TSTP Solution File: SEU132+1 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU132+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 15:22:29 EDT 2024
% Result : Theorem 0.21s 0.51s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 277
% Syntax : Number of formulae : 983 ( 42 unt; 0 def)
% Number of atoms : 3521 ( 51 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 4292 (1754 ~;2221 |; 42 &)
% ( 265 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 264 ( 262 usr; 259 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-3 aty)
% Number of variables : 1771 (1754 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6208,plain,
$false,
inference(avatar_sat_refutation,[],[f70,f75,f80,f85,f90,f94,f98,f102,f106,f110,f116,f120,f125,f133,f139,f143,f151,f155,f161,f166,f170,f176,f181,f185,f201,f211,f215,f227,f231,f235,f243,f247,f251,f267,f271,f276,f298,f311,f315,f337,f341,f349,f353,f365,f369,f383,f391,f395,f427,f431,f443,f447,f451,f472,f480,f484,f488,f492,f500,f509,f513,f517,f521,f549,f553,f587,f591,f595,f599,f603,f607,f702,f706,f724,f749,f764,f768,f772,f776,f886,f922,f975,f1002,f1006,f1034,f1038,f1042,f1046,f1071,f1075,f1099,f1103,f1107,f1111,f1115,f1119,f1123,f1171,f1195,f1199,f1215,f1222,f1226,f1230,f1234,f1238,f1242,f1497,f1511,f1515,f1519,f1528,f1538,f1542,f1546,f1551,f1560,f1565,f1573,f1579,f1600,f1611,f1619,f1623,f1627,f1631,f1635,f1639,f1754,f1758,f1762,f1766,f1770,f1886,f1890,f1894,f1898,f1906,f1912,f1936,f1942,f2062,f2066,f2070,f2074,f2078,f2082,f2086,f2090,f2094,f2115,f2363,f2367,f2438,f2539,f2543,f2547,f2551,f2555,f2566,f2783,f2787,f2791,f2795,f2799,f2907,f2931,f2935,f3028,f3032,f3036,f3040,f3044,f3048,f3052,f3056,f3060,f3064,f3975,f3979,f3983,f4138,f4164,f4168,f4325,f4376,f4430,f4554,f4600,f4605,f4610,f4615,f4619,f4624,f4628,f4632,f4636,f4640,f4694,f4706,f4710,f4714,f4737,f4742,f4746,f4751,f4755,f4759,f4763,f4769,f4773,f4779,f4783,f4789,f4793,f4799,f4804,f4808,f4812,f4816,f4820,f4958,f5127,f5131,f5135,f5202,f5206,f5210,f5214,f5218,f5222,f5226,f5230,f5234,f5238,f5242,f5446,f5513,f5521,f5525,f5529,f5601,f5656,f5660,f5664,f5668,f5925,f5929,f6163,f6167,f6171,f6175,f6179,f6183,f6187,f6191,f6195,f6205]) ).
fof(f6205,plain,
( spl8_2
| ~ spl8_238 ),
inference(avatar_contradiction_clause,[],[f6196]) ).
fof(f6196,plain,
( $false
| spl8_2
| ~ spl8_238 ),
inference(resolution,[],[f5445,f74]) ).
fof(f74,plain,
( ~ subset(set_difference(sK1,sK3),set_difference(sK2,sK3))
| spl8_2 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f72,plain,
( spl8_2
<=> subset(set_difference(sK1,sK3),set_difference(sK2,sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_2])]) ).
fof(f5445,plain,
( ! [X0] : subset(set_difference(sK1,X0),set_difference(sK2,X0))
| ~ spl8_238 ),
inference(avatar_component_clause,[],[f5444]) ).
fof(f5444,plain,
( spl8_238
<=> ! [X0] : subset(set_difference(sK1,X0),set_difference(sK2,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_238])]) ).
fof(f6195,plain,
( spl8_258
| ~ spl8_11
| ~ spl8_108 ),
inference(avatar_split_clause,[],[f1464,f1240,f114,f6193]) ).
fof(f6193,plain,
( spl8_258
<=> ! [X0,X1] :
( in(sK5(set_difference(sK2,X0),sK1,X1),X0)
| sP0(set_difference(sK2,X0),sK1,X1)
| ~ in(X1,sK5(set_difference(sK2,X0),sK1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_258])]) ).
fof(f114,plain,
( spl8_11
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_11])]) ).
fof(f1240,plain,
( spl8_108
<=> ! [X0,X1] :
( in(sK5(set_difference(sK2,X0),sK1,X1),X0)
| sP0(set_difference(sK2,X0),sK1,X1)
| in(sK5(set_difference(sK2,X0),sK1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_108])]) ).
fof(f1464,plain,
( ! [X0,X1] :
( in(sK5(set_difference(sK2,X0),sK1,X1),X0)
| sP0(set_difference(sK2,X0),sK1,X1)
| ~ in(X1,sK5(set_difference(sK2,X0),sK1,X1)) )
| ~ spl8_11
| ~ spl8_108 ),
inference(resolution,[],[f1241,f115]) ).
fof(f115,plain,
( ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) )
| ~ spl8_11 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f1241,plain,
( ! [X0,X1] :
( in(sK5(set_difference(sK2,X0),sK1,X1),X1)
| in(sK5(set_difference(sK2,X0),sK1,X1),X0)
| sP0(set_difference(sK2,X0),sK1,X1) )
| ~ spl8_108 ),
inference(avatar_component_clause,[],[f1240]) ).
fof(f6191,plain,
( spl8_257
| ~ spl8_11
| ~ spl8_107 ),
inference(avatar_split_clause,[],[f1437,f1236,f114,f6189]) ).
fof(f6189,plain,
( spl8_257
<=> ! [X2,X0,X1] :
( in(sK5(X0,set_difference(sK1,X1),X2),sK2)
| sP0(X0,set_difference(sK1,X1),X2)
| ~ in(X2,sK5(X0,set_difference(sK1,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_257])]) ).
fof(f1236,plain,
( spl8_107
<=> ! [X2,X0,X1] :
( in(sK5(X0,set_difference(sK1,X1),X2),X2)
| sP0(X0,set_difference(sK1,X1),X2)
| in(sK5(X0,set_difference(sK1,X1),X2),sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_107])]) ).
fof(f1437,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,set_difference(sK1,X1),X2),sK2)
| sP0(X0,set_difference(sK1,X1),X2)
| ~ in(X2,sK5(X0,set_difference(sK1,X1),X2)) )
| ~ spl8_11
| ~ spl8_107 ),
inference(resolution,[],[f1237,f115]) ).
fof(f1237,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,set_difference(sK1,X1),X2),sK2)
| in(sK5(X0,set_difference(sK1,X1),X2),X2)
| sP0(X0,set_difference(sK1,X1),X2) )
| ~ spl8_107 ),
inference(avatar_component_clause,[],[f1236]) ).
fof(f6187,plain,
( spl8_256
| ~ spl8_11
| ~ spl8_107 ),
inference(avatar_split_clause,[],[f1424,f1236,f114,f6185]) ).
fof(f6185,plain,
( spl8_256
<=> ! [X2,X0,X1] :
( in(sK5(X0,set_difference(sK1,X1),X2),X2)
| sP0(X0,set_difference(sK1,X1),X2)
| ~ in(sK2,sK5(X0,set_difference(sK1,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_256])]) ).
fof(f1424,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,set_difference(sK1,X1),X2),X2)
| sP0(X0,set_difference(sK1,X1),X2)
| ~ in(sK2,sK5(X0,set_difference(sK1,X1),X2)) )
| ~ spl8_11
| ~ spl8_107 ),
inference(resolution,[],[f1237,f115]) ).
fof(f6183,plain,
( spl8_255
| ~ spl8_11
| ~ spl8_106 ),
inference(avatar_split_clause,[],[f1393,f1232,f114,f6181]) ).
fof(f6181,plain,
( spl8_255
<=> ! [X2,X0,X1] :
( in(sK5(X0,X1,set_difference(sK1,X2)),sK2)
| sP0(X0,X1,set_difference(sK1,X2))
| ~ in(X1,sK5(X0,X1,set_difference(sK1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_255])]) ).
fof(f1232,plain,
( spl8_106
<=> ! [X2,X0,X1] :
( in(sK5(X0,X1,set_difference(sK1,X2)),X1)
| sP0(X0,X1,set_difference(sK1,X2))
| in(sK5(X0,X1,set_difference(sK1,X2)),sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_106])]) ).
fof(f1393,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,X1,set_difference(sK1,X2)),sK2)
| sP0(X0,X1,set_difference(sK1,X2))
| ~ in(X1,sK5(X0,X1,set_difference(sK1,X2))) )
| ~ spl8_11
| ~ spl8_106 ),
inference(resolution,[],[f1233,f115]) ).
fof(f1233,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,X1,set_difference(sK1,X2)),sK2)
| in(sK5(X0,X1,set_difference(sK1,X2)),X1)
| sP0(X0,X1,set_difference(sK1,X2)) )
| ~ spl8_106 ),
inference(avatar_component_clause,[],[f1232]) ).
fof(f6179,plain,
( spl8_254
| ~ spl8_11
| ~ spl8_106 ),
inference(avatar_split_clause,[],[f1382,f1232,f114,f6177]) ).
fof(f6177,plain,
( spl8_254
<=> ! [X2,X0,X1] :
( in(sK5(X0,X1,set_difference(sK1,X2)),X1)
| sP0(X0,X1,set_difference(sK1,X2))
| ~ in(sK2,sK5(X0,X1,set_difference(sK1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_254])]) ).
fof(f1382,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,X1,set_difference(sK1,X2)),X1)
| sP0(X0,X1,set_difference(sK1,X2))
| ~ in(sK2,sK5(X0,X1,set_difference(sK1,X2))) )
| ~ spl8_11
| ~ spl8_106 ),
inference(resolution,[],[f1233,f115]) ).
fof(f6175,plain,
( spl8_253
| ~ spl8_11
| ~ spl8_105 ),
inference(avatar_split_clause,[],[f1346,f1228,f114,f6173]) ).
fof(f6173,plain,
( spl8_253
<=> ! [X2,X0,X1] :
( in(sK5(X0,sK1,set_difference(X1,X2)),sK2)
| sP0(X0,sK1,set_difference(X1,X2))
| ~ in(X1,sK5(X0,sK1,set_difference(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_253])]) ).
fof(f1228,plain,
( spl8_105
<=> ! [X2,X0,X1] :
( in(sK5(X0,sK1,set_difference(X1,X2)),sK2)
| sP0(X0,sK1,set_difference(X1,X2))
| in(sK5(X0,sK1,set_difference(X1,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_105])]) ).
fof(f1346,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,sK1,set_difference(X1,X2)),sK2)
| sP0(X0,sK1,set_difference(X1,X2))
| ~ in(X1,sK5(X0,sK1,set_difference(X1,X2))) )
| ~ spl8_11
| ~ spl8_105 ),
inference(resolution,[],[f1229,f115]) ).
fof(f1229,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,sK1,set_difference(X1,X2)),sK2)
| in(sK5(X0,sK1,set_difference(X1,X2)),X1)
| sP0(X0,sK1,set_difference(X1,X2)) )
| ~ spl8_105 ),
inference(avatar_component_clause,[],[f1228]) ).
fof(f6171,plain,
( spl8_252
| ~ spl8_11
| ~ spl8_105 ),
inference(avatar_split_clause,[],[f1337,f1228,f114,f6169]) ).
fof(f6169,plain,
( spl8_252
<=> ! [X2,X0,X1] :
( in(sK5(X0,sK1,set_difference(X1,X2)),X1)
| sP0(X0,sK1,set_difference(X1,X2))
| ~ in(sK2,sK5(X0,sK1,set_difference(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_252])]) ).
fof(f1337,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,sK1,set_difference(X1,X2)),X1)
| sP0(X0,sK1,set_difference(X1,X2))
| ~ in(sK2,sK5(X0,sK1,set_difference(X1,X2))) )
| ~ spl8_11
| ~ spl8_105 ),
inference(resolution,[],[f1229,f115]) ).
fof(f6167,plain,
( spl8_251
| ~ spl8_11
| ~ spl8_103 ),
inference(avatar_split_clause,[],[f1279,f1220,f114,f6165]) ).
fof(f6165,plain,
( spl8_251
<=> ! [X2,X0,X1] :
( in(sK5(X0,set_difference(X1,X2),sK1),sK2)
| sP0(X0,set_difference(X1,X2),sK1)
| ~ in(X1,sK5(X0,set_difference(X1,X2),sK1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_251])]) ).
fof(f1220,plain,
( spl8_103
<=> ! [X2,X0,X1] :
( in(sK5(X0,set_difference(X1,X2),sK1),sK2)
| sP0(X0,set_difference(X1,X2),sK1)
| in(sK5(X0,set_difference(X1,X2),sK1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_103])]) ).
fof(f1279,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,set_difference(X1,X2),sK1),sK2)
| sP0(X0,set_difference(X1,X2),sK1)
| ~ in(X1,sK5(X0,set_difference(X1,X2),sK1)) )
| ~ spl8_11
| ~ spl8_103 ),
inference(resolution,[],[f1221,f115]) ).
fof(f1221,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,set_difference(X1,X2),sK1),sK2)
| in(sK5(X0,set_difference(X1,X2),sK1),X1)
| sP0(X0,set_difference(X1,X2),sK1) )
| ~ spl8_103 ),
inference(avatar_component_clause,[],[f1220]) ).
fof(f6163,plain,
( spl8_250
| ~ spl8_11
| ~ spl8_103 ),
inference(avatar_split_clause,[],[f1272,f1220,f114,f6161]) ).
fof(f6161,plain,
( spl8_250
<=> ! [X2,X0,X1] :
( in(sK5(X0,set_difference(X1,X2),sK1),X1)
| sP0(X0,set_difference(X1,X2),sK1)
| ~ in(sK2,sK5(X0,set_difference(X1,X2),sK1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_250])]) ).
fof(f1272,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,set_difference(X1,X2),sK1),X1)
| sP0(X0,set_difference(X1,X2),sK1)
| ~ in(sK2,sK5(X0,set_difference(X1,X2),sK1)) )
| ~ spl8_11
| ~ spl8_103 ),
inference(resolution,[],[f1221,f115]) ).
fof(f5929,plain,
( spl8_249
| ~ spl8_15
| ~ spl8_226 ),
inference(avatar_split_clause,[],[f5279,f5133,f137,f5927]) ).
fof(f5927,plain,
( spl8_249
<=> ! [X0] : subset(sK1,set_difference(sK2,set_difference(X0,sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_249])]) ).
fof(f137,plain,
( spl8_15
<=> ! [X0,X1] :
( subset(X0,X1)
| in(sK4(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_15])]) ).
fof(f5133,plain,
( spl8_226
<=> ! [X0,X1] :
( subset(sK1,set_difference(sK2,set_difference(X0,X1)))
| ~ in(sK4(sK1,set_difference(sK2,set_difference(X0,X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_226])]) ).
fof(f5279,plain,
( ! [X0] : subset(sK1,set_difference(sK2,set_difference(X0,sK1)))
| ~ spl8_15
| ~ spl8_226 ),
inference(duplicate_literal_removal,[],[f5270]) ).
fof(f5270,plain,
( ! [X0] :
( subset(sK1,set_difference(sK2,set_difference(X0,sK1)))
| subset(sK1,set_difference(sK2,set_difference(X0,sK1))) )
| ~ spl8_15
| ~ spl8_226 ),
inference(resolution,[],[f5134,f138]) ).
fof(f138,plain,
( ! [X0,X1] :
( in(sK4(X0,X1),X0)
| subset(X0,X1) )
| ~ spl8_15 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f5134,plain,
( ! [X0,X1] :
( ~ in(sK4(sK1,set_difference(sK2,set_difference(X0,X1))),X1)
| subset(sK1,set_difference(sK2,set_difference(X0,X1))) )
| ~ spl8_226 ),
inference(avatar_component_clause,[],[f5133]) ).
fof(f5925,plain,
( spl8_248
| ~ spl8_3
| ~ spl8_13
| ~ spl8_111 ),
inference(avatar_split_clause,[],[f1524,f1513,f122,f77,f5923]) ).
fof(f5923,plain,
( spl8_248
<=> ! [X0] : sK7 = set_difference(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_248])]) ).
fof(f77,plain,
( spl8_3
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_3])]) ).
fof(f122,plain,
( spl8_13
<=> empty_set = sK7 ),
introduced(avatar_definition,[new_symbols(naming,[spl8_13])]) ).
fof(f1513,plain,
( spl8_111
<=> ! [X0,X1] :
( ~ empty(X0)
| set_difference(X1,X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_111])]) ).
fof(f1524,plain,
( ! [X0] : sK7 = set_difference(X0,X0)
| ~ spl8_3
| ~ spl8_13
| ~ spl8_111 ),
inference(forward_demodulation,[],[f1522,f124]) ).
fof(f124,plain,
( empty_set = sK7
| ~ spl8_13 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f1522,plain,
( ! [X0] : empty_set = set_difference(X0,X0)
| ~ spl8_3
| ~ spl8_111 ),
inference(resolution,[],[f1514,f79]) ).
fof(f79,plain,
( empty(empty_set)
| ~ spl8_3 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f1514,plain,
( ! [X0,X1] :
( ~ empty(X0)
| set_difference(X1,X1) = X0 )
| ~ spl8_111 ),
inference(avatar_component_clause,[],[f1513]) ).
fof(f5668,plain,
( spl8_247
| ~ spl8_97
| ~ spl8_181 ),
inference(avatar_split_clause,[],[f4120,f3977,f1117,f5666]) ).
fof(f5666,plain,
( spl8_247
<=> ! [X2,X0,X1] :
( sP0(X0,X1,set_difference(sK1,set_difference(sK2,X2)))
| ~ empty(X1)
| in(sK5(X0,X1,set_difference(sK1,set_difference(sK2,X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_247])]) ).
fof(f1117,plain,
( spl8_97
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,X0,set_difference(sK1,X2))
| in(sK5(X1,X0,set_difference(sK1,X2)),sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_97])]) ).
fof(f3977,plain,
( spl8_181
<=> ! [X4,X0,X3,X2,X1] :
( ~ empty(X0)
| sP0(X1,X0,set_difference(X2,set_difference(X3,X4)))
| ~ in(sK5(X1,X0,set_difference(X2,set_difference(X3,X4))),X3)
| in(sK5(X1,X0,set_difference(X2,set_difference(X3,X4))),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_181])]) ).
fof(f4120,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,set_difference(sK1,set_difference(sK2,X2)))
| ~ empty(X1)
| in(sK5(X0,X1,set_difference(sK1,set_difference(sK2,X2))),X2) )
| ~ spl8_97
| ~ spl8_181 ),
inference(duplicate_literal_removal,[],[f4077]) ).
fof(f4077,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,set_difference(sK1,set_difference(sK2,X2)))
| ~ empty(X1)
| in(sK5(X0,X1,set_difference(sK1,set_difference(sK2,X2))),X2)
| sP0(X0,X1,set_difference(sK1,set_difference(sK2,X2)))
| ~ empty(X1) )
| ~ spl8_97
| ~ spl8_181 ),
inference(resolution,[],[f3978,f1118]) ).
fof(f1118,plain,
( ! [X2,X0,X1] :
( in(sK5(X1,X0,set_difference(sK1,X2)),sK2)
| sP0(X1,X0,set_difference(sK1,X2))
| ~ empty(X0) )
| ~ spl8_97 ),
inference(avatar_component_clause,[],[f1117]) ).
fof(f3978,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(sK5(X1,X0,set_difference(X2,set_difference(X3,X4))),X3)
| sP0(X1,X0,set_difference(X2,set_difference(X3,X4)))
| ~ empty(X0)
| in(sK5(X1,X0,set_difference(X2,set_difference(X3,X4))),X4) )
| ~ spl8_181 ),
inference(avatar_component_clause,[],[f3977]) ).
fof(f5664,plain,
( spl8_246
| ~ spl8_96
| ~ spl8_180 ),
inference(avatar_split_clause,[],[f4047,f3973,f1113,f5662]) ).
fof(f5662,plain,
( spl8_246
<=> ! [X2,X0,X1] :
( sP0(X0,set_difference(sK1,set_difference(sK2,X1)),X2)
| ~ empty(X2)
| in(sK5(X0,set_difference(sK1,set_difference(sK2,X1)),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_246])]) ).
fof(f1113,plain,
( spl8_96
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,set_difference(sK1,X2),X0)
| in(sK5(X1,set_difference(sK1,X2),X0),sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_96])]) ).
fof(f3973,plain,
( spl8_180
<=> ! [X4,X0,X3,X2,X1] :
( ~ empty(X0)
| sP0(X1,set_difference(X2,set_difference(X3,X4)),X0)
| ~ in(sK5(X1,set_difference(X2,set_difference(X3,X4)),X0),X3)
| in(sK5(X1,set_difference(X2,set_difference(X3,X4)),X0),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_180])]) ).
fof(f4047,plain,
( ! [X2,X0,X1] :
( sP0(X0,set_difference(sK1,set_difference(sK2,X1)),X2)
| ~ empty(X2)
| in(sK5(X0,set_difference(sK1,set_difference(sK2,X1)),X2),X1) )
| ~ spl8_96
| ~ spl8_180 ),
inference(duplicate_literal_removal,[],[f3999]) ).
fof(f3999,plain,
( ! [X2,X0,X1] :
( sP0(X0,set_difference(sK1,set_difference(sK2,X1)),X2)
| ~ empty(X2)
| in(sK5(X0,set_difference(sK1,set_difference(sK2,X1)),X2),X1)
| sP0(X0,set_difference(sK1,set_difference(sK2,X1)),X2)
| ~ empty(X2) )
| ~ spl8_96
| ~ spl8_180 ),
inference(resolution,[],[f3974,f1114]) ).
fof(f1114,plain,
( ! [X2,X0,X1] :
( in(sK5(X1,set_difference(sK1,X2),X0),sK2)
| sP0(X1,set_difference(sK1,X2),X0)
| ~ empty(X0) )
| ~ spl8_96 ),
inference(avatar_component_clause,[],[f1113]) ).
fof(f3974,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(sK5(X1,set_difference(X2,set_difference(X3,X4)),X0),X3)
| sP0(X1,set_difference(X2,set_difference(X3,X4)),X0)
| ~ empty(X0)
| in(sK5(X1,set_difference(X2,set_difference(X3,X4)),X0),X4) )
| ~ spl8_180 ),
inference(avatar_component_clause,[],[f3973]) ).
fof(f5660,plain,
( spl8_245
| ~ spl8_19
| ~ spl8_160 ),
inference(avatar_split_clause,[],[f2733,f2553,f159,f5658]) ).
fof(f5658,plain,
( spl8_245
<=> ! [X0,X3,X2,X1] :
( sP0(X0,X1,set_difference(set_difference(sK1,X2),X3))
| ~ empty(X1)
| in(sK5(X0,X1,set_difference(set_difference(sK1,X2),X3)),sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_245])]) ).
fof(f159,plain,
( spl8_19
<=> ! [X0] :
( ~ in(X0,sK1)
| in(X0,sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_19])]) ).
fof(f2553,plain,
( spl8_160
<=> ! [X4,X0,X3,X2,X1] :
( ~ empty(X0)
| sP0(X1,X0,set_difference(set_difference(X2,X3),X4))
| in(sK5(X1,X0,set_difference(set_difference(X2,X3),X4)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_160])]) ).
fof(f2733,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,X1,set_difference(set_difference(sK1,X2),X3))
| ~ empty(X1)
| in(sK5(X0,X1,set_difference(set_difference(sK1,X2),X3)),sK2) )
| ~ spl8_19
| ~ spl8_160 ),
inference(resolution,[],[f2554,f160]) ).
fof(f160,plain,
( ! [X0] :
( ~ in(X0,sK1)
| in(X0,sK2) )
| ~ spl8_19 ),
inference(avatar_component_clause,[],[f159]) ).
fof(f2554,plain,
( ! [X2,X3,X0,X1,X4] :
( in(sK5(X1,X0,set_difference(set_difference(X2,X3),X4)),X2)
| sP0(X1,X0,set_difference(set_difference(X2,X3),X4))
| ~ empty(X0) )
| ~ spl8_160 ),
inference(avatar_component_clause,[],[f2553]) ).
fof(f5656,plain,
( spl8_244
| ~ spl8_19
| ~ spl8_158 ),
inference(avatar_split_clause,[],[f2631,f2545,f159,f5654]) ).
fof(f5654,plain,
( spl8_244
<=> ! [X0,X3,X2,X1] :
( sP0(X0,set_difference(set_difference(sK1,X1),X2),X3)
| ~ empty(X3)
| in(sK5(X0,set_difference(set_difference(sK1,X1),X2),X3),sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_244])]) ).
fof(f2545,plain,
( spl8_158
<=> ! [X4,X0,X3,X2,X1] :
( ~ empty(X0)
| sP0(X1,set_difference(set_difference(X2,X3),X4),X0)
| in(sK5(X1,set_difference(set_difference(X2,X3),X4),X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_158])]) ).
fof(f2631,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,set_difference(set_difference(sK1,X1),X2),X3)
| ~ empty(X3)
| in(sK5(X0,set_difference(set_difference(sK1,X1),X2),X3),sK2) )
| ~ spl8_19
| ~ spl8_158 ),
inference(resolution,[],[f2546,f160]) ).
fof(f2546,plain,
( ! [X2,X3,X0,X1,X4] :
( in(sK5(X1,set_difference(set_difference(X2,X3),X4),X0),X2)
| sP0(X1,set_difference(set_difference(X2,X3),X4),X0)
| ~ empty(X0) )
| ~ spl8_158 ),
inference(avatar_component_clause,[],[f2545]) ).
fof(f5601,plain,
( spl8_243
| ~ spl8_30
| ~ spl8_226 ),
inference(avatar_split_clause,[],[f5278,f5133,f233,f5599]) ).
fof(f5599,plain,
( spl8_243
<=> ! [X0] : subset(sK1,set_difference(sK2,set_difference(X0,sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_243])]) ).
fof(f233,plain,
( spl8_30
<=> ! [X0] :
( in(sK4(sK1,X0),sK2)
| subset(sK1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_30])]) ).
fof(f5278,plain,
( ! [X0] : subset(sK1,set_difference(sK2,set_difference(X0,sK2)))
| ~ spl8_30
| ~ spl8_226 ),
inference(duplicate_literal_removal,[],[f5271]) ).
fof(f5271,plain,
( ! [X0] :
( subset(sK1,set_difference(sK2,set_difference(X0,sK2)))
| subset(sK1,set_difference(sK2,set_difference(X0,sK2))) )
| ~ spl8_30
| ~ spl8_226 ),
inference(resolution,[],[f5134,f234]) ).
fof(f234,plain,
( ! [X0] :
( in(sK4(sK1,X0),sK2)
| subset(sK1,X0) )
| ~ spl8_30 ),
inference(avatar_component_clause,[],[f233]) ).
fof(f5529,plain,
( spl8_242
| ~ spl8_90
| ~ spl8_171 ),
inference(avatar_split_clause,[],[f3118,f3030,f1069,f5527]) ).
fof(f5527,plain,
( spl8_242
<=> ! [X0,X1] :
( sP0(X0,X0,set_difference(sK1,set_difference(sK2,X1)))
| in(sK5(X0,X0,set_difference(sK1,set_difference(sK2,X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_242])]) ).
fof(f1069,plain,
( spl8_90
<=> ! [X0,X1] :
( sP0(X0,X0,set_difference(sK1,X1))
| in(sK5(X0,X0,set_difference(sK1,X1)),sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_90])]) ).
fof(f3030,plain,
( spl8_171
<=> ! [X0,X3,X2,X1] :
( sP0(X0,X0,set_difference(X1,set_difference(X2,X3)))
| ~ in(sK5(X0,X0,set_difference(X1,set_difference(X2,X3))),X2)
| in(sK5(X0,X0,set_difference(X1,set_difference(X2,X3))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_171])]) ).
fof(f3118,plain,
( ! [X0,X1] :
( sP0(X0,X0,set_difference(sK1,set_difference(sK2,X1)))
| in(sK5(X0,X0,set_difference(sK1,set_difference(sK2,X1))),X1) )
| ~ spl8_90
| ~ spl8_171 ),
inference(duplicate_literal_removal,[],[f3067]) ).
fof(f3067,plain,
( ! [X0,X1] :
( sP0(X0,X0,set_difference(sK1,set_difference(sK2,X1)))
| in(sK5(X0,X0,set_difference(sK1,set_difference(sK2,X1))),X1)
| sP0(X0,X0,set_difference(sK1,set_difference(sK2,X1))) )
| ~ spl8_90
| ~ spl8_171 ),
inference(resolution,[],[f3031,f1070]) ).
fof(f1070,plain,
( ! [X0,X1] :
( in(sK5(X0,X0,set_difference(sK1,X1)),sK2)
| sP0(X0,X0,set_difference(sK1,X1)) )
| ~ spl8_90 ),
inference(avatar_component_clause,[],[f1069]) ).
fof(f3031,plain,
( ! [X2,X3,X0,X1] :
( ~ in(sK5(X0,X0,set_difference(X1,set_difference(X2,X3))),X2)
| sP0(X0,X0,set_difference(X1,set_difference(X2,X3)))
| in(sK5(X0,X0,set_difference(X1,set_difference(X2,X3))),X3) )
| ~ spl8_171 ),
inference(avatar_component_clause,[],[f3030]) ).
fof(f5525,plain,
( spl8_241
| ~ spl8_19
| ~ spl8_154 ),
inference(avatar_split_clause,[],[f2486,f2365,f159,f5523]) ).
fof(f5523,plain,
( spl8_241
<=> ! [X2,X0,X1] :
( sP0(X0,X0,set_difference(set_difference(sK1,X1),X2))
| in(sK5(X0,X0,set_difference(set_difference(sK1,X1),X2)),sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_241])]) ).
fof(f2365,plain,
( spl8_154
<=> ! [X0,X3,X2,X1] :
( sP0(X0,X0,set_difference(set_difference(X1,X2),X3))
| in(sK5(X0,X0,set_difference(set_difference(X1,X2),X3)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_154])]) ).
fof(f2486,plain,
( ! [X2,X0,X1] :
( sP0(X0,X0,set_difference(set_difference(sK1,X1),X2))
| in(sK5(X0,X0,set_difference(set_difference(sK1,X1),X2)),sK2) )
| ~ spl8_19
| ~ spl8_154 ),
inference(resolution,[],[f2366,f160]) ).
fof(f2366,plain,
( ! [X2,X3,X0,X1] :
( in(sK5(X0,X0,set_difference(set_difference(X1,X2),X3)),X1)
| sP0(X0,X0,set_difference(set_difference(X1,X2),X3)) )
| ~ spl8_154 ),
inference(avatar_component_clause,[],[f2365]) ).
fof(f5521,plain,
( spl8_240
| ~ spl8_11
| ~ spl8_99 ),
inference(avatar_split_clause,[],[f1174,f1169,f114,f5519]) ).
fof(f5519,plain,
( spl8_240
<=> ! [X0,X1] :
( sP0(X0,set_difference(sK1,X1),set_difference(sK1,X1))
| ~ in(sK2,sK5(X0,set_difference(sK1,X1),set_difference(sK1,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_240])]) ).
fof(f1169,plain,
( spl8_99
<=> ! [X0,X1] :
( sP0(X0,set_difference(sK1,X1),set_difference(sK1,X1))
| in(sK5(X0,set_difference(sK1,X1),set_difference(sK1,X1)),sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_99])]) ).
fof(f1174,plain,
( ! [X0,X1] :
( sP0(X0,set_difference(sK1,X1),set_difference(sK1,X1))
| ~ in(sK2,sK5(X0,set_difference(sK1,X1),set_difference(sK1,X1))) )
| ~ spl8_11
| ~ spl8_99 ),
inference(resolution,[],[f1170,f115]) ).
fof(f1170,plain,
( ! [X0,X1] :
( in(sK5(X0,set_difference(sK1,X1),set_difference(sK1,X1)),sK2)
| sP0(X0,set_difference(sK1,X1),set_difference(sK1,X1)) )
| ~ spl8_99 ),
inference(avatar_component_clause,[],[f1169]) ).
fof(f5513,plain,
( spl8_239
| ~ spl8_7
| ~ spl8_13
| ~ spl8_109 ),
inference(avatar_split_clause,[],[f1506,f1495,f122,f96,f5511]) ).
fof(f5511,plain,
( spl8_239
<=> ! [X0] : sP0(X0,X0,sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_239])]) ).
fof(f96,plain,
( spl8_7
<=> ! [X0] : empty_set = set_difference(empty_set,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_7])]) ).
fof(f1495,plain,
( spl8_109
<=> ! [X0,X1] : sP0(X0,X0,set_difference(X1,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_109])]) ).
fof(f1506,plain,
( ! [X0] : sP0(X0,X0,sK7)
| ~ spl8_7
| ~ spl8_13
| ~ spl8_109 ),
inference(forward_demodulation,[],[f1502,f124]) ).
fof(f1502,plain,
( ! [X0] : sP0(X0,X0,empty_set)
| ~ spl8_7
| ~ spl8_109 ),
inference(superposition,[],[f1496,f97]) ).
fof(f97,plain,
( ! [X0] : empty_set = set_difference(empty_set,X0)
| ~ spl8_7 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f1496,plain,
( ! [X0,X1] : sP0(X0,X0,set_difference(X1,X1))
| ~ spl8_109 ),
inference(avatar_component_clause,[],[f1495]) ).
fof(f5446,plain,
( spl8_238
| ~ spl8_62
| ~ spl8_225 ),
inference(avatar_split_clause,[],[f5267,f5129,f511,f5444]) ).
fof(f511,plain,
( spl8_62
<=> ! [X2,X0,X1] :
( ~ in(sK4(set_difference(X0,X1),X2),X1)
| subset(set_difference(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_62])]) ).
fof(f5129,plain,
( spl8_225
<=> ! [X0,X1] :
( subset(set_difference(sK1,X0),set_difference(sK2,X1))
| in(sK4(set_difference(sK1,X0),set_difference(sK2,X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_225])]) ).
fof(f5267,plain,
( ! [X0] : subset(set_difference(sK1,X0),set_difference(sK2,X0))
| ~ spl8_62
| ~ spl8_225 ),
inference(duplicate_literal_removal,[],[f5248]) ).
fof(f5248,plain,
( ! [X0] :
( subset(set_difference(sK1,X0),set_difference(sK2,X0))
| subset(set_difference(sK1,X0),set_difference(sK2,X0)) )
| ~ spl8_62
| ~ spl8_225 ),
inference(resolution,[],[f5130,f512]) ).
fof(f512,plain,
( ! [X2,X0,X1] :
( ~ in(sK4(set_difference(X0,X1),X2),X1)
| subset(set_difference(X0,X1),X2) )
| ~ spl8_62 ),
inference(avatar_component_clause,[],[f511]) ).
fof(f5130,plain,
( ! [X0,X1] :
( in(sK4(set_difference(sK1,X0),set_difference(sK2,X1)),X1)
| subset(set_difference(sK1,X0),set_difference(sK2,X1)) )
| ~ spl8_225 ),
inference(avatar_component_clause,[],[f5129]) ).
fof(f5242,plain,
( spl8_237
| ~ spl8_10
| ~ spl8_207 ),
inference(avatar_split_clause,[],[f4867,f4749,f108,f5240]) ).
fof(f5240,plain,
( spl8_237
<=> ! [X0,X1] :
( sP0(sK2,sK1,set_difference(X0,X1))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_237])]) ).
fof(f108,plain,
( spl8_10
<=> ! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_10])]) ).
fof(f4749,plain,
( spl8_207
<=> ! [X0,X1] :
( sP0(sK2,sK1,set_difference(X0,X1))
| in(sK5(sK2,sK1,set_difference(X0,X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_207])]) ).
fof(f4867,plain,
( ! [X0,X1] :
( sP0(sK2,sK1,set_difference(X0,X1))
| ~ empty(X0) )
| ~ spl8_10
| ~ spl8_207 ),
inference(resolution,[],[f4750,f109]) ).
fof(f109,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) )
| ~ spl8_10 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f4750,plain,
( ! [X0,X1] :
( in(sK5(sK2,sK1,set_difference(X0,X1)),X0)
| sP0(sK2,sK1,set_difference(X0,X1)) )
| ~ spl8_207 ),
inference(avatar_component_clause,[],[f4749]) ).
fof(f5238,plain,
( spl8_236
| ~ spl8_88
| ~ spl8_167 ),
inference(avatar_split_clause,[],[f2921,f2905,f1040,f5236]) ).
fof(f5236,plain,
( spl8_236
<=> ! [X0,X1] :
( subset(set_difference(sK1,set_difference(sK2,X0)),X1)
| in(sK4(set_difference(sK1,set_difference(sK2,X0)),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_236])]) ).
fof(f1040,plain,
( spl8_88
<=> ! [X0,X1] :
( subset(set_difference(sK1,X0),X1)
| in(sK4(set_difference(sK1,X0),X1),sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_88])]) ).
fof(f2905,plain,
( spl8_167
<=> ! [X0,X3,X2,X1] :
( subset(set_difference(X0,set_difference(X1,X2)),X3)
| ~ in(sK4(set_difference(X0,set_difference(X1,X2)),X3),X1)
| in(sK4(set_difference(X0,set_difference(X1,X2)),X3),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_167])]) ).
fof(f2921,plain,
( ! [X0,X1] :
( subset(set_difference(sK1,set_difference(sK2,X0)),X1)
| in(sK4(set_difference(sK1,set_difference(sK2,X0)),X1),X0) )
| ~ spl8_88
| ~ spl8_167 ),
inference(duplicate_literal_removal,[],[f2912]) ).
fof(f2912,plain,
( ! [X0,X1] :
( subset(set_difference(sK1,set_difference(sK2,X0)),X1)
| in(sK4(set_difference(sK1,set_difference(sK2,X0)),X1),X0)
| subset(set_difference(sK1,set_difference(sK2,X0)),X1) )
| ~ spl8_88
| ~ spl8_167 ),
inference(resolution,[],[f2906,f1041]) ).
fof(f1041,plain,
( ! [X0,X1] :
( in(sK4(set_difference(sK1,X0),X1),sK2)
| subset(set_difference(sK1,X0),X1) )
| ~ spl8_88 ),
inference(avatar_component_clause,[],[f1040]) ).
fof(f2906,plain,
( ! [X2,X3,X0,X1] :
( ~ in(sK4(set_difference(X0,set_difference(X1,X2)),X3),X1)
| subset(set_difference(X0,set_difference(X1,X2)),X3)
| in(sK4(set_difference(X0,set_difference(X1,X2)),X3),X2) )
| ~ spl8_167 ),
inference(avatar_component_clause,[],[f2905]) ).
fof(f5234,plain,
( spl8_235
| ~ spl8_19
| ~ spl8_147 ),
inference(avatar_split_clause,[],[f2159,f2076,f159,f5232]) ).
fof(f5232,plain,
( spl8_235
<=> ! [X0,X1] :
( subset(set_difference(X0,X1),set_difference(X0,sK1))
| in(sK4(set_difference(X0,X1),set_difference(X0,sK1)),sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_235])]) ).
fof(f2076,plain,
( spl8_147
<=> ! [X2,X0,X1] :
( in(sK4(set_difference(X0,X1),set_difference(X0,X2)),X2)
| subset(set_difference(X0,X1),set_difference(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_147])]) ).
fof(f2159,plain,
( ! [X0,X1] :
( subset(set_difference(X0,X1),set_difference(X0,sK1))
| in(sK4(set_difference(X0,X1),set_difference(X0,sK1)),sK2) )
| ~ spl8_19
| ~ spl8_147 ),
inference(resolution,[],[f2077,f160]) ).
fof(f2077,plain,
( ! [X2,X0,X1] :
( in(sK4(set_difference(X0,X1),set_difference(X0,X2)),X2)
| subset(set_difference(X0,X1),set_difference(X0,X2)) )
| ~ spl8_147 ),
inference(avatar_component_clause,[],[f2076]) ).
fof(f5230,plain,
( spl8_234
| ~ spl8_19
| ~ spl8_144 ),
inference(avatar_split_clause,[],[f2124,f2064,f159,f5228]) ).
fof(f5228,plain,
( spl8_234
<=> ! [X2,X0,X1] :
( subset(set_difference(set_difference(sK1,X0),X1),X2)
| in(sK4(set_difference(set_difference(sK1,X0),X1),X2),sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_234])]) ).
fof(f2064,plain,
( spl8_144
<=> ! [X0,X3,X2,X1] :
( subset(set_difference(set_difference(X0,X1),X2),X3)
| in(sK4(set_difference(set_difference(X0,X1),X2),X3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_144])]) ).
fof(f2124,plain,
( ! [X2,X0,X1] :
( subset(set_difference(set_difference(sK1,X0),X1),X2)
| in(sK4(set_difference(set_difference(sK1,X0),X1),X2),sK2) )
| ~ spl8_19
| ~ spl8_144 ),
inference(resolution,[],[f2065,f160]) ).
fof(f2065,plain,
( ! [X2,X3,X0,X1] :
( in(sK4(set_difference(set_difference(X0,X1),X2),X3),X0)
| subset(set_difference(set_difference(X0,X1),X2),X3) )
| ~ spl8_144 ),
inference(avatar_component_clause,[],[f2064]) ).
fof(f5226,plain,
( spl8_233
| ~ spl8_10
| ~ spl8_108 ),
inference(avatar_split_clause,[],[f1473,f1240,f108,f5224]) ).
fof(f5224,plain,
( spl8_233
<=> ! [X0,X1] :
( in(sK5(set_difference(sK2,X0),sK1,X1),X1)
| sP0(set_difference(sK2,X0),sK1,X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_233])]) ).
fof(f1473,plain,
( ! [X0,X1] :
( in(sK5(set_difference(sK2,X0),sK1,X1),X1)
| sP0(set_difference(sK2,X0),sK1,X1)
| ~ empty(X0) )
| ~ spl8_10
| ~ spl8_108 ),
inference(resolution,[],[f1241,f109]) ).
fof(f5222,plain,
( spl8_232
| ~ spl8_10
| ~ spl8_108 ),
inference(avatar_split_clause,[],[f1465,f1240,f108,f5220]) ).
fof(f5220,plain,
( spl8_232
<=> ! [X0,X1] :
( in(sK5(set_difference(sK2,X0),sK1,X1),X0)
| sP0(set_difference(sK2,X0),sK1,X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_232])]) ).
fof(f1465,plain,
( ! [X0,X1] :
( in(sK5(set_difference(sK2,X0),sK1,X1),X0)
| sP0(set_difference(sK2,X0),sK1,X1)
| ~ empty(X1) )
| ~ spl8_10
| ~ spl8_108 ),
inference(resolution,[],[f1241,f109]) ).
fof(f5218,plain,
( spl8_231
| ~ spl8_10
| ~ spl8_105 ),
inference(avatar_split_clause,[],[f1347,f1228,f108,f5216]) ).
fof(f5216,plain,
( spl8_231
<=> ! [X2,X0,X1] :
( in(sK5(X0,sK1,set_difference(X1,X2)),sK2)
| sP0(X0,sK1,set_difference(X1,X2))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_231])]) ).
fof(f1347,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,sK1,set_difference(X1,X2)),sK2)
| sP0(X0,sK1,set_difference(X1,X2))
| ~ empty(X1) )
| ~ spl8_10
| ~ spl8_105 ),
inference(resolution,[],[f1229,f109]) ).
fof(f5214,plain,
( spl8_230
| ~ spl8_10
| ~ spl8_103 ),
inference(avatar_split_clause,[],[f1280,f1220,f108,f5212]) ).
fof(f5212,plain,
( spl8_230
<=> ! [X2,X0,X1] :
( in(sK5(X0,set_difference(X1,X2),sK1),sK2)
| sP0(X0,set_difference(X1,X2),sK1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_230])]) ).
fof(f1280,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,set_difference(X1,X2),sK1),sK2)
| sP0(X0,set_difference(X1,X2),sK1)
| ~ empty(X1) )
| ~ spl8_10
| ~ spl8_103 ),
inference(resolution,[],[f1221,f109]) ).
fof(f5210,plain,
( spl8_229
| ~ spl8_11
| ~ spl8_97 ),
inference(avatar_split_clause,[],[f1150,f1117,f114,f5208]) ).
fof(f5208,plain,
( spl8_229
<=> ! [X2,X0,X1] :
( sP0(X0,X1,set_difference(sK1,X2))
| ~ empty(X1)
| ~ in(sK2,sK5(X0,X1,set_difference(sK1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_229])]) ).
fof(f1150,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,set_difference(sK1,X2))
| ~ empty(X1)
| ~ in(sK2,sK5(X0,X1,set_difference(sK1,X2))) )
| ~ spl8_11
| ~ spl8_97 ),
inference(resolution,[],[f1118,f115]) ).
fof(f5206,plain,
( spl8_228
| ~ spl8_11
| ~ spl8_96 ),
inference(avatar_split_clause,[],[f1126,f1113,f114,f5204]) ).
fof(f5204,plain,
( spl8_228
<=> ! [X2,X0,X1] :
( sP0(X0,set_difference(sK1,X1),X2)
| ~ empty(X2)
| ~ in(sK2,sK5(X0,set_difference(sK1,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_228])]) ).
fof(f1126,plain,
( ! [X2,X0,X1] :
( sP0(X0,set_difference(sK1,X1),X2)
| ~ empty(X2)
| ~ in(sK2,sK5(X0,set_difference(sK1,X1),X2)) )
| ~ spl8_11
| ~ spl8_96 ),
inference(resolution,[],[f1114,f115]) ).
fof(f5202,plain,
( spl8_227
| ~ spl8_32
| ~ spl8_89 ),
inference(avatar_split_clause,[],[f1061,f1044,f245,f5200]) ).
fof(f5200,plain,
( spl8_227
<=> ! [X0,X1] :
( subset(sK1,set_difference(sK2,set_difference(X0,X1)))
| in(sK4(sK1,set_difference(sK2,set_difference(X0,X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_227])]) ).
fof(f245,plain,
( spl8_32
<=> ! [X2,X0,X1] :
( ~ in(X0,set_difference(X1,X2))
| in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_32])]) ).
fof(f1044,plain,
( spl8_89
<=> ! [X0] :
( in(sK4(sK1,set_difference(sK2,X0)),X0)
| subset(sK1,set_difference(sK2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_89])]) ).
fof(f1061,plain,
( ! [X0,X1] :
( subset(sK1,set_difference(sK2,set_difference(X0,X1)))
| in(sK4(sK1,set_difference(sK2,set_difference(X0,X1))),X0) )
| ~ spl8_32
| ~ spl8_89 ),
inference(resolution,[],[f1045,f246]) ).
fof(f246,plain,
( ! [X2,X0,X1] :
( ~ in(X0,set_difference(X1,X2))
| in(X0,X1) )
| ~ spl8_32 ),
inference(avatar_component_clause,[],[f245]) ).
fof(f1045,plain,
( ! [X0] :
( in(sK4(sK1,set_difference(sK2,X0)),X0)
| subset(sK1,set_difference(sK2,X0)) )
| ~ spl8_89 ),
inference(avatar_component_clause,[],[f1044]) ).
fof(f5135,plain,
( spl8_226
| ~ spl8_33
| ~ spl8_89 ),
inference(avatar_split_clause,[],[f1060,f1044,f249,f5133]) ).
fof(f249,plain,
( spl8_33
<=> ! [X2,X0,X1] :
( ~ in(X0,set_difference(X1,X2))
| ~ in(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_33])]) ).
fof(f1060,plain,
( ! [X0,X1] :
( subset(sK1,set_difference(sK2,set_difference(X0,X1)))
| ~ in(sK4(sK1,set_difference(sK2,set_difference(X0,X1))),X1) )
| ~ spl8_33
| ~ spl8_89 ),
inference(resolution,[],[f1045,f250]) ).
fof(f250,plain,
( ! [X2,X0,X1] :
( ~ in(X0,set_difference(X1,X2))
| ~ in(X0,X2) )
| ~ spl8_33 ),
inference(avatar_component_clause,[],[f249]) ).
fof(f5131,plain,
( spl8_225
| ~ spl8_76
| ~ spl8_88 ),
inference(avatar_split_clause,[],[f1054,f1040,f747,f5129]) ).
fof(f747,plain,
( spl8_76
<=> ! [X2,X0,X1] :
( ~ in(sK4(X0,set_difference(X1,X2)),X1)
| in(sK4(X0,set_difference(X1,X2)),X2)
| subset(X0,set_difference(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_76])]) ).
fof(f1054,plain,
( ! [X0,X1] :
( subset(set_difference(sK1,X0),set_difference(sK2,X1))
| in(sK4(set_difference(sK1,X0),set_difference(sK2,X1)),X1) )
| ~ spl8_76
| ~ spl8_88 ),
inference(duplicate_literal_removal,[],[f1049]) ).
fof(f1049,plain,
( ! [X0,X1] :
( subset(set_difference(sK1,X0),set_difference(sK2,X1))
| in(sK4(set_difference(sK1,X0),set_difference(sK2,X1)),X1)
| subset(set_difference(sK1,X0),set_difference(sK2,X1)) )
| ~ spl8_76
| ~ spl8_88 ),
inference(resolution,[],[f1041,f748]) ).
fof(f748,plain,
( ! [X2,X0,X1] :
( ~ in(sK4(X0,set_difference(X1,X2)),X1)
| in(sK4(X0,set_difference(X1,X2)),X2)
| subset(X0,set_difference(X1,X2)) )
| ~ spl8_76 ),
inference(avatar_component_clause,[],[f747]) ).
fof(f5127,plain,
( spl8_224
| ~ spl8_25
| ~ spl8_84 ),
inference(avatar_split_clause,[],[f1018,f1000,f199,f5125]) ).
fof(f5125,plain,
( spl8_224
<=> ! [X0] :
( sP0(X0,sK1,sK2)
| in(sK5(X0,sK1,sK2),X0)
| ~ in(sK5(X0,sK1,sK2),sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_224])]) ).
fof(f199,plain,
( spl8_25
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(sK5(X0,X1,X2),X0)
| ~ in(sK5(X0,X1,X2),X1)
| ~ in(sK5(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_25])]) ).
fof(f1000,plain,
( spl8_84
<=> ! [X0] :
( in(sK5(X0,sK1,sK2),sK2)
| sP0(X0,sK1,sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_84])]) ).
fof(f1018,plain,
( ! [X0] :
( sP0(X0,sK1,sK2)
| in(sK5(X0,sK1,sK2),X0)
| ~ in(sK5(X0,sK1,sK2),sK1) )
| ~ spl8_25
| ~ spl8_84 ),
inference(duplicate_literal_removal,[],[f1017]) ).
fof(f1017,plain,
( ! [X0] :
( sP0(X0,sK1,sK2)
| in(sK5(X0,sK1,sK2),X0)
| ~ in(sK5(X0,sK1,sK2),sK1)
| sP0(X0,sK1,sK2) )
| ~ spl8_25
| ~ spl8_84 ),
inference(resolution,[],[f1001,f200]) ).
fof(f200,plain,
( ! [X2,X0,X1] :
( ~ in(sK5(X0,X1,X2),X2)
| in(sK5(X0,X1,X2),X0)
| ~ in(sK5(X0,X1,X2),X1)
| sP0(X0,X1,X2) )
| ~ spl8_25 ),
inference(avatar_component_clause,[],[f199]) ).
fof(f1001,plain,
( ! [X0] :
( in(sK5(X0,sK1,sK2),sK2)
| sP0(X0,sK1,sK2) )
| ~ spl8_84 ),
inference(avatar_component_clause,[],[f1000]) ).
fof(f4958,plain,
( spl8_223
| ~ spl8_73
| ~ spl8_197 ),
inference(avatar_split_clause,[],[f4679,f4630,f700,f4956]) ).
fof(f4956,plain,
( spl8_223
<=> ! [X0] : sP0(sK1,set_difference(X0,sK2),set_difference(X0,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_223])]) ).
fof(f700,plain,
( spl8_73
<=> ! [X2,X0,X1] :
( sP0(X0,set_difference(X1,X2),set_difference(X1,X2))
| ~ in(sK5(X0,set_difference(X1,X2),set_difference(X1,X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_73])]) ).
fof(f4630,plain,
( spl8_197
<=> ! [X0] :
( sP0(sK1,X0,X0)
| in(sK5(sK1,X0,X0),sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_197])]) ).
fof(f4679,plain,
( ! [X0] : sP0(sK1,set_difference(X0,sK2),set_difference(X0,sK2))
| ~ spl8_73
| ~ spl8_197 ),
inference(duplicate_literal_removal,[],[f4646]) ).
fof(f4646,plain,
( ! [X0] :
( sP0(sK1,set_difference(X0,sK2),set_difference(X0,sK2))
| sP0(sK1,set_difference(X0,sK2),set_difference(X0,sK2)) )
| ~ spl8_73
| ~ spl8_197 ),
inference(resolution,[],[f4631,f701]) ).
fof(f701,plain,
( ! [X2,X0,X1] :
( ~ in(sK5(X0,set_difference(X1,X2),set_difference(X1,X2)),X2)
| sP0(X0,set_difference(X1,X2),set_difference(X1,X2)) )
| ~ spl8_73 ),
inference(avatar_component_clause,[],[f700]) ).
fof(f4631,plain,
( ! [X0] :
( in(sK5(sK1,X0,X0),sK2)
| sP0(sK1,X0,X0) )
| ~ spl8_197 ),
inference(avatar_component_clause,[],[f4630]) ).
fof(f4820,plain,
( spl8_222
| ~ spl8_19
| ~ spl8_138 ),
inference(avatar_split_clause,[],[f2038,f1896,f159,f4818]) ).
fof(f4818,plain,
( spl8_222
<=> ! [X0,X1] :
( sP0(X0,set_difference(X0,X1),sK1)
| in(sK5(X0,set_difference(X0,X1),sK1),sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_222])]) ).
fof(f1896,plain,
( spl8_138
<=> ! [X2,X0,X1] :
( in(sK5(X0,set_difference(X0,X1),X2),X2)
| sP0(X0,set_difference(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_138])]) ).
fof(f2038,plain,
( ! [X0,X1] :
( sP0(X0,set_difference(X0,X1),sK1)
| in(sK5(X0,set_difference(X0,X1),sK1),sK2) )
| ~ spl8_19
| ~ spl8_138 ),
inference(resolution,[],[f1897,f160]) ).
fof(f1897,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,set_difference(X0,X1),X2),X2)
| sP0(X0,set_difference(X0,X1),X2) )
| ~ spl8_138 ),
inference(avatar_component_clause,[],[f1896]) ).
fof(f4816,plain,
( spl8_221
| ~ spl8_19
| ~ spl8_137 ),
inference(avatar_split_clause,[],[f2009,f1892,f159,f4814]) ).
fof(f4814,plain,
( spl8_221
<=> ! [X0,X1] :
( sP0(X0,set_difference(sK1,X1),sK1)
| in(sK5(X0,set_difference(sK1,X1),sK1),sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_221])]) ).
fof(f1892,plain,
( spl8_137
<=> ! [X2,X0,X1] :
( in(sK5(X0,set_difference(X1,X2),X1),X1)
| sP0(X0,set_difference(X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_137])]) ).
fof(f2009,plain,
( ! [X0,X1] :
( sP0(X0,set_difference(sK1,X1),sK1)
| in(sK5(X0,set_difference(sK1,X1),sK1),sK2) )
| ~ spl8_19
| ~ spl8_137 ),
inference(resolution,[],[f1893,f160]) ).
fof(f1893,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,set_difference(X1,X2),X1),X1)
| sP0(X0,set_difference(X1,X2),X1) )
| ~ spl8_137 ),
inference(avatar_component_clause,[],[f1892]) ).
fof(f4812,plain,
( spl8_220
| ~ spl8_19
| ~ spl8_136 ),
inference(avatar_split_clause,[],[f1978,f1888,f159,f4810]) ).
fof(f4810,plain,
( spl8_220
<=> ! [X0,X1] :
( sP0(X0,sK1,set_difference(sK1,X1))
| in(sK5(X0,sK1,set_difference(sK1,X1)),sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_220])]) ).
fof(f1888,plain,
( spl8_136
<=> ! [X2,X0,X1] :
( in(sK5(X0,X1,set_difference(X1,X2)),X1)
| sP0(X0,X1,set_difference(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_136])]) ).
fof(f1978,plain,
( ! [X0,X1] :
( sP0(X0,sK1,set_difference(sK1,X1))
| in(sK5(X0,sK1,set_difference(sK1,X1)),sK2) )
| ~ spl8_19
| ~ spl8_136 ),
inference(resolution,[],[f1889,f160]) ).
fof(f1889,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,X1,set_difference(X1,X2)),X1)
| sP0(X0,X1,set_difference(X1,X2)) )
| ~ spl8_136 ),
inference(avatar_component_clause,[],[f1888]) ).
fof(f4808,plain,
( spl8_219
| ~ spl8_108 ),
inference(avatar_split_clause,[],[f1483,f1240,f4806]) ).
fof(f4806,plain,
( spl8_219
<=> ! [X0] :
( in(sK5(set_difference(sK2,X0),sK1,X0),X0)
| sP0(set_difference(sK2,X0),sK1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_219])]) ).
fof(f1483,plain,
( ! [X0] :
( in(sK5(set_difference(sK2,X0),sK1,X0),X0)
| sP0(set_difference(sK2,X0),sK1,X0) )
| ~ spl8_108 ),
inference(factoring,[],[f1241]) ).
fof(f4804,plain,
( spl8_218
| ~ spl8_24
| ~ spl8_107 ),
inference(avatar_split_clause,[],[f1461,f1236,f183,f4802]) ).
fof(f4802,plain,
( spl8_218
<=> ! [X0,X1] :
( in(sK5(sK2,set_difference(sK1,X0),X1),X1)
| sP0(sK2,set_difference(sK1,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_218])]) ).
fof(f183,plain,
( spl8_24
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ in(sK5(X0,X1,X2),X0)
| in(sK5(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_24])]) ).
fof(f1461,plain,
( ! [X0,X1] :
( in(sK5(sK2,set_difference(sK1,X0),X1),X1)
| sP0(sK2,set_difference(sK1,X0),X1) )
| ~ spl8_24
| ~ spl8_107 ),
inference(duplicate_literal_removal,[],[f1422]) ).
fof(f1422,plain,
( ! [X0,X1] :
( in(sK5(sK2,set_difference(sK1,X0),X1),X1)
| sP0(sK2,set_difference(sK1,X0),X1)
| sP0(sK2,set_difference(sK1,X0),X1)
| in(sK5(sK2,set_difference(sK1,X0),X1),X1) )
| ~ spl8_24
| ~ spl8_107 ),
inference(resolution,[],[f1237,f184]) ).
fof(f184,plain,
( ! [X2,X0,X1] :
( ~ in(sK5(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| in(sK5(X0,X1,X2),X2) )
| ~ spl8_24 ),
inference(avatar_component_clause,[],[f183]) ).
fof(f4799,plain,
( spl8_217
| ~ spl8_21
| ~ spl8_132 ),
inference(avatar_split_clause,[],[f2055,f1760,f168,f4797]) ).
fof(f4797,plain,
( spl8_217
<=> ! [X0,X1] :
( ~ in(X0,set_difference(sK1,sK2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_217])]) ).
fof(f168,plain,
( spl8_21
<=> ! [X4,X0,X2,X1] :
( ~ in(X4,X0)
| ~ in(X4,X2)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_21])]) ).
fof(f1760,plain,
( spl8_132
<=> ! [X0] : sP0(X0,X0,set_difference(sK1,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_132])]) ).
fof(f2055,plain,
( ! [X0,X1] :
( ~ in(X0,set_difference(sK1,sK2))
| ~ in(X0,X1) )
| ~ spl8_21
| ~ spl8_132 ),
inference(resolution,[],[f1761,f169]) ).
fof(f169,plain,
( ! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| ~ in(X4,X2)
| ~ in(X4,X0) )
| ~ spl8_21 ),
inference(avatar_component_clause,[],[f168]) ).
fof(f1761,plain,
( ! [X0] : sP0(X0,X0,set_difference(sK1,sK2))
| ~ spl8_132 ),
inference(avatar_component_clause,[],[f1760]) ).
fof(f4793,plain,
( spl8_216
| ~ spl8_80
| ~ spl8_107 ),
inference(avatar_split_clause,[],[f1459,f1236,f774,f4791]) ).
fof(f4791,plain,
( spl8_216
<=> ! [X0,X1] :
( in(sK5(X0,set_difference(sK1,sK2),X1),X1)
| sP0(X0,set_difference(sK1,sK2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_216])]) ).
fof(f774,plain,
( spl8_80
<=> ! [X0,X3,X2,X1] :
( ~ in(sK5(X0,set_difference(X1,X2),X3),X2)
| in(sK5(X0,set_difference(X1,X2),X3),X3)
| sP0(X0,set_difference(X1,X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_80])]) ).
fof(f1459,plain,
( ! [X0,X1] :
( in(sK5(X0,set_difference(sK1,sK2),X1),X1)
| sP0(X0,set_difference(sK1,sK2),X1) )
| ~ spl8_80
| ~ spl8_107 ),
inference(duplicate_literal_removal,[],[f1426]) ).
fof(f1426,plain,
( ! [X0,X1] :
( in(sK5(X0,set_difference(sK1,sK2),X1),X1)
| sP0(X0,set_difference(sK1,sK2),X1)
| in(sK5(X0,set_difference(sK1,sK2),X1),X1)
| sP0(X0,set_difference(sK1,sK2),X1) )
| ~ spl8_80
| ~ spl8_107 ),
inference(resolution,[],[f1237,f775]) ).
fof(f775,plain,
( ! [X2,X3,X0,X1] :
( ~ in(sK5(X0,set_difference(X1,X2),X3),X2)
| in(sK5(X0,set_difference(X1,X2),X3),X3)
| sP0(X0,set_difference(X1,X2),X3) )
| ~ spl8_80 ),
inference(avatar_component_clause,[],[f774]) ).
fof(f4789,plain,
( spl8_215
| ~ spl8_107 ),
inference(avatar_split_clause,[],[f1447,f1236,f4787]) ).
fof(f4787,plain,
( spl8_215
<=> ! [X0,X1] :
( in(sK5(X0,set_difference(sK1,X1),sK2),sK2)
| sP0(X0,set_difference(sK1,X1),sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_215])]) ).
fof(f1447,plain,
( ! [X0,X1] :
( in(sK5(X0,set_difference(sK1,X1),sK2),sK2)
| sP0(X0,set_difference(sK1,X1),sK2) )
| ~ spl8_107 ),
inference(factoring,[],[f1237]) ).
fof(f4783,plain,
( spl8_214
| ~ spl8_79
| ~ spl8_106 ),
inference(avatar_split_clause,[],[f1417,f1232,f770,f4781]) ).
fof(f4781,plain,
( spl8_214
<=> ! [X0,X1] :
( in(sK5(X0,X1,set_difference(sK1,sK2)),X1)
| sP0(X0,X1,set_difference(sK1,sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_214])]) ).
fof(f770,plain,
( spl8_79
<=> ! [X0,X3,X2,X1] :
( ~ in(sK5(X0,X1,set_difference(X2,X3)),X3)
| in(sK5(X0,X1,set_difference(X2,X3)),X1)
| sP0(X0,X1,set_difference(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_79])]) ).
fof(f1417,plain,
( ! [X0,X1] :
( in(sK5(X0,X1,set_difference(sK1,sK2)),X1)
| sP0(X0,X1,set_difference(sK1,sK2)) )
| ~ spl8_79
| ~ spl8_106 ),
inference(duplicate_literal_removal,[],[f1389]) ).
fof(f1389,plain,
( ! [X0,X1] :
( in(sK5(X0,X1,set_difference(sK1,sK2)),X1)
| sP0(X0,X1,set_difference(sK1,sK2))
| in(sK5(X0,X1,set_difference(sK1,sK2)),X1)
| sP0(X0,X1,set_difference(sK1,sK2)) )
| ~ spl8_79
| ~ spl8_106 ),
inference(resolution,[],[f1233,f771]) ).
fof(f771,plain,
( ! [X2,X3,X0,X1] :
( ~ in(sK5(X0,X1,set_difference(X2,X3)),X3)
| in(sK5(X0,X1,set_difference(X2,X3)),X1)
| sP0(X0,X1,set_difference(X2,X3)) )
| ~ spl8_79 ),
inference(avatar_component_clause,[],[f770]) ).
fof(f4779,plain,
( spl8_213
| ~ spl8_106 ),
inference(avatar_split_clause,[],[f1405,f1232,f4777]) ).
fof(f4777,plain,
( spl8_213
<=> ! [X0,X1] :
( in(sK5(X0,sK2,set_difference(sK1,X1)),sK2)
| sP0(X0,sK2,set_difference(sK1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_213])]) ).
fof(f1405,plain,
( ! [X0,X1] :
( in(sK5(X0,sK2,set_difference(sK1,X1)),sK2)
| sP0(X0,sK2,set_difference(sK1,X1)) )
| ~ spl8_106 ),
inference(factoring,[],[f1233]) ).
fof(f4773,plain,
( spl8_212
| ~ spl8_104
| ~ spl8_105 ),
inference(avatar_split_clause,[],[f1370,f1228,f1224,f4771]) ).
fof(f4771,plain,
( spl8_212
<=> ! [X0,X1] :
( in(sK5(X0,sK1,set_difference(X1,X1)),sK2)
| sP0(X0,sK1,set_difference(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_212])]) ).
fof(f1224,plain,
( spl8_104
<=> ! [X2,X0,X1] :
( in(sK5(X0,sK1,set_difference(X1,X2)),sK2)
| sP0(X0,sK1,set_difference(X1,X2))
| ~ in(sK5(X0,sK1,set_difference(X1,X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_104])]) ).
fof(f1370,plain,
( ! [X0,X1] :
( in(sK5(X0,sK1,set_difference(X1,X1)),sK2)
| sP0(X0,sK1,set_difference(X1,X1)) )
| ~ spl8_104
| ~ spl8_105 ),
inference(duplicate_literal_removal,[],[f1348]) ).
fof(f1348,plain,
( ! [X0,X1] :
( in(sK5(X0,sK1,set_difference(X1,X1)),sK2)
| sP0(X0,sK1,set_difference(X1,X1))
| sP0(X0,sK1,set_difference(X1,X1))
| in(sK5(X0,sK1,set_difference(X1,X1)),sK2) )
| ~ spl8_104
| ~ spl8_105 ),
inference(resolution,[],[f1229,f1225]) ).
fof(f1225,plain,
( ! [X2,X0,X1] :
( ~ in(sK5(X0,sK1,set_difference(X1,X2)),X2)
| sP0(X0,sK1,set_difference(X1,X2))
| in(sK5(X0,sK1,set_difference(X1,X2)),sK2) )
| ~ spl8_104 ),
inference(avatar_component_clause,[],[f1224]) ).
fof(f4769,plain,
( spl8_211
| ~ spl8_105 ),
inference(avatar_split_clause,[],[f1357,f1228,f4767]) ).
fof(f4767,plain,
( spl8_211
<=> ! [X0,X1] :
( in(sK5(X0,sK1,set_difference(sK2,X1)),sK2)
| sP0(X0,sK1,set_difference(sK2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_211])]) ).
fof(f1357,plain,
( ! [X0,X1] :
( in(sK5(X0,sK1,set_difference(sK2,X1)),sK2)
| sP0(X0,sK1,set_difference(sK2,X1)) )
| ~ spl8_105 ),
inference(factoring,[],[f1229]) ).
fof(f4763,plain,
( spl8_210
| ~ spl8_102
| ~ spl8_103 ),
inference(avatar_split_clause,[],[f1300,f1220,f1213,f4761]) ).
fof(f4761,plain,
( spl8_210
<=> ! [X0,X1] :
( in(sK5(X0,set_difference(X1,X1),sK1),sK2)
| sP0(X0,set_difference(X1,X1),sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_210])]) ).
fof(f1213,plain,
( spl8_102
<=> ! [X2,X0,X1] :
( in(sK5(X0,set_difference(X1,X2),sK1),sK2)
| sP0(X0,set_difference(X1,X2),sK1)
| ~ in(sK5(X0,set_difference(X1,X2),sK1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_102])]) ).
fof(f1300,plain,
( ! [X0,X1] :
( in(sK5(X0,set_difference(X1,X1),sK1),sK2)
| sP0(X0,set_difference(X1,X1),sK1) )
| ~ spl8_102
| ~ spl8_103 ),
inference(duplicate_literal_removal,[],[f1281]) ).
fof(f1281,plain,
( ! [X0,X1] :
( in(sK5(X0,set_difference(X1,X1),sK1),sK2)
| sP0(X0,set_difference(X1,X1),sK1)
| sP0(X0,set_difference(X1,X1),sK1)
| in(sK5(X0,set_difference(X1,X1),sK1),sK2) )
| ~ spl8_102
| ~ spl8_103 ),
inference(resolution,[],[f1221,f1214]) ).
fof(f1214,plain,
( ! [X2,X0,X1] :
( ~ in(sK5(X0,set_difference(X1,X2),sK1),X2)
| sP0(X0,set_difference(X1,X2),sK1)
| in(sK5(X0,set_difference(X1,X2),sK1),sK2) )
| ~ spl8_102 ),
inference(avatar_component_clause,[],[f1213]) ).
fof(f4759,plain,
( spl8_209
| ~ spl8_103 ),
inference(avatar_split_clause,[],[f1289,f1220,f4757]) ).
fof(f4757,plain,
( spl8_209
<=> ! [X0,X1] :
( in(sK5(X0,set_difference(sK2,X1),sK1),sK2)
| sP0(X0,set_difference(sK2,X1),sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_209])]) ).
fof(f1289,plain,
( ! [X0,X1] :
( in(sK5(X0,set_difference(sK2,X1),sK1),sK2)
| sP0(X0,set_difference(sK2,X1),sK1) )
| ~ spl8_103 ),
inference(factoring,[],[f1221]) ).
fof(f4755,plain,
( spl8_208
| ~ spl8_11
| ~ spl8_90 ),
inference(avatar_split_clause,[],[f1078,f1069,f114,f4753]) ).
fof(f4753,plain,
( spl8_208
<=> ! [X0,X1] :
( sP0(X0,X0,set_difference(sK1,X1))
| ~ in(sK2,sK5(X0,X0,set_difference(sK1,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_208])]) ).
fof(f1078,plain,
( ! [X0,X1] :
( sP0(X0,X0,set_difference(sK1,X1))
| ~ in(sK2,sK5(X0,X0,set_difference(sK1,X1))) )
| ~ spl8_11
| ~ spl8_90 ),
inference(resolution,[],[f1070,f115]) ).
fof(f4751,plain,
( spl8_207
| ~ spl8_32
| ~ spl8_85 ),
inference(avatar_split_clause,[],[f1026,f1004,f245,f4749]) ).
fof(f1004,plain,
( spl8_85
<=> ! [X0] :
( in(sK5(sK2,sK1,X0),X0)
| sP0(sK2,sK1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_85])]) ).
fof(f1026,plain,
( ! [X0,X1] :
( sP0(sK2,sK1,set_difference(X0,X1))
| in(sK5(sK2,sK1,set_difference(X0,X1)),X0) )
| ~ spl8_32
| ~ spl8_85 ),
inference(resolution,[],[f1005,f246]) ).
fof(f1005,plain,
( ! [X0] :
( in(sK5(sK2,sK1,X0),X0)
| sP0(sK2,sK1,X0) )
| ~ spl8_85 ),
inference(avatar_component_clause,[],[f1004]) ).
fof(f4746,plain,
( spl8_206
| ~ spl8_17
| ~ spl8_98 ),
inference(avatar_split_clause,[],[f1379,f1121,f149,f4744]) ).
fof(f4744,plain,
( spl8_206
<=> ! [X0,X1] :
( ~ in(X0,set_difference(sK1,sK2))
| in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_206])]) ).
fof(f149,plain,
( spl8_17
<=> ! [X0,X1,X3] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_17])]) ).
fof(f1121,plain,
( spl8_98
<=> ! [X0] : subset(set_difference(sK1,sK2),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_98])]) ).
fof(f1379,plain,
( ! [X0,X1] :
( ~ in(X0,set_difference(sK1,sK2))
| in(X0,X1) )
| ~ spl8_17
| ~ spl8_98 ),
inference(resolution,[],[f1122,f150]) ).
fof(f150,plain,
( ! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) )
| ~ spl8_17 ),
inference(avatar_component_clause,[],[f149]) ).
fof(f1122,plain,
( ! [X0] : subset(set_difference(sK1,sK2),X0)
| ~ spl8_98 ),
inference(avatar_component_clause,[],[f1121]) ).
fof(f4742,plain,
( spl8_205
| ~ spl8_33
| ~ spl8_85 ),
inference(avatar_split_clause,[],[f1025,f1004,f249,f4740]) ).
fof(f4740,plain,
( spl8_205
<=> ! [X0,X1] :
( sP0(sK2,sK1,set_difference(X0,X1))
| ~ in(sK5(sK2,sK1,set_difference(X0,X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_205])]) ).
fof(f1025,plain,
( ! [X0,X1] :
( sP0(sK2,sK1,set_difference(X0,X1))
| ~ in(sK5(sK2,sK1,set_difference(X0,X1)),X1) )
| ~ spl8_33
| ~ spl8_85 ),
inference(resolution,[],[f1005,f250]) ).
fof(f4737,plain,
( spl8_204
| ~ spl8_7
| ~ spl8_13
| ~ spl8_101 ),
inference(avatar_split_clause,[],[f1210,f1197,f122,f96,f4735]) ).
fof(f4735,plain,
( spl8_204
<=> ! [X0] : subset(sK7,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_204])]) ).
fof(f1197,plain,
( spl8_101
<=> ! [X0,X1] : subset(set_difference(X0,X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_101])]) ).
fof(f1210,plain,
( ! [X0] : subset(sK7,X0)
| ~ spl8_7
| ~ spl8_13
| ~ spl8_101 ),
inference(forward_demodulation,[],[f1206,f124]) ).
fof(f1206,plain,
( ! [X0] : subset(empty_set,X0)
| ~ spl8_7
| ~ spl8_101 ),
inference(superposition,[],[f1198,f97]) ).
fof(f1198,plain,
( ! [X0,X1] : subset(set_difference(X0,X0),X1)
| ~ spl8_101 ),
inference(avatar_component_clause,[],[f1197]) ).
fof(f4714,plain,
( spl8_203
| ~ spl8_19
| ~ spl8_134 ),
inference(avatar_split_clause,[],[f1871,f1768,f159,f4712]) ).
fof(f4712,plain,
( spl8_203
<=> ! [X0] :
( subset(X0,set_difference(X0,sK1))
| in(sK4(X0,set_difference(X0,sK1)),sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_203])]) ).
fof(f1768,plain,
( spl8_134
<=> ! [X0,X1] :
( in(sK4(X0,set_difference(X0,X1)),X1)
| subset(X0,set_difference(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_134])]) ).
fof(f1871,plain,
( ! [X0] :
( subset(X0,set_difference(X0,sK1))
| in(sK4(X0,set_difference(X0,sK1)),sK2) )
| ~ spl8_19
| ~ spl8_134 ),
inference(resolution,[],[f1769,f160]) ).
fof(f1769,plain,
( ! [X0,X1] :
( in(sK4(X0,set_difference(X0,X1)),X1)
| subset(X0,set_difference(X0,X1)) )
| ~ spl8_134 ),
inference(avatar_component_clause,[],[f1768]) ).
fof(f4710,plain,
( spl8_202
| ~ spl8_11
| ~ spl8_89 ),
inference(avatar_split_clause,[],[f1058,f1044,f114,f4708]) ).
fof(f4708,plain,
( spl8_202
<=> ! [X0] :
( subset(sK1,set_difference(sK2,X0))
| ~ in(X0,sK4(sK1,set_difference(sK2,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_202])]) ).
fof(f1058,plain,
( ! [X0] :
( subset(sK1,set_difference(sK2,X0))
| ~ in(X0,sK4(sK1,set_difference(sK2,X0))) )
| ~ spl8_11
| ~ spl8_89 ),
inference(resolution,[],[f1045,f115]) ).
fof(f4706,plain,
( spl8_201
| ~ spl8_11
| ~ spl8_88 ),
inference(avatar_split_clause,[],[f1050,f1040,f114,f4704]) ).
fof(f4704,plain,
( spl8_201
<=> ! [X0,X1] :
( subset(set_difference(sK1,X0),X1)
| ~ in(sK2,sK4(set_difference(sK1,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_201])]) ).
fof(f1050,plain,
( ! [X0,X1] :
( subset(set_difference(sK1,X0),X1)
| ~ in(sK2,sK4(set_difference(sK1,X0),X1)) )
| ~ spl8_11
| ~ spl8_88 ),
inference(resolution,[],[f1041,f115]) ).
fof(f4694,plain,
( spl8_200
| ~ spl8_17
| ~ spl8_91 ),
inference(avatar_split_clause,[],[f1216,f1073,f149,f4692]) ).
fof(f4692,plain,
( spl8_200
<=> ! [X0,X1] :
( ~ in(X0,set_difference(sK1,X1))
| in(X0,sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_200])]) ).
fof(f1073,plain,
( spl8_91
<=> ! [X0] : subset(set_difference(sK1,X0),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_91])]) ).
fof(f1216,plain,
( ! [X0,X1] :
( ~ in(X0,set_difference(sK1,X1))
| in(X0,sK2) )
| ~ spl8_17
| ~ spl8_91 ),
inference(resolution,[],[f1074,f150]) ).
fof(f1074,plain,
( ! [X0] : subset(set_difference(sK1,X0),sK2)
| ~ spl8_91 ),
inference(avatar_component_clause,[],[f1073]) ).
fof(f4640,plain,
( spl8_199
| ~ spl8_19
| ~ spl8_142 ),
inference(avatar_split_clause,[],[f1950,f1940,f159,f4638]) ).
fof(f4638,plain,
( spl8_199
<=> ! [X0] :
( sP0(X0,sK7,sK1)
| in(sK5(X0,sK7,sK1),sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_199])]) ).
fof(f1940,plain,
( spl8_142
<=> ! [X2,X0] :
( sP0(X0,sK7,X2)
| in(sK5(X0,sK7,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_142])]) ).
fof(f1950,plain,
( ! [X0] :
( sP0(X0,sK7,sK1)
| in(sK5(X0,sK7,sK1),sK2) )
| ~ spl8_19
| ~ spl8_142 ),
inference(resolution,[],[f1941,f160]) ).
fof(f1941,plain,
( ! [X2,X0] :
( in(sK5(X0,sK7,X2),X2)
| sP0(X0,sK7,X2) )
| ~ spl8_142 ),
inference(avatar_component_clause,[],[f1940]) ).
fof(f4636,plain,
( spl8_198
| ~ spl8_19
| ~ spl8_140 ),
inference(avatar_split_clause,[],[f1920,f1910,f159,f4634]) ).
fof(f4634,plain,
( spl8_198
<=> ! [X0] :
( sP0(X0,sK1,sK7)
| in(sK5(X0,sK1,sK7),sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_198])]) ).
fof(f1910,plain,
( spl8_140
<=> ! [X0,X1] :
( sP0(X0,X1,sK7)
| in(sK5(X0,X1,sK7),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_140])]) ).
fof(f1920,plain,
( ! [X0] :
( sP0(X0,sK1,sK7)
| in(sK5(X0,sK1,sK7),sK2) )
| ~ spl8_19
| ~ spl8_140 ),
inference(resolution,[],[f1911,f160]) ).
fof(f1911,plain,
( ! [X0,X1] :
( in(sK5(X0,X1,sK7),X1)
| sP0(X0,X1,sK7) )
| ~ spl8_140 ),
inference(avatar_component_clause,[],[f1910]) ).
fof(f4632,plain,
( spl8_197
| ~ spl8_19
| ~ spl8_125 ),
inference(avatar_split_clause,[],[f1690,f1621,f159,f4630]) ).
fof(f1621,plain,
( spl8_125
<=> ! [X0,X1] :
( in(sK5(X0,X1,X1),X0)
| sP0(X0,X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_125])]) ).
fof(f1690,plain,
( ! [X0] :
( sP0(sK1,X0,X0)
| in(sK5(sK1,X0,X0),sK2) )
| ~ spl8_19
| ~ spl8_125 ),
inference(resolution,[],[f1622,f160]) ).
fof(f1622,plain,
( ! [X0,X1] :
( in(sK5(X0,X1,X1),X0)
| sP0(X0,X1,X1) )
| ~ spl8_125 ),
inference(avatar_component_clause,[],[f1621]) ).
fof(f4628,plain,
( spl8_196
| ~ spl8_11
| ~ spl8_85 ),
inference(avatar_split_clause,[],[f1022,f1004,f114,f4626]) ).
fof(f4626,plain,
( spl8_196
<=> ! [X0] :
( sP0(sK2,sK1,X0)
| ~ in(X0,sK5(sK2,sK1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_196])]) ).
fof(f1022,plain,
( ! [X0] :
( sP0(sK2,sK1,X0)
| ~ in(X0,sK5(sK2,sK1,X0)) )
| ~ spl8_11
| ~ spl8_85 ),
inference(resolution,[],[f1005,f115]) ).
fof(f4624,plain,
( spl8_195
| ~ spl8_11
| ~ spl8_84 ),
inference(avatar_split_clause,[],[f1015,f1000,f114,f4622]) ).
fof(f4622,plain,
( spl8_195
<=> ! [X0] :
( sP0(X0,sK1,sK2)
| ~ in(sK2,sK5(X0,sK1,sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_195])]) ).
fof(f1015,plain,
( ! [X0] :
( sP0(X0,sK1,sK2)
| ~ in(sK2,sK5(X0,sK1,sK2)) )
| ~ spl8_11
| ~ spl8_84 ),
inference(resolution,[],[f1001,f115]) ).
fof(f4619,plain,
( spl8_194
| ~ spl8_18
| ~ spl8_113 ),
inference(avatar_split_clause,[],[f1902,f1526,f153,f4617]) ).
fof(f4617,plain,
( spl8_194
<=> ! [X0] :
( ~ empty(X0)
| set_difference(sK1,sK2) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_194])]) ).
fof(f153,plain,
( spl8_18
<=> ! [X2,X0,X1] :
( set_difference(X0,X1) = X2
| ~ sP0(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_18])]) ).
fof(f1526,plain,
( spl8_113
<=> ! [X0] :
( sP0(sK2,sK1,X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_113])]) ).
fof(f1902,plain,
( ! [X0] :
( ~ empty(X0)
| set_difference(sK1,sK2) = X0 )
| ~ spl8_18
| ~ spl8_113 ),
inference(resolution,[],[f1527,f154]) ).
fof(f154,plain,
( ! [X2,X0,X1] :
( ~ sP0(X1,X0,X2)
| set_difference(X0,X1) = X2 )
| ~ spl8_18 ),
inference(avatar_component_clause,[],[f153]) ).
fof(f1527,plain,
( ! [X0] :
( sP0(sK2,sK1,X0)
| ~ empty(X0) )
| ~ spl8_113 ),
inference(avatar_component_clause,[],[f1526]) ).
fof(f4615,plain,
( spl8_193
| ~ spl8_11
| ~ spl8_81 ),
inference(avatar_split_clause,[],[f1009,f884,f114,f4613]) ).
fof(f4613,plain,
( spl8_193
<=> ! [X0] :
( sP0(X0,sK2,sK1)
| ~ in(sK2,sK5(X0,sK2,sK1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_193])]) ).
fof(f884,plain,
( spl8_81
<=> ! [X0] :
( in(sK5(X0,sK2,sK1),sK2)
| sP0(X0,sK2,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_81])]) ).
fof(f1009,plain,
( ! [X0] :
( sP0(X0,sK2,sK1)
| ~ in(sK2,sK5(X0,sK2,sK1)) )
| ~ spl8_11
| ~ spl8_81 ),
inference(resolution,[],[f885,f115]) ).
fof(f885,plain,
( ! [X0] :
( in(sK5(X0,sK2,sK1),sK2)
| sP0(X0,sK2,sK1) )
| ~ spl8_81 ),
inference(avatar_component_clause,[],[f884]) ).
fof(f4610,plain,
( spl8_192
| ~ spl8_73
| ~ spl8_99 ),
inference(avatar_split_clause,[],[f1189,f1169,f700,f4608]) ).
fof(f4608,plain,
( spl8_192
<=> ! [X0] : sP0(X0,set_difference(sK1,sK2),set_difference(sK1,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_192])]) ).
fof(f1189,plain,
( ! [X0] : sP0(X0,set_difference(sK1,sK2),set_difference(sK1,sK2))
| ~ spl8_73
| ~ spl8_99 ),
inference(duplicate_literal_removal,[],[f1176]) ).
fof(f1176,plain,
( ! [X0] :
( sP0(X0,set_difference(sK1,sK2),set_difference(sK1,sK2))
| sP0(X0,set_difference(sK1,sK2),set_difference(sK1,sK2)) )
| ~ spl8_73
| ~ spl8_99 ),
inference(resolution,[],[f1170,f701]) ).
fof(f4605,plain,
( spl8_191
| ~ spl8_71
| ~ spl8_97 ),
inference(avatar_split_clause,[],[f1160,f1117,f601,f4603]) ).
fof(f4603,plain,
( spl8_191
<=> ! [X0,X1] :
( sP0(X0,X1,set_difference(sK1,sK2))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_191])]) ).
fof(f601,plain,
( spl8_71
<=> ! [X0,X3,X2,X1] :
( sP0(X0,X1,set_difference(X2,X3))
| ~ empty(X1)
| ~ in(sK5(X0,X1,set_difference(X2,X3)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_71])]) ).
fof(f1160,plain,
( ! [X0,X1] :
( sP0(X0,X1,set_difference(sK1,sK2))
| ~ empty(X1) )
| ~ spl8_71
| ~ spl8_97 ),
inference(duplicate_literal_removal,[],[f1157]) ).
fof(f1157,plain,
( ! [X0,X1] :
( sP0(X0,X1,set_difference(sK1,sK2))
| ~ empty(X1)
| ~ empty(X1)
| sP0(X0,X1,set_difference(sK1,sK2)) )
| ~ spl8_71
| ~ spl8_97 ),
inference(resolution,[],[f1118,f602]) ).
fof(f602,plain,
( ! [X2,X3,X0,X1] :
( ~ in(sK5(X0,X1,set_difference(X2,X3)),X3)
| ~ empty(X1)
| sP0(X0,X1,set_difference(X2,X3)) )
| ~ spl8_71 ),
inference(avatar_component_clause,[],[f601]) ).
fof(f4600,plain,
( spl8_190
| ~ spl8_68
| ~ spl8_96 ),
inference(avatar_split_clause,[],[f1144,f1113,f589,f4598]) ).
fof(f4598,plain,
( spl8_190
<=> ! [X0,X1] :
( sP0(X0,set_difference(sK1,sK2),X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_190])]) ).
fof(f589,plain,
( spl8_68
<=> ! [X0,X3,X2,X1] :
( sP0(X0,set_difference(X1,X2),X3)
| ~ empty(X3)
| ~ in(sK5(X0,set_difference(X1,X2),X3),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_68])]) ).
fof(f1144,plain,
( ! [X0,X1] :
( sP0(X0,set_difference(sK1,sK2),X1)
| ~ empty(X1) )
| ~ spl8_68
| ~ spl8_96 ),
inference(duplicate_literal_removal,[],[f1129]) ).
fof(f1129,plain,
( ! [X0,X1] :
( sP0(X0,set_difference(sK1,sK2),X1)
| ~ empty(X1)
| ~ empty(X1)
| sP0(X0,set_difference(sK1,sK2),X1) )
| ~ spl8_68
| ~ spl8_96 ),
inference(resolution,[],[f1114,f590]) ).
fof(f590,plain,
( ! [X2,X3,X0,X1] :
( ~ in(sK5(X0,set_difference(X1,X2),X3),X2)
| ~ empty(X3)
| sP0(X0,set_difference(X1,X2),X3) )
| ~ spl8_68 ),
inference(avatar_component_clause,[],[f589]) ).
fof(f4554,plain,
( spl8_189
| ~ spl8_37
| ~ spl8_83 ),
inference(avatar_split_clause,[],[f987,f973,f296,f4552]) ).
fof(f4552,plain,
( spl8_189
<=> ! [X4,X0,X3,X2,X1] :
( in(sK5(X0,X1,set_difference(set_difference(X2,X3),X4)),X4)
| in(sK5(X0,X1,set_difference(set_difference(X2,X3),X4)),X0)
| ~ in(sK5(X0,X1,set_difference(set_difference(X2,X3),X4)),X1)
| sP0(X0,X1,set_difference(set_difference(X2,X3),X4))
| ~ in(sK5(X0,X1,set_difference(set_difference(X2,X3),X4)),X2)
| in(sK5(X0,X1,set_difference(set_difference(X2,X3),X4)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_189])]) ).
fof(f296,plain,
( spl8_37
<=> ! [X2,X0,X1] :
( in(X0,X1)
| ~ in(X0,X2)
| in(X0,set_difference(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_37])]) ).
fof(f973,plain,
( spl8_83
<=> ! [X0,X3,X2,X1] :
( ~ in(sK5(X0,X1,set_difference(X2,X3)),X2)
| in(sK5(X0,X1,set_difference(X2,X3)),X3)
| in(sK5(X0,X1,set_difference(X2,X3)),X0)
| ~ in(sK5(X0,X1,set_difference(X2,X3)),X1)
| sP0(X0,X1,set_difference(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_83])]) ).
fof(f987,plain,
( ! [X2,X3,X0,X1,X4] :
( in(sK5(X0,X1,set_difference(set_difference(X2,X3),X4)),X4)
| in(sK5(X0,X1,set_difference(set_difference(X2,X3),X4)),X0)
| ~ in(sK5(X0,X1,set_difference(set_difference(X2,X3),X4)),X1)
| sP0(X0,X1,set_difference(set_difference(X2,X3),X4))
| ~ in(sK5(X0,X1,set_difference(set_difference(X2,X3),X4)),X2)
| in(sK5(X0,X1,set_difference(set_difference(X2,X3),X4)),X3) )
| ~ spl8_37
| ~ spl8_83 ),
inference(resolution,[],[f974,f297]) ).
fof(f297,plain,
( ! [X2,X0,X1] :
( in(X0,set_difference(X2,X1))
| ~ in(X0,X2)
| in(X0,X1) )
| ~ spl8_37 ),
inference(avatar_component_clause,[],[f296]) ).
fof(f974,plain,
( ! [X2,X3,X0,X1] :
( ~ in(sK5(X0,X1,set_difference(X2,X3)),X2)
| in(sK5(X0,X1,set_difference(X2,X3)),X3)
| in(sK5(X0,X1,set_difference(X2,X3)),X0)
| ~ in(sK5(X0,X1,set_difference(X2,X3)),X1)
| sP0(X0,X1,set_difference(X2,X3)) )
| ~ spl8_83 ),
inference(avatar_component_clause,[],[f973]) ).
fof(f4430,plain,
( spl8_188
| ~ spl8_37
| ~ spl8_82 ),
inference(avatar_split_clause,[],[f945,f920,f296,f4428]) ).
fof(f4428,plain,
( spl8_188
<=> ! [X4,X0,X3,X2,X1] :
( in(sK5(set_difference(set_difference(X0,X1),X2),X3,X4),X2)
| sP0(set_difference(set_difference(X0,X1),X2),X3,X4)
| in(sK5(set_difference(set_difference(X0,X1),X2),X3,X4),X4)
| ~ in(sK5(set_difference(set_difference(X0,X1),X2),X3,X4),X0)
| in(sK5(set_difference(set_difference(X0,X1),X2),X3,X4),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_188])]) ).
fof(f920,plain,
( spl8_82
<=> ! [X0,X3,X2,X1] :
( ~ in(sK5(set_difference(X0,X1),X2,X3),X0)
| in(sK5(set_difference(X0,X1),X2,X3),X1)
| sP0(set_difference(X0,X1),X2,X3)
| in(sK5(set_difference(X0,X1),X2,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_82])]) ).
fof(f945,plain,
( ! [X2,X3,X0,X1,X4] :
( in(sK5(set_difference(set_difference(X0,X1),X2),X3,X4),X2)
| sP0(set_difference(set_difference(X0,X1),X2),X3,X4)
| in(sK5(set_difference(set_difference(X0,X1),X2),X3,X4),X4)
| ~ in(sK5(set_difference(set_difference(X0,X1),X2),X3,X4),X0)
| in(sK5(set_difference(set_difference(X0,X1),X2),X3,X4),X1) )
| ~ spl8_37
| ~ spl8_82 ),
inference(resolution,[],[f921,f297]) ).
fof(f921,plain,
( ! [X2,X3,X0,X1] :
( ~ in(sK5(set_difference(X0,X1),X2,X3),X0)
| in(sK5(set_difference(X0,X1),X2,X3),X1)
| sP0(set_difference(X0,X1),X2,X3)
| in(sK5(set_difference(X0,X1),X2,X3),X3) )
| ~ spl8_82 ),
inference(avatar_component_clause,[],[f920]) ).
fof(f4376,plain,
( spl8_187
| ~ spl8_69
| ~ spl8_83 ),
inference(avatar_split_clause,[],[f993,f973,f593,f4374]) ).
fof(f4374,plain,
( spl8_187
<=> ! [X0,X3,X2,X1] :
( in(sK5(X0,set_difference(X1,X2),set_difference(X1,X3)),X3)
| in(sK5(X0,set_difference(X1,X2),set_difference(X1,X3)),X0)
| ~ in(sK5(X0,set_difference(X1,X2),set_difference(X1,X3)),set_difference(X1,X2))
| sP0(X0,set_difference(X1,X2),set_difference(X1,X3))
| ~ empty(set_difference(X1,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_187])]) ).
fof(f593,plain,
( spl8_69
<=> ! [X0,X3,X2,X1] :
( sP0(X0,set_difference(X1,X2),X3)
| ~ empty(X3)
| in(sK5(X0,set_difference(X1,X2),X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_69])]) ).
fof(f993,plain,
( ! [X2,X3,X0,X1] :
( in(sK5(X0,set_difference(X1,X2),set_difference(X1,X3)),X3)
| in(sK5(X0,set_difference(X1,X2),set_difference(X1,X3)),X0)
| ~ in(sK5(X0,set_difference(X1,X2),set_difference(X1,X3)),set_difference(X1,X2))
| sP0(X0,set_difference(X1,X2),set_difference(X1,X3))
| ~ empty(set_difference(X1,X3)) )
| ~ spl8_69
| ~ spl8_83 ),
inference(duplicate_literal_removal,[],[f984]) ).
fof(f984,plain,
( ! [X2,X3,X0,X1] :
( in(sK5(X0,set_difference(X1,X2),set_difference(X1,X3)),X3)
| in(sK5(X0,set_difference(X1,X2),set_difference(X1,X3)),X0)
| ~ in(sK5(X0,set_difference(X1,X2),set_difference(X1,X3)),set_difference(X1,X2))
| sP0(X0,set_difference(X1,X2),set_difference(X1,X3))
| ~ empty(set_difference(X1,X3))
| sP0(X0,set_difference(X1,X2),set_difference(X1,X3)) )
| ~ spl8_69
| ~ spl8_83 ),
inference(resolution,[],[f974,f594]) ).
fof(f594,plain,
( ! [X2,X3,X0,X1] :
( in(sK5(X0,set_difference(X1,X2),X3),X1)
| ~ empty(X3)
| sP0(X0,set_difference(X1,X2),X3) )
| ~ spl8_69 ),
inference(avatar_component_clause,[],[f593]) ).
fof(f4325,plain,
( spl8_186
| ~ spl8_37
| ~ spl8_73 ),
inference(avatar_split_clause,[],[f710,f700,f296,f4323]) ).
fof(f4323,plain,
( spl8_186
<=> ! [X0,X3,X2,X1] :
( sP0(X0,set_difference(X1,set_difference(X2,X3)),set_difference(X1,set_difference(X2,X3)))
| ~ in(sK5(X0,set_difference(X1,set_difference(X2,X3)),set_difference(X1,set_difference(X2,X3))),X2)
| in(sK5(X0,set_difference(X1,set_difference(X2,X3)),set_difference(X1,set_difference(X2,X3))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_186])]) ).
fof(f710,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,set_difference(X1,set_difference(X2,X3)),set_difference(X1,set_difference(X2,X3)))
| ~ in(sK5(X0,set_difference(X1,set_difference(X2,X3)),set_difference(X1,set_difference(X2,X3))),X2)
| in(sK5(X0,set_difference(X1,set_difference(X2,X3)),set_difference(X1,set_difference(X2,X3))),X3) )
| ~ spl8_37
| ~ spl8_73 ),
inference(resolution,[],[f701,f297]) ).
fof(f4168,plain,
( spl8_185
| ~ spl8_37
| ~ spl8_80 ),
inference(avatar_split_clause,[],[f900,f774,f296,f4166]) ).
fof(f4166,plain,
( spl8_185
<=> ! [X4,X0,X3,X2,X1] :
( in(sK5(X0,set_difference(X1,set_difference(X2,X3)),X4),X4)
| sP0(X0,set_difference(X1,set_difference(X2,X3)),X4)
| ~ in(sK5(X0,set_difference(X1,set_difference(X2,X3)),X4),X2)
| in(sK5(X0,set_difference(X1,set_difference(X2,X3)),X4),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_185])]) ).
fof(f900,plain,
( ! [X2,X3,X0,X1,X4] :
( in(sK5(X0,set_difference(X1,set_difference(X2,X3)),X4),X4)
| sP0(X0,set_difference(X1,set_difference(X2,X3)),X4)
| ~ in(sK5(X0,set_difference(X1,set_difference(X2,X3)),X4),X2)
| in(sK5(X0,set_difference(X1,set_difference(X2,X3)),X4),X3) )
| ~ spl8_37
| ~ spl8_80 ),
inference(resolution,[],[f775,f297]) ).
fof(f4164,plain,
( spl8_184
| ~ spl8_37
| ~ spl8_79 ),
inference(avatar_split_clause,[],[f866,f770,f296,f4162]) ).
fof(f4162,plain,
( spl8_184
<=> ! [X4,X0,X3,X2,X1] :
( in(sK5(X0,X1,set_difference(X2,set_difference(X3,X4))),X1)
| sP0(X0,X1,set_difference(X2,set_difference(X3,X4)))
| ~ in(sK5(X0,X1,set_difference(X2,set_difference(X3,X4))),X3)
| in(sK5(X0,X1,set_difference(X2,set_difference(X3,X4))),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_184])]) ).
fof(f866,plain,
( ! [X2,X3,X0,X1,X4] :
( in(sK5(X0,X1,set_difference(X2,set_difference(X3,X4))),X1)
| sP0(X0,X1,set_difference(X2,set_difference(X3,X4)))
| ~ in(sK5(X0,X1,set_difference(X2,set_difference(X3,X4))),X3)
| in(sK5(X0,X1,set_difference(X2,set_difference(X3,X4))),X4) )
| ~ spl8_37
| ~ spl8_79 ),
inference(resolution,[],[f771,f297]) ).
fof(f4138,plain,
( spl8_183
| ~ spl8_37
| ~ spl8_76 ),
inference(avatar_split_clause,[],[f753,f747,f296,f4136]) ).
fof(f4136,plain,
( spl8_183
<=> ! [X0,X3,X2,X1] :
( in(sK4(X0,set_difference(set_difference(X1,X2),X3)),X3)
| subset(X0,set_difference(set_difference(X1,X2),X3))
| ~ in(sK4(X0,set_difference(set_difference(X1,X2),X3)),X1)
| in(sK4(X0,set_difference(set_difference(X1,X2),X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_183])]) ).
fof(f753,plain,
( ! [X2,X3,X0,X1] :
( in(sK4(X0,set_difference(set_difference(X1,X2),X3)),X3)
| subset(X0,set_difference(set_difference(X1,X2),X3))
| ~ in(sK4(X0,set_difference(set_difference(X1,X2),X3)),X1)
| in(sK4(X0,set_difference(set_difference(X1,X2),X3)),X2) )
| ~ spl8_37
| ~ spl8_76 ),
inference(resolution,[],[f748,f297]) ).
fof(f3983,plain,
( spl8_182
| ~ spl8_10
| ~ spl8_89 ),
inference(avatar_split_clause,[],[f1059,f1044,f108,f3981]) ).
fof(f3981,plain,
( spl8_182
<=> ! [X0] :
( subset(sK1,set_difference(sK2,X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_182])]) ).
fof(f1059,plain,
( ! [X0] :
( subset(sK1,set_difference(sK2,X0))
| ~ empty(X0) )
| ~ spl8_10
| ~ spl8_89 ),
inference(resolution,[],[f1045,f109]) ).
fof(f3979,plain,
( spl8_181
| ~ spl8_37
| ~ spl8_71 ),
inference(avatar_split_clause,[],[f667,f601,f296,f3977]) ).
fof(f667,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ empty(X0)
| sP0(X1,X0,set_difference(X2,set_difference(X3,X4)))
| ~ in(sK5(X1,X0,set_difference(X2,set_difference(X3,X4))),X3)
| in(sK5(X1,X0,set_difference(X2,set_difference(X3,X4))),X4) )
| ~ spl8_37
| ~ spl8_71 ),
inference(resolution,[],[f602,f297]) ).
fof(f3975,plain,
( spl8_180
| ~ spl8_37
| ~ spl8_68 ),
inference(avatar_split_clause,[],[f628,f589,f296,f3973]) ).
fof(f628,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ empty(X0)
| sP0(X1,set_difference(X2,set_difference(X3,X4)),X0)
| ~ in(sK5(X1,set_difference(X2,set_difference(X3,X4)),X0),X3)
| in(sK5(X1,set_difference(X2,set_difference(X3,X4)),X0),X4) )
| ~ spl8_37
| ~ spl8_68 ),
inference(resolution,[],[f590,f297]) ).
fof(f3064,plain,
( spl8_179
| ~ spl8_78
| ~ spl8_82 ),
inference(avatar_split_clause,[],[f957,f920,f766,f3062]) ).
fof(f3062,plain,
( spl8_179
<=> ! [X0,X3,X2,X1] :
( in(sK5(set_difference(X0,X1),set_difference(X0,X2),X3),X1)
| sP0(set_difference(X0,X1),set_difference(X0,X2),X3)
| in(sK5(set_difference(X0,X1),set_difference(X0,X2),X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_179])]) ).
fof(f766,plain,
( spl8_78
<=> ! [X0,X3,X2,X1] :
( in(sK5(X0,set_difference(X1,X2),X3),X1)
| in(sK5(X0,set_difference(X1,X2),X3),X3)
| sP0(X0,set_difference(X1,X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_78])]) ).
fof(f957,plain,
( ! [X2,X3,X0,X1] :
( in(sK5(set_difference(X0,X1),set_difference(X0,X2),X3),X1)
| sP0(set_difference(X0,X1),set_difference(X0,X2),X3)
| in(sK5(set_difference(X0,X1),set_difference(X0,X2),X3),X3) )
| ~ spl8_78
| ~ spl8_82 ),
inference(duplicate_literal_removal,[],[f937]) ).
fof(f937,plain,
( ! [X2,X3,X0,X1] :
( in(sK5(set_difference(X0,X1),set_difference(X0,X2),X3),X1)
| sP0(set_difference(X0,X1),set_difference(X0,X2),X3)
| in(sK5(set_difference(X0,X1),set_difference(X0,X2),X3),X3)
| in(sK5(set_difference(X0,X1),set_difference(X0,X2),X3),X3)
| sP0(set_difference(X0,X1),set_difference(X0,X2),X3) )
| ~ spl8_78
| ~ spl8_82 ),
inference(resolution,[],[f921,f767]) ).
fof(f767,plain,
( ! [X2,X3,X0,X1] :
( in(sK5(X0,set_difference(X1,X2),X3),X3)
| in(sK5(X0,set_difference(X1,X2),X3),X1)
| sP0(X0,set_difference(X1,X2),X3) )
| ~ spl8_78 ),
inference(avatar_component_clause,[],[f766]) ).
fof(f3060,plain,
( spl8_178
| ~ spl8_32
| ~ spl8_78 ),
inference(avatar_split_clause,[],[f835,f766,f245,f3058]) ).
fof(f3058,plain,
( spl8_178
<=> ! [X4,X0,X3,X2,X1] :
( in(sK5(X0,set_difference(set_difference(X1,X2),X3),X4),X4)
| sP0(X0,set_difference(set_difference(X1,X2),X3),X4)
| in(sK5(X0,set_difference(set_difference(X1,X2),X3),X4),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_178])]) ).
fof(f835,plain,
( ! [X2,X3,X0,X1,X4] :
( in(sK5(X0,set_difference(set_difference(X1,X2),X3),X4),X4)
| sP0(X0,set_difference(set_difference(X1,X2),X3),X4)
| in(sK5(X0,set_difference(set_difference(X1,X2),X3),X4),X1) )
| ~ spl8_32
| ~ spl8_78 ),
inference(resolution,[],[f767,f246]) ).
fof(f3056,plain,
( spl8_177
| ~ spl8_33
| ~ spl8_78 ),
inference(avatar_split_clause,[],[f834,f766,f249,f3054]) ).
fof(f3054,plain,
( spl8_177
<=> ! [X4,X0,X3,X2,X1] :
( in(sK5(X0,set_difference(set_difference(X1,X2),X3),X4),X4)
| sP0(X0,set_difference(set_difference(X1,X2),X3),X4)
| ~ in(sK5(X0,set_difference(set_difference(X1,X2),X3),X4),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_177])]) ).
fof(f834,plain,
( ! [X2,X3,X0,X1,X4] :
( in(sK5(X0,set_difference(set_difference(X1,X2),X3),X4),X4)
| sP0(X0,set_difference(set_difference(X1,X2),X3),X4)
| ~ in(sK5(X0,set_difference(set_difference(X1,X2),X3),X4),X2) )
| ~ spl8_33
| ~ spl8_78 ),
inference(resolution,[],[f767,f250]) ).
fof(f3052,plain,
( spl8_176
| ~ spl8_33
| ~ spl8_78 ),
inference(avatar_split_clause,[],[f822,f766,f249,f3050]) ).
fof(f3050,plain,
( spl8_176
<=> ! [X4,X0,X3,X2,X1] :
( in(sK5(X0,set_difference(X1,X2),set_difference(X3,X4)),X1)
| sP0(X0,set_difference(X1,X2),set_difference(X3,X4))
| ~ in(sK5(X0,set_difference(X1,X2),set_difference(X3,X4)),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_176])]) ).
fof(f822,plain,
( ! [X2,X3,X0,X1,X4] :
( in(sK5(X0,set_difference(X1,X2),set_difference(X3,X4)),X1)
| sP0(X0,set_difference(X1,X2),set_difference(X3,X4))
| ~ in(sK5(X0,set_difference(X1,X2),set_difference(X3,X4)),X4) )
| ~ spl8_33
| ~ spl8_78 ),
inference(resolution,[],[f767,f250]) ).
fof(f3048,plain,
( spl8_175
| ~ spl8_32
| ~ spl8_77 ),
inference(avatar_split_clause,[],[f795,f762,f245,f3046]) ).
fof(f3046,plain,
( spl8_175
<=> ! [X4,X0,X3,X2,X1] :
( in(sK5(X0,set_difference(X1,X2),set_difference(X3,X4)),X3)
| sP0(X0,set_difference(X1,X2),set_difference(X3,X4))
| in(sK5(X0,set_difference(X1,X2),set_difference(X3,X4)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_175])]) ).
fof(f762,plain,
( spl8_77
<=> ! [X0,X3,X2,X1] :
( in(sK5(X0,X1,set_difference(X2,X3)),X2)
| in(sK5(X0,X1,set_difference(X2,X3)),X1)
| sP0(X0,X1,set_difference(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_77])]) ).
fof(f795,plain,
( ! [X2,X3,X0,X1,X4] :
( in(sK5(X0,set_difference(X1,X2),set_difference(X3,X4)),X3)
| sP0(X0,set_difference(X1,X2),set_difference(X3,X4))
| in(sK5(X0,set_difference(X1,X2),set_difference(X3,X4)),X1) )
| ~ spl8_32
| ~ spl8_77 ),
inference(resolution,[],[f763,f246]) ).
fof(f763,plain,
( ! [X2,X3,X0,X1] :
( in(sK5(X0,X1,set_difference(X2,X3)),X2)
| in(sK5(X0,X1,set_difference(X2,X3)),X1)
| sP0(X0,X1,set_difference(X2,X3)) )
| ~ spl8_77 ),
inference(avatar_component_clause,[],[f762]) ).
fof(f3044,plain,
( spl8_174
| ~ spl8_33
| ~ spl8_77 ),
inference(avatar_split_clause,[],[f794,f762,f249,f3042]) ).
fof(f3042,plain,
( spl8_174
<=> ! [X4,X0,X3,X2,X1] :
( in(sK5(X0,set_difference(X1,X2),set_difference(X3,X4)),X3)
| sP0(X0,set_difference(X1,X2),set_difference(X3,X4))
| ~ in(sK5(X0,set_difference(X1,X2),set_difference(X3,X4)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_174])]) ).
fof(f794,plain,
( ! [X2,X3,X0,X1,X4] :
( in(sK5(X0,set_difference(X1,X2),set_difference(X3,X4)),X3)
| sP0(X0,set_difference(X1,X2),set_difference(X3,X4))
| ~ in(sK5(X0,set_difference(X1,X2),set_difference(X3,X4)),X2) )
| ~ spl8_33
| ~ spl8_77 ),
inference(resolution,[],[f763,f250]) ).
fof(f3040,plain,
( spl8_173
| ~ spl8_32
| ~ spl8_77 ),
inference(avatar_split_clause,[],[f785,f762,f245,f3038]) ).
fof(f3038,plain,
( spl8_173
<=> ! [X4,X0,X3,X2,X1] :
( in(sK5(X0,X1,set_difference(set_difference(X2,X3),X4)),X1)
| sP0(X0,X1,set_difference(set_difference(X2,X3),X4))
| in(sK5(X0,X1,set_difference(set_difference(X2,X3),X4)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_173])]) ).
fof(f785,plain,
( ! [X2,X3,X0,X1,X4] :
( in(sK5(X0,X1,set_difference(set_difference(X2,X3),X4)),X1)
| sP0(X0,X1,set_difference(set_difference(X2,X3),X4))
| in(sK5(X0,X1,set_difference(set_difference(X2,X3),X4)),X2) )
| ~ spl8_32
| ~ spl8_77 ),
inference(resolution,[],[f763,f246]) ).
fof(f3036,plain,
( spl8_172
| ~ spl8_33
| ~ spl8_77 ),
inference(avatar_split_clause,[],[f784,f762,f249,f3034]) ).
fof(f3034,plain,
( spl8_172
<=> ! [X4,X0,X3,X2,X1] :
( in(sK5(X0,X1,set_difference(set_difference(X2,X3),X4)),X1)
| sP0(X0,X1,set_difference(set_difference(X2,X3),X4))
| ~ in(sK5(X0,X1,set_difference(set_difference(X2,X3),X4)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_172])]) ).
fof(f784,plain,
( ! [X2,X3,X0,X1,X4] :
( in(sK5(X0,X1,set_difference(set_difference(X2,X3),X4)),X1)
| sP0(X0,X1,set_difference(set_difference(X2,X3),X4))
| ~ in(sK5(X0,X1,set_difference(set_difference(X2,X3),X4)),X3) )
| ~ spl8_33
| ~ spl8_77 ),
inference(resolution,[],[f763,f250]) ).
fof(f3032,plain,
( spl8_171
| ~ spl8_37
| ~ spl8_65 ),
inference(avatar_split_clause,[],[f558,f547,f296,f3030]) ).
fof(f547,plain,
( spl8_65
<=> ! [X2,X0,X1] :
( sP0(X0,X0,set_difference(X1,X2))
| ~ in(sK5(X0,X0,set_difference(X1,X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_65])]) ).
fof(f558,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,X0,set_difference(X1,set_difference(X2,X3)))
| ~ in(sK5(X0,X0,set_difference(X1,set_difference(X2,X3))),X2)
| in(sK5(X0,X0,set_difference(X1,set_difference(X2,X3))),X3) )
| ~ spl8_37
| ~ spl8_65 ),
inference(resolution,[],[f548,f297]) ).
fof(f548,plain,
( ! [X2,X0,X1] :
( ~ in(sK5(X0,X0,set_difference(X1,X2)),X2)
| sP0(X0,X0,set_difference(X1,X2)) )
| ~ spl8_65 ),
inference(avatar_component_clause,[],[f547]) ).
fof(f3028,plain,
( spl8_170
| ~ spl8_32
| ~ spl8_152 ),
inference(avatar_split_clause,[],[f2381,f2112,f245,f3026]) ).
fof(f3026,plain,
( spl8_170
<=> ! [X0] :
( ~ in(X0,sK7)
| in(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_170])]) ).
fof(f2112,plain,
( spl8_152
<=> sK7 = set_difference(sK1,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_152])]) ).
fof(f2381,plain,
( ! [X0] :
( ~ in(X0,sK7)
| in(X0,sK1) )
| ~ spl8_32
| ~ spl8_152 ),
inference(superposition,[],[f246,f2114]) ).
fof(f2114,plain,
( sK7 = set_difference(sK1,sK2)
| ~ spl8_152 ),
inference(avatar_component_clause,[],[f2112]) ).
fof(f2935,plain,
( spl8_169
| ~ spl8_32
| ~ spl8_74 ),
inference(avatar_split_clause,[],[f733,f704,f245,f2933]) ).
fof(f2933,plain,
( spl8_169
<=> ! [X0,X3,X2,X1] :
( sP0(X0,set_difference(set_difference(X1,X2),X3),set_difference(set_difference(X1,X2),X3))
| in(sK5(X0,set_difference(set_difference(X1,X2),X3),set_difference(set_difference(X1,X2),X3)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_169])]) ).
fof(f704,plain,
( spl8_74
<=> ! [X2,X0,X1] :
( sP0(X0,set_difference(X1,X2),set_difference(X1,X2))
| in(sK5(X0,set_difference(X1,X2),set_difference(X1,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_74])]) ).
fof(f733,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,set_difference(set_difference(X1,X2),X3),set_difference(set_difference(X1,X2),X3))
| in(sK5(X0,set_difference(set_difference(X1,X2),X3),set_difference(set_difference(X1,X2),X3)),X1) )
| ~ spl8_32
| ~ spl8_74 ),
inference(resolution,[],[f705,f246]) ).
fof(f705,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,set_difference(X1,X2),set_difference(X1,X2)),X1)
| sP0(X0,set_difference(X1,X2),set_difference(X1,X2)) )
| ~ spl8_74 ),
inference(avatar_component_clause,[],[f704]) ).
fof(f2931,plain,
( spl8_168
| ~ spl8_33
| ~ spl8_74 ),
inference(avatar_split_clause,[],[f732,f704,f249,f2929]) ).
fof(f2929,plain,
( spl8_168
<=> ! [X0,X3,X2,X1] :
( sP0(X0,set_difference(set_difference(X1,X2),X3),set_difference(set_difference(X1,X2),X3))
| ~ in(sK5(X0,set_difference(set_difference(X1,X2),X3),set_difference(set_difference(X1,X2),X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_168])]) ).
fof(f732,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,set_difference(set_difference(X1,X2),X3),set_difference(set_difference(X1,X2),X3))
| ~ in(sK5(X0,set_difference(set_difference(X1,X2),X3),set_difference(set_difference(X1,X2),X3)),X2) )
| ~ spl8_33
| ~ spl8_74 ),
inference(resolution,[],[f705,f250]) ).
fof(f2907,plain,
( spl8_167
| ~ spl8_37
| ~ spl8_62 ),
inference(avatar_split_clause,[],[f537,f511,f296,f2905]) ).
fof(f537,plain,
( ! [X2,X3,X0,X1] :
( subset(set_difference(X0,set_difference(X1,X2)),X3)
| ~ in(sK4(set_difference(X0,set_difference(X1,X2)),X3),X1)
| in(sK4(set_difference(X0,set_difference(X1,X2)),X3),X2) )
| ~ spl8_37
| ~ spl8_62 ),
inference(resolution,[],[f512,f297]) ).
fof(f2799,plain,
( spl8_166
| ~ spl8_23
| ~ spl8_82 ),
inference(avatar_split_clause,[],[f964,f920,f179,f2797]) ).
fof(f2797,plain,
( spl8_166
<=> ! [X2,X0,X1] :
( in(sK5(set_difference(X0,X1),X0,X2),X1)
| sP0(set_difference(X0,X1),X0,X2)
| in(sK5(set_difference(X0,X1),X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_166])]) ).
fof(f179,plain,
( spl8_23
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(sK5(X0,X1,X2),X1)
| in(sK5(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_23])]) ).
fof(f964,plain,
( ! [X2,X0,X1] :
( in(sK5(set_difference(X0,X1),X0,X2),X1)
| sP0(set_difference(X0,X1),X0,X2)
| in(sK5(set_difference(X0,X1),X0,X2),X2) )
| ~ spl8_23
| ~ spl8_82 ),
inference(duplicate_literal_removal,[],[f930]) ).
fof(f930,plain,
( ! [X2,X0,X1] :
( in(sK5(set_difference(X0,X1),X0,X2),X1)
| sP0(set_difference(X0,X1),X0,X2)
| in(sK5(set_difference(X0,X1),X0,X2),X2)
| in(sK5(set_difference(X0,X1),X0,X2),X2)
| sP0(set_difference(X0,X1),X0,X2) )
| ~ spl8_23
| ~ spl8_82 ),
inference(resolution,[],[f921,f180]) ).
fof(f180,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,X1,X2),X2)
| in(sK5(X0,X1,X2),X1)
| sP0(X0,X1,X2) )
| ~ spl8_23 ),
inference(avatar_component_clause,[],[f179]) ).
fof(f2795,plain,
( spl8_165
| ~ spl8_11
| ~ spl8_78 ),
inference(avatar_split_clause,[],[f827,f766,f114,f2793]) ).
fof(f2793,plain,
( spl8_165
<=> ! [X0,X3,X2,X1] :
( in(sK5(X0,set_difference(X1,X2),X3),X3)
| sP0(X0,set_difference(X1,X2),X3)
| ~ in(X1,sK5(X0,set_difference(X1,X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_165])]) ).
fof(f827,plain,
( ! [X2,X3,X0,X1] :
( in(sK5(X0,set_difference(X1,X2),X3),X3)
| sP0(X0,set_difference(X1,X2),X3)
| ~ in(X1,sK5(X0,set_difference(X1,X2),X3)) )
| ~ spl8_11
| ~ spl8_78 ),
inference(resolution,[],[f767,f115]) ).
fof(f2791,plain,
( spl8_164
| ~ spl8_11
| ~ spl8_78 ),
inference(avatar_split_clause,[],[f818,f766,f114,f2789]) ).
fof(f2789,plain,
( spl8_164
<=> ! [X0,X3,X2,X1] :
( in(sK5(X0,set_difference(X1,X2),X3),X1)
| sP0(X0,set_difference(X1,X2),X3)
| ~ in(X3,sK5(X0,set_difference(X1,X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_164])]) ).
fof(f818,plain,
( ! [X2,X3,X0,X1] :
( in(sK5(X0,set_difference(X1,X2),X3),X1)
| sP0(X0,set_difference(X1,X2),X3)
| ~ in(X3,sK5(X0,set_difference(X1,X2),X3)) )
| ~ spl8_11
| ~ spl8_78 ),
inference(resolution,[],[f767,f115]) ).
fof(f2787,plain,
( spl8_163
| ~ spl8_11
| ~ spl8_77 ),
inference(avatar_split_clause,[],[f789,f762,f114,f2785]) ).
fof(f2785,plain,
( spl8_163
<=> ! [X0,X3,X2,X1] :
( in(sK5(X0,X1,set_difference(X2,X3)),X2)
| sP0(X0,X1,set_difference(X2,X3))
| ~ in(X1,sK5(X0,X1,set_difference(X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_163])]) ).
fof(f789,plain,
( ! [X2,X3,X0,X1] :
( in(sK5(X0,X1,set_difference(X2,X3)),X2)
| sP0(X0,X1,set_difference(X2,X3))
| ~ in(X1,sK5(X0,X1,set_difference(X2,X3))) )
| ~ spl8_11
| ~ spl8_77 ),
inference(resolution,[],[f763,f115]) ).
fof(f2783,plain,
( spl8_162
| ~ spl8_11
| ~ spl8_77 ),
inference(avatar_split_clause,[],[f778,f762,f114,f2781]) ).
fof(f2781,plain,
( spl8_162
<=> ! [X0,X3,X2,X1] :
( in(sK5(X0,X1,set_difference(X2,X3)),X1)
| sP0(X0,X1,set_difference(X2,X3))
| ~ in(X2,sK5(X0,X1,set_difference(X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_162])]) ).
fof(f778,plain,
( ! [X2,X3,X0,X1] :
( in(sK5(X0,X1,set_difference(X2,X3)),X1)
| sP0(X0,X1,set_difference(X2,X3))
| ~ in(X2,sK5(X0,X1,set_difference(X2,X3))) )
| ~ spl8_11
| ~ spl8_77 ),
inference(resolution,[],[f763,f115]) ).
fof(f2566,plain,
( spl8_161
| ~ spl8_12
| ~ spl8_152 ),
inference(avatar_split_clause,[],[f2380,f2112,f118,f2563]) ).
fof(f2563,plain,
( spl8_161
<=> sP0(sK2,sK1,sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_161])]) ).
fof(f118,plain,
( spl8_12
<=> ! [X0,X1] : sP0(X1,X0,set_difference(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_12])]) ).
fof(f2380,plain,
( sP0(sK2,sK1,sK7)
| ~ spl8_12
| ~ spl8_152 ),
inference(superposition,[],[f119,f2114]) ).
fof(f119,plain,
( ! [X0,X1] : sP0(X1,X0,set_difference(X0,X1))
| ~ spl8_12 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f2555,plain,
( spl8_160
| ~ spl8_32
| ~ spl8_72 ),
inference(avatar_split_clause,[],[f686,f605,f245,f2553]) ).
fof(f605,plain,
( spl8_72
<=> ! [X0,X3,X2,X1] :
( sP0(X0,X1,set_difference(X2,X3))
| ~ empty(X1)
| in(sK5(X0,X1,set_difference(X2,X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_72])]) ).
fof(f686,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ empty(X0)
| sP0(X1,X0,set_difference(set_difference(X2,X3),X4))
| in(sK5(X1,X0,set_difference(set_difference(X2,X3),X4)),X2) )
| ~ spl8_32
| ~ spl8_72 ),
inference(resolution,[],[f606,f246]) ).
fof(f606,plain,
( ! [X2,X3,X0,X1] :
( in(sK5(X0,X1,set_difference(X2,X3)),X2)
| ~ empty(X1)
| sP0(X0,X1,set_difference(X2,X3)) )
| ~ spl8_72 ),
inference(avatar_component_clause,[],[f605]) ).
fof(f2551,plain,
( spl8_159
| ~ spl8_33
| ~ spl8_72 ),
inference(avatar_split_clause,[],[f685,f605,f249,f2549]) ).
fof(f2549,plain,
( spl8_159
<=> ! [X4,X0,X3,X2,X1] :
( ~ empty(X0)
| sP0(X1,X0,set_difference(set_difference(X2,X3),X4))
| ~ in(sK5(X1,X0,set_difference(set_difference(X2,X3),X4)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_159])]) ).
fof(f685,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ empty(X0)
| sP0(X1,X0,set_difference(set_difference(X2,X3),X4))
| ~ in(sK5(X1,X0,set_difference(set_difference(X2,X3),X4)),X3) )
| ~ spl8_33
| ~ spl8_72 ),
inference(resolution,[],[f606,f250]) ).
fof(f2547,plain,
( spl8_158
| ~ spl8_32
| ~ spl8_69 ),
inference(avatar_split_clause,[],[f648,f593,f245,f2545]) ).
fof(f648,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ empty(X0)
| sP0(X1,set_difference(set_difference(X2,X3),X4),X0)
| in(sK5(X1,set_difference(set_difference(X2,X3),X4),X0),X2) )
| ~ spl8_32
| ~ spl8_69 ),
inference(resolution,[],[f594,f246]) ).
fof(f2543,plain,
( spl8_157
| ~ spl8_33
| ~ spl8_69 ),
inference(avatar_split_clause,[],[f647,f593,f249,f2541]) ).
fof(f2541,plain,
( spl8_157
<=> ! [X4,X0,X3,X2,X1] :
( ~ empty(X0)
| sP0(X1,set_difference(set_difference(X2,X3),X4),X0)
| ~ in(sK5(X1,set_difference(set_difference(X2,X3),X4),X0),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_157])]) ).
fof(f647,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ empty(X0)
| sP0(X1,set_difference(set_difference(X2,X3),X4),X0)
| ~ in(sK5(X1,set_difference(set_difference(X2,X3),X4),X0),X3) )
| ~ spl8_33
| ~ spl8_69 ),
inference(resolution,[],[f594,f250]) ).
fof(f2539,plain,
( spl8_156
| ~ spl8_37
| ~ spl8_60 ),
inference(avatar_split_clause,[],[f501,f498,f296,f2537]) ).
fof(f2537,plain,
( spl8_156
<=> ! [X0,X3,X2,X1] :
( in(set_difference(X0,X1),X2)
| ~ in(set_difference(X0,X1),X3)
| ~ in(set_difference(X3,X2),X0)
| in(set_difference(X3,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_156])]) ).
fof(f498,plain,
( spl8_60
<=> ! [X2,X0,X1] :
( ~ in(X0,X1)
| in(X0,X2)
| ~ in(set_difference(X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_60])]) ).
fof(f501,plain,
( ! [X2,X3,X0,X1] :
( in(set_difference(X0,X1),X2)
| ~ in(set_difference(X0,X1),X3)
| ~ in(set_difference(X3,X2),X0)
| in(set_difference(X3,X2),X1) )
| ~ spl8_37
| ~ spl8_60 ),
inference(resolution,[],[f499,f297]) ).
fof(f499,plain,
( ! [X2,X0,X1] :
( ~ in(set_difference(X1,X2),X0)
| in(X0,X2)
| ~ in(X0,X1) )
| ~ spl8_60 ),
inference(avatar_component_clause,[],[f498]) ).
fof(f2438,plain,
( spl8_155
| ~ spl8_11
| ~ spl8_74 ),
inference(avatar_split_clause,[],[f726,f704,f114,f2436]) ).
fof(f2436,plain,
( spl8_155
<=> ! [X2,X0,X1] :
( sP0(X0,set_difference(X1,X2),set_difference(X1,X2))
| ~ in(X1,sK5(X0,set_difference(X1,X2),set_difference(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_155])]) ).
fof(f726,plain,
( ! [X2,X0,X1] :
( sP0(X0,set_difference(X1,X2),set_difference(X1,X2))
| ~ in(X1,sK5(X0,set_difference(X1,X2),set_difference(X1,X2))) )
| ~ spl8_11
| ~ spl8_74 ),
inference(resolution,[],[f705,f115]) ).
fof(f2367,plain,
( spl8_154
| ~ spl8_32
| ~ spl8_66 ),
inference(avatar_split_clause,[],[f573,f551,f245,f2365]) ).
fof(f551,plain,
( spl8_66
<=> ! [X2,X0,X1] :
( sP0(X0,X0,set_difference(X1,X2))
| in(sK5(X0,X0,set_difference(X1,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_66])]) ).
fof(f573,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,X0,set_difference(set_difference(X1,X2),X3))
| in(sK5(X0,X0,set_difference(set_difference(X1,X2),X3)),X1) )
| ~ spl8_32
| ~ spl8_66 ),
inference(resolution,[],[f552,f246]) ).
fof(f552,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,X0,set_difference(X1,X2)),X1)
| sP0(X0,X0,set_difference(X1,X2)) )
| ~ spl8_66 ),
inference(avatar_component_clause,[],[f551]) ).
fof(f2363,plain,
( spl8_153
| ~ spl8_33
| ~ spl8_66 ),
inference(avatar_split_clause,[],[f572,f551,f249,f2361]) ).
fof(f2361,plain,
( spl8_153
<=> ! [X0,X3,X2,X1] :
( sP0(X0,X0,set_difference(set_difference(X1,X2),X3))
| ~ in(sK5(X0,X0,set_difference(set_difference(X1,X2),X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_153])]) ).
fof(f572,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,X0,set_difference(set_difference(X1,X2),X3))
| ~ in(sK5(X0,X0,set_difference(set_difference(X1,X2),X3)),X2) )
| ~ spl8_33
| ~ spl8_66 ),
inference(resolution,[],[f552,f250]) ).
fof(f2115,plain,
( spl8_152
| ~ spl8_3
| ~ spl8_13
| ~ spl8_18
| ~ spl8_111
| ~ spl8_132 ),
inference(avatar_split_clause,[],[f2058,f1760,f1513,f153,f122,f77,f2112]) ).
fof(f2058,plain,
( sK7 = set_difference(sK1,sK2)
| ~ spl8_3
| ~ spl8_13
| ~ spl8_18
| ~ spl8_111
| ~ spl8_132 ),
inference(forward_demodulation,[],[f2057,f1524]) ).
fof(f2057,plain,
( ! [X0] : set_difference(X0,X0) = set_difference(sK1,sK2)
| ~ spl8_18
| ~ spl8_132 ),
inference(resolution,[],[f1761,f154]) ).
fof(f2094,plain,
( spl8_151
| ~ spl8_8
| ~ spl8_13
| ~ spl8_80 ),
inference(avatar_split_clause,[],[f918,f774,f122,f100,f2092]) ).
fof(f2092,plain,
( spl8_151
<=> ! [X2,X0,X1] :
( ~ in(sK5(X1,X0,X2),sK7)
| in(sK5(X1,X0,X2),X2)
| sP0(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_151])]) ).
fof(f100,plain,
( spl8_8
<=> ! [X0] : set_difference(X0,empty_set) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl8_8])]) ).
fof(f918,plain,
( ! [X2,X0,X1] :
( ~ in(sK5(X1,X0,X2),sK7)
| in(sK5(X1,X0,X2),X2)
| sP0(X1,X0,X2) )
| ~ spl8_8
| ~ spl8_13
| ~ spl8_80 ),
inference(forward_demodulation,[],[f902,f124]) ).
fof(f902,plain,
( ! [X2,X0,X1] :
( ~ in(sK5(X1,X0,X2),empty_set)
| in(sK5(X1,X0,X2),X2)
| sP0(X1,X0,X2) )
| ~ spl8_8
| ~ spl8_80 ),
inference(superposition,[],[f775,f101]) ).
fof(f101,plain,
( ! [X0] : set_difference(X0,empty_set) = X0
| ~ spl8_8 ),
inference(avatar_component_clause,[],[f100]) ).
fof(f2090,plain,
( spl8_150
| ~ spl8_8
| ~ spl8_13
| ~ spl8_79 ),
inference(avatar_split_clause,[],[f882,f770,f122,f100,f2088]) ).
fof(f2088,plain,
( spl8_150
<=> ! [X2,X0,X1] :
( ~ in(sK5(X1,X2,X0),sK7)
| in(sK5(X1,X2,X0),X2)
| sP0(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_150])]) ).
fof(f882,plain,
( ! [X2,X0,X1] :
( ~ in(sK5(X1,X2,X0),sK7)
| in(sK5(X1,X2,X0),X2)
| sP0(X1,X2,X0) )
| ~ spl8_8
| ~ spl8_13
| ~ spl8_79 ),
inference(forward_demodulation,[],[f868,f124]) ).
fof(f868,plain,
( ! [X2,X0,X1] :
( ~ in(sK5(X1,X2,X0),empty_set)
| in(sK5(X1,X2,X0),X2)
| sP0(X1,X2,X0) )
| ~ spl8_8
| ~ spl8_79 ),
inference(superposition,[],[f771,f101]) ).
fof(f2086,plain,
( spl8_149
| ~ spl8_10
| ~ spl8_78 ),
inference(avatar_split_clause,[],[f828,f766,f108,f2084]) ).
fof(f2084,plain,
( spl8_149
<=> ! [X0,X3,X2,X1] :
( in(sK5(X0,set_difference(X1,X2),X3),X3)
| sP0(X0,set_difference(X1,X2),X3)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_149])]) ).
fof(f828,plain,
( ! [X2,X3,X0,X1] :
( in(sK5(X0,set_difference(X1,X2),X3),X3)
| sP0(X0,set_difference(X1,X2),X3)
| ~ empty(X1) )
| ~ spl8_10
| ~ spl8_78 ),
inference(resolution,[],[f767,f109]) ).
fof(f2082,plain,
( spl8_148
| ~ spl8_10
| ~ spl8_77 ),
inference(avatar_split_clause,[],[f779,f762,f108,f2080]) ).
fof(f2080,plain,
( spl8_148
<=> ! [X0,X3,X2,X1] :
( in(sK5(X0,X1,set_difference(X2,X3)),X1)
| sP0(X0,X1,set_difference(X2,X3))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_148])]) ).
fof(f779,plain,
( ! [X2,X3,X0,X1] :
( in(sK5(X0,X1,set_difference(X2,X3)),X1)
| sP0(X0,X1,set_difference(X2,X3))
| ~ empty(X2) )
| ~ spl8_10
| ~ spl8_77 ),
inference(resolution,[],[f763,f109]) ).
fof(f2078,plain,
( spl8_147
| ~ spl8_61
| ~ spl8_76 ),
inference(avatar_split_clause,[],[f759,f747,f507,f2076]) ).
fof(f507,plain,
( spl8_61
<=> ! [X2,X0,X1] :
( in(sK4(set_difference(X0,X1),X2),X0)
| subset(set_difference(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_61])]) ).
fof(f759,plain,
( ! [X2,X0,X1] :
( in(sK4(set_difference(X0,X1),set_difference(X0,X2)),X2)
| subset(set_difference(X0,X1),set_difference(X0,X2)) )
| ~ spl8_61
| ~ spl8_76 ),
inference(duplicate_literal_removal,[],[f751]) ).
fof(f751,plain,
( ! [X2,X0,X1] :
( in(sK4(set_difference(X0,X1),set_difference(X0,X2)),X2)
| subset(set_difference(X0,X1),set_difference(X0,X2))
| subset(set_difference(X0,X1),set_difference(X0,X2)) )
| ~ spl8_61
| ~ spl8_76 ),
inference(resolution,[],[f748,f508]) ).
fof(f508,plain,
( ! [X2,X0,X1] :
( in(sK4(set_difference(X0,X1),X2),X0)
| subset(set_difference(X0,X1),X2) )
| ~ spl8_61 ),
inference(avatar_component_clause,[],[f507]) ).
fof(f2074,plain,
( spl8_146
| ~ spl8_11
| ~ spl8_72 ),
inference(avatar_split_clause,[],[f680,f605,f114,f2072]) ).
fof(f2072,plain,
( spl8_146
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP0(X1,X0,set_difference(X2,X3))
| ~ in(X2,sK5(X1,X0,set_difference(X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_146])]) ).
fof(f680,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP0(X1,X0,set_difference(X2,X3))
| ~ in(X2,sK5(X1,X0,set_difference(X2,X3))) )
| ~ spl8_11
| ~ spl8_72 ),
inference(resolution,[],[f606,f115]) ).
fof(f2070,plain,
( spl8_145
| ~ spl8_11
| ~ spl8_69 ),
inference(avatar_split_clause,[],[f642,f593,f114,f2068]) ).
fof(f2068,plain,
( spl8_145
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP0(X1,set_difference(X2,X3),X0)
| ~ in(X2,sK5(X1,set_difference(X2,X3),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_145])]) ).
fof(f642,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP0(X1,set_difference(X2,X3),X0)
| ~ in(X2,sK5(X1,set_difference(X2,X3),X0)) )
| ~ spl8_11
| ~ spl8_69 ),
inference(resolution,[],[f594,f115]) ).
fof(f2066,plain,
( spl8_144
| ~ spl8_32
| ~ spl8_61 ),
inference(avatar_split_clause,[],[f526,f507,f245,f2064]) ).
fof(f526,plain,
( ! [X2,X3,X0,X1] :
( subset(set_difference(set_difference(X0,X1),X2),X3)
| in(sK4(set_difference(set_difference(X0,X1),X2),X3),X0) )
| ~ spl8_32
| ~ spl8_61 ),
inference(resolution,[],[f508,f246]) ).
fof(f2062,plain,
( spl8_143
| ~ spl8_33
| ~ spl8_61 ),
inference(avatar_split_clause,[],[f525,f507,f249,f2060]) ).
fof(f2060,plain,
( spl8_143
<=> ! [X0,X3,X2,X1] :
( subset(set_difference(set_difference(X0,X1),X2),X3)
| ~ in(sK4(set_difference(set_difference(X0,X1),X2),X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_143])]) ).
fof(f525,plain,
( ! [X2,X3,X0,X1] :
( subset(set_difference(set_difference(X0,X1),X2),X3)
| ~ in(sK4(set_difference(set_difference(X0,X1),X2),X3),X1) )
| ~ spl8_33
| ~ spl8_61 ),
inference(resolution,[],[f508,f250]) ).
fof(f1942,plain,
( spl8_142
| ~ spl8_3
| ~ spl8_13
| ~ spl8_111
| ~ spl8_141 ),
inference(avatar_split_clause,[],[f1938,f1934,f1513,f122,f77,f1940]) ).
fof(f1934,plain,
( spl8_141
<=> ! [X2,X0,X1] :
( in(sK5(X0,set_difference(X1,X1),X2),X2)
| sP0(X0,set_difference(X1,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_141])]) ).
fof(f1938,plain,
( ! [X2,X0] :
( sP0(X0,sK7,X2)
| in(sK5(X0,sK7,X2),X2) )
| ~ spl8_3
| ~ spl8_13
| ~ spl8_111
| ~ spl8_141 ),
inference(forward_demodulation,[],[f1937,f1524]) ).
fof(f1937,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,sK7,X2),X2)
| sP0(X0,set_difference(X1,X1),X2) )
| ~ spl8_3
| ~ spl8_13
| ~ spl8_111
| ~ spl8_141 ),
inference(forward_demodulation,[],[f1935,f1524]) ).
fof(f1935,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,set_difference(X1,X1),X2),X2)
| sP0(X0,set_difference(X1,X1),X2) )
| ~ spl8_141 ),
inference(avatar_component_clause,[],[f1934]) ).
fof(f1936,plain,
( spl8_141
| ~ spl8_78
| ~ spl8_80 ),
inference(avatar_split_clause,[],[f914,f774,f766,f1934]) ).
fof(f914,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,set_difference(X1,X1),X2),X2)
| sP0(X0,set_difference(X1,X1),X2) )
| ~ spl8_78
| ~ spl8_80 ),
inference(duplicate_literal_removal,[],[f887]) ).
fof(f887,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,set_difference(X1,X1),X2),X2)
| sP0(X0,set_difference(X1,X1),X2)
| in(sK5(X0,set_difference(X1,X1),X2),X2)
| sP0(X0,set_difference(X1,X1),X2) )
| ~ spl8_78
| ~ spl8_80 ),
inference(resolution,[],[f775,f767]) ).
fof(f1912,plain,
( spl8_140
| ~ spl8_3
| ~ spl8_13
| ~ spl8_111
| ~ spl8_139 ),
inference(avatar_split_clause,[],[f1908,f1904,f1513,f122,f77,f1910]) ).
fof(f1904,plain,
( spl8_139
<=> ! [X2,X0,X1] :
( in(sK5(X0,X1,set_difference(X2,X2)),X1)
| sP0(X0,X1,set_difference(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_139])]) ).
fof(f1908,plain,
( ! [X0,X1] :
( sP0(X0,X1,sK7)
| in(sK5(X0,X1,sK7),X1) )
| ~ spl8_3
| ~ spl8_13
| ~ spl8_111
| ~ spl8_139 ),
inference(forward_demodulation,[],[f1907,f1524]) ).
fof(f1907,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,X1,sK7),X1)
| sP0(X0,X1,set_difference(X2,X2)) )
| ~ spl8_3
| ~ spl8_13
| ~ spl8_111
| ~ spl8_139 ),
inference(forward_demodulation,[],[f1905,f1524]) ).
fof(f1905,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,X1,set_difference(X2,X2)),X1)
| sP0(X0,X1,set_difference(X2,X2)) )
| ~ spl8_139 ),
inference(avatar_component_clause,[],[f1904]) ).
fof(f1906,plain,
( spl8_139
| ~ spl8_77
| ~ spl8_79 ),
inference(avatar_split_clause,[],[f877,f770,f762,f1904]) ).
fof(f877,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,X1,set_difference(X2,X2)),X1)
| sP0(X0,X1,set_difference(X2,X2)) )
| ~ spl8_77
| ~ spl8_79 ),
inference(duplicate_literal_removal,[],[f856]) ).
fof(f856,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,X1,set_difference(X2,X2)),X1)
| sP0(X0,X1,set_difference(X2,X2))
| in(sK5(X0,X1,set_difference(X2,X2)),X1)
| sP0(X0,X1,set_difference(X2,X2)) )
| ~ spl8_77
| ~ spl8_79 ),
inference(resolution,[],[f771,f763]) ).
fof(f1898,plain,
( spl8_138
| ~ spl8_24
| ~ spl8_78 ),
inference(avatar_split_clause,[],[f848,f766,f183,f1896]) ).
fof(f848,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,set_difference(X0,X1),X2),X2)
| sP0(X0,set_difference(X0,X1),X2) )
| ~ spl8_24
| ~ spl8_78 ),
inference(duplicate_literal_removal,[],[f826]) ).
fof(f826,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,set_difference(X0,X1),X2),X2)
| sP0(X0,set_difference(X0,X1),X2)
| sP0(X0,set_difference(X0,X1),X2)
| in(sK5(X0,set_difference(X0,X1),X2),X2) )
| ~ spl8_24
| ~ spl8_78 ),
inference(resolution,[],[f767,f184]) ).
fof(f1894,plain,
( spl8_137
| ~ spl8_78 ),
inference(avatar_split_clause,[],[f838,f766,f1892]) ).
fof(f838,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,set_difference(X1,X2),X1),X1)
| sP0(X0,set_difference(X1,X2),X1) )
| ~ spl8_78 ),
inference(factoring,[],[f767]) ).
fof(f1890,plain,
( spl8_136
| ~ spl8_77 ),
inference(avatar_split_clause,[],[f798,f762,f1888]) ).
fof(f798,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,X1,set_difference(X1,X2)),X1)
| sP0(X0,X1,set_difference(X1,X2)) )
| ~ spl8_77 ),
inference(factoring,[],[f763]) ).
fof(f1886,plain,
( spl8_135
| ~ spl8_11
| ~ spl8_66 ),
inference(avatar_split_clause,[],[f569,f551,f114,f1884]) ).
fof(f1884,plain,
( spl8_135
<=> ! [X2,X0,X1] :
( sP0(X0,X0,set_difference(X1,X2))
| ~ in(X1,sK5(X0,X0,set_difference(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_135])]) ).
fof(f569,plain,
( ! [X2,X0,X1] :
( sP0(X0,X0,set_difference(X1,X2))
| ~ in(X1,sK5(X0,X0,set_difference(X1,X2))) )
| ~ spl8_11
| ~ spl8_66 ),
inference(resolution,[],[f552,f115]) ).
fof(f1770,plain,
( spl8_134
| ~ spl8_15
| ~ spl8_76 ),
inference(avatar_split_clause,[],[f760,f747,f137,f1768]) ).
fof(f760,plain,
( ! [X0,X1] :
( in(sK4(X0,set_difference(X0,X1)),X1)
| subset(X0,set_difference(X0,X1)) )
| ~ spl8_15
| ~ spl8_76 ),
inference(duplicate_literal_removal,[],[f750]) ).
fof(f750,plain,
( ! [X0,X1] :
( in(sK4(X0,set_difference(X0,X1)),X1)
| subset(X0,set_difference(X0,X1))
| subset(X0,set_difference(X0,X1)) )
| ~ spl8_15
| ~ spl8_76 ),
inference(resolution,[],[f748,f138]) ).
fof(f1766,plain,
( spl8_133
| ~ spl8_8
| ~ spl8_13
| ~ spl8_71 ),
inference(avatar_split_clause,[],[f678,f601,f122,f100,f1764]) ).
fof(f1764,plain,
( spl8_133
<=> ! [X2,X0,X1] :
( ~ in(sK5(X1,X2,X0),sK7)
| ~ empty(X2)
| sP0(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_133])]) ).
fof(f678,plain,
( ! [X2,X0,X1] :
( ~ in(sK5(X1,X2,X0),sK7)
| ~ empty(X2)
| sP0(X1,X2,X0) )
| ~ spl8_8
| ~ spl8_13
| ~ spl8_71 ),
inference(forward_demodulation,[],[f669,f124]) ).
fof(f669,plain,
( ! [X2,X0,X1] :
( ~ in(sK5(X1,X2,X0),empty_set)
| ~ empty(X2)
| sP0(X1,X2,X0) )
| ~ spl8_8
| ~ spl8_71 ),
inference(superposition,[],[f602,f101]) ).
fof(f1762,plain,
( spl8_132
| ~ spl8_65
| ~ spl8_90 ),
inference(avatar_split_clause,[],[f1093,f1069,f547,f1760]) ).
fof(f1093,plain,
( ! [X0] : sP0(X0,X0,set_difference(sK1,sK2))
| ~ spl8_65
| ~ spl8_90 ),
inference(duplicate_literal_removal,[],[f1080]) ).
fof(f1080,plain,
( ! [X0] :
( sP0(X0,X0,set_difference(sK1,sK2))
| sP0(X0,X0,set_difference(sK1,sK2)) )
| ~ spl8_65
| ~ spl8_90 ),
inference(resolution,[],[f1070,f548]) ).
fof(f1758,plain,
( spl8_131
| ~ spl8_8
| ~ spl8_13
| ~ spl8_68 ),
inference(avatar_split_clause,[],[f640,f589,f122,f100,f1756]) ).
fof(f1756,plain,
( spl8_131
<=> ! [X2,X0,X1] :
( ~ in(sK5(X1,X0,X2),sK7)
| ~ empty(X2)
| sP0(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_131])]) ).
fof(f640,plain,
( ! [X2,X0,X1] :
( ~ in(sK5(X1,X0,X2),sK7)
| ~ empty(X2)
| sP0(X1,X0,X2) )
| ~ spl8_8
| ~ spl8_13
| ~ spl8_68 ),
inference(forward_demodulation,[],[f630,f124]) ).
fof(f630,plain,
( ! [X2,X0,X1] :
( ~ in(sK5(X1,X0,X2),empty_set)
| ~ empty(X2)
| sP0(X1,X0,X2) )
| ~ spl8_8
| ~ spl8_68 ),
inference(superposition,[],[f590,f101]) ).
fof(f1754,plain,
( spl8_130
| ~ spl8_11
| ~ spl8_61 ),
inference(avatar_split_clause,[],[f523,f507,f114,f1752]) ).
fof(f1752,plain,
( spl8_130
<=> ! [X2,X0,X1] :
( subset(set_difference(X0,X1),X2)
| ~ in(X0,sK4(set_difference(X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_130])]) ).
fof(f523,plain,
( ! [X2,X0,X1] :
( subset(set_difference(X0,X1),X2)
| ~ in(X0,sK4(set_difference(X0,X1),X2)) )
| ~ spl8_11
| ~ spl8_61 ),
inference(resolution,[],[f508,f115]) ).
fof(f1639,plain,
( spl8_129
| ~ spl8_10
| ~ spl8_74 ),
inference(avatar_split_clause,[],[f727,f704,f108,f1637]) ).
fof(f1637,plain,
( spl8_129
<=> ! [X2,X0,X1] :
( sP0(X0,set_difference(X1,X2),set_difference(X1,X2))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_129])]) ).
fof(f727,plain,
( ! [X2,X0,X1] :
( sP0(X0,set_difference(X1,X2),set_difference(X1,X2))
| ~ empty(X1) )
| ~ spl8_10
| ~ spl8_74 ),
inference(resolution,[],[f705,f109]) ).
fof(f1635,plain,
( spl8_128
| ~ spl8_8
| ~ spl8_13
| ~ spl8_73 ),
inference(avatar_split_clause,[],[f720,f700,f122,f100,f1633]) ).
fof(f1633,plain,
( spl8_128
<=> ! [X0,X1] :
( ~ in(sK5(X1,X0,X0),sK7)
| sP0(X1,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_128])]) ).
fof(f720,plain,
( ! [X0,X1] :
( ~ in(sK5(X1,X0,X0),sK7)
| sP0(X1,X0,X0) )
| ~ spl8_8
| ~ spl8_13
| ~ spl8_73 ),
inference(forward_demodulation,[],[f712,f124]) ).
fof(f712,plain,
( ! [X0,X1] :
( ~ in(sK5(X1,X0,X0),empty_set)
| sP0(X1,X0,X0) )
| ~ spl8_8
| ~ spl8_73 ),
inference(superposition,[],[f701,f101]) ).
fof(f1631,plain,
( spl8_127
| ~ spl8_10
| ~ spl8_72 ),
inference(avatar_split_clause,[],[f681,f605,f108,f1629]) ).
fof(f1629,plain,
( spl8_127
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP0(X1,X0,set_difference(X2,X3))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_127])]) ).
fof(f681,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP0(X1,X0,set_difference(X2,X3))
| ~ empty(X2) )
| ~ spl8_10
| ~ spl8_72 ),
inference(resolution,[],[f606,f109]) ).
fof(f1627,plain,
( spl8_126
| ~ spl8_10
| ~ spl8_69 ),
inference(avatar_split_clause,[],[f643,f593,f108,f1625]) ).
fof(f1625,plain,
( spl8_126
<=> ! [X0,X3,X2,X1] :
( ~ empty(X0)
| sP0(X1,set_difference(X2,X3),X0)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_126])]) ).
fof(f643,plain,
( ! [X2,X3,X0,X1] :
( ~ empty(X0)
| sP0(X1,set_difference(X2,X3),X0)
| ~ empty(X2) )
| ~ spl8_10
| ~ spl8_69 ),
inference(resolution,[],[f594,f109]) ).
fof(f1623,plain,
( spl8_125
| ~ spl8_34
| ~ spl8_67 ),
inference(avatar_split_clause,[],[f618,f585,f265,f1621]) ).
fof(f265,plain,
( spl8_34
<=> ! [X0,X1] :
( in(sK5(X0,X1,X1),X1)
| sP0(X0,X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_34])]) ).
fof(f585,plain,
( spl8_67
<=> ! [X0,X1] :
( sP0(X0,X1,X1)
| in(sK5(X0,X1,X1),X0)
| ~ in(sK5(X0,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_67])]) ).
fof(f618,plain,
( ! [X0,X1] :
( in(sK5(X0,X1,X1),X0)
| sP0(X0,X1,X1) )
| ~ spl8_34
| ~ spl8_67 ),
inference(duplicate_literal_removal,[],[f612]) ).
fof(f612,plain,
( ! [X0,X1] :
( in(sK5(X0,X1,X1),X0)
| sP0(X0,X1,X1)
| sP0(X0,X1,X1) )
| ~ spl8_34
| ~ spl8_67 ),
inference(resolution,[],[f586,f266]) ).
fof(f266,plain,
( ! [X0,X1] :
( in(sK5(X0,X1,X1),X1)
| sP0(X0,X1,X1) )
| ~ spl8_34 ),
inference(avatar_component_clause,[],[f265]) ).
fof(f586,plain,
( ! [X0,X1] :
( ~ in(sK5(X0,X1,X1),X1)
| in(sK5(X0,X1,X1),X0)
| sP0(X0,X1,X1) )
| ~ spl8_67 ),
inference(avatar_component_clause,[],[f585]) ).
fof(f1619,plain,
( spl8_124
| ~ spl8_8
| ~ spl8_13
| ~ spl8_65 ),
inference(avatar_split_clause,[],[f567,f547,f122,f100,f1617]) ).
fof(f1617,plain,
( spl8_124
<=> ! [X0,X1] :
( ~ in(sK5(X1,X1,X0),sK7)
| sP0(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_124])]) ).
fof(f567,plain,
( ! [X0,X1] :
( ~ in(sK5(X1,X1,X0),sK7)
| sP0(X1,X1,X0) )
| ~ spl8_8
| ~ spl8_13
| ~ spl8_65 ),
inference(forward_demodulation,[],[f560,f124]) ).
fof(f560,plain,
( ! [X0,X1] :
( ~ in(sK5(X1,X1,X0),empty_set)
| sP0(X1,X1,X0) )
| ~ spl8_8
| ~ spl8_65 ),
inference(superposition,[],[f548,f101]) ).
fof(f1611,plain,
( spl8_123
| ~ spl8_18
| ~ spl8_55 ),
inference(avatar_split_clause,[],[f476,f470,f153,f1609]) ).
fof(f1609,plain,
( spl8_123
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ empty(X1)
| set_difference(X1,X2) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_123])]) ).
fof(f470,plain,
( spl8_55
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(X2)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_55])]) ).
fof(f476,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ empty(X1)
| set_difference(X1,X2) = X0 )
| ~ spl8_18
| ~ spl8_55 ),
inference(resolution,[],[f471,f154]) ).
fof(f471,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(X2)
| ~ empty(X1) )
| ~ spl8_55 ),
inference(avatar_component_clause,[],[f470]) ).
fof(f1600,plain,
( spl8_122
| ~ spl8_44
| ~ spl8_83 ),
inference(avatar_split_clause,[],[f992,f973,f363,f1598]) ).
fof(f1598,plain,
( spl8_122
<=> ! [X0,X1] :
( in(sK5(X0,sK1,set_difference(sK2,X1)),X1)
| in(sK5(X0,sK1,set_difference(sK2,X1)),X0)
| ~ in(sK5(X0,sK1,set_difference(sK2,X1)),sK1)
| sP0(X0,sK1,set_difference(sK2,X1))
| ~ empty(set_difference(sK2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_122])]) ).
fof(f363,plain,
( spl8_44
<=> ! [X0,X1] :
( sP0(X0,sK1,X1)
| ~ empty(X1)
| in(sK5(X0,sK1,X1),sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_44])]) ).
fof(f992,plain,
( ! [X0,X1] :
( in(sK5(X0,sK1,set_difference(sK2,X1)),X1)
| in(sK5(X0,sK1,set_difference(sK2,X1)),X0)
| ~ in(sK5(X0,sK1,set_difference(sK2,X1)),sK1)
| sP0(X0,sK1,set_difference(sK2,X1))
| ~ empty(set_difference(sK2,X1)) )
| ~ spl8_44
| ~ spl8_83 ),
inference(duplicate_literal_removal,[],[f986]) ).
fof(f986,plain,
( ! [X0,X1] :
( in(sK5(X0,sK1,set_difference(sK2,X1)),X1)
| in(sK5(X0,sK1,set_difference(sK2,X1)),X0)
| ~ in(sK5(X0,sK1,set_difference(sK2,X1)),sK1)
| sP0(X0,sK1,set_difference(sK2,X1))
| ~ empty(set_difference(sK2,X1))
| sP0(X0,sK1,set_difference(sK2,X1)) )
| ~ spl8_44
| ~ spl8_83 ),
inference(resolution,[],[f974,f364]) ).
fof(f364,plain,
( ! [X0,X1] :
( in(sK5(X0,sK1,X1),sK2)
| ~ empty(X1)
| sP0(X0,sK1,X1) )
| ~ spl8_44 ),
inference(avatar_component_clause,[],[f363]) ).
fof(f1579,plain,
( ~ spl8_121
| spl8_2
| ~ spl8_112 ),
inference(avatar_split_clause,[],[f1529,f1517,f72,f1576]) ).
fof(f1576,plain,
( spl8_121
<=> empty(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_121])]) ).
fof(f1517,plain,
( spl8_112
<=> ! [X2,X0,X1] :
( subset(set_difference(X0,X1),X2)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_112])]) ).
fof(f1529,plain,
( ~ empty(sK1)
| spl8_2
| ~ spl8_112 ),
inference(resolution,[],[f1518,f74]) ).
fof(f1518,plain,
( ! [X2,X0,X1] :
( subset(set_difference(X0,X1),X2)
| ~ empty(X0) )
| ~ spl8_112 ),
inference(avatar_component_clause,[],[f1517]) ).
fof(f1573,plain,
( spl8_120
| ~ spl8_73
| ~ spl8_74 ),
inference(avatar_split_clause,[],[f743,f704,f700,f1571]) ).
fof(f1571,plain,
( spl8_120
<=> ! [X0,X1] : sP0(X0,set_difference(X1,X1),set_difference(X1,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_120])]) ).
fof(f743,plain,
( ! [X0,X1] : sP0(X0,set_difference(X1,X1),set_difference(X1,X1))
| ~ spl8_73
| ~ spl8_74 ),
inference(duplicate_literal_removal,[],[f728]) ).
fof(f728,plain,
( ! [X0,X1] :
( sP0(X0,set_difference(X1,X1),set_difference(X1,X1))
| sP0(X0,set_difference(X1,X1),set_difference(X1,X1)) )
| ~ spl8_73
| ~ spl8_74 ),
inference(resolution,[],[f705,f701]) ).
fof(f1565,plain,
( spl8_119
| ~ spl8_3
| ~ spl8_13
| ~ spl8_111
| ~ spl8_118 ),
inference(avatar_split_clause,[],[f1561,f1558,f1513,f122,f77,f1563]) ).
fof(f1563,plain,
( spl8_119
<=> ! [X0,X1] :
( sP0(X1,X0,sK7)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_119])]) ).
fof(f1558,plain,
( spl8_118
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,X0,set_difference(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_118])]) ).
fof(f1561,plain,
( ! [X0,X1] :
( sP0(X1,X0,sK7)
| ~ empty(X0) )
| ~ spl8_3
| ~ spl8_13
| ~ spl8_111
| ~ spl8_118 ),
inference(forward_demodulation,[],[f1559,f1524]) ).
fof(f1559,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,X0,set_difference(X2,X2)) )
| ~ spl8_118 ),
inference(avatar_component_clause,[],[f1558]) ).
fof(f1560,plain,
( spl8_118
| ~ spl8_71
| ~ spl8_72 ),
inference(avatar_split_clause,[],[f693,f605,f601,f1558]) ).
fof(f693,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,X0,set_difference(X2,X2)) )
| ~ spl8_71
| ~ spl8_72 ),
inference(duplicate_literal_removal,[],[f684]) ).
fof(f684,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,X0,set_difference(X2,X2))
| ~ empty(X0)
| sP0(X1,X0,set_difference(X2,X2)) )
| ~ spl8_71
| ~ spl8_72 ),
inference(resolution,[],[f606,f602]) ).
fof(f1551,plain,
( spl8_117
| ~ spl8_3
| ~ spl8_13
| ~ spl8_111
| ~ spl8_116 ),
inference(avatar_split_clause,[],[f1547,f1544,f1513,f122,f77,f1549]) ).
fof(f1549,plain,
( spl8_117
<=> ! [X0,X1] :
( sP0(X1,sK7,X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_117])]) ).
fof(f1544,plain,
( spl8_116
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,set_difference(X2,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_116])]) ).
fof(f1547,plain,
( ! [X0,X1] :
( sP0(X1,sK7,X0)
| ~ empty(X0) )
| ~ spl8_3
| ~ spl8_13
| ~ spl8_111
| ~ spl8_116 ),
inference(forward_demodulation,[],[f1545,f1524]) ).
fof(f1545,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,set_difference(X2,X2),X0) )
| ~ spl8_116 ),
inference(avatar_component_clause,[],[f1544]) ).
fof(f1546,plain,
( spl8_116
| ~ spl8_68
| ~ spl8_69 ),
inference(avatar_split_clause,[],[f657,f593,f589,f1544]) ).
fof(f657,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,set_difference(X2,X2),X0) )
| ~ spl8_68
| ~ spl8_69 ),
inference(duplicate_literal_removal,[],[f644]) ).
fof(f644,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,set_difference(X2,X2),X0)
| ~ empty(X0)
| sP0(X1,set_difference(X2,X2),X0) )
| ~ spl8_68
| ~ spl8_69 ),
inference(resolution,[],[f594,f590]) ).
fof(f1542,plain,
( spl8_115
| ~ spl8_10
| ~ spl8_66 ),
inference(avatar_split_clause,[],[f570,f551,f108,f1540]) ).
fof(f1540,plain,
( spl8_115
<=> ! [X2,X0,X1] :
( sP0(X0,X0,set_difference(X1,X2))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_115])]) ).
fof(f570,plain,
( ! [X2,X0,X1] :
( sP0(X0,X0,set_difference(X1,X2))
| ~ empty(X1) )
| ~ spl8_10
| ~ spl8_66 ),
inference(resolution,[],[f552,f109]) ).
fof(f1538,plain,
( spl8_114
| ~ spl8_8
| ~ spl8_13
| ~ spl8_62 ),
inference(avatar_split_clause,[],[f545,f511,f122,f100,f1536]) ).
fof(f1536,plain,
( spl8_114
<=> ! [X0,X1] :
( ~ in(sK4(X0,X1),sK7)
| subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_114])]) ).
fof(f545,plain,
( ! [X0,X1] :
( ~ in(sK4(X0,X1),sK7)
| subset(X0,X1) )
| ~ spl8_8
| ~ spl8_13
| ~ spl8_62 ),
inference(forward_demodulation,[],[f539,f124]) ).
fof(f539,plain,
( ! [X0,X1] :
( ~ in(sK4(X0,X1),empty_set)
| subset(X0,X1) )
| ~ spl8_8
| ~ spl8_62 ),
inference(superposition,[],[f512,f101]) ).
fof(f1528,plain,
( spl8_113
| ~ spl8_10
| ~ spl8_85 ),
inference(avatar_split_clause,[],[f1023,f1004,f108,f1526]) ).
fof(f1023,plain,
( ! [X0] :
( sP0(sK2,sK1,X0)
| ~ empty(X0) )
| ~ spl8_10
| ~ spl8_85 ),
inference(resolution,[],[f1005,f109]) ).
fof(f1519,plain,
( spl8_112
| ~ spl8_10
| ~ spl8_61 ),
inference(avatar_split_clause,[],[f524,f507,f108,f1517]) ).
fof(f524,plain,
( ! [X2,X0,X1] :
( subset(set_difference(X0,X1),X2)
| ~ empty(X0) )
| ~ spl8_10
| ~ spl8_61 ),
inference(resolution,[],[f508,f109]) ).
fof(f1515,plain,
( spl8_111
| ~ spl8_18
| ~ spl8_54 ),
inference(avatar_split_clause,[],[f468,f449,f153,f1513]) ).
fof(f449,plain,
( spl8_54
<=> ! [X0,X1] :
( sP0(X0,X0,X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_54])]) ).
fof(f468,plain,
( ! [X0,X1] :
( ~ empty(X0)
| set_difference(X1,X1) = X0 )
| ~ spl8_18
| ~ spl8_54 ),
inference(resolution,[],[f450,f154]) ).
fof(f450,plain,
( ! [X0,X1] :
( sP0(X0,X0,X1)
| ~ empty(X1) )
| ~ spl8_54 ),
inference(avatar_component_clause,[],[f449]) ).
fof(f1511,plain,
( spl8_110
| ~ spl8_18
| ~ spl8_53 ),
inference(avatar_split_clause,[],[f464,f445,f153,f1509]) ).
fof(f1509,plain,
( spl8_110
<=> ! [X0,X1] :
( ~ empty(X0)
| set_difference(X0,X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_110])]) ).
fof(f445,plain,
( spl8_53
<=> ! [X0,X1] :
( sP0(X0,X1,X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_53])]) ).
fof(f464,plain,
( ! [X0,X1] :
( ~ empty(X0)
| set_difference(X0,X1) = X0 )
| ~ spl8_18
| ~ spl8_53 ),
inference(resolution,[],[f446,f154]) ).
fof(f446,plain,
( ! [X0,X1] :
( sP0(X0,X1,X1)
| ~ empty(X1) )
| ~ spl8_53 ),
inference(avatar_component_clause,[],[f445]) ).
fof(f1497,plain,
( spl8_109
| ~ spl8_65
| ~ spl8_66 ),
inference(avatar_split_clause,[],[f580,f551,f547,f1495]) ).
fof(f580,plain,
( ! [X0,X1] : sP0(X0,X0,set_difference(X1,X1))
| ~ spl8_65
| ~ spl8_66 ),
inference(duplicate_literal_removal,[],[f571]) ).
fof(f571,plain,
( ! [X0,X1] :
( sP0(X0,X0,set_difference(X1,X1))
| sP0(X0,X0,set_difference(X1,X1)) )
| ~ spl8_65
| ~ spl8_66 ),
inference(resolution,[],[f552,f548]) ).
fof(f1242,plain,
( spl8_108
| ~ spl8_49
| ~ spl8_82 ),
inference(avatar_split_clause,[],[f952,f920,f393,f1240]) ).
fof(f393,plain,
( spl8_49
<=> ! [X0,X1] :
( in(sK5(X0,sK1,X1),sK2)
| in(sK5(X0,sK1,X1),X1)
| sP0(X0,sK1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_49])]) ).
fof(f952,plain,
( ! [X0,X1] :
( in(sK5(set_difference(sK2,X0),sK1,X1),X0)
| sP0(set_difference(sK2,X0),sK1,X1)
| in(sK5(set_difference(sK2,X0),sK1,X1),X1) )
| ~ spl8_49
| ~ spl8_82 ),
inference(duplicate_literal_removal,[],[f942]) ).
fof(f942,plain,
( ! [X0,X1] :
( in(sK5(set_difference(sK2,X0),sK1,X1),X0)
| sP0(set_difference(sK2,X0),sK1,X1)
| in(sK5(set_difference(sK2,X0),sK1,X1),X1)
| in(sK5(set_difference(sK2,X0),sK1,X1),X1)
| sP0(set_difference(sK2,X0),sK1,X1) )
| ~ spl8_49
| ~ spl8_82 ),
inference(resolution,[],[f921,f394]) ).
fof(f394,plain,
( ! [X0,X1] :
( in(sK5(X0,sK1,X1),sK2)
| in(sK5(X0,sK1,X1),X1)
| sP0(X0,sK1,X1) )
| ~ spl8_49 ),
inference(avatar_component_clause,[],[f393]) ).
fof(f1238,plain,
( spl8_107
| ~ spl8_19
| ~ spl8_78 ),
inference(avatar_split_clause,[],[f836,f766,f159,f1236]) ).
fof(f836,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,set_difference(sK1,X1),X2),X2)
| sP0(X0,set_difference(sK1,X1),X2)
| in(sK5(X0,set_difference(sK1,X1),X2),sK2) )
| ~ spl8_19
| ~ spl8_78 ),
inference(resolution,[],[f767,f160]) ).
fof(f1234,plain,
( spl8_106
| ~ spl8_19
| ~ spl8_77 ),
inference(avatar_split_clause,[],[f786,f762,f159,f1232]) ).
fof(f786,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,X1,set_difference(sK1,X2)),X1)
| sP0(X0,X1,set_difference(sK1,X2))
| in(sK5(X0,X1,set_difference(sK1,X2)),sK2) )
| ~ spl8_19
| ~ spl8_77 ),
inference(resolution,[],[f763,f160]) ).
fof(f1230,plain,
( spl8_105
| ~ spl8_32
| ~ spl8_49 ),
inference(avatar_split_clause,[],[f418,f393,f245,f1228]) ).
fof(f418,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,sK1,set_difference(X1,X2)),sK2)
| sP0(X0,sK1,set_difference(X1,X2))
| in(sK5(X0,sK1,set_difference(X1,X2)),X1) )
| ~ spl8_32
| ~ spl8_49 ),
inference(resolution,[],[f394,f246]) ).
fof(f1226,plain,
( spl8_104
| ~ spl8_33
| ~ spl8_49 ),
inference(avatar_split_clause,[],[f417,f393,f249,f1224]) ).
fof(f417,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,sK1,set_difference(X1,X2)),sK2)
| sP0(X0,sK1,set_difference(X1,X2))
| ~ in(sK5(X0,sK1,set_difference(X1,X2)),X2) )
| ~ spl8_33
| ~ spl8_49 ),
inference(resolution,[],[f394,f250]) ).
fof(f1222,plain,
( spl8_103
| ~ spl8_32
| ~ spl8_48 ),
inference(avatar_split_clause,[],[f404,f389,f245,f1220]) ).
fof(f389,plain,
( spl8_48
<=> ! [X0,X1] :
( in(sK5(X0,X1,sK1),sK2)
| in(sK5(X0,X1,sK1),X1)
| sP0(X0,X1,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_48])]) ).
fof(f404,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,set_difference(X1,X2),sK1),sK2)
| sP0(X0,set_difference(X1,X2),sK1)
| in(sK5(X0,set_difference(X1,X2),sK1),X1) )
| ~ spl8_32
| ~ spl8_48 ),
inference(resolution,[],[f390,f246]) ).
fof(f390,plain,
( ! [X0,X1] :
( in(sK5(X0,X1,sK1),sK2)
| in(sK5(X0,X1,sK1),X1)
| sP0(X0,X1,sK1) )
| ~ spl8_48 ),
inference(avatar_component_clause,[],[f389]) ).
fof(f1215,plain,
( spl8_102
| ~ spl8_33
| ~ spl8_48 ),
inference(avatar_split_clause,[],[f403,f389,f249,f1213]) ).
fof(f403,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,set_difference(X1,X2),sK1),sK2)
| sP0(X0,set_difference(X1,X2),sK1)
| ~ in(sK5(X0,set_difference(X1,X2),sK1),X2) )
| ~ spl8_33
| ~ spl8_48 ),
inference(resolution,[],[f390,f250]) ).
fof(f1199,plain,
( spl8_101
| ~ spl8_61
| ~ spl8_62 ),
inference(avatar_split_clause,[],[f542,f511,f507,f1197]) ).
fof(f542,plain,
( ! [X0,X1] : subset(set_difference(X0,X0),X1)
| ~ spl8_61
| ~ spl8_62 ),
inference(duplicate_literal_removal,[],[f536]) ).
fof(f536,plain,
( ! [X0,X1] :
( subset(set_difference(X0,X0),X1)
| subset(set_difference(X0,X0),X1) )
| ~ spl8_61
| ~ spl8_62 ),
inference(resolution,[],[f512,f508]) ).
fof(f1195,plain,
( spl8_100
| ~ spl8_16
| ~ spl8_61 ),
inference(avatar_split_clause,[],[f533,f507,f141,f1193]) ).
fof(f1193,plain,
( spl8_100
<=> ! [X0,X1] : subset(set_difference(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_100])]) ).
fof(f141,plain,
( spl8_16
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ in(sK4(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_16])]) ).
fof(f533,plain,
( ! [X0,X1] : subset(set_difference(X0,X1),X0)
| ~ spl8_16
| ~ spl8_61 ),
inference(duplicate_literal_removal,[],[f522]) ).
fof(f522,plain,
( ! [X0,X1] :
( subset(set_difference(X0,X1),X0)
| subset(set_difference(X0,X1),X0) )
| ~ spl8_16
| ~ spl8_61 ),
inference(resolution,[],[f508,f142]) ).
fof(f142,plain,
( ! [X0,X1] :
( ~ in(sK4(X0,X1),X1)
| subset(X0,X1) )
| ~ spl8_16 ),
inference(avatar_component_clause,[],[f141]) ).
fof(f1171,plain,
( spl8_99
| ~ spl8_19
| ~ spl8_74 ),
inference(avatar_split_clause,[],[f734,f704,f159,f1169]) ).
fof(f734,plain,
( ! [X0,X1] :
( sP0(X0,set_difference(sK1,X1),set_difference(sK1,X1))
| in(sK5(X0,set_difference(sK1,X1),set_difference(sK1,X1)),sK2) )
| ~ spl8_19
| ~ spl8_74 ),
inference(resolution,[],[f705,f160]) ).
fof(f1123,plain,
( spl8_98
| ~ spl8_62
| ~ spl8_88 ),
inference(avatar_split_clause,[],[f1056,f1040,f511,f1121]) ).
fof(f1056,plain,
( ! [X0] : subset(set_difference(sK1,sK2),X0)
| ~ spl8_62
| ~ spl8_88 ),
inference(duplicate_literal_removal,[],[f1047]) ).
fof(f1047,plain,
( ! [X0] :
( subset(set_difference(sK1,sK2),X0)
| subset(set_difference(sK1,sK2),X0) )
| ~ spl8_62
| ~ spl8_88 ),
inference(resolution,[],[f1041,f512]) ).
fof(f1119,plain,
( spl8_97
| ~ spl8_19
| ~ spl8_72 ),
inference(avatar_split_clause,[],[f687,f605,f159,f1117]) ).
fof(f687,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,X0,set_difference(sK1,X2))
| in(sK5(X1,X0,set_difference(sK1,X2)),sK2) )
| ~ spl8_19
| ~ spl8_72 ),
inference(resolution,[],[f606,f160]) ).
fof(f1115,plain,
( spl8_96
| ~ spl8_19
| ~ spl8_69 ),
inference(avatar_split_clause,[],[f649,f593,f159,f1113]) ).
fof(f649,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| sP0(X1,set_difference(sK1,X2),X0)
| in(sK5(X1,set_difference(sK1,X2),X0),sK2) )
| ~ spl8_19
| ~ spl8_69 ),
inference(resolution,[],[f594,f160]) ).
fof(f1111,plain,
( spl8_95
| ~ spl8_11
| ~ spl8_49 ),
inference(avatar_split_clause,[],[f414,f393,f114,f1109]) ).
fof(f1109,plain,
( spl8_95
<=> ! [X0,X1] :
( in(sK5(X0,sK1,X1),sK2)
| sP0(X0,sK1,X1)
| ~ in(X1,sK5(X0,sK1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_95])]) ).
fof(f414,plain,
( ! [X0,X1] :
( in(sK5(X0,sK1,X1),sK2)
| sP0(X0,sK1,X1)
| ~ in(X1,sK5(X0,sK1,X1)) )
| ~ spl8_11
| ~ spl8_49 ),
inference(resolution,[],[f394,f115]) ).
fof(f1107,plain,
( spl8_94
| ~ spl8_11
| ~ spl8_49 ),
inference(avatar_split_clause,[],[f410,f393,f114,f1105]) ).
fof(f1105,plain,
( spl8_94
<=> ! [X0,X1] :
( in(sK5(X0,sK1,X1),X1)
| sP0(X0,sK1,X1)
| ~ in(sK2,sK5(X0,sK1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_94])]) ).
fof(f410,plain,
( ! [X0,X1] :
( in(sK5(X0,sK1,X1),X1)
| sP0(X0,sK1,X1)
| ~ in(sK2,sK5(X0,sK1,X1)) )
| ~ spl8_11
| ~ spl8_49 ),
inference(resolution,[],[f394,f115]) ).
fof(f1103,plain,
( spl8_93
| ~ spl8_11
| ~ spl8_48 ),
inference(avatar_split_clause,[],[f400,f389,f114,f1101]) ).
fof(f1101,plain,
( spl8_93
<=> ! [X0,X1] :
( in(sK5(X0,X1,sK1),sK2)
| sP0(X0,X1,sK1)
| ~ in(X1,sK5(X0,X1,sK1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_93])]) ).
fof(f400,plain,
( ! [X0,X1] :
( in(sK5(X0,X1,sK1),sK2)
| sP0(X0,X1,sK1)
| ~ in(X1,sK5(X0,X1,sK1)) )
| ~ spl8_11
| ~ spl8_48 ),
inference(resolution,[],[f390,f115]) ).
fof(f1099,plain,
( spl8_92
| ~ spl8_11
| ~ spl8_48 ),
inference(avatar_split_clause,[],[f397,f389,f114,f1097]) ).
fof(f1097,plain,
( spl8_92
<=> ! [X0,X1] :
( in(sK5(X0,X1,sK1),X1)
| sP0(X0,X1,sK1)
| ~ in(sK2,sK5(X0,X1,sK1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_92])]) ).
fof(f397,plain,
( ! [X0,X1] :
( in(sK5(X0,X1,sK1),X1)
| sP0(X0,X1,sK1)
| ~ in(sK2,sK5(X0,X1,sK1)) )
| ~ spl8_11
| ~ spl8_48 ),
inference(resolution,[],[f390,f115]) ).
fof(f1075,plain,
( spl8_91
| ~ spl8_16
| ~ spl8_88 ),
inference(avatar_split_clause,[],[f1055,f1040,f141,f1073]) ).
fof(f1055,plain,
( ! [X0] : subset(set_difference(sK1,X0),sK2)
| ~ spl8_16
| ~ spl8_88 ),
inference(duplicate_literal_removal,[],[f1048]) ).
fof(f1048,plain,
( ! [X0] :
( subset(set_difference(sK1,X0),sK2)
| subset(set_difference(sK1,X0),sK2) )
| ~ spl8_16
| ~ spl8_88 ),
inference(resolution,[],[f1041,f142]) ).
fof(f1071,plain,
( spl8_90
| ~ spl8_19
| ~ spl8_66 ),
inference(avatar_split_clause,[],[f574,f551,f159,f1069]) ).
fof(f574,plain,
( ! [X0,X1] :
( sP0(X0,X0,set_difference(sK1,X1))
| in(sK5(X0,X0,set_difference(sK1,X1)),sK2) )
| ~ spl8_19
| ~ spl8_66 ),
inference(resolution,[],[f552,f160]) ).
fof(f1046,plain,
( spl8_89
| ~ spl8_30
| ~ spl8_76 ),
inference(avatar_split_clause,[],[f758,f747,f233,f1044]) ).
fof(f758,plain,
( ! [X0] :
( in(sK4(sK1,set_difference(sK2,X0)),X0)
| subset(sK1,set_difference(sK2,X0)) )
| ~ spl8_30
| ~ spl8_76 ),
inference(duplicate_literal_removal,[],[f752]) ).
fof(f752,plain,
( ! [X0] :
( in(sK4(sK1,set_difference(sK2,X0)),X0)
| subset(sK1,set_difference(sK2,X0))
| subset(sK1,set_difference(sK2,X0)) )
| ~ spl8_30
| ~ spl8_76 ),
inference(resolution,[],[f748,f234]) ).
fof(f1042,plain,
( spl8_88
| ~ spl8_19
| ~ spl8_61 ),
inference(avatar_split_clause,[],[f527,f507,f159,f1040]) ).
fof(f527,plain,
( ! [X0,X1] :
( subset(set_difference(sK1,X0),X1)
| in(sK4(set_difference(sK1,X0),X1),sK2) )
| ~ spl8_19
| ~ spl8_61 ),
inference(resolution,[],[f508,f160]) ).
fof(f1038,plain,
( spl8_87
| ~ spl8_11
| ~ spl8_45 ),
inference(avatar_split_clause,[],[f385,f367,f114,f1036]) ).
fof(f1036,plain,
( spl8_87
<=> ! [X0,X1] :
( ~ empty(X0)
| sP0(X1,X0,sK1)
| ~ in(sK2,sK5(X1,X0,sK1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_87])]) ).
fof(f367,plain,
( spl8_45
<=> ! [X0,X1] :
( sP0(X0,X1,sK1)
| ~ empty(X1)
| in(sK5(X0,X1,sK1),sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_45])]) ).
fof(f385,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sP0(X1,X0,sK1)
| ~ in(sK2,sK5(X1,X0,sK1)) )
| ~ spl8_11
| ~ spl8_45 ),
inference(resolution,[],[f368,f115]) ).
fof(f368,plain,
( ! [X0,X1] :
( in(sK5(X0,X1,sK1),sK2)
| ~ empty(X1)
| sP0(X0,X1,sK1) )
| ~ spl8_45 ),
inference(avatar_component_clause,[],[f367]) ).
fof(f1034,plain,
( spl8_86
| ~ spl8_11
| ~ spl8_44 ),
inference(avatar_split_clause,[],[f371,f363,f114,f1032]) ).
fof(f1032,plain,
( spl8_86
<=> ! [X0,X1] :
( ~ empty(X0)
| sP0(X1,sK1,X0)
| ~ in(sK2,sK5(X1,sK1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_86])]) ).
fof(f371,plain,
( ! [X0,X1] :
( ~ empty(X0)
| sP0(X1,sK1,X0)
| ~ in(sK2,sK5(X1,sK1,X0)) )
| ~ spl8_11
| ~ spl8_44 ),
inference(resolution,[],[f364,f115]) ).
fof(f1006,plain,
( spl8_85
| ~ spl8_24
| ~ spl8_49 ),
inference(avatar_split_clause,[],[f423,f393,f183,f1004]) ).
fof(f423,plain,
( ! [X0] :
( in(sK5(sK2,sK1,X0),X0)
| sP0(sK2,sK1,X0) )
| ~ spl8_24
| ~ spl8_49 ),
inference(duplicate_literal_removal,[],[f409]) ).
fof(f409,plain,
( ! [X0] :
( in(sK5(sK2,sK1,X0),X0)
| sP0(sK2,sK1,X0)
| sP0(sK2,sK1,X0)
| in(sK5(sK2,sK1,X0),X0) )
| ~ spl8_24
| ~ spl8_49 ),
inference(resolution,[],[f394,f184]) ).
fof(f1002,plain,
( spl8_84
| ~ spl8_49 ),
inference(avatar_split_clause,[],[f420,f393,f1000]) ).
fof(f420,plain,
( ! [X0] :
( in(sK5(X0,sK1,sK2),sK2)
| sP0(X0,sK1,sK2) )
| ~ spl8_49 ),
inference(factoring,[],[f394]) ).
fof(f975,plain,
( spl8_83
| ~ spl8_25
| ~ spl8_37 ),
inference(avatar_split_clause,[],[f305,f296,f199,f973]) ).
fof(f305,plain,
( ! [X2,X3,X0,X1] :
( ~ in(sK5(X0,X1,set_difference(X2,X3)),X2)
| in(sK5(X0,X1,set_difference(X2,X3)),X3)
| in(sK5(X0,X1,set_difference(X2,X3)),X0)
| ~ in(sK5(X0,X1,set_difference(X2,X3)),X1)
| sP0(X0,X1,set_difference(X2,X3)) )
| ~ spl8_25
| ~ spl8_37 ),
inference(resolution,[],[f297,f200]) ).
fof(f922,plain,
( spl8_82
| ~ spl8_24
| ~ spl8_37 ),
inference(avatar_split_clause,[],[f301,f296,f183,f920]) ).
fof(f301,plain,
( ! [X2,X3,X0,X1] :
( ~ in(sK5(set_difference(X0,X1),X2,X3),X0)
| in(sK5(set_difference(X0,X1),X2,X3),X1)
| sP0(set_difference(X0,X1),X2,X3)
| in(sK5(set_difference(X0,X1),X2,X3),X3) )
| ~ spl8_24
| ~ spl8_37 ),
inference(resolution,[],[f297,f184]) ).
fof(f886,plain,
( spl8_81
| ~ spl8_48 ),
inference(avatar_split_clause,[],[f406,f389,f884]) ).
fof(f406,plain,
( ! [X0] :
( in(sK5(X0,sK2,sK1),sK2)
| sP0(X0,sK2,sK1) )
| ~ spl8_48 ),
inference(factoring,[],[f390]) ).
fof(f776,plain,
( spl8_80
| ~ spl8_23
| ~ spl8_33 ),
inference(avatar_split_clause,[],[f259,f249,f179,f774]) ).
fof(f259,plain,
( ! [X2,X3,X0,X1] :
( ~ in(sK5(X0,set_difference(X1,X2),X3),X2)
| in(sK5(X0,set_difference(X1,X2),X3),X3)
| sP0(X0,set_difference(X1,X2),X3) )
| ~ spl8_23
| ~ spl8_33 ),
inference(resolution,[],[f250,f180]) ).
fof(f772,plain,
( spl8_79
| ~ spl8_23
| ~ spl8_33 ),
inference(avatar_split_clause,[],[f258,f249,f179,f770]) ).
fof(f258,plain,
( ! [X2,X3,X0,X1] :
( ~ in(sK5(X0,X1,set_difference(X2,X3)),X3)
| in(sK5(X0,X1,set_difference(X2,X3)),X1)
| sP0(X0,X1,set_difference(X2,X3)) )
| ~ spl8_23
| ~ spl8_33 ),
inference(resolution,[],[f250,f180]) ).
fof(f768,plain,
( spl8_78
| ~ spl8_23
| ~ spl8_32 ),
inference(avatar_split_clause,[],[f254,f245,f179,f766]) ).
fof(f254,plain,
( ! [X2,X3,X0,X1] :
( in(sK5(X0,set_difference(X1,X2),X3),X1)
| in(sK5(X0,set_difference(X1,X2),X3),X3)
| sP0(X0,set_difference(X1,X2),X3) )
| ~ spl8_23
| ~ spl8_32 ),
inference(resolution,[],[f246,f180]) ).
fof(f764,plain,
( spl8_77
| ~ spl8_23
| ~ spl8_32 ),
inference(avatar_split_clause,[],[f253,f245,f179,f762]) ).
fof(f253,plain,
( ! [X2,X3,X0,X1] :
( in(sK5(X0,X1,set_difference(X2,X3)),X2)
| in(sK5(X0,X1,set_difference(X2,X3)),X1)
| sP0(X0,X1,set_difference(X2,X3)) )
| ~ spl8_23
| ~ spl8_32 ),
inference(resolution,[],[f246,f180]) ).
fof(f749,plain,
( spl8_76
| ~ spl8_16
| ~ spl8_37 ),
inference(avatar_split_clause,[],[f304,f296,f141,f747]) ).
fof(f304,plain,
( ! [X2,X0,X1] :
( ~ in(sK4(X0,set_difference(X1,X2)),X1)
| in(sK4(X0,set_difference(X1,X2)),X2)
| subset(X0,set_difference(X1,X2)) )
| ~ spl8_16
| ~ spl8_37 ),
inference(resolution,[],[f297,f142]) ).
fof(f724,plain,
( spl8_75
| ~ spl8_11
| ~ spl8_43 ),
inference(avatar_split_clause,[],[f359,f351,f114,f722]) ).
fof(f722,plain,
( spl8_75
<=> ! [X0] :
( sP0(X0,X0,sK1)
| ~ in(sK2,sK5(X0,X0,sK1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_75])]) ).
fof(f351,plain,
( spl8_43
<=> ! [X0] :
( sP0(X0,X0,sK1)
| in(sK5(X0,X0,sK1),sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_43])]) ).
fof(f359,plain,
( ! [X0] :
( sP0(X0,X0,sK1)
| ~ in(sK2,sK5(X0,X0,sK1)) )
| ~ spl8_11
| ~ spl8_43 ),
inference(resolution,[],[f352,f115]) ).
fof(f352,plain,
( ! [X0] :
( in(sK5(X0,X0,sK1),sK2)
| sP0(X0,X0,sK1) )
| ~ spl8_43 ),
inference(avatar_component_clause,[],[f351]) ).
fof(f706,plain,
( spl8_74
| ~ spl8_32
| ~ spl8_34 ),
inference(avatar_split_clause,[],[f282,f265,f245,f704]) ).
fof(f282,plain,
( ! [X2,X0,X1] :
( sP0(X0,set_difference(X1,X2),set_difference(X1,X2))
| in(sK5(X0,set_difference(X1,X2),set_difference(X1,X2)),X1) )
| ~ spl8_32
| ~ spl8_34 ),
inference(resolution,[],[f266,f246]) ).
fof(f702,plain,
( spl8_73
| ~ spl8_33
| ~ spl8_34 ),
inference(avatar_split_clause,[],[f281,f265,f249,f700]) ).
fof(f281,plain,
( ! [X2,X0,X1] :
( sP0(X0,set_difference(X1,X2),set_difference(X1,X2))
| ~ in(sK5(X0,set_difference(X1,X2),set_difference(X1,X2)),X2) )
| ~ spl8_33
| ~ spl8_34 ),
inference(resolution,[],[f266,f250]) ).
fof(f607,plain,
( spl8_72
| ~ spl8_32
| ~ spl8_39 ),
inference(avatar_split_clause,[],[f330,f313,f245,f605]) ).
fof(f313,plain,
( spl8_39
<=> ! [X2,X0,X1] :
( in(sK5(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_39])]) ).
fof(f330,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,X1,set_difference(X2,X3))
| ~ empty(X1)
| in(sK5(X0,X1,set_difference(X2,X3)),X2) )
| ~ spl8_32
| ~ spl8_39 ),
inference(resolution,[],[f314,f246]) ).
fof(f314,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| ~ empty(X1) )
| ~ spl8_39 ),
inference(avatar_component_clause,[],[f313]) ).
fof(f603,plain,
( spl8_71
| ~ spl8_33
| ~ spl8_39 ),
inference(avatar_split_clause,[],[f329,f313,f249,f601]) ).
fof(f329,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,X1,set_difference(X2,X3))
| ~ empty(X1)
| ~ in(sK5(X0,X1,set_difference(X2,X3)),X3) )
| ~ spl8_33
| ~ spl8_39 ),
inference(resolution,[],[f314,f250]) ).
fof(f599,plain,
( spl8_70
| ~ spl8_11
| ~ spl8_42 ),
inference(avatar_split_clause,[],[f355,f347,f114,f597]) ).
fof(f597,plain,
( spl8_70
<=> ! [X0] :
( sP0(X0,sK1,sK1)
| ~ in(sK2,sK5(X0,sK1,sK1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_70])]) ).
fof(f347,plain,
( spl8_42
<=> ! [X0] :
( sP0(X0,sK1,sK1)
| in(sK5(X0,sK1,sK1),sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_42])]) ).
fof(f355,plain,
( ! [X0] :
( sP0(X0,sK1,sK1)
| ~ in(sK2,sK5(X0,sK1,sK1)) )
| ~ spl8_11
| ~ spl8_42 ),
inference(resolution,[],[f348,f115]) ).
fof(f348,plain,
( ! [X0] :
( in(sK5(X0,sK1,sK1),sK2)
| sP0(X0,sK1,sK1) )
| ~ spl8_42 ),
inference(avatar_component_clause,[],[f347]) ).
fof(f595,plain,
( spl8_69
| ~ spl8_32
| ~ spl8_38 ),
inference(avatar_split_clause,[],[f321,f309,f245,f593]) ).
fof(f309,plain,
( spl8_38
<=> ! [X2,X0,X1] :
( in(sK5(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_38])]) ).
fof(f321,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,set_difference(X1,X2),X3)
| ~ empty(X3)
| in(sK5(X0,set_difference(X1,X2),X3),X1) )
| ~ spl8_32
| ~ spl8_38 ),
inference(resolution,[],[f310,f246]) ).
fof(f310,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ empty(X2) )
| ~ spl8_38 ),
inference(avatar_component_clause,[],[f309]) ).
fof(f591,plain,
( spl8_68
| ~ spl8_33
| ~ spl8_38 ),
inference(avatar_split_clause,[],[f320,f309,f249,f589]) ).
fof(f320,plain,
( ! [X2,X3,X0,X1] :
( sP0(X0,set_difference(X1,X2),X3)
| ~ empty(X3)
| ~ in(sK5(X0,set_difference(X1,X2),X3),X2) )
| ~ spl8_33
| ~ spl8_38 ),
inference(resolution,[],[f310,f250]) ).
fof(f587,plain,
( spl8_67
| ~ spl8_25
| ~ spl8_34 ),
inference(avatar_split_clause,[],[f284,f265,f199,f585]) ).
fof(f284,plain,
( ! [X0,X1] :
( sP0(X0,X1,X1)
| in(sK5(X0,X1,X1),X0)
| ~ in(sK5(X0,X1,X1),X1) )
| ~ spl8_25
| ~ spl8_34 ),
inference(duplicate_literal_removal,[],[f280]) ).
fof(f280,plain,
( ! [X0,X1] :
( sP0(X0,X1,X1)
| in(sK5(X0,X1,X1),X0)
| ~ in(sK5(X0,X1,X1),X1)
| sP0(X0,X1,X1) )
| ~ spl8_25
| ~ spl8_34 ),
inference(resolution,[],[f266,f200]) ).
fof(f553,plain,
( spl8_66
| ~ spl8_32
| ~ spl8_35 ),
inference(avatar_split_clause,[],[f291,f269,f245,f551]) ).
fof(f269,plain,
( spl8_35
<=> ! [X0,X1] :
( sP0(X0,X0,X1)
| in(sK5(X0,X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_35])]) ).
fof(f291,plain,
( ! [X2,X0,X1] :
( sP0(X0,X0,set_difference(X1,X2))
| in(sK5(X0,X0,set_difference(X1,X2)),X1) )
| ~ spl8_32
| ~ spl8_35 ),
inference(resolution,[],[f270,f246]) ).
fof(f270,plain,
( ! [X0,X1] :
( in(sK5(X0,X0,X1),X1)
| sP0(X0,X0,X1) )
| ~ spl8_35 ),
inference(avatar_component_clause,[],[f269]) ).
fof(f549,plain,
( spl8_65
| ~ spl8_33
| ~ spl8_35 ),
inference(avatar_split_clause,[],[f290,f269,f249,f547]) ).
fof(f290,plain,
( ! [X2,X0,X1] :
( sP0(X0,X0,set_difference(X1,X2))
| ~ in(sK5(X0,X0,set_difference(X1,X2)),X2) )
| ~ spl8_33
| ~ spl8_35 ),
inference(resolution,[],[f270,f250]) ).
fof(f521,plain,
( spl8_64
| ~ spl8_11
| ~ spl8_39 ),
inference(avatar_split_clause,[],[f326,f313,f114,f519]) ).
fof(f519,plain,
( spl8_64
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(X1)
| ~ in(X2,sK5(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_64])]) ).
fof(f326,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(X1)
| ~ in(X2,sK5(X0,X1,X2)) )
| ~ spl8_11
| ~ spl8_39 ),
inference(resolution,[],[f314,f115]) ).
fof(f517,plain,
( spl8_63
| ~ spl8_11
| ~ spl8_38 ),
inference(avatar_split_clause,[],[f317,f309,f114,f515]) ).
fof(f515,plain,
( spl8_63
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(X2)
| ~ in(X1,sK5(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_63])]) ).
fof(f317,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(X2)
| ~ in(X1,sK5(X0,X1,X2)) )
| ~ spl8_11
| ~ spl8_38 ),
inference(resolution,[],[f310,f115]) ).
fof(f513,plain,
( spl8_62
| ~ spl8_15
| ~ spl8_33 ),
inference(avatar_split_clause,[],[f257,f249,f137,f511]) ).
fof(f257,plain,
( ! [X2,X0,X1] :
( ~ in(sK4(set_difference(X0,X1),X2),X1)
| subset(set_difference(X0,X1),X2) )
| ~ spl8_15
| ~ spl8_33 ),
inference(resolution,[],[f250,f138]) ).
fof(f509,plain,
( spl8_61
| ~ spl8_15
| ~ spl8_32 ),
inference(avatar_split_clause,[],[f252,f245,f137,f507]) ).
fof(f252,plain,
( ! [X2,X0,X1] :
( in(sK4(set_difference(X0,X1),X2),X0)
| subset(set_difference(X0,X1),X2) )
| ~ spl8_15
| ~ spl8_32 ),
inference(resolution,[],[f246,f138]) ).
fof(f500,plain,
( spl8_60
| ~ spl8_11
| ~ spl8_37 ),
inference(avatar_split_clause,[],[f302,f296,f114,f498]) ).
fof(f302,plain,
( ! [X2,X0,X1] :
( ~ in(X0,X1)
| in(X0,X2)
| ~ in(set_difference(X1,X2),X0) )
| ~ spl8_11
| ~ spl8_37 ),
inference(resolution,[],[f297,f115]) ).
fof(f492,plain,
( spl8_59
| ~ spl8_11
| ~ spl8_30 ),
inference(avatar_split_clause,[],[f343,f233,f114,f490]) ).
fof(f490,plain,
( spl8_59
<=> ! [X0] :
( subset(sK1,X0)
| ~ in(sK2,sK4(sK1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_59])]) ).
fof(f343,plain,
( ! [X0] :
( subset(sK1,X0)
| ~ in(sK2,sK4(sK1,X0)) )
| ~ spl8_11
| ~ spl8_30 ),
inference(resolution,[],[f234,f115]) ).
fof(f488,plain,
( spl8_58
| ~ spl8_10
| ~ spl8_37 ),
inference(avatar_split_clause,[],[f303,f296,f108,f486]) ).
fof(f486,plain,
( spl8_58
<=> ! [X2,X0,X1] :
( ~ in(X0,X1)
| in(X0,X2)
| ~ empty(set_difference(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_58])]) ).
fof(f303,plain,
( ! [X2,X0,X1] :
( ~ in(X0,X1)
| in(X0,X2)
| ~ empty(set_difference(X1,X2)) )
| ~ spl8_10
| ~ spl8_37 ),
inference(resolution,[],[f297,f109]) ).
fof(f484,plain,
( spl8_57
| ~ spl8_11
| ~ spl8_35 ),
inference(avatar_split_clause,[],[f287,f269,f114,f482]) ).
fof(f482,plain,
( spl8_57
<=> ! [X0,X1] :
( sP0(X0,X0,X1)
| ~ in(X1,sK5(X0,X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_57])]) ).
fof(f287,plain,
( ! [X0,X1] :
( sP0(X0,X0,X1)
| ~ in(X1,sK5(X0,X0,X1)) )
| ~ spl8_11
| ~ spl8_35 ),
inference(resolution,[],[f270,f115]) ).
fof(f480,plain,
( spl8_56
| ~ spl8_11
| ~ spl8_34 ),
inference(avatar_split_clause,[],[f278,f265,f114,f478]) ).
fof(f478,plain,
( spl8_56
<=> ! [X0,X1] :
( sP0(X0,X1,X1)
| ~ in(X1,sK5(X0,X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_56])]) ).
fof(f278,plain,
( ! [X0,X1] :
( sP0(X0,X1,X1)
| ~ in(X1,sK5(X0,X1,X1)) )
| ~ spl8_11
| ~ spl8_34 ),
inference(resolution,[],[f266,f115]) ).
fof(f472,plain,
( spl8_55
| ~ spl8_10
| ~ spl8_38 ),
inference(avatar_split_clause,[],[f318,f309,f108,f470]) ).
fof(f318,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(X2)
| ~ empty(X1) )
| ~ spl8_10
| ~ spl8_38 ),
inference(resolution,[],[f310,f109]) ).
fof(f451,plain,
( spl8_54
| ~ spl8_10
| ~ spl8_35 ),
inference(avatar_split_clause,[],[f288,f269,f108,f449]) ).
fof(f288,plain,
( ! [X0,X1] :
( sP0(X0,X0,X1)
| ~ empty(X1) )
| ~ spl8_10
| ~ spl8_35 ),
inference(resolution,[],[f270,f109]) ).
fof(f447,plain,
( spl8_53
| ~ spl8_10
| ~ spl8_34 ),
inference(avatar_split_clause,[],[f279,f265,f108,f445]) ).
fof(f279,plain,
( ! [X0,X1] :
( sP0(X0,X1,X1)
| ~ empty(X1) )
| ~ spl8_10
| ~ spl8_34 ),
inference(resolution,[],[f266,f109]) ).
fof(f443,plain,
( spl8_52
| ~ spl8_21
| ~ spl8_26 ),
inference(avatar_split_clause,[],[f217,f209,f168,f441]) ).
fof(f441,plain,
( spl8_52
<=> ! [X0,X1] :
( ~ in(X0,sK7)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_52])]) ).
fof(f209,plain,
( spl8_26
<=> ! [X0] : sP0(X0,sK7,sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_26])]) ).
fof(f217,plain,
( ! [X0,X1] :
( ~ in(X0,sK7)
| ~ in(X0,X1) )
| ~ spl8_21
| ~ spl8_26 ),
inference(resolution,[],[f210,f169]) ).
fof(f210,plain,
( ! [X0] : sP0(X0,sK7,sK7)
| ~ spl8_26 ),
inference(avatar_component_clause,[],[f209]) ).
fof(f431,plain,
( spl8_51
| ~ spl8_7
| ~ spl8_13 ),
inference(avatar_split_clause,[],[f206,f122,f96,f429]) ).
fof(f429,plain,
( spl8_51
<=> ! [X0] : sK7 = set_difference(sK7,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_51])]) ).
fof(f206,plain,
( ! [X0] : sK7 = set_difference(sK7,X0)
| ~ spl8_7
| ~ spl8_13 ),
inference(superposition,[],[f97,f124]) ).
fof(f427,plain,
( spl8_50
| ~ spl8_8
| ~ spl8_13 ),
inference(avatar_split_clause,[],[f205,f122,f100,f425]) ).
fof(f425,plain,
( spl8_50
<=> ! [X0] : set_difference(X0,sK7) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl8_50])]) ).
fof(f205,plain,
( ! [X0] : set_difference(X0,sK7) = X0
| ~ spl8_8
| ~ spl8_13 ),
inference(superposition,[],[f101,f124]) ).
fof(f395,plain,
( spl8_49
| ~ spl8_19
| ~ spl8_23 ),
inference(avatar_split_clause,[],[f193,f179,f159,f393]) ).
fof(f193,plain,
( ! [X0,X1] :
( in(sK5(X0,sK1,X1),sK2)
| in(sK5(X0,sK1,X1),X1)
| sP0(X0,sK1,X1) )
| ~ spl8_19
| ~ spl8_23 ),
inference(resolution,[],[f160,f180]) ).
fof(f391,plain,
( spl8_48
| ~ spl8_19
| ~ spl8_23 ),
inference(avatar_split_clause,[],[f192,f179,f159,f389]) ).
fof(f192,plain,
( ! [X0,X1] :
( in(sK5(X0,X1,sK1),sK2)
| in(sK5(X0,X1,sK1),X1)
| sP0(X0,X1,sK1) )
| ~ spl8_19
| ~ spl8_23 ),
inference(resolution,[],[f160,f180]) ).
fof(f383,plain,
( ~ spl8_46
| spl8_47
| ~ spl8_10
| ~ spl8_30 ),
inference(avatar_split_clause,[],[f344,f233,f108,f381,f377]) ).
fof(f377,plain,
( spl8_46
<=> empty(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_46])]) ).
fof(f381,plain,
( spl8_47
<=> ! [X0] : subset(sK1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_47])]) ).
fof(f344,plain,
( ! [X0] :
( subset(sK1,X0)
| ~ empty(sK2) )
| ~ spl8_10
| ~ spl8_30 ),
inference(resolution,[],[f234,f109]) ).
fof(f369,plain,
( spl8_45
| ~ spl8_19
| ~ spl8_39 ),
inference(avatar_split_clause,[],[f331,f313,f159,f367]) ).
fof(f331,plain,
( ! [X0,X1] :
( sP0(X0,X1,sK1)
| ~ empty(X1)
| in(sK5(X0,X1,sK1),sK2) )
| ~ spl8_19
| ~ spl8_39 ),
inference(resolution,[],[f314,f160]) ).
fof(f365,plain,
( spl8_44
| ~ spl8_19
| ~ spl8_38 ),
inference(avatar_split_clause,[],[f322,f309,f159,f363]) ).
fof(f322,plain,
( ! [X0,X1] :
( sP0(X0,sK1,X1)
| ~ empty(X1)
| in(sK5(X0,sK1,X1),sK2) )
| ~ spl8_19
| ~ spl8_38 ),
inference(resolution,[],[f310,f160]) ).
fof(f353,plain,
( spl8_43
| ~ spl8_19
| ~ spl8_35 ),
inference(avatar_split_clause,[],[f292,f269,f159,f351]) ).
fof(f292,plain,
( ! [X0] :
( sP0(X0,X0,sK1)
| in(sK5(X0,X0,sK1),sK2) )
| ~ spl8_19
| ~ spl8_35 ),
inference(resolution,[],[f270,f160]) ).
fof(f349,plain,
( spl8_42
| ~ spl8_19
| ~ spl8_34 ),
inference(avatar_split_clause,[],[f283,f265,f159,f347]) ).
fof(f283,plain,
( ! [X0] :
( sP0(X0,sK1,sK1)
| in(sK5(X0,sK1,sK1),sK2) )
| ~ spl8_19
| ~ spl8_34 ),
inference(resolution,[],[f266,f160]) ).
fof(f341,plain,
( spl8_41
| ~ spl8_11
| ~ spl8_23 ),
inference(avatar_split_clause,[],[f188,f179,f114,f339]) ).
fof(f339,plain,
( spl8_41
<=> ! [X2,X0,X1] :
( in(sK5(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| ~ in(X1,sK5(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_41])]) ).
fof(f188,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| ~ in(X1,sK5(X0,X1,X2)) )
| ~ spl8_11
| ~ spl8_23 ),
inference(resolution,[],[f180,f115]) ).
fof(f337,plain,
( spl8_40
| ~ spl8_11
| ~ spl8_23 ),
inference(avatar_split_clause,[],[f186,f179,f114,f335]) ).
fof(f335,plain,
( spl8_40
<=> ! [X2,X0,X1] :
( in(sK5(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ in(X2,sK5(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_40])]) ).
fof(f186,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ in(X2,sK5(X0,X1,X2)) )
| ~ spl8_11
| ~ spl8_23 ),
inference(resolution,[],[f180,f115]) ).
fof(f315,plain,
( spl8_39
| ~ spl8_10
| ~ spl8_23 ),
inference(avatar_split_clause,[],[f189,f179,f108,f313]) ).
fof(f189,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| ~ empty(X1) )
| ~ spl8_10
| ~ spl8_23 ),
inference(resolution,[],[f180,f109]) ).
fof(f311,plain,
( spl8_38
| ~ spl8_10
| ~ spl8_23 ),
inference(avatar_split_clause,[],[f187,f179,f108,f309]) ).
fof(f187,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ empty(X2) )
| ~ spl8_10
| ~ spl8_23 ),
inference(resolution,[],[f180,f109]) ).
fof(f298,plain,
( spl8_37
| ~ spl8_12
| ~ spl8_22 ),
inference(avatar_split_clause,[],[f177,f174,f118,f296]) ).
fof(f174,plain,
( spl8_22
<=> ! [X4,X0,X2,X1] :
( in(X4,X2)
| in(X4,X0)
| ~ in(X4,X1)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_22])]) ).
fof(f177,plain,
( ! [X2,X0,X1] :
( in(X0,X1)
| ~ in(X0,X2)
| in(X0,set_difference(X2,X1)) )
| ~ spl8_12
| ~ spl8_22 ),
inference(resolution,[],[f175,f119]) ).
fof(f175,plain,
( ! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| in(X4,X0)
| ~ in(X4,X1)
| in(X4,X2) )
| ~ spl8_22 ),
inference(avatar_component_clause,[],[f174]) ).
fof(f276,plain,
( ~ spl8_36
| spl8_2
| ~ spl8_29 ),
inference(avatar_split_clause,[],[f238,f229,f72,f273]) ).
fof(f273,plain,
( spl8_36
<=> empty(set_difference(sK1,sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_36])]) ).
fof(f229,plain,
( spl8_29
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_29])]) ).
fof(f238,plain,
( ~ empty(set_difference(sK1,sK3))
| spl8_2
| ~ spl8_29 ),
inference(resolution,[],[f230,f74]) ).
fof(f230,plain,
( ! [X0,X1] :
( subset(X0,X1)
| ~ empty(X0) )
| ~ spl8_29 ),
inference(avatar_component_clause,[],[f229]) ).
fof(f271,plain,
( spl8_35
| ~ spl8_23
| ~ spl8_24 ),
inference(avatar_split_clause,[],[f196,f183,f179,f269]) ).
fof(f196,plain,
( ! [X0,X1] :
( sP0(X0,X0,X1)
| in(sK5(X0,X0,X1),X1) )
| ~ spl8_23
| ~ spl8_24 ),
inference(duplicate_literal_removal,[],[f195]) ).
fof(f195,plain,
( ! [X0,X1] :
( sP0(X0,X0,X1)
| in(sK5(X0,X0,X1),X1)
| in(sK5(X0,X0,X1),X1)
| sP0(X0,X0,X1) )
| ~ spl8_23
| ~ spl8_24 ),
inference(resolution,[],[f184,f180]) ).
fof(f267,plain,
( spl8_34
| ~ spl8_23 ),
inference(avatar_split_clause,[],[f190,f179,f265]) ).
fof(f190,plain,
( ! [X0,X1] :
( in(sK5(X0,X1,X1),X1)
| sP0(X0,X1,X1) )
| ~ spl8_23 ),
inference(factoring,[],[f180]) ).
fof(f251,plain,
( spl8_33
| ~ spl8_12
| ~ spl8_21 ),
inference(avatar_split_clause,[],[f172,f168,f118,f249]) ).
fof(f172,plain,
( ! [X2,X0,X1] :
( ~ in(X0,set_difference(X1,X2))
| ~ in(X0,X2) )
| ~ spl8_12
| ~ spl8_21 ),
inference(resolution,[],[f169,f119]) ).
fof(f247,plain,
( spl8_32
| ~ spl8_12
| ~ spl8_20 ),
inference(avatar_split_clause,[],[f171,f164,f118,f245]) ).
fof(f164,plain,
( spl8_20
<=> ! [X4,X0,X1,X2] :
( in(X4,X1)
| ~ in(X4,X2)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_20])]) ).
fof(f171,plain,
( ! [X2,X0,X1] :
( ~ in(X0,set_difference(X1,X2))
| in(X0,X1) )
| ~ spl8_12
| ~ spl8_20 ),
inference(resolution,[],[f165,f119]) ).
fof(f165,plain,
( ! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| ~ in(X4,X2)
| in(X4,X1) )
| ~ spl8_20 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f243,plain,
( spl8_31
| ~ spl8_11
| ~ spl8_15 ),
inference(avatar_split_clause,[],[f144,f137,f114,f241]) ).
fof(f241,plain,
( spl8_31
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ in(X0,sK4(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_31])]) ).
fof(f144,plain,
( ! [X0,X1] :
( subset(X0,X1)
| ~ in(X0,sK4(X0,X1)) )
| ~ spl8_11
| ~ spl8_15 ),
inference(resolution,[],[f138,f115]) ).
fof(f235,plain,
( spl8_30
| ~ spl8_15
| ~ spl8_19 ),
inference(avatar_split_clause,[],[f191,f159,f137,f233]) ).
fof(f191,plain,
( ! [X0] :
( in(sK4(sK1,X0),sK2)
| subset(sK1,X0) )
| ~ spl8_15
| ~ spl8_19 ),
inference(resolution,[],[f160,f138]) ).
fof(f231,plain,
( spl8_29
| ~ spl8_10
| ~ spl8_15 ),
inference(avatar_split_clause,[],[f145,f137,f108,f229]) ).
fof(f145,plain,
( ! [X0,X1] :
( subset(X0,X1)
| ~ empty(X0) )
| ~ spl8_10
| ~ spl8_15 ),
inference(resolution,[],[f138,f109]) ).
fof(f227,plain,
( spl8_28
| ~ spl8_5
| ~ spl8_14 ),
inference(avatar_split_clause,[],[f135,f131,f87,f225]) ).
fof(f225,plain,
( spl8_28
<=> ! [X0] :
( sK7 = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_28])]) ).
fof(f87,plain,
( spl8_5
<=> empty(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_5])]) ).
fof(f131,plain,
( spl8_14
<=> ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_14])]) ).
fof(f135,plain,
( ! [X0] :
( sK7 = X0
| ~ empty(X0) )
| ~ spl8_5
| ~ spl8_14 ),
inference(resolution,[],[f132,f89]) ).
fof(f89,plain,
( empty(sK7)
| ~ spl8_5 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f132,plain,
( ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) )
| ~ spl8_14 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f215,plain,
( spl8_27
| ~ spl8_8
| ~ spl8_12
| ~ spl8_13 ),
inference(avatar_split_clause,[],[f129,f122,f118,f100,f213]) ).
fof(f213,plain,
( spl8_27
<=> ! [X0] : sP0(sK7,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_27])]) ).
fof(f129,plain,
( ! [X0] : sP0(sK7,X0,X0)
| ~ spl8_8
| ~ spl8_12
| ~ spl8_13 ),
inference(forward_demodulation,[],[f127,f124]) ).
fof(f127,plain,
( ! [X0] : sP0(empty_set,X0,X0)
| ~ spl8_8
| ~ spl8_12 ),
inference(superposition,[],[f119,f101]) ).
fof(f211,plain,
( spl8_26
| ~ spl8_7
| ~ spl8_12
| ~ spl8_13 ),
inference(avatar_split_clause,[],[f128,f122,f118,f96,f209]) ).
fof(f128,plain,
( ! [X0] : sP0(X0,sK7,sK7)
| ~ spl8_7
| ~ spl8_12
| ~ spl8_13 ),
inference(forward_demodulation,[],[f126,f124]) ).
fof(f126,plain,
( ! [X0] : sP0(X0,empty_set,empty_set)
| ~ spl8_7
| ~ spl8_12 ),
inference(superposition,[],[f119,f97]) ).
fof(f201,plain,
spl8_25,
inference(avatar_split_clause,[],[f60,f199]) ).
fof(f60,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(sK5(X0,X1,X2),X0)
| ~ in(sK5(X0,X1,X2),X1)
| ~ in(sK5(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f36]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ( ( in(sK5(X0,X1,X2),X0)
| ~ in(sK5(X0,X1,X2),X1)
| ~ in(sK5(X0,X1,X2),X2) )
& ( ( ~ in(sK5(X0,X1,X2),X0)
& in(sK5(X0,X1,X2),X1) )
| in(sK5(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| in(X4,X0)
| ~ in(X4,X1) )
& ( ( ~ in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f34,f35]) ).
fof(f35,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) )
=> ( ( in(sK5(X0,X1,X2),X0)
| ~ in(sK5(X0,X1,X2),X1)
| ~ in(sK5(X0,X1,X2),X2) )
& ( ( ~ in(sK5(X0,X1,X2),X0)
& in(sK5(X0,X1,X2),X1) )
| in(sK5(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ? [X3] :
( ( in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| in(X4,X0)
| ~ in(X4,X1) )
& ( ( ~ in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f33]) ).
fof(f33,plain,
! [X1,X0,X2] :
( ( sP0(X1,X0,X2)
| ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| ~ sP0(X1,X0,X2) ) ),
inference(flattening,[],[f32]) ).
fof(f32,plain,
! [X1,X0,X2] :
( ( sP0(X1,X0,X2)
| ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| ~ sP0(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X1,X0,X2] :
( sP0(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ( ~ in(X3,X1)
& in(X3,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f185,plain,
spl8_24,
inference(avatar_split_clause,[],[f59,f183]) ).
fof(f59,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ in(sK5(X0,X1,X2),X0)
| in(sK5(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f36]) ).
fof(f181,plain,
spl8_23,
inference(avatar_split_clause,[],[f58,f179]) ).
fof(f58,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(sK5(X0,X1,X2),X1)
| in(sK5(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f36]) ).
fof(f176,plain,
spl8_22,
inference(avatar_split_clause,[],[f57,f174]) ).
fof(f57,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| in(X4,X0)
| ~ in(X4,X1)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f36]) ).
fof(f170,plain,
spl8_21,
inference(avatar_split_clause,[],[f56,f168]) ).
fof(f56,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,X0)
| ~ in(X4,X2)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f36]) ).
fof(f166,plain,
spl8_20,
inference(avatar_split_clause,[],[f55,f164]) ).
fof(f55,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X2)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f36]) ).
fof(f161,plain,
( spl8_19
| ~ spl8_1
| ~ spl8_17 ),
inference(avatar_split_clause,[],[f156,f149,f67,f159]) ).
fof(f67,plain,
( spl8_1
<=> subset(sK1,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_1])]) ).
fof(f156,plain,
( ! [X0] :
( ~ in(X0,sK1)
| in(X0,sK2) )
| ~ spl8_1
| ~ spl8_17 ),
inference(resolution,[],[f150,f69]) ).
fof(f69,plain,
( subset(sK1,sK2)
| ~ spl8_1 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f155,plain,
spl8_18,
inference(avatar_split_clause,[],[f62,f153]) ).
fof(f62,plain,
! [X2,X0,X1] :
( set_difference(X0,X1) = X2
| ~ sP0(X1,X0,X2) ),
inference(cnf_transformation,[],[f37]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) = X2
| ~ sP0(X1,X0,X2) )
& ( sP0(X1,X0,X2)
| set_difference(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1,X2] :
( set_difference(X0,X1) = X2
<=> sP0(X1,X0,X2) ),
inference(definition_folding,[],[f3,f24]) ).
fof(f3,axiom,
! [X0,X1,X2] :
( set_difference(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( ~ in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f151,plain,
spl8_17,
inference(avatar_split_clause,[],[f50,f149]) ).
fof(f50,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f31,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK4(X0,X1),X1)
& in(sK4(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f29,f30]) ).
fof(f30,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK4(X0,X1),X1)
& in(sK4(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f28]) ).
fof(f28,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f21]) ).
fof(f21,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f143,plain,
spl8_16,
inference(avatar_split_clause,[],[f52,f141]) ).
fof(f52,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK4(X0,X1),X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f139,plain,
spl8_15,
inference(avatar_split_clause,[],[f51,f137]) ).
fof(f51,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK4(X0,X1),X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f133,plain,
spl8_14,
inference(avatar_split_clause,[],[f53,f131]) ).
fof(f53,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(f125,plain,
( spl8_13
| ~ spl8_5
| ~ spl8_9 ),
inference(avatar_split_clause,[],[f112,f104,f87,f122]) ).
fof(f104,plain,
( spl8_9
<=> ! [X0] :
( empty_set = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_9])]) ).
fof(f112,plain,
( empty_set = sK7
| ~ spl8_5
| ~ spl8_9 ),
inference(resolution,[],[f105,f89]) ).
fof(f105,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = X0 )
| ~ spl8_9 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f120,plain,
spl8_12,
inference(avatar_split_clause,[],[f65,f118]) ).
fof(f65,plain,
! [X0,X1] : sP0(X1,X0,set_difference(X0,X1)),
inference(equality_resolution,[],[f61]) ).
fof(f61,plain,
! [X2,X0,X1] :
( sP0(X1,X0,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f37]) ).
fof(f116,plain,
spl8_11,
inference(avatar_split_clause,[],[f49,f114]) ).
fof(f49,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f20,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f110,plain,
spl8_10,
inference(avatar_split_clause,[],[f54,f108]) ).
fof(f54,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f106,plain,
spl8_9,
inference(avatar_split_clause,[],[f47,f104]) ).
fof(f47,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f19,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f102,plain,
spl8_8,
inference(avatar_split_clause,[],[f46,f100]) ).
fof(f46,plain,
! [X0] : set_difference(X0,empty_set) = X0,
inference(cnf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0] : set_difference(X0,empty_set) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
fof(f98,plain,
spl8_7,
inference(avatar_split_clause,[],[f45,f96]) ).
fof(f45,plain,
! [X0] : empty_set = set_difference(empty_set,X0),
inference(cnf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0] : empty_set = set_difference(empty_set,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
fof(f94,plain,
spl8_6,
inference(avatar_split_clause,[],[f48,f92]) ).
fof(f92,plain,
( spl8_6
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_6])]) ).
fof(f48,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f17]) ).
fof(f17,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f9]) ).
fof(f9,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f90,plain,
spl8_5,
inference(avatar_split_clause,[],[f64,f87]) ).
fof(f64,plain,
empty(sK7),
inference(cnf_transformation,[],[f41]) ).
fof(f41,plain,
empty(sK7),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f7,f40]) ).
fof(f40,plain,
( ? [X0] : empty(X0)
=> empty(sK7) ),
introduced(choice_axiom,[]) ).
fof(f7,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f85,plain,
~ spl8_4,
inference(avatar_split_clause,[],[f63,f82]) ).
fof(f82,plain,
( spl8_4
<=> empty(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_4])]) ).
fof(f63,plain,
~ empty(sK6),
inference(cnf_transformation,[],[f39]) ).
fof(f39,plain,
~ empty(sK6),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f8,f38]) ).
fof(f38,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK6) ),
introduced(choice_axiom,[]) ).
fof(f8,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f80,plain,
spl8_3,
inference(avatar_split_clause,[],[f44,f77]) ).
fof(f44,plain,
empty(empty_set),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f75,plain,
~ spl8_2,
inference(avatar_split_clause,[],[f43,f72]) ).
fof(f43,plain,
~ subset(set_difference(sK1,sK3),set_difference(sK2,sK3)),
inference(cnf_transformation,[],[f27]) ).
fof(f27,plain,
( ~ subset(set_difference(sK1,sK3),set_difference(sK2,sK3))
& subset(sK1,sK2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f18,f26]) ).
fof(f26,plain,
( ? [X0,X1,X2] :
( ~ subset(set_difference(X0,X2),set_difference(X1,X2))
& subset(X0,X1) )
=> ( ~ subset(set_difference(sK1,sK3),set_difference(sK2,sK3))
& subset(sK1,sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
? [X0,X1,X2] :
( ~ subset(set_difference(X0,X2),set_difference(X1,X2))
& subset(X0,X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,negated_conjecture,
~ ! [X0,X1,X2] :
( subset(X0,X1)
=> subset(set_difference(X0,X2),set_difference(X1,X2)) ),
inference(negated_conjecture,[],[f10]) ).
fof(f10,conjecture,
! [X0,X1,X2] :
( subset(X0,X1)
=> subset(set_difference(X0,X2),set_difference(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_xboole_1) ).
fof(f70,plain,
spl8_1,
inference(avatar_split_clause,[],[f42,f67]) ).
fof(f42,plain,
subset(sK1,sK2),
inference(cnf_transformation,[],[f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU132+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.34 % Computer : n026.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Apr 29 20:36:34 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (15934)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.36 % (15938)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.37 % (15937)WARNING: value z3 for option sas not known
% 0.14/0.37 TRYING [1]
% 0.14/0.37 TRYING [2]
% 0.14/0.37 TRYING [3]
% 0.14/0.37 % (15935)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.37 % (15936)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.37 % (15939)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)
% 0.14/0.37 % (15937)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)
% 0.14/0.37 % (15940)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)
% 0.14/0.37 % (15941)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)
% 0.14/0.37 TRYING [4]
% 0.14/0.37 TRYING [1]
% 0.14/0.37 TRYING [2]
% 0.21/0.38 TRYING [5]
% 0.21/0.38 TRYING [3]
% 0.21/0.40 TRYING [6]
% 0.21/0.42 TRYING [4]
% 0.21/0.44 TRYING [7]
% 0.21/0.50 % (15939)First to succeed.
% 0.21/0.50 TRYING [5]
% 0.21/0.50 % (15941)Also succeeded, but the first one will report.
% 0.21/0.51 % (15939)Refutation found. Thanks to Tanya!
% 0.21/0.51 % SZS status Theorem for theBenchmark
% 0.21/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.51 % (15939)------------------------------
% 0.21/0.51 % (15939)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.21/0.51 % (15939)Termination reason: Refutation
% 0.21/0.51
% 0.21/0.51 % (15939)Memory used [KB]: 3000
% 0.21/0.51 % (15939)Time elapsed: 0.138 s
% 0.21/0.51 % (15939)Instructions burned: 242 (million)
% 0.21/0.51 % (15939)------------------------------
% 0.21/0.51 % (15939)------------------------------
% 0.21/0.51 % (15934)Success in time 0.158 s
%------------------------------------------------------------------------------