1)) )
| ~ spl10_126
| ~ spl10_194 ),
inference(duplicate_literal_removal,[],[f2516]) ).
fof(f2516,plain,
( ! [X0,X1] :
( member(sK6(domain_of(X0),complement(X1)),X1)
| subclass(domain_of(X0),complement(X1))
| subclass(domain_of(X0),complement(X1)) )
| ~ spl10_126
| ~ spl10_194 ),
inference(resolution,[],[f2505,f1200]) ).
fof(f20641,plain,
( spl10_615
| ~ spl10_128
| ~ spl10_194 ),
inference(avatar_split_clause,[],[f2528,f2504,f1207,f20639]) ).
fof(f20639,plain,
( spl10_615
<=> ! [X0,X1] :
( member(sK6(power_class(X0),complement(X1)),X1)
| subclass(power_class(X0),complement(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_615])]) ).
fof(f2528,plain,
( ! [X0,X1] :
( member(sK6(power_class(X0),complement(X1)),X1)
| subclass(power_class(X0),complement(X1)) )
| ~ spl10_128
| ~ spl10_194 ),
inference(duplicate_literal_removal,[],[f2517]) ).
fof(f2517,plain,
( ! [X0,X1] :
( member(sK6(power_class(X0),complement(X1)),X1)
| subclass(power_class(X0),complement(X1))
| subclass(power_class(X0),complement(X1)) )
| ~ spl10_128
| ~ spl10_194 ),
inference(resolution,[],[f2505,f1208]) ).
fof(f20637,plain,
( spl10_614
| ~ spl10_7
| ~ spl10_191 ),
inference(avatar_split_clause,[],[f2475,f2362,f300,f20634]) ).
fof(f20634,plain,
( spl10_614
<=> sK9 = first(unordered_pair(unordered_pair(sK9,sK9),unordered_pair(sK9,unordered_pair(sK9,sK9)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_614])]) ).
fof(f2475,plain,
( sK9 = first(unordered_pair(unordered_pair(sK9,sK9),unordered_pair(sK9,unordered_pair(sK9,sK9))))
| ~ spl10_7
| ~ spl10_191 ),
inference(resolution,[],[f2363,f302]) ).
fof(f20632,plain,
( spl10_613
| ~ spl10_30
| ~ spl10_191 ),
inference(avatar_split_clause,[],[f2460,f2362,f409,f20629]) ).
fof(f20629,plain,
( spl10_613
<=> null_class = first(unordered_pair(unordered_pair(null_class,null_class),unordered_pair(null_class,unordered_pair(sK9,sK9)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_613])]) ).
fof(f409,plain,
( spl10_30
<=> member(null_class,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_30])]) ).
fof(f2460,plain,
( null_class = first(unordered_pair(unordered_pair(null_class,null_class),unordered_pair(null_class,unordered_pair(sK9,sK9))))
| ~ spl10_30
| ~ spl10_191 ),
inference(resolution,[],[f2363,f411]) ).
fof(f411,plain,
( member(null_class,universal_class)
| ~ spl10_30 ),
inference(avatar_component_clause,[],[f409]) ).
fof(f20627,plain,
( spl10_612
| ~ spl10_7
| ~ spl10_190 ),
inference(avatar_split_clause,[],[f2439,f2358,f300,f20624]) ).
fof(f20624,plain,
( spl10_612
<=> sK9 = second(unordered_pair(unordered_pair(sK9,sK9),unordered_pair(sK9,unordered_pair(sK9,sK9)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_612])]) ).
fof(f2439,plain,
( sK9 = second(unordered_pair(unordered_pair(sK9,sK9),unordered_pair(sK9,unordered_pair(sK9,sK9))))
| ~ spl10_7
| ~ spl10_190 ),
inference(resolution,[],[f2359,f302]) ).
fof(f20622,plain,
( spl10_611
| ~ spl10_30
| ~ spl10_190 ),
inference(avatar_split_clause,[],[f2424,f2358,f409,f20619]) ).
fof(f20619,plain,
( spl10_611
<=> sK9 = second(unordered_pair(unordered_pair(null_class,null_class),unordered_pair(null_class,unordered_pair(sK9,sK9)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_611])]) ).
fof(f2424,plain,
( sK9 = second(unordered_pair(unordered_pair(null_class,null_class),unordered_pair(null_class,unordered_pair(sK9,sK9))))
| ~ spl10_30
| ~ spl10_190 ),
inference(resolution,[],[f2359,f411]) ).
fof(f20617,plain,
( spl10_610
| ~ spl10_7
| ~ spl10_189 ),
inference(avatar_split_clause,[],[f2400,f2339,f300,f20615]) ).
fof(f20615,plain,
( spl10_610
<=> ! [X0,X1] :
( ~ member(universal_class,X0)
| member(sK9,sum_class(intersection(X0,X1)))
| ~ member(universal_class,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_610])]) ).
fof(f2339,plain,
( spl10_189
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X3,sum_class(intersection(X2,X1)))
| ~ member(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_189])]) ).
fof(f2400,plain,
( ! [X0,X1] :
( ~ member(universal_class,X0)
| member(sK9,sum_class(intersection(X0,X1)))
| ~ member(universal_class,X1) )
| ~ spl10_7
| ~ spl10_189 ),
inference(resolution,[],[f2340,f302]) ).
fof(f2340,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X3,X0)
| ~ member(X0,X2)
| member(X3,sum_class(intersection(X2,X1)))
| ~ member(X0,X1) )
| ~ spl10_189 ),
inference(avatar_component_clause,[],[f2339]) ).
fof(f20613,plain,
( spl10_609
| ~ spl10_30
| ~ spl10_189 ),
inference(avatar_split_clause,[],[f2385,f2339,f409,f20611]) ).
fof(f20611,plain,
( spl10_609
<=> ! [X0,X1] :
( ~ member(universal_class,X0)
| member(null_class,sum_class(intersection(X0,X1)))
| ~ member(universal_class,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_609])]) ).
fof(f2385,plain,
( ! [X0,X1] :
( ~ member(universal_class,X0)
| member(null_class,sum_class(intersection(X0,X1)))
| ~ member(universal_class,X1) )
| ~ spl10_30
| ~ spl10_189 ),
inference(resolution,[],[f2340,f411]) ).
fof(f20609,plain,
( spl10_608
| ~ spl10_12
| ~ spl10_182 ),
inference(avatar_split_clause,[],[f2210,f2125,f324,f20607]) ).
fof(f20607,plain,
( spl10_608
<=> ! [X0,X1] :
( member(null_class,sum_class(X0))
| ~ member(X1,sum_class(X0))
| ~ inductive(sK7(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_608])]) ).
fof(f324,plain,
( spl10_12
<=> ! [X0] :
( member(null_class,X0)
| ~ inductive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_12])]) ).
fof(f2125,plain,
( spl10_182
<=> ! [X2,X0,X1] :
( member(X0,sum_class(X1))
| ~ member(X0,sK7(X2,X1))
| ~ member(X2,sum_class(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_182])]) ).
fof(f2210,plain,
( ! [X0,X1] :
( member(null_class,sum_class(X0))
| ~ member(X1,sum_class(X0))
| ~ inductive(sK7(X1,X0)) )
| ~ spl10_12
| ~ spl10_182 ),
inference(resolution,[],[f2126,f325]) ).
fof(f325,plain,
( ! [X0] :
( member(null_class,X0)
| ~ inductive(X0) )
| ~ spl10_12 ),
inference(avatar_component_clause,[],[f324]) ).
fof(f2126,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sK7(X2,X1))
| member(X0,sum_class(X1))
| ~ member(X2,sum_class(X1)) )
| ~ spl10_182 ),
inference(avatar_component_clause,[],[f2125]) ).
fof(f20605,plain,
( spl10_607
| ~ spl10_163
| ~ spl10_311 ),
inference(avatar_split_clause,[],[f5991,f5976,f1728,f20603]) ).
fof(f20603,plain,
( spl10_607
<=> ! [X0,X1] : subclass(intersection(X0,sK0),union(sum_class(universal_class),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_607])]) ).
fof(f5991,plain,
( ! [X0,X1] : subclass(intersection(X0,sK0),union(sum_class(universal_class),X1))
| ~ spl10_163
| ~ spl10_311 ),
inference(duplicate_literal_removal,[],[f5986]) ).
fof(f5986,plain,
( ! [X0,X1] :
( subclass(intersection(X0,sK0),union(sum_class(universal_class),X1))
| subclass(intersection(X0,sK0),union(sum_class(universal_class),X1)) )
| ~ spl10_163
| ~ spl10_311 ),
inference(resolution,[],[f5977,f1729]) ).
fof(f20601,plain,
( spl10_606
| ~ spl10_20
| ~ spl10_149 ),
inference(avatar_split_clause,[],[f1611,f1469,f358,f20599]) ).
fof(f20599,plain,
( spl10_606
<=> ! [X2,X0,X1] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,X1)
| ~ function(union(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_606])]) ).
fof(f1469,plain,
( spl10_149
<=> ! [X0,X3,X2,X1] :
( member(X0,X1)
| ~ subclass(union(X2,X3),X1)
| ~ member(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_149])]) ).
fof(f1611,plain,
( ! [X2,X0,X1] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,X1)
| ~ function(union(X1,X2)) )
| ~ spl10_20
| ~ spl10_149 ),
inference(resolution,[],[f1470,f359]) ).
fof(f1470,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(union(X2,X3),X1)
| member(X0,X1)
| ~ member(X0,X2) )
| ~ spl10_149 ),
inference(avatar_component_clause,[],[f1469]) ).
fof(f20597,plain,
( spl10_605
| ~ spl10_20
| ~ spl10_148 ),
inference(avatar_split_clause,[],[f1606,f1465,f358,f20595]) ).
fof(f20595,plain,
( spl10_605
<=> ! [X2,X0,X1] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,X1)
| ~ function(union(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_605])]) ).
fof(f1465,plain,
( spl10_148
<=> ! [X0,X3,X2,X1] :
( member(X0,X1)
| ~ subclass(union(X2,X3),X1)
| ~ member(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_148])]) ).
fof(f1606,plain,
( ! [X2,X0,X1] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,X1)
| ~ function(union(X2,X1)) )
| ~ spl10_20
| ~ spl10_148 ),
inference(resolution,[],[f1466,f359]) ).
fof(f1466,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(union(X2,X3),X1)
| member(X0,X1)
| ~ member(X0,X3) )
| ~ spl10_148 ),
inference(avatar_component_clause,[],[f1465]) ).
fof(f20593,plain,
( spl10_604
| ~ spl10_20
| ~ spl10_147 ),
inference(avatar_split_clause,[],[f1602,f1461,f358,f20591]) ).
fof(f20591,plain,
( spl10_604
<=> ! [X0,X1] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,universal_class)
| ~ function(unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_604])]) ).
fof(f1461,plain,
( spl10_147
<=> ! [X2,X0,X1] :
( member(X0,X1)
| ~ subclass(unordered_pair(X0,X2),X1)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_147])]) ).
fof(f1602,plain,
( ! [X0,X1] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,universal_class)
| ~ function(unordered_pair(X0,X1)) )
| ~ spl10_20
| ~ spl10_147 ),
inference(resolution,[],[f1462,f359]) ).
fof(f1462,plain,
( ! [X2,X0,X1] :
( ~ subclass(unordered_pair(X0,X2),X1)
| member(X0,X1)
| ~ member(X0,universal_class) )
| ~ spl10_147 ),
inference(avatar_component_clause,[],[f1461]) ).
fof(f20589,plain,
( spl10_603
| ~ spl10_20
| ~ spl10_146 ),
inference(avatar_split_clause,[],[f1598,f1457,f358,f20587]) ).
fof(f20587,plain,
( spl10_603
<=> ! [X0,X1] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,universal_class)
| ~ function(unordered_pair(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_603])]) ).
fof(f1457,plain,
( spl10_146
<=> ! [X2,X0,X1] :
( member(X0,X1)
| ~ subclass(unordered_pair(X2,X0),X1)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_146])]) ).
fof(f1598,plain,
( ! [X0,X1] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,universal_class)
| ~ function(unordered_pair(X1,X0)) )
| ~ spl10_20
| ~ spl10_146 ),
inference(resolution,[],[f1458,f359]) ).
fof(f1458,plain,
( ! [X2,X0,X1] :
( ~ subclass(unordered_pair(X2,X0),X1)
| member(X0,X1)
| ~ member(X0,universal_class) )
| ~ spl10_146 ),
inference(avatar_component_clause,[],[f1457]) ).
fof(f20585,plain,
( spl10_602
| ~ spl10_27
| ~ spl10_145 ),
inference(avatar_split_clause,[],[f1589,f1453,f387,f20583]) ).
fof(f20583,plain,
( spl10_602
<=> ! [X2,X0,X1] :
( ~ subclass(X0,power_class(X1))
| subclass(X0,X2)
| subclass(sK6(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_602])]) ).
fof(f1589,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,power_class(X1))
| subclass(X0,X2)
| subclass(sK6(X0,X2),X1) )
| ~ spl10_27
| ~ spl10_145 ),
inference(resolution,[],[f1454,f388]) ).
fof(f20581,plain,
( spl10_601
| ~ spl10_25
| ~ spl10_145 ),
inference(avatar_split_clause,[],[f1582,f1453,f379,f20579]) ).
fof(f20579,plain,
( spl10_601
<=> ! [X2,X0,X1] :
( ~ subclass(X0,complement(X1))
| subclass(X0,X2)
| ~ member(sK6(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_601])]) ).
fof(f1582,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,complement(X1))
| subclass(X0,X2)
| ~ member(sK6(X0,X2),X1) )
| ~ spl10_25
| ~ spl10_145 ),
inference(resolution,[],[f1454,f380]) ).
fof(f20577,plain,
( spl10_600
| ~ spl10_35
| ~ spl10_140 ),
inference(avatar_split_clause,[],[f1430,f1259,f430,f20575]) ).
fof(f20575,plain,
( spl10_600
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| ~ member(X2,identity_relation)
| member(sK5(X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_600])]) ).
fof(f1430,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| ~ member(X2,identity_relation)
| member(sK5(X2),X0) )
| ~ spl10_35
| ~ spl10_140 ),
inference(resolution,[],[f1260,f431]) ).
fof(f20573,plain,
( spl10_599
| ~ spl10_36
| ~ spl10_140 ),
inference(avatar_split_clause,[],[f1429,f1259,f434,f20571]) ).
fof(f20571,plain,
( spl10_599
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| ~ member(X2,identity_relation)
| member(sK5(X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_599])]) ).
fof(f1429,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| ~ member(X2,identity_relation)
| member(sK5(X2),X1) )
| ~ spl10_36
| ~ spl10_140 ),
inference(resolution,[],[f1260,f435]) ).
fof(f20569,plain,
( spl10_598
| ~ spl10_35
| ~ spl10_139 ),
inference(avatar_split_clause,[],[f1404,f1255,f430,f20567]) ).
fof(f20567,plain,
( spl10_598
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| null_class = X2
| member(sK4(X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_598])]) ).
fof(f1404,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| null_class = X2
| member(sK4(X2),X0) )
| ~ spl10_35
| ~ spl10_139 ),
inference(resolution,[],[f1256,f431]) ).
fof(f20565,plain,
( spl10_597
| ~ spl10_36
| ~ spl10_139 ),
inference(avatar_split_clause,[],[f1403,f1255,f434,f20563]) ).
fof(f20563,plain,
( spl10_597
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| null_class = X2
| member(sK4(X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_597])]) ).
fof(f1403,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| null_class = X2
| member(sK4(X2),X1) )
| ~ spl10_36
| ~ spl10_139 ),
inference(resolution,[],[f1256,f435]) ).
fof(f20561,plain,
( spl10_596
| ~ spl10_35
| ~ spl10_137 ),
inference(avatar_split_clause,[],[f1378,f1246,f430,f20559]) ).
fof(f20559,plain,
( spl10_596
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| ~ member(X2,universal_class)
| member(power_class(X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_596])]) ).
fof(f1378,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| ~ member(X2,universal_class)
| member(power_class(X2),X0) )
| ~ spl10_35
| ~ spl10_137 ),
inference(resolution,[],[f1247,f431]) ).
fof(f20557,plain,
( spl10_595
| ~ spl10_36
| ~ spl10_137 ),
inference(avatar_split_clause,[],[f1377,f1246,f434,f20555]) ).
fof(f20555,plain,
( spl10_595
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| ~ member(X2,universal_class)
| member(power_class(X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_595])]) ).
fof(f1377,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| ~ member(X2,universal_class)
| member(power_class(X2),X1) )
| ~ spl10_36
| ~ spl10_137 ),
inference(resolution,[],[f1247,f435]) ).
fof(f20553,plain,
( spl10_594
| ~ spl10_35
| ~ spl10_136 ),
inference(avatar_split_clause,[],[f1353,f1242,f430,f20551]) ).
fof(f20551,plain,
( spl10_594
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| ~ member(X2,universal_class)
| member(sum_class(X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_594])]) ).
fof(f1353,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| ~ member(X2,universal_class)
| member(sum_class(X2),X0) )
| ~ spl10_35
| ~ spl10_136 ),
inference(resolution,[],[f1243,f431]) ).
fof(f20549,plain,
( spl10_593
| ~ spl10_36
| ~ spl10_136 ),
inference(avatar_split_clause,[],[f1352,f1242,f434,f20547]) ).
fof(f20547,plain,
( spl10_593
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| ~ member(X2,universal_class)
| member(sum_class(X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_593])]) ).
fof(f1352,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| ~ member(X2,universal_class)
| member(sum_class(X2),X1) )
| ~ spl10_36
| ~ spl10_136 ),
inference(resolution,[],[f1243,f435]) ).
fof(f20545,plain,
( spl10_592
| ~ spl10_35
| ~ spl10_135 ),
inference(avatar_split_clause,[],[f1327,f1238,f430,f20543]) ).
fof(f20543,plain,
( spl10_592
<=> ! [X2,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| null_class = X0
| member(sK4(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_592])]) ).
fof(f1327,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| null_class = X0
| member(sK4(X0),X1) )
| ~ spl10_35
| ~ spl10_135 ),
inference(resolution,[],[f1239,f431]) ).
fof(f20541,plain,
( spl10_591
| ~ spl10_36
| ~ spl10_135 ),
inference(avatar_split_clause,[],[f1326,f1238,f434,f20539]) ).
fof(f20539,plain,
( spl10_591
<=> ! [X2,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| null_class = X0
| member(sK4(X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_591])]) ).
fof(f1326,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| null_class = X0
| member(sK4(X0),X2) )
| ~ spl10_36
| ~ spl10_135 ),
inference(resolution,[],[f1239,f435]) ).
fof(f20537,plain,
( spl10_590
| ~ spl10_119
| ~ spl10_134 ),
inference(avatar_split_clause,[],[f1313,f1234,f1071,f20535]) ).
fof(f20535,plain,
( spl10_590
<=> ! [X2,X0,X1] :
( ~ member(unordered_pair(X0,X1),X2)
| null_class = X2
| ~ subclass(universal_class,sK4(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_590])]) ).
fof(f1313,plain,
( ! [X2,X0,X1] :
( ~ member(unordered_pair(X0,X1),X2)
| null_class = X2
| ~ subclass(universal_class,sK4(X2)) )
| ~ spl10_119
| ~ spl10_134 ),
inference(resolution,[],[f1235,f1072]) ).
fof(f20533,plain,
( spl10_589
| ~ spl10_16
| ~ spl10_134 ),
inference(avatar_split_clause,[],[f1310,f1234,f342,f20531]) ).
fof(f20531,plain,
( spl10_589
<=> ! [X0] :
( ~ member(sK4(sK4(X0)),X0)
| null_class = X0
| null_class = sK4(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_589])]) ).
fof(f1310,plain,
( ! [X0] :
( ~ member(sK4(sK4(X0)),X0)
| null_class = X0
| null_class = sK4(X0) )
| ~ spl10_16
| ~ spl10_134 ),
inference(resolution,[],[f1235,f343]) ).
fof(f20529,plain,
( spl10_588
| ~ spl10_118
| ~ spl10_127 ),
inference(avatar_split_clause,[],[f1297,f1203,f1067,f20527]) ).
fof(f20527,plain,
( spl10_588
<=> ! [X0,X1] :
( subclass(power_class(X0),X1)
| member(null_class,X0)
| ~ inductive(sK6(power_class(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_588])]) ).
fof(f1203,plain,
( spl10_127
<=> ! [X0,X1] :
( subclass(power_class(X0),X1)
| subclass(sK6(power_class(X0),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_127])]) ).
fof(f1297,plain,
( ! [X0,X1] :
( subclass(power_class(X0),X1)
| member(null_class,X0)
| ~ inductive(sK6(power_class(X0),X1)) )
| ~ spl10_118
| ~ spl10_127 ),
inference(resolution,[],[f1204,f1068]) ).
fof(f1204,plain,
( ! [X0,X1] :
( subclass(sK6(power_class(X0),X1),X0)
| subclass(power_class(X0),X1) )
| ~ spl10_127 ),
inference(avatar_component_clause,[],[f1203]) ).
fof(f20525,plain,
( spl10_587
| ~ spl10_114
| ~ spl10_124 ),
inference(avatar_split_clause,[],[f1275,f1191,f1049,f20523]) ).
fof(f20523,plain,
( spl10_587
<=> ! [X0] :
( subclass(complement(sum_class(universal_class)),X0)
| ~ member(sK6(complement(sum_class(universal_class)),X0),sK9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_587])]) ).
fof(f1275,plain,
( ! [X0] :
( subclass(complement(sum_class(universal_class)),X0)
| ~ member(sK6(complement(sum_class(universal_class)),X0),sK9) )
| ~ spl10_114
| ~ spl10_124 ),
inference(resolution,[],[f1192,f1050]) ).
fof(f20521,plain,
( ~ spl10_586
| ~ spl10_12
| spl10_578 ),
inference(avatar_split_clause,[],[f20455,f19606,f324,f20518]) ).
fof(f20518,plain,
( spl10_586
<=> inductive(sum_class(sum_class(universal_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_586])]) ).
fof(f19606,plain,
( spl10_578
<=> member(null_class,sum_class(sum_class(universal_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_578])]) ).
fof(f20455,plain,
( ~ inductive(sum_class(sum_class(universal_class)))
| ~ spl10_12
| spl10_578 ),
inference(resolution,[],[f19607,f325]) ).
fof(f19607,plain,
( ~ member(null_class,sum_class(sum_class(universal_class)))
| spl10_578 ),
inference(avatar_component_clause,[],[f19606]) ).
fof(f20516,plain,
( spl10_585
| ~ spl10_16
| ~ spl10_123 ),
inference(avatar_split_clause,[],[f1185,f1163,f342,f20514]) ).
fof(f20514,plain,
( spl10_585
<=> ! [X0,X1] :
( member(sK4(unordered_pair(X0,X1)),sum_class(universal_class))
| unordered_pair(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_585])]) ).
fof(f1185,plain,
( ! [X0,X1] :
( member(sK4(unordered_pair(X0,X1)),sum_class(universal_class))
| unordered_pair(X0,X1) = null_class )
| ~ spl10_16
| ~ spl10_123 ),
inference(resolution,[],[f1164,f343]) ).
fof(f20512,plain,
( spl10_584
| ~ spl10_51
| ~ spl10_119 ),
inference(avatar_split_clause,[],[f1110,f1071,f554,f20510]) ).
fof(f20510,plain,
( spl10_584
<=> ! [X0,X3,X2,X1] :
( ~ subclass(universal_class,X0)
| member(X1,sum_class(X0))
| ~ member(X1,unordered_pair(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_584])]) ).
fof(f1110,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(universal_class,X0)
| member(X1,sum_class(X0))
| ~ member(X1,unordered_pair(X2,X3)) )
| ~ spl10_51
| ~ spl10_119 ),
inference(resolution,[],[f1072,f555]) ).
fof(f20506,plain,
( spl10_583
| ~ spl10_108
| ~ spl10_144 ),
inference(avatar_split_clause,[],[f1551,f1449,f1004,f20504]) ).
fof(f20504,plain,
( spl10_583
<=> ! [X0] :
( null_class = intersection(X0,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| unordered_pair(sK0,sK0) = sK4(intersection(X0,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))))
| unordered_pair(sK0,unordered_pair(sK1,sK1)) = sK4(intersection(X0,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_583])]) ).
fof(f1551,plain,
( ! [X0] :
( null_class = intersection(X0,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| unordered_pair(sK0,sK0) = sK4(intersection(X0,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))))
| unordered_pair(sK0,unordered_pair(sK1,sK1)) = sK4(intersection(X0,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))) )
| ~ spl10_108
| ~ spl10_144 ),
inference(resolution,[],[f1450,f1005]) ).
fof(f20500,plain,
( spl10_582
| ~ spl10_108
| ~ spl10_143 ),
inference(avatar_split_clause,[],[f1526,f1445,f1004,f20498]) ).
fof(f20498,plain,
( spl10_582
<=> ! [X0] :
( null_class = intersection(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X0)
| unordered_pair(sK0,sK0) = sK4(intersection(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X0))
| unordered_pair(sK0,unordered_pair(sK1,sK1)) = sK4(intersection(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_582])]) ).
fof(f1526,plain,
( ! [X0] :
( null_class = intersection(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X0)
| unordered_pair(sK0,sK0) = sK4(intersection(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X0))
| unordered_pair(sK0,unordered_pair(sK1,sK1)) = sK4(intersection(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X0)) )
| ~ spl10_108
| ~ spl10_143 ),
inference(resolution,[],[f1446,f1005]) ).
fof(f20471,plain,
( ~ spl10_541
| spl10_581
| ~ spl10_107
| ~ spl10_214
| ~ spl10_361 ),
inference(avatar_split_clause,[],[f19152,f8770,f3013,f993,f20469,f19140]) ).
fof(f19140,plain,
( spl10_541
<=> member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_541])]) ).
fof(f20469,plain,
( spl10_581
<=> ! [X0] :
( member(unordered_pair(sK2,unordered_pair(sK3,sK3)),sum_class(domain_of(X0)))
| null_class = intersection(X0,cross_product(unordered_pair(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))),universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_581])]) ).
fof(f993,plain,
( spl10_107
<=> member(unordered_pair(sK0,unordered_pair(sK1,sK1)),unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_107])]) ).
fof(f3013,plain,
( spl10_214
<=> ! [X2,X0,X1] :
( null_class = intersection(X0,cross_product(unordered_pair(X1,X1),universal_class))
| ~ member(X1,universal_class)
| member(X2,sum_class(domain_of(X0)))
| ~ member(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_214])]) ).
fof(f19152,plain,
( ! [X0] :
( member(unordered_pair(sK2,unordered_pair(sK3,sK3)),sum_class(domain_of(X0)))
| ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),universal_class)
| null_class = intersection(X0,cross_product(unordered_pair(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))),universal_class)) )
| ~ spl10_107
| ~ spl10_214
| ~ spl10_361 ),
inference(forward_demodulation,[],[f3204,f8772]) ).
fof(f3204,plain,
( ! [X0] :
( ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),universal_class)
| member(unordered_pair(sK0,unordered_pair(sK1,sK1)),sum_class(domain_of(X0)))
| null_class = intersection(X0,cross_product(unordered_pair(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))),universal_class)) )
| ~ spl10_107
| ~ spl10_214 ),
inference(resolution,[],[f3014,f995]) ).
fof(f995,plain,
( member(unordered_pair(sK0,unordered_pair(sK1,sK1)),unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| ~ spl10_107 ),
inference(avatar_component_clause,[],[f993]) ).
fof(f3014,plain,
( ! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X1,universal_class)
| member(X2,sum_class(domain_of(X0)))
| null_class = intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)) )
| ~ spl10_214 ),
inference(avatar_component_clause,[],[f3013]) ).
fof(f20467,plain,
( ~ spl10_579
| spl10_580
| ~ spl10_108
| ~ spl10_216 ),
inference(avatar_split_clause,[],[f3303,f3021,f1004,f20465,f20461]) ).
fof(f20461,plain,
( spl10_579
<=> subclass(element_relation,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_579])]) ).
fof(f20465,plain,
( spl10_580
<=> ! [X0,X1] :
( ~ member(X0,universal_class)
| unordered_pair(sK0,unordered_pair(sK1,sK1)) = unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))
| unordered_pair(sK0,sK0) = unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))
| ~ member(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_580])]) ).
fof(f3303,plain,
( ! [X0,X1] :
( ~ member(X0,universal_class)
| ~ member(X1,X0)
| ~ subclass(element_relation,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| unordered_pair(sK0,sK0) = unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))
| unordered_pair(sK0,unordered_pair(sK1,sK1)) = unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))) )
| ~ spl10_108
| ~ spl10_216 ),
inference(resolution,[],[f3022,f1005]) ).
fof(f19609,plain,
( ~ spl10_577
| spl10_578
| ~ spl10_30
| ~ spl10_290 ),
inference(avatar_split_clause,[],[f5718,f5660,f409,f19606,f19602]) ).
fof(f19602,plain,
( spl10_577
<=> member(universal_class,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_577])]) ).
fof(f5660,plain,
( spl10_290
<=> ! [X0,X1] :
( ~ member(X0,sK0)
| member(X1,sum_class(sum_class(universal_class)))
| ~ member(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_290])]) ).
fof(f5718,plain,
( member(null_class,sum_class(sum_class(universal_class)))
| ~ member(universal_class,sK0)
| ~ spl10_30
| ~ spl10_290 ),
inference(resolution,[],[f5661,f411]) ).
fof(f5661,plain,
( ! [X0,X1] :
( ~ member(X1,X0)
| member(X1,sum_class(sum_class(universal_class)))
| ~ member(X0,sK0) )
| ~ spl10_290 ),
inference(avatar_component_clause,[],[f5660]) ).
fof(f19489,plain,
( spl10_576
| ~ spl10_68
| ~ spl10_245 ),
inference(avatar_split_clause,[],[f4449,f4119,f681,f19487]) ).
fof(f19487,plain,
( spl10_576
<=> ! [X0,X1] :
( ~ member(sK4(identity_relation),cross_product(X0,X1))
| member(sK5(sK4(identity_relation)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_576])]) ).
fof(f681,plain,
( spl10_68
<=> ! [X0,X3,X2,X1] :
( member(X0,X2)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_68])]) ).
fof(f4119,plain,
( spl10_245
<=> sK4(identity_relation) = unordered_pair(unordered_pair(sK5(sK4(identity_relation)),sK5(sK4(identity_relation))),unordered_pair(sK5(sK4(identity_relation)),unordered_pair(sK5(sK4(identity_relation)),sK5(sK4(identity_relation))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_245])]) ).
fof(f4449,plain,
( ! [X0,X1] :
( ~ member(sK4(identity_relation),cross_product(X0,X1))
| member(sK5(sK4(identity_relation)),X0) )
| ~ spl10_68
| ~ spl10_245 ),
inference(superposition,[],[f682,f4121]) ).
fof(f4121,plain,
( sK4(identity_relation) = unordered_pair(unordered_pair(sK5(sK4(identity_relation)),sK5(sK4(identity_relation))),unordered_pair(sK5(sK4(identity_relation)),unordered_pair(sK5(sK4(identity_relation)),sK5(sK4(identity_relation)))))
| ~ spl10_245 ),
inference(avatar_component_clause,[],[f4119]) ).
fof(f682,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3))
| member(X0,X2) )
| ~ spl10_68 ),
inference(avatar_component_clause,[],[f681]) ).
fof(f19485,plain,
( spl10_575
| ~ spl10_67
| ~ spl10_245 ),
inference(avatar_split_clause,[],[f4448,f4119,f677,f19483]) ).
fof(f19483,plain,
( spl10_575
<=> ! [X0,X1] :
( ~ member(sK4(identity_relation),cross_product(X0,X1))
| member(sK5(sK4(identity_relation)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_575])]) ).
fof(f677,plain,
( spl10_67
<=> ! [X0,X3,X2,X1] :
( member(X1,X3)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_67])]) ).
fof(f4448,plain,
( ! [X0,X1] :
( ~ member(sK4(identity_relation),cross_product(X0,X1))
| member(sK5(sK4(identity_relation)),X1) )
| ~ spl10_67
| ~ spl10_245 ),
inference(superposition,[],[f678,f4121]) ).
fof(f678,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3))
| member(X1,X3) )
| ~ spl10_67 ),
inference(avatar_component_clause,[],[f677]) ).
fof(f19479,plain,
( spl10_512
| spl10_574
| ~ spl10_66
| ~ spl10_245 ),
inference(avatar_split_clause,[],[f4447,f4119,f673,f19477,f18616]) ).
fof(f18616,plain,
( spl10_512
<=> member(sK5(sK4(identity_relation)),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_512])]) ).
fof(f19477,plain,
( spl10_574
<=> ! [X0,X1] : ~ member(sK4(identity_relation),compose(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_574])]) ).
fof(f673,plain,
( spl10_66
<=> ! [X0,X3,X2,X1] :
( member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),compose(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_66])]) ).
fof(f4447,plain,
( ! [X0,X1] :
( ~ member(sK4(identity_relation),compose(X0,X1))
| member(sK5(sK4(identity_relation)),universal_class) )
| ~ spl10_66
| ~ spl10_245 ),
inference(superposition,[],[f674,f4121]) ).
fof(f674,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),compose(X1,X0))
| member(X2,universal_class) )
| ~ spl10_66 ),
inference(avatar_component_clause,[],[f673]) ).
fof(f19475,plain,
( spl10_573
| ~ spl10_67
| ~ spl10_199 ),
inference(avatar_split_clause,[],[f2671,f2556,f677,f19473]) ).
fof(f19473,plain,
( spl10_573
<=> ! [X2,X0,X1] :
( ~ member(X0,universal_class)
| ~ subclass(identity_relation,cross_product(X1,X2))
| member(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_573])]) ).
fof(f2671,plain,
( ! [X2,X0,X1] :
( ~ member(X0,universal_class)
| ~ subclass(identity_relation,cross_product(X1,X2))
| member(X0,X2) )
| ~ spl10_67
| ~ spl10_199 ),
inference(resolution,[],[f2557,f678]) ).
fof(f19471,plain,
( spl10_572
| ~ spl10_68
| ~ spl10_199 ),
inference(avatar_split_clause,[],[f2670,f2556,f681,f19469]) ).
fof(f19469,plain,
( spl10_572
<=> ! [X2,X0,X1] :
( ~ member(X0,universal_class)
| ~ subclass(identity_relation,cross_product(X1,X2))
| member(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_572])]) ).
fof(f2670,plain,
( ! [X2,X0,X1] :
( ~ member(X0,universal_class)
| ~ subclass(identity_relation,cross_product(X1,X2))
| member(X0,X1) )
| ~ spl10_68
| ~ spl10_199 ),
inference(resolution,[],[f2557,f682]) ).
fof(f19467,plain,
( spl10_571
| ~ spl10_197 ),
inference(avatar_split_clause,[],[f2627,f2548,f19465]) ).
fof(f19465,plain,
( spl10_571
<=> ! [X0] :
( member(sK4(union(X0,X0)),X0)
| null_class = union(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_571])]) ).
fof(f2548,plain,
( spl10_197
<=> ! [X0,X1] :
( member(sK4(union(X0,X1)),X0)
| member(sK4(union(X0,X1)),X1)
| null_class = union(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_197])]) ).
fof(f2627,plain,
( ! [X0] :
( member(sK4(union(X0,X0)),X0)
| null_class = union(X0,X0) )
| ~ spl10_197 ),
inference(factoring,[],[f2549]) ).
fof(f2549,plain,
( ! [X0,X1] :
( member(sK4(union(X0,X1)),X1)
| member(sK4(union(X0,X1)),X0)
| null_class = union(X0,X1) )
| ~ spl10_197 ),
inference(avatar_component_clause,[],[f2548]) ).
fof(f19463,plain,
( spl10_570
| ~ spl10_5
| ~ spl10_197 ),
inference(avatar_split_clause,[],[f2613,f2548,f292,f19461]) ).
fof(f19461,plain,
( spl10_570
<=> ! [X0] :
( member(sK4(union(null_class,X0)),X0)
| null_class = union(null_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_570])]) ).
fof(f2613,plain,
( ! [X0] :
( member(sK4(union(null_class,X0)),X0)
| null_class = union(null_class,X0) )
| ~ spl10_5
| ~ spl10_197 ),
inference(resolution,[],[f2549,f293]) ).
fof(f19459,plain,
( spl10_569
| ~ spl10_5
| ~ spl10_197 ),
inference(avatar_split_clause,[],[f2579,f2548,f292,f19457]) ).
fof(f19457,plain,
( spl10_569
<=> ! [X0] :
( member(sK4(union(X0,null_class)),X0)
| null_class = union(X0,null_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_569])]) ).
fof(f2579,plain,
( ! [X0] :
( member(sK4(union(X0,null_class)),X0)
| null_class = union(X0,null_class) )
| ~ spl10_5
| ~ spl10_197 ),
inference(resolution,[],[f2549,f293]) ).
fof(f19455,plain,
( spl10_568
| ~ spl10_7
| ~ spl10_187 ),
inference(avatar_split_clause,[],[f2315,f2256,f300,f19453]) ).
fof(f19453,plain,
( spl10_568
<=> ! [X0,X1] :
( ~ member(X0,sK9)
| ~ subclass(sK9,X1)
| member(X0,sum_class(power_class(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_568])]) ).
fof(f2256,plain,
( spl10_187
<=> ! [X2,X0,X1] :
( member(X0,sum_class(power_class(X1)))
| ~ member(X0,X2)
| ~ subclass(X2,X1)
| ~ member(X2,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_187])]) ).
fof(f2315,plain,
( ! [X0,X1] :
( ~ member(X0,sK9)
| ~ subclass(sK9,X1)
| member(X0,sum_class(power_class(X1))) )
| ~ spl10_7
| ~ spl10_187 ),
inference(resolution,[],[f2257,f302]) ).
fof(f2257,plain,
( ! [X2,X0,X1] :
( ~ member(X2,universal_class)
| ~ member(X0,X2)
| ~ subclass(X2,X1)
| member(X0,sum_class(power_class(X1))) )
| ~ spl10_187 ),
inference(avatar_component_clause,[],[f2256]) ).
fof(f19451,plain,
( spl10_567
| ~ spl10_7
| ~ spl10_186 ),
inference(avatar_split_clause,[],[f2279,f2252,f300,f19449]) ).
fof(f19449,plain,
( spl10_567
<=> ! [X0,X1] :
( ~ member(X0,sK9)
| member(sK9,X1)
| member(X0,sum_class(complement(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_567])]) ).
fof(f2252,plain,
( spl10_186
<=> ! [X2,X0,X1] :
( member(X0,sum_class(complement(X1)))
| ~ member(X0,X2)
| member(X2,X1)
| ~ member(X2,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_186])]) ).
fof(f2279,plain,
( ! [X0,X1] :
( ~ member(X0,sK9)
| member(sK9,X1)
| member(X0,sum_class(complement(X1))) )
| ~ spl10_7
| ~ spl10_186 ),
inference(resolution,[],[f2253,f302]) ).
fof(f2253,plain,
( ! [X2,X0,X1] :
( ~ member(X2,universal_class)
| ~ member(X0,X2)
| member(X2,X1)
| member(X0,sum_class(complement(X1))) )
| ~ spl10_186 ),
inference(avatar_component_clause,[],[f2252]) ).
fof(f19446,plain,
( spl10_566
| ~ spl10_13
| ~ spl10_174 ),
inference(avatar_split_clause,[],[f2051,f1775,f328,f19444]) ).
fof(f19444,plain,
( spl10_566
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| member(X0,sum_class(union(universal_class,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_566])]) ).
fof(f2051,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| member(X0,sum_class(union(universal_class,X3))) )
| ~ spl10_13
| ~ spl10_174 ),
inference(resolution,[],[f1776,f329]) ).
fof(f19441,plain,
( spl10_565
| ~ spl10_13
| ~ spl10_173 ),
inference(avatar_split_clause,[],[f1995,f1771,f328,f19439]) ).
fof(f19439,plain,
( spl10_565
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| member(X0,sum_class(union(X3,universal_class))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_565])]) ).
fof(f1995,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| member(X0,sum_class(union(X3,universal_class))) )
| ~ spl10_13
| ~ spl10_173 ),
inference(resolution,[],[f1772,f329]) ).
fof(f19437,plain,
( spl10_564
| ~ spl10_12
| ~ spl10_170 ),
inference(avatar_split_clause,[],[f1939,f1756,f324,f19435]) ).
fof(f19435,plain,
( spl10_564
<=> ! [X0,X1] :
( member(null_class,sum_class(X0))
| subclass(X0,X1)
| ~ inductive(sK6(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_564])]) ).
fof(f1939,plain,
( ! [X0,X1] :
( member(null_class,sum_class(X0))
| subclass(X0,X1)
| ~ inductive(sK6(X0,X1)) )
| ~ spl10_12
| ~ spl10_170 ),
inference(resolution,[],[f1757,f325]) ).
fof(f19433,plain,
( spl10_563
| ~ spl10_27
| ~ spl10_140 ),
inference(avatar_split_clause,[],[f1438,f1259,f387,f19431]) ).
fof(f19431,plain,
( spl10_563
<=> ! [X0,X1] :
( ~ subclass(universal_class,power_class(X0))
| ~ member(X1,identity_relation)
| subclass(sK5(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_563])]) ).
fof(f1438,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,power_class(X0))
| ~ member(X1,identity_relation)
| subclass(sK5(X1),X0) )
| ~ spl10_27
| ~ spl10_140 ),
inference(resolution,[],[f1260,f388]) ).
fof(f19429,plain,
( spl10_562
| ~ spl10_25
| ~ spl10_140 ),
inference(avatar_split_clause,[],[f1431,f1259,f379,f19427]) ).
fof(f19427,plain,
( spl10_562
<=> ! [X0,X1] :
( ~ subclass(universal_class,complement(X0))
| ~ member(X1,identity_relation)
| ~ member(sK5(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_562])]) ).
fof(f1431,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,complement(X0))
| ~ member(X1,identity_relation)
| ~ member(sK5(X1),X0) )
| ~ spl10_25
| ~ spl10_140 ),
inference(resolution,[],[f1260,f380]) ).
fof(f19425,plain,
( spl10_561
| ~ spl10_27
| ~ spl10_139 ),
inference(avatar_split_clause,[],[f1412,f1255,f387,f19423]) ).
fof(f19423,plain,
( spl10_561
<=> ! [X0,X1] :
( ~ subclass(universal_class,power_class(X0))
| null_class = X1
| subclass(sK4(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_561])]) ).
fof(f1412,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,power_class(X0))
| null_class = X1
| subclass(sK4(X1),X0) )
| ~ spl10_27
| ~ spl10_139 ),
inference(resolution,[],[f1256,f388]) ).
fof(f19421,plain,
( spl10_560
| ~ spl10_25
| ~ spl10_139 ),
inference(avatar_split_clause,[],[f1405,f1255,f379,f19419]) ).
fof(f19419,plain,
( spl10_560
<=> ! [X0,X1] :
( ~ subclass(universal_class,complement(X0))
| null_class = X1
| ~ member(sK4(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_560])]) ).
fof(f1405,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,complement(X0))
| null_class = X1
| ~ member(sK4(X1),X0) )
| ~ spl10_25
| ~ spl10_139 ),
inference(resolution,[],[f1256,f380]) ).
fof(f19417,plain,
( spl10_559
| ~ spl10_27
| ~ spl10_137 ),
inference(avatar_split_clause,[],[f1386,f1246,f387,f19415]) ).
fof(f19415,plain,
( spl10_559
<=> ! [X0,X1] :
( ~ subclass(universal_class,power_class(X0))
| ~ member(X1,universal_class)
| subclass(power_class(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_559])]) ).
fof(f1386,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,power_class(X0))
| ~ member(X1,universal_class)
| subclass(power_class(X1),X0) )
| ~ spl10_27
| ~ spl10_137 ),
inference(resolution,[],[f1247,f388]) ).
fof(f19413,plain,
( ~ spl10_558
| spl10_233
| ~ spl10_20
| ~ spl10_381 ),
inference(avatar_split_clause,[],[f10831,f10602,f358,f3853,f19410]) ).
fof(f19410,plain,
( spl10_558
<=> function(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_558])]) ).
fof(f3853,plain,
( spl10_233
<=> member(null_class,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_233])]) ).
fof(f10602,plain,
( spl10_381
<=> ! [X0] :
( member(null_class,X0)
| ~ subclass(sK9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_381])]) ).
fof(f10831,plain,
( member(null_class,cross_product(universal_class,universal_class))
| ~ function(sK9)
| ~ spl10_20
| ~ spl10_381 ),
inference(resolution,[],[f10603,f359]) ).
fof(f10603,plain,
( ! [X0] :
( ~ subclass(sK9,X0)
| member(null_class,X0) )
| ~ spl10_381 ),
inference(avatar_component_clause,[],[f10602]) ).
fof(f19408,plain,
( spl10_557
| ~ spl10_25
| ~ spl10_137 ),
inference(avatar_split_clause,[],[f1379,f1246,f379,f19406]) ).
fof(f19406,plain,
( spl10_557
<=> ! [X0,X1] :
( ~ subclass(universal_class,complement(X0))
| ~ member(X1,universal_class)
| ~ member(power_class(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_557])]) ).
fof(f1379,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,complement(X0))
| ~ member(X1,universal_class)
| ~ member(power_class(X1),X0) )
| ~ spl10_25
| ~ spl10_137 ),
inference(resolution,[],[f1247,f380]) ).
fof(f19404,plain,
( spl10_556
| ~ spl10_27
| ~ spl10_136 ),
inference(avatar_split_clause,[],[f1361,f1242,f387,f19402]) ).
fof(f19402,plain,
( spl10_556
<=> ! [X0,X1] :
( ~ subclass(universal_class,power_class(X0))
| ~ member(X1,universal_class)
| subclass(sum_class(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_556])]) ).
fof(f1361,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,power_class(X0))
| ~ member(X1,universal_class)
| subclass(sum_class(X1),X0) )
| ~ spl10_27
| ~ spl10_136 ),
inference(resolution,[],[f1243,f388]) ).
fof(f19400,plain,
( spl10_555
| ~ spl10_25
| ~ spl10_136 ),
inference(avatar_split_clause,[],[f1354,f1242,f379,f19398]) ).
fof(f19398,plain,
( spl10_555
<=> ! [X0,X1] :
( ~ subclass(universal_class,complement(X0))
| ~ member(X1,universal_class)
| ~ member(sum_class(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_555])]) ).
fof(f1354,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,complement(X0))
| ~ member(X1,universal_class)
| ~ member(sum_class(X1),X0) )
| ~ spl10_25
| ~ spl10_136 ),
inference(resolution,[],[f1243,f380]) ).
fof(f19396,plain,
( spl10_554
| ~ spl10_27
| ~ spl10_135 ),
inference(avatar_split_clause,[],[f1335,f1238,f387,f19394]) ).
fof(f19394,plain,
( spl10_554
<=> ! [X0,X1] :
( ~ subclass(X0,power_class(X1))
| null_class = X0
| subclass(sK4(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_554])]) ).
fof(f1335,plain,
( ! [X0,X1] :
( ~ subclass(X0,power_class(X1))
| null_class = X0
| subclass(sK4(X0),X1) )
| ~ spl10_27
| ~ spl10_135 ),
inference(resolution,[],[f1239,f388]) ).
fof(f19392,plain,
( spl10_553
| ~ spl10_25
| ~ spl10_135 ),
inference(avatar_split_clause,[],[f1328,f1238,f379,f19390]) ).
fof(f19390,plain,
( spl10_553
<=> ! [X0,X1] :
( ~ subclass(X0,complement(X1))
| null_class = X0
| ~ member(sK4(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_553])]) ).
fof(f1328,plain,
( ! [X0,X1] :
( ~ subclass(X0,complement(X1))
| null_class = X0
| ~ member(sK4(X0),X1) )
| ~ spl10_25
| ~ spl10_135 ),
inference(resolution,[],[f1239,f380]) ).
fof(f19381,plain,
( spl10_551
| spl10_552
| ~ spl10_119
| ~ spl10_123 ),
inference(avatar_split_clause,[],[f1188,f1163,f1071,f19379,f19376]) ).
fof(f19376,plain,
( spl10_551
<=> ! [X2,X3] : ~ subclass(universal_class,unordered_pair(X2,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_551])]) ).
fof(f1188,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(X0,X1),sum_class(universal_class))
| ~ subclass(universal_class,unordered_pair(X2,X3)) )
| ~ spl10_119
| ~ spl10_123 ),
inference(resolution,[],[f1164,f1072]) ).
fof(f19374,plain,
( spl10_550
| ~ spl10_118
| ~ spl10_122 ),
inference(avatar_split_clause,[],[f1176,f1159,f1067,f19372]) ).
fof(f19372,plain,
( spl10_550
<=> ! [X0] :
( null_class = power_class(X0)
| member(null_class,X0)
| ~ inductive(sK4(power_class(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_550])]) ).
fof(f1176,plain,
( ! [X0] :
( null_class = power_class(X0)
| member(null_class,X0)
| ~ inductive(sK4(power_class(X0))) )
| ~ spl10_118
| ~ spl10_122 ),
inference(resolution,[],[f1160,f1068]) ).
fof(f19368,plain,
( ~ spl10_549
| spl10_292
| ~ spl10_114
| ~ spl10_121 ),
inference(avatar_split_clause,[],[f1172,f1144,f1049,f5668,f19365]) ).
fof(f19365,plain,
( spl10_549
<=> member(sK4(complement(sum_class(universal_class))),sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_549])]) ).
fof(f5668,plain,
( spl10_292
<=> null_class = complement(sum_class(universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_292])]) ).
fof(f1172,plain,
( null_class = complement(sum_class(universal_class))
| ~ member(sK4(complement(sum_class(universal_class))),sK9)
| ~ spl10_114
| ~ spl10_121 ),
inference(resolution,[],[f1145,f1050]) ).
fof(f19353,plain,
( spl10_548
| ~ spl10_45
| ~ spl10_119 ),
inference(avatar_split_clause,[],[f1111,f1071,f494,f19351]) ).
fof(f19351,plain,
( spl10_548
<=> ! [X0,X3,X2,X1] :
( ~ subclass(universal_class,X0)
| member(unordered_pair(X1,X2),X3)
| ~ subclass(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_548])]) ).
fof(f1111,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(universal_class,X0)
| member(unordered_pair(X1,X2),X3)
| ~ subclass(X0,X3) )
| ~ spl10_45
| ~ spl10_119 ),
inference(resolution,[],[f1072,f495]) ).
fof(f19349,plain,
( spl10_547
| ~ spl10_51
| ~ spl10_114 ),
inference(avatar_split_clause,[],[f1059,f1049,f554,f19347]) ).
fof(f19347,plain,
( spl10_547
<=> ! [X0,X1] :
( ~ member(X0,sK9)
| member(X1,sum_class(sum_class(universal_class)))
| ~ member(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_547])]) ).
fof(f1059,plain,
( ! [X0,X1] :
( ~ member(X0,sK9)
| member(X1,sum_class(sum_class(universal_class)))
| ~ member(X1,X0) )
| ~ spl10_51
| ~ spl10_114 ),
inference(resolution,[],[f1050,f555]) ).
fof(f19216,plain,
( spl10_546
| ~ spl10_72
| ~ spl10_464 ),
inference(avatar_split_clause,[],[f14587,f14520,f706,f19214]) ).
fof(f19214,plain,
( spl10_546
<=> ! [X0,X1] :
( sK0 = second(unordered_pair(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(X1,universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(X1,universal_class)),universal_class))))),unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(X1,universal_class)),universal_class)))),unordered_pair(sK2,sK2))))
| ~ function(X0)
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_546])]) ).
fof(f14587,plain,
( ! [X0,X1] :
( sK0 = second(unordered_pair(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(X1,universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(X1,universal_class)),universal_class))))),unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(X1,universal_class)),universal_class)))),unordered_pair(sK2,sK2))))
| ~ function(X0)
| ~ member(X1,universal_class) )
| ~ spl10_72
| ~ spl10_464 ),
inference(resolution,[],[f14521,f707]) ).
fof(f19212,plain,
( spl10_545
| ~ spl10_1
| ~ spl10_273 ),
inference(avatar_split_clause,[],[f5155,f5139,f272,f19210]) ).
fof(f19210,plain,
( spl10_545
<=> ! [X0,X1] :
( ~ member(X0,universal_class)
| ~ function(X1)
| domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(sK0,universal_class)),universal_class)))) = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(sK0,universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(sK0,universal_class)),universal_class)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_545])]) ).
fof(f5139,plain,
( spl10_273
<=> ! [X2,X0,X1] :
( domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X2,universal_class)),universal_class)))) = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X2,universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X2,universal_class)),universal_class))))))))
| ~ member(X0,universal_class)
| ~ function(X1)
| ~ member(X2,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_273])]) ).
fof(f5155,plain,
( ! [X0,X1] :
( ~ member(X0,universal_class)
| ~ function(X1)
| domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(sK0,universal_class)),universal_class)))) = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(sK0,universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(sK0,universal_class)),universal_class)))))))) )
| ~ spl10_1
| ~ spl10_273 ),
inference(resolution,[],[f5140,f274]) ).
fof(f5140,plain,
( ! [X2,X0,X1] :
( ~ member(X2,universal_class)
| ~ member(X0,universal_class)
| ~ function(X1)
| domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X2,universal_class)),universal_class)))) = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X2,universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X2,universal_class)),universal_class)))))))) )
| ~ spl10_273 ),
inference(avatar_component_clause,[],[f5139]) ).
fof(f19206,plain,
( spl10_544
| ~ spl10_47
| ~ spl10_108 ),
inference(avatar_split_clause,[],[f1015,f1004,f502,f19204]) ).
fof(f19204,plain,
( spl10_544
<=> ! [X0] :
( unordered_pair(sK0,sK0) = sK7(X0,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| unordered_pair(sK0,unordered_pair(sK1,sK1)) = sK7(X0,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| ~ member(X0,sum_class(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_544])]) ).
fof(f1015,plain,
( ! [X0] :
( unordered_pair(sK0,sK0) = sK7(X0,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| unordered_pair(sK0,unordered_pair(sK1,sK1)) = sK7(X0,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| ~ member(X0,sum_class(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))) )
| ~ spl10_47
| ~ spl10_108 ),
inference(resolution,[],[f1005,f503]) ).
fof(f19201,plain,
( spl10_543
| ~ spl10_72
| ~ spl10_95 ),
inference(avatar_split_clause,[],[f900,f891,f706,f19199]) ).
fof(f19199,plain,
( spl10_543
<=> ! [X0,X1] :
( sK0 = second(unordered_pair(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(X1,universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(X1,universal_class)),universal_class))))),unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(X1,universal_class)),universal_class)))),unordered_pair(sK0,sK0))))
| ~ function(X0)
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_543])]) ).
fof(f900,plain,
( ! [X0,X1] :
( sK0 = second(unordered_pair(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(X1,universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(X1,universal_class)),universal_class))))),unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(X1,universal_class)),universal_class)))),unordered_pair(sK0,sK0))))
| ~ function(X0)
| ~ member(X1,universal_class) )
| ~ spl10_72
| ~ spl10_95 ),
inference(resolution,[],[f892,f707]) ).
fof(f892,plain,
( ! [X0] :
( ~ member(X0,universal_class)
| sK0 = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK0,sK0)))) )
| ~ spl10_95 ),
inference(avatar_component_clause,[],[f891]) ).
fof(f19173,plain,
( spl10_542
| ~ spl10_314
| ~ spl10_540 ),
inference(avatar_split_clause,[],[f19159,f19137,f6012,f19171]) ).
fof(f19171,plain,
( spl10_542
<=> ! [X0] :
( member(unordered_pair(sK2,sK2),sum_class(domain_of(X0)))
| null_class = intersection(X0,cross_product(unordered_pair(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))),universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_542])]) ).
fof(f19137,plain,
( spl10_540
<=> ! [X0] :
( member(unordered_pair(sK0,sK0),sum_class(domain_of(X0)))
| null_class = intersection(X0,cross_product(unordered_pair(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))),universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_540])]) ).
fof(f19159,plain,
( ! [X0] :
( member(unordered_pair(sK2,sK2),sum_class(domain_of(X0)))
| null_class = intersection(X0,cross_product(unordered_pair(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))),universal_class)) )
| ~ spl10_314
| ~ spl10_540 ),
inference(forward_demodulation,[],[f19138,f6014]) ).
fof(f19138,plain,
( ! [X0] :
( member(unordered_pair(sK0,sK0),sum_class(domain_of(X0)))
| null_class = intersection(X0,cross_product(unordered_pair(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))),universal_class)) )
| ~ spl10_540 ),
inference(avatar_component_clause,[],[f19137]) ).
fof(f19147,plain,
( ~ spl10_13
| spl10_541 ),
inference(avatar_contradiction_clause,[],[f19144]) ).
fof(f19144,plain,
( $false
| ~ spl10_13
| spl10_541 ),
inference(resolution,[],[f19142,f329]) ).
fof(f19142,plain,
( ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),universal_class)
| spl10_541 ),
inference(avatar_component_clause,[],[f19140]) ).
fof(f19143,plain,
( spl10_540
| ~ spl10_541
| ~ spl10_103
| ~ spl10_214 ),
inference(avatar_split_clause,[],[f3203,f3013,f961,f19140,f19137]) ).
fof(f961,plain,
( spl10_103
<=> member(unordered_pair(sK0,sK0),unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_103])]) ).
fof(f3203,plain,
( ! [X0] :
( ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),universal_class)
| member(unordered_pair(sK0,sK0),sum_class(domain_of(X0)))
| null_class = intersection(X0,cross_product(unordered_pair(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))),universal_class)) )
| ~ spl10_103
| ~ spl10_214 ),
inference(resolution,[],[f3014,f963]) ).
fof(f963,plain,
( member(unordered_pair(sK0,sK0),unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| ~ spl10_103 ),
inference(avatar_component_clause,[],[f961]) ).
fof(f19133,plain,
( spl10_539
| ~ spl10_33
| ~ spl10_108 ),
inference(avatar_split_clause,[],[f1014,f1004,f422,f19131]) ).
fof(f19131,plain,
( spl10_539
<=> ! [X0] :
( unordered_pair(sK0,sK0) = sK6(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X0)
| unordered_pair(sK0,unordered_pair(sK1,sK1)) = sK6(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X0)
| subclass(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_539])]) ).
fof(f1014,plain,
( ! [X0] :
( unordered_pair(sK0,sK0) = sK6(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X0)
| unordered_pair(sK0,unordered_pair(sK1,sK1)) = sK6(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X0)
| subclass(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X0) )
| ~ spl10_33
| ~ spl10_108 ),
inference(resolution,[],[f1005,f423]) ).
fof(f19128,plain,
( ~ spl10_537
| spl10_538
| ~ spl10_108
| ~ spl10_199 ),
inference(avatar_split_clause,[],[f2700,f2556,f1004,f19126,f19122]) ).
fof(f19122,plain,
( spl10_537
<=> subclass(identity_relation,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_537])]) ).
fof(f19126,plain,
( spl10_538
<=> ! [X0] :
( ~ member(X0,universal_class)
| unordered_pair(sK0,unordered_pair(sK1,sK1)) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0)))
| unordered_pair(sK0,sK0) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_538])]) ).
fof(f2700,plain,
( ! [X0] :
( ~ member(X0,universal_class)
| ~ subclass(identity_relation,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| unordered_pair(sK0,sK0) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0)))
| unordered_pair(sK0,unordered_pair(sK1,sK1)) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0))) )
| ~ spl10_108
| ~ spl10_199 ),
inference(resolution,[],[f2557,f1005]) ).
fof(f19116,plain,
( spl10_536
| ~ spl10_96
| ~ spl10_211 ),
inference(avatar_split_clause,[],[f3096,f2986,f895,f19114]) ).
fof(f19114,plain,
( spl10_536
<=> ! [X0,X1] :
( member(sK7(X0,union(universal_class,X1)),X1)
| ~ member(X0,sum_class(union(universal_class,X1)))
| sK7(X0,union(universal_class,X1)) = first(unordered_pair(unordered_pair(sK7(X0,union(universal_class,X1)),sK7(X0,union(universal_class,X1))),unordered_pair(sK7(X0,union(universal_class,X1)),unordered_pair(sK0,sK0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_536])]) ).
fof(f3096,plain,
( ! [X0,X1] :
( member(sK7(X0,union(universal_class,X1)),X1)
| ~ member(X0,sum_class(union(universal_class,X1)))
| sK7(X0,union(universal_class,X1)) = first(unordered_pair(unordered_pair(sK7(X0,union(universal_class,X1)),sK7(X0,union(universal_class,X1))),unordered_pair(sK7(X0,union(universal_class,X1)),unordered_pair(sK0,sK0)))) )
| ~ spl10_96
| ~ spl10_211 ),
inference(resolution,[],[f2987,f896]) ).
fof(f19108,plain,
( spl10_535
| ~ spl10_96
| ~ spl10_211 ),
inference(avatar_split_clause,[],[f3060,f2986,f895,f19106]) ).
fof(f19106,plain,
( spl10_535
<=> ! [X0,X1] :
( member(sK7(X0,union(X1,universal_class)),X1)
| ~ member(X0,sum_class(union(X1,universal_class)))
| sK7(X0,union(X1,universal_class)) = first(unordered_pair(unordered_pair(sK7(X0,union(X1,universal_class)),sK7(X0,union(X1,universal_class))),unordered_pair(sK7(X0,union(X1,universal_class)),unordered_pair(sK0,sK0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_535])]) ).
fof(f3060,plain,
( ! [X0,X1] :
( member(sK7(X0,union(X1,universal_class)),X1)
| ~ member(X0,sum_class(union(X1,universal_class)))
| sK7(X0,union(X1,universal_class)) = first(unordered_pair(unordered_pair(sK7(X0,union(X1,universal_class)),sK7(X0,union(X1,universal_class))),unordered_pair(sK7(X0,union(X1,universal_class)),unordered_pair(sK0,sK0)))) )
| ~ spl10_96
| ~ spl10_211 ),
inference(resolution,[],[f2987,f896]) ).
fof(f19088,plain,
( spl10_534
| ~ spl10_361
| ~ spl10_530 ),
inference(avatar_split_clause,[],[f19072,f19063,f8770,f19085]) ).
fof(f19072,plain,
( unordered_pair(sK2,unordered_pair(sK3,sK3)) = sK4(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| ~ spl10_361
| ~ spl10_530 ),
inference(forward_demodulation,[],[f19065,f8772]) ).
fof(f19081,plain,
( spl10_533
| ~ spl10_372
| ~ spl10_475 ),
inference(avatar_split_clause,[],[f18580,f17364,f9484,f19079]) ).
fof(f19079,plain,
( spl10_533
<=> ! [X0] : member(sK9,union(X0,sum_class(universal_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_533])]) ).
fof(f9484,plain,
( spl10_372
<=> ! [X0,X1] : subclass(X0,union(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_372])]) ).
fof(f17364,plain,
( spl10_475
<=> ! [X0] :
( member(sK9,X0)
| ~ subclass(sum_class(universal_class),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_475])]) ).
fof(f18580,plain,
( ! [X0] : member(sK9,union(X0,sum_class(universal_class)))
| ~ spl10_372
| ~ spl10_475 ),
inference(resolution,[],[f17365,f9485]) ).
fof(f9485,plain,
( ! [X0,X1] : subclass(X0,union(X1,X0))
| ~ spl10_372 ),
inference(avatar_component_clause,[],[f9484]) ).
fof(f17365,plain,
( ! [X0] :
( ~ subclass(sum_class(universal_class),X0)
| member(sK9,X0) )
| ~ spl10_475 ),
inference(avatar_component_clause,[],[f17364]) ).
fof(f19077,plain,
( ~ spl10_532
| ~ spl10_314
| spl10_531 ),
inference(avatar_split_clause,[],[f19071,f19067,f6012,f19074]) ).
fof(f19074,plain,
( spl10_532
<=> unordered_pair(sK2,sK2) = sK4(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_532])]) ).
fof(f19071,plain,
( unordered_pair(sK2,sK2) != sK4(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| ~ spl10_314
| spl10_531 ),
inference(forward_demodulation,[],[f19068,f6014]) ).
fof(f19070,plain,
( spl10_529
| spl10_530
| spl10_531
| ~ spl10_16
| ~ spl10_108 ),
inference(avatar_split_clause,[],[f1013,f1004,f342,f19067,f19063,f19059]) ).
fof(f1013,plain,
( unordered_pair(sK0,sK0) = sK4(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| unordered_pair(sK0,unordered_pair(sK1,sK1)) = sK4(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| null_class = unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))
| ~ spl10_16
| ~ spl10_108 ),
inference(resolution,[],[f1005,f343]) ).
fof(f18835,plain,
( spl10_528
| ~ spl10_33
| ~ spl10_195 ),
inference(avatar_split_clause,[],[f2542,f2508,f422,f18833]) ).
fof(f18833,plain,
( spl10_528
<=> ! [X0] :
( ~ subclass(sK6(universal_class,power_class(X0)),X0)
| subclass(universal_class,power_class(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_528])]) ).
fof(f2542,plain,
( ! [X0] :
( ~ subclass(sK6(universal_class,power_class(X0)),X0)
| subclass(universal_class,power_class(X0)) )
| ~ spl10_33
| ~ spl10_195 ),
inference(duplicate_literal_removal,[],[f2535]) ).
fof(f2535,plain,
( ! [X0] :
( ~ subclass(sK6(universal_class,power_class(X0)),X0)
| subclass(universal_class,power_class(X0))
| subclass(universal_class,power_class(X0)) )
| ~ spl10_33
| ~ spl10_195 ),
inference(resolution,[],[f2509,f423]) ).
fof(f18831,plain,
( spl10_527
| ~ spl10_33
| ~ spl10_194 ),
inference(avatar_split_clause,[],[f2526,f2504,f422,f18829]) ).
fof(f18829,plain,
( spl10_527
<=> ! [X0] :
( member(sK6(universal_class,complement(X0)),X0)
| subclass(universal_class,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_527])]) ).
fof(f2526,plain,
( ! [X0] :
( member(sK6(universal_class,complement(X0)),X0)
| subclass(universal_class,complement(X0)) )
| ~ spl10_33
| ~ spl10_194 ),
inference(duplicate_literal_removal,[],[f2519]) ).
fof(f2519,plain,
( ! [X0] :
( member(sK6(universal_class,complement(X0)),X0)
| subclass(universal_class,complement(X0))
| subclass(universal_class,complement(X0)) )
| ~ spl10_33
| ~ spl10_194 ),
inference(resolution,[],[f2505,f423]) ).
fof(f18827,plain,
( spl10_526
| ~ spl10_12
| ~ spl10_155 ),
inference(avatar_split_clause,[],[f1644,f1493,f324,f18825]) ).
fof(f18825,plain,
( spl10_526
<=> ! [X0] :
( member(null_class,sum_class(X0))
| null_class = X0
| ~ inductive(sK4(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_526])]) ).
fof(f1644,plain,
( ! [X0] :
( member(null_class,sum_class(X0))
| null_class = X0
| ~ inductive(sK4(X0)) )
| ~ spl10_12
| ~ spl10_155 ),
inference(resolution,[],[f1494,f325]) ).
fof(f18823,plain,
( spl10_525
| ~ spl10_35
| ~ spl10_119 ),
inference(avatar_split_clause,[],[f1121,f1071,f430,f18821]) ).
fof(f18821,plain,
( spl10_525
<=> ! [X2,X0,X1,X3] :
( ~ subclass(universal_class,intersection(X0,X1))
| member(unordered_pair(X2,X3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_525])]) ).
fof(f1121,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| member(unordered_pair(X2,X3),X0) )
| ~ spl10_35
| ~ spl10_119 ),
inference(resolution,[],[f1072,f431]) ).
fof(f18819,plain,
( spl10_524
| ~ spl10_36
| ~ spl10_119 ),
inference(avatar_split_clause,[],[f1120,f1071,f434,f18817]) ).
fof(f18817,plain,
( spl10_524
<=> ! [X2,X0,X1,X3] :
( ~ subclass(universal_class,intersection(X0,X1))
| member(unordered_pair(X2,X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_524])]) ).
fof(f1120,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| member(unordered_pair(X2,X3),X1) )
| ~ spl10_36
| ~ spl10_119 ),
inference(resolution,[],[f1072,f435]) ).
fof(f18815,plain,
( spl10_523
| spl10_522
| ~ spl10_32
| ~ spl10_118 ),
inference(avatar_split_clause,[],[f1086,f1067,f418,f18807,f18813]) ).
fof(f18813,plain,
( spl10_523
<=> ! [X0] : ~ inductive(flip(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_523])]) ).
fof(f18807,plain,
( spl10_522
<=> member(null_class,cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_522])]) ).
fof(f418,plain,
( spl10_32
<=> ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_32])]) ).
fof(f1086,plain,
( ! [X0] :
( member(null_class,cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ inductive(flip(X0)) )
| ~ spl10_32
| ~ spl10_118 ),
inference(resolution,[],[f1068,f419]) ).
fof(f419,plain,
( ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ spl10_32 ),
inference(avatar_component_clause,[],[f418]) ).
fof(f18810,plain,
( spl10_521
| spl10_522
| ~ spl10_31
| ~ spl10_118 ),
inference(avatar_split_clause,[],[f1085,f1067,f414,f18807,f18804]) ).
fof(f18804,plain,
( spl10_521
<=> ! [X0] : ~ inductive(rotate(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_521])]) ).
fof(f414,plain,
( spl10_31
<=> ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_31])]) ).
fof(f1085,plain,
( ! [X0] :
( member(null_class,cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ inductive(rotate(X0)) )
| ~ spl10_31
| ~ spl10_118 ),
inference(resolution,[],[f1068,f415]) ).
fof(f415,plain,
( ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ spl10_31 ),
inference(avatar_component_clause,[],[f414]) ).
fof(f18802,plain,
( ~ spl10_520
| ~ spl10_156
| ~ spl10_502 ),
inference(avatar_split_clause,[],[f18657,f18565,f1497,f18799]) ).
fof(f18799,plain,
( spl10_520
<=> subclass(universal_class,complement(sum_class(universal_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_520])]) ).
fof(f1497,plain,
( spl10_156
<=> member(unordered_pair(sK0,sK0),sum_class(universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_156])]) ).
fof(f18657,plain,
( ~ subclass(universal_class,complement(sum_class(universal_class)))
| ~ spl10_156
| ~ spl10_502 ),
inference(resolution,[],[f18566,f1499]) ).
fof(f1499,plain,
( member(unordered_pair(sK0,sK0),sum_class(universal_class))
| ~ spl10_156 ),
inference(avatar_component_clause,[],[f1497]) ).
fof(f18797,plain,
( spl10_519
| ~ spl10_34
| ~ spl10_114 ),
inference(avatar_split_clause,[],[f1061,f1049,f426,f18795]) ).
fof(f18795,plain,
( spl10_519
<=> ! [X0] :
( ~ member(sK6(X0,sum_class(universal_class)),sK9)
| subclass(X0,sum_class(universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_519])]) ).
fof(f1061,plain,
( ! [X0] :
( ~ member(sK6(X0,sum_class(universal_class)),sK9)
| subclass(X0,sum_class(universal_class)) )
| ~ spl10_34
| ~ spl10_114 ),
inference(resolution,[],[f1050,f427]) ).
fof(f18793,plain,
( spl10_518
| ~ spl10_45
| ~ spl10_114 ),
inference(avatar_split_clause,[],[f1060,f1049,f494,f18791]) ).
fof(f18791,plain,
( spl10_518
<=> ! [X0,X1] :
( ~ member(X0,sK9)
| member(X0,X1)
| ~ subclass(sum_class(universal_class),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_518])]) ).
fof(f1060,plain,
( ! [X0,X1] :
( ~ member(X0,sK9)
| member(X0,X1)
| ~ subclass(sum_class(universal_class),X1) )
| ~ spl10_45
| ~ spl10_114 ),
inference(resolution,[],[f1050,f495]) ).
fof(f18785,plain,
( spl10_517
| ~ spl10_95
| ~ spl10_211 ),
inference(avatar_split_clause,[],[f3095,f2986,f891,f18783]) ).
fof(f18783,plain,
( spl10_517
<=> ! [X0,X1] :
( member(sK7(X0,union(universal_class,X1)),X1)
| ~ member(X0,sum_class(union(universal_class,X1)))
| sK0 = second(unordered_pair(unordered_pair(sK7(X0,union(universal_class,X1)),sK7(X0,union(universal_class,X1))),unordered_pair(sK7(X0,union(universal_class,X1)),unordered_pair(sK0,sK0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_517])]) ).
fof(f3095,plain,
( ! [X0,X1] :
( member(sK7(X0,union(universal_class,X1)),X1)
| ~ member(X0,sum_class(union(universal_class,X1)))
| sK0 = second(unordered_pair(unordered_pair(sK7(X0,union(universal_class,X1)),sK7(X0,union(universal_class,X1))),unordered_pair(sK7(X0,union(universal_class,X1)),unordered_pair(sK0,sK0)))) )
| ~ spl10_95
| ~ spl10_211 ),
inference(resolution,[],[f2987,f892]) ).
fof(f18777,plain,
( spl10_516
| ~ spl10_95
| ~ spl10_211 ),
inference(avatar_split_clause,[],[f3059,f2986,f891,f18775]) ).
fof(f18775,plain,
( spl10_516
<=> ! [X0,X1] :
( member(sK7(X0,union(X1,universal_class)),X1)
| ~ member(X0,sum_class(union(X1,universal_class)))
| sK0 = second(unordered_pair(unordered_pair(sK7(X0,union(X1,universal_class)),sK7(X0,union(X1,universal_class))),unordered_pair(sK7(X0,union(X1,universal_class)),unordered_pair(sK0,sK0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_516])]) ).
fof(f3059,plain,
( ! [X0,X1] :
( member(sK7(X0,union(X1,universal_class)),X1)
| ~ member(X0,sum_class(union(X1,universal_class)))
| sK0 = second(unordered_pair(unordered_pair(sK7(X0,union(X1,universal_class)),sK7(X0,union(X1,universal_class))),unordered_pair(sK7(X0,union(X1,universal_class)),unordered_pair(sK0,sK0)))) )
| ~ spl10_95
| ~ spl10_211 ),
inference(resolution,[],[f2987,f892]) ).
fof(f18636,plain,
( spl10_512
| ~ spl10_515
| ~ spl10_61
| ~ spl10_245 ),
inference(avatar_split_clause,[],[f6557,f4119,f643,f18633,f18616]) ).
fof(f18633,plain,
( spl10_515
<=> member(sK4(identity_relation),successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_515])]) ).
fof(f643,plain,
( spl10_61
<=> ! [X0,X1] :
( member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_61])]) ).
fof(f6557,plain,
( ~ member(sK4(identity_relation),successor_relation)
| member(sK5(sK4(identity_relation)),universal_class)
| ~ spl10_61
| ~ spl10_245 ),
inference(superposition,[],[f644,f4121]) ).
fof(f644,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation)
| member(X1,universal_class) )
| ~ spl10_61 ),
inference(avatar_component_clause,[],[f643]) ).
fof(f18631,plain,
( spl10_514
| ~ spl10_371
| ~ spl10_475 ),
inference(avatar_split_clause,[],[f18579,f17364,f9480,f18629]) ).
fof(f18629,plain,
( spl10_514
<=> ! [X0] : member(sK9,union(sum_class(universal_class),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_514])]) ).
fof(f9480,plain,
( spl10_371
<=> ! [X0,X1] : subclass(X0,union(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_371])]) ).
fof(f18579,plain,
( ! [X0] : member(sK9,union(sum_class(universal_class),X0))
| ~ spl10_371
| ~ spl10_475 ),
inference(resolution,[],[f17365,f9481]) ).
fof(f9481,plain,
( ! [X0,X1] : subclass(X0,union(X0,X1))
| ~ spl10_371 ),
inference(avatar_component_clause,[],[f9480]) ).
fof(f18623,plain,
( spl10_512
| ~ spl10_513
| ~ spl10_60
| ~ spl10_245 ),
inference(avatar_split_clause,[],[f4444,f4119,f639,f18620,f18616]) ).
fof(f18620,plain,
( spl10_513
<=> member(sK4(identity_relation),element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_513])]) ).
fof(f639,plain,
( spl10_60
<=> ! [X0,X1] :
( member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_60])]) ).
fof(f4444,plain,
( ~ member(sK4(identity_relation),element_relation)
| member(sK5(sK4(identity_relation)),universal_class)
| ~ spl10_60
| ~ spl10_245 ),
inference(superposition,[],[f640,f4121]) ).
fof(f640,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| member(X1,universal_class) )
| ~ spl10_60 ),
inference(avatar_component_clause,[],[f639]) ).
fof(f18614,plain,
( ~ spl10_510
| spl10_511
| ~ spl10_5
| ~ spl10_216 ),
inference(avatar_split_clause,[],[f3309,f3021,f292,f18612,f18608]) ).
fof(f18608,plain,
( spl10_510
<=> subclass(element_relation,null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_510])]) ).
fof(f18612,plain,
( spl10_511
<=> ! [X0,X1] :
( ~ member(X0,universal_class)
| ~ member(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_511])]) ).
fof(f3309,plain,
( ! [X0,X1] :
( ~ member(X0,universal_class)
| ~ member(X1,X0)
| ~ subclass(element_relation,null_class) )
| ~ spl10_5
| ~ spl10_216 ),
inference(resolution,[],[f3022,f293]) ).
fof(f18605,plain,
( ~ spl10_508
| spl10_509
| ~ spl10_58
| ~ spl10_199 ),
inference(avatar_split_clause,[],[f2673,f2556,f631,f18603,f18599]) ).
fof(f18599,plain,
( spl10_508
<=> subclass(identity_relation,element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_508])]) ).
fof(f18603,plain,
( spl10_509
<=> ! [X0] :
( ~ member(X0,universal_class)
| member(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_509])]) ).
fof(f631,plain,
( spl10_58
<=> ! [X0,X1] :
( member(X0,X1)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_58])]) ).
fof(f2673,plain,
( ! [X0] :
( ~ member(X0,universal_class)
| ~ subclass(identity_relation,element_relation)
| member(X0,X0) )
| ~ spl10_58
| ~ spl10_199 ),
inference(resolution,[],[f2557,f632]) ).
fof(f632,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| member(X0,X1) )
| ~ spl10_58 ),
inference(avatar_component_clause,[],[f631]) ).
fof(f18596,plain,
( spl10_507
| ~ spl10_7
| ~ spl10_174 ),
inference(avatar_split_clause,[],[f2066,f1775,f300,f18594]) ).
fof(f18594,plain,
( spl10_507
<=> ! [X0,X1] :
( ~ member(X0,sK9)
| member(X0,sum_class(union(universal_class,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_507])]) ).
fof(f2066,plain,
( ! [X0,X1] :
( ~ member(X0,sK9)
| member(X0,sum_class(union(universal_class,X1))) )
| ~ spl10_7
| ~ spl10_174 ),
inference(resolution,[],[f1776,f302]) ).
fof(f18591,plain,
( spl10_506
| ~ spl10_7
| ~ spl10_173 ),
inference(avatar_split_clause,[],[f2010,f1771,f300,f18589]) ).
fof(f18589,plain,
( spl10_506
<=> ! [X0,X1] :
( ~ member(X0,sK9)
| member(X0,sum_class(union(X1,universal_class))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_506])]) ).
fof(f2010,plain,
( ! [X0,X1] :
( ~ member(X0,sK9)
| member(X0,sum_class(union(X1,universal_class))) )
| ~ spl10_7
| ~ spl10_173 ),
inference(resolution,[],[f1772,f302]) ).
fof(f18587,plain,
( spl10_505
| ~ spl10_150
| ~ spl10_169 ),
inference(avatar_split_clause,[],[f1937,f1752,f1473,f18585]) ).
fof(f18585,plain,
( spl10_505
<=> ! [X0,X1] :
( ~ member(X0,sum_class(complement(X1)))
| ~ subclass(complement(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_505])]) ).
fof(f1937,plain,
( ! [X0,X1] :
( ~ member(X0,sum_class(complement(X1)))
| ~ subclass(complement(X1),X1) )
| ~ spl10_150
| ~ spl10_169 ),
inference(duplicate_literal_removal,[],[f1911]) ).
fof(f1911,plain,
( ! [X0,X1] :
( ~ member(X0,sum_class(complement(X1)))
| ~ subclass(complement(X1),X1)
| ~ member(X0,sum_class(complement(X1))) )
| ~ spl10_150
| ~ spl10_169 ),
inference(resolution,[],[f1753,f1474]) ).
fof(f18575,plain,
( spl10_504
| ~ spl10_12
| ~ spl10_134 ),
inference(avatar_split_clause,[],[f1308,f1234,f324,f18573]) ).
fof(f18573,plain,
( spl10_504
<=> ! [X0] :
( ~ member(null_class,X0)
| null_class = X0
| ~ inductive(sK4(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_504])]) ).
fof(f1308,plain,
( ! [X0] :
( ~ member(null_class,X0)
| null_class = X0
| ~ inductive(sK4(X0)) )
| ~ spl10_12
| ~ spl10_134 ),
inference(resolution,[],[f1235,f325]) ).
fof(f18571,plain,
( spl10_503
| ~ spl10_27
| ~ spl10_119 ),
inference(avatar_split_clause,[],[f1129,f1071,f387,f18569]) ).
fof(f18569,plain,
( spl10_503
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,power_class(X0))
| subclass(unordered_pair(X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_503])]) ).
fof(f1129,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,power_class(X0))
| subclass(unordered_pair(X1,X2),X0) )
| ~ spl10_27
| ~ spl10_119 ),
inference(resolution,[],[f1072,f388]) ).
fof(f18567,plain,
( spl10_502
| ~ spl10_25
| ~ spl10_119 ),
inference(avatar_split_clause,[],[f1122,f1071,f379,f18565]) ).
fof(f1122,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,complement(X0))
| ~ member(unordered_pair(X1,X2),X0) )
| ~ spl10_25
| ~ spl10_119 ),
inference(resolution,[],[f1072,f380]) ).
fof(f18563,plain,
( spl10_501
| spl10_233
| ~ spl10_23
| ~ spl10_118 ),
inference(avatar_split_clause,[],[f1088,f1067,f371,f3853,f18561]) ).
fof(f18561,plain,
( spl10_501
<=> ! [X0,X1] : ~ inductive(compose(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_501])]) ).
fof(f371,plain,
( spl10_23
<=> ! [X0,X1] : subclass(compose(X1,X0),cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_23])]) ).
fof(f1088,plain,
( ! [X0,X1] :
( member(null_class,cross_product(universal_class,universal_class))
| ~ inductive(compose(X0,X1)) )
| ~ spl10_23
| ~ spl10_118 ),
inference(resolution,[],[f1068,f372]) ).
fof(f372,plain,
( ! [X0,X1] : subclass(compose(X1,X0),cross_product(universal_class,universal_class))
| ~ spl10_23 ),
inference(avatar_component_clause,[],[f371]) ).
fof(f18558,plain,
( spl10_500
| spl10_233
| ~ spl10_20
| ~ spl10_118 ),
inference(avatar_split_clause,[],[f1081,f1067,f358,f3853,f18556]) ).
fof(f18556,plain,
( spl10_500
<=> ! [X0] :
( ~ inductive(X0)
| ~ function(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_500])]) ).
fof(f1081,plain,
( ! [X0] :
( member(null_class,cross_product(universal_class,universal_class))
| ~ inductive(X0)
| ~ function(X0) )
| ~ spl10_20
| ~ spl10_118 ),
inference(resolution,[],[f1068,f359]) ).
fof(f18490,plain,
( spl10_499
| ~ spl10_1
| ~ spl10_264 ),
inference(avatar_split_clause,[],[f4985,f4964,f272,f18488]) ).
fof(f18488,plain,
( spl10_499
<=> ! [X0,X1] :
( ~ member(X0,universal_class)
| ~ function(X1)
| first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(sK0,universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(sK0,universal_class)),universal_class)))))))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_499])]) ).
fof(f4964,plain,
( spl10_264
<=> ! [X2,X0,X1] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X2,universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X2,universal_class)),universal_class)))))))) = X0
| ~ member(X0,universal_class)
| ~ function(X1)
| ~ member(X2,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_264])]) ).
fof(f4985,plain,
( ! [X0,X1] :
( ~ member(X0,universal_class)
| ~ function(X1)
| first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(sK0,universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(sK0,universal_class)),universal_class)))))))) = X0 )
| ~ spl10_1
| ~ spl10_264 ),
inference(resolution,[],[f4965,f274]) ).
fof(f4965,plain,
( ! [X2,X0,X1] :
( ~ member(X2,universal_class)
| ~ member(X0,universal_class)
| ~ function(X1)
| first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X2,universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X2,universal_class)),universal_class)))))))) = X0 )
| ~ spl10_264 ),
inference(avatar_component_clause,[],[f4964]) ).
fof(f18345,plain,
( spl10_498
| ~ spl10_314
| ~ spl10_493 ),
inference(avatar_split_clause,[],[f18323,f18320,f6012,f18343]) ).
fof(f18343,plain,
( spl10_498
<=> ! [X2,X0,X1] :
( sK7(X0,unordered_pair(X1,X2)) = first(unordered_pair(unordered_pair(sK7(X0,unordered_pair(X1,X2)),sK7(X0,unordered_pair(X1,X2))),unordered_pair(sK7(X0,unordered_pair(X1,X2)),unordered_pair(sK2,sK2))))
| ~ member(X0,sum_class(unordered_pair(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_498])]) ).
fof(f18320,plain,
( spl10_493
<=> ! [X2,X0,X1] :
( ~ member(X0,sum_class(unordered_pair(X1,X2)))
| sK7(X0,unordered_pair(X1,X2)) = first(unordered_pair(unordered_pair(sK7(X0,unordered_pair(X1,X2)),sK7(X0,unordered_pair(X1,X2))),unordered_pair(sK7(X0,unordered_pair(X1,X2)),unordered_pair(sK0,sK0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_493])]) ).
fof(f18323,plain,
( ! [X2,X0,X1] :
( sK7(X0,unordered_pair(X1,X2)) = first(unordered_pair(unordered_pair(sK7(X0,unordered_pair(X1,X2)),sK7(X0,unordered_pair(X1,X2))),unordered_pair(sK7(X0,unordered_pair(X1,X2)),unordered_pair(sK2,sK2))))
| ~ member(X0,sum_class(unordered_pair(X1,X2))) )
| ~ spl10_314
| ~ spl10_493 ),
inference(forward_demodulation,[],[f18321,f6014]) ).
fof(f18321,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum_class(unordered_pair(X1,X2)))
| sK7(X0,unordered_pair(X1,X2)) = first(unordered_pair(unordered_pair(sK7(X0,unordered_pair(X1,X2)),sK7(X0,unordered_pair(X1,X2))),unordered_pair(sK7(X0,unordered_pair(X1,X2)),unordered_pair(sK0,sK0)))) )
| ~ spl10_493 ),
inference(avatar_component_clause,[],[f18320]) ).
fof(f18341,plain,
( spl10_497
| ~ spl10_178
| ~ spl10_463 ),
inference(avatar_split_clause,[],[f14564,f14516,f2095,f18339]) ).
fof(f18339,plain,
( spl10_497
<=> ! [X0,X1] :
( sK7(X0,intersection(X1,universal_class)) = first(unordered_pair(unordered_pair(sK7(X0,intersection(X1,universal_class)),sK7(X0,intersection(X1,universal_class))),unordered_pair(sK7(X0,intersection(X1,universal_class)),unordered_pair(sK2,sK2))))
| ~ member(X0,sum_class(intersection(X1,universal_class))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_497])]) ).
fof(f14564,plain,
( ! [X0,X1] :
( sK7(X0,intersection(X1,universal_class)) = first(unordered_pair(unordered_pair(sK7(X0,intersection(X1,universal_class)),sK7(X0,intersection(X1,universal_class))),unordered_pair(sK7(X0,intersection(X1,universal_class)),unordered_pair(sK2,sK2))))
| ~ member(X0,sum_class(intersection(X1,universal_class))) )
| ~ spl10_178
| ~ spl10_463 ),
inference(resolution,[],[f14517,f2096]) ).
fof(f18337,plain,
( spl10_496
| ~ spl10_179
| ~ spl10_463 ),
inference(avatar_split_clause,[],[f14559,f14516,f2099,f18335]) ).
fof(f18335,plain,
( spl10_496
<=> ! [X0,X1] :
( sK7(X0,intersection(universal_class,X1)) = first(unordered_pair(unordered_pair(sK7(X0,intersection(universal_class,X1)),sK7(X0,intersection(universal_class,X1))),unordered_pair(sK7(X0,intersection(universal_class,X1)),unordered_pair(sK2,sK2))))
| ~ member(X0,sum_class(intersection(universal_class,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_496])]) ).
fof(f14559,plain,
( ! [X0,X1] :
( sK7(X0,intersection(universal_class,X1)) = first(unordered_pair(unordered_pair(sK7(X0,intersection(universal_class,X1)),sK7(X0,intersection(universal_class,X1))),unordered_pair(sK7(X0,intersection(universal_class,X1)),unordered_pair(sK2,sK2))))
| ~ member(X0,sum_class(intersection(universal_class,X1))) )
| ~ spl10_179
| ~ spl10_463 ),
inference(resolution,[],[f14517,f2100]) ).
fof(f18332,plain,
( spl10_495
| ~ spl10_96
| ~ spl10_179 ),
inference(avatar_split_clause,[],[f2176,f2099,f895,f18330]) ).
fof(f18330,plain,
( spl10_495
<=> ! [X0,X1] :
( ~ member(X0,sum_class(intersection(universal_class,X1)))
| sK7(X0,intersection(universal_class,X1)) = first(unordered_pair(unordered_pair(sK7(X0,intersection(universal_class,X1)),sK7(X0,intersection(universal_class,X1))),unordered_pair(sK7(X0,intersection(universal_class,X1)),unordered_pair(sK0,sK0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_495])]) ).
fof(f2176,plain,
( ! [X0,X1] :
( ~ member(X0,sum_class(intersection(universal_class,X1)))
| sK7(X0,intersection(universal_class,X1)) = first(unordered_pair(unordered_pair(sK7(X0,intersection(universal_class,X1)),sK7(X0,intersection(universal_class,X1))),unordered_pair(sK7(X0,intersection(universal_class,X1)),unordered_pair(sK0,sK0)))) )
| ~ spl10_96
| ~ spl10_179 ),
inference(resolution,[],[f2100,f896]) ).
fof(f18327,plain,
( spl10_494
| ~ spl10_96
| ~ spl10_178 ),
inference(avatar_split_clause,[],[f2145,f2095,f895,f18325]) ).
fof(f18325,plain,
( spl10_494
<=> ! [X0,X1] :
( ~ member(X0,sum_class(intersection(X1,universal_class)))
| sK7(X0,intersection(X1,universal_class)) = first(unordered_pair(unordered_pair(sK7(X0,intersection(X1,universal_class)),sK7(X0,intersection(X1,universal_class))),unordered_pair(sK7(X0,intersection(X1,universal_class)),unordered_pair(sK0,sK0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_494])]) ).
fof(f2145,plain,
( ! [X0,X1] :
( ~ member(X0,sum_class(intersection(X1,universal_class)))
| sK7(X0,intersection(X1,universal_class)) = first(unordered_pair(unordered_pair(sK7(X0,intersection(X1,universal_class)),sK7(X0,intersection(X1,universal_class))),unordered_pair(sK7(X0,intersection(X1,universal_class)),unordered_pair(sK0,sK0)))) )
| ~ spl10_96
| ~ spl10_178 ),
inference(resolution,[],[f2096,f896]) ).
fof(f18322,plain,
( spl10_493
| ~ spl10_96
| ~ spl10_177 ),
inference(avatar_split_clause,[],[f2132,f2091,f895,f18320]) ).
fof(f2091,plain,
( spl10_177
<=> ! [X2,X0,X1] :
( ~ member(X0,sum_class(unordered_pair(X1,X2)))
| member(sK7(X0,unordered_pair(X1,X2)),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_177])]) ).
fof(f2132,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum_class(unordered_pair(X1,X2)))
| sK7(X0,unordered_pair(X1,X2)) = first(unordered_pair(unordered_pair(sK7(X0,unordered_pair(X1,X2)),sK7(X0,unordered_pair(X1,X2))),unordered_pair(sK7(X0,unordered_pair(X1,X2)),unordered_pair(sK0,sK0)))) )
| ~ spl10_96
| ~ spl10_177 ),
inference(resolution,[],[f2092,f896]) ).
fof(f2092,plain,
( ! [X2,X0,X1] :
( member(sK7(X0,unordered_pair(X1,X2)),universal_class)
| ~ member(X0,sum_class(unordered_pair(X1,X2))) )
| ~ spl10_177 ),
inference(avatar_component_clause,[],[f2091]) ).
fof(f18188,plain,
( spl10_492
| ~ spl10_153
| ~ spl10_168 ),
inference(avatar_split_clause,[],[f1910,f1748,f1485,f18186]) ).
fof(f18186,plain,
( spl10_492
<=> ! [X0,X1] :
( member(X0,X1)
| ~ member(X0,sum_class(power_class(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_492])]) ).
fof(f1910,plain,
( ! [X0,X1] :
( member(X0,X1)
| ~ member(X0,sum_class(power_class(X1))) )
| ~ spl10_153
| ~ spl10_168 ),
inference(duplicate_literal_removal,[],[f1906]) ).
fof(f1906,plain,
( ! [X0,X1] :
( member(X0,X1)
| ~ member(X0,sum_class(power_class(X1)))
| ~ member(X0,sum_class(power_class(X1))) )
| ~ spl10_153
| ~ spl10_168 ),
inference(resolution,[],[f1749,f1486]) ).
fof(f18184,plain,
( spl10_491
| ~ spl10_145
| ~ spl10_165 ),
inference(avatar_split_clause,[],[f1878,f1736,f1453,f18182]) ).
fof(f18182,plain,
( spl10_491
<=> ! [X2,X0,X1] :
( subclass(X0,union(X1,X2))
| ~ subclass(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_491])]) ).
fof(f1878,plain,
( ! [X2,X0,X1] :
( subclass(X0,union(X1,X2))
| ~ subclass(X0,X2) )
| ~ spl10_145
| ~ spl10_165 ),
inference(duplicate_literal_removal,[],[f1863]) ).
fof(f1863,plain,
( ! [X2,X0,X1] :
( subclass(X0,union(X1,X2))
| ~ subclass(X0,X2)
| subclass(X0,union(X1,X2)) )
| ~ spl10_145
| ~ spl10_165 ),
inference(resolution,[],[f1737,f1454]) ).
fof(f18180,plain,
( spl10_490
| ~ spl10_145
| ~ spl10_164 ),
inference(avatar_split_clause,[],[f1856,f1732,f1453,f18178]) ).
fof(f18178,plain,
( spl10_490
<=> ! [X2,X0,X1] :
( subclass(X0,union(X1,X2))
| ~ subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_490])]) ).
fof(f1856,plain,
( ! [X2,X0,X1] :
( subclass(X0,union(X1,X2))
| ~ subclass(X0,X1) )
| ~ spl10_145
| ~ spl10_164 ),
inference(duplicate_literal_removal,[],[f1841]) ).
fof(f1841,plain,
( ! [X2,X0,X1] :
( subclass(X0,union(X1,X2))
| ~ subclass(X0,X1)
| subclass(X0,union(X1,X2)) )
| ~ spl10_145
| ~ spl10_164 ),
inference(resolution,[],[f1733,f1454]) ).
fof(f18176,plain,
( spl10_489
| ~ spl10_124
| ~ spl10_145 ),
inference(avatar_split_clause,[],[f1593,f1453,f1191,f18174]) ).
fof(f18174,plain,
( spl10_489
<=> ! [X0,X1] :
( ~ subclass(complement(X0),X0)
| subclass(complement(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_489])]) ).
fof(f1593,plain,
( ! [X0,X1] :
( ~ subclass(complement(X0),X0)
| subclass(complement(X0),X1) )
| ~ spl10_124
| ~ spl10_145 ),
inference(duplicate_literal_removal,[],[f1568]) ).
fof(f1568,plain,
( ! [X0,X1] :
( ~ subclass(complement(X0),X0)
| subclass(complement(X0),X1)
| subclass(complement(X0),X1) )
| ~ spl10_124
| ~ spl10_145 ),
inference(resolution,[],[f1454,f1192]) ).
fof(f18172,plain,
( spl10_488
| ~ spl10_121
| ~ spl10_135 ),
inference(avatar_split_clause,[],[f1339,f1238,f1144,f18170]) ).
fof(f18170,plain,
( spl10_488
<=> ! [X0] :
( ~ subclass(complement(X0),X0)
| complement(X0) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_488])]) ).
fof(f1339,plain,
( ! [X0] :
( ~ subclass(complement(X0),X0)
| complement(X0) = null_class )
| ~ spl10_121
| ~ spl10_135 ),
inference(duplicate_literal_removal,[],[f1314]) ).
fof(f1314,plain,
( ! [X0] :
( ~ subclass(complement(X0),X0)
| complement(X0) = null_class
| complement(X0) = null_class )
| ~ spl10_121
| ~ spl10_135 ),
inference(resolution,[],[f1239,f1145]) ).
fof(f18168,plain,
( spl10_487
| ~ spl10_372
| ~ spl10_468 ),
inference(avatar_split_clause,[],[f17598,f17107,f9484,f18166]) ).
fof(f18166,plain,
( spl10_487
<=> ! [X0] : member(null_class,union(X0,sum_class(universal_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_487])]) ).
fof(f17107,plain,
( spl10_468
<=> ! [X0] :
( member(null_class,X0)
| ~ subclass(sum_class(universal_class),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_468])]) ).
fof(f17598,plain,
( ! [X0] : member(null_class,union(X0,sum_class(universal_class)))
| ~ spl10_372
| ~ spl10_468 ),
inference(resolution,[],[f17108,f9485]) ).
fof(f17108,plain,
( ! [X0] :
( ~ subclass(sum_class(universal_class),X0)
| member(null_class,X0) )
| ~ spl10_468 ),
inference(avatar_component_clause,[],[f17107]) ).
fof(f18086,plain,
( spl10_486
| ~ spl10_178
| ~ spl10_464 ),
inference(avatar_split_clause,[],[f14621,f14520,f2095,f18084]) ).
fof(f18084,plain,
( spl10_486
<=> ! [X0,X1] :
( sK0 = second(unordered_pair(unordered_pair(sK7(X0,intersection(X1,universal_class)),sK7(X0,intersection(X1,universal_class))),unordered_pair(sK7(X0,intersection(X1,universal_class)),unordered_pair(sK2,sK2))))
| ~ member(X0,sum_class(intersection(X1,universal_class))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_486])]) ).
fof(f14621,plain,
( ! [X0,X1] :
( sK0 = second(unordered_pair(unordered_pair(sK7(X0,intersection(X1,universal_class)),sK7(X0,intersection(X1,universal_class))),unordered_pair(sK7(X0,intersection(X1,universal_class)),unordered_pair(sK2,sK2))))
| ~ member(X0,sum_class(intersection(X1,universal_class))) )
| ~ spl10_178
| ~ spl10_464 ),
inference(resolution,[],[f14521,f2096]) ).
fof(f18082,plain,
( spl10_485
| ~ spl10_179
| ~ spl10_464 ),
inference(avatar_split_clause,[],[f14616,f14520,f2099,f18080]) ).
fof(f18080,plain,
( spl10_485
<=> ! [X0,X1] :
( sK0 = second(unordered_pair(unordered_pair(sK7(X0,intersection(universal_class,X1)),sK7(X0,intersection(universal_class,X1))),unordered_pair(sK7(X0,intersection(universal_class,X1)),unordered_pair(sK2,sK2))))
| ~ member(X0,sum_class(intersection(universal_class,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_485])]) ).
fof(f14616,plain,
( ! [X0,X1] :
( sK0 = second(unordered_pair(unordered_pair(sK7(X0,intersection(universal_class,X1)),sK7(X0,intersection(universal_class,X1))),unordered_pair(sK7(X0,intersection(universal_class,X1)),unordered_pair(sK2,sK2))))
| ~ member(X0,sum_class(intersection(universal_class,X1))) )
| ~ spl10_179
| ~ spl10_464 ),
inference(resolution,[],[f14521,f2100]) ).
fof(f17955,plain,
( spl10_484
| ~ spl10_169
| ~ spl10_463 ),
inference(avatar_split_clause,[],[f14563,f14516,f1752,f17953]) ).
fof(f17953,plain,
( spl10_484
<=> ! [X0,X1] :
( sK7(X0,X1) = first(unordered_pair(unordered_pair(sK7(X0,X1),sK7(X0,X1)),unordered_pair(sK7(X0,X1),unordered_pair(sK2,sK2))))
| ~ member(X0,sum_class(X1))
| ~ subclass(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_484])]) ).
fof(f14563,plain,
( ! [X0,X1] :
( sK7(X0,X1) = first(unordered_pair(unordered_pair(sK7(X0,X1),sK7(X0,X1)),unordered_pair(sK7(X0,X1),unordered_pair(sK2,sK2))))
| ~ member(X0,sum_class(X1))
| ~ subclass(X1,universal_class) )
| ~ spl10_169
| ~ spl10_463 ),
inference(resolution,[],[f14517,f1753]) ).
fof(f17934,plain,
( spl10_483
| ~ spl10_145
| ~ spl10_463 ),
inference(avatar_split_clause,[],[f14562,f14516,f1453,f17932]) ).
fof(f17932,plain,
( spl10_483
<=> ! [X0,X1] :
( sK6(X0,X1) = first(unordered_pair(unordered_pair(sK6(X0,X1),sK6(X0,X1)),unordered_pair(sK6(X0,X1),unordered_pair(sK2,sK2))))
| ~ subclass(X0,universal_class)
| subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_483])]) ).
fof(f14562,plain,
( ! [X0,X1] :
( sK6(X0,X1) = first(unordered_pair(unordered_pair(sK6(X0,X1),sK6(X0,X1)),unordered_pair(sK6(X0,X1),unordered_pair(sK2,sK2))))
| ~ subclass(X0,universal_class)
| subclass(X0,X1) )
| ~ spl10_145
| ~ spl10_463 ),
inference(resolution,[],[f14517,f1454]) ).
fof(f17844,plain,
( spl10_482
| ~ spl10_371
| ~ spl10_468 ),
inference(avatar_split_clause,[],[f17597,f17107,f9480,f17842]) ).
fof(f17842,plain,
( spl10_482
<=> ! [X0] : member(null_class,union(sum_class(universal_class),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_482])]) ).
fof(f17597,plain,
( ! [X0] : member(null_class,union(sum_class(universal_class),X0))
| ~ spl10_371
| ~ spl10_468 ),
inference(resolution,[],[f17108,f9481]) ).
fof(f17840,plain,
( spl10_481
| ~ spl10_169
| ~ spl10_464 ),
inference(avatar_split_clause,[],[f14620,f14520,f1752,f17838]) ).
fof(f17838,plain,
( spl10_481
<=> ! [X0,X1] :
( sK0 = second(unordered_pair(unordered_pair(sK7(X0,X1),sK7(X0,X1)),unordered_pair(sK7(X0,X1),unordered_pair(sK2,sK2))))
| ~ member(X0,sum_class(X1))
| ~ subclass(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_481])]) ).
fof(f14620,plain,
( ! [X0,X1] :
( sK0 = second(unordered_pair(unordered_pair(sK7(X0,X1),sK7(X0,X1)),unordered_pair(sK7(X0,X1),unordered_pair(sK2,sK2))))
| ~ member(X0,sum_class(X1))
| ~ subclass(X1,universal_class) )
| ~ spl10_169
| ~ spl10_464 ),
inference(resolution,[],[f14521,f1753]) ).
fof(f17666,plain,
( spl10_480
| ~ spl10_145
| ~ spl10_464 ),
inference(avatar_split_clause,[],[f14619,f14520,f1453,f17664]) ).
fof(f17664,plain,
( spl10_480
<=> ! [X0,X1] :
( sK0 = second(unordered_pair(unordered_pair(sK6(X0,X1),sK6(X0,X1)),unordered_pair(sK6(X0,X1),unordered_pair(sK2,sK2))))
| ~ subclass(X0,universal_class)
| subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_480])]) ).
fof(f14619,plain,
( ! [X0,X1] :
( sK0 = second(unordered_pair(unordered_pair(sK6(X0,X1),sK6(X0,X1)),unordered_pair(sK6(X0,X1),unordered_pair(sK2,sK2))))
| ~ subclass(X0,universal_class)
| subclass(X0,X1) )
| ~ spl10_145
| ~ spl10_464 ),
inference(resolution,[],[f14521,f1454]) ).
fof(f17662,plain,
( spl10_479
| ~ spl10_47
| ~ spl10_463 ),
inference(avatar_split_clause,[],[f14558,f14516,f502,f17660]) ).
fof(f17660,plain,
( spl10_479
<=> ! [X0] :
( sK7(X0,universal_class) = first(unordered_pair(unordered_pair(sK7(X0,universal_class),sK7(X0,universal_class)),unordered_pair(sK7(X0,universal_class),unordered_pair(sK2,sK2))))
| ~ member(X0,sum_class(universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_479])]) ).
fof(f14558,plain,
( ! [X0] :
( sK7(X0,universal_class) = first(unordered_pair(unordered_pair(sK7(X0,universal_class),sK7(X0,universal_class)),unordered_pair(sK7(X0,universal_class),unordered_pair(sK2,sK2))))
| ~ member(X0,sum_class(universal_class)) )
| ~ spl10_47
| ~ spl10_463 ),
inference(resolution,[],[f14517,f503]) ).
fof(f17603,plain,
( spl10_478
| ~ spl10_33
| ~ spl10_463 ),
inference(avatar_split_clause,[],[f14545,f14516,f422,f17601]) ).
fof(f17601,plain,
( spl10_478
<=> ! [X0] :
( sK6(universal_class,X0) = first(unordered_pair(unordered_pair(sK6(universal_class,X0),sK6(universal_class,X0)),unordered_pair(sK6(universal_class,X0),unordered_pair(sK2,sK2))))
| subclass(universal_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_478])]) ).
fof(f14545,plain,
( ! [X0] :
( sK6(universal_class,X0) = first(unordered_pair(unordered_pair(sK6(universal_class,X0),sK6(universal_class,X0)),unordered_pair(sK6(universal_class,X0),unordered_pair(sK2,sK2))))
| subclass(universal_class,X0) )
| ~ spl10_33
| ~ spl10_463 ),
inference(resolution,[],[f14517,f423]) ).
fof(f17548,plain,
( spl10_477
| ~ spl10_47
| ~ spl10_464 ),
inference(avatar_split_clause,[],[f14615,f14520,f502,f17546]) ).
fof(f17546,plain,
( spl10_477
<=> ! [X0] :
( sK0 = second(unordered_pair(unordered_pair(sK7(X0,universal_class),sK7(X0,universal_class)),unordered_pair(sK7(X0,universal_class),unordered_pair(sK2,sK2))))
| ~ member(X0,sum_class(universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_477])]) ).
fof(f14615,plain,
( ! [X0] :
( sK0 = second(unordered_pair(unordered_pair(sK7(X0,universal_class),sK7(X0,universal_class)),unordered_pair(sK7(X0,universal_class),unordered_pair(sK2,sK2))))
| ~ member(X0,sum_class(universal_class)) )
| ~ spl10_47
| ~ spl10_464 ),
inference(resolution,[],[f14521,f503]) ).
fof(f17489,plain,
( spl10_476
| ~ spl10_33
| ~ spl10_464 ),
inference(avatar_split_clause,[],[f14602,f14520,f422,f17487]) ).
fof(f17487,plain,
( spl10_476
<=> ! [X0] :
( sK0 = second(unordered_pair(unordered_pair(sK6(universal_class,X0),sK6(universal_class,X0)),unordered_pair(sK6(universal_class,X0),unordered_pair(sK2,sK2))))
| subclass(universal_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_476])]) ).
fof(f14602,plain,
( ! [X0] :
( sK0 = second(unordered_pair(unordered_pair(sK6(universal_class,X0),sK6(universal_class,X0)),unordered_pair(sK6(universal_class,X0),unordered_pair(sK2,sK2))))
| subclass(universal_class,X0) )
| ~ spl10_33
| ~ spl10_464 ),
inference(resolution,[],[f14521,f423]) ).
fof(f17467,plain,
( spl10_388
| ~ spl10_314
| ~ spl10_387 ),
inference(avatar_split_clause,[],[f13857,f10802,f6012,f10876]) ).
fof(f10876,plain,
( spl10_388
<=> ! [X0] :
( sK6(universal_class,X0) = second(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,unordered_pair(sK6(universal_class,X0),sK6(universal_class,X0)))))
| subclass(universal_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_388])]) ).
fof(f13857,plain,
( ! [X0] :
( sK6(universal_class,X0) = second(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,unordered_pair(sK6(universal_class,X0),sK6(universal_class,X0)))))
| subclass(universal_class,X0) )
| ~ spl10_314
| ~ spl10_387 ),
inference(forward_demodulation,[],[f10803,f6014]) ).
fof(f10803,plain,
( ! [X0] :
( subclass(universal_class,X0)
| sK6(universal_class,X0) = second(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK6(universal_class,X0),sK6(universal_class,X0))))) )
| ~ spl10_387 ),
inference(avatar_component_clause,[],[f10802]) ).
fof(f17366,plain,
( spl10_475
| ~ spl10_45
| ~ spl10_445 ),
inference(avatar_split_clause,[],[f14302,f12631,f494,f17364]) ).
fof(f12631,plain,
( spl10_445
<=> member(sK9,sum_class(universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_445])]) ).
fof(f14302,plain,
( ! [X0] :
( member(sK9,X0)
| ~ subclass(sum_class(universal_class),X0) )
| ~ spl10_45
| ~ spl10_445 ),
inference(resolution,[],[f12633,f495]) ).
fof(f12633,plain,
( member(sK9,sum_class(universal_class))
| ~ spl10_445 ),
inference(avatar_component_clause,[],[f12631]) ).
fof(f17297,plain,
( spl10_474
| ~ spl10_22
| ~ spl10_463 ),
inference(avatar_split_clause,[],[f14535,f14516,f367,f17295]) ).
fof(f17295,plain,
( spl10_474
<=> ! [X0] :
( sK5(X0) = first(unordered_pair(unordered_pair(sK5(X0),sK5(X0)),unordered_pair(sK5(X0),unordered_pair(sK2,sK2))))
| ~ member(X0,identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_474])]) ).
fof(f367,plain,
( spl10_22
<=> ! [X0] :
( member(sK5(X0),universal_class)
| ~ member(X0,identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_22])]) ).
fof(f14535,plain,
( ! [X0] :
( sK5(X0) = first(unordered_pair(unordered_pair(sK5(X0),sK5(X0)),unordered_pair(sK5(X0),unordered_pair(sK2,sK2))))
| ~ member(X0,identity_relation) )
| ~ spl10_22
| ~ spl10_463 ),
inference(resolution,[],[f14517,f368]) ).
fof(f368,plain,
( ! [X0] :
( member(sK5(X0),universal_class)
| ~ member(X0,identity_relation) )
| ~ spl10_22 ),
inference(avatar_component_clause,[],[f367]) ).
fof(f17293,plain,
( spl10_473
| ~ spl10_18
| ~ spl10_463 ),
inference(avatar_split_clause,[],[f14532,f14516,f350,f17291]) ).
fof(f17291,plain,
( spl10_473
<=> ! [X0] :
( power_class(X0) = first(unordered_pair(unordered_pair(power_class(X0),power_class(X0)),unordered_pair(power_class(X0),unordered_pair(sK2,sK2))))
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_473])]) ).
fof(f14532,plain,
( ! [X0] :
( power_class(X0) = first(unordered_pair(unordered_pair(power_class(X0),power_class(X0)),unordered_pair(power_class(X0),unordered_pair(sK2,sK2))))
| ~ member(X0,universal_class) )
| ~ spl10_18
| ~ spl10_463 ),
inference(resolution,[],[f14517,f351]) ).
fof(f17289,plain,
( spl10_472
| ~ spl10_19
| ~ spl10_463 ),
inference(avatar_split_clause,[],[f14531,f14516,f354,f17287]) ).
fof(f17287,plain,
( spl10_472
<=> ! [X0] :
( sum_class(X0) = first(unordered_pair(unordered_pair(sum_class(X0),sum_class(X0)),unordered_pair(sum_class(X0),unordered_pair(sK2,sK2))))
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_472])]) ).
fof(f14531,plain,
( ! [X0] :
( sum_class(X0) = first(unordered_pair(unordered_pair(sum_class(X0),sum_class(X0)),unordered_pair(sum_class(X0),unordered_pair(sK2,sK2))))
| ~ member(X0,universal_class) )
| ~ spl10_19
| ~ spl10_463 ),
inference(resolution,[],[f14517,f355]) ).
fof(f17121,plain,
( spl10_471
| ~ spl10_22
| ~ spl10_464 ),
inference(avatar_split_clause,[],[f14592,f14520,f367,f17119]) ).
fof(f17119,plain,
( spl10_471
<=> ! [X0] :
( sK0 = second(unordered_pair(unordered_pair(sK5(X0),sK5(X0)),unordered_pair(sK5(X0),unordered_pair(sK2,sK2))))
| ~ member(X0,identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_471])]) ).
fof(f14592,plain,
( ! [X0] :
( sK0 = second(unordered_pair(unordered_pair(sK5(X0),sK5(X0)),unordered_pair(sK5(X0),unordered_pair(sK2,sK2))))
| ~ member(X0,identity_relation) )
| ~ spl10_22
| ~ spl10_464 ),
inference(resolution,[],[f14521,f368]) ).
fof(f17117,plain,
( spl10_470
| ~ spl10_18
| ~ spl10_464 ),
inference(avatar_split_clause,[],[f14589,f14520,f350,f17115]) ).
fof(f17115,plain,
( spl10_470
<=> ! [X0] :
( sK0 = second(unordered_pair(unordered_pair(power_class(X0),power_class(X0)),unordered_pair(power_class(X0),unordered_pair(sK2,sK2))))
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_470])]) ).
fof(f14589,plain,
( ! [X0] :
( sK0 = second(unordered_pair(unordered_pair(power_class(X0),power_class(X0)),unordered_pair(power_class(X0),unordered_pair(sK2,sK2))))
| ~ member(X0,universal_class) )
| ~ spl10_18
| ~ spl10_464 ),
inference(resolution,[],[f14521,f351]) ).
fof(f17113,plain,
( spl10_469
| ~ spl10_19
| ~ spl10_464 ),
inference(avatar_split_clause,[],[f14588,f14520,f354,f17111]) ).
fof(f17111,plain,
( spl10_469
<=> ! [X0] :
( sK0 = second(unordered_pair(unordered_pair(sum_class(X0),sum_class(X0)),unordered_pair(sum_class(X0),unordered_pair(sK2,sK2))))
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_469])]) ).
fof(f14588,plain,
( ! [X0] :
( sK0 = second(unordered_pair(unordered_pair(sum_class(X0),sum_class(X0)),unordered_pair(sum_class(X0),unordered_pair(sK2,sK2))))
| ~ member(X0,universal_class) )
| ~ spl10_19
| ~ spl10_464 ),
inference(resolution,[],[f14521,f355]) ).
fof(f17109,plain,
( spl10_468
| ~ spl10_45
| ~ spl10_303 ),
inference(avatar_split_clause,[],[f7983,f5852,f494,f17107]) ).
fof(f5852,plain,
( spl10_303
<=> member(null_class,sum_class(universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_303])]) ).
fof(f7983,plain,
( ! [X0] :
( member(null_class,X0)
| ~ subclass(sum_class(universal_class),X0) )
| ~ spl10_45
| ~ spl10_303 ),
inference(resolution,[],[f5854,f495]) ).
fof(f5854,plain,
( member(null_class,sum_class(universal_class))
| ~ spl10_303 ),
inference(avatar_component_clause,[],[f5852]) ).
fof(f15541,plain,
( spl10_466
| ~ spl10_467
| ~ spl10_142
| ~ spl10_314 ),
inference(avatar_split_clause,[],[f12698,f6012,f1267,f15538,f15534]) ).
fof(f15534,plain,
( spl10_466
<=> null_class = sK0 ),
introduced(avatar_definition,[new_symbols(naming,[spl10_466])]) ).
fof(f15538,plain,
( spl10_467
<=> inductive(unordered_pair(sK2,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_467])]) ).
fof(f1267,plain,
( spl10_142
<=> ! [X0,X1] :
( null_class = X0
| null_class = X1
| ~ inductive(unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_142])]) ).
fof(f12698,plain,
( ~ inductive(unordered_pair(sK2,sK2))
| null_class = sK0
| ~ spl10_142
| ~ spl10_314 ),
inference(duplicate_literal_removal,[],[f10150]) ).
fof(f10150,plain,
( ~ inductive(unordered_pair(sK2,sK2))
| null_class = sK0
| null_class = sK0
| ~ spl10_142
| ~ spl10_314 ),
inference(superposition,[],[f1268,f6014]) ).
fof(f1268,plain,
( ! [X0,X1] :
( ~ inductive(unordered_pair(X0,X1))
| null_class = X1
| null_class = X0 )
| ~ spl10_142 ),
inference(avatar_component_clause,[],[f1267]) ).
fof(f14527,plain,
( ~ spl10_465
| ~ spl10_314
| spl10_378 ),
inference(avatar_split_clause,[],[f12890,f10587,f6012,f14524]) ).
fof(f14524,plain,
( spl10_465
<=> null_class = unordered_pair(sK2,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_465])]) ).
fof(f10587,plain,
( spl10_378
<=> null_class = unordered_pair(sK0,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_378])]) ).
fof(f12890,plain,
( null_class != unordered_pair(sK2,sK2)
| ~ spl10_314
| spl10_378 ),
inference(superposition,[],[f10588,f6014]) ).
fof(f10588,plain,
( null_class != unordered_pair(sK0,sK0)
| spl10_378 ),
inference(avatar_component_clause,[],[f10587]) ).
fof(f14522,plain,
( spl10_464
| ~ spl10_95
| ~ spl10_314 ),
inference(avatar_split_clause,[],[f14157,f6012,f891,f14520]) ).
fof(f14157,plain,
( ! [X0] :
( sK0 = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK2,sK2))))
| ~ member(X0,universal_class) )
| ~ spl10_95
| ~ spl10_314 ),
inference(forward_demodulation,[],[f892,f6014]) ).
fof(f14518,plain,
( spl10_463
| ~ spl10_96
| ~ spl10_314 ),
inference(avatar_split_clause,[],[f14089,f6012,f895,f14516]) ).
fof(f14089,plain,
( ! [X0] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK2,sK2)))) = X0
| ~ member(X0,universal_class) )
| ~ spl10_96
| ~ spl10_314 ),
inference(forward_demodulation,[],[f896,f6014]) ).
fof(f13725,plain,
( spl10_270
| ~ spl10_461 ),
inference(avatar_contradiction_clause,[],[f13695]) ).
fof(f13695,plain,
( $false
| spl10_270
| ~ spl10_461 ),
inference(resolution,[],[f13652,f5082]) ).
fof(f5082,plain,
( ~ member(universal_class,universal_class)
| spl10_270 ),
inference(avatar_component_clause,[],[f5080]) ).
fof(f5080,plain,
( spl10_270
<=> member(universal_class,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_270])]) ).
fof(f13652,plain,
( ! [X2] : member(X2,universal_class)
| ~ spl10_461 ),
inference(avatar_component_clause,[],[f13651]) ).
fof(f13651,plain,
( spl10_461
<=> ! [X2] : member(X2,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_461])]) ).
fof(f13724,plain,
( spl10_443
| ~ spl10_461 ),
inference(avatar_contradiction_clause,[],[f13701]) ).
fof(f13701,plain,
( $false
| spl10_443
| ~ spl10_461 ),
inference(resolution,[],[f13652,f12512]) ).
fof(f12512,plain,
( ~ member(complement(sum_class(universal_class)),universal_class)
| spl10_443 ),
inference(avatar_component_clause,[],[f12510]) ).
fof(f12510,plain,
( spl10_443
<=> member(complement(sum_class(universal_class)),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_443])]) ).
fof(f13723,plain,
( spl10_395
| ~ spl10_461 ),
inference(avatar_contradiction_clause,[],[f13702]) ).
fof(f13702,plain,
( $false
| spl10_395
| ~ spl10_461 ),
inference(resolution,[],[f13652,f11063]) ).
fof(f11063,plain,
( ~ member(sum_class(universal_class),universal_class)
| spl10_395 ),
inference(avatar_component_clause,[],[f11061]) ).
fof(f11061,plain,
( spl10_395
<=> member(sum_class(universal_class),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_395])]) ).
fof(f13722,plain,
( spl10_287
| ~ spl10_461 ),
inference(avatar_contradiction_clause,[],[f13705]) ).
fof(f13705,plain,
( $false
| spl10_287
| ~ spl10_461 ),
inference(resolution,[],[f13652,f5635]) ).
fof(f5635,plain,
( ~ member(identity_relation,universal_class)
| spl10_287 ),
inference(avatar_component_clause,[],[f5633]) ).
fof(f5633,plain,
( spl10_287
<=> member(identity_relation,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_287])]) ).
fof(f13721,plain,
( ~ spl10_176
| ~ spl10_461 ),
inference(avatar_contradiction_clause,[],[f13706]) ).
fof(f13706,plain,
( $false
| ~ spl10_176
| ~ spl10_461 ),
inference(resolution,[],[f13652,f1904]) ).
fof(f1904,plain,
( ! [X0] : ~ member(sK1,X0)
| ~ spl10_176 ),
inference(avatar_component_clause,[],[f1903]) ).
fof(f1903,plain,
( spl10_176
<=> ! [X0] : ~ member(sK1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_176])]) ).
fof(f13720,plain,
( ~ spl10_115
| ~ spl10_461 ),
inference(avatar_contradiction_clause,[],[f13707]) ).
fof(f13707,plain,
( $false
| ~ spl10_115
| ~ spl10_461 ),
inference(resolution,[],[f13652,f1054]) ).
fof(f1054,plain,
( ! [X1] : ~ member(sK2,X1)
| ~ spl10_115 ),
inference(avatar_component_clause,[],[f1053]) ).
fof(f1053,plain,
( spl10_115
<=> ! [X1] : ~ member(sK2,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_115])]) ).
fof(f13719,plain,
( spl10_99
| ~ spl10_461 ),
inference(avatar_contradiction_clause,[],[f13708]) ).
fof(f13708,plain,
( $false
| spl10_99
| ~ spl10_461 ),
inference(resolution,[],[f13652,f937]) ).
fof(f937,plain,
( ~ member(sK3,universal_class)
| spl10_99 ),
inference(avatar_component_clause,[],[f935]) ).
fof(f935,plain,
( spl10_99
<=> member(sK3,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_99])]) ).
fof(f13657,plain,
( ~ spl10_7
| ~ spl10_428
| spl10_445 ),
inference(avatar_split_clause,[],[f13410,f12631,f11768,f300]) ).
fof(f11768,plain,
( spl10_428
<=> ! [X0] :
( member(X0,sum_class(universal_class))
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_428])]) ).
fof(f13410,plain,
( ~ member(sK9,universal_class)
| ~ spl10_428
| spl10_445 ),
inference(resolution,[],[f12632,f11769]) ).
fof(f11769,plain,
( ! [X0] :
( member(X0,sum_class(universal_class))
| ~ member(X0,universal_class) )
| ~ spl10_428 ),
inference(avatar_component_clause,[],[f11768]) ).
fof(f12632,plain,
( ~ member(sK9,sum_class(universal_class))
| spl10_445 ),
inference(avatar_component_clause,[],[f12631]) ).
fof(f13656,plain,
( spl10_461
| spl10_462
| ~ spl10_66
| ~ spl10_119 ),
inference(avatar_split_clause,[],[f1099,f1071,f673,f13654,f13651]) ).
fof(f13654,plain,
( spl10_462
<=> ! [X0,X1] : ~ subclass(universal_class,compose(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_462])]) ).
fof(f1099,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,compose(X0,X1))
| member(X2,universal_class) )
| ~ spl10_66
| ~ spl10_119 ),
inference(resolution,[],[f1072,f674]) ).
fof(f13649,plain,
( spl10_460
| ~ spl10_67
| ~ spl10_119 ),
inference(avatar_split_clause,[],[f1092,f1071,f677,f13647]) ).
fof(f13647,plain,
( spl10_460
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,cross_product(X0,X1))
| member(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_460])]) ).
fof(f1092,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,cross_product(X0,X1))
| member(X2,X1) )
| ~ spl10_67
| ~ spl10_119 ),
inference(resolution,[],[f1072,f678]) ).
fof(f13645,plain,
( spl10_459
| ~ spl10_68
| ~ spl10_119 ),
inference(avatar_split_clause,[],[f1091,f1071,f681,f13643]) ).
fof(f13643,plain,
( spl10_459
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,cross_product(X0,X1))
| member(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_459])]) ).
fof(f1091,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,cross_product(X0,X1))
| member(X2,X0) )
| ~ spl10_68
| ~ spl10_119 ),
inference(resolution,[],[f1072,f682]) ).
fof(f13588,plain,
( spl10_458
| ~ spl10_361
| ~ spl10_457 ),
inference(avatar_split_clause,[],[f13584,f13581,f8770,f13586]) ).
fof(f13586,plain,
( spl10_458
<=> ! [X0,X1] :
( member(unordered_pair(sK2,unordered_pair(sK3,sK3)),sum_class(intersection(X0,X1)))
| ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X0)
| ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_458])]) ).
fof(f13584,plain,
( ! [X0,X1] :
( member(unordered_pair(sK2,unordered_pair(sK3,sK3)),sum_class(intersection(X0,X1)))
| ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X0)
| ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X1) )
| ~ spl10_361
| ~ spl10_457 ),
inference(forward_demodulation,[],[f13582,f8772]) ).
fof(f13583,plain,
( spl10_457
| ~ spl10_107
| ~ spl10_189 ),
inference(avatar_split_clause,[],[f2404,f2339,f993,f13581]) ).
fof(f2404,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X0)
| member(unordered_pair(sK0,unordered_pair(sK1,sK1)),sum_class(intersection(X0,X1)))
| ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X1) )
| ~ spl10_107
| ~ spl10_189 ),
inference(resolution,[],[f2340,f995]) ).
fof(f13577,plain,
( spl10_456
| ~ spl10_108
| ~ spl10_169 ),
inference(avatar_split_clause,[],[f1920,f1752,f1004,f13575]) ).
fof(f13575,plain,
( spl10_456
<=> ! [X0,X1] :
( ~ member(X0,sum_class(X1))
| ~ subclass(X1,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| sK7(X0,X1) = unordered_pair(sK0,sK0)
| sK7(X0,X1) = unordered_pair(sK0,unordered_pair(sK1,sK1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_456])]) ).
fof(f1920,plain,
( ! [X0,X1] :
( ~ member(X0,sum_class(X1))
| ~ subclass(X1,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| sK7(X0,X1) = unordered_pair(sK0,sK0)
| sK7(X0,X1) = unordered_pair(sK0,unordered_pair(sK1,sK1)) )
| ~ spl10_108
| ~ spl10_169 ),
inference(resolution,[],[f1753,f1005]) ).
fof(f13572,plain,
( spl10_455
| ~ spl10_314
| ~ spl10_444 ),
inference(avatar_split_clause,[],[f13017,f12625,f6012,f13570]) ).
fof(f13017,plain,
( ! [X0,X1] :
( sK6(X0,X1) = unordered_pair(sK2,sK2)
| ~ subclass(X0,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| subclass(X0,X1)
| sK6(X0,X1) = unordered_pair(sK0,unordered_pair(sK1,sK1)) )
| ~ spl10_314
| ~ spl10_444 ),
inference(forward_demodulation,[],[f12626,f6014]) ).
fof(f13242,plain,
( spl10_454
| ~ spl10_314
| ~ spl10_420 ),
inference(avatar_split_clause,[],[f13016,f11732,f6012,f13240]) ).
fof(f13016,plain,
( ! [X0] :
( sK4(X0) = unordered_pair(sK2,sK2)
| ~ subclass(X0,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| null_class = X0
| sK4(X0) = unordered_pair(sK0,unordered_pair(sK1,sK1)) )
| ~ spl10_314
| ~ spl10_420 ),
inference(forward_demodulation,[],[f11733,f6014]) ).
fof(f13162,plain,
( spl10_453
| ~ spl10_314
| ~ spl10_385 ),
inference(avatar_split_clause,[],[f13036,f10621,f6012,f13160]) ).
fof(f13160,plain,
( spl10_453
<=> ! [X0,X1] :
( member(X0,sum_class(union(X1,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,sK2)))))
| ~ member(X0,unordered_pair(sK2,unordered_pair(sK3,sK3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_453])]) ).
fof(f10621,plain,
( spl10_385
<=> ! [X0,X1] :
( ~ member(X0,unordered_pair(sK2,unordered_pair(sK3,sK3)))
| member(X0,sum_class(union(X1,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_385])]) ).
fof(f13036,plain,
( ! [X0,X1] :
( member(X0,sum_class(union(X1,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,sK2)))))
| ~ member(X0,unordered_pair(sK2,unordered_pair(sK3,sK3))) )
| ~ spl10_314
| ~ spl10_385 ),
inference(forward_demodulation,[],[f10622,f6014]) ).
fof(f10622,plain,
( ! [X0,X1] :
( member(X0,sum_class(union(X1,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0)))))
| ~ member(X0,unordered_pair(sK2,unordered_pair(sK3,sK3))) )
| ~ spl10_385 ),
inference(avatar_component_clause,[],[f10621]) ).
fof(f13157,plain,
( spl10_452
| ~ spl10_314
| ~ spl10_376 ),
inference(avatar_split_clause,[],[f13035,f9713,f6012,f13155]) ).
fof(f9713,plain,
( spl10_376
<=> ! [X0,X1] :
( member(X0,sum_class(union(X1,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0)))))
| ~ member(X0,unordered_pair(sK0,unordered_pair(sK1,sK1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_376])]) ).
fof(f13035,plain,
( ! [X0,X1] :
( member(X0,sum_class(union(X1,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,sK2)))))
| ~ member(X0,unordered_pair(sK0,unordered_pair(sK1,sK1))) )
| ~ spl10_314
| ~ spl10_376 ),
inference(forward_demodulation,[],[f9714,f6014]) ).
fof(f9714,plain,
( ! [X0,X1] :
( member(X0,sum_class(union(X1,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0)))))
| ~ member(X0,unordered_pair(sK0,unordered_pair(sK1,sK1))) )
| ~ spl10_376 ),
inference(avatar_component_clause,[],[f9713]) ).
fof(f13059,plain,
( ~ spl10_362
| ~ spl10_314
| spl10_363 ),
inference(avatar_split_clause,[],[f10311,f8780,f6012,f8774]) ).
fof(f10311,plain,
( unordered_pair(sK0,unordered_pair(sK1,sK1)) != unordered_pair(sK2,sK2)
| ~ spl10_314
| spl10_363 ),
inference(forward_demodulation,[],[f8781,f6014]) ).
fof(f13010,plain,
( ~ spl10_314
| ~ spl10_362
| spl10_363 ),
inference(avatar_split_clause,[],[f10935,f8780,f8774,f6012]) ).
fof(f12660,plain,
( spl10_451
| ~ spl10_313
| ~ spl10_450 ),
inference(avatar_split_clause,[],[f12656,f12652,f6008,f12658]) ).
fof(f12658,plain,
( spl10_451
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0)),X1)
| ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0)),X0)
| member(unordered_pair(sK0,sK0),sum_class(intersection(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_451])]) ).
fof(f12652,plain,
( spl10_450
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X0)
| member(unordered_pair(sK0,sK0),sum_class(intersection(X0,X1)))
| ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_450])]) ).
fof(f12656,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0)),X1)
| ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0)),X0)
| member(unordered_pair(sK0,sK0),sum_class(intersection(X0,X1))) )
| ~ spl10_313
| ~ spl10_450 ),
inference(forward_demodulation,[],[f12655,f6010]) ).
fof(f12655,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0)),X0)
| member(unordered_pair(sK0,sK0),sum_class(intersection(X0,X1)))
| ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X1) )
| ~ spl10_313
| ~ spl10_450 ),
inference(forward_demodulation,[],[f12653,f6010]) ).
fof(f12653,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X1)
| member(unordered_pair(sK0,sK0),sum_class(intersection(X0,X1)))
| ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X0) )
| ~ spl10_450 ),
inference(avatar_component_clause,[],[f12652]) ).
fof(f12654,plain,
( spl10_450
| ~ spl10_103
| ~ spl10_189 ),
inference(avatar_split_clause,[],[f2403,f2339,f961,f12652]) ).
fof(f2403,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X0)
| member(unordered_pair(sK0,sK0),sum_class(intersection(X0,X1)))
| ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X1) )
| ~ spl10_103
| ~ spl10_189 ),
inference(resolution,[],[f2340,f963]) ).
fof(f12650,plain,
( spl10_449
| ~ spl10_95
| ~ spl10_179 ),
inference(avatar_split_clause,[],[f2177,f2099,f891,f12648]) ).
fof(f12648,plain,
( spl10_449
<=> ! [X0,X1] :
( ~ member(X0,sum_class(intersection(universal_class,X1)))
| sK0 = second(unordered_pair(unordered_pair(sK7(X0,intersection(universal_class,X1)),sK7(X0,intersection(universal_class,X1))),unordered_pair(sK7(X0,intersection(universal_class,X1)),unordered_pair(sK0,sK0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_449])]) ).
fof(f2177,plain,
( ! [X0,X1] :
( ~ member(X0,sum_class(intersection(universal_class,X1)))
| sK0 = second(unordered_pair(unordered_pair(sK7(X0,intersection(universal_class,X1)),sK7(X0,intersection(universal_class,X1))),unordered_pair(sK7(X0,intersection(universal_class,X1)),unordered_pair(sK0,sK0)))) )
| ~ spl10_95
| ~ spl10_179 ),
inference(resolution,[],[f2100,f892]) ).
fof(f12646,plain,
( spl10_448
| ~ spl10_95
| ~ spl10_178 ),
inference(avatar_split_clause,[],[f2146,f2095,f891,f12644]) ).
fof(f12644,plain,
( spl10_448
<=> ! [X0,X1] :
( ~ member(X0,sum_class(intersection(X1,universal_class)))
| sK0 = second(unordered_pair(unordered_pair(sK7(X0,intersection(X1,universal_class)),sK7(X0,intersection(X1,universal_class))),unordered_pair(sK7(X0,intersection(X1,universal_class)),unordered_pair(sK0,sK0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_448])]) ).
fof(f2146,plain,
( ! [X0,X1] :
( ~ member(X0,sum_class(intersection(X1,universal_class)))
| sK0 = second(unordered_pair(unordered_pair(sK7(X0,intersection(X1,universal_class)),sK7(X0,intersection(X1,universal_class))),unordered_pair(sK7(X0,intersection(X1,universal_class)),unordered_pair(sK0,sK0)))) )
| ~ spl10_95
| ~ spl10_178 ),
inference(resolution,[],[f2096,f892]) ).
fof(f12642,plain,
( spl10_447
| ~ spl10_95
| ~ spl10_177 ),
inference(avatar_split_clause,[],[f2133,f2091,f891,f12640]) ).
fof(f12640,plain,
( spl10_447
<=> ! [X2,X0,X1] :
( ~ member(X0,sum_class(unordered_pair(X1,X2)))
| sK0 = second(unordered_pair(unordered_pair(sK7(X0,unordered_pair(X1,X2)),sK7(X0,unordered_pair(X1,X2))),unordered_pair(sK7(X0,unordered_pair(X1,X2)),unordered_pair(sK0,sK0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_447])]) ).
fof(f2133,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum_class(unordered_pair(X1,X2)))
| sK0 = second(unordered_pair(unordered_pair(sK7(X0,unordered_pair(X1,X2)),sK7(X0,unordered_pair(X1,X2))),unordered_pair(sK7(X0,unordered_pair(X1,X2)),unordered_pair(sK0,sK0)))) )
| ~ spl10_95
| ~ spl10_177 ),
inference(resolution,[],[f2092,f892]) ).
fof(f12638,plain,
( spl10_445
| ~ spl10_446
| ~ spl10_111
| ~ spl10_422 ),
inference(avatar_split_clause,[],[f12472,f11742,f1031,f12635,f12631]) ).
fof(f12635,plain,
( spl10_446
<=> subclass(universal_class,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_446])]) ).
fof(f1031,plain,
( spl10_111
<=> ! [X0] :
( member(sK9,X0)
| ~ subclass(universal_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_111])]) ).
fof(f11742,plain,
( spl10_422
<=> ! [X0] :
( subclass(X0,sum_class(universal_class))
| ~ subclass(X0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_422])]) ).
fof(f12472,plain,
( ~ subclass(universal_class,sK0)
| member(sK9,sum_class(universal_class))
| ~ spl10_111
| ~ spl10_422 ),
inference(resolution,[],[f11743,f1032]) ).
fof(f1032,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| member(sK9,X0) )
| ~ spl10_111 ),
inference(avatar_component_clause,[],[f1031]) ).
fof(f11743,plain,
( ! [X0] :
( subclass(X0,sum_class(universal_class))
| ~ subclass(X0,sK0) )
| ~ spl10_422 ),
inference(avatar_component_clause,[],[f11742]) ).
fof(f12627,plain,
( spl10_444
| ~ spl10_108
| ~ spl10_145 ),
inference(avatar_split_clause,[],[f1578,f1453,f1004,f12625]) ).
fof(f1578,plain,
( ! [X0,X1] :
( ~ subclass(X0,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| subclass(X0,X1)
| sK6(X0,X1) = unordered_pair(sK0,sK0)
| sK6(X0,X1) = unordered_pair(sK0,unordered_pair(sK1,sK1)) )
| ~ spl10_108
| ~ spl10_145 ),
inference(resolution,[],[f1454,f1005]) ).
fof(f12513,plain,
( ~ spl10_442
| spl10_292
| ~ spl10_443
| ~ spl10_59
| ~ spl10_247 ),
inference(avatar_split_clause,[],[f4522,f4139,f635,f12510,f5668,f12506]) ).
fof(f12506,plain,
( spl10_442
<=> member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(complement(sum_class(universal_class)),complement(sum_class(universal_class))),universal_class)),universal_class))))),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_442])]) ).
fof(f635,plain,
( spl10_59
<=> ! [X0] :
( member(X0,sum_class(universal_class))
| ~ member(X0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_59])]) ).
fof(f4139,plain,
( spl10_247
<=> ! [X0] :
( complement(X0) = null_class
| ~ member(complement(X0),universal_class)
| ~ member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(complement(X0),complement(X0)),universal_class)),universal_class))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_247])]) ).
fof(f4522,plain,
( ~ member(complement(sum_class(universal_class)),universal_class)
| null_class = complement(sum_class(universal_class))
| ~ member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(complement(sum_class(universal_class)),complement(sum_class(universal_class))),universal_class)),universal_class))))),sK0)
| ~ spl10_59
| ~ spl10_247 ),
inference(resolution,[],[f4140,f636]) ).
fof(f636,plain,
( ! [X0] :
( member(X0,sum_class(universal_class))
| ~ member(X0,sK0) )
| ~ spl10_59 ),
inference(avatar_component_clause,[],[f635]) ).
fof(f4140,plain,
( ! [X0] :
( ~ member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(complement(X0),complement(X0)),universal_class)),universal_class))))),X0)
| ~ member(complement(X0),universal_class)
| complement(X0) = null_class )
| ~ spl10_247 ),
inference(avatar_component_clause,[],[f4139]) ).
fof(f12504,plain,
( spl10_441
| ~ spl10_96
| ~ spl10_154 ),
inference(avatar_split_clause,[],[f1638,f1489,f895,f12502]) ).
fof(f12502,plain,
( spl10_441
<=> ! [X0,X1] :
( ~ member(X0,sum_class(power_class(X1)))
| sK7(X0,power_class(X1)) = first(unordered_pair(unordered_pair(sK7(X0,power_class(X1)),sK7(X0,power_class(X1))),unordered_pair(sK7(X0,power_class(X1)),unordered_pair(sK0,sK0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_441])]) ).
fof(f1638,plain,
( ! [X0,X1] :
( ~ member(X0,sum_class(power_class(X1)))
| sK7(X0,power_class(X1)) = first(unordered_pair(unordered_pair(sK7(X0,power_class(X1)),sK7(X0,power_class(X1))),unordered_pair(sK7(X0,power_class(X1)),unordered_pair(sK0,sK0)))) )
| ~ spl10_96
| ~ spl10_154 ),
inference(resolution,[],[f1490,f896]) ).
fof(f12500,plain,
( spl10_440
| ~ spl10_96
| ~ spl10_152 ),
inference(avatar_split_clause,[],[f1629,f1481,f895,f12498]) ).
fof(f12498,plain,
( spl10_440
<=> ! [X0,X1] :
( ~ member(X0,sum_class(domain_of(X1)))
| sK7(X0,domain_of(X1)) = first(unordered_pair(unordered_pair(sK7(X0,domain_of(X1)),sK7(X0,domain_of(X1))),unordered_pair(sK7(X0,domain_of(X1)),unordered_pair(sK0,sK0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_440])]) ).
fof(f1629,plain,
( ! [X0,X1] :
( ~ member(X0,sum_class(domain_of(X1)))
| sK7(X0,domain_of(X1)) = first(unordered_pair(unordered_pair(sK7(X0,domain_of(X1)),sK7(X0,domain_of(X1))),unordered_pair(sK7(X0,domain_of(X1)),unordered_pair(sK0,sK0)))) )
| ~ spl10_96
| ~ spl10_152 ),
inference(resolution,[],[f1482,f896]) ).
fof(f12496,plain,
( spl10_439
| ~ spl10_96
| ~ spl10_151 ),
inference(avatar_split_clause,[],[f1621,f1477,f895,f12494]) ).
fof(f12494,plain,
( spl10_439
<=> ! [X0,X1] :
( ~ member(X0,sum_class(complement(X1)))
| sK7(X0,complement(X1)) = first(unordered_pair(unordered_pair(sK7(X0,complement(X1)),sK7(X0,complement(X1))),unordered_pair(sK7(X0,complement(X1)),unordered_pair(sK0,sK0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_439])]) ).
fof(f1621,plain,
( ! [X0,X1] :
( ~ member(X0,sum_class(complement(X1)))
| sK7(X0,complement(X1)) = first(unordered_pair(unordered_pair(sK7(X0,complement(X1)),sK7(X0,complement(X1))),unordered_pair(sK7(X0,complement(X1)),unordered_pair(sK0,sK0)))) )
| ~ spl10_96
| ~ spl10_151 ),
inference(resolution,[],[f1478,f896]) ).
fof(f11844,plain,
( spl10_438
| ~ spl10_244
| ~ spl10_317 ),
inference(avatar_split_clause,[],[f11829,f6188,f4115,f11841]) ).
fof(f11841,plain,
( spl10_438
<=> member(identity_relation,sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_438])]) ).
fof(f4115,plain,
( spl10_244
<=> null_class = identity_relation ),
introduced(avatar_definition,[new_symbols(naming,[spl10_244])]) ).
fof(f6188,plain,
( spl10_317
<=> member(null_class,sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_317])]) ).
fof(f11829,plain,
( member(identity_relation,sK9)
| ~ spl10_244
| ~ spl10_317 ),
inference(superposition,[],[f6189,f4117]) ).
fof(f4117,plain,
( null_class = identity_relation
| ~ spl10_244 ),
inference(avatar_component_clause,[],[f4115]) ).
fof(f6189,plain,
( member(null_class,sK9)
| ~ spl10_317 ),
inference(avatar_component_clause,[],[f6188]) ).
fof(f11809,plain,
( spl10_437
| ~ spl10_119
| ~ spl10_245 ),
inference(avatar_split_clause,[],[f4470,f4119,f1071,f11807]) ).
fof(f11807,plain,
( spl10_437
<=> ! [X0] :
( member(sK4(identity_relation),X0)
| ~ subclass(universal_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_437])]) ).
fof(f4470,plain,
( ! [X0] :
( member(sK4(identity_relation),X0)
| ~ subclass(universal_class,X0) )
| ~ spl10_119
| ~ spl10_245 ),
inference(superposition,[],[f1072,f4121]) ).
fof(f11805,plain,
( spl10_436
| ~ spl10_5
| ~ spl10_169 ),
inference(avatar_split_clause,[],[f1925,f1752,f292,f11803]) ).
fof(f11803,plain,
( spl10_436
<=> ! [X0,X1] :
( ~ member(X0,sum_class(X1))
| ~ subclass(X1,null_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_436])]) ).
fof(f1925,plain,
( ! [X0,X1] :
( ~ member(X0,sum_class(X1))
| ~ subclass(X1,null_class) )
| ~ spl10_5
| ~ spl10_169 ),
inference(resolution,[],[f1753,f293]) ).
fof(f11800,plain,
( spl10_435
| ~ spl10_164
| ~ spl10_166 ),
inference(avatar_split_clause,[],[f1893,f1740,f1732,f11798]) ).
fof(f11798,plain,
( spl10_435
<=> ! [X2,X0,X1] : subclass(unordered_pair(X0,X1),union(universal_class,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_435])]) ).
fof(f1740,plain,
( spl10_166
<=> ! [X2,X0,X1] :
( member(sK6(unordered_pair(X0,X1),X2),universal_class)
| subclass(unordered_pair(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_166])]) ).
fof(f1893,plain,
( ! [X2,X0,X1] : subclass(unordered_pair(X0,X1),union(universal_class,X2))
| ~ spl10_164
| ~ spl10_166 ),
inference(duplicate_literal_removal,[],[f1883]) ).
fof(f1883,plain,
( ! [X2,X0,X1] :
( subclass(unordered_pair(X0,X1),union(universal_class,X2))
| subclass(unordered_pair(X0,X1),union(universal_class,X2)) )
| ~ spl10_164
| ~ spl10_166 ),
inference(resolution,[],[f1741,f1733]) ).
fof(f1741,plain,
( ! [X2,X0,X1] :
( member(sK6(unordered_pair(X0,X1),X2),universal_class)
| subclass(unordered_pair(X0,X1),X2) )
| ~ spl10_166 ),
inference(avatar_component_clause,[],[f1740]) ).
fof(f11795,plain,
( spl10_434
| ~ spl10_165
| ~ spl10_166 ),
inference(avatar_split_clause,[],[f1892,f1740,f1736,f11793]) ).
fof(f11793,plain,
( spl10_434
<=> ! [X2,X0,X1] : subclass(unordered_pair(X0,X1),union(X2,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_434])]) ).
fof(f1892,plain,
( ! [X2,X0,X1] : subclass(unordered_pair(X0,X1),union(X2,universal_class))
| ~ spl10_165
| ~ spl10_166 ),
inference(duplicate_literal_removal,[],[f1884]) ).
fof(f1884,plain,
( ! [X2,X0,X1] :
( subclass(unordered_pair(X0,X1),union(X2,universal_class))
| subclass(unordered_pair(X0,X1),union(X2,universal_class)) )
| ~ spl10_165
| ~ spl10_166 ),
inference(resolution,[],[f1741,f1737]) ).
fof(f11791,plain,
( spl10_433
| ~ spl10_162
| ~ spl10_165 ),
inference(avatar_split_clause,[],[f1880,f1736,f1724,f11789]) ).
fof(f11789,plain,
( spl10_433
<=> ! [X2,X0,X1] : subclass(intersection(X0,X1),union(X2,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_433])]) ).
fof(f1880,plain,
( ! [X2,X0,X1] : subclass(intersection(X0,X1),union(X2,X0))
| ~ spl10_162
| ~ spl10_165 ),
inference(duplicate_literal_removal,[],[f1861]) ).
fof(f1861,plain,
( ! [X2,X0,X1] :
( subclass(intersection(X0,X1),union(X2,X0))
| subclass(intersection(X0,X1),union(X2,X0)) )
| ~ spl10_162
| ~ spl10_165 ),
inference(resolution,[],[f1737,f1725]) ).
fof(f11787,plain,
( spl10_432
| ~ spl10_163
| ~ spl10_165 ),
inference(avatar_split_clause,[],[f1879,f1736,f1728,f11785]) ).
fof(f11785,plain,
( spl10_432
<=> ! [X2,X0,X1] : subclass(intersection(X0,X1),union(X2,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_432])]) ).
fof(f1879,plain,
( ! [X2,X0,X1] : subclass(intersection(X0,X1),union(X2,X1))
| ~ spl10_163
| ~ spl10_165 ),
inference(duplicate_literal_removal,[],[f1862]) ).
fof(f1862,plain,
( ! [X2,X0,X1] :
( subclass(intersection(X0,X1),union(X2,X1))
| subclass(intersection(X0,X1),union(X2,X1)) )
| ~ spl10_163
| ~ spl10_165 ),
inference(resolution,[],[f1737,f1729]) ).
fof(f11783,plain,
( spl10_431
| ~ spl10_162
| ~ spl10_164 ),
inference(avatar_split_clause,[],[f1858,f1732,f1724,f11781]) ).
fof(f11781,plain,
( spl10_431
<=> ! [X2,X0,X1] : subclass(intersection(X0,X1),union(X0,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_431])]) ).
fof(f1858,plain,
( ! [X2,X0,X1] : subclass(intersection(X0,X1),union(X0,X2))
| ~ spl10_162
| ~ spl10_164 ),
inference(duplicate_literal_removal,[],[f1839]) ).
fof(f1839,plain,
( ! [X2,X0,X1] :
( subclass(intersection(X0,X1),union(X0,X2))
| subclass(intersection(X0,X1),union(X0,X2)) )
| ~ spl10_162
| ~ spl10_164 ),
inference(resolution,[],[f1733,f1725]) ).
fof(f11779,plain,
( ~ spl10_314
| ~ spl10_313
| spl10_318 ),
inference(avatar_split_clause,[],[f10532,f6193,f6008,f6012]) ).
fof(f6193,plain,
( spl10_318
<=> unordered_pair(sK2,sK2) = unordered_pair(sK2,unordered_pair(sK3,sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_318])]) ).
fof(f10532,plain,
( unordered_pair(sK0,sK0) != unordered_pair(sK2,sK2)
| ~ spl10_313
| spl10_318 ),
inference(superposition,[],[f6195,f6010]) ).
fof(f6195,plain,
( unordered_pair(sK2,sK2) != unordered_pair(sK2,unordered_pair(sK3,sK3))
| spl10_318 ),
inference(avatar_component_clause,[],[f6193]) ).
fof(f11778,plain,
( spl10_430
| ~ spl10_163
| ~ spl10_164 ),
inference(avatar_split_clause,[],[f1857,f1732,f1728,f11776]) ).
fof(f11776,plain,
( spl10_430
<=> ! [X2,X0,X1] : subclass(intersection(X0,X1),union(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_430])]) ).
fof(f1857,plain,
( ! [X2,X0,X1] : subclass(intersection(X0,X1),union(X1,X2))
| ~ spl10_163
| ~ spl10_164 ),
inference(duplicate_literal_removal,[],[f1840]) ).
fof(f1840,plain,
( ! [X2,X0,X1] :
( subclass(intersection(X0,X1),union(X1,X2))
| subclass(intersection(X0,X1),union(X1,X2)) )
| ~ spl10_163
| ~ spl10_164 ),
inference(resolution,[],[f1733,f1729]) ).
fof(f11774,plain,
( spl10_429
| ~ spl10_121
| ~ spl10_139 ),
inference(avatar_split_clause,[],[f1416,f1255,f1144,f11772]) ).
fof(f11772,plain,
( spl10_429
<=> ! [X0] :
( ~ subclass(universal_class,X0)
| complement(X0) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_429])]) ).
fof(f1416,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| complement(X0) = null_class )
| ~ spl10_121
| ~ spl10_139 ),
inference(duplicate_literal_removal,[],[f1391]) ).
fof(f1391,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| complement(X0) = null_class
| complement(X0) = null_class )
| ~ spl10_121
| ~ spl10_139 ),
inference(resolution,[],[f1256,f1145]) ).
fof(f11770,plain,
( spl10_428
| ~ spl10_40
| ~ spl10_123 ),
inference(avatar_split_clause,[],[f1179,f1163,f450,f11768]) ).
fof(f450,plain,
( spl10_40
<=> ! [X2,X1] :
( member(X2,unordered_pair(X1,X2))
| ~ member(X2,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_40])]) ).
fof(f1179,plain,
( ! [X0] :
( member(X0,sum_class(universal_class))
| ~ member(X0,universal_class) )
| ~ spl10_40
| ~ spl10_123 ),
inference(resolution,[],[f1164,f451]) ).
fof(f451,plain,
( ! [X2,X1] :
( member(X2,unordered_pair(X1,X2))
| ~ member(X2,universal_class) )
| ~ spl10_40 ),
inference(avatar_component_clause,[],[f450]) ).
fof(f11766,plain,
( ~ spl10_427
| spl10_233
| ~ spl10_11
| ~ spl10_118 ),
inference(avatar_split_clause,[],[f1087,f1067,f319,f3853,f11763]) ).
fof(f11763,plain,
( spl10_427
<=> inductive(successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_427])]) ).
fof(f319,plain,
( spl10_11
<=> subclass(successor_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_11])]) ).
fof(f1087,plain,
( member(null_class,cross_product(universal_class,universal_class))
| ~ inductive(successor_relation)
| ~ spl10_11
| ~ spl10_118 ),
inference(resolution,[],[f1068,f321]) ).
fof(f321,plain,
( subclass(successor_relation,cross_product(universal_class,universal_class))
| ~ spl10_11 ),
inference(avatar_component_clause,[],[f319]) ).
fof(f11761,plain,
( ~ spl10_426
| spl10_233
| ~ spl10_10
| ~ spl10_118 ),
inference(avatar_split_clause,[],[f1082,f1067,f314,f3853,f11758]) ).
fof(f11758,plain,
( spl10_426
<=> inductive(element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_426])]) ).
fof(f314,plain,
( spl10_10
<=> subclass(element_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_10])]) ).
fof(f1082,plain,
( member(null_class,cross_product(universal_class,universal_class))
| ~ inductive(element_relation)
| ~ spl10_10
| ~ spl10_118 ),
inference(resolution,[],[f1068,f316]) ).
fof(f316,plain,
( subclass(element_relation,cross_product(universal_class,universal_class))
| ~ spl10_10 ),
inference(avatar_component_clause,[],[f314]) ).
fof(f11756,plain,
( spl10_425
| ~ spl10_418
| ~ spl10_108
| ~ spl10_140 ),
inference(avatar_split_clause,[],[f6408,f1259,f1004,f11641,f11754]) ).
fof(f11754,plain,
( spl10_425
<=> ! [X0] :
( ~ member(X0,identity_relation)
| sK5(X0) = unordered_pair(sK0,unordered_pair(sK1,sK1))
| sK5(X0) = unordered_pair(sK0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_425])]) ).
fof(f11641,plain,
( spl10_418
<=> subclass(universal_class,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_418])]) ).
fof(f6408,plain,
( ! [X0] :
( ~ subclass(universal_class,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| ~ member(X0,identity_relation)
| sK5(X0) = unordered_pair(sK0,sK0)
| sK5(X0) = unordered_pair(sK0,unordered_pair(sK1,sK1)) )
| ~ spl10_108
| ~ spl10_140 ),
inference(resolution,[],[f1260,f1005]) ).
fof(f11752,plain,
( spl10_424
| ~ spl10_418
| ~ spl10_108
| ~ spl10_139 ),
inference(avatar_split_clause,[],[f1401,f1255,f1004,f11641,f11750]) ).
fof(f11750,plain,
( spl10_424
<=> ! [X0] :
( null_class = X0
| sK4(X0) = unordered_pair(sK0,unordered_pair(sK1,sK1))
| sK4(X0) = unordered_pair(sK0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_424])]) ).
fof(f1401,plain,
( ! [X0] :
( ~ subclass(universal_class,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| null_class = X0
| sK4(X0) = unordered_pair(sK0,sK0)
| sK4(X0) = unordered_pair(sK0,unordered_pair(sK1,sK1)) )
| ~ spl10_108
| ~ spl10_139 ),
inference(resolution,[],[f1256,f1005]) ).
fof(f11748,plain,
( spl10_423
| ~ spl10_418
| ~ spl10_108
| ~ spl10_137 ),
inference(avatar_split_clause,[],[f1375,f1246,f1004,f11641,f11746]) ).
fof(f11746,plain,
( spl10_423
<=> ! [X0] :
( ~ member(X0,universal_class)
| power_class(X0) = unordered_pair(sK0,unordered_pair(sK1,sK1))
| power_class(X0) = unordered_pair(sK0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_423])]) ).
fof(f1375,plain,
( ! [X0] :
( ~ subclass(universal_class,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| ~ member(X0,universal_class)
| power_class(X0) = unordered_pair(sK0,sK0)
| power_class(X0) = unordered_pair(sK0,unordered_pair(sK1,sK1)) )
| ~ spl10_108
| ~ spl10_137 ),
inference(resolution,[],[f1247,f1005]) ).
fof(f11744,plain,
( spl10_422
| ~ spl10_145
| ~ spl10_241 ),
inference(avatar_split_clause,[],[f4793,f4103,f1453,f11742]) ).
fof(f4793,plain,
( ! [X0] :
( subclass(X0,sum_class(universal_class))
| ~ subclass(X0,sK0) )
| ~ spl10_145
| ~ spl10_241 ),
inference(duplicate_literal_removal,[],[f4792]) ).
fof(f4792,plain,
( ! [X0] :
( subclass(X0,sum_class(universal_class))
| ~ subclass(X0,sK0)
| subclass(X0,sum_class(universal_class)) )
| ~ spl10_145
| ~ spl10_241 ),
inference(resolution,[],[f4104,f1454]) ).
fof(f11740,plain,
( spl10_421
| ~ spl10_418
| ~ spl10_108
| ~ spl10_136 ),
inference(avatar_split_clause,[],[f1350,f1242,f1004,f11641,f11738]) ).
fof(f11738,plain,
( spl10_421
<=> ! [X0] :
( ~ member(X0,universal_class)
| sum_class(X0) = unordered_pair(sK0,unordered_pair(sK1,sK1))
| sum_class(X0) = unordered_pair(sK0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_421])]) ).
fof(f1350,plain,
( ! [X0] :
( ~ subclass(universal_class,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| ~ member(X0,universal_class)
| sum_class(X0) = unordered_pair(sK0,sK0)
| sum_class(X0) = unordered_pair(sK0,unordered_pair(sK1,sK1)) )
| ~ spl10_108
| ~ spl10_136 ),
inference(resolution,[],[f1243,f1005]) ).
fof(f11734,plain,
( spl10_420
| ~ spl10_108
| ~ spl10_135 ),
inference(avatar_split_clause,[],[f1324,f1238,f1004,f11732]) ).
fof(f1324,plain,
( ! [X0] :
( ~ subclass(X0,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| null_class = X0
| sK4(X0) = unordered_pair(sK0,sK0)
| sK4(X0) = unordered_pair(sK0,unordered_pair(sK1,sK1)) )
| ~ spl10_108
| ~ spl10_135 ),
inference(resolution,[],[f1239,f1005]) ).
fof(f11649,plain,
( spl10_419
| ~ spl10_96
| ~ spl10_169 ),
inference(avatar_split_clause,[],[f1914,f1752,f895,f11647]) ).
fof(f11647,plain,
( spl10_419
<=> ! [X0,X1] :
( ~ member(X0,sum_class(X1))
| ~ subclass(X1,universal_class)
| sK7(X0,X1) = first(unordered_pair(unordered_pair(sK7(X0,X1),sK7(X0,X1)),unordered_pair(sK7(X0,X1),unordered_pair(sK0,sK0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_419])]) ).
fof(f1914,plain,
( ! [X0,X1] :
( ~ member(X0,sum_class(X1))
| ~ subclass(X1,universal_class)
| sK7(X0,X1) = first(unordered_pair(unordered_pair(sK7(X0,X1),sK7(X0,X1)),unordered_pair(sK7(X0,X1),unordered_pair(sK0,sK0)))) )
| ~ spl10_96
| ~ spl10_169 ),
inference(resolution,[],[f1753,f896]) ).
fof(f11644,plain,
( spl10_417
| ~ spl10_418
| ~ spl10_108
| ~ spl10_119 ),
inference(avatar_split_clause,[],[f1118,f1071,f1004,f11641,f11638]) ).
fof(f11638,plain,
( spl10_417
<=> ! [X0,X1] :
( unordered_pair(X0,X1) = unordered_pair(sK0,sK0)
| unordered_pair(X0,X1) = unordered_pair(sK0,unordered_pair(sK1,sK1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_417])]) ).
fof(f1118,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| unordered_pair(X0,X1) = unordered_pair(sK0,sK0)
| unordered_pair(X0,X1) = unordered_pair(sK0,unordered_pair(sK1,sK1)) )
| ~ spl10_108
| ~ spl10_119 ),
inference(resolution,[],[f1072,f1005]) ).
fof(f11511,plain,
( spl10_416
| ~ spl10_95
| ~ spl10_154 ),
inference(avatar_split_clause,[],[f1639,f1489,f891,f11509]) ).
fof(f11509,plain,
( spl10_416
<=> ! [X0,X1] :
( ~ member(X0,sum_class(power_class(X1)))
| sK0 = second(unordered_pair(unordered_pair(sK7(X0,power_class(X1)),sK7(X0,power_class(X1))),unordered_pair(sK7(X0,power_class(X1)),unordered_pair(sK0,sK0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_416])]) ).
fof(f1639,plain,
( ! [X0,X1] :
( ~ member(X0,sum_class(power_class(X1)))
| sK0 = second(unordered_pair(unordered_pair(sK7(X0,power_class(X1)),sK7(X0,power_class(X1))),unordered_pair(sK7(X0,power_class(X1)),unordered_pair(sK0,sK0)))) )
| ~ spl10_95
| ~ spl10_154 ),
inference(resolution,[],[f1490,f892]) ).
fof(f11497,plain,
( spl10_415
| ~ spl10_95
| ~ spl10_152 ),
inference(avatar_split_clause,[],[f1630,f1481,f891,f11495]) ).
fof(f11495,plain,
( spl10_415
<=> ! [X0,X1] :
( ~ member(X0,sum_class(domain_of(X1)))
| sK0 = second(unordered_pair(unordered_pair(sK7(X0,domain_of(X1)),sK7(X0,domain_of(X1))),unordered_pair(sK7(X0,domain_of(X1)),unordered_pair(sK0,sK0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_415])]) ).
fof(f1630,plain,
( ! [X0,X1] :
( ~ member(X0,sum_class(domain_of(X1)))
| sK0 = second(unordered_pair(unordered_pair(sK7(X0,domain_of(X1)),sK7(X0,domain_of(X1))),unordered_pair(sK7(X0,domain_of(X1)),unordered_pair(sK0,sK0)))) )
| ~ spl10_95
| ~ spl10_152 ),
inference(resolution,[],[f1482,f892]) ).
fof(f11493,plain,
( spl10_414
| ~ spl10_95
| ~ spl10_151 ),
inference(avatar_split_clause,[],[f1622,f1477,f891,f11491]) ).
fof(f11491,plain,
( spl10_414
<=> ! [X0,X1] :
( ~ member(X0,sum_class(complement(X1)))
| sK0 = second(unordered_pair(unordered_pair(sK7(X0,complement(X1)),sK7(X0,complement(X1))),unordered_pair(sK7(X0,complement(X1)),unordered_pair(sK0,sK0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_414])]) ).
fof(f1622,plain,
( ! [X0,X1] :
( ~ member(X0,sum_class(complement(X1)))
| sK0 = second(unordered_pair(unordered_pair(sK7(X0,complement(X1)),sK7(X0,complement(X1))),unordered_pair(sK7(X0,complement(X1)),unordered_pair(sK0,sK0)))) )
| ~ spl10_95
| ~ spl10_151 ),
inference(resolution,[],[f1478,f892]) ).
fof(f11489,plain,
( spl10_413
| ~ spl10_96
| ~ spl10_145 ),
inference(avatar_split_clause,[],[f1571,f1453,f895,f11487]) ).
fof(f11487,plain,
( spl10_413
<=> ! [X0,X1] :
( ~ subclass(X0,universal_class)
| subclass(X0,X1)
| sK6(X0,X1) = first(unordered_pair(unordered_pair(sK6(X0,X1),sK6(X0,X1)),unordered_pair(sK6(X0,X1),unordered_pair(sK0,sK0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_413])]) ).
fof(f1571,plain,
( ! [X0,X1] :
( ~ subclass(X0,universal_class)
| subclass(X0,X1)
| sK6(X0,X1) = first(unordered_pair(unordered_pair(sK6(X0,X1),sK6(X0,X1)),unordered_pair(sK6(X0,X1),unordered_pair(sK0,sK0)))) )
| ~ spl10_96
| ~ spl10_145 ),
inference(resolution,[],[f1454,f896]) ).
fof(f11404,plain,
( spl10_412
| ~ spl10_95
| ~ spl10_169 ),
inference(avatar_split_clause,[],[f1915,f1752,f891,f11402]) ).
fof(f11402,plain,
( spl10_412
<=> ! [X0,X1] :
( ~ member(X0,sum_class(X1))
| ~ subclass(X1,universal_class)
| sK0 = second(unordered_pair(unordered_pair(sK7(X0,X1),sK7(X0,X1)),unordered_pair(sK7(X0,X1),unordered_pair(sK0,sK0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_412])]) ).
fof(f1915,plain,
( ! [X0,X1] :
( ~ member(X0,sum_class(X1))
| ~ subclass(X1,universal_class)
| sK0 = second(unordered_pair(unordered_pair(sK7(X0,X1),sK7(X0,X1)),unordered_pair(sK7(X0,X1),unordered_pair(sK0,sK0)))) )
| ~ spl10_95
| ~ spl10_169 ),
inference(resolution,[],[f1753,f892]) ).
fof(f11242,plain,
( ~ spl10_410
| spl10_411
| ~ spl10_5
| ~ spl10_199 ),
inference(avatar_split_clause,[],[f2705,f2556,f292,f11240,f11236]) ).
fof(f11236,plain,
( spl10_410
<=> subclass(identity_relation,null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_410])]) ).
fof(f11240,plain,
( spl10_411
<=> ! [X0] : ~ member(X0,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_411])]) ).
fof(f2705,plain,
( ! [X0] :
( ~ member(X0,universal_class)
| ~ subclass(identity_relation,null_class) )
| ~ spl10_5
| ~ spl10_199 ),
inference(resolution,[],[f2557,f293]) ).
fof(f11233,plain,
( spl10_409
| ~ spl10_125
| ~ spl10_165 ),
inference(avatar_split_clause,[],[f1877,f1736,f1195,f11231]) ).
fof(f11231,plain,
( spl10_409
<=> ! [X0,X1] : subclass(complement(X0),union(X1,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_409])]) ).
fof(f1877,plain,
( ! [X0,X1] : subclass(complement(X0),union(X1,universal_class))
| ~ spl10_125
| ~ spl10_165 ),
inference(duplicate_literal_removal,[],[f1864]) ).
fof(f1864,plain,
( ! [X0,X1] :
( subclass(complement(X0),union(X1,universal_class))
| subclass(complement(X0),union(X1,universal_class)) )
| ~ spl10_125
| ~ spl10_165 ),
inference(resolution,[],[f1737,f1196]) ).
fof(f11228,plain,
( spl10_408
| ~ spl10_126
| ~ spl10_165 ),
inference(avatar_split_clause,[],[f1876,f1736,f1199,f11226]) ).
fof(f11226,plain,
( spl10_408
<=> ! [X0,X1] : subclass(domain_of(X0),union(X1,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_408])]) ).
fof(f1876,plain,
( ! [X0,X1] : subclass(domain_of(X0),union(X1,universal_class))
| ~ spl10_126
| ~ spl10_165 ),
inference(duplicate_literal_removal,[],[f1865]) ).
fof(f1865,plain,
( ! [X0,X1] :
( subclass(domain_of(X0),union(X1,universal_class))
| subclass(domain_of(X0),union(X1,universal_class)) )
| ~ spl10_126
| ~ spl10_165 ),
inference(resolution,[],[f1737,f1200]) ).
fof(f11223,plain,
( spl10_407
| ~ spl10_128
| ~ spl10_165 ),
inference(avatar_split_clause,[],[f1875,f1736,f1207,f11221]) ).
fof(f11221,plain,
( spl10_407
<=> ! [X0,X1] : subclass(power_class(X0),union(X1,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_407])]) ).
fof(f1875,plain,
( ! [X0,X1] : subclass(power_class(X0),union(X1,universal_class))
| ~ spl10_128
| ~ spl10_165 ),
inference(duplicate_literal_removal,[],[f1866]) ).
fof(f1866,plain,
( ! [X0,X1] :
( subclass(power_class(X0),union(X1,universal_class))
| subclass(power_class(X0),union(X1,universal_class)) )
| ~ spl10_128
| ~ spl10_165 ),
inference(resolution,[],[f1737,f1208]) ).
fof(f11218,plain,
( spl10_406
| ~ spl10_125
| ~ spl10_164 ),
inference(avatar_split_clause,[],[f1855,f1732,f1195,f11216]) ).
fof(f11216,plain,
( spl10_406
<=> ! [X0,X1] : subclass(complement(X0),union(universal_class,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_406])]) ).
fof(f1855,plain,
( ! [X0,X1] : subclass(complement(X0),union(universal_class,X1))
| ~ spl10_125
| ~ spl10_164 ),
inference(duplicate_literal_removal,[],[f1842]) ).
fof(f1842,plain,
( ! [X0,X1] :
( subclass(complement(X0),union(universal_class,X1))
| subclass(complement(X0),union(universal_class,X1)) )
| ~ spl10_125
| ~ spl10_164 ),
inference(resolution,[],[f1733,f1196]) ).
fof(f11213,plain,
( spl10_405
| ~ spl10_126
| ~ spl10_164 ),
inference(avatar_split_clause,[],[f1854,f1732,f1199,f11211]) ).
fof(f11211,plain,
( spl10_405
<=> ! [X0,X1] : subclass(domain_of(X0),union(universal_class,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_405])]) ).
fof(f1854,plain,
( ! [X0,X1] : subclass(domain_of(X0),union(universal_class,X1))
| ~ spl10_126
| ~ spl10_164 ),
inference(duplicate_literal_removal,[],[f1843]) ).
fof(f1843,plain,
( ! [X0,X1] :
( subclass(domain_of(X0),union(universal_class,X1))
| subclass(domain_of(X0),union(universal_class,X1)) )
| ~ spl10_126
| ~ spl10_164 ),
inference(resolution,[],[f1733,f1200]) ).
fof(f11208,plain,
( spl10_404
| ~ spl10_128
| ~ spl10_164 ),
inference(avatar_split_clause,[],[f1853,f1732,f1207,f11206]) ).
fof(f11206,plain,
( spl10_404
<=> ! [X0,X1] : subclass(power_class(X0),union(universal_class,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_404])]) ).
fof(f1853,plain,
( ! [X0,X1] : subclass(power_class(X0),union(universal_class,X1))
| ~ spl10_128
| ~ spl10_164 ),
inference(duplicate_literal_removal,[],[f1844]) ).
fof(f1844,plain,
( ! [X0,X1] :
( subclass(power_class(X0),union(universal_class,X1))
| subclass(power_class(X0),union(universal_class,X1)) )
| ~ spl10_128
| ~ spl10_164 ),
inference(resolution,[],[f1733,f1208]) ).
fof(f11204,plain,
( spl10_403
| ~ spl10_6
| ~ spl10_148 ),
inference(avatar_split_clause,[],[f1604,f1465,f296,f11202]) ).
fof(f11202,plain,
( spl10_403
<=> ! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_403])]) ).
fof(f296,plain,
( spl10_6
<=> ! [X0] : subclass(X0,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_6])]) ).
fof(f1604,plain,
( ! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) )
| ~ spl10_6
| ~ spl10_148 ),
inference(resolution,[],[f1466,f297]) ).
fof(f297,plain,
( ! [X0] : subclass(X0,universal_class)
| ~ spl10_6 ),
inference(avatar_component_clause,[],[f296]) ).
fof(f11200,plain,
( spl10_402
| ~ spl10_5
| ~ spl10_145 ),
inference(avatar_split_clause,[],[f1584,f1453,f292,f11198]) ).
fof(f11198,plain,
( spl10_402
<=> ! [X0,X1] :
( ~ subclass(X0,null_class)
| subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_402])]) ).
fof(f1584,plain,
( ! [X0,X1] :
( ~ subclass(X0,null_class)
| subclass(X0,X1) )
| ~ spl10_5
| ~ spl10_145 ),
inference(resolution,[],[f1454,f293]) ).
fof(f11196,plain,
( spl10_401
| ~ spl10_42
| ~ spl10_43 ),
inference(avatar_split_clause,[],[f870,f486,f478,f11194]) ).
fof(f11194,plain,
( spl10_401
<=> ! [X0] :
( null_class = X0
| ~ subclass(X0,null_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_401])]) ).
fof(f478,plain,
( spl10_42
<=> ! [X0] : subclass(null_class,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_42])]) ).
fof(f870,plain,
( ! [X0] :
( null_class = X0
| ~ subclass(X0,null_class) )
| ~ spl10_42
| ~ spl10_43 ),
inference(resolution,[],[f479,f487]) ).
fof(f479,plain,
( ! [X0] : subclass(null_class,X0)
| ~ spl10_42 ),
inference(avatar_component_clause,[],[f478]) ).
fof(f11192,plain,
( spl10_400
| ~ spl10_372
| ~ spl10_381 ),
inference(avatar_split_clause,[],[f10833,f10602,f9484,f11190]) ).
fof(f11190,plain,
( spl10_400
<=> ! [X0] : member(null_class,union(X0,sK9)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_400])]) ).
fof(f10833,plain,
( ! [X0] : member(null_class,union(X0,sK9))
| ~ spl10_372
| ~ spl10_381 ),
inference(resolution,[],[f10603,f9485]) ).
fof(f11188,plain,
( spl10_399
| ~ spl10_30
| ~ spl10_45 ),
inference(avatar_split_clause,[],[f519,f494,f409,f11186]) ).
fof(f11186,plain,
( spl10_399
<=> ! [X0] :
( member(null_class,X0)
| ~ subclass(universal_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_399])]) ).
fof(f519,plain,
( ! [X0] :
( member(null_class,X0)
| ~ subclass(universal_class,X0) )
| ~ spl10_30
| ~ spl10_45 ),
inference(resolution,[],[f495,f411]) ).
fof(f11089,plain,
( spl10_398
| ~ spl10_59
| ~ spl10_243 ),
inference(avatar_split_clause,[],[f4199,f4111,f635,f11087]) ).
fof(f11087,plain,
( spl10_398
<=> ! [X0,X1] :
( ~ member(X0,universal_class)
| sK7(X1,universal_class) = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK7(X1,universal_class),sK7(X1,universal_class)))))
| ~ member(X1,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_398])]) ).
fof(f4111,plain,
( spl10_243
<=> ! [X0,X1] :
( sK7(X1,universal_class) = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK7(X1,universal_class),sK7(X1,universal_class)))))
| ~ member(X0,universal_class)
| ~ member(X1,sum_class(universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_243])]) ).
fof(f4199,plain,
( ! [X0,X1] :
( ~ member(X0,universal_class)
| sK7(X1,universal_class) = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK7(X1,universal_class),sK7(X1,universal_class)))))
| ~ member(X1,sK0) )
| ~ spl10_59
| ~ spl10_243 ),
inference(resolution,[],[f4112,f636]) ).
fof(f4112,plain,
( ! [X0,X1] :
( ~ member(X1,sum_class(universal_class))
| ~ member(X0,universal_class)
| sK7(X1,universal_class) = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK7(X1,universal_class),sK7(X1,universal_class))))) )
| ~ spl10_243 ),
inference(avatar_component_clause,[],[f4111]) ).
fof(f11085,plain,
( spl10_397
| ~ spl10_95
| ~ spl10_145 ),
inference(avatar_split_clause,[],[f1572,f1453,f891,f11083]) ).
fof(f11083,plain,
( spl10_397
<=> ! [X0,X1] :
( ~ subclass(X0,universal_class)
| subclass(X0,X1)
| sK0 = second(unordered_pair(unordered_pair(sK6(X0,X1),sK6(X0,X1)),unordered_pair(sK6(X0,X1),unordered_pair(sK0,sK0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_397])]) ).
fof(f1572,plain,
( ! [X0,X1] :
( ~ subclass(X0,universal_class)
| subclass(X0,X1)
| sK0 = second(unordered_pair(unordered_pair(sK6(X0,X1),sK6(X0,X1)),unordered_pair(sK6(X0,X1),unordered_pair(sK0,sK0)))) )
| ~ spl10_95
| ~ spl10_145 ),
inference(resolution,[],[f1454,f892]) ).
fof(f11081,plain,
( spl10_396
| ~ spl10_47
| ~ spl10_96 ),
inference(avatar_split_clause,[],[f925,f895,f502,f11079]) ).
fof(f11079,plain,
( spl10_396
<=> ! [X0] :
( sK7(X0,universal_class) = first(unordered_pair(unordered_pair(sK7(X0,universal_class),sK7(X0,universal_class)),unordered_pair(sK7(X0,universal_class),unordered_pair(sK0,sK0))))
| ~ member(X0,sum_class(universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_396])]) ).
fof(f925,plain,
( ! [X0] :
( sK7(X0,universal_class) = first(unordered_pair(unordered_pair(sK7(X0,universal_class),sK7(X0,universal_class)),unordered_pair(sK7(X0,universal_class),unordered_pair(sK0,sK0))))
| ~ member(X0,sum_class(universal_class)) )
| ~ spl10_47
| ~ spl10_96 ),
inference(resolution,[],[f896,f503]) ).
fof(f11064,plain,
( spl10_394
| ~ spl10_395
| ~ spl10_59
| ~ spl10_214 ),
inference(avatar_split_clause,[],[f3214,f3013,f635,f11061,f11058]) ).
fof(f11058,plain,
( spl10_394
<=> ! [X0,X1] :
( member(X0,sum_class(domain_of(X1)))
| ~ member(X0,sK0)
| null_class = intersection(X1,cross_product(unordered_pair(sum_class(universal_class),sum_class(universal_class)),universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_394])]) ).
fof(f3214,plain,
( ! [X0,X1] :
( ~ member(sum_class(universal_class),universal_class)
| member(X0,sum_class(domain_of(X1)))
| null_class = intersection(X1,cross_product(unordered_pair(sum_class(universal_class),sum_class(universal_class)),universal_class))
| ~ member(X0,sK0) )
| ~ spl10_59
| ~ spl10_214 ),
inference(resolution,[],[f3014,f636]) ).
fof(f11056,plain,
( spl10_393
| ~ spl10_371
| ~ spl10_381 ),
inference(avatar_split_clause,[],[f10832,f10602,f9480,f11054]) ).
fof(f11054,plain,
( spl10_393
<=> ! [X0] : member(null_class,union(sK9,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_393])]) ).
fof(f10832,plain,
( ! [X0] : member(null_class,union(sK9,X0))
| ~ spl10_371
| ~ spl10_381 ),
inference(resolution,[],[f10603,f9481]) ).
fof(f11052,plain,
( spl10_392
| ~ spl10_33
| ~ spl10_96 ),
inference(avatar_split_clause,[],[f924,f895,f422,f11050]) ).
fof(f11050,plain,
( spl10_392
<=> ! [X0] :
( sK6(universal_class,X0) = first(unordered_pair(unordered_pair(sK6(universal_class,X0),sK6(universal_class,X0)),unordered_pair(sK6(universal_class,X0),unordered_pair(sK0,sK0))))
| subclass(universal_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_392])]) ).
fof(f924,plain,
( ! [X0] :
( sK6(universal_class,X0) = first(unordered_pair(unordered_pair(sK6(universal_class,X0),sK6(universal_class,X0)),unordered_pair(sK6(universal_class,X0),unordered_pair(sK0,sK0))))
| subclass(universal_class,X0) )
| ~ spl10_33
| ~ spl10_96 ),
inference(resolution,[],[f896,f423]) ).
fof(f10958,plain,
( spl10_391
| ~ spl10_59
| ~ spl10_237 ),
inference(avatar_split_clause,[],[f3928,f3920,f635,f10956]) ).
fof(f10956,plain,
( spl10_391
<=> ! [X0,X1] :
( ~ member(X0,universal_class)
| first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK7(X1,universal_class),sK7(X1,universal_class))))) = X0
| ~ member(X1,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_391])]) ).
fof(f3920,plain,
( spl10_237
<=> ! [X0,X1] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK7(X1,universal_class),sK7(X1,universal_class))))) = X0
| ~ member(X0,universal_class)
| ~ member(X1,sum_class(universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_237])]) ).
fof(f3928,plain,
( ! [X0,X1] :
( ~ member(X0,universal_class)
| first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK7(X1,universal_class),sK7(X1,universal_class))))) = X0
| ~ member(X1,sK0) )
| ~ spl10_59
| ~ spl10_237 ),
inference(resolution,[],[f3921,f636]) ).
fof(f3921,plain,
( ! [X0,X1] :
( ~ member(X1,sum_class(universal_class))
| ~ member(X0,universal_class)
| first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK7(X1,universal_class),sK7(X1,universal_class))))) = X0 )
| ~ spl10_237 ),
inference(avatar_component_clause,[],[f3920]) ).
fof(f10954,plain,
( spl10_390
| ~ spl10_59
| ~ spl10_206 ),
inference(avatar_split_clause,[],[f2821,f2774,f635,f10952]) ).
fof(f10952,plain,
( spl10_390
<=> ! [X0,X1] :
( ~ member(sK6(X0,intersection(X1,sum_class(universal_class))),X1)
| subclass(X0,intersection(X1,sum_class(universal_class)))
| ~ member(sK6(X0,intersection(X1,sum_class(universal_class))),sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_390])]) ).
fof(f2821,plain,
( ! [X0,X1] :
( ~ member(sK6(X0,intersection(X1,sum_class(universal_class))),X1)
| subclass(X0,intersection(X1,sum_class(universal_class)))
| ~ member(sK6(X0,intersection(X1,sum_class(universal_class))),sK0) )
| ~ spl10_59
| ~ spl10_206 ),
inference(resolution,[],[f2775,f636]) ).
fof(f10950,plain,
( spl10_389
| ~ spl10_47
| ~ spl10_95 ),
inference(avatar_split_clause,[],[f911,f891,f502,f10948]) ).
fof(f10948,plain,
( spl10_389
<=> ! [X0] :
( sK0 = second(unordered_pair(unordered_pair(sK7(X0,universal_class),sK7(X0,universal_class)),unordered_pair(sK7(X0,universal_class),unordered_pair(sK0,sK0))))
| ~ member(X0,sum_class(universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_389])]) ).
fof(f911,plain,
( ! [X0] :
( sK0 = second(unordered_pair(unordered_pair(sK7(X0,universal_class),sK7(X0,universal_class)),unordered_pair(sK7(X0,universal_class),unordered_pair(sK0,sK0))))
| ~ member(X0,sum_class(universal_class)) )
| ~ spl10_47
| ~ spl10_95 ),
inference(resolution,[],[f892,f503]) ).
fof(f10878,plain,
( spl10_388
| ~ spl10_362
| ~ spl10_363
| ~ spl10_387 ),
inference(avatar_split_clause,[],[f10805,f10802,f8780,f8774,f10876]) ).
fof(f10805,plain,
( ! [X0] :
( sK6(universal_class,X0) = second(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,unordered_pair(sK6(universal_class,X0),sK6(universal_class,X0)))))
| subclass(universal_class,X0) )
| ~ spl10_362
| ~ spl10_363
| ~ spl10_387 ),
inference(forward_demodulation,[],[f10803,f10663]) ).
fof(f10663,plain,
( unordered_pair(sK0,sK0) = unordered_pair(sK2,sK2)
| ~ spl10_362
| ~ spl10_363 ),
inference(superposition,[],[f8776,f8782]) ).
fof(f10804,plain,
( spl10_387
| ~ spl10_1
| ~ spl10_239 ),
inference(avatar_split_clause,[],[f4007,f3995,f272,f10802]) ).
fof(f4007,plain,
( ! [X0] :
( sK6(universal_class,X0) = second(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK6(universal_class,X0),sK6(universal_class,X0)))))
| subclass(universal_class,X0) )
| ~ spl10_1
| ~ spl10_239 ),
inference(resolution,[],[f3996,f274]) ).
fof(f10799,plain,
( spl10_386
| ~ spl10_107
| ~ spl10_174 ),
inference(avatar_split_clause,[],[f2070,f1775,f993,f10797]) ).
fof(f10797,plain,
( spl10_386
<=> ! [X0,X1] :
( ~ member(X0,unordered_pair(sK0,unordered_pair(sK1,sK1)))
| member(X0,sum_class(union(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_386])]) ).
fof(f2070,plain,
( ! [X0,X1] :
( ~ member(X0,unordered_pair(sK0,unordered_pair(sK1,sK1)))
| member(X0,sum_class(union(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X1))) )
| ~ spl10_107
| ~ spl10_174 ),
inference(resolution,[],[f1776,f995]) ).
fof(f10623,plain,
( spl10_385
| ~ spl10_361
| ~ spl10_376 ),
inference(avatar_split_clause,[],[f10392,f9713,f8770,f10621]) ).
fof(f10392,plain,
( ! [X0,X1] :
( ~ member(X0,unordered_pair(sK2,unordered_pair(sK3,sK3)))
| member(X0,sum_class(union(X1,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0))))) )
| ~ spl10_361
| ~ spl10_376 ),
inference(forward_demodulation,[],[f9714,f8772]) ).
fof(f10618,plain,
( ~ spl10_383
| spl10_384
| ~ spl10_108
| ~ spl10_140
| ~ spl10_313
| ~ spl10_361
| ~ spl10_363 ),
inference(avatar_split_clause,[],[f10446,f8780,f8770,f6008,f1259,f1004,f10616,f10612]) ).
fof(f10612,plain,
( spl10_383
<=> subclass(universal_class,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_383])]) ).
fof(f10616,plain,
( spl10_384
<=> ! [X0] :
( sK5(X0) = unordered_pair(sK0,sK0)
| ~ member(X0,identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_384])]) ).
fof(f10446,plain,
( ! [X0] :
( sK5(X0) = unordered_pair(sK0,sK0)
| ~ subclass(universal_class,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0)))
| ~ member(X0,identity_relation) )
| ~ spl10_108
| ~ spl10_140
| ~ spl10_313
| ~ spl10_361
| ~ spl10_363 ),
inference(duplicate_literal_removal,[],[f10445]) ).
fof(f10445,plain,
( ! [X0] :
( sK5(X0) = unordered_pair(sK0,sK0)
| ~ subclass(universal_class,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0)))
| ~ member(X0,identity_relation)
| sK5(X0) = unordered_pair(sK0,sK0) )
| ~ spl10_108
| ~ spl10_140
| ~ spl10_313
| ~ spl10_361
| ~ spl10_363 ),
inference(forward_demodulation,[],[f10444,f9752]) ).
fof(f9752,plain,
( unordered_pair(sK0,sK0) = unordered_pair(sK2,unordered_pair(sK3,sK3))
| ~ spl10_361
| ~ spl10_363 ),
inference(forward_demodulation,[],[f8772,f8782]) ).
fof(f10444,plain,
( ! [X0] :
( sK5(X0) = unordered_pair(sK2,unordered_pair(sK3,sK3))
| ~ subclass(universal_class,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0)))
| ~ member(X0,identity_relation)
| sK5(X0) = unordered_pair(sK0,sK0) )
| ~ spl10_108
| ~ spl10_140
| ~ spl10_313
| ~ spl10_361 ),
inference(forward_demodulation,[],[f6312,f8772]) ).
fof(f6312,plain,
( ! [X0] :
( ~ subclass(universal_class,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0)))
| ~ member(X0,identity_relation)
| sK5(X0) = unordered_pair(sK0,sK0)
| sK5(X0) = unordered_pair(sK0,unordered_pair(sK1,sK1)) )
| ~ spl10_108
| ~ spl10_140
| ~ spl10_313 ),
inference(forward_demodulation,[],[f1427,f6010]) ).
fof(f1427,plain,
( ! [X0] :
( ~ subclass(universal_class,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| ~ member(X0,identity_relation)
| sK5(X0) = unordered_pair(sK0,sK0)
| sK5(X0) = unordered_pair(sK0,unordered_pair(sK1,sK1)) )
| ~ spl10_108
| ~ spl10_140 ),
inference(resolution,[],[f1260,f1005]) ).
fof(f10609,plain,
( ~ spl10_382
| spl10_378
| ~ spl10_12
| ~ spl10_108
| ~ spl10_363 ),
inference(avatar_split_clause,[],[f9800,f8780,f1004,f324,f10587,f10606]) ).
fof(f9800,plain,
( null_class = unordered_pair(sK0,sK0)
| ~ inductive(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| ~ spl10_12
| ~ spl10_108
| ~ spl10_363 ),
inference(duplicate_literal_removal,[],[f9799]) ).
fof(f9799,plain,
( null_class = unordered_pair(sK0,sK0)
| null_class = unordered_pair(sK0,sK0)
| ~ inductive(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| ~ spl10_12
| ~ spl10_108
| ~ spl10_363 ),
inference(forward_demodulation,[],[f1011,f8782]) ).
fof(f1011,plain,
( null_class = unordered_pair(sK0,sK0)
| null_class = unordered_pair(sK0,unordered_pair(sK1,sK1))
| ~ inductive(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| ~ spl10_12
| ~ spl10_108 ),
inference(resolution,[],[f1005,f325]) ).
fof(f10604,plain,
( spl10_381
| ~ spl10_45
| ~ spl10_317 ),
inference(avatar_split_clause,[],[f7148,f6188,f494,f10602]) ).
fof(f7148,plain,
( ! [X0] :
( member(null_class,X0)
| ~ subclass(sK9,X0) )
| ~ spl10_45
| ~ spl10_317 ),
inference(resolution,[],[f6189,f495]) ).
fof(f10600,plain,
( ~ spl10_380
| ~ spl10_9
| ~ spl10_361
| ~ spl10_363
| spl10_379 ),
inference(avatar_split_clause,[],[f10595,f10591,f8780,f8770,f309,f10597]) ).
fof(f10597,plain,
( spl10_380
<=> inductive(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_380])]) ).
fof(f10595,plain,
( ~ inductive(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0)))
| ~ spl10_9
| ~ spl10_361
| ~ spl10_363
| spl10_379 ),
inference(forward_demodulation,[],[f10593,f9756]) ).
fof(f9756,plain,
( unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,sK0)) = unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0))
| ~ spl10_9
| ~ spl10_361
| ~ spl10_363 ),
inference(forward_demodulation,[],[f8950,f9752]) ).
fof(f8950,plain,
( unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))) = unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK2,unordered_pair(sK3,sK3)))
| ~ spl10_9
| ~ spl10_361 ),
inference(superposition,[],[f311,f8772]) ).
fof(f10594,plain,
( spl10_378
| ~ spl10_379
| ~ spl10_9
| ~ spl10_12
| ~ spl10_108
| ~ spl10_363 ),
inference(avatar_split_clause,[],[f9801,f8780,f1004,f324,f309,f10591,f10587]) ).
fof(f9801,plain,
( ~ inductive(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,sK0)))
| null_class = unordered_pair(sK0,sK0)
| ~ spl10_9
| ~ spl10_12
| ~ spl10_108
| ~ spl10_363 ),
inference(forward_demodulation,[],[f9800,f9663]) ).
fof(f9663,plain,
( unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))) = unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,sK0))
| ~ spl10_9
| ~ spl10_363 ),
inference(superposition,[],[f311,f8782]) ).
fof(f10519,plain,
( spl10_313
| ~ spl10_361
| ~ spl10_363 ),
inference(avatar_split_clause,[],[f9752,f8780,f8770,f6008]) ).
fof(f10386,plain,
( spl10_377
| ~ spl10_314
| ~ spl10_357 ),
inference(avatar_split_clause,[],[f8257,f8254,f6012,f10384]) ).
fof(f10384,plain,
( spl10_377
<=> ! [X0] :
( sK0 = first(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,unordered_pair(sK6(universal_class,X0),sK6(universal_class,X0)))))
| subclass(universal_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_377])]) ).
fof(f8257,plain,
( ! [X0] :
( sK0 = first(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,unordered_pair(sK6(universal_class,X0),sK6(universal_class,X0)))))
| subclass(universal_class,X0) )
| ~ spl10_314
| ~ spl10_357 ),
inference(forward_demodulation,[],[f8255,f6014]) ).
fof(f8255,plain,
( ! [X0] :
( subclass(universal_class,X0)
| sK0 = first(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK6(universal_class,X0),sK6(universal_class,X0))))) )
| ~ spl10_357 ),
inference(avatar_component_clause,[],[f8254]) ).
fof(f10283,plain,
( spl10_313
| ~ spl10_361
| ~ spl10_363 ),
inference(avatar_split_clause,[],[f9752,f8780,f8770,f6008]) ).
fof(f9715,plain,
( spl10_376
| ~ spl10_313
| ~ spl10_374 ),
inference(avatar_split_clause,[],[f9620,f9611,f6008,f9713]) ).
fof(f9620,plain,
( ! [X0,X1] :
( member(X0,sum_class(union(X1,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0)))))
| ~ member(X0,unordered_pair(sK0,unordered_pair(sK1,sK1))) )
| ~ spl10_313
| ~ spl10_374 ),
inference(forward_demodulation,[],[f9612,f6010]) ).
fof(f9619,plain,
( spl10_375
| ~ spl10_313
| ~ spl10_362
| ~ spl10_374 ),
inference(avatar_split_clause,[],[f9615,f9611,f8774,f6008,f9617]) ).
fof(f9617,plain,
( spl10_375
<=> ! [X0,X1] :
( member(X0,sum_class(union(X1,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0)))))
| ~ member(X0,unordered_pair(sK2,sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_375])]) ).
fof(f9615,plain,
( ! [X0,X1] :
( member(X0,sum_class(union(X1,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0)))))
| ~ member(X0,unordered_pair(sK2,sK2)) )
| ~ spl10_313
| ~ spl10_362
| ~ spl10_374 ),
inference(forward_demodulation,[],[f9614,f6010]) ).
fof(f9613,plain,
( spl10_374
| ~ spl10_107
| ~ spl10_173 ),
inference(avatar_split_clause,[],[f2014,f1771,f993,f9611]) ).
fof(f2014,plain,
( ! [X0,X1] :
( ~ member(X0,unordered_pair(sK0,unordered_pair(sK1,sK1)))
| member(X0,sum_class(union(X1,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))))) )
| ~ spl10_107
| ~ spl10_173 ),
inference(resolution,[],[f1772,f995]) ).
fof(f9609,plain,
( spl10_373
| ~ spl10_33
| ~ spl10_95 ),
inference(avatar_split_clause,[],[f910,f891,f422,f9607]) ).
fof(f9607,plain,
( spl10_373
<=> ! [X0] :
( sK0 = second(unordered_pair(unordered_pair(sK6(universal_class,X0),sK6(universal_class,X0)),unordered_pair(sK6(universal_class,X0),unordered_pair(sK0,sK0))))
| subclass(universal_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_373])]) ).
fof(f910,plain,
( ! [X0] :
( sK0 = second(unordered_pair(unordered_pair(sK6(universal_class,X0),sK6(universal_class,X0)),unordered_pair(sK6(universal_class,X0),unordered_pair(sK0,sK0))))
| subclass(universal_class,X0) )
| ~ spl10_33
| ~ spl10_95 ),
inference(resolution,[],[f892,f423]) ).
fof(f9486,plain,
( spl10_372
| ~ spl10_33
| ~ spl10_165 ),
inference(avatar_split_clause,[],[f1881,f1736,f422,f9484]) ).
fof(f1881,plain,
( ! [X0,X1] : subclass(X0,union(X1,X0))
| ~ spl10_33
| ~ spl10_165 ),
inference(duplicate_literal_removal,[],[f1860]) ).
fof(f1860,plain,
( ! [X0,X1] :
( subclass(X0,union(X1,X0))
| subclass(X0,union(X1,X0)) )
| ~ spl10_33
| ~ spl10_165 ),
inference(resolution,[],[f1737,f423]) ).
fof(f9482,plain,
( spl10_371
| ~ spl10_33
| ~ spl10_164 ),
inference(avatar_split_clause,[],[f1859,f1732,f422,f9480]) ).
fof(f1859,plain,
( ! [X0,X1] : subclass(X0,union(X0,X1))
| ~ spl10_33
| ~ spl10_164 ),
inference(duplicate_literal_removal,[],[f1838]) ).
fof(f1838,plain,
( ! [X0,X1] :
( subclass(X0,union(X0,X1))
| subclass(X0,union(X0,X1)) )
| ~ spl10_33
| ~ spl10_164 ),
inference(resolution,[],[f1733,f423]) ).
fof(f9478,plain,
( spl10_370
| ~ spl10_34
| ~ spl10_163 ),
inference(avatar_split_clause,[],[f1834,f1728,f426,f9476]) ).
fof(f9476,plain,
( spl10_370
<=> ! [X0,X1] : subclass(intersection(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_370])]) ).
fof(f1834,plain,
( ! [X0,X1] : subclass(intersection(X0,X1),X1)
| ~ spl10_34
| ~ spl10_163 ),
inference(duplicate_literal_removal,[],[f1808]) ).
fof(f1808,plain,
( ! [X0,X1] :
( subclass(intersection(X0,X1),X1)
| subclass(intersection(X0,X1),X1) )
| ~ spl10_34
| ~ spl10_163 ),
inference(resolution,[],[f1729,f427]) ).
fof(f9474,plain,
( spl10_369
| ~ spl10_34
| ~ spl10_162 ),
inference(avatar_split_clause,[],[f1804,f1724,f426,f9472]) ).
fof(f9472,plain,
( spl10_369
<=> ! [X0,X1] : subclass(intersection(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_369])]) ).
fof(f1804,plain,
( ! [X0,X1] : subclass(intersection(X0,X1),X0)
| ~ spl10_34
| ~ spl10_162 ),
inference(duplicate_literal_removal,[],[f1778]) ).
fof(f1778,plain,
( ! [X0,X1] :
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) )
| ~ spl10_34
| ~ spl10_162 ),
inference(resolution,[],[f1725,f427]) ).
fof(f9470,plain,
( spl10_368
| ~ spl10_5
| ~ spl10_144 ),
inference(avatar_split_clause,[],[f1557,f1449,f292,f9468]) ).
fof(f9468,plain,
( spl10_368
<=> ! [X0] : null_class = intersection(X0,null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_368])]) ).
fof(f1557,plain,
( ! [X0] : null_class = intersection(X0,null_class)
| ~ spl10_5
| ~ spl10_144 ),
inference(resolution,[],[f1450,f293]) ).
fof(f9466,plain,
( spl10_367
| ~ spl10_5
| ~ spl10_143 ),
inference(avatar_split_clause,[],[f1532,f1445,f292,f9464]) ).
fof(f9464,plain,
( spl10_367
<=> ! [X0] : null_class = intersection(null_class,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_367])]) ).
fof(f1532,plain,
( ! [X0] : null_class = intersection(null_class,X0)
| ~ spl10_5
| ~ spl10_143 ),
inference(resolution,[],[f1446,f293]) ).
fof(f9273,plain,
( ~ spl10_4
| ~ spl10_365 ),
inference(avatar_contradiction_clause,[],[f9272]) ).
fof(f9272,plain,
( $false
| ~ spl10_4
| ~ spl10_365 ),
inference(resolution,[],[f9219,f289]) ).
fof(f289,plain,
( inductive(sK9)
| ~ spl10_4 ),
inference(avatar_component_clause,[],[f287]) ).
fof(f287,plain,
( spl10_4
<=> inductive(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_4])]) ).
fof(f9219,plain,
( ! [X0] : ~ inductive(X0)
| ~ spl10_365 ),
inference(avatar_component_clause,[],[f9218]) ).
fof(f9218,plain,
( spl10_365
<=> ! [X0] : ~ inductive(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_365])]) ).
fof(f9270,plain,
( spl10_366
| ~ spl10_30
| ~ spl10_96 ),
inference(avatar_split_clause,[],[f913,f895,f409,f9267]) ).
fof(f9267,plain,
( spl10_366
<=> null_class = first(unordered_pair(unordered_pair(null_class,null_class),unordered_pair(null_class,unordered_pair(sK0,sK0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_366])]) ).
fof(f913,plain,
( null_class = first(unordered_pair(unordered_pair(null_class,null_class),unordered_pair(null_class,unordered_pair(sK0,sK0))))
| ~ spl10_30
| ~ spl10_96 ),
inference(resolution,[],[f896,f411]) ).
fof(f9220,plain,
( spl10_365
| spl10_30
| ~ spl10_6
| ~ spl10_118 ),
inference(avatar_split_clause,[],[f1079,f1067,f296,f409,f9218]) ).
fof(f1079,plain,
( ! [X0] :
( member(null_class,universal_class)
| ~ inductive(X0) )
| ~ spl10_6
| ~ spl10_118 ),
inference(resolution,[],[f1068,f297]) ).
fof(f9022,plain,
( spl10_364
| ~ spl10_156
| ~ spl10_314 ),
inference(avatar_split_clause,[],[f6080,f6012,f1497,f9019]) ).
fof(f9019,plain,
( spl10_364
<=> member(unordered_pair(sK2,sK2),sum_class(universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_364])]) ).
fof(f6080,plain,
( member(unordered_pair(sK2,sK2),sum_class(universal_class))
| ~ spl10_156
| ~ spl10_314 ),
inference(superposition,[],[f1499,f6014]) ).
fof(f8783,plain,
( spl10_363
| ~ spl10_313
| ~ spl10_361 ),
inference(avatar_split_clause,[],[f8778,f8770,f6008,f8780]) ).
fof(f8778,plain,
( unordered_pair(sK0,sK0) = unordered_pair(sK0,unordered_pair(sK1,sK1))
| ~ spl10_313
| ~ spl10_361 ),
inference(forward_demodulation,[],[f8772,f6010]) ).
fof(f8777,plain,
( spl10_361
| spl10_362
| ~ spl10_54
| ~ spl10_107 ),
inference(avatar_split_clause,[],[f999,f993,f596,f8774,f8770]) ).
fof(f999,plain,
( unordered_pair(sK0,unordered_pair(sK1,sK1)) = unordered_pair(sK2,sK2)
| unordered_pair(sK0,unordered_pair(sK1,sK1)) = unordered_pair(sK2,unordered_pair(sK3,sK3))
| ~ spl10_54
| ~ spl10_107 ),
inference(resolution,[],[f995,f597]) ).
fof(f8768,plain,
( spl10_360
| ~ spl10_13
| ~ spl10_96 ),
inference(avatar_split_clause,[],[f912,f895,f328,f8766]) ).
fof(f8766,plain,
( spl10_360
<=> ! [X0,X1] : unordered_pair(X0,X1) = first(unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),unordered_pair(unordered_pair(X0,X1),unordered_pair(sK0,sK0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_360])]) ).
fof(f912,plain,
( ! [X0,X1] : unordered_pair(X0,X1) = first(unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),unordered_pair(unordered_pair(X0,X1),unordered_pair(sK0,sK0))))
| ~ spl10_13
| ~ spl10_96 ),
inference(resolution,[],[f896,f329]) ).
fof(f8683,plain,
( spl10_359
| ~ spl10_33
| ~ spl10_312 ),
inference(avatar_split_clause,[],[f6006,f5980,f422,f8681]) ).
fof(f8681,plain,
( spl10_359
<=> ! [X0] : subclass(sK0,union(X0,sum_class(universal_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_359])]) ).
fof(f6006,plain,
( ! [X0] : subclass(sK0,union(X0,sum_class(universal_class)))
| ~ spl10_33
| ~ spl10_312 ),
inference(duplicate_literal_removal,[],[f5995]) ).
fof(f5995,plain,
( ! [X0] :
( subclass(sK0,union(X0,sum_class(universal_class)))
| subclass(sK0,union(X0,sum_class(universal_class))) )
| ~ spl10_33
| ~ spl10_312 ),
inference(resolution,[],[f5981,f423]) ).
fof(f8616,plain,
( spl10_358
| ~ spl10_314
| ~ spl10_355 ),
inference(avatar_split_clause,[],[f8248,f8245,f6012,f8614]) ).
fof(f8614,plain,
( spl10_358
<=> ! [X0,X1] :
( ~ member(X0,unordered_pair(sK2,sK2))
| member(X0,sum_class(union(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_358])]) ).
fof(f8245,plain,
( spl10_355
<=> ! [X0,X1] :
( ~ member(X0,unordered_pair(sK0,sK0))
| member(X0,sum_class(union(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_355])]) ).
fof(f8248,plain,
( ! [X0,X1] :
( ~ member(X0,unordered_pair(sK2,sK2))
| member(X0,sum_class(union(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X1))) )
| ~ spl10_314
| ~ spl10_355 ),
inference(forward_demodulation,[],[f8246,f6014]) ).
fof(f8246,plain,
( ! [X0,X1] :
( member(X0,sum_class(union(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X1)))
| ~ member(X0,unordered_pair(sK0,sK0)) )
| ~ spl10_355 ),
inference(avatar_component_clause,[],[f8245]) ).
fof(f8256,plain,
( spl10_357
| ~ spl10_1
| ~ spl10_235 ),
inference(avatar_split_clause,[],[f3875,f3863,f272,f8254]) ).
fof(f3875,plain,
( ! [X0] :
( sK0 = first(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK6(universal_class,X0),sK6(universal_class,X0)))))
| subclass(universal_class,X0) )
| ~ spl10_1
| ~ spl10_235 ),
inference(resolution,[],[f3864,f274]) ).
fof(f8252,plain,
( spl10_356
| ~ spl10_33
| ~ spl10_311 ),
inference(avatar_split_clause,[],[f5994,f5976,f422,f8250]) ).
fof(f8250,plain,
( spl10_356
<=> ! [X0] : subclass(sK0,union(sum_class(universal_class),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_356])]) ).
fof(f5994,plain,
( ! [X0] : subclass(sK0,union(sum_class(universal_class),X0))
| ~ spl10_33
| ~ spl10_311 ),
inference(duplicate_literal_removal,[],[f5983]) ).
fof(f5983,plain,
( ! [X0] :
( subclass(sK0,union(sum_class(universal_class),X0))
| subclass(sK0,union(sum_class(universal_class),X0)) )
| ~ spl10_33
| ~ spl10_311 ),
inference(resolution,[],[f5977,f423]) ).
fof(f8247,plain,
( spl10_355
| ~ spl10_103
| ~ spl10_174 ),
inference(avatar_split_clause,[],[f2069,f1775,f961,f8245]) ).
fof(f2069,plain,
( ! [X0,X1] :
( ~ member(X0,unordered_pair(sK0,sK0))
| member(X0,sum_class(union(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X1))) )
| ~ spl10_103
| ~ spl10_174 ),
inference(resolution,[],[f1776,f963]) ).
fof(f8089,plain,
( spl10_354
| ~ spl10_313
| ~ spl10_353 ),
inference(avatar_split_clause,[],[f8085,f8082,f6008,f8087]) ).
fof(f8087,plain,
( spl10_354
<=> ! [X0,X1] :
( member(X0,sum_class(union(X1,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0)))))
| ~ member(X0,unordered_pair(sK0,sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_354])]) ).
fof(f8082,plain,
( spl10_353
<=> ! [X0,X1] :
( ~ member(X0,unordered_pair(sK0,sK0))
| member(X0,sum_class(union(X1,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_353])]) ).
fof(f8085,plain,
( ! [X0,X1] :
( member(X0,sum_class(union(X1,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0)))))
| ~ member(X0,unordered_pair(sK0,sK0)) )
| ~ spl10_313
| ~ spl10_353 ),
inference(forward_demodulation,[],[f8083,f6010]) ).
fof(f8083,plain,
( ! [X0,X1] :
( member(X0,sum_class(union(X1,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))))
| ~ member(X0,unordered_pair(sK0,sK0)) )
| ~ spl10_353 ),
inference(avatar_component_clause,[],[f8082]) ).
fof(f8084,plain,
( spl10_353
| ~ spl10_103
| ~ spl10_173 ),
inference(avatar_split_clause,[],[f2013,f1771,f961,f8082]) ).
fof(f2013,plain,
( ! [X0,X1] :
( ~ member(X0,unordered_pair(sK0,sK0))
| member(X0,sum_class(union(X1,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))))) )
| ~ spl10_103
| ~ spl10_173 ),
inference(resolution,[],[f1772,f963]) ).
fof(f7994,plain,
( spl10_352
| ~ spl10_314
| ~ spl10_344 ),
inference(avatar_split_clause,[],[f7319,f7316,f6012,f7992]) ).
fof(f7992,plain,
( spl10_352
<=> ! [X0] :
( sK4(X0) = second(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,unordered_pair(sK4(X0),sK4(X0)))))
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_352])]) ).
fof(f7319,plain,
( ! [X0] :
( sK4(X0) = second(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,unordered_pair(sK4(X0),sK4(X0)))))
| null_class = X0 )
| ~ spl10_314
| ~ spl10_344 ),
inference(forward_demodulation,[],[f7317,f6014]) ).
fof(f7317,plain,
( ! [X0] :
( sK4(X0) = second(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK4(X0),sK4(X0)))))
| null_class = X0 )
| ~ spl10_344 ),
inference(avatar_component_clause,[],[f7316]) ).
fof(f7837,plain,
( spl10_351
| ~ spl10_313
| ~ spl10_350 ),
inference(avatar_split_clause,[],[f7833,f7830,f6008,f7835]) ).
fof(f7835,plain,
( spl10_351
<=> ! [X0] :
( member(X0,sum_class(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0))))
| ~ member(X0,unordered_pair(sK0,unordered_pair(sK1,sK1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_351])]) ).
fof(f7830,plain,
( spl10_350
<=> ! [X0] :
( member(X0,sum_class(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))))
| ~ member(X0,unordered_pair(sK0,unordered_pair(sK1,sK1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_350])]) ).
fof(f7833,plain,
( ! [X0] :
( member(X0,sum_class(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0))))
| ~ member(X0,unordered_pair(sK0,unordered_pair(sK1,sK1))) )
| ~ spl10_313
| ~ spl10_350 ),
inference(forward_demodulation,[],[f7831,f6010]) ).
fof(f7831,plain,
( ! [X0] :
( member(X0,sum_class(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))))
| ~ member(X0,unordered_pair(sK0,unordered_pair(sK1,sK1))) )
| ~ spl10_350 ),
inference(avatar_component_clause,[],[f7830]) ).
fof(f7832,plain,
( spl10_350
| ~ spl10_51
| ~ spl10_107 ),
inference(avatar_split_clause,[],[f1001,f993,f554,f7830]) ).
fof(f1001,plain,
( ! [X0] :
( member(X0,sum_class(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))))
| ~ member(X0,unordered_pair(sK0,unordered_pair(sK1,sK1))) )
| ~ spl10_51
| ~ spl10_107 ),
inference(resolution,[],[f995,f555]) ).
fof(f7828,plain,
( spl10_349
| ~ spl10_22
| ~ spl10_96 ),
inference(avatar_split_clause,[],[f919,f895,f367,f7826]) ).
fof(f7826,plain,
( spl10_349
<=> ! [X0] :
( sK5(X0) = first(unordered_pair(unordered_pair(sK5(X0),sK5(X0)),unordered_pair(sK5(X0),unordered_pair(sK0,sK0))))
| ~ member(X0,identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_349])]) ).
fof(f919,plain,
( ! [X0] :
( sK5(X0) = first(unordered_pair(unordered_pair(sK5(X0),sK5(X0)),unordered_pair(sK5(X0),unordered_pair(sK0,sK0))))
| ~ member(X0,identity_relation) )
| ~ spl10_22
| ~ spl10_96 ),
inference(resolution,[],[f896,f368]) ).
fof(f7824,plain,
( spl10_348
| ~ spl10_15
| ~ spl10_96 ),
inference(avatar_split_clause,[],[f918,f895,f338,f7822]) ).
fof(f7822,plain,
( spl10_348
<=> ! [X0] :
( sK4(X0) = first(unordered_pair(unordered_pair(sK4(X0),sK4(X0)),unordered_pair(sK4(X0),unordered_pair(sK0,sK0))))
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_348])]) ).
fof(f918,plain,
( ! [X0] :
( sK4(X0) = first(unordered_pair(unordered_pair(sK4(X0),sK4(X0)),unordered_pair(sK4(X0),unordered_pair(sK0,sK0))))
| null_class = X0 )
| ~ spl10_15
| ~ spl10_96 ),
inference(resolution,[],[f896,f339]) ).
fof(f7820,plain,
( spl10_347
| ~ spl10_18
| ~ spl10_96 ),
inference(avatar_split_clause,[],[f916,f895,f350,f7818]) ).
fof(f7818,plain,
( spl10_347
<=> ! [X0] :
( power_class(X0) = first(unordered_pair(unordered_pair(power_class(X0),power_class(X0)),unordered_pair(power_class(X0),unordered_pair(sK0,sK0))))
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_347])]) ).
fof(f916,plain,
( ! [X0] :
( power_class(X0) = first(unordered_pair(unordered_pair(power_class(X0),power_class(X0)),unordered_pair(power_class(X0),unordered_pair(sK0,sK0))))
| ~ member(X0,universal_class) )
| ~ spl10_18
| ~ spl10_96 ),
inference(resolution,[],[f896,f351]) ).
fof(f7816,plain,
( spl10_346
| ~ spl10_19
| ~ spl10_96 ),
inference(avatar_split_clause,[],[f915,f895,f354,f7814]) ).
fof(f7814,plain,
( spl10_346
<=> ! [X0] :
( sum_class(X0) = first(unordered_pair(unordered_pair(sum_class(X0),sum_class(X0)),unordered_pair(sum_class(X0),unordered_pair(sK0,sK0))))
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_346])]) ).
fof(f915,plain,
( ! [X0] :
( sum_class(X0) = first(unordered_pair(unordered_pair(sum_class(X0),sum_class(X0)),unordered_pair(sum_class(X0),unordered_pair(sK0,sK0))))
| ~ member(X0,universal_class) )
| ~ spl10_19
| ~ spl10_96 ),
inference(resolution,[],[f896,f355]) ).
fof(f7629,plain,
( spl10_345
| ~ spl10_314
| ~ spl10_341 ),
inference(avatar_split_clause,[],[f7306,f7303,f6012,f7627]) ).
fof(f7627,plain,
( spl10_345
<=> ! [X0,X1] : unordered_pair(X0,X1) = second(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_345])]) ).
fof(f7306,plain,
( ! [X0,X1] : unordered_pair(X0,X1) = second(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)))))
| ~ spl10_314
| ~ spl10_341 ),
inference(forward_demodulation,[],[f7304,f6014]) ).
fof(f7304,plain,
( ! [X0,X1] : unordered_pair(X0,X1) = second(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)))))
| ~ spl10_341 ),
inference(avatar_component_clause,[],[f7303]) ).
fof(f7318,plain,
( spl10_344
| ~ spl10_1
| ~ spl10_229 ),
inference(avatar_split_clause,[],[f3777,f3556,f272,f7316]) ).
fof(f3777,plain,
( ! [X0] :
( sK4(X0) = second(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK4(X0),sK4(X0)))))
| null_class = X0 )
| ~ spl10_1
| ~ spl10_229 ),
inference(resolution,[],[f3557,f274]) ).
fof(f7314,plain,
( spl10_343
| ~ spl10_1
| ~ spl10_228 ),
inference(avatar_split_clause,[],[f3731,f3552,f272,f7312]) ).
fof(f7312,plain,
( spl10_343
<=> ! [X0] :
( ~ member(X0,universal_class)
| power_class(sK0) = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(power_class(sK0),power_class(sK0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_343])]) ).
fof(f3552,plain,
( spl10_228
<=> ! [X0,X1] :
( power_class(X1) = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(power_class(X1),power_class(X1)))))
| ~ member(X0,universal_class)
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_228])]) ).
fof(f3731,plain,
( ! [X0] :
( ~ member(X0,universal_class)
| power_class(sK0) = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(power_class(sK0),power_class(sK0))))) )
| ~ spl10_1
| ~ spl10_228 ),
inference(resolution,[],[f3553,f274]) ).
fof(f3553,plain,
( ! [X0,X1] :
( ~ member(X1,universal_class)
| ~ member(X0,universal_class)
| power_class(X1) = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(power_class(X1),power_class(X1))))) )
| ~ spl10_228 ),
inference(avatar_component_clause,[],[f3552]) ).
fof(f7310,plain,
( spl10_342
| ~ spl10_1
| ~ spl10_227 ),
inference(avatar_split_clause,[],[f3683,f3548,f272,f7308]) ).
fof(f7308,plain,
( spl10_342
<=> ! [X0] :
( ~ member(X0,universal_class)
| sum_class(sK0) = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sum_class(sK0),sum_class(sK0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_342])]) ).
fof(f3548,plain,
( spl10_227
<=> ! [X0,X1] :
( sum_class(X1) = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sum_class(X1),sum_class(X1)))))
| ~ member(X0,universal_class)
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_227])]) ).
fof(f3683,plain,
( ! [X0] :
( ~ member(X0,universal_class)
| sum_class(sK0) = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sum_class(sK0),sum_class(sK0))))) )
| ~ spl10_1
| ~ spl10_227 ),
inference(resolution,[],[f3549,f274]) ).
fof(f3549,plain,
( ! [X0,X1] :
( ~ member(X1,universal_class)
| ~ member(X0,universal_class)
| sum_class(X1) = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sum_class(X1),sum_class(X1))))) )
| ~ spl10_227 ),
inference(avatar_component_clause,[],[f3548]) ).
fof(f7305,plain,
( spl10_341
| ~ spl10_1
| ~ spl10_226 ),
inference(avatar_split_clause,[],[f3637,f3544,f272,f7303]) ).
fof(f3637,plain,
( ! [X0,X1] : unordered_pair(X0,X1) = second(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)))))
| ~ spl10_1
| ~ spl10_226 ),
inference(resolution,[],[f3545,f274]) ).
fof(f7168,plain,
( spl10_340
| ~ spl10_313
| ~ spl10_339 ),
inference(avatar_split_clause,[],[f7164,f7161,f6008,f7166]) ).
fof(f7166,plain,
( spl10_340
<=> ! [X0] :
( ~ subclass(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0)),X0)
| member(unordered_pair(sK0,unordered_pair(sK1,sK1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_340])]) ).
fof(f7161,plain,
( spl10_339
<=> ! [X0] :
( member(unordered_pair(sK0,unordered_pair(sK1,sK1)),X0)
| ~ subclass(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_339])]) ).
fof(f7164,plain,
( ! [X0] :
( ~ subclass(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0)),X0)
| member(unordered_pair(sK0,unordered_pair(sK1,sK1)),X0) )
| ~ spl10_313
| ~ spl10_339 ),
inference(forward_demodulation,[],[f7162,f6010]) ).
fof(f7162,plain,
( ! [X0] :
( ~ subclass(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X0)
| member(unordered_pair(sK0,unordered_pair(sK1,sK1)),X0) )
| ~ spl10_339 ),
inference(avatar_component_clause,[],[f7161]) ).
fof(f7163,plain,
( spl10_339
| ~ spl10_45
| ~ spl10_107 ),
inference(avatar_split_clause,[],[f1002,f993,f494,f7161]) ).
fof(f1002,plain,
( ! [X0] :
( member(unordered_pair(sK0,unordered_pair(sK1,sK1)),X0)
| ~ subclass(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X0) )
| ~ spl10_45
| ~ spl10_107 ),
inference(resolution,[],[f995,f495]) ).
fof(f7159,plain,
( spl10_338
| ~ spl10_22
| ~ spl10_95 ),
inference(avatar_split_clause,[],[f905,f891,f367,f7157]) ).
fof(f7157,plain,
( spl10_338
<=> ! [X0] :
( sK0 = second(unordered_pair(unordered_pair(sK5(X0),sK5(X0)),unordered_pair(sK5(X0),unordered_pair(sK0,sK0))))
| ~ member(X0,identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_338])]) ).
fof(f905,plain,
( ! [X0] :
( sK0 = second(unordered_pair(unordered_pair(sK5(X0),sK5(X0)),unordered_pair(sK5(X0),unordered_pair(sK0,sK0))))
| ~ member(X0,identity_relation) )
| ~ spl10_22
| ~ spl10_95 ),
inference(resolution,[],[f892,f368]) ).
fof(f7147,plain,
( spl10_337
| ~ spl10_15
| ~ spl10_95 ),
inference(avatar_split_clause,[],[f904,f891,f338,f7145]) ).
fof(f7145,plain,
( spl10_337
<=> ! [X0] :
( sK0 = second(unordered_pair(unordered_pair(sK4(X0),sK4(X0)),unordered_pair(sK4(X0),unordered_pair(sK0,sK0))))
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_337])]) ).
fof(f904,plain,
( ! [X0] :
( sK0 = second(unordered_pair(unordered_pair(sK4(X0),sK4(X0)),unordered_pair(sK4(X0),unordered_pair(sK0,sK0))))
| null_class = X0 )
| ~ spl10_15
| ~ spl10_95 ),
inference(resolution,[],[f892,f339]) ).
fof(f7143,plain,
( spl10_336
| ~ spl10_18
| ~ spl10_95 ),
inference(avatar_split_clause,[],[f902,f891,f350,f7141]) ).
fof(f7141,plain,
( spl10_336
<=> ! [X0] :
( sK0 = second(unordered_pair(unordered_pair(power_class(X0),power_class(X0)),unordered_pair(power_class(X0),unordered_pair(sK0,sK0))))
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_336])]) ).
fof(f902,plain,
( ! [X0] :
( sK0 = second(unordered_pair(unordered_pair(power_class(X0),power_class(X0)),unordered_pair(power_class(X0),unordered_pair(sK0,sK0))))
| ~ member(X0,universal_class) )
| ~ spl10_18
| ~ spl10_95 ),
inference(resolution,[],[f892,f351]) ).
fof(f7139,plain,
( spl10_335
| ~ spl10_19
| ~ spl10_95 ),
inference(avatar_split_clause,[],[f901,f891,f354,f7137]) ).
fof(f7137,plain,
( spl10_335
<=> ! [X0] :
( sK0 = second(unordered_pair(unordered_pair(sum_class(X0),sum_class(X0)),unordered_pair(sum_class(X0),unordered_pair(sK0,sK0))))
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_335])]) ).
fof(f901,plain,
( ! [X0] :
( sK0 = second(unordered_pair(unordered_pair(sum_class(X0),sum_class(X0)),unordered_pair(sum_class(X0),unordered_pair(sK0,sK0))))
| ~ member(X0,universal_class) )
| ~ spl10_19
| ~ spl10_95 ),
inference(resolution,[],[f892,f355]) ).
fof(f7135,plain,
( spl10_334
| ~ spl10_13
| ~ spl10_95 ),
inference(avatar_split_clause,[],[f898,f891,f328,f7133]) ).
fof(f7133,plain,
( spl10_334
<=> ! [X0,X1] : sK0 = second(unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),unordered_pair(unordered_pair(X0,X1),unordered_pair(sK0,sK0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_334])]) ).
fof(f898,plain,
( ! [X0,X1] : sK0 = second(unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),unordered_pair(unordered_pair(X0,X1),unordered_pair(sK0,sK0))))
| ~ spl10_13
| ~ spl10_95 ),
inference(resolution,[],[f892,f329]) ).
fof(f7048,plain,
( spl10_333
| ~ spl10_314
| ~ spl10_332 ),
inference(avatar_split_clause,[],[f6869,f6866,f6012,f7046]) ).
fof(f7046,plain,
( spl10_333
<=> ! [X0] :
( sK0 = first(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,unordered_pair(sK4(X0),sK4(X0)))))
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_333])]) ).
fof(f6869,plain,
( ! [X0] :
( sK0 = first(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,unordered_pair(sK4(X0),sK4(X0)))))
| null_class = X0 )
| ~ spl10_314
| ~ spl10_332 ),
inference(forward_demodulation,[],[f6867,f6014]) ).
fof(f6867,plain,
( ! [X0] :
( sK0 = first(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK4(X0),sK4(X0)))))
| null_class = X0 )
| ~ spl10_332 ),
inference(avatar_component_clause,[],[f6866]) ).
fof(f6987,plain,
( ~ spl10_4
| ~ spl10_12
| spl10_317 ),
inference(avatar_split_clause,[],[f6724,f6188,f324,f287]) ).
fof(f6724,plain,
( ~ inductive(sK9)
| ~ spl10_12
| spl10_317 ),
inference(resolution,[],[f6190,f325]) ).
fof(f6190,plain,
( ~ member(null_class,sK9)
| spl10_317 ),
inference(avatar_component_clause,[],[f6188]) ).
fof(f6868,plain,
( spl10_332
| ~ spl10_1
| ~ spl10_219 ),
inference(avatar_split_clause,[],[f3423,f3033,f272,f6866]) ).
fof(f3423,plain,
( ! [X0] :
( sK0 = first(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK4(X0),sK4(X0)))))
| null_class = X0 )
| ~ spl10_1
| ~ spl10_219 ),
inference(resolution,[],[f3034,f274]) ).
fof(f6864,plain,
( spl10_331
| ~ spl10_1
| ~ spl10_218 ),
inference(avatar_split_clause,[],[f3378,f3029,f272,f6862]) ).
fof(f6862,plain,
( spl10_331
<=> ! [X0] :
( ~ member(X0,universal_class)
| first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(power_class(sK0),power_class(sK0))))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_331])]) ).
fof(f3029,plain,
( spl10_218
<=> ! [X0,X1] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(power_class(X1),power_class(X1))))) = X0
| ~ member(X0,universal_class)
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_218])]) ).
fof(f3378,plain,
( ! [X0] :
( ~ member(X0,universal_class)
| first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(power_class(sK0),power_class(sK0))))) = X0 )
| ~ spl10_1
| ~ spl10_218 ),
inference(resolution,[],[f3030,f274]) ).
fof(f3030,plain,
( ! [X0,X1] :
( ~ member(X1,universal_class)
| ~ member(X0,universal_class)
| first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(power_class(X1),power_class(X1))))) = X0 )
| ~ spl10_218 ),
inference(avatar_component_clause,[],[f3029]) ).
fof(f6860,plain,
( spl10_330
| ~ spl10_1
| ~ spl10_217 ),
inference(avatar_split_clause,[],[f3331,f3025,f272,f6858]) ).
fof(f6858,plain,
( spl10_330
<=> ! [X0] :
( ~ member(X0,universal_class)
| first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sum_class(sK0),sum_class(sK0))))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_330])]) ).
fof(f3025,plain,
( spl10_217
<=> ! [X0,X1] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sum_class(X1),sum_class(X1))))) = X0
| ~ member(X0,universal_class)
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_217])]) ).
fof(f3331,plain,
( ! [X0] :
( ~ member(X0,universal_class)
| first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sum_class(sK0),sum_class(sK0))))) = X0 )
| ~ spl10_1
| ~ spl10_217 ),
inference(resolution,[],[f3026,f274]) ).
fof(f3026,plain,
( ! [X0,X1] :
( ~ member(X1,universal_class)
| ~ member(X0,universal_class)
| first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sum_class(X1),sum_class(X1))))) = X0 )
| ~ spl10_217 ),
inference(avatar_component_clause,[],[f3025]) ).
fof(f6856,plain,
( spl10_329
| ~ spl10_59
| ~ spl10_189 ),
inference(avatar_split_clause,[],[f2414,f2339,f635,f6854]) ).
fof(f6854,plain,
( spl10_329
<=> ! [X2,X0,X1] :
( ~ member(sum_class(universal_class),X0)
| member(X1,sum_class(intersection(X0,X2)))
| ~ member(sum_class(universal_class),X2)
| ~ member(X1,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_329])]) ).
fof(f2414,plain,
( ! [X2,X0,X1] :
( ~ member(sum_class(universal_class),X0)
| member(X1,sum_class(intersection(X0,X2)))
| ~ member(sum_class(universal_class),X2)
| ~ member(X1,sK0) )
| ~ spl10_59
| ~ spl10_189 ),
inference(resolution,[],[f2340,f636]) ).
fof(f6728,plain,
( spl10_328
| ~ spl10_313
| ~ spl10_327 ),
inference(avatar_split_clause,[],[f6723,f6720,f6008,f6726]) ).
fof(f6726,plain,
( spl10_328
<=> ! [X0] :
( member(X0,sum_class(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0))))
| ~ member(X0,unordered_pair(sK0,sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_328])]) ).
fof(f6720,plain,
( spl10_327
<=> ! [X0] :
( member(X0,sum_class(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))))
| ~ member(X0,unordered_pair(sK0,sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_327])]) ).
fof(f6723,plain,
( ! [X0] :
( member(X0,sum_class(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0))))
| ~ member(X0,unordered_pair(sK0,sK0)) )
| ~ spl10_313
| ~ spl10_327 ),
inference(forward_demodulation,[],[f6721,f6010]) ).
fof(f6721,plain,
( ! [X0] :
( member(X0,sum_class(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))))
| ~ member(X0,unordered_pair(sK0,sK0)) )
| ~ spl10_327 ),
inference(avatar_component_clause,[],[f6720]) ).
fof(f6722,plain,
( spl10_327
| ~ spl10_51
| ~ spl10_103 ),
inference(avatar_split_clause,[],[f969,f961,f554,f6720]) ).
fof(f969,plain,
( ! [X0] :
( member(X0,sum_class(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))))
| ~ member(X0,unordered_pair(sK0,sK0)) )
| ~ spl10_51
| ~ spl10_103 ),
inference(resolution,[],[f963,f555]) ).
fof(f6479,plain,
( ~ spl10_326
| ~ spl10_12
| spl10_303 ),
inference(avatar_split_clause,[],[f5974,f5852,f324,f6476]) ).
fof(f6476,plain,
( spl10_326
<=> inductive(sum_class(universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_326])]) ).
fof(f5974,plain,
( ~ inductive(sum_class(universal_class))
| ~ spl10_12
| spl10_303 ),
inference(resolution,[],[f5853,f325]) ).
fof(f5853,plain,
( ~ member(null_class,sum_class(universal_class))
| spl10_303 ),
inference(avatar_component_clause,[],[f5852]) ).
fof(f6310,plain,
( spl10_325
| ~ spl10_244
| ~ spl10_247 ),
inference(avatar_split_clause,[],[f4142,f4139,f4115,f6308]) ).
fof(f6308,plain,
( spl10_325
<=> ! [X0] :
( complement(X0) = identity_relation
| ~ member(complement(X0),universal_class)
| ~ member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(complement(X0),complement(X0)),universal_class)),universal_class))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_325])]) ).
fof(f4142,plain,
( ! [X0] :
( complement(X0) = identity_relation
| ~ member(complement(X0),universal_class)
| ~ member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(complement(X0),complement(X0)),universal_class)),universal_class))))),X0) )
| ~ spl10_244
| ~ spl10_247 ),
inference(forward_demodulation,[],[f4140,f4117]) ).
fof(f6293,plain,
( spl10_324
| ~ spl10_13
| ~ spl10_245 ),
inference(avatar_split_clause,[],[f4466,f4119,f328,f6290]) ).
fof(f6290,plain,
( spl10_324
<=> member(sK4(identity_relation),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_324])]) ).
fof(f4466,plain,
( member(sK4(identity_relation),universal_class)
| ~ spl10_13
| ~ spl10_245 ),
inference(superposition,[],[f329,f4121]) ).
fof(f6288,plain,
( spl10_323
| ~ spl10_15
| ~ spl10_121 ),
inference(avatar_split_clause,[],[f1175,f1144,f338,f6285]) ).
fof(f6285,plain,
( spl10_323
<=> null_class = complement(universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_323])]) ).
fof(f1175,plain,
( null_class = complement(universal_class)
| ~ spl10_15
| ~ spl10_121 ),
inference(duplicate_literal_removal,[],[f1166]) ).
fof(f1166,plain,
( null_class = complement(universal_class)
| null_class = complement(universal_class)
| ~ spl10_15
| ~ spl10_121 ),
inference(resolution,[],[f1145,f339]) ).
fof(f6283,plain,
( ~ spl10_322
| ~ spl10_59
| spl10_303 ),
inference(avatar_split_clause,[],[f5973,f5852,f635,f6280]) ).
fof(f6280,plain,
( spl10_322
<=> member(null_class,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_322])]) ).
fof(f5973,plain,
( ~ member(null_class,sK0)
| ~ spl10_59
| spl10_303 ),
inference(resolution,[],[f5853,f636]) ).
fof(f6278,plain,
( spl10_321
| ~ spl10_16
| ~ spl10_101 ),
inference(avatar_split_clause,[],[f951,f946,f342,f6275]) ).
fof(f6275,plain,
( spl10_321
<=> null_class = sum_class(null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_321])]) ).
fof(f946,plain,
( spl10_101
<=> ! [X0] : ~ member(X0,sum_class(null_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_101])]) ).
fof(f951,plain,
( null_class = sum_class(null_class)
| ~ spl10_16
| ~ spl10_101 ),
inference(resolution,[],[f947,f343]) ).
fof(f947,plain,
( ! [X0] : ~ member(X0,sum_class(null_class))
| ~ spl10_101 ),
inference(avatar_component_clause,[],[f946]) ).
fof(f6211,plain,
( spl10_320
| ~ spl10_314
| ~ spl10_319 ),
inference(avatar_split_clause,[],[f6201,f6198,f6012,f6209]) ).
fof(f6209,plain,
( spl10_320
<=> ! [X0,X1] : sK0 = first(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_320])]) ).
fof(f6201,plain,
( ! [X0,X1] : sK0 = first(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)))))
| ~ spl10_314
| ~ spl10_319 ),
inference(forward_demodulation,[],[f6199,f6014]) ).
fof(f6199,plain,
( ! [X0,X1] : sK0 = first(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)))))
| ~ spl10_319 ),
inference(avatar_component_clause,[],[f6198]) ).
fof(f6200,plain,
( spl10_319
| ~ spl10_1
| ~ spl10_210 ),
inference(avatar_split_clause,[],[f2949,f2804,f272,f6198]) ).
fof(f2949,plain,
( ! [X0,X1] : sK0 = first(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)))))
| ~ spl10_1
| ~ spl10_210 ),
inference(resolution,[],[f2805,f274]) ).
fof(f6196,plain,
( ~ spl10_318
| spl10_313
| ~ spl10_314 ),
inference(avatar_split_clause,[],[f6077,f6012,f6008,f6193]) ).
fof(f6077,plain,
( unordered_pair(sK2,sK2) != unordered_pair(sK2,unordered_pair(sK3,sK3))
| spl10_313
| ~ spl10_314 ),
inference(forward_demodulation,[],[f6009,f6014]) ).
fof(f6009,plain,
( unordered_pair(sK0,sK0) != unordered_pair(sK2,unordered_pair(sK3,sK3))
| spl10_313 ),
inference(avatar_component_clause,[],[f6008]) ).
fof(f6191,plain,
( ~ spl10_317
| ~ spl10_114
| spl10_303 ),
inference(avatar_split_clause,[],[f5972,f5852,f1049,f6188]) ).
fof(f5972,plain,
( ~ member(null_class,sK9)
| ~ spl10_114
| spl10_303 ),
inference(resolution,[],[f5853,f1050]) ).
fof(f6076,plain,
( spl10_316
| ~ spl10_313
| ~ spl10_315 ),
inference(avatar_split_clause,[],[f6072,f6069,f6008,f6074]) ).
fof(f6074,plain,
( spl10_316
<=> ! [X0] :
( ~ subclass(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0)),X0)
| member(unordered_pair(sK0,sK0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_316])]) ).
fof(f6069,plain,
( spl10_315
<=> ! [X0] :
( member(unordered_pair(sK0,sK0),X0)
| ~ subclass(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_315])]) ).
fof(f6072,plain,
( ! [X0] :
( ~ subclass(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK0,sK0)),X0)
| member(unordered_pair(sK0,sK0),X0) )
| ~ spl10_313
| ~ spl10_315 ),
inference(forward_demodulation,[],[f6070,f6010]) ).
fof(f6070,plain,
( ! [X0] :
( ~ subclass(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X0)
| member(unordered_pair(sK0,sK0),X0) )
| ~ spl10_315 ),
inference(avatar_component_clause,[],[f6069]) ).
fof(f6071,plain,
( spl10_315
| ~ spl10_45
| ~ spl10_103 ),
inference(avatar_split_clause,[],[f970,f961,f494,f6069]) ).
fof(f970,plain,
( ! [X0] :
( member(unordered_pair(sK0,sK0),X0)
| ~ subclass(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),X0) )
| ~ spl10_45
| ~ spl10_103 ),
inference(resolution,[],[f963,f495]) ).
fof(f6015,plain,
( spl10_313
| spl10_314
| ~ spl10_54
| ~ spl10_103 ),
inference(avatar_split_clause,[],[f967,f961,f596,f6012,f6008]) ).
fof(f967,plain,
( unordered_pair(sK0,sK0) = unordered_pair(sK2,sK2)
| unordered_pair(sK0,sK0) = unordered_pair(sK2,unordered_pair(sK3,sK3))
| ~ spl10_54
| ~ spl10_103 ),
inference(resolution,[],[f963,f597]) ).
fof(f5982,plain,
( spl10_312
| ~ spl10_59
| ~ spl10_165 ),
inference(avatar_split_clause,[],[f1873,f1736,f635,f5980]) ).
fof(f1873,plain,
( ! [X0,X1] :
( subclass(X0,union(X1,sum_class(universal_class)))
| ~ member(sK6(X0,union(X1,sum_class(universal_class))),sK0) )
| ~ spl10_59
| ~ spl10_165 ),
inference(resolution,[],[f1737,f636]) ).
fof(f5978,plain,
( spl10_311
| ~ spl10_59
| ~ spl10_164 ),
inference(avatar_split_clause,[],[f1851,f1732,f635,f5976]) ).
fof(f1851,plain,
( ! [X0,X1] :
( subclass(X0,union(sum_class(universal_class),X1))
| ~ member(sK6(X0,union(sum_class(universal_class),X1)),sK0) )
| ~ spl10_59
| ~ spl10_164 ),
inference(resolution,[],[f1733,f636]) ).
fof(f5899,plain,
( spl10_310
| ~ spl10_59
| ~ spl10_174 ),
inference(avatar_split_clause,[],[f2082,f1775,f635,f5897]) ).
fof(f5897,plain,
( spl10_310
<=> ! [X2,X0,X1] :
( ~ member(X0,X1)
| member(X0,sum_class(union(sum_class(universal_class),X2)))
| ~ member(X1,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_310])]) ).
fof(f2082,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| member(X0,sum_class(union(sum_class(universal_class),X2)))
| ~ member(X1,sK0) )
| ~ spl10_59
| ~ spl10_174 ),
inference(resolution,[],[f1776,f636]) ).
fof(f5895,plain,
( spl10_309
| ~ spl10_59
| ~ spl10_173 ),
inference(avatar_split_clause,[],[f2026,f1771,f635,f5893]) ).
fof(f5893,plain,
( spl10_309
<=> ! [X2,X0,X1] :
( ~ member(X0,X1)
| member(X0,sum_class(union(X2,sum_class(universal_class))))
| ~ member(X1,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_309])]) ).
fof(f2026,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| member(X0,sum_class(union(X2,sum_class(universal_class))))
| ~ member(X1,sK0) )
| ~ spl10_59
| ~ spl10_173 ),
inference(resolution,[],[f1772,f636]) ).
fof(f5891,plain,
( spl10_308
| ~ spl10_59
| ~ spl10_150 ),
inference(avatar_split_clause,[],[f1618,f1473,f635,f5889]) ).
fof(f5889,plain,
( spl10_308
<=> ! [X0] :
( ~ member(X0,sum_class(complement(sum_class(universal_class))))
| ~ member(sK7(X0,complement(sum_class(universal_class))),sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_308])]) ).
fof(f1618,plain,
( ! [X0] :
( ~ member(X0,sum_class(complement(sum_class(universal_class))))
| ~ member(sK7(X0,complement(sum_class(universal_class))),sK0) )
| ~ spl10_59
| ~ spl10_150 ),
inference(resolution,[],[f1474,f636]) ).
fof(f5887,plain,
( ~ spl10_307
| ~ spl10_5
| ~ spl10_119 ),
inference(avatar_split_clause,[],[f1124,f1071,f292,f5884]) ).
fof(f5884,plain,
( spl10_307
<=> subclass(universal_class,null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_307])]) ).
fof(f1124,plain,
( ~ subclass(universal_class,null_class)
| ~ spl10_5
| ~ spl10_119 ),
inference(resolution,[],[f1072,f293]) ).
fof(f5881,plain,
( ~ spl10_306
| ~ spl10_12
| ~ spl10_101 ),
inference(avatar_split_clause,[],[f949,f946,f324,f5878]) ).
fof(f5878,plain,
( spl10_306
<=> inductive(sum_class(null_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_306])]) ).
fof(f949,plain,
( ~ inductive(sum_class(null_class))
| ~ spl10_12
| ~ spl10_101 ),
inference(resolution,[],[f947,f325]) ).
fof(f5865,plain,
( spl10_305
| ~ spl10_1
| ~ spl10_191 ),
inference(avatar_split_clause,[],[f2464,f2362,f272,f5862]) ).
fof(f2464,plain,
( sK0 = first(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK9,sK9))))
| ~ spl10_1
| ~ spl10_191 ),
inference(resolution,[],[f2363,f274]) ).
fof(f5860,plain,
( spl10_304
| ~ spl10_1
| ~ spl10_190 ),
inference(avatar_split_clause,[],[f2428,f2358,f272,f5857]) ).
fof(f2428,plain,
( sK9 = second(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK9,sK9))))
| ~ spl10_1
| ~ spl10_190 ),
inference(resolution,[],[f2359,f274]) ).
fof(f5855,plain,
( ~ spl10_302
| spl10_303
| ~ spl10_118
| ~ spl10_266 ),
inference(avatar_split_clause,[],[f5103,f4972,f1067,f5852,f5848]) ).
fof(f5848,plain,
( spl10_302
<=> inductive(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_302])]) ).
fof(f4972,plain,
( spl10_266
<=> subclass(sK0,sum_class(universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_266])]) ).
fof(f5103,plain,
( member(null_class,sum_class(universal_class))
| ~ inductive(sK0)
| ~ spl10_118
| ~ spl10_266 ),
inference(resolution,[],[f4974,f1068]) ).
fof(f4974,plain,
( subclass(sK0,sum_class(universal_class))
| ~ spl10_266 ),
inference(avatar_component_clause,[],[f4972]) ).
fof(f5846,plain,
( spl10_301
| ~ spl10_1
| ~ spl10_189 ),
inference(avatar_split_clause,[],[f2389,f2339,f272,f5844]) ).
fof(f5844,plain,
( spl10_301
<=> ! [X0,X1] :
( ~ member(universal_class,X0)
| member(sK0,sum_class(intersection(X0,X1)))
| ~ member(universal_class,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_301])]) ).
fof(f2389,plain,
( ! [X0,X1] :
( ~ member(universal_class,X0)
| member(sK0,sum_class(intersection(X0,X1)))
| ~ member(universal_class,X1) )
| ~ spl10_1
| ~ spl10_189 ),
inference(resolution,[],[f2340,f274]) ).
fof(f5842,plain,
( spl10_300
| ~ spl10_59
| ~ spl10_124 ),
inference(avatar_split_clause,[],[f1276,f1191,f635,f5840]) ).
fof(f1276,plain,
( ! [X0] :
( subclass(complement(sum_class(universal_class)),X0)
| ~ member(sK6(complement(sum_class(universal_class)),X0),sK0) )
| ~ spl10_59
| ~ spl10_124 ),
inference(resolution,[],[f1192,f636]) ).
fof(f5838,plain,
( spl10_299
| ~ spl10_7
| ~ spl10_96 ),
inference(avatar_split_clause,[],[f920,f895,f300,f5835]) ).
fof(f5835,plain,
( spl10_299
<=> sK9 = first(unordered_pair(unordered_pair(sK9,sK9),unordered_pair(sK9,unordered_pair(sK0,sK0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_299])]) ).
fof(f920,plain,
( sK9 = first(unordered_pair(unordered_pair(sK9,sK9),unordered_pair(sK9,unordered_pair(sK0,sK0))))
| ~ spl10_7
| ~ spl10_96 ),
inference(resolution,[],[f896,f302]) ).
fof(f5833,plain,
( spl10_298
| ~ spl10_1
| ~ spl10_96 ),
inference(avatar_split_clause,[],[f917,f895,f272,f5830]) ).
fof(f5830,plain,
( spl10_298
<=> sK0 = first(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK0,sK0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_298])]) ).
fof(f917,plain,
( sK0 = first(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK0,sK0))))
| ~ spl10_1
| ~ spl10_96 ),
inference(resolution,[],[f896,f274]) ).
fof(f5828,plain,
( spl10_297
| ~ spl10_7
| ~ spl10_95 ),
inference(avatar_split_clause,[],[f906,f891,f300,f5825]) ).
fof(f5825,plain,
( spl10_297
<=> sK0 = second(unordered_pair(unordered_pair(sK9,sK9),unordered_pair(sK9,unordered_pair(sK0,sK0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_297])]) ).
fof(f906,plain,
( sK0 = second(unordered_pair(unordered_pair(sK9,sK9),unordered_pair(sK9,unordered_pair(sK0,sK0))))
| ~ spl10_7
| ~ spl10_95 ),
inference(resolution,[],[f892,f302]) ).
fof(f5823,plain,
( spl10_296
| ~ spl10_1
| ~ spl10_95 ),
inference(avatar_split_clause,[],[f903,f891,f272,f5820]) ).
fof(f5820,plain,
( spl10_296
<=> sK0 = second(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK0,sK0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_296])]) ).
fof(f903,plain,
( sK0 = second(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK0,sK0))))
| ~ spl10_1
| ~ spl10_95 ),
inference(resolution,[],[f892,f274]) ).
fof(f5818,plain,
( ~ spl10_105
| ~ spl10_12
| spl10_30 ),
inference(avatar_split_clause,[],[f987,f409,f324,f983]) ).
fof(f983,plain,
( spl10_105
<=> inductive(universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_105])]) ).
fof(f987,plain,
( ~ inductive(universal_class)
| ~ spl10_12
| spl10_30 ),
inference(resolution,[],[f410,f325]) ).
fof(f410,plain,
( ~ member(null_class,universal_class)
| spl10_30 ),
inference(avatar_component_clause,[],[f409]) ).
fof(f5813,plain,
( spl10_295
| ~ spl10_30
| ~ spl10_95 ),
inference(avatar_split_clause,[],[f899,f891,f409,f5810]) ).
fof(f5810,plain,
( spl10_295
<=> sK0 = second(unordered_pair(unordered_pair(null_class,null_class),unordered_pair(null_class,unordered_pair(sK0,sK0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_295])]) ).
fof(f899,plain,
( sK0 = second(unordered_pair(unordered_pair(null_class,null_class),unordered_pair(null_class,unordered_pair(sK0,sK0))))
| ~ spl10_30
| ~ spl10_95 ),
inference(resolution,[],[f892,f411]) ).
fof(f5681,plain,
( spl10_294
| ~ spl10_1
| ~ spl10_187 ),
inference(avatar_split_clause,[],[f2304,f2256,f272,f5679]) ).
fof(f5679,plain,
( spl10_294
<=> ! [X0,X1] :
( ~ member(X0,sK0)
| ~ subclass(sK0,X1)
| member(X0,sum_class(power_class(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_294])]) ).
fof(f2304,plain,
( ! [X0,X1] :
( ~ member(X0,sK0)
| ~ subclass(sK0,X1)
| member(X0,sum_class(power_class(X1))) )
| ~ spl10_1
| ~ spl10_187 ),
inference(resolution,[],[f2257,f274]) ).
fof(f5677,plain,
( spl10_293
| ~ spl10_1
| ~ spl10_186 ),
inference(avatar_split_clause,[],[f2268,f2252,f272,f5675]) ).
fof(f5675,plain,
( spl10_293
<=> ! [X0,X1] :
( ~ member(X0,sK0)
| member(sK0,X1)
| member(X0,sum_class(complement(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_293])]) ).
fof(f2268,plain,
( ! [X0,X1] :
( ~ member(X0,sK0)
| member(sK0,X1)
| member(X0,sum_class(complement(X1))) )
| ~ spl10_1
| ~ spl10_186 ),
inference(resolution,[],[f2253,f274]) ).
fof(f5671,plain,
( ~ spl10_291
| spl10_292
| ~ spl10_59
| ~ spl10_121 ),
inference(avatar_split_clause,[],[f1173,f1144,f635,f5668,f5664]) ).
fof(f5664,plain,
( spl10_291
<=> member(sK4(complement(sum_class(universal_class))),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_291])]) ).
fof(f1173,plain,
( null_class = complement(sum_class(universal_class))
| ~ member(sK4(complement(sum_class(universal_class))),sK0)
| ~ spl10_59
| ~ spl10_121 ),
inference(resolution,[],[f1145,f636]) ).
fof(f5662,plain,
( spl10_290
| ~ spl10_51
| ~ spl10_59 ),
inference(avatar_split_clause,[],[f661,f635,f554,f5660]) ).
fof(f661,plain,
( ! [X0,X1] :
( ~ member(X0,sK0)
| member(X1,sum_class(sum_class(universal_class)))
| ~ member(X1,X0) )
| ~ spl10_51
| ~ spl10_59 ),
inference(resolution,[],[f636,f555]) ).
fof(f5644,plain,
( spl10_289
| ~ spl10_80
| ~ spl10_83 ),
inference(avatar_split_clause,[],[f830,f825,f785,f5642]) ).
fof(f5642,plain,
( spl10_289
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class))))),sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class)))))))),compose(X1,X2))
| ~ member(X0,universal_class)
| null_class = domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))
| ~ member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_289])]) ).
fof(f785,plain,
( spl10_80
<=> ! [X1] :
( member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))),X1)
| null_class = X1
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_80])]) ).
fof(f825,plain,
( spl10_83
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),compose(X1,X0))
| ~ member(X3,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X2,X2),universal_class)),universal_class)))),universal_class)),universal_class)))))
| ~ member(X2,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_83])]) ).
fof(f830,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class))))),sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class)))))))),compose(X1,X2))
| ~ member(X0,universal_class)
| null_class = domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))
| ~ member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),universal_class) )
| ~ spl10_80
| ~ spl10_83 ),
inference(resolution,[],[f826,f786]) ).
fof(f786,plain,
( ! [X1] :
( member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))),X1)
| null_class = X1
| ~ member(X1,universal_class) )
| ~ spl10_80 ),
inference(avatar_component_clause,[],[f785]) ).
fof(f826,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X3,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X2,X2),universal_class)),universal_class)))),universal_class)),universal_class)))))
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),compose(X1,X0))
| ~ member(X2,universal_class) )
| ~ spl10_83 ),
inference(avatar_component_clause,[],[f825]) ).
fof(f5640,plain,
( spl10_288
| ~ spl10_79
| ~ spl10_80 ),
inference(avatar_split_clause,[],[f799,f785,f781,f5638]) ).
fof(f5638,plain,
( spl10_288
<=> ! [X0,X1] :
( cross_product(X0,X1) = null_class
| ~ member(cross_product(X0,X1),universal_class)
| sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))) = unordered_pair(unordered_pair(first(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))),first(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))),unordered_pair(first(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))),unordered_pair(second(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))),second(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_288])]) ).
fof(f781,plain,
( spl10_79
<=> ! [X2,X0,X1] :
( unordered_pair(unordered_pair(first(X2),first(X2)),unordered_pair(first(X2),unordered_pair(second(X2),second(X2)))) = X2
| ~ member(X2,cross_product(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_79])]) ).
fof(f799,plain,
( ! [X0,X1] :
( cross_product(X0,X1) = null_class
| ~ member(cross_product(X0,X1),universal_class)
| sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))) = unordered_pair(unordered_pair(first(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))),first(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))),unordered_pair(first(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))),unordered_pair(second(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))),second(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))))) )
| ~ spl10_79
| ~ spl10_80 ),
inference(resolution,[],[f786,f782]) ).
fof(f782,plain,
( ! [X2,X0,X1] :
( ~ member(X2,cross_product(X0,X1))
| unordered_pair(unordered_pair(first(X2),first(X2)),unordered_pair(first(X2),unordered_pair(second(X2),second(X2)))) = X2 )
| ~ spl10_79 ),
inference(avatar_component_clause,[],[f781]) ).
fof(f5636,plain,
( spl10_286
| ~ spl10_287
| spl10_244
| ~ spl10_77
| ~ spl10_80 ),
inference(avatar_split_clause,[],[f809,f785,f763,f4115,f5633,f5629]) ).
fof(f5629,plain,
( spl10_286
<=> sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class))))) = unordered_pair(unordered_pair(sK5(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class)))))),sK5(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class))))))),unordered_pair(sK5(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class)))))),unordered_pair(sK5(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class)))))),sK5(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class))))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_286])]) ).
fof(f763,plain,
( spl10_77
<=> ! [X0] :
( unordered_pair(unordered_pair(sK5(X0),sK5(X0)),unordered_pair(sK5(X0),unordered_pair(sK5(X0),sK5(X0)))) = X0
| ~ member(X0,identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_77])]) ).
fof(f809,plain,
( null_class = identity_relation
| ~ member(identity_relation,universal_class)
| sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class))))) = unordered_pair(unordered_pair(sK5(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class)))))),sK5(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class))))))),unordered_pair(sK5(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class)))))),unordered_pair(sK5(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class)))))),sK5(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class)))))))))
| ~ spl10_77
| ~ spl10_80 ),
inference(resolution,[],[f786,f764]) ).
fof(f764,plain,
( ! [X0] :
( ~ member(X0,identity_relation)
| unordered_pair(unordered_pair(sK5(X0),sK5(X0)),unordered_pair(sK5(X0),unordered_pair(sK5(X0),sK5(X0)))) = X0 )
| ~ spl10_77 ),
inference(avatar_component_clause,[],[f763]) ).
fof(f5556,plain,
( spl10_285
| ~ spl10_78
| ~ spl10_90 ),
inference(avatar_split_clause,[],[f868,f863,f767,f5554]) ).
fof(f5554,plain,
( spl10_285
<=> ! [X0,X3,X2,X1] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),X3)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),flip(X3))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_285])]) ).
fof(f767,plain,
( spl10_78
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3))
| ~ member(X1,X3)
| ~ member(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_78])]) ).
fof(f863,plain,
( spl10_90
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_90])]) ).
fof(f868,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),X3)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),flip(X3))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),cross_product(universal_class,universal_class)) )
| ~ spl10_78
| ~ spl10_90 ),
inference(resolution,[],[f864,f768]) ).
fof(f768,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3))
| ~ member(X1,X3)
| ~ member(X0,X2) )
| ~ spl10_78 ),
inference(avatar_component_clause,[],[f767]) ).
fof(f864,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3)) )
| ~ spl10_90 ),
inference(avatar_component_clause,[],[f863]) ).
fof(f5552,plain,
( spl10_284
| ~ spl10_162
| ~ spl10_241 ),
inference(avatar_split_clause,[],[f4797,f4103,f1724,f5550]) ).
fof(f5550,plain,
( spl10_284
<=> ! [X0] : subclass(intersection(sK0,X0),sum_class(universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_284])]) ).
fof(f4797,plain,
( ! [X0] : subclass(intersection(sK0,X0),sum_class(universal_class))
| ~ spl10_162
| ~ spl10_241 ),
inference(duplicate_literal_removal,[],[f4788]) ).
fof(f4788,plain,
( ! [X0] :
( subclass(intersection(sK0,X0),sum_class(universal_class))
| subclass(intersection(sK0,X0),sum_class(universal_class)) )
| ~ spl10_162
| ~ spl10_241 ),
inference(resolution,[],[f4104,f1725]) ).
fof(f5548,plain,
( spl10_283
| ~ spl10_78
| ~ spl10_89 ),
inference(avatar_split_clause,[],[f866,f859,f767,f5546]) ).
fof(f5546,plain,
( spl10_283
<=> ! [X0,X3,X2,X1] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),X3)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),unordered_pair(X1,X1))),rotate(X3))
| ~ member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_283])]) ).
fof(f859,plain,
( spl10_89
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),rotate(X0))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X1,X1))),X0)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_89])]) ).
fof(f866,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),X3)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),unordered_pair(X1,X1))),rotate(X3))
| ~ member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class)) )
| ~ spl10_78
| ~ spl10_89 ),
inference(resolution,[],[f860,f768]) ).
fof(f860,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X1,X1))),X0)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),rotate(X0)) )
| ~ spl10_89 ),
inference(avatar_component_clause,[],[f859]) ).
fof(f5535,plain,
( spl10_282
| ~ spl10_47
| ~ spl10_83 ),
inference(avatar_split_clause,[],[f833,f825,f502,f5533]) ).
fof(f5533,plain,
( spl10_282
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK7(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))),sK7(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))))))),compose(X2,X3))
| ~ member(X0,universal_class)
| ~ member(X1,sum_class(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_282])]) ).
fof(f833,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK7(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))),sK7(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))))))),compose(X2,X3))
| ~ member(X0,universal_class)
| ~ member(X1,sum_class(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))))) )
| ~ spl10_47
| ~ spl10_83 ),
inference(resolution,[],[f826,f503]) ).
fof(f5522,plain,
( spl10_281
| ~ spl10_33
| ~ spl10_83 ),
inference(avatar_split_clause,[],[f832,f825,f422,f5520]) ).
fof(f5520,plain,
( spl10_281
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK6(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),X3),sK6(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),X3)))),compose(X1,X2))
| ~ member(X0,universal_class)
| subclass(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_281])]) ).
fof(f832,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK6(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),X3),sK6(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),X3)))),compose(X1,X2))
| ~ member(X0,universal_class)
| subclass(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),X3) )
| ~ spl10_33
| ~ spl10_83 ),
inference(resolution,[],[f826,f423]) ).
fof(f5509,plain,
( spl10_280
| ~ spl10_16
| ~ spl10_83 ),
inference(avatar_split_clause,[],[f831,f825,f342,f5507]) ).
fof(f5507,plain,
( spl10_280
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK4(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))),sK4(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))))))),compose(X1,X2))
| ~ member(X0,universal_class)
| null_class = domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_280])]) ).
fof(f831,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK4(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))),sK4(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))))))),compose(X1,X2))
| ~ member(X0,universal_class)
| null_class = domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))) )
| ~ spl10_16
| ~ spl10_83 ),
inference(resolution,[],[f826,f343]) ).
fof(f5424,plain,
( spl10_279
| ~ spl10_78
| ~ spl10_79 ),
inference(avatar_split_clause,[],[f788,f781,f767,f5422]) ).
fof(f5422,plain,
( spl10_279
<=> ! [X0,X3,X2,X1] :
( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))) = unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))
| ~ member(X1,X2)
| ~ member(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_279])]) ).
fof(f788,plain,
( ! [X2,X3,X0,X1] :
( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))) = unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))
| ~ member(X1,X2)
| ~ member(X0,X3) )
| ~ spl10_78
| ~ spl10_79 ),
inference(resolution,[],[f782,f768]) ).
fof(f5364,plain,
( spl10_278
| ~ spl10_163
| ~ spl10_241 ),
inference(avatar_split_clause,[],[f4795,f4103,f1728,f5362]) ).
fof(f5362,plain,
( spl10_278
<=> ! [X0] : subclass(intersection(X0,sK0),sum_class(universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_278])]) ).
fof(f4795,plain,
( ! [X0] : subclass(intersection(X0,sK0),sum_class(universal_class))
| ~ spl10_163
| ~ spl10_241 ),
inference(duplicate_literal_removal,[],[f4790]) ).
fof(f4790,plain,
( ! [X0] :
( subclass(intersection(X0,sK0),sum_class(universal_class))
| subclass(intersection(X0,sK0),sum_class(universal_class)) )
| ~ spl10_163
| ~ spl10_241 ),
inference(resolution,[],[f4104,f1729]) ).
fof(f5360,plain,
( spl10_277
| ~ spl10_63
| ~ spl10_77 ),
inference(avatar_split_clause,[],[f770,f763,f651,f5358]) ).
fof(f5358,plain,
( spl10_277
<=> ! [X0] :
( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0))) = unordered_pair(unordered_pair(sK5(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0)))),sK5(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0))))),unordered_pair(sK5(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0)))),unordered_pair(sK5(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0)))),sK5(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0)))))))
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_277])]) ).
fof(f651,plain,
( spl10_63
<=> ! [X1] :
( member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X1,X1))),identity_relation)
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_63])]) ).
fof(f770,plain,
( ! [X0] :
( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0))) = unordered_pair(unordered_pair(sK5(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0)))),sK5(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0))))),unordered_pair(sK5(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0)))),unordered_pair(sK5(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0)))),sK5(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0)))))))
| ~ member(X0,universal_class) )
| ~ spl10_63
| ~ spl10_77 ),
inference(resolution,[],[f764,f652]) ).
fof(f652,plain,
( ! [X1] :
( member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X1,X1))),identity_relation)
| ~ member(X1,universal_class) )
| ~ spl10_63 ),
inference(avatar_component_clause,[],[f651]) ).
fof(f5219,plain,
( spl10_276
| ~ spl10_53
| ~ spl10_80 ),
inference(avatar_split_clause,[],[f806,f785,f589,f5217]) ).
fof(f5217,plain,
( spl10_276
<=> ! [X0,X1] :
( null_class = union(X0,X1)
| ~ member(union(X0,X1),universal_class)
| member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(union(X0,X1),union(X0,X1)),universal_class)),universal_class))))),X0)
| member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(union(X0,X1),union(X0,X1)),universal_class)),universal_class))))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_276])]) ).
fof(f589,plain,
( spl10_53
<=> ! [X2,X0,X1] :
( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_53])]) ).
fof(f806,plain,
( ! [X0,X1] :
( null_class = union(X0,X1)
| ~ member(union(X0,X1),universal_class)
| member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(union(X0,X1),union(X0,X1)),universal_class)),universal_class))))),X0)
| member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(union(X0,X1),union(X0,X1)),universal_class)),universal_class))))),X1) )
| ~ spl10_53
| ~ spl10_80 ),
inference(resolution,[],[f786,f590]) ).
fof(f590,plain,
( ! [X2,X0,X1] :
( ~ member(X2,union(X0,X1))
| member(X2,X0)
| member(X2,X1) )
| ~ spl10_53 ),
inference(avatar_component_clause,[],[f589]) ).
fof(f5215,plain,
( spl10_275
| ~ spl10_54
| ~ spl10_80 ),
inference(avatar_split_clause,[],[f797,f785,f596,f5213]) ).
fof(f5213,plain,
( spl10_275
<=> ! [X0,X1] :
( unordered_pair(X0,X1) = null_class
| ~ member(unordered_pair(X0,X1),universal_class)
| sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))) = X0
| sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_275])]) ).
fof(f797,plain,
( ! [X0,X1] :
( unordered_pair(X0,X1) = null_class
| ~ member(unordered_pair(X0,X1),universal_class)
| sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))) = X0
| sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))) = X1 )
| ~ spl10_54
| ~ spl10_80 ),
inference(resolution,[],[f786,f597]) ).
fof(f5145,plain,
( spl10_274
| ~ spl10_65
| ~ spl10_83 ),
inference(avatar_split_clause,[],[f828,f825,f669,f5143]) ).
fof(f5143,plain,
( spl10_274
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
| ~ member(X0,universal_class)
| null_class = intersection(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))),cross_product(unordered_pair(X1,X1),universal_class))
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_274])]) ).
fof(f669,plain,
( spl10_65
<=> ! [X0,X1] :
( member(X1,domain_of(X0))
| null_class = intersection(X0,cross_product(unordered_pair(X1,X1),universal_class))
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_65])]) ).
fof(f828,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
| ~ member(X0,universal_class)
| null_class = intersection(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))),cross_product(unordered_pair(X1,X1),universal_class))
| ~ member(X1,universal_class) )
| ~ spl10_65
| ~ spl10_83 ),
inference(resolution,[],[f826,f670]) ).
fof(f670,plain,
( ! [X0,X1] :
( member(X1,domain_of(X0))
| null_class = intersection(X0,cross_product(unordered_pair(X1,X1),universal_class))
| ~ member(X1,universal_class) )
| ~ spl10_65 ),
inference(avatar_component_clause,[],[f669]) ).
fof(f5141,plain,
( spl10_273
| ~ spl10_72
| ~ spl10_74 ),
inference(avatar_split_clause,[],[f737,f724,f706,f5139]) ).
fof(f737,plain,
( ! [X2,X0,X1] :
( domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X2,universal_class)),universal_class)))) = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X2,universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X2,universal_class)),universal_class))))))))
| ~ member(X0,universal_class)
| ~ function(X1)
| ~ member(X2,universal_class) )
| ~ spl10_72
| ~ spl10_74 ),
inference(resolution,[],[f725,f707]) ).
fof(f5102,plain,
( spl10_272
| ~ spl10_47
| ~ spl10_79 ),
inference(avatar_split_clause,[],[f792,f781,f502,f5100]) ).
fof(f5100,plain,
( spl10_272
<=> ! [X2,X0,X1] :
( sK7(X0,cross_product(X1,X2)) = unordered_pair(unordered_pair(first(sK7(X0,cross_product(X1,X2))),first(sK7(X0,cross_product(X1,X2)))),unordered_pair(first(sK7(X0,cross_product(X1,X2))),unordered_pair(second(sK7(X0,cross_product(X1,X2))),second(sK7(X0,cross_product(X1,X2))))))
| ~ member(X0,sum_class(cross_product(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_272])]) ).
fof(f792,plain,
( ! [X2,X0,X1] :
( sK7(X0,cross_product(X1,X2)) = unordered_pair(unordered_pair(first(sK7(X0,cross_product(X1,X2))),first(sK7(X0,cross_product(X1,X2)))),unordered_pair(first(sK7(X0,cross_product(X1,X2))),unordered_pair(second(sK7(X0,cross_product(X1,X2))),second(sK7(X0,cross_product(X1,X2))))))
| ~ member(X0,sum_class(cross_product(X1,X2))) )
| ~ spl10_47
| ~ spl10_79 ),
inference(resolution,[],[f782,f503]) ).
fof(f5087,plain,
( spl10_269
| ~ spl10_270
| spl10_271
| ~ spl10_75
| ~ spl10_80 ),
inference(avatar_split_clause,[],[f795,f785,f728,f5084,f5080,f5077]) ).
fof(f5077,plain,
( spl10_269
<=> ! [X0] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(universal_class,universal_class),universal_class)),universal_class))))),sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(universal_class,universal_class),universal_class)),universal_class))))))))) = X0
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_269])]) ).
fof(f5084,plain,
( spl10_271
<=> universal_class = null_class ),
introduced(avatar_definition,[new_symbols(naming,[spl10_271])]) ).
fof(f795,plain,
( ! [X0] :
( universal_class = null_class
| ~ member(universal_class,universal_class)
| first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(universal_class,universal_class),universal_class)),universal_class))))),sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(universal_class,universal_class),universal_class)),universal_class))))))))) = X0
| ~ member(X0,universal_class) )
| ~ spl10_75
| ~ spl10_80 ),
inference(resolution,[],[f786,f729]) ).
fof(f5075,plain,
( spl10_268
| ~ spl10_33
| ~ spl10_79 ),
inference(avatar_split_clause,[],[f791,f781,f422,f5073]) ).
fof(f5073,plain,
( spl10_268
<=> ! [X2,X0,X1] :
( sK6(cross_product(X0,X1),X2) = unordered_pair(unordered_pair(first(sK6(cross_product(X0,X1),X2)),first(sK6(cross_product(X0,X1),X2))),unordered_pair(first(sK6(cross_product(X0,X1),X2)),unordered_pair(second(sK6(cross_product(X0,X1),X2)),second(sK6(cross_product(X0,X1),X2)))))
| subclass(cross_product(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_268])]) ).
fof(f791,plain,
( ! [X2,X0,X1] :
( sK6(cross_product(X0,X1),X2) = unordered_pair(unordered_pair(first(sK6(cross_product(X0,X1),X2)),first(sK6(cross_product(X0,X1),X2))),unordered_pair(first(sK6(cross_product(X0,X1),X2)),unordered_pair(second(sK6(cross_product(X0,X1),X2)),second(sK6(cross_product(X0,X1),X2)))))
| subclass(cross_product(X0,X1),X2) )
| ~ spl10_33
| ~ spl10_79 ),
inference(resolution,[],[f782,f423]) ).
fof(f5033,plain,
( spl10_267
| ~ spl10_16
| ~ spl10_79 ),
inference(avatar_split_clause,[],[f790,f781,f342,f5031]) ).
fof(f5031,plain,
( spl10_267
<=> ! [X0,X1] :
( sK4(cross_product(X0,X1)) = unordered_pair(unordered_pair(first(sK4(cross_product(X0,X1))),first(sK4(cross_product(X0,X1)))),unordered_pair(first(sK4(cross_product(X0,X1))),unordered_pair(second(sK4(cross_product(X0,X1))),second(sK4(cross_product(X0,X1))))))
| cross_product(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_267])]) ).
fof(f790,plain,
( ! [X0,X1] :
( sK4(cross_product(X0,X1)) = unordered_pair(unordered_pair(first(sK4(cross_product(X0,X1))),first(sK4(cross_product(X0,X1)))),unordered_pair(first(sK4(cross_product(X0,X1))),unordered_pair(second(sK4(cross_product(X0,X1))),second(sK4(cross_product(X0,X1))))))
| cross_product(X0,X1) = null_class )
| ~ spl10_16
| ~ spl10_79 ),
inference(resolution,[],[f782,f343]) ).
fof(f4975,plain,
( spl10_266
| ~ spl10_33
| ~ spl10_241 ),
inference(avatar_split_clause,[],[f4798,f4103,f422,f4972]) ).
fof(f4798,plain,
( subclass(sK0,sum_class(universal_class))
| ~ spl10_33
| ~ spl10_241 ),
inference(duplicate_literal_removal,[],[f4787]) ).
fof(f4787,plain,
( subclass(sK0,sum_class(universal_class))
| subclass(sK0,sum_class(universal_class))
| ~ spl10_33
| ~ spl10_241 ),
inference(resolution,[],[f4104,f423]) ).
fof(f4970,plain,
( spl10_265
| ~ spl10_12
| ~ spl10_83 ),
inference(avatar_split_clause,[],[f829,f825,f324,f4968]) ).
fof(f4968,plain,
( spl10_265
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X1,X2))
| ~ member(X0,universal_class)
| ~ inductive(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_265])]) ).
fof(f829,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X1,X2))
| ~ member(X0,universal_class)
| ~ inductive(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))) )
| ~ spl10_12
| ~ spl10_83 ),
inference(resolution,[],[f826,f325]) ).
fof(f4966,plain,
( spl10_264
| ~ spl10_72
| ~ spl10_75 ),
inference(avatar_split_clause,[],[f750,f728,f706,f4964]) ).
fof(f750,plain,
( ! [X2,X0,X1] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X2,universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X2,universal_class)),universal_class)))))))) = X0
| ~ member(X0,universal_class)
| ~ function(X1)
| ~ member(X2,universal_class) )
| ~ spl10_72
| ~ spl10_75 ),
inference(resolution,[],[f729,f707]) ).
fof(f4927,plain,
( spl10_263
| ~ spl10_51
| ~ spl10_81 ),
inference(avatar_split_clause,[],[f817,f811,f554,f4925]) ).
fof(f4925,plain,
( spl10_263
<=> ! [X0,X1] :
( ~ member(union(X0,unordered_pair(X0,X0)),universal_class)
| ~ member(X0,universal_class)
| member(X1,sum_class(successor_relation))
| ~ member(X1,unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(union(X0,unordered_pair(X0,X0)),union(X0,unordered_pair(X0,X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_263])]) ).
fof(f811,plain,
( spl10_81
<=> ! [X0] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(union(X0,unordered_pair(X0,X0)),union(X0,unordered_pair(X0,X0))))),successor_relation)
| ~ member(union(X0,unordered_pair(X0,X0)),universal_class)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_81])]) ).
fof(f817,plain,
( ! [X0,X1] :
( ~ member(union(X0,unordered_pair(X0,X0)),universal_class)
| ~ member(X0,universal_class)
| member(X1,sum_class(successor_relation))
| ~ member(X1,unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(union(X0,unordered_pair(X0,X0)),union(X0,unordered_pair(X0,X0)))))) )
| ~ spl10_51
| ~ spl10_81 ),
inference(resolution,[],[f812,f555]) ).
fof(f812,plain,
( ! [X0] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(union(X0,unordered_pair(X0,X0)),union(X0,unordered_pair(X0,X0))))),successor_relation)
| ~ member(union(X0,unordered_pair(X0,X0)),universal_class)
| ~ member(X0,universal_class) )
| ~ spl10_81 ),
inference(avatar_component_clause,[],[f811]) ).
fof(f4815,plain,
( spl10_262
| ~ spl10_45
| ~ spl10_81 ),
inference(avatar_split_clause,[],[f818,f811,f494,f4813]) ).
fof(f818,plain,
( ! [X0,X1] :
( ~ member(union(X0,unordered_pair(X0,X0)),universal_class)
| ~ member(X0,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(union(X0,unordered_pair(X0,X0)),union(X0,unordered_pair(X0,X0))))),X1)
| ~ subclass(successor_relation,X1) )
| ~ spl10_45
| ~ spl10_81 ),
inference(resolution,[],[f812,f495]) ).
fof(f4811,plain,
( spl10_261
| ~ spl10_47
| ~ spl10_77 ),
inference(avatar_split_clause,[],[f774,f763,f502,f4809]) ).
fof(f4809,plain,
( spl10_261
<=> ! [X0] :
( sK7(X0,identity_relation) = unordered_pair(unordered_pair(sK5(sK7(X0,identity_relation)),sK5(sK7(X0,identity_relation))),unordered_pair(sK5(sK7(X0,identity_relation)),unordered_pair(sK5(sK7(X0,identity_relation)),sK5(sK7(X0,identity_relation)))))
| ~ member(X0,sum_class(identity_relation)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_261])]) ).
fof(f774,plain,
( ! [X0] :
( sK7(X0,identity_relation) = unordered_pair(unordered_pair(sK5(sK7(X0,identity_relation)),sK5(sK7(X0,identity_relation))),unordered_pair(sK5(sK7(X0,identity_relation)),unordered_pair(sK5(sK7(X0,identity_relation)),sK5(sK7(X0,identity_relation)))))
| ~ member(X0,sum_class(identity_relation)) )
| ~ spl10_47
| ~ spl10_77 ),
inference(resolution,[],[f764,f503]) ).
fof(f4802,plain,
( spl10_260
| ~ spl10_33
| ~ spl10_77 ),
inference(avatar_split_clause,[],[f773,f763,f422,f4800]) ).
fof(f4800,plain,
( spl10_260
<=> ! [X0] :
( sK6(identity_relation,X0) = unordered_pair(unordered_pair(sK5(sK6(identity_relation,X0)),sK5(sK6(identity_relation,X0))),unordered_pair(sK5(sK6(identity_relation,X0)),unordered_pair(sK5(sK6(identity_relation,X0)),sK5(sK6(identity_relation,X0)))))
| subclass(identity_relation,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_260])]) ).
fof(f773,plain,
( ! [X0] :
( sK6(identity_relation,X0) = unordered_pair(unordered_pair(sK5(sK6(identity_relation,X0)),sK5(sK6(identity_relation,X0))),unordered_pair(sK5(sK6(identity_relation,X0)),unordered_pair(sK5(sK6(identity_relation,X0)),sK5(sK6(identity_relation,X0)))))
| subclass(identity_relation,X0) )
| ~ spl10_33
| ~ spl10_77 ),
inference(resolution,[],[f764,f423]) ).
fof(f4644,plain,
( spl10_259
| ~ spl10_35
| ~ spl10_80 ),
inference(avatar_split_clause,[],[f801,f785,f430,f4642]) ).
fof(f4642,plain,
( spl10_259
<=> ! [X0,X1] :
( intersection(X0,X1) = null_class
| ~ member(intersection(X0,X1),universal_class)
| member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_259])]) ).
fof(f801,plain,
( ! [X0,X1] :
( intersection(X0,X1) = null_class
| ~ member(intersection(X0,X1),universal_class)
| member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))),X0) )
| ~ spl10_35
| ~ spl10_80 ),
inference(resolution,[],[f786,f431]) ).
fof(f4640,plain,
( spl10_258
| ~ spl10_36
| ~ spl10_80 ),
inference(avatar_split_clause,[],[f800,f785,f434,f4638]) ).
fof(f4638,plain,
( spl10_258
<=> ! [X0,X1] :
( intersection(X0,X1) = null_class
| ~ member(intersection(X0,X1),universal_class)
| member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_258])]) ).
fof(f800,plain,
( ! [X0,X1] :
( intersection(X0,X1) = null_class
| ~ member(intersection(X0,X1),universal_class)
| member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))),X1) )
| ~ spl10_36
| ~ spl10_80 ),
inference(resolution,[],[f786,f435]) ).
fof(f4636,plain,
( spl10_257
| ~ spl10_39
| ~ spl10_80 ),
inference(avatar_split_clause,[],[f798,f785,f446,f4634]) ).
fof(f4634,plain,
( spl10_257
<=> ! [X0,X1] :
( unordered_pair(X0,X1) = null_class
| ~ member(unordered_pair(X0,X1),universal_class)
| member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_257])]) ).
fof(f446,plain,
( spl10_39
<=> ! [X2,X0,X1] :
( member(X0,universal_class)
| ~ member(X0,unordered_pair(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_39])]) ).
fof(f798,plain,
( ! [X0,X1] :
( unordered_pair(X0,X1) = null_class
| ~ member(unordered_pair(X0,X1),universal_class)
| member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))),universal_class) )
| ~ spl10_39
| ~ spl10_80 ),
inference(resolution,[],[f786,f447]) ).
fof(f447,plain,
( ! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| member(X0,universal_class) )
| ~ spl10_39 ),
inference(avatar_component_clause,[],[f446]) ).
fof(f4624,plain,
( spl10_256
| ~ spl10_9
| ~ spl10_90 ),
inference(avatar_split_clause,[],[f869,f863,f309,f4622]) ).
fof(f4622,plain,
( spl10_256
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))),unordered_pair(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),unordered_pair(X0,X0))),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(sK0,sK0))),unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(sK0,sK0)))),unordered_pair(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(sK0,sK0))),unordered_pair(X0,X0))),X1)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))),unordered_pair(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),unordered_pair(X0,X0))),flip(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_256])]) ).
fof(f869,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))),unordered_pair(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),unordered_pair(X0,X0))),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(sK0,sK0))),unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(sK0,sK0)))),unordered_pair(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(sK0,sK0))),unordered_pair(X0,X0))),X1)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))),unordered_pair(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),unordered_pair(X0,X0))),flip(X1)) )
| ~ spl10_9
| ~ spl10_90 ),
inference(superposition,[],[f864,f311]) ).
fof(f4620,plain,
( spl10_255
| ~ spl10_9
| ~ spl10_89 ),
inference(avatar_split_clause,[],[f867,f859,f309,f4618]) ).
fof(f4618,plain,
( spl10_255
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))),unordered_pair(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),unordered_pair(X0,X0))),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(X0,X0))),unordered_pair(sK0,sK0))),X1)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))),unordered_pair(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),unordered_pair(X0,X0))),rotate(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_255])]) ).
fof(f867,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))),unordered_pair(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),unordered_pair(X0,X0))),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(X0,X0))),unordered_pair(sK0,sK0))),X1)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))),unordered_pair(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),unordered_pair(X0,X0))),rotate(X1)) )
| ~ spl10_9
| ~ spl10_89 ),
inference(superposition,[],[f860,f311]) ).
fof(f4610,plain,
( spl10_254
| ~ spl10_43
| ~ spl10_57 ),
inference(avatar_split_clause,[],[f654,f627,f486,f4608]) ).
fof(f4608,plain,
( spl10_254
<=> ! [X0] :
( ~ inductive(X0)
| domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))) = X0
| ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_254])]) ).
fof(f627,plain,
( spl10_57
<=> ! [X0] :
( subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| ~ inductive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_57])]) ).
fof(f654,plain,
( ! [X0] :
( ~ inductive(X0)
| domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))) = X0
| ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class))))) )
| ~ spl10_43
| ~ spl10_57 ),
inference(resolution,[],[f628,f487]) ).
fof(f628,plain,
( ! [X0] :
( subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| ~ inductive(X0) )
| ~ spl10_57 ),
inference(avatar_component_clause,[],[f627]) ).
fof(f4244,plain,
( spl10_253
| ~ spl10_244
| ~ spl10_246 ),
inference(avatar_split_clause,[],[f4137,f4134,f4115,f4242]) ).
fof(f4242,plain,
( spl10_253
<=> ! [X0,X1] :
( identity_relation = X0
| ~ member(X0,universal_class)
| member(X1,sum_class(X0))
| ~ member(X1,sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_253])]) ).
fof(f4134,plain,
( spl10_246
<=> ! [X0,X1] :
( null_class = X0
| ~ member(X0,universal_class)
| member(X1,sum_class(X0))
| ~ member(X1,sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_246])]) ).
fof(f4137,plain,
( ! [X0,X1] :
( identity_relation = X0
| ~ member(X0,universal_class)
| member(X1,sum_class(X0))
| ~ member(X1,sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))) )
| ~ spl10_244
| ~ spl10_246 ),
inference(forward_demodulation,[],[f4135,f4117]) ).
fof(f4135,plain,
( ! [X0,X1] :
( ~ member(X1,sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))
| ~ member(X0,universal_class)
| member(X1,sum_class(X0))
| null_class = X0 )
| ~ spl10_246 ),
inference(avatar_component_clause,[],[f4134]) ).
fof(f4166,plain,
( spl10_252
| ~ spl10_26
| ~ spl10_80 ),
inference(avatar_split_clause,[],[f808,f785,f383,f4164]) ).
fof(f4164,plain,
( spl10_252
<=> ! [X0] :
( null_class = power_class(X0)
| ~ member(power_class(X0),universal_class)
| member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(power_class(X0),power_class(X0)),universal_class)),universal_class))))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_252])]) ).
fof(f383,plain,
( spl10_26
<=> ! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,power_class(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_26])]) ).
fof(f808,plain,
( ! [X0] :
( null_class = power_class(X0)
| ~ member(power_class(X0),universal_class)
| member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(power_class(X0),power_class(X0)),universal_class)),universal_class))))),universal_class) )
| ~ spl10_26
| ~ spl10_80 ),
inference(resolution,[],[f786,f384]) ).
fof(f384,plain,
( ! [X0,X1] :
( ~ member(X0,power_class(X1))
| member(X0,universal_class) )
| ~ spl10_26 ),
inference(avatar_component_clause,[],[f383]) ).
fof(f4162,plain,
( ~ spl10_251
| spl10_231
| ~ spl10_244 ),
inference(avatar_split_clause,[],[f4131,f4115,f3628,f4159]) ).
fof(f4159,plain,
( spl10_251
<=> subclass(sum_class(universal_class),identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_251])]) ).
fof(f3628,plain,
( spl10_231
<=> subclass(sum_class(universal_class),null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_231])]) ).
fof(f4131,plain,
( ~ subclass(sum_class(universal_class),identity_relation)
| spl10_231
| ~ spl10_244 ),
inference(superposition,[],[f3630,f4117]) ).
fof(f3630,plain,
( ~ subclass(sum_class(universal_class),null_class)
| spl10_231 ),
inference(avatar_component_clause,[],[f3628]) ).
fof(f4156,plain,
( spl10_250
| ~ spl10_27
| ~ spl10_80 ),
inference(avatar_split_clause,[],[f807,f785,f387,f4154]) ).
fof(f4154,plain,
( spl10_250
<=> ! [X0] :
( null_class = power_class(X0)
| ~ member(power_class(X0),universal_class)
| subclass(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(power_class(X0),power_class(X0)),universal_class)),universal_class))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_250])]) ).
fof(f807,plain,
( ! [X0] :
( null_class = power_class(X0)
| ~ member(power_class(X0),universal_class)
| subclass(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(power_class(X0),power_class(X0)),universal_class)),universal_class))))),X0) )
| ~ spl10_27
| ~ spl10_80 ),
inference(resolution,[],[f786,f388]) ).
fof(f4151,plain,
( spl10_249
| ~ spl10_28
| ~ spl10_80 ),
inference(avatar_split_clause,[],[f805,f785,f391,f4149]) ).
fof(f4149,plain,
( spl10_249
<=> ! [X0] :
( null_class = domain_of(X0)
| ~ member(domain_of(X0),universal_class)
| member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(domain_of(X0),domain_of(X0)),universal_class)),universal_class))))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_249])]) ).
fof(f391,plain,
( spl10_28
<=> ! [X0,X1] :
( member(X1,universal_class)
| ~ member(X1,domain_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_28])]) ).
fof(f805,plain,
( ! [X0] :
( null_class = domain_of(X0)
| ~ member(domain_of(X0),universal_class)
| member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(domain_of(X0),domain_of(X0)),universal_class)),universal_class))))),universal_class) )
| ~ spl10_28
| ~ spl10_80 ),
inference(resolution,[],[f786,f392]) ).
fof(f392,plain,
( ! [X0,X1] :
( ~ member(X1,domain_of(X0))
| member(X1,universal_class) )
| ~ spl10_28 ),
inference(avatar_component_clause,[],[f391]) ).
fof(f4146,plain,
( spl10_248
| ~ spl10_24
| ~ spl10_80 ),
inference(avatar_split_clause,[],[f803,f785,f375,f4144]) ).
fof(f4144,plain,
( spl10_248
<=> ! [X0] :
( complement(X0) = null_class
| ~ member(complement(X0),universal_class)
| member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(complement(X0),complement(X0)),universal_class)),universal_class))))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_248])]) ).
fof(f375,plain,
( spl10_24
<=> ! [X0,X1] :
( member(X1,universal_class)
| ~ member(X1,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_24])]) ).
fof(f803,plain,
( ! [X0] :
( complement(X0) = null_class
| ~ member(complement(X0),universal_class)
| member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(complement(X0),complement(X0)),universal_class)),universal_class))))),universal_class) )
| ~ spl10_24
| ~ spl10_80 ),
inference(resolution,[],[f786,f376]) ).
fof(f376,plain,
( ! [X0,X1] :
( ~ member(X1,complement(X0))
| member(X1,universal_class) )
| ~ spl10_24 ),
inference(avatar_component_clause,[],[f375]) ).
fof(f4141,plain,
( spl10_247
| ~ spl10_25
| ~ spl10_80 ),
inference(avatar_split_clause,[],[f802,f785,f379,f4139]) ).
fof(f802,plain,
( ! [X0] :
( complement(X0) = null_class
| ~ member(complement(X0),universal_class)
| ~ member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(complement(X0),complement(X0)),universal_class)),universal_class))))),X0) )
| ~ spl10_25
| ~ spl10_80 ),
inference(resolution,[],[f786,f380]) ).
fof(f4136,plain,
( spl10_246
| ~ spl10_51
| ~ spl10_80 ),
inference(avatar_split_clause,[],[f793,f785,f554,f4134]) ).
fof(f793,plain,
( ! [X0,X1] :
( null_class = X0
| ~ member(X0,universal_class)
| member(X1,sum_class(X0))
| ~ member(X1,sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))) )
| ~ spl10_51
| ~ spl10_80 ),
inference(resolution,[],[f786,f555]) ).
fof(f4122,plain,
( spl10_244
| spl10_245
| ~ spl10_16
| ~ spl10_77 ),
inference(avatar_split_clause,[],[f772,f763,f342,f4119,f4115]) ).
fof(f772,plain,
( sK4(identity_relation) = unordered_pair(unordered_pair(sK5(sK4(identity_relation)),sK5(sK4(identity_relation))),unordered_pair(sK5(sK4(identity_relation)),unordered_pair(sK5(sK4(identity_relation)),sK5(sK4(identity_relation)))))
| null_class = identity_relation
| ~ spl10_16
| ~ spl10_77 ),
inference(resolution,[],[f764,f343]) ).
fof(f4113,plain,
( spl10_243
| ~ spl10_47
| ~ spl10_74 ),
inference(avatar_split_clause,[],[f747,f724,f502,f4111]) ).
fof(f747,plain,
( ! [X0,X1] :
( sK7(X1,universal_class) = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK7(X1,universal_class),sK7(X1,universal_class)))))
| ~ member(X0,universal_class)
| ~ member(X1,sum_class(universal_class)) )
| ~ spl10_47
| ~ spl10_74 ),
inference(resolution,[],[f725,f503]) ).
fof(f4109,plain,
( spl10_242
| ~ spl10_34
| ~ spl10_65 ),
inference(avatar_split_clause,[],[f688,f669,f426,f4107]) ).
fof(f4107,plain,
( spl10_242
<=> ! [X0,X1] :
( null_class = intersection(X0,cross_product(unordered_pair(sK6(X1,domain_of(X0)),sK6(X1,domain_of(X0))),universal_class))
| ~ member(sK6(X1,domain_of(X0)),universal_class)
| subclass(X1,domain_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_242])]) ).
fof(f688,plain,
( ! [X0,X1] :
( null_class = intersection(X0,cross_product(unordered_pair(sK6(X1,domain_of(X0)),sK6(X1,domain_of(X0))),universal_class))
| ~ member(sK6(X1,domain_of(X0)),universal_class)
| subclass(X1,domain_of(X0)) )
| ~ spl10_34
| ~ spl10_65 ),
inference(resolution,[],[f670,f427]) ).
fof(f4105,plain,
( spl10_241
| ~ spl10_34
| ~ spl10_59 ),
inference(avatar_split_clause,[],[f663,f635,f426,f4103]) ).
fof(f663,plain,
( ! [X0] :
( ~ member(sK6(X0,sum_class(universal_class)),sK0)
| subclass(X0,sum_class(universal_class)) )
| ~ spl10_34
| ~ spl10_59 ),
inference(resolution,[],[f636,f427]) ).
fof(f4001,plain,
( spl10_240
| ~ spl10_45
| ~ spl10_80 ),
inference(avatar_split_clause,[],[f794,f785,f494,f3999]) ).
fof(f794,plain,
( ! [X0,X1] :
( null_class = X0
| ~ member(X0,universal_class)
| member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))),X1)
| ~ subclass(X0,X1) )
| ~ spl10_45
| ~ spl10_80 ),
inference(resolution,[],[f786,f495]) ).
fof(f3997,plain,
( spl10_239
| ~ spl10_33
| ~ spl10_74 ),
inference(avatar_split_clause,[],[f746,f724,f422,f3995]) ).
fof(f746,plain,
( ! [X0,X1] :
( sK6(universal_class,X1) = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK6(universal_class,X1),sK6(universal_class,X1)))))
| ~ member(X0,universal_class)
| subclass(universal_class,X1) )
| ~ spl10_33
| ~ spl10_74 ),
inference(resolution,[],[f725,f423]) ).
fof(f3926,plain,
( spl10_238
| ~ spl10_51
| ~ spl10_78 ),
inference(avatar_split_clause,[],[f777,f767,f554,f3924]) ).
fof(f3924,plain,
( spl10_238
<=> ! [X4,X0,X3,X2,X1] :
( ~ member(X0,X1)
| ~ member(X2,X3)
| member(X4,sum_class(cross_product(X3,X1)))
| ~ member(X4,unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_238])]) ).
fof(f777,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ member(X0,X1)
| ~ member(X2,X3)
| member(X4,sum_class(cross_product(X3,X1)))
| ~ member(X4,unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0)))) )
| ~ spl10_51
| ~ spl10_78 ),
inference(resolution,[],[f768,f555]) ).
fof(f3922,plain,
( spl10_237
| ~ spl10_47
| ~ spl10_75 ),
inference(avatar_split_clause,[],[f760,f728,f502,f3920]) ).
fof(f760,plain,
( ! [X0,X1] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK7(X1,universal_class),sK7(X1,universal_class))))) = X0
| ~ member(X0,universal_class)
| ~ member(X1,sum_class(universal_class)) )
| ~ spl10_47
| ~ spl10_75 ),
inference(resolution,[],[f729,f503]) ).
fof(f3869,plain,
( spl10_236
| ~ spl10_45
| ~ spl10_78 ),
inference(avatar_split_clause,[],[f778,f767,f494,f3867]) ).
fof(f3867,plain,
( spl10_236
<=> ! [X4,X0,X3,X2,X1] :
( ~ member(X0,X1)
| ~ member(X2,X3)
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),X4)
| ~ subclass(cross_product(X3,X1),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_236])]) ).
fof(f778,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ member(X0,X1)
| ~ member(X2,X3)
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),X4)
| ~ subclass(cross_product(X3,X1),X4) )
| ~ spl10_45
| ~ spl10_78 ),
inference(resolution,[],[f768,f495]) ).
fof(f3865,plain,
( spl10_235
| ~ spl10_33
| ~ spl10_75 ),
inference(avatar_split_clause,[],[f759,f728,f422,f3863]) ).
fof(f759,plain,
( ! [X0,X1] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK6(universal_class,X1),sK6(universal_class,X1))))) = X0
| ~ member(X0,universal_class)
| subclass(universal_class,X1) )
| ~ spl10_33
| ~ spl10_75 ),
inference(resolution,[],[f729,f423]) ).
fof(f3860,plain,
( ~ spl10_232
| ~ spl10_233
| spl10_234
| ~ spl10_20
| ~ spl10_71 ),
inference(avatar_split_clause,[],[f715,f702,f358,f3857,f3853,f3849]) ).
fof(f3849,plain,
( spl10_232
<=> function(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(cross_product(universal_class,universal_class),universal_class)),universal_class))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_232])]) ).
fof(f3857,plain,
( spl10_234
<=> inductive(cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_234])]) ).
fof(f702,plain,
( spl10_71
<=> ! [X0] :
( inductive(X0)
| ~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| ~ member(null_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_71])]) ).
fof(f715,plain,
( inductive(cross_product(universal_class,universal_class))
| ~ member(null_class,cross_product(universal_class,universal_class))
| ~ function(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(cross_product(universal_class,universal_class),universal_class)),universal_class)))))
| ~ spl10_20
| ~ spl10_71 ),
inference(resolution,[],[f703,f359]) ).
fof(f703,plain,
( ! [X0] :
( ~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| inductive(X0)
| ~ member(null_class,X0) )
| ~ spl10_71 ),
inference(avatar_component_clause,[],[f702]) ).
fof(f3631,plain,
( ~ spl10_231
| ~ spl10_5
| ~ spl10_223 ),
inference(avatar_split_clause,[],[f3489,f3049,f292,f3628]) ).
fof(f3049,plain,
( spl10_223
<=> ! [X0] :
( member(unordered_pair(sK0,sK0),X0)
| ~ subclass(sum_class(universal_class),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_223])]) ).
fof(f3489,plain,
( ~ subclass(sum_class(universal_class),null_class)
| ~ spl10_5
| ~ spl10_223 ),
inference(resolution,[],[f3050,f293]) ).
fof(f3050,plain,
( ! [X0] :
( member(unordered_pair(sK0,sK0),X0)
| ~ subclass(sum_class(universal_class),X0) )
| ~ spl10_223 ),
inference(avatar_component_clause,[],[f3049]) ).
fof(f3562,plain,
( spl10_230
| ~ spl10_22
| ~ spl10_74 ),
inference(avatar_split_clause,[],[f742,f724,f367,f3560]) ).
fof(f3560,plain,
( spl10_230
<=> ! [X0,X1] :
( sK5(X1) = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK5(X1),sK5(X1)))))
| ~ member(X0,universal_class)
| ~ member(X1,identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_230])]) ).
fof(f742,plain,
( ! [X0,X1] :
( sK5(X1) = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK5(X1),sK5(X1)))))
| ~ member(X0,universal_class)
| ~ member(X1,identity_relation) )
| ~ spl10_22
| ~ spl10_74 ),
inference(resolution,[],[f725,f368]) ).
fof(f3558,plain,
( spl10_229
| ~ spl10_15
| ~ spl10_74 ),
inference(avatar_split_clause,[],[f741,f724,f338,f3556]) ).
fof(f741,plain,
( ! [X0,X1] :
( sK4(X1) = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK4(X1),sK4(X1)))))
| ~ member(X0,universal_class)
| null_class = X1 )
| ~ spl10_15
| ~ spl10_74 ),
inference(resolution,[],[f725,f339]) ).
fof(f3554,plain,
( spl10_228
| ~ spl10_18
| ~ spl10_74 ),
inference(avatar_split_clause,[],[f739,f724,f350,f3552]) ).
fof(f739,plain,
( ! [X0,X1] :
( power_class(X1) = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(power_class(X1),power_class(X1)))))
| ~ member(X0,universal_class)
| ~ member(X1,universal_class) )
| ~ spl10_18
| ~ spl10_74 ),
inference(resolution,[],[f725,f351]) ).
fof(f3550,plain,
( spl10_227
| ~ spl10_19
| ~ spl10_74 ),
inference(avatar_split_clause,[],[f738,f724,f354,f3548]) ).
fof(f738,plain,
( ! [X0,X1] :
( sum_class(X1) = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sum_class(X1),sum_class(X1)))))
| ~ member(X0,universal_class)
| ~ member(X1,universal_class) )
| ~ spl10_19
| ~ spl10_74 ),
inference(resolution,[],[f725,f355]) ).
fof(f3546,plain,
( spl10_226
| ~ spl10_13
| ~ spl10_74 ),
inference(avatar_split_clause,[],[f735,f724,f328,f3544]) ).
fof(f735,plain,
( ! [X2,X0,X1] :
( unordered_pair(X1,X2) = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X2)))))
| ~ member(X0,universal_class) )
| ~ spl10_13
| ~ spl10_74 ),
inference(resolution,[],[f725,f329]) ).
fof(f3542,plain,
( spl10_225
| ~ spl10_51
| ~ spl10_73 ),
inference(avatar_split_clause,[],[f720,f710,f554,f3540]) ).
fof(f3540,plain,
( spl10_225
<=> ! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(X1,universal_class)
| member(X2,sum_class(element_relation))
| ~ member(X2,unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_225])]) ).
fof(f710,plain,
( spl10_73
<=> ! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| ~ member(X0,X1)
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_73])]) ).
fof(f720,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(X1,universal_class)
| member(X2,sum_class(element_relation))
| ~ member(X2,unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))) )
| ~ spl10_51
| ~ spl10_73 ),
inference(resolution,[],[f711,f555]) ).
fof(f711,plain,
( ! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| ~ member(X0,X1)
| ~ member(X1,universal_class) )
| ~ spl10_73 ),
inference(avatar_component_clause,[],[f710]) ).
fof(f3538,plain,
( spl10_224
| ~ spl10_51
| ~ spl10_72 ),
inference(avatar_split_clause,[],[f716,f706,f554,f3536]) ).
fof(f3536,plain,
( spl10_224
<=> ! [X2,X0,X1] :
( ~ function(X0)
| ~ member(X1,universal_class)
| member(X2,sum_class(universal_class))
| ~ member(X2,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(X1,universal_class)),universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_224])]) ).
fof(f716,plain,
( ! [X2,X0,X1] :
( ~ function(X0)
| ~ member(X1,universal_class)
| member(X2,sum_class(universal_class))
| ~ member(X2,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(X1,universal_class)),universal_class))))) )
| ~ spl10_51
| ~ spl10_72 ),
inference(resolution,[],[f707,f555]) ).
fof(f3051,plain,
( spl10_223
| ~ spl10_45
| ~ spl10_156 ),
inference(avatar_split_clause,[],[f1608,f1497,f494,f3049]) ).
fof(f1608,plain,
( ! [X0] :
( member(unordered_pair(sK0,sK0),X0)
| ~ subclass(sum_class(universal_class),X0) )
| ~ spl10_45
| ~ spl10_156 ),
inference(resolution,[],[f1499,f495]) ).
fof(f3047,plain,
( spl10_221
| spl10_222
| ~ spl10_12
| ~ spl10_79 ),
inference(avatar_split_clause,[],[f789,f781,f324,f3044,f3041]) ).
fof(f3041,plain,
( spl10_221
<=> ! [X0,X1] : ~ inductive(cross_product(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_221])]) ).
fof(f3044,plain,
( spl10_222
<=> null_class = unordered_pair(unordered_pair(first(null_class),first(null_class)),unordered_pair(first(null_class),unordered_pair(second(null_class),second(null_class)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_222])]) ).
fof(f789,plain,
( ! [X0,X1] :
( null_class = unordered_pair(unordered_pair(first(null_class),first(null_class)),unordered_pair(first(null_class),unordered_pair(second(null_class),second(null_class))))
| ~ inductive(cross_product(X0,X1)) )
| ~ spl10_12
| ~ spl10_79 ),
inference(resolution,[],[f782,f325]) ).
fof(f3039,plain,
( spl10_220
| ~ spl10_22
| ~ spl10_75 ),
inference(avatar_split_clause,[],[f755,f728,f367,f3037]) ).
fof(f3037,plain,
( spl10_220
<=> ! [X0,X1] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK5(X1),sK5(X1))))) = X0
| ~ member(X0,universal_class)
| ~ member(X1,identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_220])]) ).
fof(f755,plain,
( ! [X0,X1] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK5(X1),sK5(X1))))) = X0
| ~ member(X0,universal_class)
| ~ member(X1,identity_relation) )
| ~ spl10_22
| ~ spl10_75 ),
inference(resolution,[],[f729,f368]) ).
fof(f3035,plain,
( spl10_219
| ~ spl10_15
| ~ spl10_75 ),
inference(avatar_split_clause,[],[f754,f728,f338,f3033]) ).
fof(f754,plain,
( ! [X0,X1] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK4(X1),sK4(X1))))) = X0
| ~ member(X0,universal_class)
| null_class = X1 )
| ~ spl10_15
| ~ spl10_75 ),
inference(resolution,[],[f729,f339]) ).
fof(f3031,plain,
( spl10_218
| ~ spl10_18
| ~ spl10_75 ),
inference(avatar_split_clause,[],[f752,f728,f350,f3029]) ).
fof(f752,plain,
( ! [X0,X1] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(power_class(X1),power_class(X1))))) = X0
| ~ member(X0,universal_class)
| ~ member(X1,universal_class) )
| ~ spl10_18
| ~ spl10_75 ),
inference(resolution,[],[f729,f351]) ).
fof(f3027,plain,
( spl10_217
| ~ spl10_19
| ~ spl10_75 ),
inference(avatar_split_clause,[],[f751,f728,f354,f3025]) ).
fof(f751,plain,
( ! [X0,X1] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sum_class(X1),sum_class(X1))))) = X0
| ~ member(X0,universal_class)
| ~ member(X1,universal_class) )
| ~ spl10_19
| ~ spl10_75 ),
inference(resolution,[],[f729,f355]) ).
fof(f3023,plain,
( spl10_216
| ~ spl10_45
| ~ spl10_73 ),
inference(avatar_split_clause,[],[f721,f710,f494,f3021]) ).
fof(f721,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(X1,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2)
| ~ subclass(element_relation,X2) )
| ~ spl10_45
| ~ spl10_73 ),
inference(resolution,[],[f711,f495]) ).
fof(f3019,plain,
( spl10_215
| ~ spl10_45
| ~ spl10_72 ),
inference(avatar_split_clause,[],[f717,f706,f494,f3017]) ).
fof(f3017,plain,
( spl10_215
<=> ! [X2,X0,X1] :
( ~ function(X0)
| ~ member(X1,universal_class)
| member(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(X1,universal_class)),universal_class)))),X2)
| ~ subclass(universal_class,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_215])]) ).
fof(f717,plain,
( ! [X2,X0,X1] :
( ~ function(X0)
| ~ member(X1,universal_class)
| member(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(X1,universal_class)),universal_class)))),X2)
| ~ subclass(universal_class,X2) )
| ~ spl10_45
| ~ spl10_72 ),
inference(resolution,[],[f707,f495]) ).
fof(f3015,plain,
( spl10_214
| ~ spl10_51
| ~ spl10_65 ),
inference(avatar_split_clause,[],[f686,f669,f554,f3013]) ).
fof(f686,plain,
( ! [X2,X0,X1] :
( null_class = intersection(X0,cross_product(unordered_pair(X1,X1),universal_class))
| ~ member(X1,universal_class)
| member(X2,sum_class(domain_of(X0)))
| ~ member(X2,X1) )
| ~ spl10_51
| ~ spl10_65 ),
inference(resolution,[],[f670,f555]) ).
fof(f3011,plain,
( spl10_213
| ~ spl10_43
| ~ spl10_55 ),
inference(avatar_split_clause,[],[f621,f600,f486,f3009]) ).
fof(f3009,plain,
( spl10_213
<=> ! [X0] :
( ~ function(X0)
| identity_relation = compose(X0,domain_of(flip(cross_product(X0,universal_class))))
| ~ subclass(identity_relation,compose(X0,domain_of(flip(cross_product(X0,universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_213])]) ).
fof(f600,plain,
( spl10_55
<=> ! [X0] :
( subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation)
| ~ function(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_55])]) ).
fof(f621,plain,
( ! [X0] :
( ~ function(X0)
| identity_relation = compose(X0,domain_of(flip(cross_product(X0,universal_class))))
| ~ subclass(identity_relation,compose(X0,domain_of(flip(cross_product(X0,universal_class))))) )
| ~ spl10_43
| ~ spl10_55 ),
inference(resolution,[],[f601,f487]) ).
fof(f601,plain,
( ! [X0] :
( subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation)
| ~ function(X0) )
| ~ spl10_55 ),
inference(avatar_component_clause,[],[f600]) ).
fof(f2992,plain,
( spl10_212
| ~ spl10_47
| ~ spl10_54 ),
inference(avatar_split_clause,[],[f619,f596,f502,f2990]) ).
fof(f2990,plain,
( spl10_212
<=> ! [X2,X0,X1] :
( sK7(X0,unordered_pair(X1,X2)) = X1
| sK7(X0,unordered_pair(X1,X2)) = X2
| ~ member(X0,sum_class(unordered_pair(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_212])]) ).
fof(f619,plain,
( ! [X2,X0,X1] :
( sK7(X0,unordered_pair(X1,X2)) = X1
| sK7(X0,unordered_pair(X1,X2)) = X2
| ~ member(X0,sum_class(unordered_pair(X1,X2))) )
| ~ spl10_47
| ~ spl10_54 ),
inference(resolution,[],[f597,f503]) ).
fof(f2988,plain,
( spl10_211
| ~ spl10_47
| ~ spl10_53 ),
inference(avatar_split_clause,[],[f613,f589,f502,f2986]) ).
fof(f613,plain,
( ! [X2,X0,X1] :
( member(sK7(X0,union(X1,X2)),X1)
| member(sK7(X0,union(X1,X2)),X2)
| ~ member(X0,sum_class(union(X1,X2))) )
| ~ spl10_47
| ~ spl10_53 ),
inference(resolution,[],[f590,f503]) ).
fof(f2806,plain,
( spl10_210
| ~ spl10_13
| ~ spl10_75 ),
inference(avatar_split_clause,[],[f748,f728,f328,f2804]) ).
fof(f748,plain,
( ! [X2,X0,X1] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X2))))) = X0
| ~ member(X0,universal_class) )
| ~ spl10_13
| ~ spl10_75 ),
inference(resolution,[],[f729,f329]) ).
fof(f2802,plain,
( spl10_209
| ~ spl10_45
| ~ spl10_65 ),
inference(avatar_split_clause,[],[f687,f669,f494,f2800]) ).
fof(f2800,plain,
( spl10_209
<=> ! [X2,X0,X1] :
( null_class = intersection(X0,cross_product(unordered_pair(X1,X1),universal_class))
| ~ member(X1,universal_class)
| member(X1,X2)
| ~ subclass(domain_of(X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_209])]) ).
fof(f687,plain,
( ! [X2,X0,X1] :
( null_class = intersection(X0,cross_product(unordered_pair(X1,X1),universal_class))
| ~ member(X1,universal_class)
| member(X1,X2)
| ~ subclass(domain_of(X0),X2) )
| ~ spl10_45
| ~ spl10_65 ),
inference(resolution,[],[f670,f495]) ).
fof(f2798,plain,
( spl10_208
| ~ spl10_33
| ~ spl10_54 ),
inference(avatar_split_clause,[],[f618,f596,f422,f2796]) ).
fof(f2796,plain,
( spl10_208
<=> ! [X2,X0,X1] :
( sK6(unordered_pair(X0,X1),X2) = X0
| sK6(unordered_pair(X0,X1),X2) = X1
| subclass(unordered_pair(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_208])]) ).
fof(f618,plain,
( ! [X2,X0,X1] :
( sK6(unordered_pair(X0,X1),X2) = X0
| sK6(unordered_pair(X0,X1),X2) = X1
| subclass(unordered_pair(X0,X1),X2) )
| ~ spl10_33
| ~ spl10_54 ),
inference(resolution,[],[f597,f423]) ).
fof(f2780,plain,
( spl10_207
| ~ spl10_33
| ~ spl10_53 ),
inference(avatar_split_clause,[],[f612,f589,f422,f2778]) ).
fof(f612,plain,
( ! [X2,X0,X1] :
( member(sK6(union(X0,X1),X2),X0)
| member(sK6(union(X0,X1),X2),X1)
| subclass(union(X0,X1),X2) )
| ~ spl10_33
| ~ spl10_53 ),
inference(resolution,[],[f590,f423]) ).
fof(f2776,plain,
( spl10_206
| ~ spl10_34
| ~ spl10_52 ),
inference(avatar_split_clause,[],[f607,f585,f426,f2774]) ).
fof(f585,plain,
( spl10_52
<=> ! [X2,X0,X1] :
( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_52])]) ).
fof(f607,plain,
( ! [X2,X0,X1] :
( ~ member(sK6(X0,intersection(X1,X2)),X2)
| ~ member(sK6(X0,intersection(X1,X2)),X1)
| subclass(X0,intersection(X1,X2)) )
| ~ spl10_34
| ~ spl10_52 ),
inference(resolution,[],[f586,f427]) ).
fof(f586,plain,
( ! [X2,X0,X1] :
( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) )
| ~ spl10_52 ),
inference(avatar_component_clause,[],[f585]) ).
fof(f2748,plain,
( ~ spl10_204
| spl10_205
| ~ spl10_12
| ~ spl10_77 ),
inference(avatar_split_clause,[],[f771,f763,f324,f2745,f2741]) ).
fof(f2741,plain,
( spl10_204
<=> inductive(identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_204])]) ).
fof(f2745,plain,
( spl10_205
<=> null_class = unordered_pair(unordered_pair(sK5(null_class),sK5(null_class)),unordered_pair(sK5(null_class),unordered_pair(sK5(null_class),sK5(null_class)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_205])]) ).
fof(f771,plain,
( null_class = unordered_pair(unordered_pair(sK5(null_class),sK5(null_class)),unordered_pair(sK5(null_class),unordered_pair(sK5(null_class),sK5(null_class))))
| ~ inductive(identity_relation)
| ~ spl10_12
| ~ spl10_77 ),
inference(resolution,[],[f764,f325]) ).
fof(f2739,plain,
( spl10_203
| ~ spl10_51
| ~ spl10_63 ),
inference(avatar_split_clause,[],[f659,f651,f554,f2737]) ).
fof(f2737,plain,
( spl10_203
<=> ! [X0,X1] :
( ~ member(X0,universal_class)
| member(X1,sum_class(identity_relation))
| ~ member(X1,unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_203])]) ).
fof(f659,plain,
( ! [X0,X1] :
( ~ member(X0,universal_class)
| member(X1,sum_class(identity_relation))
| ~ member(X1,unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0)))) )
| ~ spl10_51
| ~ spl10_63 ),
inference(resolution,[],[f652,f555]) ).
fof(f2731,plain,
( spl10_202
| ~ spl10_9
| ~ spl10_85 ),
inference(avatar_split_clause,[],[f843,f839,f309,f2729]) ).
fof(f839,plain,
( spl10_85
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_85])]) ).
fof(f843,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))),unordered_pair(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),unordered_pair(X0,X0))),flip(X1))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(sK0,sK0))),unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(sK0,sK0)))),unordered_pair(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(sK0,sK0))),unordered_pair(X0,X0))),X1) )
| ~ spl10_9
| ~ spl10_85 ),
inference(superposition,[],[f840,f311]) ).
fof(f840,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3) )
| ~ spl10_85 ),
inference(avatar_component_clause,[],[f839]) ).
fof(f2727,plain,
( spl10_201
| ~ spl10_1
| ~ spl10_174 ),
inference(avatar_split_clause,[],[f2056,f1775,f272,f2725]) ).
fof(f2725,plain,
( spl10_201
<=> ! [X0,X1] :
( ~ member(X0,sK0)
| member(X0,sum_class(union(universal_class,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_201])]) ).
fof(f2056,plain,
( ! [X0,X1] :
( ~ member(X0,sK0)
| member(X0,sum_class(union(universal_class,X1))) )
| ~ spl10_1
| ~ spl10_174 ),
inference(resolution,[],[f1776,f274]) ).
fof(f2723,plain,
( spl10_200
| ~ spl10_9
| ~ spl10_84 ),
inference(avatar_split_clause,[],[f842,f835,f309,f2721]) ).
fof(f835,plain,
( spl10_84
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X1,X1))),X0)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),rotate(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_84])]) ).
fof(f842,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3)))),unordered_pair(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),unordered_pair(X0,X0))),rotate(X1))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(X0,X0))),unordered_pair(sK0,sK0))),X1) )
| ~ spl10_9
| ~ spl10_84 ),
inference(superposition,[],[f836,f311]) ).
fof(f836,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),rotate(X0))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X1,X1))),X0) )
| ~ spl10_84 ),
inference(avatar_component_clause,[],[f835]) ).
fof(f2558,plain,
( spl10_199
| ~ spl10_45
| ~ spl10_63 ),
inference(avatar_split_clause,[],[f660,f651,f494,f2556]) ).
fof(f660,plain,
( ! [X0,X1] :
( ~ member(X0,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0))),X1)
| ~ subclass(identity_relation,X1) )
| ~ spl10_45
| ~ spl10_63 ),
inference(resolution,[],[f652,f495]) ).
fof(f2554,plain,
( spl10_198
| ~ spl10_16
| ~ spl10_54 ),
inference(avatar_split_clause,[],[f617,f596,f342,f2552]) ).
fof(f2552,plain,
( spl10_198
<=> ! [X0,X1] :
( sK4(unordered_pair(X0,X1)) = X0
| sK4(unordered_pair(X0,X1)) = X1
| unordered_pair(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_198])]) ).
fof(f617,plain,
( ! [X0,X1] :
( sK4(unordered_pair(X0,X1)) = X0
| sK4(unordered_pair(X0,X1)) = X1
| unordered_pair(X0,X1) = null_class )
| ~ spl10_16
| ~ spl10_54 ),
inference(resolution,[],[f597,f343]) ).
fof(f2550,plain,
( spl10_197
| ~ spl10_16
| ~ spl10_53 ),
inference(avatar_split_clause,[],[f611,f589,f342,f2548]) ).
fof(f611,plain,
( ! [X0,X1] :
( member(sK4(union(X0,X1)),X0)
| member(sK4(union(X0,X1)),X1)
| null_class = union(X0,X1) )
| ~ spl10_16
| ~ spl10_53 ),
inference(resolution,[],[f590,f343]) ).
fof(f2514,plain,
( spl10_196
| ~ spl10_1
| ~ spl10_173 ),
inference(avatar_split_clause,[],[f2000,f1771,f272,f2512]) ).
fof(f2512,plain,
( spl10_196
<=> ! [X0,X1] :
( ~ member(X0,sK0)
| member(X0,sum_class(union(X1,universal_class))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_196])]) ).
fof(f2000,plain,
( ! [X0,X1] :
( ~ member(X0,sK0)
| member(X0,sum_class(union(X1,universal_class))) )
| ~ spl10_1
| ~ spl10_173 ),
inference(resolution,[],[f1772,f274]) ).
fof(f2510,plain,
( spl10_195
| ~ spl10_34
| ~ spl10_50 ),
inference(avatar_split_clause,[],[f564,f550,f426,f2508]) ).
fof(f550,plain,
( spl10_50
<=> ! [X0,X1] :
( member(X0,power_class(X1))
| ~ subclass(X0,X1)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_50])]) ).
fof(f564,plain,
( ! [X0,X1] :
( ~ subclass(sK6(X0,power_class(X1)),X1)
| ~ member(sK6(X0,power_class(X1)),universal_class)
| subclass(X0,power_class(X1)) )
| ~ spl10_34
| ~ spl10_50 ),
inference(resolution,[],[f551,f427]) ).
fof(f551,plain,
( ! [X0,X1] :
( member(X0,power_class(X1))
| ~ subclass(X0,X1)
| ~ member(X0,universal_class) )
| ~ spl10_50 ),
inference(avatar_component_clause,[],[f550]) ).
fof(f2506,plain,
( spl10_194
| ~ spl10_34
| ~ spl10_49 ),
inference(avatar_split_clause,[],[f560,f546,f426,f2504]) ).
fof(f546,plain,
( spl10_49
<=> ! [X0,X1] :
( member(X1,complement(X0))
| member(X1,X0)
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_49])]) ).
fof(f560,plain,
( ! [X0,X1] :
( member(sK6(X0,complement(X1)),X1)
| ~ member(sK6(X0,complement(X1)),universal_class)
| subclass(X0,complement(X1)) )
| ~ spl10_34
| ~ spl10_49 ),
inference(resolution,[],[f547,f427]) ).
fof(f547,plain,
( ! [X0,X1] :
( member(X1,complement(X0))
| member(X1,X0)
| ~ member(X1,universal_class) )
| ~ spl10_49 ),
inference(avatar_component_clause,[],[f546]) ).
fof(f2502,plain,
( spl10_193
| ~ spl10_32
| ~ spl10_43 ),
inference(avatar_split_clause,[],[f510,f486,f418,f2500]) ).
fof(f2500,plain,
( spl10_193
<=> ! [X0] :
( cross_product(cross_product(universal_class,universal_class),universal_class) = flip(X0)
| ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_193])]) ).
fof(f510,plain,
( ! [X0] :
( cross_product(cross_product(universal_class,universal_class),universal_class) = flip(X0)
| ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0)) )
| ~ spl10_32
| ~ spl10_43 ),
inference(resolution,[],[f487,f419]) ).
fof(f2498,plain,
( spl10_192
| ~ spl10_31
| ~ spl10_43 ),
inference(avatar_split_clause,[],[f509,f486,f414,f2496]) ).
fof(f2496,plain,
( spl10_192
<=> ! [X0] :
( rotate(X0) = cross_product(cross_product(universal_class,universal_class),universal_class)
| ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_192])]) ).
fof(f509,plain,
( ! [X0] :
( rotate(X0) = cross_product(cross_product(universal_class,universal_class),universal_class)
| ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0)) )
| ~ spl10_31
| ~ spl10_43 ),
inference(resolution,[],[f487,f415]) ).
fof(f2364,plain,
( spl10_191
| ~ spl10_7
| ~ spl10_75 ),
inference(avatar_split_clause,[],[f756,f728,f300,f2362]) ).
fof(f756,plain,
( ! [X0] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK9,sK9)))) = X0
| ~ member(X0,universal_class) )
| ~ spl10_7
| ~ spl10_75 ),
inference(resolution,[],[f729,f302]) ).
fof(f2360,plain,
( spl10_190
| ~ spl10_7
| ~ spl10_74 ),
inference(avatar_split_clause,[],[f743,f724,f300,f2358]) ).
fof(f743,plain,
( ! [X0] :
( sK9 = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK9,sK9))))
| ~ member(X0,universal_class) )
| ~ spl10_7
| ~ spl10_74 ),
inference(resolution,[],[f725,f302]) ).
fof(f2341,plain,
( spl10_189
| ~ spl10_51
| ~ spl10_52 ),
inference(avatar_split_clause,[],[f605,f585,f554,f2339]) ).
fof(f605,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X3,sum_class(intersection(X2,X1)))
| ~ member(X3,X0) )
| ~ spl10_51
| ~ spl10_52 ),
inference(resolution,[],[f586,f555]) ).
fof(f2262,plain,
( spl10_188
| ~ spl10_45
| ~ spl10_52 ),
inference(avatar_split_clause,[],[f606,f585,f494,f2260]) ).
fof(f2260,plain,
( spl10_188
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,X3)
| ~ subclass(intersection(X2,X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_188])]) ).
fof(f606,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,X3)
| ~ subclass(intersection(X2,X1),X3) )
| ~ spl10_45
| ~ spl10_52 ),
inference(resolution,[],[f586,f495]) ).
fof(f2258,plain,
( spl10_187
| ~ spl10_50
| ~ spl10_51 ),
inference(avatar_split_clause,[],[f582,f554,f550,f2256]) ).
fof(f582,plain,
( ! [X2,X0,X1] :
( member(X0,sum_class(power_class(X1)))
| ~ member(X0,X2)
| ~ subclass(X2,X1)
| ~ member(X2,universal_class) )
| ~ spl10_50
| ~ spl10_51 ),
inference(resolution,[],[f555,f551]) ).
fof(f2254,plain,
( spl10_186
| ~ spl10_49
| ~ spl10_51 ),
inference(avatar_split_clause,[],[f579,f554,f546,f2252]) ).
fof(f579,plain,
( ! [X2,X0,X1] :
( member(X0,sum_class(complement(X1)))
| ~ member(X0,X2)
| member(X2,X1)
| ~ member(X2,universal_class) )
| ~ spl10_49
| ~ spl10_51 ),
inference(resolution,[],[f555,f547]) ).
fof(f2250,plain,
( spl10_185
| ~ spl10_23
| ~ spl10_43 ),
inference(avatar_split_clause,[],[f512,f486,f371,f2248]) ).
fof(f2248,plain,
( spl10_185
<=> ! [X0,X1] :
( cross_product(universal_class,universal_class) = compose(X0,X1)
| ~ subclass(cross_product(universal_class,universal_class),compose(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_185])]) ).
fof(f512,plain,
( ! [X0,X1] :
( cross_product(universal_class,universal_class) = compose(X0,X1)
| ~ subclass(cross_product(universal_class,universal_class),compose(X0,X1)) )
| ~ spl10_23
| ~ spl10_43 ),
inference(resolution,[],[f487,f372]) ).
fof(f2234,plain,
( spl10_184
| ~ spl10_1
| ~ spl10_175 ),
inference(avatar_split_clause,[],[f2102,f1900,f272,f2231]) ).
fof(f2231,plain,
( spl10_184
<=> member(sK2,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_184])]) ).
fof(f1900,plain,
( spl10_175
<=> ! [X1] :
( ~ member(sK0,X1)
| member(sK2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_175])]) ).
fof(f2102,plain,
( member(sK2,universal_class)
| ~ spl10_1
| ~ spl10_175 ),
inference(resolution,[],[f1901,f274]) ).
fof(f1901,plain,
( ! [X1] :
( ~ member(sK0,X1)
| member(sK2,X1) )
| ~ spl10_175 ),
inference(avatar_component_clause,[],[f1900]) ).
fof(f2131,plain,
( spl10_183
| ~ spl10_46
| ~ spl10_51 ),
inference(avatar_split_clause,[],[f583,f554,f498,f2129]) ).
fof(f2129,plain,
( spl10_183
<=> ! [X2,X0,X1] :
( member(X0,sum_class(sK7(X1,X2)))
| ~ member(X0,X1)
| ~ member(X1,sum_class(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_183])]) ).
fof(f498,plain,
( spl10_46
<=> ! [X0,X1] :
( member(X0,sK7(X0,X1))
| ~ member(X0,sum_class(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_46])]) ).
fof(f583,plain,
( ! [X2,X0,X1] :
( member(X0,sum_class(sK7(X1,X2)))
| ~ member(X0,X1)
| ~ member(X1,sum_class(X2)) )
| ~ spl10_46
| ~ spl10_51 ),
inference(resolution,[],[f555,f499]) ).
fof(f499,plain,
( ! [X0,X1] :
( member(X0,sK7(X0,X1))
| ~ member(X0,sum_class(X1)) )
| ~ spl10_46 ),
inference(avatar_component_clause,[],[f498]) ).
fof(f2127,plain,
( spl10_182
| ~ spl10_47
| ~ spl10_51 ),
inference(avatar_split_clause,[],[f568,f554,f502,f2125]) ).
fof(f568,plain,
( ! [X2,X0,X1] :
( member(X0,sum_class(X1))
| ~ member(X0,sK7(X2,X1))
| ~ member(X2,sum_class(X1)) )
| ~ spl10_47
| ~ spl10_51 ),
inference(resolution,[],[f555,f503]) ).
fof(f2123,plain,
( spl10_181
| ~ spl10_45
| ~ spl10_50 ),
inference(avatar_split_clause,[],[f563,f550,f494,f2121]) ).
fof(f2121,plain,
( spl10_181
<=> ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X0,universal_class)
| member(X0,X2)
| ~ subclass(power_class(X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_181])]) ).
fof(f563,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X0,universal_class)
| member(X0,X2)
| ~ subclass(power_class(X1),X2) )
| ~ spl10_45
| ~ spl10_50 ),
inference(resolution,[],[f551,f495]) ).
fof(f2119,plain,
( spl10_180
| ~ spl10_45
| ~ spl10_49 ),
inference(avatar_split_clause,[],[f559,f546,f494,f2117]) ).
fof(f2117,plain,
( spl10_180
<=> ! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,universal_class)
| member(X0,X2)
| ~ subclass(complement(X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_180])]) ).
fof(f559,plain,
( ! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,universal_class)
| member(X0,X2)
| ~ subclass(complement(X1),X2) )
| ~ spl10_45
| ~ spl10_49 ),
inference(resolution,[],[f547,f495]) ).
fof(f2101,plain,
( spl10_179
| ~ spl10_35
| ~ spl10_47 ),
inference(avatar_split_clause,[],[f538,f502,f430,f2099]) ).
fof(f538,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum_class(intersection(X1,X2)))
| member(sK7(X0,intersection(X1,X2)),X1) )
| ~ spl10_35
| ~ spl10_47 ),
inference(resolution,[],[f503,f431]) ).
fof(f2097,plain,
( spl10_178
| ~ spl10_36
| ~ spl10_47 ),
inference(avatar_split_clause,[],[f537,f502,f434,f2095]) ).
fof(f537,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum_class(intersection(X1,X2)))
| member(sK7(X0,intersection(X1,X2)),X2) )
| ~ spl10_36
| ~ spl10_47 ),
inference(resolution,[],[f503,f435]) ).
fof(f2093,plain,
( spl10_177
| ~ spl10_39
| ~ spl10_47 ),
inference(avatar_split_clause,[],[f536,f502,f446,f2091]) ).
fof(f536,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum_class(unordered_pair(X1,X2)))
| member(sK7(X0,unordered_pair(X1,X2)),universal_class) )
| ~ spl10_39
| ~ spl10_47 ),
inference(resolution,[],[f503,f447]) ).
fof(f1905,plain,
( spl10_175
| spl10_176
| ~ spl10_68
| ~ spl10_104 ),
inference(avatar_split_clause,[],[f977,f972,f681,f1903,f1900]) ).
fof(f972,plain,
( spl10_104
<=> ! [X0,X1] :
( member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),cross_product(X0,X1))
| ~ member(sK1,X1)
| ~ member(sK0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_104])]) ).
fof(f977,plain,
( ! [X0,X1] :
( ~ member(sK1,X0)
| ~ member(sK0,X1)
| member(sK2,X1) )
| ~ spl10_68
| ~ spl10_104 ),
inference(resolution,[],[f973,f682]) ).
fof(f973,plain,
( ! [X0,X1] :
( member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),cross_product(X0,X1))
| ~ member(sK1,X1)
| ~ member(sK0,X0) )
| ~ spl10_104 ),
inference(avatar_component_clause,[],[f972]) ).
fof(f1777,plain,
( spl10_174
| ~ spl10_37
| ~ spl10_51 ),
inference(avatar_split_clause,[],[f581,f554,f438,f1775]) ).
fof(f581,plain,
( ! [X2,X3,X0,X1] :
( member(X0,sum_class(union(X1,X2)))
| ~ member(X0,X3)
| ~ member(X3,X1) )
| ~ spl10_37
| ~ spl10_51 ),
inference(resolution,[],[f555,f439]) ).
fof(f1773,plain,
( spl10_173
| ~ spl10_38
| ~ spl10_51 ),
inference(avatar_split_clause,[],[f580,f554,f442,f1771]) ).
fof(f580,plain,
( ! [X2,X3,X0,X1] :
( member(X0,sum_class(union(X1,X2)))
| ~ member(X0,X3)
| ~ member(X3,X2) )
| ~ spl10_38
| ~ spl10_51 ),
inference(resolution,[],[f555,f443]) ).
fof(f1769,plain,
( spl10_172
| ~ spl10_41
| ~ spl10_51 ),
inference(avatar_split_clause,[],[f578,f554,f454,f1767]) ).
fof(f1767,plain,
( spl10_172
<=> ! [X2,X0,X1] :
( member(X0,sum_class(unordered_pair(X1,X2)))
| ~ member(X0,X1)
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_172])]) ).
fof(f578,plain,
( ! [X2,X0,X1] :
( member(X0,sum_class(unordered_pair(X1,X2)))
| ~ member(X0,X1)
| ~ member(X1,universal_class) )
| ~ spl10_41
| ~ spl10_51 ),
inference(resolution,[],[f555,f455]) ).
fof(f1765,plain,
( spl10_171
| ~ spl10_40
| ~ spl10_51 ),
inference(avatar_split_clause,[],[f577,f554,f450,f1763]) ).
fof(f1763,plain,
( spl10_171
<=> ! [X2,X0,X1] :
( member(X0,sum_class(unordered_pair(X1,X2)))
| ~ member(X0,X2)
| ~ member(X2,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_171])]) ).
fof(f577,plain,
( ! [X2,X0,X1] :
( member(X0,sum_class(unordered_pair(X1,X2)))
| ~ member(X0,X2)
| ~ member(X2,universal_class) )
| ~ spl10_40
| ~ spl10_51 ),
inference(resolution,[],[f555,f451]) ).
fof(f1758,plain,
( spl10_170
| ~ spl10_33
| ~ spl10_51 ),
inference(avatar_split_clause,[],[f567,f554,f422,f1756]) ).
fof(f567,plain,
( ! [X2,X0,X1] :
( member(X0,sum_class(X1))
| ~ member(X0,sK6(X1,X2))
| subclass(X1,X2) )
| ~ spl10_33
| ~ spl10_51 ),
inference(resolution,[],[f555,f423]) ).
fof(f1754,plain,
( spl10_169
| ~ spl10_45
| ~ spl10_47 ),
inference(avatar_split_clause,[],[f535,f502,f494,f1752]) ).
fof(f535,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum_class(X1))
| member(sK7(X0,X1),X2)
| ~ subclass(X1,X2) )
| ~ spl10_45
| ~ spl10_47 ),
inference(resolution,[],[f503,f495]) ).
fof(f1750,plain,
( spl10_168
| ~ spl10_45
| ~ spl10_46 ),
inference(avatar_split_clause,[],[f534,f498,f494,f1748]) ).
fof(f534,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum_class(X1))
| member(X0,X2)
| ~ subclass(sK7(X0,X1),X2) )
| ~ spl10_45
| ~ spl10_46 ),
inference(resolution,[],[f499,f495]) ).
fof(f1746,plain,
( spl10_167
| ~ spl10_20
| ~ spl10_43 ),
inference(avatar_split_clause,[],[f507,f486,f358,f1744]) ).
fof(f1744,plain,
( spl10_167
<=> ! [X0] :
( cross_product(universal_class,universal_class) = X0
| ~ subclass(cross_product(universal_class,universal_class),X0)
| ~ function(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_167])]) ).
fof(f507,plain,
( ! [X0] :
( cross_product(universal_class,universal_class) = X0
| ~ subclass(cross_product(universal_class,universal_class),X0)
| ~ function(X0) )
| ~ spl10_20
| ~ spl10_43 ),
inference(resolution,[],[f487,f359]) ).
fof(f1742,plain,
( spl10_166
| ~ spl10_33
| ~ spl10_39 ),
inference(avatar_split_clause,[],[f475,f446,f422,f1740]) ).
fof(f475,plain,
( ! [X2,X0,X1] :
( member(sK6(unordered_pair(X0,X1),X2),universal_class)
| subclass(unordered_pair(X0,X1),X2) )
| ~ spl10_33
| ~ spl10_39 ),
inference(resolution,[],[f447,f423]) ).
fof(f1738,plain,
( spl10_165
| ~ spl10_34
| ~ spl10_38 ),
inference(avatar_split_clause,[],[f472,f442,f426,f1736]) ).
fof(f472,plain,
( ! [X2,X0,X1] :
( ~ member(sK6(X0,union(X1,X2)),X2)
| subclass(X0,union(X1,X2)) )
| ~ spl10_34
| ~ spl10_38 ),
inference(resolution,[],[f443,f427]) ).
fof(f1734,plain,
( spl10_164
| ~ spl10_34
| ~ spl10_37 ),
inference(avatar_split_clause,[],[f471,f438,f426,f1732]) ).
fof(f471,plain,
( ! [X2,X0,X1] :
( ~ member(sK6(X0,union(X1,X2)),X1)
| subclass(X0,union(X1,X2)) )
| ~ spl10_34
| ~ spl10_37 ),
inference(resolution,[],[f439,f427]) ).
fof(f1730,plain,
( spl10_163
| ~ spl10_33
| ~ spl10_36 ),
inference(avatar_split_clause,[],[f470,f434,f422,f1728]) ).
fof(f470,plain,
( ! [X2,X0,X1] :
( member(sK6(intersection(X0,X1),X2),X1)
| subclass(intersection(X0,X1),X2) )
| ~ spl10_33
| ~ spl10_36 ),
inference(resolution,[],[f435,f423]) ).
fof(f1726,plain,
( spl10_162
| ~ spl10_33
| ~ spl10_35 ),
inference(avatar_split_clause,[],[f467,f430,f422,f1724]) ).
fof(f467,plain,
( ! [X2,X0,X1] :
( member(sK6(intersection(X0,X1),X2),X0)
| subclass(intersection(X0,X1),X2) )
| ~ spl10_33
| ~ spl10_35 ),
inference(resolution,[],[f431,f423]) ).
fof(f1708,plain,
( spl10_161
| ~ spl10_107
| ~ spl10_123 ),
inference(avatar_split_clause,[],[f1182,f1163,f993,f1705]) ).
fof(f1182,plain,
( member(unordered_pair(sK0,unordered_pair(sK1,sK1)),sum_class(universal_class))
| ~ spl10_107
| ~ spl10_123 ),
inference(resolution,[],[f1164,f995]) ).
fof(f1516,plain,
( spl10_160
| ~ spl10_22
| ~ spl10_51 ),
inference(avatar_split_clause,[],[f575,f554,f367,f1514]) ).
fof(f575,plain,
( ! [X0,X1] :
( member(X0,sum_class(universal_class))
| ~ member(X0,sK5(X1))
| ~ member(X1,identity_relation) )
| ~ spl10_22
| ~ spl10_51 ),
inference(resolution,[],[f555,f368]) ).
fof(f1512,plain,
( spl10_159
| ~ spl10_15
| ~ spl10_51 ),
inference(avatar_split_clause,[],[f574,f554,f338,f1510]) ).
fof(f574,plain,
( ! [X0,X1] :
( member(X0,sum_class(universal_class))
| ~ member(X0,sK4(X1))
| null_class = X1 )
| ~ spl10_15
| ~ spl10_51 ),
inference(resolution,[],[f555,f339]) ).
fof(f1508,plain,
( spl10_158
| ~ spl10_18
| ~ spl10_51 ),
inference(avatar_split_clause,[],[f572,f554,f350,f1506]) ).
fof(f572,plain,
( ! [X0,X1] :
( member(X0,sum_class(universal_class))
| ~ member(X0,power_class(X1))
| ~ member(X1,universal_class) )
| ~ spl10_18
| ~ spl10_51 ),
inference(resolution,[],[f555,f351]) ).
fof(f1504,plain,
( spl10_157
| ~ spl10_19
| ~ spl10_51 ),
inference(avatar_split_clause,[],[f571,f554,f354,f1502]) ).
fof(f571,plain,
( ! [X0,X1] :
( member(X0,sum_class(universal_class))
| ~ member(X0,sum_class(X1))
| ~ member(X1,universal_class) )
| ~ spl10_19
| ~ spl10_51 ),
inference(resolution,[],[f555,f355]) ).
fof(f1500,plain,
( spl10_156
| ~ spl10_103
| ~ spl10_123 ),
inference(avatar_split_clause,[],[f1181,f1163,f961,f1497]) ).
fof(f1181,plain,
( member(unordered_pair(sK0,sK0),sum_class(universal_class))
| ~ spl10_103
| ~ spl10_123 ),
inference(resolution,[],[f1164,f963]) ).
fof(f1495,plain,
( spl10_155
| ~ spl10_16
| ~ spl10_51 ),
inference(avatar_split_clause,[],[f566,f554,f342,f1493]) ).
fof(f566,plain,
( ! [X0,X1] :
( member(X0,sum_class(X1))
| ~ member(X0,sK4(X1))
| null_class = X1 )
| ~ spl10_16
| ~ spl10_51 ),
inference(resolution,[],[f555,f343]) ).
fof(f1491,plain,
( spl10_154
| ~ spl10_26
| ~ spl10_47 ),
inference(avatar_split_clause,[],[f544,f502,f383,f1489]) ).
fof(f544,plain,
( ! [X0,X1] :
( ~ member(X0,sum_class(power_class(X1)))
| member(sK7(X0,power_class(X1)),universal_class) )
| ~ spl10_26
| ~ spl10_47 ),
inference(resolution,[],[f503,f384]) ).
fof(f1487,plain,
( spl10_153
| ~ spl10_27
| ~ spl10_47 ),
inference(avatar_split_clause,[],[f543,f502,f387,f1485]) ).
fof(f543,plain,
( ! [X0,X1] :
( ~ member(X0,sum_class(power_class(X1)))
| subclass(sK7(X0,power_class(X1)),X1) )
| ~ spl10_27
| ~ spl10_47 ),
inference(resolution,[],[f503,f388]) ).
fof(f1483,plain,
( spl10_152
| ~ spl10_28
| ~ spl10_47 ),
inference(avatar_split_clause,[],[f542,f502,f391,f1481]) ).
fof(f542,plain,
( ! [X0,X1] :
( ~ member(X0,sum_class(domain_of(X1)))
| member(sK7(X0,domain_of(X1)),universal_class) )
| ~ spl10_28
| ~ spl10_47 ),
inference(resolution,[],[f503,f392]) ).
fof(f1479,plain,
( spl10_151
| ~ spl10_24
| ~ spl10_47 ),
inference(avatar_split_clause,[],[f540,f502,f375,f1477]) ).
fof(f540,plain,
( ! [X0,X1] :
( ~ member(X0,sum_class(complement(X1)))
| member(sK7(X0,complement(X1)),universal_class) )
| ~ spl10_24
| ~ spl10_47 ),
inference(resolution,[],[f503,f376]) ).
fof(f1475,plain,
( spl10_150
| ~ spl10_25
| ~ spl10_47 ),
inference(avatar_split_clause,[],[f539,f502,f379,f1473]) ).
fof(f539,plain,
( ! [X0,X1] :
( ~ member(X0,sum_class(complement(X1)))
| ~ member(sK7(X0,complement(X1)),X1) )
| ~ spl10_25
| ~ spl10_47 ),
inference(resolution,[],[f503,f380]) ).
fof(f1471,plain,
( spl10_149
| ~ spl10_37
| ~ spl10_45 ),
inference(avatar_split_clause,[],[f529,f494,f438,f1469]) ).
fof(f529,plain,
( ! [X2,X3,X0,X1] :
( member(X0,X1)
| ~ subclass(union(X2,X3),X1)
| ~ member(X0,X2) )
| ~ spl10_37
| ~ spl10_45 ),
inference(resolution,[],[f495,f439]) ).
fof(f1467,plain,
( spl10_148
| ~ spl10_38
| ~ spl10_45 ),
inference(avatar_split_clause,[],[f528,f494,f442,f1465]) ).
fof(f528,plain,
( ! [X2,X3,X0,X1] :
( member(X0,X1)
| ~ subclass(union(X2,X3),X1)
| ~ member(X0,X3) )
| ~ spl10_38
| ~ spl10_45 ),
inference(resolution,[],[f495,f443]) ).
fof(f1463,plain,
( spl10_147
| ~ spl10_41
| ~ spl10_45 ),
inference(avatar_split_clause,[],[f527,f494,f454,f1461]) ).
fof(f527,plain,
( ! [X2,X0,X1] :
( member(X0,X1)
| ~ subclass(unordered_pair(X0,X2),X1)
| ~ member(X0,universal_class) )
| ~ spl10_41
| ~ spl10_45 ),
inference(resolution,[],[f495,f455]) ).
fof(f1459,plain,
( spl10_146
| ~ spl10_40
| ~ spl10_45 ),
inference(avatar_split_clause,[],[f526,f494,f450,f1457]) ).
fof(f526,plain,
( ! [X2,X0,X1] :
( member(X0,X1)
| ~ subclass(unordered_pair(X2,X0),X1)
| ~ member(X0,universal_class) )
| ~ spl10_40
| ~ spl10_45 ),
inference(resolution,[],[f495,f451]) ).
fof(f1455,plain,
( spl10_145
| ~ spl10_33
| ~ spl10_45 ),
inference(avatar_split_clause,[],[f517,f494,f422,f1453]) ).
fof(f517,plain,
( ! [X2,X0,X1] :
( member(sK6(X0,X1),X2)
| ~ subclass(X0,X2)
| subclass(X0,X1) )
| ~ spl10_33
| ~ spl10_45 ),
inference(resolution,[],[f495,f423]) ).
fof(f1451,plain,
( spl10_144
| ~ spl10_16
| ~ spl10_36 ),
inference(avatar_split_clause,[],[f469,f434,f342,f1449]) ).
fof(f469,plain,
( ! [X0,X1] :
( member(sK4(intersection(X0,X1)),X1)
| intersection(X0,X1) = null_class )
| ~ spl10_16
| ~ spl10_36 ),
inference(resolution,[],[f435,f343]) ).
fof(f1447,plain,
( spl10_143
| ~ spl10_16
| ~ spl10_35 ),
inference(avatar_split_clause,[],[f466,f430,f342,f1445]) ).
fof(f466,plain,
( ! [X0,X1] :
( member(sK4(intersection(X0,X1)),X0)
| intersection(X0,X1) = null_class )
| ~ spl10_16
| ~ spl10_35 ),
inference(resolution,[],[f431,f343]) ).
fof(f1269,plain,
( spl10_142
| ~ spl10_12
| ~ spl10_54 ),
inference(avatar_split_clause,[],[f616,f596,f324,f1267]) ).
fof(f616,plain,
( ! [X0,X1] :
( null_class = X0
| null_class = X1
| ~ inductive(unordered_pair(X0,X1)) )
| ~ spl10_12
| ~ spl10_54 ),
inference(resolution,[],[f597,f325]) ).
fof(f1265,plain,
( spl10_141
| ~ spl10_12
| ~ spl10_53 ),
inference(avatar_split_clause,[],[f610,f589,f324,f1263]) ).
fof(f1263,plain,
( spl10_141
<=> ! [X0,X1] :
( member(null_class,X0)
| member(null_class,X1)
| ~ inductive(union(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_141])]) ).
fof(f610,plain,
( ! [X0,X1] :
( member(null_class,X0)
| member(null_class,X1)
| ~ inductive(union(X0,X1)) )
| ~ spl10_12
| ~ spl10_53 ),
inference(resolution,[],[f590,f325]) ).
fof(f1261,plain,
( spl10_140
| ~ spl10_22
| ~ spl10_45 ),
inference(avatar_split_clause,[],[f524,f494,f367,f1259]) ).
fof(f524,plain,
( ! [X0,X1] :
( member(sK5(X0),X1)
| ~ subclass(universal_class,X1)
| ~ member(X0,identity_relation) )
| ~ spl10_22
| ~ spl10_45 ),
inference(resolution,[],[f495,f368]) ).
fof(f1257,plain,
( spl10_139
| ~ spl10_15
| ~ spl10_45 ),
inference(avatar_split_clause,[],[f523,f494,f338,f1255]) ).
fof(f523,plain,
( ! [X0,X1] :
( member(sK4(X0),X1)
| ~ subclass(universal_class,X1)
| null_class = X0 )
| ~ spl10_15
| ~ spl10_45 ),
inference(resolution,[],[f495,f339]) ).
fof(f1253,plain,
( ~ spl10_138
| spl10_94
| ~ spl10_119 ),
inference(avatar_split_clause,[],[f1107,f1071,f886,f1250]) ).
fof(f1250,plain,
( spl10_138
<=> subclass(universal_class,successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_138])]) ).
fof(f886,plain,
( spl10_94
<=> member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_94])]) ).
fof(f1107,plain,
( ~ subclass(universal_class,successor_relation)
| spl10_94
| ~ spl10_119 ),
inference(resolution,[],[f1072,f888]) ).
fof(f888,plain,
( ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),successor_relation)
| spl10_94 ),
inference(avatar_component_clause,[],[f886]) ).
fof(f1248,plain,
( spl10_137
| ~ spl10_18
| ~ spl10_45 ),
inference(avatar_split_clause,[],[f521,f494,f350,f1246]) ).
fof(f521,plain,
( ! [X0,X1] :
( member(power_class(X0),X1)
| ~ subclass(universal_class,X1)
| ~ member(X0,universal_class) )
| ~ spl10_18
| ~ spl10_45 ),
inference(resolution,[],[f495,f351]) ).
fof(f1244,plain,
( spl10_136
| ~ spl10_19
| ~ spl10_45 ),
inference(avatar_split_clause,[],[f520,f494,f354,f1242]) ).
fof(f520,plain,
( ! [X0,X1] :
( member(sum_class(X0),X1)
| ~ subclass(universal_class,X1)
| ~ member(X0,universal_class) )
| ~ spl10_19
| ~ spl10_45 ),
inference(resolution,[],[f495,f355]) ).
fof(f1240,plain,
( spl10_135
| ~ spl10_16
| ~ spl10_45 ),
inference(avatar_split_clause,[],[f516,f494,f342,f1238]) ).
fof(f516,plain,
( ! [X0,X1] :
( member(sK4(X0),X1)
| ~ subclass(X0,X1)
| null_class = X0 )
| ~ spl10_16
| ~ spl10_45 ),
inference(resolution,[],[f495,f343]) ).
fof(f1236,plain,
( spl10_134
| ~ spl10_17
| ~ spl10_44 ),
inference(avatar_split_clause,[],[f514,f490,f346,f1234]) ).
fof(f346,plain,
( spl10_17
<=> ! [X0] :
( disjoint(sK4(X0),X0)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_17])]) ).
fof(f490,plain,
( spl10_44
<=> ! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,X0)
| ~ disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_44])]) ).
fof(f514,plain,
( ! [X0,X1] :
( ~ member(X0,sK4(X1))
| ~ member(X0,X1)
| null_class = X1 )
| ~ spl10_17
| ~ spl10_44 ),
inference(resolution,[],[f491,f347]) ).
fof(f347,plain,
( ! [X0] :
( disjoint(sK4(X0),X0)
| null_class = X0 )
| ~ spl10_17 ),
inference(avatar_component_clause,[],[f346]) ).
fof(f491,plain,
( ! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ member(X2,X0)
| ~ member(X2,X1) )
| ~ spl10_44 ),
inference(avatar_component_clause,[],[f490]) ).
fof(f1232,plain,
( ~ spl10_132
| spl10_133
| ~ spl10_11
| ~ spl10_43 ),
inference(avatar_split_clause,[],[f511,f486,f319,f1229,f1225]) ).
fof(f1225,plain,
( spl10_132
<=> subclass(cross_product(universal_class,universal_class),successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_132])]) ).
fof(f1229,plain,
( spl10_133
<=> cross_product(universal_class,universal_class) = successor_relation ),
introduced(avatar_definition,[new_symbols(naming,[spl10_133])]) ).
fof(f511,plain,
( cross_product(universal_class,universal_class) = successor_relation
| ~ subclass(cross_product(universal_class,universal_class),successor_relation)
| ~ spl10_11
| ~ spl10_43 ),
inference(resolution,[],[f487,f321]) ).
fof(f1223,plain,
( ~ spl10_130
| spl10_131
| ~ spl10_10
| ~ spl10_43 ),
inference(avatar_split_clause,[],[f508,f486,f314,f1220,f1216]) ).
fof(f1216,plain,
( spl10_130
<=> subclass(cross_product(universal_class,universal_class),element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_130])]) ).
fof(f1220,plain,
( spl10_131
<=> element_relation = cross_product(universal_class,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_131])]) ).
fof(f508,plain,
( element_relation = cross_product(universal_class,universal_class)
| ~ subclass(cross_product(universal_class,universal_class),element_relation)
| ~ spl10_10
| ~ spl10_43 ),
inference(resolution,[],[f487,f316]) ).
fof(f1214,plain,
( ~ spl10_129
| spl10_92
| ~ spl10_119 ),
inference(avatar_split_clause,[],[f1106,f1071,f876,f1211]) ).
fof(f1211,plain,
( spl10_129
<=> subclass(universal_class,element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_129])]) ).
fof(f876,plain,
( spl10_92
<=> member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_92])]) ).
fof(f1106,plain,
( ~ subclass(universal_class,element_relation)
| spl10_92
| ~ spl10_119 ),
inference(resolution,[],[f1072,f878]) ).
fof(f878,plain,
( ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),element_relation)
| spl10_92 ),
inference(avatar_component_clause,[],[f876]) ).
fof(f1209,plain,
( spl10_128
| ~ spl10_26
| ~ spl10_33 ),
inference(avatar_split_clause,[],[f462,f422,f383,f1207]) ).
fof(f462,plain,
( ! [X0,X1] :
( subclass(power_class(X0),X1)
| member(sK6(power_class(X0),X1),universal_class) )
| ~ spl10_26
| ~ spl10_33 ),
inference(resolution,[],[f423,f384]) ).
fof(f1205,plain,
( spl10_127
| ~ spl10_27
| ~ spl10_33 ),
inference(avatar_split_clause,[],[f461,f422,f387,f1203]) ).
fof(f461,plain,
( ! [X0,X1] :
( subclass(power_class(X0),X1)
| subclass(sK6(power_class(X0),X1),X0) )
| ~ spl10_27
| ~ spl10_33 ),
inference(resolution,[],[f423,f388]) ).
fof(f1201,plain,
( spl10_126
| ~ spl10_28
| ~ spl10_33 ),
inference(avatar_split_clause,[],[f460,f422,f391,f1199]) ).
fof(f460,plain,
( ! [X0,X1] :
( subclass(domain_of(X0),X1)
| member(sK6(domain_of(X0),X1),universal_class) )
| ~ spl10_28
| ~ spl10_33 ),
inference(resolution,[],[f423,f392]) ).
fof(f1197,plain,
( spl10_125
| ~ spl10_24
| ~ spl10_33 ),
inference(avatar_split_clause,[],[f458,f422,f375,f1195]) ).
fof(f458,plain,
( ! [X0,X1] :
( subclass(complement(X0),X1)
| member(sK6(complement(X0),X1),universal_class) )
| ~ spl10_24
| ~ spl10_33 ),
inference(resolution,[],[f423,f376]) ).
fof(f1193,plain,
( spl10_124
| ~ spl10_25
| ~ spl10_33 ),
inference(avatar_split_clause,[],[f457,f422,f379,f1191]) ).
fof(f457,plain,
( ! [X0,X1] :
( subclass(complement(X0),X1)
| ~ member(sK6(complement(X0),X1),X0) )
| ~ spl10_25
| ~ spl10_33 ),
inference(resolution,[],[f423,f380]) ).
fof(f1165,plain,
( spl10_123
| ~ spl10_13
| ~ spl10_51 ),
inference(avatar_split_clause,[],[f569,f554,f328,f1163]) ).
fof(f569,plain,
( ! [X2,X0,X1] :
( member(X0,sum_class(universal_class))
| ~ member(X0,unordered_pair(X1,X2)) )
| ~ spl10_13
| ~ spl10_51 ),
inference(resolution,[],[f555,f329]) ).
fof(f1161,plain,
( spl10_122
| ~ spl10_16
| ~ spl10_27 ),
inference(avatar_split_clause,[],[f402,f387,f342,f1159]) ).
fof(f402,plain,
( ! [X0] :
( subclass(sK4(power_class(X0)),X0)
| null_class = power_class(X0) )
| ~ spl10_16
| ~ spl10_27 ),
inference(resolution,[],[f388,f343]) ).
fof(f1146,plain,
( spl10_121
| ~ spl10_16
| ~ spl10_25 ),
inference(avatar_split_clause,[],[f398,f379,f342,f1144]) ).
fof(f398,plain,
( ! [X0] :
( ~ member(sK4(complement(X0)),X0)
| complement(X0) = null_class )
| ~ spl10_16
| ~ spl10_25 ),
inference(resolution,[],[f380,f343]) ).
fof(f1137,plain,
( spl10_120
| ~ spl10_9
| ~ spl10_82 ),
inference(avatar_split_clause,[],[f823,f820,f309,f1135]) ).
fof(f1135,plain,
( spl10_120
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),compose(X0,X1))
| member(sK1,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(sK0,sK0),universal_class)),universal_class)))),universal_class)),universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_120])]) ).
fof(f820,plain,
( spl10_82
<=> ! [X0,X3,X2,X1] :
( member(X3,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X2,X2),universal_class)),universal_class)))),universal_class)),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),compose(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_82])]) ).
fof(f823,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),compose(X0,X1))
| member(sK1,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(sK0,sK0),universal_class)),universal_class)))),universal_class)),universal_class))))) )
| ~ spl10_9
| ~ spl10_82 ),
inference(superposition,[],[f821,f311]) ).
fof(f821,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),compose(X1,X0))
| member(X3,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X2,X2),universal_class)),universal_class)))),universal_class)),universal_class))))) )
| ~ spl10_82 ),
inference(avatar_component_clause,[],[f820]) ).
fof(f1073,plain,
( spl10_119
| ~ spl10_13
| ~ spl10_45 ),
inference(avatar_split_clause,[],[f518,f494,f328,f1071]) ).
fof(f518,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(X0,X1),X2)
| ~ subclass(universal_class,X2) )
| ~ spl10_13
| ~ spl10_45 ),
inference(resolution,[],[f495,f329]) ).
fof(f1069,plain,
( spl10_118
| ~ spl10_12
| ~ spl10_45 ),
inference(avatar_split_clause,[],[f515,f494,f324,f1067]) ).
fof(f515,plain,
( ! [X0,X1] :
( member(null_class,X0)
| ~ subclass(X1,X0)
| ~ inductive(X1) )
| ~ spl10_12
| ~ spl10_45 ),
inference(resolution,[],[f495,f325]) ).
fof(f1065,plain,
( spl10_117
| ~ spl10_14
| ~ spl10_43 ),
inference(avatar_split_clause,[],[f513,f486,f332,f1063]) ).
fof(f332,plain,
( spl10_14
<=> ! [X1] :
( subclass(sK9,X1)
| ~ inductive(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_14])]) ).
fof(f513,plain,
( ! [X0] :
( sK9 = X0
| ~ subclass(X0,sK9)
| ~ inductive(X0) )
| ~ spl10_14
| ~ spl10_43 ),
inference(resolution,[],[f487,f333]) ).
fof(f333,plain,
( ! [X1] :
( subclass(sK9,X1)
| ~ inductive(X1) )
| ~ spl10_14 ),
inference(avatar_component_clause,[],[f332]) ).
fof(f1058,plain,
( spl10_115
| spl10_116
| ~ spl10_78
| ~ spl10_97 ),
inference(avatar_split_clause,[],[f943,f927,f767,f1056,f1053]) ).
fof(f1056,plain,
( spl10_116
<=> ! [X0] :
( member(sK1,X0)
| ~ member(sK3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_116])]) ).
fof(f927,plain,
( spl10_97
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),cross_product(X0,X1))
| member(sK1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_97])]) ).
fof(f943,plain,
( ! [X0,X1] :
( member(sK1,X0)
| ~ member(sK3,X0)
| ~ member(sK2,X1) )
| ~ spl10_78
| ~ spl10_97 ),
inference(resolution,[],[f928,f768]) ).
fof(f928,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),cross_product(X0,X1))
| member(sK1,X1) )
| ~ spl10_97 ),
inference(avatar_component_clause,[],[f927]) ).
fof(f1051,plain,
( spl10_114
| ~ spl10_7
| ~ spl10_51 ),
inference(avatar_split_clause,[],[f576,f554,f300,f1049]) ).
fof(f576,plain,
( ! [X0] :
( member(X0,sum_class(universal_class))
| ~ member(X0,sK9) )
| ~ spl10_7
| ~ spl10_51 ),
inference(resolution,[],[f555,f302]) ).
fof(f1047,plain,
( spl10_113
| ~ spl10_12
| ~ spl10_36 ),
inference(avatar_split_clause,[],[f468,f434,f324,f1045]) ).
fof(f1045,plain,
( spl10_113
<=> ! [X0,X1] :
( member(null_class,X0)
| ~ inductive(intersection(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_113])]) ).
fof(f468,plain,
( ! [X0,X1] :
( member(null_class,X0)
| ~ inductive(intersection(X1,X0)) )
| ~ spl10_12
| ~ spl10_36 ),
inference(resolution,[],[f435,f325]) ).
fof(f1043,plain,
( spl10_112
| ~ spl10_12
| ~ spl10_35 ),
inference(avatar_split_clause,[],[f465,f430,f324,f1041]) ).
fof(f1041,plain,
( spl10_112
<=> ! [X0,X1] :
( member(null_class,X0)
| ~ inductive(intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_112])]) ).
fof(f465,plain,
( ! [X0,X1] :
( member(null_class,X0)
| ~ inductive(intersection(X0,X1)) )
| ~ spl10_12
| ~ spl10_35 ),
inference(resolution,[],[f431,f325]) ).
fof(f1033,plain,
( spl10_111
| ~ spl10_7
| ~ spl10_45 ),
inference(avatar_split_clause,[],[f525,f494,f300,f1031]) ).
fof(f525,plain,
( ! [X0] :
( member(sK9,X0)
| ~ subclass(universal_class,X0) )
| ~ spl10_7
| ~ spl10_45 ),
inference(resolution,[],[f495,f302]) ).
fof(f1029,plain,
( spl10_110
| ~ spl10_6
| ~ spl10_43 ),
inference(avatar_split_clause,[],[f505,f486,f296,f1027]) ).
fof(f1027,plain,
( spl10_110
<=> ! [X0] :
( universal_class = X0
| ~ subclass(universal_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_110])]) ).
fof(f505,plain,
( ! [X0] :
( universal_class = X0
| ~ subclass(universal_class,X0) )
| ~ spl10_6
| ~ spl10_43 ),
inference(resolution,[],[f487,f297]) ).
fof(f1019,plain,
( spl10_109
| spl10_30
| ~ spl10_12
| ~ spl10_26 ),
inference(avatar_split_clause,[],[f399,f383,f324,f409,f1017]) ).
fof(f1017,plain,
( spl10_109
<=> ! [X0] : ~ inductive(power_class(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_109])]) ).
fof(f399,plain,
( ! [X0] :
( member(null_class,universal_class)
| ~ inductive(power_class(X0)) )
| ~ spl10_12
| ~ spl10_26 ),
inference(resolution,[],[f384,f325]) ).
fof(f1006,plain,
( spl10_108
| ~ spl10_9
| ~ spl10_54 ),
inference(avatar_split_clause,[],[f620,f596,f309,f1004]) ).
fof(f620,plain,
( ! [X0] :
( ~ member(X0,unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| unordered_pair(sK0,sK0) = X0
| unordered_pair(sK0,unordered_pair(sK1,sK1)) = X0 )
| ~ spl10_9
| ~ spl10_54 ),
inference(superposition,[],[f597,f311]) ).
fof(f998,plain,
( ~ spl10_13
| spl10_106 ),
inference(avatar_contradiction_clause,[],[f997]) ).
fof(f997,plain,
( $false
| ~ spl10_13
| spl10_106 ),
inference(resolution,[],[f991,f329]) ).
fof(f991,plain,
( ~ member(unordered_pair(sK0,unordered_pair(sK1,sK1)),universal_class)
| spl10_106 ),
inference(avatar_component_clause,[],[f989]) ).
fof(f989,plain,
( spl10_106
<=> member(unordered_pair(sK0,unordered_pair(sK1,sK1)),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_106])]) ).
fof(f996,plain,
( ~ spl10_106
| spl10_107
| ~ spl10_9
| ~ spl10_40 ),
inference(avatar_split_clause,[],[f482,f450,f309,f993,f989]) ).
fof(f482,plain,
( member(unordered_pair(sK0,unordered_pair(sK1,sK1)),unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| ~ member(unordered_pair(sK0,unordered_pair(sK1,sK1)),universal_class)
| ~ spl10_9
| ~ spl10_40 ),
inference(superposition,[],[f451,f311]) ).
fof(f986,plain,
( ~ spl10_30
| spl10_105
| ~ spl10_6
| ~ spl10_71 ),
inference(avatar_split_clause,[],[f714,f702,f296,f983,f409]) ).
fof(f714,plain,
( inductive(universal_class)
| ~ member(null_class,universal_class)
| ~ spl10_6
| ~ spl10_71 ),
inference(resolution,[],[f703,f297]) ).
fof(f974,plain,
( spl10_104
| ~ spl10_9
| ~ spl10_78 ),
inference(avatar_split_clause,[],[f779,f767,f309,f972]) ).
fof(f779,plain,
( ! [X0,X1] :
( member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),cross_product(X0,X1))
| ~ member(sK1,X1)
| ~ member(sK0,X0) )
| ~ spl10_9
| ~ spl10_78 ),
inference(superposition,[],[f768,f311]) ).
fof(f966,plain,
( ~ spl10_13
| spl10_102 ),
inference(avatar_contradiction_clause,[],[f965]) ).
fof(f965,plain,
( $false
| ~ spl10_13
| spl10_102 ),
inference(resolution,[],[f959,f329]) ).
fof(f959,plain,
( ~ member(unordered_pair(sK0,sK0),universal_class)
| spl10_102 ),
inference(avatar_component_clause,[],[f957]) ).
fof(f957,plain,
( spl10_102
<=> member(unordered_pair(sK0,sK0),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_102])]) ).
fof(f964,plain,
( ~ spl10_102
| spl10_103
| ~ spl10_9
| ~ spl10_41 ),
inference(avatar_split_clause,[],[f484,f454,f309,f961,f957]) ).
fof(f484,plain,
( member(unordered_pair(sK0,sK0),unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))))
| ~ member(unordered_pair(sK0,sK0),universal_class)
| ~ spl10_9
| ~ spl10_41 ),
inference(superposition,[],[f455,f311]) ).
fof(f948,plain,
( spl10_101
| ~ spl10_5
| ~ spl10_47 ),
inference(avatar_split_clause,[],[f541,f502,f292,f946]) ).
fof(f541,plain,
( ! [X0] : ~ member(X0,sum_class(null_class))
| ~ spl10_5
| ~ spl10_47 ),
inference(resolution,[],[f503,f293]) ).
fof(f942,plain,
( ~ spl10_99
| ~ spl10_100
| ~ spl10_73
| spl10_92 ),
inference(avatar_split_clause,[],[f880,f876,f710,f939,f935]) ).
fof(f939,plain,
( spl10_100
<=> member(sK2,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_100])]) ).
fof(f880,plain,
( ~ member(sK2,sK3)
| ~ member(sK3,universal_class)
| ~ spl10_73
| spl10_92 ),
inference(resolution,[],[f878,f711]) ).
fof(f933,plain,
( spl10_98
| ~ spl10_9
| ~ spl10_68 ),
inference(avatar_split_clause,[],[f691,f681,f309,f931]) ).
fof(f931,plain,
( spl10_98
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),cross_product(X0,X1))
| member(sK0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_98])]) ).
fof(f691,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),cross_product(X0,X1))
| member(sK0,X0) )
| ~ spl10_9
| ~ spl10_68 ),
inference(superposition,[],[f682,f311]) ).
fof(f929,plain,
( spl10_97
| ~ spl10_9
| ~ spl10_67 ),
inference(avatar_split_clause,[],[f690,f677,f309,f927]) ).
fof(f690,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),cross_product(X0,X1))
| member(sK1,X1) )
| ~ spl10_9
| ~ spl10_67 ),
inference(superposition,[],[f678,f311]) ).
fof(f897,plain,
( spl10_96
| ~ spl10_1
| ~ spl10_75 ),
inference(avatar_split_clause,[],[f753,f728,f272,f895]) ).
fof(f753,plain,
( ! [X0] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK0,sK0)))) = X0
| ~ member(X0,universal_class) )
| ~ spl10_1
| ~ spl10_75 ),
inference(resolution,[],[f729,f274]) ).
fof(f893,plain,
( spl10_95
| ~ spl10_1
| ~ spl10_74 ),
inference(avatar_split_clause,[],[f740,f724,f272,f891]) ).
fof(f740,plain,
( ! [X0] :
( sK0 = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK0,sK0))))
| ~ member(X0,universal_class) )
| ~ spl10_1
| ~ spl10_74 ),
inference(resolution,[],[f725,f274]) ).
fof(f889,plain,
( spl10_93
| ~ spl10_94
| ~ spl10_9
| ~ spl10_61 ),
inference(avatar_split_clause,[],[f657,f643,f309,f886,f882]) ).
fof(f882,plain,
( spl10_93
<=> member(sK1,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_93])]) ).
fof(f657,plain,
( ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),successor_relation)
| member(sK1,universal_class)
| ~ spl10_9
| ~ spl10_61 ),
inference(superposition,[],[f644,f311]) ).
fof(f879,plain,
( spl10_91
| ~ spl10_92
| ~ spl10_9
| ~ spl10_58 ),
inference(avatar_split_clause,[],[f655,f631,f309,f876,f872]) ).
fof(f872,plain,
( spl10_91
<=> member(sK0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_91])]) ).
fof(f655,plain,
( ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),element_relation)
| member(sK0,sK1)
| ~ spl10_9
| ~ spl10_58 ),
inference(superposition,[],[f632,f311]) ).
fof(f865,plain,
spl10_90,
inference(avatar_split_clause,[],[f261,f863]) ).
fof(f261,plain,
! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(definition_unfolding,[],[f221,f230,f230,f230,f230,f230,f230]) ).
fof(f230,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
inference(definition_unfolding,[],[f168,f145,f145]) ).
fof(f145,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set_defn) ).
fof(f168,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair_defn) ).
fof(f221,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(ordered_pair(X0,X1),X2),flip(X3))
| ~ member(ordered_pair(ordered_pair(X1,X0),X2),X3)
| ~ member(ordered_pair(ordered_pair(X0,X1),X2),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(cnf_transformation,[],[f132]) ).
fof(f132,plain,
! [X0,X1,X2,X3] :
( ( member(ordered_pair(ordered_pair(X0,X1),X2),flip(X3))
| ~ member(ordered_pair(ordered_pair(X1,X0),X2),X3)
| ~ member(ordered_pair(ordered_pair(X0,X1),X2),cross_product(cross_product(universal_class,universal_class),universal_class)) )
& ( ( member(ordered_pair(ordered_pair(X1,X0),X2),X3)
& member(ordered_pair(ordered_pair(X0,X1),X2),cross_product(cross_product(universal_class,universal_class),universal_class)) )
| ~ member(ordered_pair(ordered_pair(X0,X1),X2),flip(X3)) ) ),
inference(flattening,[],[f131]) ).
fof(f131,plain,
! [X0,X1,X2,X3] :
( ( member(ordered_pair(ordered_pair(X0,X1),X2),flip(X3))
| ~ member(ordered_pair(ordered_pair(X1,X0),X2),X3)
| ~ member(ordered_pair(ordered_pair(X0,X1),X2),cross_product(cross_product(universal_class,universal_class),universal_class)) )
& ( ( member(ordered_pair(ordered_pair(X1,X0),X2),X3)
& member(ordered_pair(ordered_pair(X0,X1),X2),cross_product(cross_product(universal_class,universal_class),universal_class)) )
| ~ member(ordered_pair(ordered_pair(X0,X1),X2),flip(X3)) ) ),
inference(nnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0,X1,X2,X3] :
( member(ordered_pair(ordered_pair(X0,X1),X2),flip(X3))
<=> ( member(ordered_pair(ordered_pair(X1,X0),X2),X3)
& member(ordered_pair(ordered_pair(X0,X1),X2),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
inference(rectify,[],[f20]) ).
fof(f20,axiom,
! [X2,X3,X6,X0] :
( member(ordered_pair(ordered_pair(X2,X3),X6),flip(X0))
<=> ( member(ordered_pair(ordered_pair(X3,X2),X6),X0)
& member(ordered_pair(ordered_pair(X2,X3),X6),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip_defn) ).
fof(f861,plain,
spl10_89,
inference(avatar_split_clause,[],[f258,f859]) ).
fof(f258,plain,
! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),rotate(X0))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X1,X1))),X0)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(definition_unfolding,[],[f218,f230,f230,f230,f230,f230,f230]) ).
fof(f218,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(ordered_pair(X1,X2),X3),rotate(X0))
| ~ member(ordered_pair(ordered_pair(X2,X3),X1),X0)
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(cnf_transformation,[],[f130]) ).
fof(f130,plain,
! [X0,X1,X2,X3] :
( ( member(ordered_pair(ordered_pair(X1,X2),X3),rotate(X0))
| ~ member(ordered_pair(ordered_pair(X2,X3),X1),X0)
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class)) )
& ( ( member(ordered_pair(ordered_pair(X2,X3),X1),X0)
& member(ordered_pair(ordered_pair(X1,X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class)) )
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),rotate(X0)) ) ),
inference(flattening,[],[f129]) ).
fof(f129,plain,
! [X0,X1,X2,X3] :
( ( member(ordered_pair(ordered_pair(X1,X2),X3),rotate(X0))
| ~ member(ordered_pair(ordered_pair(X2,X3),X1),X0)
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class)) )
& ( ( member(ordered_pair(ordered_pair(X2,X3),X1),X0)
& member(ordered_pair(ordered_pair(X1,X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class)) )
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),rotate(X0)) ) ),
inference(nnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0,X1,X2,X3] :
( member(ordered_pair(ordered_pair(X1,X2),X3),rotate(X0))
<=> ( member(ordered_pair(ordered_pair(X2,X3),X1),X0)
& member(ordered_pair(ordered_pair(X1,X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
inference(rectify,[],[f18]) ).
fof(f18,axiom,
! [X0,X2,X3,X6] :
( member(ordered_pair(ordered_pair(X2,X3),X6),rotate(X0))
<=> ( member(ordered_pair(ordered_pair(X3,X6),X2),X0)
& member(ordered_pair(ordered_pair(X2,X3),X6),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate_defn) ).
fof(f855,plain,
spl10_88,
inference(avatar_split_clause,[],[f263,f853]) ).
fof(f853,plain,
( spl10_88
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_88])]) ).
fof(f263,plain,
! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3)) ),
inference(definition_unfolding,[],[f219,f230,f230,f230,f230]) ).
fof(f219,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(ordered_pair(X0,X1),X2),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(ordered_pair(ordered_pair(X0,X1),X2),flip(X3)) ),
inference(cnf_transformation,[],[f132]) ).
fof(f851,plain,
spl10_87,
inference(avatar_split_clause,[],[f260,f849]) ).
fof(f849,plain,
( spl10_87
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),rotate(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_87])]) ).
fof(f260,plain,
! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),rotate(X0)) ),
inference(definition_unfolding,[],[f216,f230,f230,f230,f230]) ).
fof(f216,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(ordered_pair(X1,X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),rotate(X0)) ),
inference(cnf_transformation,[],[f130]) ).
fof(f847,plain,
( spl10_86
| ~ spl10_45
| ~ spl10_59 ),
inference(avatar_split_clause,[],[f662,f635,f494,f845]) ).
fof(f845,plain,
( spl10_86
<=> ! [X0,X1] :
( ~ member(X0,sK0)
| member(X0,X1)
| ~ subclass(sum_class(universal_class),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_86])]) ).
fof(f662,plain,
( ! [X0,X1] :
( ~ member(X0,sK0)
| member(X0,X1)
| ~ subclass(sum_class(universal_class),X1) )
| ~ spl10_45
| ~ spl10_59 ),
inference(resolution,[],[f636,f495]) ).
fof(f841,plain,
spl10_85,
inference(avatar_split_clause,[],[f262,f839]) ).
fof(f262,plain,
! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3)) ),
inference(definition_unfolding,[],[f220,f230,f230,f230,f230]) ).
fof(f220,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(ordered_pair(X1,X0),X2),X3)
| ~ member(ordered_pair(ordered_pair(X0,X1),X2),flip(X3)) ),
inference(cnf_transformation,[],[f132]) ).
fof(f837,plain,
spl10_84,
inference(avatar_split_clause,[],[f259,f835]) ).
fof(f259,plain,
! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X1,X1))),X0)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),rotate(X0)) ),
inference(definition_unfolding,[],[f217,f230,f230,f230,f230]) ).
fof(f217,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(ordered_pair(X2,X3),X1),X0)
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),rotate(X0)) ),
inference(cnf_transformation,[],[f130]) ).
fof(f827,plain,
spl10_83,
inference(avatar_split_clause,[],[f252,f825]) ).
fof(f252,plain,
! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),compose(X1,X0))
| ~ member(X3,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X2,X2),universal_class)),universal_class)))),universal_class)),universal_class)))))
| ~ member(X2,universal_class) ),
inference(definition_unfolding,[],[f212,f230,f229,f229,f145]) ).
fof(f229,plain,
! [X0,X1] : image(X1,X0) = domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class)))),
inference(definition_unfolding,[],[f167,f228,f198]) ).
fof(f198,plain,
! [X2,X0,X1] : restrict(X1,X0,X2) = intersection(X1,cross_product(X0,X2)),
inference(cnf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0,X1,X2] : restrict(X1,X0,X2) = intersection(X1,cross_product(X0,X2)),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X0,X5,X1] : restrict(X5,X0,X1) = intersection(X5,cross_product(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',restrict_defn) ).
fof(f228,plain,
! [X0] : range_of(X0) = domain_of(domain_of(flip(cross_product(X0,universal_class)))),
inference(definition_unfolding,[],[f144,f147]) ).
fof(f147,plain,
! [X0] : inverse(X0) = domain_of(flip(cross_product(X0,universal_class))),
inference(cnf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0] : inverse(X0) = domain_of(flip(cross_product(X0,universal_class))),
inference(rectify,[],[f26]) ).
fof(f26,axiom,
! [X1] : inverse(X1) = domain_of(flip(cross_product(X1,universal_class))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_defn) ).
fof(f144,plain,
! [X0] : range_of(X0) = domain_of(inverse(X0)),
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0] : range_of(X0) = domain_of(inverse(X0)),
inference(rectify,[],[f27]) ).
fof(f27,axiom,
! [X4] : range_of(X4) = domain_of(inverse(X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',range_of_defn) ).
fof(f167,plain,
! [X0,X1] : image(X1,X0) = range_of(restrict(X1,X0,universal_class)),
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0,X1] : image(X1,X0) = range_of(restrict(X1,X0,universal_class)),
inference(rectify,[],[f28]) ).
fof(f28,axiom,
! [X0,X5] : image(X5,X0) = range_of(restrict(X5,X0,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image_defn) ).
fof(f212,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X2,X3),compose(X1,X0))
| ~ member(X3,image(X1,image(X0,singleton(X2))))
| ~ member(X2,universal_class) ),
inference(cnf_transformation,[],[f126]) ).
fof(f126,plain,
! [X0,X1,X2,X3] :
( ( member(ordered_pair(X2,X3),compose(X1,X0))
| ~ member(X3,image(X1,image(X0,singleton(X2))))
| ~ member(X2,universal_class) )
& ( ( member(X3,image(X1,image(X0,singleton(X2))))
& member(X2,universal_class) )
| ~ member(ordered_pair(X2,X3),compose(X1,X0)) ) ),
inference(flattening,[],[f125]) ).
fof(f125,plain,
! [X0,X1,X2,X3] :
( ( member(ordered_pair(X2,X3),compose(X1,X0))
| ~ member(X3,image(X1,image(X0,singleton(X2))))
| ~ member(X2,universal_class) )
& ( ( member(X3,image(X1,image(X0,singleton(X2))))
& member(X2,universal_class) )
| ~ member(ordered_pair(X2,X3),compose(X1,X0)) ) ),
inference(nnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0,X1,X2,X3] :
( member(ordered_pair(X2,X3),compose(X1,X0))
<=> ( member(X3,image(X1,image(X0,singleton(X2))))
& member(X2,universal_class) ) ),
inference(rectify,[],[f36]) ).
fof(f36,axiom,
! [X5,X7,X2,X3] :
( member(ordered_pair(X2,X3),compose(X7,X5))
<=> ( member(X3,image(X7,image(X5,singleton(X2))))
& member(X2,universal_class) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_defn2) ).
fof(f822,plain,
spl10_82,
inference(avatar_split_clause,[],[f253,f820]) ).
fof(f253,plain,
! [X2,X3,X0,X1] :
( member(X3,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X2,X2),universal_class)),universal_class)))),universal_class)),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),compose(X1,X0)) ),
inference(definition_unfolding,[],[f211,f229,f229,f145,f230]) ).
fof(f211,plain,
! [X2,X3,X0,X1] :
( member(X3,image(X1,image(X0,singleton(X2))))
| ~ member(ordered_pair(X2,X3),compose(X1,X0)) ),
inference(cnf_transformation,[],[f126]) ).
fof(f813,plain,
spl10_81,
inference(avatar_split_clause,[],[f268,f811]) ).
fof(f268,plain,
! [X0] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(union(X0,unordered_pair(X0,X0)),union(X0,unordered_pair(X0,X0))))),successor_relation)
| ~ member(union(X0,unordered_pair(X0,X0)),universal_class)
| ~ member(X0,universal_class) ),
inference(equality_resolution,[],[f247]) ).
fof(f247,plain,
! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation)
| union(X0,unordered_pair(X0,X0)) != X1
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ),
inference(definition_unfolding,[],[f197,f230,f227]) ).
fof(f227,plain,
! [X0] : successor(X0) = union(X0,unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f146,f145]) ).
fof(f146,plain,
! [X0] : successor(X0) = union(X0,singleton(X0)),
inference(cnf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0] : successor(X0) = union(X0,singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_defn) ).
fof(f197,plain,
! [X0,X1] :
( member(ordered_pair(X0,X1),successor_relation)
| successor(X0) != X1
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f118]) ).
fof(f118,plain,
! [X0,X1] :
( ( member(ordered_pair(X0,X1),successor_relation)
| successor(X0) != X1
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) )
& ( ( successor(X0) = X1
& member(X1,universal_class)
& member(X0,universal_class) )
| ~ member(ordered_pair(X0,X1),successor_relation) ) ),
inference(flattening,[],[f117]) ).
fof(f117,plain,
! [X0,X1] :
( ( member(ordered_pair(X0,X1),successor_relation)
| successor(X0) != X1
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) )
& ( ( successor(X0) = X1
& member(X1,universal_class)
& member(X0,universal_class) )
| ~ member(ordered_pair(X0,X1),successor_relation) ) ),
inference(nnf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0,X1] :
( member(ordered_pair(X0,X1),successor_relation)
<=> ( successor(X0) = X1
& member(X1,universal_class)
& member(X0,universal_class) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_relation_defn2) ).
fof(f787,plain,
spl10_80,
inference(avatar_split_clause,[],[f264,f785]) ).
fof(f264,plain,
! [X1] :
( member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK8,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))),X1)
| null_class = X1
| ~ member(X1,universal_class) ),
inference(definition_unfolding,[],[f223,f231]) ).
fof(f231,plain,
! [X0,X1] : apply(X0,X1) = sum_class(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))),
inference(definition_unfolding,[],[f166,f229,f145]) ).
fof(f166,plain,
! [X0,X1] : apply(X0,X1) = sum_class(image(X0,singleton(X1))),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0,X1] : apply(X0,X1) = sum_class(image(X0,singleton(X1))),
inference(rectify,[],[f42]) ).
fof(f42,axiom,
! [X8,X1] : apply(X8,X1) = sum_class(image(X8,singleton(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apply_defn) ).
fof(f223,plain,
! [X1] :
( member(apply(sK8,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) ),
inference(cnf_transformation,[],[f134]) ).
fof(f134,plain,
( ! [X1] :
( member(apply(sK8,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) )
& function(sK8) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f85,f133]) ).
fof(f133,plain,
( ? [X0] :
( ! [X1] :
( member(apply(X0,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) )
& function(X0) )
=> ( ! [X1] :
( member(apply(sK8,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) )
& function(sK8) ) ),
introduced(choice_axiom,[]) ).
fof(f85,plain,
? [X0] :
( ! [X1] :
( member(apply(X0,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) )
& function(X0) ),
inference(flattening,[],[f84]) ).
fof(f84,plain,
? [X0] :
( ! [X1] :
( member(apply(X0,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) )
& function(X0) ),
inference(ennf_transformation,[],[f70]) ).
fof(f70,plain,
? [X0] :
( ! [X1] :
( member(X1,universal_class)
=> ( member(apply(X0,X1),X1)
| null_class = X1 ) )
& function(X0) ),
inference(rectify,[],[f43]) ).
fof(f43,axiom,
? [X8] :
( ! [X1] :
( member(X1,universal_class)
=> ( member(apply(X8,X1),X1)
| null_class = X1 ) )
& function(X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choice) ).
fof(f783,plain,
spl10_79,
inference(avatar_split_clause,[],[f251,f781]) ).
fof(f251,plain,
! [X2,X0,X1] :
( unordered_pair(unordered_pair(first(X2),first(X2)),unordered_pair(first(X2),unordered_pair(second(X2),second(X2)))) = X2
| ~ member(X2,cross_product(X0,X1)) ),
inference(definition_unfolding,[],[f199,f230]) ).
fof(f199,plain,
! [X2,X0,X1] :
( ordered_pair(first(X2),second(X2)) = X2
| ~ member(X2,cross_product(X0,X1)) ),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
! [X0,X1,X2] :
( ordered_pair(first(X2),second(X2)) = X2
| ~ member(X2,cross_product(X0,X1)) ),
inference(ennf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0,X1,X2] :
( member(X2,cross_product(X0,X1))
=> ordered_pair(first(X2),second(X2)) = X2 ),
inference(rectify,[],[f10]) ).
fof(f10,axiom,
! [X0,X1,X4] :
( member(X4,cross_product(X0,X1))
=> ordered_pair(first(X4),second(X4)) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cross_product) ).
fof(f769,plain,
spl10_78,
inference(avatar_split_clause,[],[f255,f767]) ).
fof(f255,plain,
! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3))
| ~ member(X1,X3)
| ~ member(X0,X2) ),
inference(definition_unfolding,[],[f215,f230]) ).
fof(f215,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ member(X1,X3)
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f128]) ).
fof(f128,plain,
! [X0,X1,X2,X3] :
( ( member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ member(X1,X3)
| ~ member(X0,X2) )
& ( ( member(X1,X3)
& member(X0,X2) )
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ) ),
inference(flattening,[],[f127]) ).
fof(f127,plain,
! [X0,X1,X2,X3] :
( ( member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ member(X1,X3)
| ~ member(X0,X2) )
& ( ( member(X1,X3)
& member(X0,X2) )
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ) ),
inference(nnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0,X1,X2,X3] :
( member(ordered_pair(X0,X1),cross_product(X2,X3))
<=> ( member(X1,X3)
& member(X0,X2) ) ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X2,X3,X0,X1] :
( member(ordered_pair(X2,X3),cross_product(X0,X1))
<=> ( member(X3,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cross_product_defn) ).
fof(f765,plain,
spl10_77,
inference(avatar_split_clause,[],[f238,f763]) ).
fof(f238,plain,
! [X0] :
( unordered_pair(unordered_pair(sK5(X0),sK5(X0)),unordered_pair(sK5(X0),unordered_pair(sK5(X0),sK5(X0)))) = X0
| ~ member(X0,identity_relation) ),
inference(definition_unfolding,[],[f162,f230]) ).
fof(f162,plain,
! [X0] :
( ordered_pair(sK5(X0),sK5(X0)) = X0
| ~ member(X0,identity_relation) ),
inference(cnf_transformation,[],[f98]) ).
fof(f98,plain,
! [X0] :
( ( member(X0,identity_relation)
| ! [X1] :
( ordered_pair(X1,X1) != X0
| ~ member(X1,universal_class) ) )
& ( ( ordered_pair(sK5(X0),sK5(X0)) = X0
& member(sK5(X0),universal_class) )
| ~ member(X0,identity_relation) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f96,f97]) ).
fof(f97,plain,
! [X0] :
( ? [X2] :
( ordered_pair(X2,X2) = X0
& member(X2,universal_class) )
=> ( ordered_pair(sK5(X0),sK5(X0)) = X0
& member(sK5(X0),universal_class) ) ),
introduced(choice_axiom,[]) ).
fof(f96,plain,
! [X0] :
( ( member(X0,identity_relation)
| ! [X1] :
( ordered_pair(X1,X1) != X0
| ~ member(X1,universal_class) ) )
& ( ? [X2] :
( ordered_pair(X2,X2) = X0
& member(X2,universal_class) )
| ~ member(X0,identity_relation) ) ),
inference(rectify,[],[f95]) ).
fof(f95,plain,
! [X0] :
( ( member(X0,identity_relation)
| ! [X1] :
( ordered_pair(X1,X1) != X0
| ~ member(X1,universal_class) ) )
& ( ? [X1] :
( ordered_pair(X1,X1) = X0
& member(X1,universal_class) )
| ~ member(X0,identity_relation) ) ),
inference(nnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0] :
( member(X0,identity_relation)
<=> ? [X1] :
( ordered_pair(X1,X1) = X0
& member(X1,universal_class) ) ),
inference(rectify,[],[f37]) ).
fof(f37,axiom,
! [X4] :
( member(X4,identity_relation)
<=> ? [X0] :
( ordered_pair(X0,X0) = X4
& member(X0,universal_class) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_relation) ).
fof(f734,plain,
spl10_76,
inference(avatar_split_clause,[],[f248,f732]) ).
fof(f248,plain,
! [X0,X1] :
( union(X0,unordered_pair(X0,X0)) = X1
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation) ),
inference(definition_unfolding,[],[f196,f227,f230]) ).
fof(f196,plain,
! [X0,X1] :
( successor(X0) = X1
| ~ member(ordered_pair(X0,X1),successor_relation) ),
inference(cnf_transformation,[],[f118]) ).
fof(f730,plain,
spl10_75,
inference(avatar_split_clause,[],[f241,f728]) ).
fof(f241,plain,
! [X0,X1] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))) = X0
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ),
inference(definition_unfolding,[],[f170,f230]) ).
fof(f170,plain,
! [X0,X1] :
( first(ordered_pair(X0,X1)) = X0
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0,X1] :
( ( second(ordered_pair(X0,X1)) = X1
& first(ordered_pair(X0,X1)) = X0 )
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ),
inference(flattening,[],[f79]) ).
fof(f79,plain,
! [X0,X1] :
( ( second(ordered_pair(X0,X1)) = X1
& first(ordered_pair(X0,X1)) = X0 )
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1] :
( ( member(X1,universal_class)
& member(X0,universal_class) )
=> ( second(ordered_pair(X0,X1)) = X1
& first(ordered_pair(X0,X1)) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',first_second) ).
fof(f726,plain,
spl10_74,
inference(avatar_split_clause,[],[f240,f724]) ).
fof(f240,plain,
! [X0,X1] :
( second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))) = X1
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ),
inference(definition_unfolding,[],[f171,f230]) ).
fof(f171,plain,
! [X0,X1] :
( second(ordered_pair(X0,X1)) = X1
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f80]) ).
fof(f712,plain,
spl10_73,
inference(avatar_split_clause,[],[f244,f710]) ).
fof(f244,plain,
! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| ~ member(X0,X1)
| ~ member(X1,universal_class) ),
inference(definition_unfolding,[],[f193,f230]) ).
fof(f193,plain,
! [X0,X1] :
( member(ordered_pair(X0,X1),element_relation)
| ~ member(X0,X1)
| ~ member(X1,universal_class) ),
inference(cnf_transformation,[],[f116]) ).
fof(f116,plain,
! [X0,X1] :
( ( member(ordered_pair(X0,X1),element_relation)
| ~ member(X0,X1)
| ~ member(X1,universal_class) )
& ( ( member(X0,X1)
& member(X1,universal_class) )
| ~ member(ordered_pair(X0,X1),element_relation) ) ),
inference(flattening,[],[f115]) ).
fof(f115,plain,
! [X0,X1] :
( ( member(ordered_pair(X0,X1),element_relation)
| ~ member(X0,X1)
| ~ member(X1,universal_class) )
& ( ( member(X0,X1)
& member(X1,universal_class) )
| ~ member(ordered_pair(X0,X1),element_relation) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0,X1] :
( member(ordered_pair(X0,X1),element_relation)
<=> ( member(X0,X1)
& member(X1,universal_class) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation_defn) ).
fof(f708,plain,
spl10_72,
inference(avatar_split_clause,[],[f239,f706]) ).
fof(f239,plain,
! [X0,X1] :
( member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class)))),universal_class)
| ~ function(X1)
| ~ member(X0,universal_class) ),
inference(definition_unfolding,[],[f169,f229]) ).
fof(f169,plain,
! [X0,X1] :
( member(image(X1,X0),universal_class)
| ~ function(X1)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
! [X0,X1] :
( member(image(X1,X0),universal_class)
| ~ function(X1)
| ~ member(X0,universal_class) ),
inference(flattening,[],[f77]) ).
fof(f77,plain,
! [X0,X1] :
( member(image(X1,X0),universal_class)
| ~ function(X1)
| ~ member(X0,universal_class) ),
inference(ennf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0,X1] :
( ( function(X1)
& member(X0,universal_class) )
=> member(image(X1,X0),universal_class) ),
inference(rectify,[],[f39]) ).
fof(f39,axiom,
! [X0,X8] :
( ( function(X8)
& member(X0,universal_class) )
=> member(image(X8,X0),universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',replacement) ).
fof(f704,plain,
spl10_71,
inference(avatar_split_clause,[],[f233,f702]) ).
fof(f233,plain,
! [X0] :
( inductive(X0)
| ~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| ~ member(null_class,X0) ),
inference(definition_unfolding,[],[f157,f229]) ).
fof(f157,plain,
! [X0] :
( inductive(X0)
| ~ subclass(image(successor_relation,X0),X0)
| ~ member(null_class,X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f92,plain,
! [X0] :
( ( inductive(X0)
| ~ subclass(image(successor_relation,X0),X0)
| ~ member(null_class,X0) )
& ( ( subclass(image(successor_relation,X0),X0)
& member(null_class,X0) )
| ~ inductive(X0) ) ),
inference(flattening,[],[f91]) ).
fof(f91,plain,
! [X0] :
( ( inductive(X0)
| ~ subclass(image(successor_relation,X0),X0)
| ~ member(null_class,X0) )
& ( ( subclass(image(successor_relation,X0),X0)
& member(null_class,X0) )
| ~ inductive(X0) ) ),
inference(nnf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0] :
( inductive(X0)
<=> ( subclass(image(successor_relation,X0),X0)
& member(null_class,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inductive_defn) ).
fof(f700,plain,
( ~ spl10_69
| spl10_70
| ~ spl10_20
| ~ spl10_48 ),
inference(avatar_split_clause,[],[f594,f531,f358,f697,f693]) ).
fof(f693,plain,
( spl10_69
<=> function(universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_69])]) ).
fof(f697,plain,
( spl10_70
<=> member(sK0,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_70])]) ).
fof(f531,plain,
( spl10_48
<=> ! [X0] :
( member(sK0,X0)
| ~ subclass(universal_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_48])]) ).
fof(f594,plain,
( member(sK0,cross_product(universal_class,universal_class))
| ~ function(universal_class)
| ~ spl10_20
| ~ spl10_48 ),
inference(resolution,[],[f532,f359]) ).
fof(f532,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| member(sK0,X0) )
| ~ spl10_48 ),
inference(avatar_component_clause,[],[f531]) ).
fof(f683,plain,
spl10_68,
inference(avatar_split_clause,[],[f257,f681]) ).
fof(f257,plain,
! [X2,X3,X0,X1] :
( member(X0,X2)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(definition_unfolding,[],[f213,f230]) ).
fof(f213,plain,
! [X2,X3,X0,X1] :
( member(X0,X2)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[],[f128]) ).
fof(f679,plain,
spl10_67,
inference(avatar_split_clause,[],[f256,f677]) ).
fof(f256,plain,
! [X2,X3,X0,X1] :
( member(X1,X3)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(definition_unfolding,[],[f214,f230]) ).
fof(f214,plain,
! [X2,X3,X0,X1] :
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[],[f128]) ).
fof(f675,plain,
spl10_66,
inference(avatar_split_clause,[],[f254,f673]) ).
fof(f254,plain,
! [X2,X3,X0,X1] :
( member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),compose(X1,X0)) ),
inference(definition_unfolding,[],[f210,f230]) ).
fof(f210,plain,
! [X2,X3,X0,X1] :
( member(X2,universal_class)
| ~ member(ordered_pair(X2,X3),compose(X1,X0)) ),
inference(cnf_transformation,[],[f126]) ).
fof(f671,plain,
spl10_65,
inference(avatar_split_clause,[],[f242,f669]) ).
fof(f242,plain,
! [X0,X1] :
( member(X1,domain_of(X0))
| null_class = intersection(X0,cross_product(unordered_pair(X1,X1),universal_class))
| ~ member(X1,universal_class) ),
inference(definition_unfolding,[],[f187,f198,f145]) ).
fof(f187,plain,
! [X0,X1] :
( member(X1,domain_of(X0))
| null_class = restrict(X0,singleton(X1),universal_class)
| ~ member(X1,universal_class) ),
inference(cnf_transformation,[],[f110]) ).
fof(f110,plain,
! [X0,X1] :
( ( member(X1,domain_of(X0))
| null_class = restrict(X0,singleton(X1),universal_class)
| ~ member(X1,universal_class) )
& ( ( null_class != restrict(X0,singleton(X1),universal_class)
& member(X1,universal_class) )
| ~ member(X1,domain_of(X0)) ) ),
inference(flattening,[],[f109]) ).
fof(f109,plain,
! [X0,X1] :
( ( member(X1,domain_of(X0))
| null_class = restrict(X0,singleton(X1),universal_class)
| ~ member(X1,universal_class) )
& ( ( null_class != restrict(X0,singleton(X1),universal_class)
& member(X1,universal_class) )
| ~ member(X1,domain_of(X0)) ) ),
inference(nnf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0,X1] :
( member(X1,domain_of(X0))
<=> ( null_class != restrict(X0,singleton(X1),universal_class)
& member(X1,universal_class) ) ),
inference(rectify,[],[f17]) ).
fof(f17,axiom,
! [X0,X4] :
( member(X4,domain_of(X0))
<=> ( null_class != restrict(X0,singleton(X4),universal_class)
& member(X4,universal_class) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_of) ).
fof(f667,plain,
spl10_64,
inference(avatar_split_clause,[],[f235,f665]) ).
fof(f665,plain,
( spl10_64
<=> ! [X0] :
( function(X0)
| ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation)
| ~ subclass(X0,cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_64])]) ).
fof(f235,plain,
! [X0] :
( function(X0)
| ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation)
| ~ subclass(X0,cross_product(universal_class,universal_class)) ),
inference(definition_unfolding,[],[f160,f147]) ).
fof(f160,plain,
! [X0] :
( function(X0)
| ~ subclass(compose(X0,inverse(X0)),identity_relation)
| ~ subclass(X0,cross_product(universal_class,universal_class)) ),
inference(cnf_transformation,[],[f94]) ).
fof(f94,plain,
! [X0] :
( ( function(X0)
| ~ subclass(compose(X0,inverse(X0)),identity_relation)
| ~ subclass(X0,cross_product(universal_class,universal_class)) )
& ( ( subclass(compose(X0,inverse(X0)),identity_relation)
& subclass(X0,cross_product(universal_class,universal_class)) )
| ~ function(X0) ) ),
inference(flattening,[],[f93]) ).
fof(f93,plain,
! [X0] :
( ( function(X0)
| ~ subclass(compose(X0,inverse(X0)),identity_relation)
| ~ subclass(X0,cross_product(universal_class,universal_class)) )
& ( ( subclass(compose(X0,inverse(X0)),identity_relation)
& subclass(X0,cross_product(universal_class,universal_class)) )
| ~ function(X0) ) ),
inference(nnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0] :
( function(X0)
<=> ( subclass(compose(X0,inverse(X0)),identity_relation)
& subclass(X0,cross_product(universal_class,universal_class)) ) ),
inference(rectify,[],[f38]) ).
fof(f38,axiom,
! [X8] :
( function(X8)
<=> ( subclass(compose(X8,inverse(X8)),identity_relation)
& subclass(X8,cross_product(universal_class,universal_class)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',function_defn) ).
fof(f653,plain,
spl10_63,
inference(avatar_split_clause,[],[f265,f651]) ).
fof(f265,plain,
! [X1] :
( member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X1,X1))),identity_relation)
| ~ member(X1,universal_class) ),
inference(equality_resolution,[],[f237]) ).
fof(f237,plain,
! [X0,X1] :
( member(X0,identity_relation)
| unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X1,X1))) != X0
| ~ member(X1,universal_class) ),
inference(definition_unfolding,[],[f163,f230]) ).
fof(f163,plain,
! [X0,X1] :
( member(X0,identity_relation)
| ordered_pair(X1,X1) != X0
| ~ member(X1,universal_class) ),
inference(cnf_transformation,[],[f98]) ).
fof(f649,plain,
spl10_62,
inference(avatar_split_clause,[],[f250,f647]) ).
fof(f647,plain,
( spl10_62
<=> ! [X0,X1] :
( member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_62])]) ).
fof(f250,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation) ),
inference(definition_unfolding,[],[f194,f230]) ).
fof(f194,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(ordered_pair(X0,X1),successor_relation) ),
inference(cnf_transformation,[],[f118]) ).
fof(f645,plain,
spl10_61,
inference(avatar_split_clause,[],[f249,f643]) ).
fof(f249,plain,
! [X0,X1] :
( member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation) ),
inference(definition_unfolding,[],[f195,f230]) ).
fof(f195,plain,
! [X0,X1] :
( member(X1,universal_class)
| ~ member(ordered_pair(X0,X1),successor_relation) ),
inference(cnf_transformation,[],[f118]) ).
fof(f641,plain,
spl10_60,
inference(avatar_split_clause,[],[f246,f639]) ).
fof(f246,plain,
! [X0,X1] :
( member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation) ),
inference(definition_unfolding,[],[f191,f230]) ).
fof(f191,plain,
! [X0,X1] :
( member(X1,universal_class)
| ~ member(ordered_pair(X0,X1),element_relation) ),
inference(cnf_transformation,[],[f116]) ).
fof(f637,plain,
( spl10_59
| ~ spl10_1
| ~ spl10_51 ),
inference(avatar_split_clause,[],[f573,f554,f272,f635]) ).
fof(f573,plain,
( ! [X0] :
( member(X0,sum_class(universal_class))
| ~ member(X0,sK0) )
| ~ spl10_1
| ~ spl10_51 ),
inference(resolution,[],[f555,f274]) ).
fof(f633,plain,
spl10_58,
inference(avatar_split_clause,[],[f245,f631]) ).
fof(f245,plain,
! [X0,X1] :
( member(X0,X1)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation) ),
inference(definition_unfolding,[],[f192,f230]) ).
fof(f192,plain,
! [X0,X1] :
( member(X0,X1)
| ~ member(ordered_pair(X0,X1),element_relation) ),
inference(cnf_transformation,[],[f116]) ).
fof(f629,plain,
spl10_57,
inference(avatar_split_clause,[],[f234,f627]) ).
fof(f234,plain,
! [X0] :
( subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| ~ inductive(X0) ),
inference(definition_unfolding,[],[f156,f229]) ).
fof(f156,plain,
! [X0] :
( subclass(image(successor_relation,X0),X0)
| ~ inductive(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f625,plain,
spl10_56,
inference(avatar_split_clause,[],[f243,f623]) ).
fof(f623,plain,
( spl10_56
<=> ! [X0,X1] :
( null_class != intersection(X0,cross_product(unordered_pair(X1,X1),universal_class))
| ~ member(X1,domain_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_56])]) ).
fof(f243,plain,
! [X0,X1] :
( null_class != intersection(X0,cross_product(unordered_pair(X1,X1),universal_class))
| ~ member(X1,domain_of(X0)) ),
inference(definition_unfolding,[],[f186,f198,f145]) ).
fof(f186,plain,
! [X0,X1] :
( null_class != restrict(X0,singleton(X1),universal_class)
| ~ member(X1,domain_of(X0)) ),
inference(cnf_transformation,[],[f110]) ).
fof(f602,plain,
spl10_55,
inference(avatar_split_clause,[],[f236,f600]) ).
fof(f236,plain,
! [X0] :
( subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation)
| ~ function(X0) ),
inference(definition_unfolding,[],[f159,f147]) ).
fof(f159,plain,
! [X0] :
( subclass(compose(X0,inverse(X0)),identity_relation)
| ~ function(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f598,plain,
spl10_54,
inference(avatar_split_clause,[],[f207,f596]) ).
fof(f207,plain,
! [X2,X0,X1] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f124]) ).
fof(f124,plain,
! [X0,X1,X2] :
( ( member(X0,unordered_pair(X1,X2))
| ( X0 != X2
& X0 != X1 )
| ~ member(X0,universal_class) )
& ( ( ( X0 = X2
| X0 = X1 )
& member(X0,universal_class) )
| ~ member(X0,unordered_pair(X1,X2)) ) ),
inference(flattening,[],[f123]) ).
fof(f123,plain,
! [X0,X1,X2] :
( ( member(X0,unordered_pair(X1,X2))
| ( X0 != X2
& X0 != X1 )
| ~ member(X0,universal_class) )
& ( ( ( X0 = X2
| X0 = X1 )
& member(X0,universal_class) )
| ~ member(X0,unordered_pair(X1,X2)) ) ),
inference(nnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0,X1,X2] :
( member(X0,unordered_pair(X1,X2))
<=> ( ( X0 = X2
| X0 = X1 )
& member(X0,universal_class) ) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X2,X0,X1] :
( member(X2,unordered_pair(X0,X1))
<=> ( ( X1 = X2
| X0 = X2 )
& member(X2,universal_class) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_defn) ).
fof(f591,plain,
spl10_53,
inference(avatar_split_clause,[],[f203,f589]) ).
fof(f203,plain,
! [X2,X0,X1] :
( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f122]) ).
fof(f122,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X1)
& ~ member(X2,X0) ) )
& ( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ) ),
inference(flattening,[],[f121]) ).
fof(f121,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X1)
& ~ member(X2,X0) ) )
& ( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ) ),
inference(nnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X1)
| member(X2,X0) ) ),
inference(rectify,[],[f22]) ).
fof(f22,axiom,
! [X0,X1,X4] :
( member(X4,union(X0,X1))
<=> ( member(X4,X1)
| member(X4,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
fof(f587,plain,
spl10_52,
inference(avatar_split_clause,[],[f202,f585]) ).
fof(f202,plain,
! [X2,X0,X1] :
( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f120,plain,
! [X0,X1,X2] :
( ( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) )
& ( ( member(X2,X1)
& member(X2,X0) )
| ~ member(X2,intersection(X0,X1)) ) ),
inference(flattening,[],[f119]) ).
fof(f119,plain,
! [X0,X1,X2] :
( ( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) )
& ( ( member(X2,X1)
& member(X2,X0) )
| ~ member(X2,intersection(X0,X1)) ) ),
inference(nnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ),
inference(rectify,[],[f13]) ).
fof(f13,axiom,
! [X0,X1,X4] :
( member(X4,intersection(X0,X1))
<=> ( member(X4,X1)
& member(X4,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection) ).
fof(f556,plain,
spl10_51,
inference(avatar_split_clause,[],[f190,f554]) ).
fof(f190,plain,
! [X2,X0,X1] :
( member(X0,sum_class(X1))
| ~ member(X2,X1)
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f114]) ).
fof(f114,plain,
! [X0,X1] :
( ( member(X0,sum_class(X1))
| ! [X2] :
( ~ member(X2,X1)
| ~ member(X0,X2) ) )
& ( ( member(sK7(X0,X1),X1)
& member(X0,sK7(X0,X1)) )
| ~ member(X0,sum_class(X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f112,f113]) ).
fof(f113,plain,
! [X0,X1] :
( ? [X3] :
( member(X3,X1)
& member(X0,X3) )
=> ( member(sK7(X0,X1),X1)
& member(X0,sK7(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f112,plain,
! [X0,X1] :
( ( member(X0,sum_class(X1))
| ! [X2] :
( ~ member(X2,X1)
| ~ member(X0,X2) ) )
& ( ? [X3] :
( member(X3,X1)
& member(X0,X3) )
| ~ member(X0,sum_class(X1)) ) ),
inference(rectify,[],[f111]) ).
fof(f111,plain,
! [X0,X1] :
( ( member(X0,sum_class(X1))
| ! [X2] :
( ~ member(X2,X1)
| ~ member(X0,X2) ) )
& ( ? [X2] :
( member(X2,X1)
& member(X0,X2) )
| ~ member(X0,sum_class(X1)) ) ),
inference(nnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0,X1] :
( member(X0,sum_class(X1))
<=> ? [X2] :
( member(X2,X1)
& member(X0,X2) ) ),
inference(rectify,[],[f31]) ).
fof(f31,axiom,
! [X2,X0] :
( member(X2,sum_class(X0))
<=> ? [X1] :
( member(X1,X0)
& member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_class_defn) ).
fof(f552,plain,
spl10_50,
inference(avatar_split_clause,[],[f184,f550]) ).
fof(f184,plain,
! [X0,X1] :
( member(X0,power_class(X1))
| ~ subclass(X0,X1)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f108]) ).
fof(f108,plain,
! [X0,X1] :
( ( member(X0,power_class(X1))
| ~ subclass(X0,X1)
| ~ member(X0,universal_class) )
& ( ( subclass(X0,X1)
& member(X0,universal_class) )
| ~ member(X0,power_class(X1)) ) ),
inference(flattening,[],[f107]) ).
fof(f107,plain,
! [X0,X1] :
( ( member(X0,power_class(X1))
| ~ subclass(X0,X1)
| ~ member(X0,universal_class) )
& ( ( subclass(X0,X1)
& member(X0,universal_class) )
| ~ member(X0,power_class(X1)) ) ),
inference(nnf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0,X1] :
( member(X0,power_class(X1))
<=> ( subclass(X0,X1)
& member(X0,universal_class) ) ),
inference(rectify,[],[f33]) ).
fof(f33,axiom,
! [X2,X0] :
( member(X2,power_class(X0))
<=> ( subclass(X2,X0)
& member(X2,universal_class) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_class_defn) ).
fof(f548,plain,
spl10_49,
inference(avatar_split_clause,[],[f181,f546]) ).
fof(f181,plain,
! [X0,X1] :
( member(X1,complement(X0))
| member(X1,X0)
| ~ member(X1,universal_class) ),
inference(cnf_transformation,[],[f106]) ).
fof(f106,plain,
! [X0,X1] :
( ( member(X1,complement(X0))
| member(X1,X0)
| ~ member(X1,universal_class) )
& ( ( ~ member(X1,X0)
& member(X1,universal_class) )
| ~ member(X1,complement(X0)) ) ),
inference(flattening,[],[f105]) ).
fof(f105,plain,
! [X0,X1] :
( ( member(X1,complement(X0))
| member(X1,X0)
| ~ member(X1,universal_class) )
& ( ( ~ member(X1,X0)
& member(X1,universal_class) )
| ~ member(X1,complement(X0)) ) ),
inference(nnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0,X1] :
( member(X1,complement(X0))
<=> ( ~ member(X1,X0)
& member(X1,universal_class) ) ),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X0,X4] :
( member(X4,complement(X0))
<=> ( ~ member(X4,X0)
& member(X4,universal_class) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement) ).
fof(f533,plain,
( spl10_48
| ~ spl10_1
| ~ spl10_45 ),
inference(avatar_split_clause,[],[f522,f494,f272,f531]) ).
fof(f522,plain,
( ! [X0] :
( member(sK0,X0)
| ~ subclass(universal_class,X0) )
| ~ spl10_1
| ~ spl10_45 ),
inference(resolution,[],[f495,f274]) ).
fof(f504,plain,
spl10_47,
inference(avatar_split_clause,[],[f189,f502]) ).
fof(f189,plain,
! [X0,X1] :
( member(sK7(X0,X1),X1)
| ~ member(X0,sum_class(X1)) ),
inference(cnf_transformation,[],[f114]) ).
fof(f500,plain,
spl10_46,
inference(avatar_split_clause,[],[f188,f498]) ).
fof(f188,plain,
! [X0,X1] :
( member(X0,sK7(X0,X1))
| ~ member(X0,sum_class(X1)) ),
inference(cnf_transformation,[],[f114]) ).
fof(f496,plain,
spl10_45,
inference(avatar_split_clause,[],[f176,f494]) ).
fof(f176,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f104]) ).
fof(f104,plain,
! [X0,X1] :
( ( subclass(X0,X1)
| ( ~ member(sK6(X0,X1),X1)
& member(sK6(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subclass(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f102,f103]) ).
fof(f103,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK6(X0,X1),X1)
& member(sK6(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f102,plain,
! [X0,X1] :
( ( subclass(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subclass(X0,X1) ) ),
inference(rectify,[],[f101]) ).
fof(f101,plain,
! [X0,X1] :
( ( subclass(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subclass(X0,X1) ) ),
inference(nnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0,X1] :
( subclass(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( subclass(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_defn) ).
fof(f492,plain,
spl10_44,
inference(avatar_split_clause,[],[f175,f490]) ).
fof(f175,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0,X1] :
( ! [X2] :
( ~ member(X2,X1)
| ~ member(X2,X0) )
| ~ disjoint(X0,X1) ),
inference(ennf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0,X1] :
( disjoint(X0,X1)
=> ! [X2] :
~ ( member(X2,X1)
& member(X2,X0) ) ),
inference(unused_predicate_definition_removal,[],[f40]) ).
fof(f40,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> ! [X2] :
~ ( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjoint_defn) ).
fof(f488,plain,
spl10_43,
inference(avatar_split_clause,[],[f174,f486]) ).
fof(f174,plain,
! [X0,X1] :
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f100]) ).
fof(f100,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) )
& ( ( subclass(X1,X0)
& subclass(X0,X1) )
| X0 != X1 ) ),
inference(flattening,[],[f99]) ).
fof(f99,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) )
& ( ( subclass(X1,X0)
& subclass(X0,X1) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subclass(X1,X0)
& subclass(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality) ).
fof(f480,plain,
( spl10_42
| ~ spl10_5
| ~ spl10_33 ),
inference(avatar_split_clause,[],[f459,f422,f292,f478]) ).
fof(f459,plain,
( ! [X0] : subclass(null_class,X0)
| ~ spl10_5
| ~ spl10_33 ),
inference(resolution,[],[f423,f293]) ).
fof(f456,plain,
spl10_41,
inference(avatar_split_clause,[],[f270,f454]) ).
fof(f270,plain,
! [X2,X1] :
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
inference(equality_resolution,[],[f208]) ).
fof(f208,plain,
! [X2,X0,X1] :
( member(X0,unordered_pair(X1,X2))
| X0 != X1
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f124]) ).
fof(f452,plain,
spl10_40,
inference(avatar_split_clause,[],[f269,f450]) ).
fof(f269,plain,
! [X2,X1] :
( member(X2,unordered_pair(X1,X2))
| ~ member(X2,universal_class) ),
inference(equality_resolution,[],[f209]) ).
fof(f209,plain,
! [X2,X0,X1] :
( member(X0,unordered_pair(X1,X2))
| X0 != X2
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f124]) ).
fof(f448,plain,
spl10_39,
inference(avatar_split_clause,[],[f206,f446]) ).
fof(f206,plain,
! [X2,X0,X1] :
( member(X0,universal_class)
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f124]) ).
fof(f444,plain,
spl10_38,
inference(avatar_split_clause,[],[f205,f442]) ).
fof(f205,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f122]) ).
fof(f440,plain,
spl10_37,
inference(avatar_split_clause,[],[f204,f438]) ).
fof(f204,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f122]) ).
fof(f436,plain,
spl10_36,
inference(avatar_split_clause,[],[f201,f434]) ).
fof(f201,plain,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[],[f120]) ).
fof(f432,plain,
spl10_35,
inference(avatar_split_clause,[],[f200,f430]) ).
fof(f200,plain,
! [X2,X0,X1] :
( member(X2,X0)
| ~ member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[],[f120]) ).
fof(f428,plain,
spl10_34,
inference(avatar_split_clause,[],[f178,f426]) ).
fof(f178,plain,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(sK6(X0,X1),X1) ),
inference(cnf_transformation,[],[f104]) ).
fof(f424,plain,
spl10_33,
inference(avatar_split_clause,[],[f177,f422]) ).
fof(f177,plain,
! [X0,X1] :
( subclass(X0,X1)
| member(sK6(X0,X1),X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f420,plain,
spl10_32,
inference(avatar_split_clause,[],[f149,f418]) ).
fof(f149,plain,
! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
inference(cnf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip) ).
fof(f416,plain,
spl10_31,
inference(avatar_split_clause,[],[f148,f414]) ).
fof(f148,plain,
! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
inference(cnf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate) ).
fof(f412,plain,
( spl10_29
| spl10_30
| ~ spl10_12
| ~ spl10_24 ),
inference(avatar_split_clause,[],[f395,f375,f324,f409,f406]) ).
fof(f406,plain,
( spl10_29
<=> ! [X0] : ~ inductive(complement(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_29])]) ).
fof(f395,plain,
( ! [X0] :
( member(null_class,universal_class)
| ~ inductive(complement(X0)) )
| ~ spl10_12
| ~ spl10_24 ),
inference(resolution,[],[f376,f325]) ).
fof(f393,plain,
spl10_28,
inference(avatar_split_clause,[],[f185,f391]) ).
fof(f185,plain,
! [X0,X1] :
( member(X1,universal_class)
| ~ member(X1,domain_of(X0)) ),
inference(cnf_transformation,[],[f110]) ).
fof(f389,plain,
spl10_27,
inference(avatar_split_clause,[],[f183,f387]) ).
fof(f183,plain,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(X0,power_class(X1)) ),
inference(cnf_transformation,[],[f108]) ).
fof(f385,plain,
spl10_26,
inference(avatar_split_clause,[],[f182,f383]) ).
fof(f182,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,power_class(X1)) ),
inference(cnf_transformation,[],[f108]) ).
fof(f381,plain,
spl10_25,
inference(avatar_split_clause,[],[f180,f379]) ).
fof(f180,plain,
! [X0,X1] :
( ~ member(X1,X0)
| ~ member(X1,complement(X0)) ),
inference(cnf_transformation,[],[f106]) ).
fof(f377,plain,
spl10_24,
inference(avatar_split_clause,[],[f179,f375]) ).
fof(f179,plain,
! [X0,X1] :
( member(X1,universal_class)
| ~ member(X1,complement(X0)) ),
inference(cnf_transformation,[],[f106]) ).
fof(f373,plain,
spl10_23,
inference(avatar_split_clause,[],[f165,f371]) ).
fof(f165,plain,
! [X0,X1] : subclass(compose(X1,X0),cross_product(universal_class,universal_class)),
inference(cnf_transformation,[],[f53]) ).
fof(f53,plain,
! [X0,X1] : subclass(compose(X1,X0),cross_product(universal_class,universal_class)),
inference(rectify,[],[f35]) ).
fof(f35,axiom,
! [X5,X7] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_defn1) ).
fof(f369,plain,
spl10_22,
inference(avatar_split_clause,[],[f161,f367]) ).
fof(f161,plain,
! [X0] :
( member(sK5(X0),universal_class)
| ~ member(X0,identity_relation) ),
inference(cnf_transformation,[],[f98]) ).
fof(f365,plain,
( ~ spl10_21
| ~ spl10_5
| ~ spl10_12 ),
inference(avatar_split_clause,[],[f335,f324,f292,f362]) ).
fof(f362,plain,
( spl10_21
<=> inductive(null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_21])]) ).
fof(f335,plain,
( ~ inductive(null_class)
| ~ spl10_5
| ~ spl10_12 ),
inference(resolution,[],[f325,f293]) ).
fof(f360,plain,
spl10_20,
inference(avatar_split_clause,[],[f158,f358]) ).
fof(f158,plain,
! [X0] :
( subclass(X0,cross_product(universal_class,universal_class))
| ~ function(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f356,plain,
spl10_19,
inference(avatar_split_clause,[],[f154,f354]) ).
fof(f154,plain,
! [X0] :
( member(sum_class(X0),universal_class)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0] :
( member(sum_class(X0),universal_class)
| ~ member(X0,universal_class) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0] :
( member(X0,universal_class)
=> member(sum_class(X0),universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_class) ).
fof(f352,plain,
spl10_18,
inference(avatar_split_clause,[],[f153,f350]) ).
fof(f153,plain,
! [X0] :
( member(power_class(X0),universal_class)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0] :
( member(power_class(X0),universal_class)
| ~ member(X0,universal_class) ),
inference(ennf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0] :
( member(X0,universal_class)
=> member(power_class(X0),universal_class) ),
inference(rectify,[],[f34]) ).
fof(f34,axiom,
! [X2] :
( member(X2,universal_class)
=> member(power_class(X2),universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_class) ).
fof(f348,plain,
spl10_17,
inference(avatar_split_clause,[],[f152,f346]) ).
fof(f152,plain,
! [X0] :
( disjoint(sK4(X0),X0)
| null_class = X0 ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0] :
( ( disjoint(sK4(X0),X0)
& member(sK4(X0),X0)
& member(sK4(X0),universal_class) )
| null_class = X0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f74,f89]) ).
fof(f89,plain,
! [X0] :
( ? [X1] :
( disjoint(X1,X0)
& member(X1,X0)
& member(X1,universal_class) )
=> ( disjoint(sK4(X0),X0)
& member(sK4(X0),X0)
& member(sK4(X0),universal_class) ) ),
introduced(choice_axiom,[]) ).
fof(f74,plain,
! [X0] :
( ? [X1] :
( disjoint(X1,X0)
& member(X1,X0)
& member(X1,universal_class) )
| null_class = X0 ),
inference(ennf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0] :
( null_class != X0
=> ? [X1] :
( disjoint(X1,X0)
& member(X1,X0)
& member(X1,universal_class) ) ),
inference(rectify,[],[f41]) ).
fof(f41,axiom,
! [X0] :
( null_class != X0
=> ? [X2] :
( disjoint(X2,X0)
& member(X2,X0)
& member(X2,universal_class) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity) ).
fof(f344,plain,
spl10_16,
inference(avatar_split_clause,[],[f151,f342]) ).
fof(f151,plain,
! [X0] :
( member(sK4(X0),X0)
| null_class = X0 ),
inference(cnf_transformation,[],[f90]) ).
fof(f340,plain,
spl10_15,
inference(avatar_split_clause,[],[f150,f338]) ).
fof(f150,plain,
! [X0] :
( member(sK4(X0),universal_class)
| null_class = X0 ),
inference(cnf_transformation,[],[f90]) ).
fof(f334,plain,
spl10_14,
inference(avatar_split_clause,[],[f226,f332]) ).
fof(f226,plain,
! [X1] :
( subclass(sK9,X1)
| ~ inductive(X1) ),
inference(cnf_transformation,[],[f136]) ).
fof(f136,plain,
( ! [X1] :
( subclass(sK9,X1)
| ~ inductive(X1) )
& inductive(sK9)
& member(sK9,universal_class) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f86,f135]) ).
fof(f135,plain,
( ? [X0] :
( ! [X1] :
( subclass(X0,X1)
| ~ inductive(X1) )
& inductive(X0)
& member(X0,universal_class) )
=> ( ! [X1] :
( subclass(sK9,X1)
| ~ inductive(X1) )
& inductive(sK9)
& member(sK9,universal_class) ) ),
introduced(choice_axiom,[]) ).
fof(f86,plain,
? [X0] :
( ! [X1] :
( subclass(X0,X1)
| ~ inductive(X1) )
& inductive(X0)
& member(X0,universal_class) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,axiom,
? [X0] :
( ! [X1] :
( inductive(X1)
=> subclass(X0,X1) )
& inductive(X0)
& member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infinity) ).
fof(f330,plain,
spl10_13,
inference(avatar_split_clause,[],[f164,f328]) ).
fof(f164,plain,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair) ).
fof(f326,plain,
spl10_12,
inference(avatar_split_clause,[],[f155,f324]) ).
fof(f155,plain,
! [X0] :
( member(null_class,X0)
| ~ inductive(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f322,plain,
spl10_11,
inference(avatar_split_clause,[],[f141,f319]) ).
fof(f141,plain,
subclass(successor_relation,cross_product(universal_class,universal_class)),
inference(cnf_transformation,[],[f24]) ).
fof(f24,axiom,
subclass(successor_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_relation_defn1) ).
fof(f317,plain,
spl10_10,
inference(avatar_split_clause,[],[f140,f314]) ).
fof(f140,plain,
subclass(element_relation,cross_product(universal_class,universal_class)),
inference(cnf_transformation,[],[f12]) ).
fof(f12,axiom,
subclass(element_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation) ).
fof(f312,plain,
spl10_9,
inference(avatar_split_clause,[],[f232,f309]) ).
fof(f232,plain,
unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK1,sK1))) = unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(sK3,sK3))),
inference(definition_unfolding,[],[f137,f230,f230]) ).
fof(f137,plain,
ordered_pair(sK0,sK1) = ordered_pair(sK2,sK3),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
( sK0 != sK2
& member(sK0,universal_class)
& ordered_pair(sK0,sK1) = ordered_pair(sK2,sK3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f73,f87]) ).
fof(f87,plain,
( ? [X0,X1,X2,X3] :
( X0 != X2
& member(X0,universal_class)
& ordered_pair(X0,X1) = ordered_pair(X2,X3) )
=> ( sK0 != sK2
& member(sK0,universal_class)
& ordered_pair(sK0,sK1) = ordered_pair(sK2,sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f73,plain,
? [X0,X1,X2,X3] :
( X0 != X2
& member(X0,universal_class)
& ordered_pair(X0,X1) = ordered_pair(X2,X3) ),
inference(flattening,[],[f72]) ).
fof(f72,plain,
? [X0,X1,X2,X3] :
( X0 != X2
& member(X0,universal_class)
& ordered_pair(X0,X1) = ordered_pair(X2,X3) ),
inference(ennf_transformation,[],[f46]) ).
fof(f46,plain,
~ ! [X0,X1,X2,X3] :
( ( member(X0,universal_class)
& ordered_pair(X0,X1) = ordered_pair(X2,X3) )
=> X0 = X2 ),
inference(rectify,[],[f45]) ).
fof(f45,negated_conjecture,
~ ! [X6,X0,X1,X4] :
( ( member(X6,universal_class)
& ordered_pair(X6,X0) = ordered_pair(X1,X4) )
=> X1 = X6 ),
inference(negated_conjecture,[],[f44]) ).
fof(f44,conjecture,
! [X6,X0,X1,X4] :
( ( member(X6,universal_class)
& ordered_pair(X6,X0) = ordered_pair(X1,X4) )
=> X1 = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair_determines_components1) ).
fof(f307,plain,
spl10_8,
inference(avatar_split_clause,[],[f266,f305]) ).
fof(f305,plain,
( spl10_8
<=> ! [X1] : subclass(X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_8])]) ).
fof(f266,plain,
! [X1] : subclass(X1,X1),
inference(equality_resolution,[],[f173]) ).
fof(f173,plain,
! [X0,X1] :
( subclass(X1,X0)
| X0 != X1 ),
inference(cnf_transformation,[],[f100]) ).
fof(f303,plain,
spl10_7,
inference(avatar_split_clause,[],[f224,f300]) ).
fof(f224,plain,
member(sK9,universal_class),
inference(cnf_transformation,[],[f136]) ).
fof(f298,plain,
spl10_6,
inference(avatar_split_clause,[],[f143,f296]) ).
fof(f143,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f294,plain,
spl10_5,
inference(avatar_split_clause,[],[f142,f292]) ).
fof(f142,plain,
! [X0] : ~ member(X0,null_class),
inference(cnf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0] : ~ member(X0,null_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_class_defn) ).
fof(f290,plain,
spl10_4,
inference(avatar_split_clause,[],[f225,f287]) ).
fof(f225,plain,
inductive(sK9),
inference(cnf_transformation,[],[f136]) ).
fof(f285,plain,
spl10_3,
inference(avatar_split_clause,[],[f222,f282]) ).
fof(f282,plain,
( spl10_3
<=> function(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_3])]) ).
fof(f222,plain,
function(sK8),
inference(cnf_transformation,[],[f134]) ).
fof(f280,plain,
~ spl10_2,
inference(avatar_split_clause,[],[f139,f277]) ).
fof(f139,plain,
sK0 != sK2,
inference(cnf_transformation,[],[f88]) ).
fof(f275,plain,
spl10_1,
inference(avatar_split_clause,[],[f138,f272]) ).
fof(f138,plain,
member(sK0,universal_class),
inference(cnf_transformation,[],[f88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET016+1 : TPTP v8.2.0. Bugfixed v5.4.0.
% 0.08/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.16/0.36 % Computer : n013.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Mon May 20 11:45:53 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.16/0.36 % (9959)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.38 % (9962)WARNING: value z3 for option sas not known
% 0.16/0.38 % (9960)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.38 % (9961)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.38 % (9963)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.38 % (9962)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.16/0.38 % (9964)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.16/0.38 % (9965)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.16/0.38 % (9967)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.23/0.41 TRYING [1]
% 0.23/0.41 TRYING [2]
% 0.23/0.41 TRYING [1]
% 0.23/0.42 TRYING [2]
% 0.23/0.45 TRYING [3]
% 0.23/0.45 TRYING [3]
% 1.19/0.53 TRYING [4]
% 1.35/0.57 TRYING [4]
% 2.01/0.68 TRYING [5]
% 3.22/0.84 TRYING [5]
% 6.19/1.26 TRYING [6]
% 7.77/1.49 TRYING [1]
% 7.77/1.49 TRYING [2]
% 7.77/1.49 TRYING [3]
% 7.77/1.51 TRYING [4]
% 8.34/1.56 TRYING [5]
% 9.36/1.70 TRYING [6]
% 9.36/1.71 TRYING [6]
% 10.60/1.91 % (9964)First to succeed.
% 10.60/1.94 % (9964)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-9959"
% 10.60/1.94 % (9964)Refutation found. Thanks to Tanya!
% 10.60/1.94 % SZS status Theorem for theBenchmark
% 10.60/1.94 % SZS output start Proof for theBenchmark
% See solution above
% 11.20/1.97 % (9964)------------------------------
% 11.20/1.97 % (9964)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 11.20/1.97 % (9964)Termination reason: Refutation
% 11.20/1.97
% 11.20/1.97 % (9964)Memory used [KB]: 17393
% 11.20/1.97 % (9964)Time elapsed: 1.555 s
% 11.20/1.97 % (9964)Instructions burned: 4304 (million)
% 11.20/1.97 % (9959)Success in time 1.594 s
%------------------------------------------------------------------------------