TSTP Solution File: SEU104+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU104+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n003.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 15:22:12 EDT 2024
% Result : Theorem 0.17s 0.38s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 189
% Syntax : Number of formulae : 610 ( 112 unt; 0 def)
% Number of atoms : 1792 ( 76 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 2070 ( 888 ~; 852 |; 149 &)
% ( 141 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 154 ( 152 usr; 136 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 6 con; 0-2 aty)
% Number of variables : 644 ( 604 !; 40 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1381,plain,
$false,
inference(avatar_sat_refutation,[],[f192,f197,f202,f207,f212,f217,f222,f227,f232,f237,f242,f246,f250,f254,f258,f262,f266,f270,f274,f278,f282,f286,f290,f294,f305,f310,f314,f318,f322,f326,f330,f334,f339,f343,f347,f351,f355,f359,f372,f376,f380,f385,f389,f393,f397,f414,f418,f422,f426,f430,f434,f438,f462,f466,f470,f474,f478,f508,f527,f542,f546,f565,f570,f594,f603,f607,f644,f649,f656,f660,f664,f668,f672,f676,f680,f710,f718,f724,f733,f751,f756,f758,f765,f769,f773,f789,f819,f826,f830,f837,f842,f843,f844,f845,f851,f864,f944,f948,f952,f956,f961,f965,f969,f992,f996,f997,f1003,f1007,f1011,f1016,f1060,f1066,f1070,f1074,f1078,f1107,f1113,f1117,f1121,f1125,f1129,f1152,f1156,f1160,f1164,f1181,f1185,f1206,f1210,f1234,f1238,f1242,f1247,f1329,f1349,f1367,f1372,f1373,f1380]) ).
fof(f1380,plain,
( spl14_89
| ~ spl14_45
| ~ spl14_90 ),
inference(avatar_split_clause,[],[f1376,f812,f395,f808]) ).
fof(f808,plain,
( spl14_89
<=> element(set_difference(sK5(sK1),sK6(sK1)),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_89])]) ).
fof(f395,plain,
( spl14_45
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_45])]) ).
fof(f812,plain,
( spl14_90
<=> in(set_difference(sK5(sK1),sK6(sK1)),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_90])]) ).
fof(f1376,plain,
( element(set_difference(sK5(sK1),sK6(sK1)),sK1)
| ~ spl14_45
| ~ spl14_90 ),
inference(resolution,[],[f813,f396]) ).
fof(f396,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) )
| ~ spl14_45 ),
inference(avatar_component_clause,[],[f395]) ).
fof(f813,plain,
( in(set_difference(sK5(sK1),sK6(sK1)),sK1)
| ~ spl14_90 ),
inference(avatar_component_clause,[],[f812]) ).
fof(f1373,plain,
( spl14_91
| ~ spl14_99
| spl14_134 ),
inference(avatar_split_clause,[],[f1368,f1364,f950,f816]) ).
fof(f816,plain,
( spl14_91
<=> sP0(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_91])]) ).
fof(f950,plain,
( spl14_99
<=> ! [X0] :
( element(sK5(X0),X0)
| sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_99])]) ).
fof(f1364,plain,
( spl14_134
<=> element(sK5(sK1),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_134])]) ).
fof(f1368,plain,
( sP0(sK1)
| ~ spl14_99
| spl14_134 ),
inference(resolution,[],[f1366,f951]) ).
fof(f951,plain,
( ! [X0] :
( element(sK5(X0),X0)
| sP0(X0) )
| ~ spl14_99 ),
inference(avatar_component_clause,[],[f950]) ).
fof(f1366,plain,
( ~ element(sK5(sK1),sK1)
| spl14_134 ),
inference(avatar_component_clause,[],[f1364]) ).
fof(f1372,plain,
( spl14_135
| ~ spl14_76
| ~ spl14_109 ),
inference(avatar_split_clause,[],[f1047,f1014,f674,f1370]) ).
fof(f1370,plain,
( spl14_135
<=> ! [X0] :
( element(symmetric_difference(X0,X0),sK1)
| ~ element(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_135])]) ).
fof(f674,plain,
( spl14_76
<=> ! [X0,X1] :
( element(set_difference(X0,X1),sK1)
| ~ element(X1,sK1)
| ~ element(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_76])]) ).
fof(f1014,plain,
( spl14_109
<=> ! [X0] : set_difference(X0,X0) = symmetric_difference(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_109])]) ).
fof(f1047,plain,
( ! [X0] :
( element(symmetric_difference(X0,X0),sK1)
| ~ element(X0,sK1) )
| ~ spl14_76
| ~ spl14_109 ),
inference(duplicate_literal_removal,[],[f1038]) ).
fof(f1038,plain,
( ! [X0] :
( element(symmetric_difference(X0,X0),sK1)
| ~ element(X0,sK1)
| ~ element(X0,sK1) )
| ~ spl14_76
| ~ spl14_109 ),
inference(superposition,[],[f675,f1015]) ).
fof(f1015,plain,
( ! [X0] : set_difference(X0,X0) = symmetric_difference(X0,X0)
| ~ spl14_109 ),
inference(avatar_component_clause,[],[f1014]) ).
fof(f675,plain,
( ! [X0,X1] :
( element(set_difference(X0,X1),sK1)
| ~ element(X1,sK1)
| ~ element(X0,sK1) )
| ~ spl14_76 ),
inference(avatar_component_clause,[],[f674]) ).
fof(f1367,plain,
( ~ spl14_134
| ~ spl14_88
| ~ spl14_13
| spl14_90 ),
inference(avatar_split_clause,[],[f821,f812,f248,f804,f1364]) ).
fof(f804,plain,
( spl14_88
<=> element(sK6(sK1),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_88])]) ).
fof(f248,plain,
( spl14_13
<=> ! [X2,X1] :
( in(set_difference(X1,X2),sK1)
| ~ element(X2,sK1)
| ~ element(X1,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_13])]) ).
fof(f821,plain,
( ~ element(sK6(sK1),sK1)
| ~ element(sK5(sK1),sK1)
| ~ spl14_13
| spl14_90 ),
inference(resolution,[],[f814,f249]) ).
fof(f249,plain,
( ! [X2,X1] :
( in(set_difference(X1,X2),sK1)
| ~ element(X2,sK1)
| ~ element(X1,sK1) )
| ~ spl14_13 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f814,plain,
( ~ in(set_difference(sK5(sK1),sK6(sK1)),sK1)
| spl14_90 ),
inference(avatar_component_clause,[],[f812]) ).
fof(f1349,plain,
( spl14_133
| ~ spl14_67
| ~ spl14_68 ),
inference(avatar_split_clause,[],[f636,f605,f601,f1347]) ).
fof(f1347,plain,
( spl14_133
<=> ! [X2,X0,X1] :
( in(symmetric_difference(X0,X1),X2)
| ~ in(set_difference(X1,X0),X2)
| ~ in(set_difference(X0,X1),X2)
| ~ sP0(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_133])]) ).
fof(f601,plain,
( spl14_67
<=> ! [X0,X1] : symmetric_difference(X0,X1) = symmetric_difference(set_difference(X0,X1),set_difference(set_difference(X1,X0),set_difference(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_67])]) ).
fof(f605,plain,
( spl14_68
<=> ! [X4,X0,X3] :
( in(symmetric_difference(X3,set_difference(X4,X3)),X0)
| ~ in(X4,X0)
| ~ in(X3,X0)
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_68])]) ).
fof(f636,plain,
( ! [X2,X0,X1] :
( in(symmetric_difference(X0,X1),X2)
| ~ in(set_difference(X1,X0),X2)
| ~ in(set_difference(X0,X1),X2)
| ~ sP0(X2) )
| ~ spl14_67
| ~ spl14_68 ),
inference(superposition,[],[f606,f602]) ).
fof(f602,plain,
( ! [X0,X1] : symmetric_difference(X0,X1) = symmetric_difference(set_difference(X0,X1),set_difference(set_difference(X1,X0),set_difference(X0,X1)))
| ~ spl14_67 ),
inference(avatar_component_clause,[],[f601]) ).
fof(f606,plain,
( ! [X3,X0,X4] :
( in(symmetric_difference(X3,set_difference(X4,X3)),X0)
| ~ in(X4,X0)
| ~ in(X3,X0)
| ~ sP0(X0) )
| ~ spl14_68 ),
inference(avatar_component_clause,[],[f605]) ).
fof(f1329,plain,
( spl14_132
| ~ spl14_55
| ~ spl14_67 ),
inference(avatar_split_clause,[],[f621,f601,f468,f1327]) ).
fof(f1327,plain,
( spl14_132
<=> ! [X0,X1] :
( finite(symmetric_difference(X0,X1))
| ~ finite(set_difference(set_difference(X1,X0),set_difference(X0,X1)))
| ~ finite(set_difference(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_132])]) ).
fof(f468,plain,
( spl14_55
<=> ! [X0,X1] :
( finite(symmetric_difference(X0,X1))
| ~ finite(X1)
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_55])]) ).
fof(f621,plain,
( ! [X0,X1] :
( finite(symmetric_difference(X0,X1))
| ~ finite(set_difference(set_difference(X1,X0),set_difference(X0,X1)))
| ~ finite(set_difference(X0,X1)) )
| ~ spl14_55
| ~ spl14_67 ),
inference(superposition,[],[f469,f602]) ).
fof(f469,plain,
( ! [X0,X1] :
( finite(symmetric_difference(X0,X1))
| ~ finite(X1)
| ~ finite(X0) )
| ~ spl14_55 ),
inference(avatar_component_clause,[],[f468]) ).
fof(f1247,plain,
( ~ spl14_131
| ~ spl14_44
| ~ spl14_110 ),
inference(avatar_split_clause,[],[f1143,f1057,f391,f1244]) ).
fof(f1244,plain,
( spl14_131
<=> in(sK1,sK6(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_131])]) ).
fof(f391,plain,
( spl14_44
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_44])]) ).
fof(f1057,plain,
( spl14_110
<=> in(sK6(sK1),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_110])]) ).
fof(f1143,plain,
( ~ in(sK1,sK6(sK1))
| ~ spl14_44
| ~ spl14_110 ),
inference(resolution,[],[f1059,f392]) ).
fof(f392,plain,
( ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) )
| ~ spl14_44 ),
inference(avatar_component_clause,[],[f391]) ).
fof(f1059,plain,
( in(sK6(sK1),sK1)
| ~ spl14_110 ),
inference(avatar_component_clause,[],[f1057]) ).
fof(f1242,plain,
( spl14_130
| ~ spl14_44
| ~ spl14_68 ),
inference(avatar_split_clause,[],[f629,f605,f391,f1240]) ).
fof(f1240,plain,
( spl14_130
<=> ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(X2,X1)
| ~ sP0(X1)
| ~ in(X1,symmetric_difference(X2,set_difference(X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_130])]) ).
fof(f629,plain,
( ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(X2,X1)
| ~ sP0(X1)
| ~ in(X1,symmetric_difference(X2,set_difference(X0,X2))) )
| ~ spl14_44
| ~ spl14_68 ),
inference(resolution,[],[f606,f392]) ).
fof(f1238,plain,
( spl14_129
| ~ spl14_45
| ~ spl14_68 ),
inference(avatar_split_clause,[],[f628,f605,f395,f1236]) ).
fof(f1236,plain,
( spl14_129
<=> ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(X2,X1)
| ~ sP0(X1)
| element(symmetric_difference(X2,set_difference(X0,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_129])]) ).
fof(f628,plain,
( ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(X2,X1)
| ~ sP0(X1)
| element(symmetric_difference(X2,set_difference(X0,X2)),X1) )
| ~ spl14_45
| ~ spl14_68 ),
inference(resolution,[],[f606,f396]) ).
fof(f1234,plain,
( spl14_128
| ~ spl14_64
| ~ spl14_67 ),
inference(avatar_split_clause,[],[f613,f601,f563,f1232]) ).
fof(f1232,plain,
( spl14_128
<=> ! [X0,X1] : symmetric_difference(X0,X1) = symmetric_difference(set_difference(X1,X0),set_difference(set_difference(X0,X1),set_difference(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_128])]) ).
fof(f563,plain,
( spl14_64
<=> ! [X0,X1] : symmetric_difference(X0,set_difference(X1,X0)) = symmetric_difference(X1,set_difference(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_64])]) ).
fof(f613,plain,
( ! [X0,X1] : symmetric_difference(X0,X1) = symmetric_difference(set_difference(X1,X0),set_difference(set_difference(X0,X1),set_difference(X1,X0)))
| ~ spl14_64
| ~ spl14_67 ),
inference(superposition,[],[f602,f564]) ).
fof(f564,plain,
( ! [X0,X1] : symmetric_difference(X0,set_difference(X1,X0)) = symmetric_difference(X1,set_difference(X0,X1))
| ~ spl14_64 ),
inference(avatar_component_clause,[],[f563]) ).
fof(f1210,plain,
( spl14_127
| ~ spl14_44
| ~ spl14_66 ),
inference(avatar_split_clause,[],[f596,f592,f391,f1208]) ).
fof(f1208,plain,
( spl14_127
<=> ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(X2,X1)
| ~ sP0(X1)
| ~ in(X1,set_difference(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_127])]) ).
fof(f592,plain,
( spl14_66
<=> ! [X4,X0,X3] :
( in(set_difference(X3,X4),X0)
| ~ in(X4,X0)
| ~ in(X3,X0)
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_66])]) ).
fof(f596,plain,
( ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(X2,X1)
| ~ sP0(X1)
| ~ in(X1,set_difference(X2,X0)) )
| ~ spl14_44
| ~ spl14_66 ),
inference(resolution,[],[f593,f392]) ).
fof(f593,plain,
( ! [X3,X0,X4] :
( in(set_difference(X3,X4),X0)
| ~ in(X4,X0)
| ~ in(X3,X0)
| ~ sP0(X0) )
| ~ spl14_66 ),
inference(avatar_component_clause,[],[f592]) ).
fof(f1206,plain,
( spl14_126
| ~ spl14_45
| ~ spl14_66 ),
inference(avatar_split_clause,[],[f595,f592,f395,f1204]) ).
fof(f1204,plain,
( spl14_126
<=> ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(X2,X1)
| ~ sP0(X1)
| element(set_difference(X2,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_126])]) ).
fof(f595,plain,
( ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(X2,X1)
| ~ sP0(X1)
| element(set_difference(X2,X0),X1) )
| ~ spl14_45
| ~ spl14_66 ),
inference(resolution,[],[f593,f396]) ).
fof(f1185,plain,
( spl14_125
| ~ spl14_63
| ~ spl14_67 ),
inference(avatar_split_clause,[],[f618,f601,f544,f1183]) ).
fof(f1183,plain,
( spl14_125
<=> ! [X0,X1] :
( finite(symmetric_difference(X0,X1))
| ~ finite(set_difference(X1,X0))
| ~ finite(set_difference(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_125])]) ).
fof(f544,plain,
( spl14_63
<=> ! [X0,X1] :
( finite(symmetric_difference(X0,set_difference(X1,X0)))
| ~ finite(X1)
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_63])]) ).
fof(f618,plain,
( ! [X0,X1] :
( finite(symmetric_difference(X0,X1))
| ~ finite(set_difference(X1,X0))
| ~ finite(set_difference(X0,X1)) )
| ~ spl14_63
| ~ spl14_67 ),
inference(superposition,[],[f545,f602]) ).
fof(f545,plain,
( ! [X0,X1] :
( finite(symmetric_difference(X0,set_difference(X1,X0)))
| ~ finite(X1)
| ~ finite(X0) )
| ~ spl14_63 ),
inference(avatar_component_clause,[],[f544]) ).
fof(f1181,plain,
( spl14_124
| ~ spl14_55
| ~ spl14_64 ),
inference(avatar_split_clause,[],[f578,f563,f468,f1179]) ).
fof(f1179,plain,
( spl14_124
<=> ! [X0,X1] :
( finite(symmetric_difference(X1,set_difference(X0,X1)))
| ~ finite(set_difference(X1,X0))
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_124])]) ).
fof(f578,plain,
( ! [X0,X1] :
( finite(symmetric_difference(X1,set_difference(X0,X1)))
| ~ finite(set_difference(X1,X0))
| ~ finite(X0) )
| ~ spl14_55
| ~ spl14_64 ),
inference(superposition,[],[f469,f564]) ).
fof(f1164,plain,
( spl14_123
| ~ spl14_48
| ~ spl14_54 ),
inference(avatar_split_clause,[],[f489,f464,f420,f1162]) ).
fof(f1162,plain,
( spl14_123
<=> ! [X0] :
( empty(powerset(X0))
| in(sK4(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_123])]) ).
fof(f420,plain,
( spl14_48
<=> ! [X0] :
( element(sK4(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_48])]) ).
fof(f464,plain,
( spl14_54
<=> ! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_54])]) ).
fof(f489,plain,
( ! [X0] :
( empty(powerset(X0))
| in(sK4(X0),powerset(X0))
| empty(X0) )
| ~ spl14_48
| ~ spl14_54 ),
inference(resolution,[],[f465,f421]) ).
fof(f421,plain,
( ! [X0] :
( element(sK4(X0),powerset(X0))
| empty(X0) )
| ~ spl14_48 ),
inference(avatar_component_clause,[],[f420]) ).
fof(f465,plain,
( ! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) )
| ~ spl14_54 ),
inference(avatar_component_clause,[],[f464]) ).
fof(f1160,plain,
( spl14_122
| ~ spl14_47
| ~ spl14_54 ),
inference(avatar_split_clause,[],[f488,f464,f416,f1158]) ).
fof(f1158,plain,
( spl14_122
<=> ! [X0] :
( empty(powerset(X0))
| in(sK3(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_122])]) ).
fof(f416,plain,
( spl14_47
<=> ! [X0] :
( element(sK3(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_47])]) ).
fof(f488,plain,
( ! [X0] :
( empty(powerset(X0))
| in(sK3(X0),powerset(X0))
| empty(X0) )
| ~ spl14_47
| ~ spl14_54 ),
inference(resolution,[],[f465,f417]) ).
fof(f417,plain,
( ! [X0] :
( element(sK3(X0),powerset(X0))
| empty(X0) )
| ~ spl14_47 ),
inference(avatar_component_clause,[],[f416]) ).
fof(f1156,plain,
( spl14_121
| ~ spl14_46
| ~ spl14_54 ),
inference(avatar_split_clause,[],[f487,f464,f412,f1154]) ).
fof(f1154,plain,
( spl14_121
<=> ! [X0] :
( empty(powerset(X0))
| in(sK2(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_121])]) ).
fof(f412,plain,
( spl14_46
<=> ! [X0] :
( element(sK2(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_46])]) ).
fof(f487,plain,
( ! [X0] :
( empty(powerset(X0))
| in(sK2(X0),powerset(X0))
| empty(X0) )
| ~ spl14_46
| ~ spl14_54 ),
inference(resolution,[],[f465,f413]) ).
fof(f413,plain,
( ! [X0] :
( element(sK2(X0),powerset(X0))
| empty(X0) )
| ~ spl14_46 ),
inference(avatar_component_clause,[],[f412]) ).
fof(f1152,plain,
( spl14_120
| ~ spl14_50
| ~ spl14_54 ),
inference(avatar_split_clause,[],[f486,f464,f428,f1150]) ).
fof(f1150,plain,
( spl14_120
<=> ! [X0,X1] :
( empty(powerset(X0))
| in(X1,powerset(X0))
| ~ subset(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_120])]) ).
fof(f428,plain,
( spl14_50
<=> ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_50])]) ).
fof(f486,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| in(X1,powerset(X0))
| ~ subset(X1,X0) )
| ~ spl14_50
| ~ spl14_54 ),
inference(resolution,[],[f465,f429]) ).
fof(f429,plain,
( ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) )
| ~ spl14_50 ),
inference(avatar_component_clause,[],[f428]) ).
fof(f1129,plain,
( spl14_119
| ~ spl14_5
| ~ spl14_26
| ~ spl14_35
| ~ spl14_67 ),
inference(avatar_split_clause,[],[f624,f601,f345,f308,f209,f1127]) ).
fof(f1127,plain,
( spl14_119
<=> ! [X0] : symmetric_difference(X0,sK11) = symmetric_difference(set_difference(X0,sK11),sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_119])]) ).
fof(f209,plain,
( spl14_5
<=> empty(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_5])]) ).
fof(f308,plain,
( spl14_26
<=> ! [X0] : empty_set = set_difference(empty_set,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_26])]) ).
fof(f345,plain,
( spl14_35
<=> ! [X0] :
( empty_set = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_35])]) ).
fof(f624,plain,
( ! [X0] : symmetric_difference(X0,sK11) = symmetric_difference(set_difference(X0,sK11),sK11)
| ~ spl14_5
| ~ spl14_26
| ~ spl14_35
| ~ spl14_67 ),
inference(forward_demodulation,[],[f623,f366]) ).
fof(f366,plain,
( empty_set = sK11
| ~ spl14_5
| ~ spl14_35 ),
inference(resolution,[],[f346,f211]) ).
fof(f211,plain,
( empty(sK11)
| ~ spl14_5 ),
inference(avatar_component_clause,[],[f209]) ).
fof(f346,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = X0 )
| ~ spl14_35 ),
inference(avatar_component_clause,[],[f345]) ).
fof(f623,plain,
( ! [X0] : symmetric_difference(X0,empty_set) = symmetric_difference(set_difference(X0,empty_set),empty_set)
| ~ spl14_26
| ~ spl14_67 ),
inference(forward_demodulation,[],[f608,f309]) ).
fof(f309,plain,
( ! [X0] : empty_set = set_difference(empty_set,X0)
| ~ spl14_26 ),
inference(avatar_component_clause,[],[f308]) ).
fof(f608,plain,
( ! [X0] : symmetric_difference(X0,empty_set) = symmetric_difference(set_difference(X0,empty_set),set_difference(empty_set,set_difference(X0,empty_set)))
| ~ spl14_26
| ~ spl14_67 ),
inference(superposition,[],[f602,f309]) ).
fof(f1125,plain,
( spl14_118
| ~ spl14_48
| ~ spl14_62 ),
inference(avatar_split_clause,[],[f550,f540,f420,f1123]) ).
fof(f1123,plain,
( spl14_118
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK4(X1))
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_118])]) ).
fof(f540,plain,
( spl14_62
<=> ! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_62])]) ).
fof(f550,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK4(X1))
| empty(X1) )
| ~ spl14_48
| ~ spl14_62 ),
inference(resolution,[],[f541,f421]) ).
fof(f541,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| element(X0,X2)
| ~ in(X0,X1) )
| ~ spl14_62 ),
inference(avatar_component_clause,[],[f540]) ).
fof(f1121,plain,
( spl14_117
| ~ spl14_47
| ~ spl14_62 ),
inference(avatar_split_clause,[],[f549,f540,f416,f1119]) ).
fof(f1119,plain,
( spl14_117
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK3(X1))
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_117])]) ).
fof(f549,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK3(X1))
| empty(X1) )
| ~ spl14_47
| ~ spl14_62 ),
inference(resolution,[],[f541,f417]) ).
fof(f1117,plain,
( spl14_116
| ~ spl14_46
| ~ spl14_62 ),
inference(avatar_split_clause,[],[f548,f540,f412,f1115]) ).
fof(f1115,plain,
( spl14_116
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK2(X1))
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_116])]) ).
fof(f548,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK2(X1))
| empty(X1) )
| ~ spl14_46
| ~ spl14_62 ),
inference(resolution,[],[f541,f413]) ).
fof(f1113,plain,
( spl14_115
| ~ spl14_50
| ~ spl14_62 ),
inference(avatar_split_clause,[],[f547,f540,f428,f1111]) ).
fof(f1111,plain,
( spl14_115
<=> ! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_115])]) ).
fof(f547,plain,
( ! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,X1) )
| ~ spl14_50
| ~ spl14_62 ),
inference(resolution,[],[f541,f429]) ).
fof(f1107,plain,
( spl14_2
| ~ spl14_23
| ~ spl14_91 ),
inference(avatar_split_clause,[],[f1061,f816,f288,f194]) ).
fof(f194,plain,
( spl14_2
<=> preboolean(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_2])]) ).
fof(f288,plain,
( spl14_23
<=> ! [X0] :
( preboolean(X0)
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_23])]) ).
fof(f1061,plain,
( preboolean(sK1)
| ~ spl14_23
| ~ spl14_91 ),
inference(resolution,[],[f818,f289]) ).
fof(f289,plain,
( ! [X0] :
( ~ sP0(X0)
| preboolean(X0) )
| ~ spl14_23 ),
inference(avatar_component_clause,[],[f288]) ).
fof(f818,plain,
( sP0(sK1)
| ~ spl14_91 ),
inference(avatar_component_clause,[],[f816]) ).
fof(f1078,plain,
( spl14_114
| ~ spl14_56
| ~ spl14_67 ),
inference(avatar_split_clause,[],[f620,f601,f472,f1076]) ).
fof(f1076,plain,
( spl14_114
<=> ! [X0,X1] :
( ~ empty(symmetric_difference(X0,X1))
| empty(set_difference(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_114])]) ).
fof(f472,plain,
( spl14_56
<=> ! [X0,X1] :
( ~ empty(symmetric_difference(X0,set_difference(X1,X0)))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_56])]) ).
fof(f620,plain,
( ! [X0,X1] :
( ~ empty(symmetric_difference(X0,X1))
| empty(set_difference(X0,X1)) )
| ~ spl14_56
| ~ spl14_67 ),
inference(superposition,[],[f473,f602]) ).
fof(f473,plain,
( ! [X0,X1] :
( ~ empty(symmetric_difference(X0,set_difference(X1,X0)))
| empty(X0) )
| ~ spl14_56 ),
inference(avatar_component_clause,[],[f472]) ).
fof(f1074,plain,
( spl14_113
| ~ spl14_57
| ~ spl14_67 ),
inference(avatar_split_clause,[],[f619,f601,f476,f1072]) ).
fof(f1072,plain,
( spl14_113
<=> ! [X0,X1] :
( ~ empty(symmetric_difference(X0,X1))
| empty(set_difference(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_113])]) ).
fof(f476,plain,
( spl14_57
<=> ! [X0,X1] :
( ~ empty(symmetric_difference(X1,set_difference(X0,X1)))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_57])]) ).
fof(f619,plain,
( ! [X0,X1] :
( ~ empty(symmetric_difference(X0,X1))
| empty(set_difference(X1,X0)) )
| ~ spl14_57
| ~ spl14_67 ),
inference(superposition,[],[f477,f602]) ).
fof(f477,plain,
( ! [X0,X1] :
( ~ empty(symmetric_difference(X1,set_difference(X0,X1)))
| empty(X0) )
| ~ spl14_57 ),
inference(avatar_component_clause,[],[f476]) ).
fof(f1070,plain,
( spl14_112
| ~ spl14_24
| ~ spl14_62 ),
inference(avatar_split_clause,[],[f551,f540,f292,f1068]) ).
fof(f1068,plain,
( spl14_112
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK7(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_112])]) ).
fof(f292,plain,
( spl14_24
<=> ! [X0] : element(sK7(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_24])]) ).
fof(f551,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK7(powerset(X1))) )
| ~ spl14_24
| ~ spl14_62 ),
inference(resolution,[],[f541,f293]) ).
fof(f293,plain,
( ! [X0] : element(sK7(X0),X0)
| ~ spl14_24 ),
inference(avatar_component_clause,[],[f292]) ).
fof(f1066,plain,
( spl14_111
| ~ spl14_50
| ~ spl14_61 ),
inference(avatar_split_clause,[],[f528,f525,f428,f1064]) ).
fof(f1064,plain,
( spl14_111
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,X2)
| ~ subset(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_111])]) ).
fof(f525,plain,
( spl14_61
<=> ! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_61])]) ).
fof(f528,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,X2)
| ~ subset(X2,X0) )
| ~ spl14_50
| ~ spl14_61 ),
inference(resolution,[],[f526,f429]) ).
fof(f526,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X0,X1) )
| ~ spl14_61 ),
inference(avatar_component_clause,[],[f525]) ).
fof(f1060,plain,
( spl14_110
| ~ spl14_72
| ~ spl14_88 ),
inference(avatar_split_clause,[],[f998,f804,f658,f1057]) ).
fof(f658,plain,
( spl14_72
<=> ! [X0] :
( in(X0,sK1)
| ~ element(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_72])]) ).
fof(f998,plain,
( in(sK6(sK1),sK1)
| ~ spl14_72
| ~ spl14_88 ),
inference(resolution,[],[f805,f659]) ).
fof(f659,plain,
( ! [X0] :
( ~ element(X0,sK1)
| in(X0,sK1) )
| ~ spl14_72 ),
inference(avatar_component_clause,[],[f658]) ).
fof(f805,plain,
( element(sK6(sK1),sK1)
| ~ spl14_88 ),
inference(avatar_component_clause,[],[f804]) ).
fof(f1016,plain,
( spl14_109
| ~ spl14_52
| ~ spl14_67 ),
inference(avatar_split_clause,[],[f612,f601,f436,f1014]) ).
fof(f436,plain,
( spl14_52
<=> ! [X0] : symmetric_difference(X0,set_difference(X0,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl14_52])]) ).
fof(f612,plain,
( ! [X0] : set_difference(X0,X0) = symmetric_difference(X0,X0)
| ~ spl14_52
| ~ spl14_67 ),
inference(superposition,[],[f602,f437]) ).
fof(f437,plain,
( ! [X0] : symmetric_difference(X0,set_difference(X0,X0)) = X0
| ~ spl14_52 ),
inference(avatar_component_clause,[],[f436]) ).
fof(f1011,plain,
( spl14_108
| ~ spl14_5
| ~ spl14_27
| ~ spl14_28
| ~ spl14_35
| ~ spl14_49
| ~ spl14_64 ),
inference(avatar_split_clause,[],[f587,f563,f424,f345,f316,f312,f209,f1009]) ).
fof(f1009,plain,
( spl14_108
<=> ! [X0] : symmetric_difference(X0,set_difference(sK11,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl14_108])]) ).
fof(f312,plain,
( spl14_27
<=> ! [X0] : symmetric_difference(X0,empty_set) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl14_27])]) ).
fof(f316,plain,
( spl14_28
<=> ! [X0] : set_difference(X0,empty_set) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl14_28])]) ).
fof(f424,plain,
( spl14_49
<=> ! [X0,X1] : symmetric_difference(X0,X1) = symmetric_difference(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_49])]) ).
fof(f587,plain,
( ! [X0] : symmetric_difference(X0,set_difference(sK11,X0)) = X0
| ~ spl14_5
| ~ spl14_27
| ~ spl14_28
| ~ spl14_35
| ~ spl14_49
| ~ spl14_64 ),
inference(forward_demodulation,[],[f586,f445]) ).
fof(f445,plain,
( ! [X0] : symmetric_difference(sK11,X0) = X0
| ~ spl14_5
| ~ spl14_27
| ~ spl14_35
| ~ spl14_49 ),
inference(forward_demodulation,[],[f439,f366]) ).
fof(f439,plain,
( ! [X0] : symmetric_difference(empty_set,X0) = X0
| ~ spl14_27
| ~ spl14_49 ),
inference(superposition,[],[f425,f313]) ).
fof(f313,plain,
( ! [X0] : symmetric_difference(X0,empty_set) = X0
| ~ spl14_27 ),
inference(avatar_component_clause,[],[f312]) ).
fof(f425,plain,
( ! [X0,X1] : symmetric_difference(X0,X1) = symmetric_difference(X1,X0)
| ~ spl14_49 ),
inference(avatar_component_clause,[],[f424]) ).
fof(f586,plain,
( ! [X0] : symmetric_difference(sK11,X0) = symmetric_difference(X0,set_difference(sK11,X0))
| ~ spl14_5
| ~ spl14_28
| ~ spl14_35
| ~ spl14_64 ),
inference(forward_demodulation,[],[f572,f366]) ).
fof(f572,plain,
( ! [X0] : symmetric_difference(X0,set_difference(empty_set,X0)) = symmetric_difference(empty_set,X0)
| ~ spl14_28
| ~ spl14_64 ),
inference(superposition,[],[f564,f317]) ).
fof(f317,plain,
( ! [X0] : set_difference(X0,empty_set) = X0
| ~ spl14_28 ),
inference(avatar_component_clause,[],[f316]) ).
fof(f1007,plain,
( spl14_107
| ~ spl14_24
| ~ spl14_61 ),
inference(avatar_split_clause,[],[f532,f525,f292,f1005]) ).
fof(f1005,plain,
( spl14_107
<=> ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK7(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_107])]) ).
fof(f532,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK7(powerset(X0))) )
| ~ spl14_24
| ~ spl14_61 ),
inference(resolution,[],[f526,f293]) ).
fof(f1003,plain,
( spl14_106
| ~ spl14_5
| ~ spl14_15
| ~ spl14_35
| ~ spl14_36
| ~ spl14_54 ),
inference(avatar_split_clause,[],[f494,f464,f349,f345,f256,f209,f1001]) ).
fof(f1001,plain,
( spl14_106
<=> ! [X0] :
( in(sK11,powerset(X0))
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_106])]) ).
fof(f256,plain,
( spl14_15
<=> ! [X0] : empty(sK8(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_15])]) ).
fof(f349,plain,
( spl14_36
<=> ! [X0] : element(sK8(X0),powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_36])]) ).
fof(f494,plain,
( ! [X0] :
( in(sK11,powerset(X0))
| empty(powerset(X0)) )
| ~ spl14_5
| ~ spl14_15
| ~ spl14_35
| ~ spl14_36
| ~ spl14_54 ),
inference(forward_demodulation,[],[f493,f366]) ).
fof(f493,plain,
( ! [X0] :
( in(empty_set,powerset(X0))
| empty(powerset(X0)) )
| ~ spl14_15
| ~ spl14_35
| ~ spl14_36
| ~ spl14_54 ),
inference(forward_demodulation,[],[f491,f364]) ).
fof(f364,plain,
( ! [X0] : empty_set = sK8(X0)
| ~ spl14_15
| ~ spl14_35 ),
inference(resolution,[],[f346,f257]) ).
fof(f257,plain,
( ! [X0] : empty(sK8(X0))
| ~ spl14_15 ),
inference(avatar_component_clause,[],[f256]) ).
fof(f491,plain,
( ! [X0] :
( empty(powerset(X0))
| in(sK8(X0),powerset(X0)) )
| ~ spl14_36
| ~ spl14_54 ),
inference(resolution,[],[f465,f350]) ).
fof(f350,plain,
( ! [X0] : element(sK8(X0),powerset(X0))
| ~ spl14_36 ),
inference(avatar_component_clause,[],[f349]) ).
fof(f997,plain,
( spl14_91
| spl14_88
| ~ spl14_100 ),
inference(avatar_split_clause,[],[f979,f954,f804,f816]) ).
fof(f954,plain,
( spl14_100
<=> ! [X0] :
( element(sK6(X0),X0)
| sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_100])]) ).
fof(f979,plain,
( sP0(sK1)
| spl14_88
| ~ spl14_100 ),
inference(resolution,[],[f955,f806]) ).
fof(f806,plain,
( ~ element(sK6(sK1),sK1)
| spl14_88 ),
inference(avatar_component_clause,[],[f804]) ).
fof(f955,plain,
( ! [X0] :
( element(sK6(X0),X0)
| sP0(X0) )
| ~ spl14_100 ),
inference(avatar_component_clause,[],[f954]) ).
fof(f996,plain,
( spl14_105
| ~ spl14_46
| ~ spl14_53 ),
inference(avatar_split_clause,[],[f480,f460,f412,f994]) ).
fof(f994,plain,
( spl14_105
<=> ! [X0] :
( finite(sK2(X0))
| ~ finite(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_105])]) ).
fof(f460,plain,
( spl14_53
<=> ! [X0,X1] :
( finite(X1)
| ~ element(X1,powerset(X0))
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_53])]) ).
fof(f480,plain,
( ! [X0] :
( finite(sK2(X0))
| ~ finite(X0)
| empty(X0) )
| ~ spl14_46
| ~ spl14_53 ),
inference(resolution,[],[f461,f413]) ).
fof(f461,plain,
( ! [X0,X1] :
( ~ element(X1,powerset(X0))
| finite(X1)
| ~ finite(X0) )
| ~ spl14_53 ),
inference(avatar_component_clause,[],[f460]) ).
fof(f992,plain,
( spl14_104
| ~ spl14_50
| ~ spl14_53 ),
inference(avatar_split_clause,[],[f479,f460,f428,f990]) ).
fof(f990,plain,
( spl14_104
<=> ! [X0,X1] :
( finite(X0)
| ~ finite(X1)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_104])]) ).
fof(f479,plain,
( ! [X0,X1] :
( finite(X0)
| ~ finite(X1)
| ~ subset(X0,X1) )
| ~ spl14_50
| ~ spl14_53 ),
inference(resolution,[],[f461,f429]) ).
fof(f969,plain,
( spl14_103
| ~ spl14_24
| ~ spl14_54 ),
inference(avatar_split_clause,[],[f490,f464,f292,f967]) ).
fof(f967,plain,
( spl14_103
<=> ! [X0] :
( empty(X0)
| in(sK7(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_103])]) ).
fof(f490,plain,
( ! [X0] :
( empty(X0)
| in(sK7(X0),X0) )
| ~ spl14_24
| ~ spl14_54 ),
inference(resolution,[],[f465,f293]) ).
fof(f965,plain,
( spl14_102
| ~ spl14_24
| ~ spl14_53 ),
inference(avatar_split_clause,[],[f483,f460,f292,f963]) ).
fof(f963,plain,
( spl14_102
<=> ! [X0] :
( finite(sK7(powerset(X0)))
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_102])]) ).
fof(f483,plain,
( ! [X0] :
( finite(sK7(powerset(X0)))
| ~ finite(X0) )
| ~ spl14_24
| ~ spl14_53 ),
inference(resolution,[],[f461,f293]) ).
fof(f961,plain,
( ~ spl14_101
| ~ spl14_44
| ~ spl14_96 ),
inference(avatar_split_clause,[],[f881,f848,f391,f958]) ).
fof(f958,plain,
( spl14_101
<=> in(sK1,sK7(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_101])]) ).
fof(f848,plain,
( spl14_96
<=> in(sK7(sK1),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_96])]) ).
fof(f881,plain,
( ~ in(sK1,sK7(sK1))
| ~ spl14_44
| ~ spl14_96 ),
inference(resolution,[],[f850,f392]) ).
fof(f850,plain,
( in(sK7(sK1),sK1)
| ~ spl14_96 ),
inference(avatar_component_clause,[],[f848]) ).
fof(f956,plain,
( spl14_100
| ~ spl14_41
| ~ spl14_45 ),
inference(avatar_split_clause,[],[f410,f395,f378,f954]) ).
fof(f378,plain,
( spl14_41
<=> ! [X0] :
( sP0(X0)
| in(sK6(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_41])]) ).
fof(f410,plain,
( ! [X0] :
( element(sK6(X0),X0)
| sP0(X0) )
| ~ spl14_41
| ~ spl14_45 ),
inference(resolution,[],[f396,f379]) ).
fof(f379,plain,
( ! [X0] :
( in(sK6(X0),X0)
| sP0(X0) )
| ~ spl14_41 ),
inference(avatar_component_clause,[],[f378]) ).
fof(f952,plain,
( spl14_99
| ~ spl14_40
| ~ spl14_45 ),
inference(avatar_split_clause,[],[f409,f395,f374,f950]) ).
fof(f374,plain,
( spl14_40
<=> ! [X0] :
( sP0(X0)
| in(sK5(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_40])]) ).
fof(f409,plain,
( ! [X0] :
( element(sK5(X0),X0)
| sP0(X0) )
| ~ spl14_40
| ~ spl14_45 ),
inference(resolution,[],[f396,f375]) ).
fof(f375,plain,
( ! [X0] :
( in(sK5(X0),X0)
| sP0(X0) )
| ~ spl14_40 ),
inference(avatar_component_clause,[],[f374]) ).
fof(f948,plain,
( spl14_98
| ~ spl14_41
| ~ spl14_44 ),
inference(avatar_split_clause,[],[f406,f391,f378,f946]) ).
fof(f946,plain,
( spl14_98
<=> ! [X0] :
( ~ in(X0,sK6(X0))
| sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_98])]) ).
fof(f406,plain,
( ! [X0] :
( ~ in(X0,sK6(X0))
| sP0(X0) )
| ~ spl14_41
| ~ spl14_44 ),
inference(resolution,[],[f392,f379]) ).
fof(f944,plain,
( spl14_97
| ~ spl14_40
| ~ spl14_44 ),
inference(avatar_split_clause,[],[f405,f391,f374,f942]) ).
fof(f942,plain,
( spl14_97
<=> ! [X0] :
( ~ in(X0,sK5(X0))
| sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_97])]) ).
fof(f405,plain,
( ! [X0] :
( ~ in(X0,sK5(X0))
| sP0(X0) )
| ~ spl14_40
| ~ spl14_44 ),
inference(resolution,[],[f392,f375]) ).
fof(f864,plain,
( spl14_93
| ~ spl14_35
| ~ spl14_80 ),
inference(avatar_split_clause,[],[f846,f721,f345,f828]) ).
fof(f828,plain,
( spl14_93
<=> ! [X0] :
( sK11 = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_93])]) ).
fof(f721,plain,
( spl14_80
<=> empty_set = sK11 ),
introduced(avatar_definition,[new_symbols(naming,[spl14_80])]) ).
fof(f846,plain,
( ! [X0] :
( sK11 = X0
| ~ empty(X0) )
| ~ spl14_35
| ~ spl14_80 ),
inference(forward_demodulation,[],[f346,f723]) ).
fof(f723,plain,
( empty_set = sK11
| ~ spl14_80 ),
inference(avatar_component_clause,[],[f721]) ).
fof(f851,plain,
( spl14_96
| ~ spl14_24
| ~ spl14_72 ),
inference(avatar_split_clause,[],[f761,f658,f292,f848]) ).
fof(f761,plain,
( in(sK7(sK1),sK1)
| ~ spl14_24
| ~ spl14_72 ),
inference(resolution,[],[f659,f293]) ).
fof(f845,plain,
( ~ spl14_3
| ~ spl14_94 ),
inference(avatar_contradiction_clause,[],[f838]) ).
fof(f838,plain,
( $false
| ~ spl14_3
| ~ spl14_94 ),
inference(resolution,[],[f833,f201]) ).
fof(f201,plain,
( empty(empty_set)
| ~ spl14_3 ),
inference(avatar_component_clause,[],[f199]) ).
fof(f199,plain,
( spl14_3
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_3])]) ).
fof(f833,plain,
( ! [X0] : ~ empty(X0)
| ~ spl14_94 ),
inference(avatar_component_clause,[],[f832]) ).
fof(f832,plain,
( spl14_94
<=> ! [X0] : ~ empty(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_94])]) ).
fof(f844,plain,
( ~ spl14_15
| ~ spl14_94 ),
inference(avatar_contradiction_clause,[],[f839]) ).
fof(f839,plain,
( $false
| ~ spl14_15
| ~ spl14_94 ),
inference(resolution,[],[f833,f257]) ).
fof(f843,plain,
( ~ spl14_16
| ~ spl14_94 ),
inference(avatar_contradiction_clause,[],[f840]) ).
fof(f840,plain,
( $false
| ~ spl14_16
| ~ spl14_94 ),
inference(resolution,[],[f833,f261]) ).
fof(f261,plain,
( ! [X0] : empty(sK9(X0))
| ~ spl14_16 ),
inference(avatar_component_clause,[],[f260]) ).
fof(f260,plain,
( spl14_16
<=> ! [X0] : empty(sK9(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_16])]) ).
fof(f842,plain,
( ~ spl14_5
| ~ spl14_94 ),
inference(avatar_contradiction_clause,[],[f841]) ).
fof(f841,plain,
( $false
| ~ spl14_5
| ~ spl14_94 ),
inference(resolution,[],[f833,f211]) ).
fof(f837,plain,
( spl14_94
| spl14_95
| ~ spl14_5
| ~ spl14_15
| ~ spl14_35
| ~ spl14_36
| ~ spl14_61 ),
inference(avatar_split_clause,[],[f536,f525,f349,f345,f256,f209,f835,f832]) ).
fof(f835,plain,
( spl14_95
<=> ! [X1] : ~ in(X1,sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_95])]) ).
fof(f536,plain,
( ! [X0,X1] :
( ~ in(X1,sK11)
| ~ empty(X0) )
| ~ spl14_5
| ~ spl14_15
| ~ spl14_35
| ~ spl14_36
| ~ spl14_61 ),
inference(forward_demodulation,[],[f535,f366]) ).
fof(f535,plain,
( ! [X0,X1] :
( ~ in(X1,empty_set)
| ~ empty(X0) )
| ~ spl14_15
| ~ spl14_35
| ~ spl14_36
| ~ spl14_61 ),
inference(forward_demodulation,[],[f533,f364]) ).
fof(f533,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK8(X0)) )
| ~ spl14_36
| ~ spl14_61 ),
inference(resolution,[],[f526,f350]) ).
fof(f830,plain,
( spl14_93
| ~ spl14_5
| ~ spl14_51 ),
inference(avatar_split_clause,[],[f453,f432,f209,f828]) ).
fof(f432,plain,
( spl14_51
<=> ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_51])]) ).
fof(f453,plain,
( ! [X0] :
( sK11 = X0
| ~ empty(X0) )
| ~ spl14_5
| ~ spl14_51 ),
inference(resolution,[],[f433,f211]) ).
fof(f433,plain,
( ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) )
| ~ spl14_51 ),
inference(avatar_component_clause,[],[f432]) ).
fof(f826,plain,
( spl14_92
| ~ spl14_5
| ~ spl14_27
| ~ spl14_35
| ~ spl14_49 ),
inference(avatar_split_clause,[],[f445,f424,f345,f312,f209,f824]) ).
fof(f824,plain,
( spl14_92
<=> ! [X0] : symmetric_difference(sK11,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl14_92])]) ).
fof(f819,plain,
( ~ spl14_88
| ~ spl14_89
| ~ spl14_90
| spl14_91
| ~ spl14_12
| ~ spl14_70 ),
inference(avatar_split_clause,[],[f650,f647,f244,f816,f812,f808,f804]) ).
fof(f244,plain,
( spl14_12
<=> ! [X2,X1] :
( in(symmetric_difference(X1,X2),sK1)
| ~ element(X2,sK1)
| ~ element(X1,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_12])]) ).
fof(f647,plain,
( spl14_70
<=> ! [X0] :
( ~ in(symmetric_difference(sK6(X0),set_difference(sK5(X0),sK6(X0))),X0)
| sP0(X0)
| ~ in(set_difference(sK5(X0),sK6(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_70])]) ).
fof(f650,plain,
( sP0(sK1)
| ~ in(set_difference(sK5(sK1),sK6(sK1)),sK1)
| ~ element(set_difference(sK5(sK1),sK6(sK1)),sK1)
| ~ element(sK6(sK1),sK1)
| ~ spl14_12
| ~ spl14_70 ),
inference(resolution,[],[f648,f245]) ).
fof(f245,plain,
( ! [X2,X1] :
( in(symmetric_difference(X1,X2),sK1)
| ~ element(X2,sK1)
| ~ element(X1,sK1) )
| ~ spl14_12 ),
inference(avatar_component_clause,[],[f244]) ).
fof(f648,plain,
( ! [X0] :
( ~ in(symmetric_difference(sK6(X0),set_difference(sK5(X0),sK6(X0))),X0)
| sP0(X0)
| ~ in(set_difference(sK5(X0),sK6(X0)),X0) )
| ~ spl14_70 ),
inference(avatar_component_clause,[],[f647]) ).
fof(f789,plain,
( spl14_87
| ~ spl14_12
| ~ spl14_67 ),
inference(avatar_split_clause,[],[f622,f601,f244,f787]) ).
fof(f787,plain,
( spl14_87
<=> ! [X0,X1] :
( in(symmetric_difference(X0,X1),sK1)
| ~ element(set_difference(set_difference(X1,X0),set_difference(X0,X1)),sK1)
| ~ element(set_difference(X0,X1),sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_87])]) ).
fof(f622,plain,
( ! [X0,X1] :
( in(symmetric_difference(X0,X1),sK1)
| ~ element(set_difference(set_difference(X1,X0),set_difference(X0,X1)),sK1)
| ~ element(set_difference(X0,X1),sK1) )
| ~ spl14_12
| ~ spl14_67 ),
inference(superposition,[],[f245,f602]) ).
fof(f773,plain,
( spl14_86
| ~ spl14_80
| ~ spl14_83 ),
inference(avatar_split_clause,[],[f757,f754,f721,f771]) ).
fof(f771,plain,
( spl14_86
<=> ! [X0] : sK9(X0) = sK11 ),
introduced(avatar_definition,[new_symbols(naming,[spl14_86])]) ).
fof(f754,plain,
( spl14_83
<=> ! [X0] : empty_set = sK9(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_83])]) ).
fof(f757,plain,
( ! [X0] : sK9(X0) = sK11
| ~ spl14_80
| ~ spl14_83 ),
inference(forward_demodulation,[],[f755,f723]) ).
fof(f755,plain,
( ! [X0] : empty_set = sK9(X0)
| ~ spl14_83 ),
inference(avatar_component_clause,[],[f754]) ).
fof(f769,plain,
( spl14_85
| ~ spl14_80
| ~ spl14_82 ),
inference(avatar_split_clause,[],[f752,f749,f721,f767]) ).
fof(f767,plain,
( spl14_85
<=> ! [X0] : sK8(X0) = sK11 ),
introduced(avatar_definition,[new_symbols(naming,[spl14_85])]) ).
fof(f749,plain,
( spl14_82
<=> ! [X0] : empty_set = sK8(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_82])]) ).
fof(f752,plain,
( ! [X0] : sK8(X0) = sK11
| ~ spl14_80
| ~ spl14_82 ),
inference(forward_demodulation,[],[f750,f723]) ).
fof(f750,plain,
( ! [X0] : empty_set = sK8(X0)
| ~ spl14_82 ),
inference(avatar_component_clause,[],[f749]) ).
fof(f765,plain,
( spl14_84
| ~ spl14_38
| ~ spl14_40 ),
inference(avatar_split_clause,[],[f399,f374,f357,f763]) ).
fof(f763,plain,
( spl14_84
<=> ! [X0] :
( sP0(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_84])]) ).
fof(f357,plain,
( spl14_38
<=> ! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_38])]) ).
fof(f399,plain,
( ! [X0] :
( sP0(X0)
| ~ empty(X0) )
| ~ spl14_38
| ~ spl14_40 ),
inference(resolution,[],[f375,f358]) ).
fof(f358,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) )
| ~ spl14_38 ),
inference(avatar_component_clause,[],[f357]) ).
fof(f758,plain,
( spl14_72
| ~ spl14_75
| ~ spl14_78 ),
inference(avatar_split_clause,[],[f714,f708,f670,f658]) ).
fof(f670,plain,
( spl14_75
<=> ! [X0,X1] :
( element(symmetric_difference(X0,X1),sK1)
| ~ element(X1,sK1)
| ~ element(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_75])]) ).
fof(f708,plain,
( spl14_78
<=> ! [X0] :
( ~ element(symmetric_difference(X0,X0),sK1)
| in(X0,sK1)
| ~ element(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_78])]) ).
fof(f714,plain,
( ! [X0] :
( in(X0,sK1)
| ~ element(X0,sK1) )
| ~ spl14_75
| ~ spl14_78 ),
inference(duplicate_literal_removal,[],[f711]) ).
fof(f711,plain,
( ! [X0] :
( in(X0,sK1)
| ~ element(X0,sK1)
| ~ element(X0,sK1)
| ~ element(X0,sK1) )
| ~ spl14_75
| ~ spl14_78 ),
inference(resolution,[],[f709,f671]) ).
fof(f671,plain,
( ! [X0,X1] :
( element(symmetric_difference(X0,X1),sK1)
| ~ element(X1,sK1)
| ~ element(X0,sK1) )
| ~ spl14_75 ),
inference(avatar_component_clause,[],[f670]) ).
fof(f709,plain,
( ! [X0] :
( ~ element(symmetric_difference(X0,X0),sK1)
| in(X0,sK1)
| ~ element(X0,sK1) )
| ~ spl14_78 ),
inference(avatar_component_clause,[],[f708]) ).
fof(f756,plain,
( spl14_83
| ~ spl14_16
| ~ spl14_35 ),
inference(avatar_split_clause,[],[f365,f345,f260,f754]) ).
fof(f365,plain,
( ! [X0] : empty_set = sK9(X0)
| ~ spl14_16
| ~ spl14_35 ),
inference(resolution,[],[f346,f261]) ).
fof(f751,plain,
( spl14_82
| ~ spl14_15
| ~ spl14_35 ),
inference(avatar_split_clause,[],[f364,f345,f256,f749]) ).
fof(f733,plain,
( spl14_81
| ~ spl14_12
| ~ spl14_64 ),
inference(avatar_split_clause,[],[f579,f563,f244,f731]) ).
fof(f731,plain,
( spl14_81
<=> ! [X0,X1] :
( in(symmetric_difference(X1,set_difference(X0,X1)),sK1)
| ~ element(set_difference(X1,X0),sK1)
| ~ element(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_81])]) ).
fof(f579,plain,
( ! [X0,X1] :
( in(symmetric_difference(X1,set_difference(X0,X1)),sK1)
| ~ element(set_difference(X1,X0),sK1)
| ~ element(X0,sK1) )
| ~ spl14_12
| ~ spl14_64 ),
inference(superposition,[],[f245,f564]) ).
fof(f724,plain,
( spl14_80
| ~ spl14_5
| ~ spl14_35 ),
inference(avatar_split_clause,[],[f366,f345,f209,f721]) ).
fof(f718,plain,
( spl14_79
| ~ spl14_15
| ~ spl14_21 ),
inference(avatar_split_clause,[],[f298,f280,f256,f716]) ).
fof(f716,plain,
( spl14_79
<=> ! [X0] : finite(sK8(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_79])]) ).
fof(f280,plain,
( spl14_21
<=> ! [X0] :
( finite(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_21])]) ).
fof(f298,plain,
( ! [X0] : finite(sK8(X0))
| ~ spl14_15
| ~ spl14_21 ),
inference(resolution,[],[f281,f257]) ).
fof(f281,plain,
( ! [X0] :
( ~ empty(X0)
| finite(X0) )
| ~ spl14_21 ),
inference(avatar_component_clause,[],[f280]) ).
fof(f710,plain,
( spl14_78
| ~ spl14_52
| ~ spl14_67
| ~ spl14_77 ),
inference(avatar_split_clause,[],[f681,f678,f601,f436,f708]) ).
fof(f678,plain,
( spl14_77
<=> ! [X0] :
( in(X0,sK1)
| ~ element(set_difference(X0,X0),sK1)
| ~ element(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_77])]) ).
fof(f681,plain,
( ! [X0] :
( ~ element(symmetric_difference(X0,X0),sK1)
| in(X0,sK1)
| ~ element(X0,sK1) )
| ~ spl14_52
| ~ spl14_67
| ~ spl14_77 ),
inference(forward_demodulation,[],[f679,f612]) ).
fof(f679,plain,
( ! [X0] :
( in(X0,sK1)
| ~ element(set_difference(X0,X0),sK1)
| ~ element(X0,sK1) )
| ~ spl14_77 ),
inference(avatar_component_clause,[],[f678]) ).
fof(f680,plain,
( spl14_77
| ~ spl14_12
| ~ spl14_52 ),
inference(avatar_split_clause,[],[f458,f436,f244,f678]) ).
fof(f458,plain,
( ! [X0] :
( in(X0,sK1)
| ~ element(set_difference(X0,X0),sK1)
| ~ element(X0,sK1) )
| ~ spl14_12
| ~ spl14_52 ),
inference(superposition,[],[f245,f437]) ).
fof(f676,plain,
( spl14_76
| ~ spl14_13
| ~ spl14_45 ),
inference(avatar_split_clause,[],[f408,f395,f248,f674]) ).
fof(f408,plain,
( ! [X0,X1] :
( element(set_difference(X0,X1),sK1)
| ~ element(X1,sK1)
| ~ element(X0,sK1) )
| ~ spl14_13
| ~ spl14_45 ),
inference(resolution,[],[f396,f249]) ).
fof(f672,plain,
( spl14_75
| ~ spl14_12
| ~ spl14_45 ),
inference(avatar_split_clause,[],[f407,f395,f244,f670]) ).
fof(f407,plain,
( ! [X0,X1] :
( element(symmetric_difference(X0,X1),sK1)
| ~ element(X1,sK1)
| ~ element(X0,sK1) )
| ~ spl14_12
| ~ spl14_45 ),
inference(resolution,[],[f396,f245]) ).
fof(f668,plain,
( spl14_74
| ~ spl14_13
| ~ spl14_44 ),
inference(avatar_split_clause,[],[f404,f391,f248,f666]) ).
fof(f666,plain,
( spl14_74
<=> ! [X0,X1] :
( ~ in(sK1,set_difference(X0,X1))
| ~ element(X1,sK1)
| ~ element(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_74])]) ).
fof(f404,plain,
( ! [X0,X1] :
( ~ in(sK1,set_difference(X0,X1))
| ~ element(X1,sK1)
| ~ element(X0,sK1) )
| ~ spl14_13
| ~ spl14_44 ),
inference(resolution,[],[f392,f249]) ).
fof(f664,plain,
( spl14_73
| ~ spl14_12
| ~ spl14_44 ),
inference(avatar_split_clause,[],[f403,f391,f244,f662]) ).
fof(f662,plain,
( spl14_73
<=> ! [X0,X1] :
( ~ in(sK1,symmetric_difference(X0,X1))
| ~ element(X1,sK1)
| ~ element(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_73])]) ).
fof(f403,plain,
( ! [X0,X1] :
( ~ in(sK1,symmetric_difference(X0,X1))
| ~ element(X1,sK1)
| ~ element(X0,sK1) )
| ~ spl14_12
| ~ spl14_44 ),
inference(resolution,[],[f392,f245]) ).
fof(f660,plain,
( ~ spl14_58
| spl14_72
| ~ spl14_12
| ~ spl14_27 ),
inference(avatar_split_clause,[],[f361,f312,f244,f658,f498]) ).
fof(f498,plain,
( spl14_58
<=> element(empty_set,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_58])]) ).
fof(f361,plain,
( ! [X0] :
( in(X0,sK1)
| ~ element(empty_set,sK1)
| ~ element(X0,sK1) )
| ~ spl14_12
| ~ spl14_27 ),
inference(superposition,[],[f245,f313]) ).
fof(f656,plain,
( ~ spl14_71
| ~ spl14_5
| ~ spl14_35
| spl14_58 ),
inference(avatar_split_clause,[],[f510,f498,f345,f209,f653]) ).
fof(f653,plain,
( spl14_71
<=> element(sK11,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_71])]) ).
fof(f510,plain,
( ~ element(sK11,sK1)
| ~ spl14_5
| ~ spl14_35
| spl14_58 ),
inference(forward_demodulation,[],[f500,f366]) ).
fof(f500,plain,
( ~ element(empty_set,sK1)
| spl14_58 ),
inference(avatar_component_clause,[],[f498]) ).
fof(f649,plain,
( spl14_70
| ~ spl14_64
| ~ spl14_69 ),
inference(avatar_split_clause,[],[f645,f642,f563,f647]) ).
fof(f642,plain,
( spl14_69
<=> ! [X0] :
( sP0(X0)
| ~ in(set_difference(sK5(X0),sK6(X0)),X0)
| ~ in(symmetric_difference(sK5(X0),set_difference(sK6(X0),sK5(X0))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_69])]) ).
fof(f645,plain,
( ! [X0] :
( ~ in(symmetric_difference(sK6(X0),set_difference(sK5(X0),sK6(X0))),X0)
| sP0(X0)
| ~ in(set_difference(sK5(X0),sK6(X0)),X0) )
| ~ spl14_64
| ~ spl14_69 ),
inference(forward_demodulation,[],[f643,f564]) ).
fof(f643,plain,
( ! [X0] :
( sP0(X0)
| ~ in(set_difference(sK5(X0),sK6(X0)),X0)
| ~ in(symmetric_difference(sK5(X0),set_difference(sK6(X0),sK5(X0))),X0) )
| ~ spl14_69 ),
inference(avatar_component_clause,[],[f642]) ).
fof(f644,plain,
spl14_69,
inference(avatar_split_clause,[],[f180,f642]) ).
fof(f180,plain,
! [X0] :
( sP0(X0)
| ~ in(set_difference(sK5(X0),sK6(X0)),X0)
| ~ in(symmetric_difference(sK5(X0),set_difference(sK6(X0),sK5(X0))),X0) ),
inference(definition_unfolding,[],[f142,f155]) ).
fof(f155,plain,
! [X0,X1] : set_union2(X0,X1) = symmetric_difference(X0,set_difference(X1,X0)),
inference(cnf_transformation,[],[f43]) ).
fof(f43,axiom,
! [X0,X1] : set_union2(X0,X1) = symmetric_difference(X0,set_difference(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t98_xboole_1) ).
fof(f142,plain,
! [X0] :
( sP0(X0)
| ~ in(set_difference(sK5(X0),sK6(X0)),X0)
| ~ in(set_union2(sK5(X0),sK6(X0)),X0) ),
inference(cnf_transformation,[],[f98]) ).
fof(f98,plain,
! [X0] :
( ( sP0(X0)
| ( ( ~ in(set_difference(sK5(X0),sK6(X0)),X0)
| ~ in(set_union2(sK5(X0),sK6(X0)),X0) )
& in(sK6(X0),X0)
& in(sK5(X0),X0) ) )
& ( ! [X3,X4] :
( ( in(set_difference(X3,X4),X0)
& in(set_union2(X3,X4),X0) )
| ~ in(X4,X0)
| ~ in(X3,X0) )
| ~ sP0(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f96,f97]) ).
fof(f97,plain,
! [X0] :
( ? [X1,X2] :
( ( ~ in(set_difference(X1,X2),X0)
| ~ in(set_union2(X1,X2),X0) )
& in(X2,X0)
& in(X1,X0) )
=> ( ( ~ in(set_difference(sK5(X0),sK6(X0)),X0)
| ~ in(set_union2(sK5(X0),sK6(X0)),X0) )
& in(sK6(X0),X0)
& in(sK5(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f96,plain,
! [X0] :
( ( sP0(X0)
| ? [X1,X2] :
( ( ~ in(set_difference(X1,X2),X0)
| ~ in(set_union2(X1,X2),X0) )
& in(X2,X0)
& in(X1,X0) ) )
& ( ! [X3,X4] :
( ( in(set_difference(X3,X4),X0)
& in(set_union2(X3,X4),X0) )
| ~ in(X4,X0)
| ~ in(X3,X0) )
| ~ sP0(X0) ) ),
inference(rectify,[],[f95]) ).
fof(f95,plain,
! [X0] :
( ( sP0(X0)
| ? [X1,X2] :
( ( ~ in(set_difference(X1,X2),X0)
| ~ in(set_union2(X1,X2),X0) )
& in(X2,X0)
& in(X1,X0) ) )
& ( ! [X1,X2] :
( ( in(set_difference(X1,X2),X0)
& in(set_union2(X1,X2),X0) )
| ~ in(X2,X0)
| ~ in(X1,X0) )
| ~ sP0(X0) ) ),
inference(nnf_transformation,[],[f85]) ).
fof(f85,plain,
! [X0] :
( sP0(X0)
<=> ! [X1,X2] :
( ( in(set_difference(X1,X2),X0)
& in(set_union2(X1,X2),X0) )
| ~ in(X2,X0)
| ~ in(X1,X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f607,plain,
spl14_68,
inference(avatar_split_clause,[],[f181,f605]) ).
fof(f181,plain,
! [X3,X0,X4] :
( in(symmetric_difference(X3,set_difference(X4,X3)),X0)
| ~ in(X4,X0)
| ~ in(X3,X0)
| ~ sP0(X0) ),
inference(definition_unfolding,[],[f138,f155]) ).
fof(f138,plain,
! [X3,X0,X4] :
( in(set_union2(X3,X4),X0)
| ~ in(X4,X0)
| ~ in(X3,X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f98]) ).
fof(f603,plain,
spl14_67,
inference(avatar_split_clause,[],[f178,f601]) ).
fof(f178,plain,
! [X0,X1] : symmetric_difference(X0,X1) = symmetric_difference(set_difference(X0,X1),set_difference(set_difference(X1,X0),set_difference(X0,X1))),
inference(definition_unfolding,[],[f156,f155]) ).
fof(f156,plain,
! [X0,X1] : symmetric_difference(X0,X1) = set_union2(set_difference(X0,X1),set_difference(X1,X0)),
inference(cnf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1] : symmetric_difference(X0,X1) = set_union2(set_difference(X0,X1),set_difference(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_xboole_0) ).
fof(f594,plain,
spl14_66,
inference(avatar_split_clause,[],[f139,f592]) ).
fof(f139,plain,
! [X3,X0,X4] :
( in(set_difference(X3,X4),X0)
| ~ in(X4,X0)
| ~ in(X3,X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f98]) ).
fof(f570,plain,
( ~ spl14_65
| ~ spl14_5
| ~ spl14_35
| spl14_60 ),
inference(avatar_split_clause,[],[f509,f505,f345,f209,f567]) ).
fof(f567,plain,
( spl14_65
<=> in(sK11,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_65])]) ).
fof(f505,plain,
( spl14_60
<=> in(empty_set,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_60])]) ).
fof(f509,plain,
( ~ in(sK11,sK1)
| ~ spl14_5
| ~ spl14_35
| spl14_60 ),
inference(forward_demodulation,[],[f506,f366]) ).
fof(f506,plain,
( ~ in(empty_set,sK1)
| spl14_60 ),
inference(avatar_component_clause,[],[f505]) ).
fof(f565,plain,
spl14_64,
inference(avatar_split_clause,[],[f183,f563]) ).
fof(f183,plain,
! [X0,X1] : symmetric_difference(X0,set_difference(X1,X0)) = symmetric_difference(X1,set_difference(X0,X1)),
inference(definition_unfolding,[],[f154,f155,f155]) ).
fof(f154,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f546,plain,
spl14_63,
inference(avatar_split_clause,[],[f186,f544]) ).
fof(f186,plain,
! [X0,X1] :
( finite(symmetric_difference(X0,set_difference(X1,X0)))
| ~ finite(X1)
| ~ finite(X0) ),
inference(definition_unfolding,[],[f164,f155]) ).
fof(f164,plain,
! [X0,X1] :
( finite(set_union2(X0,X1))
| ~ finite(X1)
| ~ finite(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
! [X0,X1] :
( finite(set_union2(X0,X1))
| ~ finite(X1)
| ~ finite(X0) ),
inference(flattening,[],[f77]) ).
fof(f77,plain,
! [X0,X1] :
( finite(set_union2(X0,X1))
| ~ finite(X1)
| ~ finite(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0,X1] :
( ( finite(X1)
& finite(X0) )
=> finite(set_union2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_finset_1) ).
fof(f542,plain,
spl14_62,
inference(avatar_split_clause,[],[f168,f540]) ).
fof(f168,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f82]) ).
fof(f82,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f527,plain,
spl14_61,
inference(avatar_split_clause,[],[f169,f525]) ).
fof(f169,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f84,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f39,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f508,plain,
( ~ spl14_58
| spl14_59
| spl14_60
| ~ spl14_13
| ~ spl14_26 ),
inference(avatar_split_clause,[],[f360,f308,f248,f505,f502,f498]) ).
fof(f502,plain,
( spl14_59
<=> ! [X0] : ~ element(X0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_59])]) ).
fof(f360,plain,
( ! [X0] :
( in(empty_set,sK1)
| ~ element(X0,sK1)
| ~ element(empty_set,sK1) )
| ~ spl14_13
| ~ spl14_26 ),
inference(superposition,[],[f249,f309]) ).
fof(f478,plain,
spl14_57,
inference(avatar_split_clause,[],[f185,f476]) ).
fof(f185,plain,
! [X0,X1] :
( ~ empty(symmetric_difference(X1,set_difference(X0,X1)))
| empty(X0) ),
inference(definition_unfolding,[],[f158,f155]) ).
fof(f158,plain,
! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
fof(f474,plain,
spl14_56,
inference(avatar_split_clause,[],[f184,f472]) ).
fof(f184,plain,
! [X0,X1] :
( ~ empty(symmetric_difference(X0,set_difference(X1,X0)))
| empty(X0) ),
inference(definition_unfolding,[],[f157,f155]) ).
fof(f157,plain,
! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
fof(f470,plain,
spl14_55,
inference(avatar_split_clause,[],[f163,f468]) ).
fof(f163,plain,
! [X0,X1] :
( finite(symmetric_difference(X0,X1))
| ~ finite(X1)
| ~ finite(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0,X1] :
( finite(symmetric_difference(X0,X1))
| ~ finite(X1)
| ~ finite(X0) ),
inference(flattening,[],[f75]) ).
fof(f75,plain,
! [X0,X1] :
( finite(symmetric_difference(X0,X1))
| ~ finite(X1)
| ~ finite(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0,X1] :
( ( finite(X1)
& finite(X0) )
=> finite(symmetric_difference(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc17_finset_1) ).
fof(f466,plain,
spl14_54,
inference(avatar_split_clause,[],[f162,f464]) ).
fof(f162,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f73]) ).
fof(f73,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f462,plain,
spl14_53,
inference(avatar_split_clause,[],[f134,f460]) ).
fof(f134,plain,
! [X0,X1] :
( finite(X1)
| ~ element(X1,powerset(X0))
| ~ finite(X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0] :
( ! [X1] :
( finite(X1)
| ~ element(X1,powerset(X0)) )
| ~ finite(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( finite(X0)
=> ! [X1] :
( element(X1,powerset(X0))
=> finite(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
fof(f438,plain,
spl14_52,
inference(avatar_split_clause,[],[f182,f436]) ).
fof(f182,plain,
! [X0] : symmetric_difference(X0,set_difference(X0,X0)) = X0,
inference(definition_unfolding,[],[f152,f155]) ).
fof(f152,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(rectify,[],[f17]) ).
fof(f17,axiom,
! [X0,X1] : set_union2(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(f434,plain,
spl14_51,
inference(avatar_split_clause,[],[f166,f432]) ).
fof(f166,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(f430,plain,
spl14_50,
inference(avatar_split_clause,[],[f165,f428]) ).
fof(f165,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0,X1] :
( subset(X0,X1)
=> element(X0,powerset(X1)) ),
inference(unused_predicate_definition_removal,[],[f35]) ).
fof(f35,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f426,plain,
spl14_49,
inference(avatar_split_clause,[],[f153,f424]) ).
fof(f153,plain,
! [X0,X1] : symmetric_difference(X0,X1) = symmetric_difference(X1,X0),
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] : symmetric_difference(X0,X1) = symmetric_difference(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k5_xboole_0) ).
fof(f422,plain,
spl14_48,
inference(avatar_split_clause,[],[f129,f420]) ).
fof(f129,plain,
! [X0] :
( element(sK4(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f94,plain,
! [X0] :
( ( finite(sK4(X0))
& ~ empty(sK4(X0))
& element(sK4(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f59,f93]) ).
fof(f93,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( finite(sK4(X0))
& ~ empty(sK4(X0))
& element(sK4(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f59,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_finset_1) ).
fof(f418,plain,
spl14_47,
inference(avatar_split_clause,[],[f126,f416]) ).
fof(f126,plain,
! [X0] :
( element(sK3(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f92,plain,
! [X0] :
( ( finite(sK3(X0))
& ~ empty(sK3(X0))
& element(sK3(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f58,f91]) ).
fof(f91,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( finite(sK3(X0))
& ~ empty(sK3(X0))
& element(sK3(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f58,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_finset_1) ).
fof(f414,plain,
spl14_46,
inference(avatar_split_clause,[],[f124,f412]) ).
fof(f124,plain,
! [X0] :
( element(sK2(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0] :
( ( ~ empty(sK2(X0))
& element(sK2(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f57,f89]) ).
fof(f89,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( ~ empty(sK2(X0))
& element(sK2(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f57,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f397,plain,
spl14_45,
inference(avatar_split_clause,[],[f161,f395]) ).
fof(f161,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f393,plain,
spl14_44,
inference(avatar_split_clause,[],[f160,f391]) ).
fof(f160,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f389,plain,
spl14_43,
inference(avatar_split_clause,[],[f159,f387]) ).
fof(f387,plain,
( spl14_43
<=> ! [X0,X1] :
( finite(set_difference(X0,X1))
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_43])]) ).
fof(f159,plain,
! [X0,X1] :
( finite(set_difference(X0,X1))
| ~ finite(X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0,X1] :
( finite(set_difference(X0,X1))
| ~ finite(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0,X1] :
( finite(X0)
=> finite(set_difference(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_finset_1) ).
fof(f385,plain,
( spl14_42
| ~ spl14_9
| ~ spl14_22 ),
inference(avatar_split_clause,[],[f306,f284,f229,f382]) ).
fof(f382,plain,
( spl14_42
<=> sP0(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_42])]) ).
fof(f229,plain,
( spl14_9
<=> preboolean(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_9])]) ).
fof(f284,plain,
( spl14_22
<=> ! [X0] :
( sP0(X0)
| ~ preboolean(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_22])]) ).
fof(f306,plain,
( sP0(sK12)
| ~ spl14_9
| ~ spl14_22 ),
inference(resolution,[],[f285,f231]) ).
fof(f231,plain,
( preboolean(sK12)
| ~ spl14_9 ),
inference(avatar_component_clause,[],[f229]) ).
fof(f285,plain,
( ! [X0] :
( ~ preboolean(X0)
| sP0(X0) )
| ~ spl14_22 ),
inference(avatar_component_clause,[],[f284]) ).
fof(f380,plain,
spl14_41,
inference(avatar_split_clause,[],[f141,f378]) ).
fof(f141,plain,
! [X0] :
( sP0(X0)
| in(sK6(X0),X0) ),
inference(cnf_transformation,[],[f98]) ).
fof(f376,plain,
spl14_40,
inference(avatar_split_clause,[],[f140,f374]) ).
fof(f140,plain,
! [X0] :
( sP0(X0)
| in(sK5(X0),X0) ),
inference(cnf_transformation,[],[f98]) ).
fof(f372,plain,
spl14_39,
inference(avatar_split_clause,[],[f137,f370]) ).
fof(f370,plain,
( spl14_39
<=> ! [X0] :
( preboolean(X0)
| ~ diff_closed(X0)
| ~ cup_closed(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_39])]) ).
fof(f137,plain,
! [X0] :
( preboolean(X0)
| ~ diff_closed(X0)
| ~ cup_closed(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0] :
( preboolean(X0)
| ~ diff_closed(X0)
| ~ cup_closed(X0) ),
inference(flattening,[],[f64]) ).
fof(f64,plain,
! [X0] :
( preboolean(X0)
| ~ diff_closed(X0)
| ~ cup_closed(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( ( diff_closed(X0)
& cup_closed(X0) )
=> preboolean(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finsub_1) ).
fof(f359,plain,
spl14_38,
inference(avatar_split_clause,[],[f167,f357]) ).
fof(f167,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f41]) ).
fof(f41,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f355,plain,
spl14_37,
inference(avatar_split_clause,[],[f148,f353]) ).
fof(f353,plain,
( spl14_37
<=> ! [X0] : element(sK9(X0),powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_37])]) ).
fof(f148,plain,
! [X0] : element(sK9(X0),powerset(X0)),
inference(cnf_transformation,[],[f105]) ).
fof(f105,plain,
! [X0] :
( finite(sK9(X0))
& empty(sK9(X0))
& element(sK9(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f53,f104]) ).
fof(f104,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& empty(X1)
& element(X1,powerset(X0)) )
=> ( finite(sK9(X0))
& empty(sK9(X0))
& element(sK9(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f53,plain,
! [X0] :
? [X1] :
( finite(X1)
& empty(X1)
& element(X1,powerset(X0)) ),
inference(pure_predicate_removal,[],[f52]) ).
fof(f52,plain,
! [X0] :
? [X1] :
( finite(X1)
& relation(X1)
& empty(X1)
& element(X1,powerset(X0)) ),
inference(pure_predicate_removal,[],[f51]) ).
fof(f51,plain,
! [X0] :
? [X1] :
( finite(X1)
& function(X1)
& relation(X1)
& empty(X1)
& element(X1,powerset(X0)) ),
inference(pure_predicate_removal,[],[f50]) ).
fof(f50,plain,
! [X0] :
? [X1] :
( finite(X1)
& one_to_one(X1)
& function(X1)
& relation(X1)
& empty(X1)
& element(X1,powerset(X0)) ),
inference(pure_predicate_removal,[],[f49]) ).
fof(f49,plain,
! [X0] :
? [X1] :
( finite(X1)
& epsilon_transitive(X1)
& one_to_one(X1)
& function(X1)
& relation(X1)
& empty(X1)
& element(X1,powerset(X0)) ),
inference(pure_predicate_removal,[],[f48]) ).
fof(f48,plain,
! [X0] :
? [X1] :
( finite(X1)
& epsilon_connected(X1)
& epsilon_transitive(X1)
& one_to_one(X1)
& function(X1)
& relation(X1)
& empty(X1)
& element(X1,powerset(X0)) ),
inference(pure_predicate_removal,[],[f47]) ).
fof(f47,plain,
! [X0] :
? [X1] :
( finite(X1)
& ordinal(X1)
& epsilon_connected(X1)
& epsilon_transitive(X1)
& one_to_one(X1)
& function(X1)
& relation(X1)
& empty(X1)
& element(X1,powerset(X0)) ),
inference(pure_predicate_removal,[],[f22]) ).
fof(f22,axiom,
! [X0] :
? [X1] :
( finite(X1)
& natural(X1)
& ordinal(X1)
& epsilon_connected(X1)
& epsilon_transitive(X1)
& one_to_one(X1)
& function(X1)
& relation(X1)
& empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_finset_1) ).
fof(f351,plain,
spl14_36,
inference(avatar_split_clause,[],[f146,f349]) ).
fof(f146,plain,
! [X0] : element(sK8(X0),powerset(X0)),
inference(cnf_transformation,[],[f103]) ).
fof(f103,plain,
! [X0] :
( empty(sK8(X0))
& element(sK8(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f23,f102]) ).
fof(f102,plain,
! [X0] :
( ? [X1] :
( empty(X1)
& element(X1,powerset(X0)) )
=> ( empty(sK8(X0))
& element(sK8(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f23,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f347,plain,
spl14_35,
inference(avatar_split_clause,[],[f136,f345]) ).
fof(f136,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f343,plain,
spl14_34,
inference(avatar_split_clause,[],[f131,f341]) ).
fof(f341,plain,
( spl14_34
<=> ! [X0] :
( finite(sK4(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_34])]) ).
fof(f131,plain,
! [X0] :
( finite(sK4(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f339,plain,
( spl14_33
| ~ spl14_5
| ~ spl14_21 ),
inference(avatar_split_clause,[],[f300,f280,f209,f336]) ).
fof(f336,plain,
( spl14_33
<=> finite(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_33])]) ).
fof(f300,plain,
( finite(sK11)
| ~ spl14_5
| ~ spl14_21 ),
inference(resolution,[],[f281,f211]) ).
fof(f334,plain,
spl14_32,
inference(avatar_split_clause,[],[f130,f332]) ).
fof(f332,plain,
( spl14_32
<=> ! [X0] :
( ~ empty(sK4(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_32])]) ).
fof(f130,plain,
! [X0] :
( ~ empty(sK4(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f330,plain,
spl14_31,
inference(avatar_split_clause,[],[f128,f328]) ).
fof(f328,plain,
( spl14_31
<=> ! [X0] :
( finite(sK3(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_31])]) ).
fof(f128,plain,
! [X0] :
( finite(sK3(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f326,plain,
spl14_30,
inference(avatar_split_clause,[],[f127,f324]) ).
fof(f324,plain,
( spl14_30
<=> ! [X0] :
( ~ empty(sK3(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_30])]) ).
fof(f127,plain,
! [X0] :
( ~ empty(sK3(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f322,plain,
spl14_29,
inference(avatar_split_clause,[],[f125,f320]) ).
fof(f320,plain,
( spl14_29
<=> ! [X0] :
( ~ empty(sK2(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_29])]) ).
fof(f125,plain,
! [X0] :
( ~ empty(sK2(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f318,plain,
spl14_28,
inference(avatar_split_clause,[],[f122,f316]) ).
fof(f122,plain,
! [X0] : set_difference(X0,empty_set) = X0,
inference(cnf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0] : set_difference(X0,empty_set) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
fof(f314,plain,
spl14_27,
inference(avatar_split_clause,[],[f121,f312]) ).
fof(f121,plain,
! [X0] : symmetric_difference(X0,empty_set) = X0,
inference(cnf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0] : symmetric_difference(X0,empty_set) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_boole) ).
fof(f310,plain,
spl14_26,
inference(avatar_split_clause,[],[f120,f308]) ).
fof(f120,plain,
! [X0] : empty_set = set_difference(empty_set,X0),
inference(cnf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0] : empty_set = set_difference(empty_set,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
fof(f305,plain,
( spl14_25
| ~ spl14_3
| ~ spl14_21 ),
inference(avatar_split_clause,[],[f297,f280,f199,f302]) ).
fof(f302,plain,
( spl14_25
<=> finite(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_25])]) ).
fof(f297,plain,
( finite(empty_set)
| ~ spl14_3
| ~ spl14_21 ),
inference(resolution,[],[f281,f201]) ).
fof(f294,plain,
spl14_24,
inference(avatar_split_clause,[],[f145,f292]) ).
fof(f145,plain,
! [X0] : element(sK7(X0),X0),
inference(cnf_transformation,[],[f101]) ).
fof(f101,plain,
! [X0] : element(sK7(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f9,f100]) ).
fof(f100,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK7(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f9,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f290,plain,
spl14_23,
inference(avatar_split_clause,[],[f144,f288]) ).
fof(f144,plain,
! [X0] :
( preboolean(X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f99,plain,
! [X0] :
( ( preboolean(X0)
| ~ sP0(X0) )
& ( sP0(X0)
| ~ preboolean(X0) ) ),
inference(nnf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0] :
( preboolean(X0)
<=> sP0(X0) ),
inference(definition_folding,[],[f67,f85]) ).
fof(f67,plain,
! [X0] :
( preboolean(X0)
<=> ! [X1,X2] :
( ( in(set_difference(X1,X2),X0)
& in(set_union2(X1,X2),X0) )
| ~ in(X2,X0)
| ~ in(X1,X0) ) ),
inference(flattening,[],[f66]) ).
fof(f66,plain,
! [X0] :
( preboolean(X0)
<=> ! [X1,X2] :
( ( in(set_difference(X1,X2),X0)
& in(set_union2(X1,X2),X0) )
| ~ in(X2,X0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0] :
( preboolean(X0)
<=> ! [X1,X2] :
( ( in(X2,X0)
& in(X1,X0) )
=> ( in(set_difference(X1,X2),X0)
& in(set_union2(X1,X2),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_finsub_1) ).
fof(f286,plain,
spl14_22,
inference(avatar_split_clause,[],[f143,f284]) ).
fof(f143,plain,
! [X0] :
( sP0(X0)
| ~ preboolean(X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f282,plain,
spl14_21,
inference(avatar_split_clause,[],[f135,f280]) ).
fof(f135,plain,
! [X0] :
( finite(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0] :
( finite(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( empty(X0)
=> finite(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
fof(f278,plain,
spl14_20,
inference(avatar_split_clause,[],[f133,f276]) ).
fof(f276,plain,
( spl14_20
<=> ! [X0] :
( diff_closed(X0)
| ~ preboolean(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_20])]) ).
fof(f133,plain,
! [X0] :
( diff_closed(X0)
| ~ preboolean(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0] :
( ( diff_closed(X0)
& cup_closed(X0) )
| ~ preboolean(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( preboolean(X0)
=> ( diff_closed(X0)
& cup_closed(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finsub_1) ).
fof(f274,plain,
spl14_19,
inference(avatar_split_clause,[],[f132,f272]) ).
fof(f272,plain,
( spl14_19
<=> ! [X0] :
( cup_closed(X0)
| ~ preboolean(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_19])]) ).
fof(f132,plain,
! [X0] :
( cup_closed(X0)
| ~ preboolean(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f270,plain,
spl14_18,
inference(avatar_split_clause,[],[f151,f268]) ).
fof(f268,plain,
( spl14_18
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_18])]) ).
fof(f151,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f27]) ).
fof(f27,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f266,plain,
spl14_17,
inference(avatar_split_clause,[],[f150,f264]) ).
fof(f264,plain,
( spl14_17
<=> ! [X0] : finite(sK9(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_17])]) ).
fof(f150,plain,
! [X0] : finite(sK9(X0)),
inference(cnf_transformation,[],[f105]) ).
fof(f262,plain,
spl14_16,
inference(avatar_split_clause,[],[f149,f260]) ).
fof(f149,plain,
! [X0] : empty(sK9(X0)),
inference(cnf_transformation,[],[f105]) ).
fof(f258,plain,
spl14_15,
inference(avatar_split_clause,[],[f147,f256]) ).
fof(f147,plain,
! [X0] : empty(sK8(X0)),
inference(cnf_transformation,[],[f103]) ).
fof(f254,plain,
spl14_14,
inference(avatar_split_clause,[],[f119,f252]) ).
fof(f252,plain,
( spl14_14
<=> ! [X0] : ~ empty(powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_14])]) ).
fof(f119,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f250,plain,
spl14_13,
inference(avatar_split_clause,[],[f116,f248]) ).
fof(f116,plain,
! [X2,X1] :
( in(set_difference(X1,X2),sK1)
| ~ element(X2,sK1)
| ~ element(X1,sK1) ),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
( ~ preboolean(sK1)
& ! [X1] :
( ! [X2] :
( ( in(set_difference(X1,X2),sK1)
& in(symmetric_difference(X1,X2),sK1) )
| ~ element(X2,sK1) )
| ~ element(X1,sK1) )
& ~ empty(sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f56,f87]) ).
fof(f87,plain,
( ? [X0] :
( ~ preboolean(X0)
& ! [X1] :
( ! [X2] :
( ( in(set_difference(X1,X2),X0)
& in(symmetric_difference(X1,X2),X0) )
| ~ element(X2,X0) )
| ~ element(X1,X0) )
& ~ empty(X0) )
=> ( ~ preboolean(sK1)
& ! [X1] :
( ! [X2] :
( ( in(set_difference(X1,X2),sK1)
& in(symmetric_difference(X1,X2),sK1) )
| ~ element(X2,sK1) )
| ~ element(X1,sK1) )
& ~ empty(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f56,plain,
? [X0] :
( ~ preboolean(X0)
& ! [X1] :
( ! [X2] :
( ( in(set_difference(X1,X2),X0)
& in(symmetric_difference(X1,X2),X0) )
| ~ element(X2,X0) )
| ~ element(X1,X0) )
& ~ empty(X0) ),
inference(flattening,[],[f55]) ).
fof(f55,plain,
? [X0] :
( ~ preboolean(X0)
& ! [X1] :
( ! [X2] :
( ( in(set_difference(X1,X2),X0)
& in(symmetric_difference(X1,X2),X0) )
| ~ element(X2,X0) )
| ~ element(X1,X0) )
& ~ empty(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,negated_conjecture,
~ ! [X0] :
( ~ empty(X0)
=> ( ! [X1] :
( element(X1,X0)
=> ! [X2] :
( element(X2,X0)
=> ( in(set_difference(X1,X2),X0)
& in(symmetric_difference(X1,X2),X0) ) ) )
=> preboolean(X0) ) ),
inference(negated_conjecture,[],[f29]) ).
fof(f29,conjecture,
! [X0] :
( ~ empty(X0)
=> ( ! [X1] :
( element(X1,X0)
=> ! [X2] :
( element(X2,X0)
=> ( in(set_difference(X1,X2),X0)
& in(symmetric_difference(X1,X2),X0) ) ) )
=> preboolean(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_finsub_1) ).
fof(f246,plain,
spl14_12,
inference(avatar_split_clause,[],[f115,f244]) ).
fof(f115,plain,
! [X2,X1] :
( in(symmetric_difference(X1,X2),sK1)
| ~ element(X2,sK1)
| ~ element(X1,sK1) ),
inference(cnf_transformation,[],[f88]) ).
fof(f242,plain,
spl14_11,
inference(avatar_split_clause,[],[f177,f239]) ).
fof(f239,plain,
( spl14_11
<=> finite(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_11])]) ).
fof(f177,plain,
finite(sK13),
inference(cnf_transformation,[],[f113]) ).
fof(f113,plain,
( finite(sK13)
& ~ empty(sK13) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f18,f112]) ).
fof(f112,plain,
( ? [X0] :
( finite(X0)
& ~ empty(X0) )
=> ( finite(sK13)
& ~ empty(sK13) ) ),
introduced(choice_axiom,[]) ).
fof(f18,axiom,
? [X0] :
( finite(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
fof(f237,plain,
~ spl14_10,
inference(avatar_split_clause,[],[f176,f234]) ).
fof(f234,plain,
( spl14_10
<=> empty(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_10])]) ).
fof(f176,plain,
~ empty(sK13),
inference(cnf_transformation,[],[f113]) ).
fof(f232,plain,
spl14_9,
inference(avatar_split_clause,[],[f175,f229]) ).
fof(f175,plain,
preboolean(sK12),
inference(cnf_transformation,[],[f111]) ).
fof(f111,plain,
( preboolean(sK12)
& diff_closed(sK12)
& cup_closed(sK12)
& ~ empty(sK12) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f54,f110]) ).
fof(f110,plain,
( ? [X0] :
( preboolean(X0)
& diff_closed(X0)
& cup_closed(X0)
& ~ empty(X0) )
=> ( preboolean(sK12)
& diff_closed(sK12)
& cup_closed(sK12)
& ~ empty(sK12) ) ),
introduced(choice_axiom,[]) ).
fof(f54,plain,
? [X0] :
( preboolean(X0)
& diff_closed(X0)
& cup_closed(X0)
& ~ empty(X0) ),
inference(pure_predicate_removal,[],[f19]) ).
fof(f19,axiom,
? [X0] :
( preboolean(X0)
& diff_closed(X0)
& cap_closed(X0)
& cup_closed(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finsub_1) ).
fof(f227,plain,
spl14_8,
inference(avatar_split_clause,[],[f174,f224]) ).
fof(f224,plain,
( spl14_8
<=> diff_closed(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_8])]) ).
fof(f174,plain,
diff_closed(sK12),
inference(cnf_transformation,[],[f111]) ).
fof(f222,plain,
spl14_7,
inference(avatar_split_clause,[],[f173,f219]) ).
fof(f219,plain,
( spl14_7
<=> cup_closed(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_7])]) ).
fof(f173,plain,
cup_closed(sK12),
inference(cnf_transformation,[],[f111]) ).
fof(f217,plain,
~ spl14_6,
inference(avatar_split_clause,[],[f172,f214]) ).
fof(f214,plain,
( spl14_6
<=> empty(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_6])]) ).
fof(f172,plain,
~ empty(sK12),
inference(cnf_transformation,[],[f111]) ).
fof(f212,plain,
spl14_5,
inference(avatar_split_clause,[],[f171,f209]) ).
fof(f171,plain,
empty(sK11),
inference(cnf_transformation,[],[f109]) ).
fof(f109,plain,
empty(sK11),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f21,f108]) ).
fof(f108,plain,
( ? [X0] : empty(X0)
=> empty(sK11) ),
introduced(choice_axiom,[]) ).
fof(f21,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f207,plain,
~ spl14_4,
inference(avatar_split_clause,[],[f170,f204]) ).
fof(f204,plain,
( spl14_4
<=> empty(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_4])]) ).
fof(f170,plain,
~ empty(sK10),
inference(cnf_transformation,[],[f107]) ).
fof(f107,plain,
~ empty(sK10),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f24,f106]) ).
fof(f106,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK10) ),
introduced(choice_axiom,[]) ).
fof(f24,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f202,plain,
spl14_3,
inference(avatar_split_clause,[],[f118,f199]) ).
fof(f118,plain,
empty(empty_set),
inference(cnf_transformation,[],[f13]) ).
fof(f13,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f197,plain,
~ spl14_2,
inference(avatar_split_clause,[],[f117,f194]) ).
fof(f117,plain,
~ preboolean(sK1),
inference(cnf_transformation,[],[f88]) ).
fof(f192,plain,
~ spl14_1,
inference(avatar_split_clause,[],[f114,f189]) ).
fof(f189,plain,
( spl14_1
<=> empty(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_1])]) ).
fof(f114,plain,
~ empty(sK1),
inference(cnf_transformation,[],[f88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU104+1 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.33 % Computer : n003.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon Apr 29 20:34:48 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.11/0.33 % (6169)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.35 % (6174)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)
% 0.11/0.35 % (6176)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)
% 0.11/0.35 % (6175)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)
% 0.11/0.35 % (6172)WARNING: value z3 for option sas not known
% 0.17/0.36 % (6172)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)
% 0.17/0.36 % (6171)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.17/0.36 % (6173)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.17/0.36 TRYING [1]
% 0.17/0.36 TRYING [2]
% 0.17/0.37 TRYING [3]
% 0.17/0.37 % (6170)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.17/0.37 % (6174)First to succeed.
% 0.17/0.37 TRYING [4]
% 0.17/0.38 % (6174)Refutation found. Thanks to Tanya!
% 0.17/0.38 % SZS status Theorem for theBenchmark
% 0.17/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.38 % (6174)------------------------------
% 0.17/0.38 % (6174)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.17/0.38 % (6174)Termination reason: Refutation
% 0.17/0.38
% 0.17/0.38 % (6174)Memory used [KB]: 1357
% 0.17/0.38 % (6174)Time elapsed: 0.029 s
% 0.17/0.38 % (6174)Instructions burned: 51 (million)
% 0.17/0.38 % (6174)------------------------------
% 0.17/0.38 % (6174)------------------------------
% 0.17/0.38 % (6169)Success in time 0.044 s
%------------------------------------------------------------------------------