TSTP Solution File: SEU105+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU105+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 : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 09:27:01 EDT 2024
% Result : Theorem 0.21s 0.50s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 224
% Syntax : Number of formulae : 746 ( 128 unt; 0 def)
% Number of atoms : 2294 ( 126 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 2772 (1224 ~;1186 |; 149 &)
% ( 171 <=>; 42 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 184 ( 182 usr; 166 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 6 con; 0-2 aty)
% Number of variables : 847 ( 807 !; 40 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5507,plain,
$false,
inference(avatar_sat_refutation,[],[f218,f223,f228,f233,f238,f243,f248,f253,f258,f263,f268,f272,f276,f280,f284,f288,f292,f296,f300,f304,f308,f312,f316,f320,f331,f336,f340,f344,f348,f352,f356,f360,f365,f369,f373,f377,f381,f385,f399,f403,f407,f411,f415,f419,f423,f427,f447,f451,f455,f459,f463,f467,f471,f475,f480,f485,f519,f532,f539,f543,f547,f578,f593,f598,f602,f606,f649,f666,f670,f716,f721,f745,f751,f757,f816,f821,f825,f829,f833,f866,f871,f876,f884,f889,f894,f898,f902,f921,f956,f960,f964,f971,f1065,f1069,f1073,f1077,f1081,f1085,f1089,f1093,f1133,f1140,f1149,f1153,f1157,f1161,f1165,f1169,f1174,f1212,f1293,f1297,f1301,f1318,f1319,f1324,f1328,f1332,f1352,f1356,f1357,f1361,f1365,f1369,f1373,f1377,f1381,f1466,f1470,f1504,f1509,f1513,f1517,f1521,f1525,f1689,f1828,f1881,f1885,f1889,f2023,f2027,f2358,f2531,f2535,f2539,f2543,f2548,f2552,f2556,f3512,f3598,f3602,f3890,f4164,f4168,f4676,f4951,f4955,f5180,f5485,f5489,f5497,f5505,f5506]) ).
fof(f5506,plain,
( ~ spl14_108
| ~ spl14_102
| ~ spl14_12
| spl14_105 ),
inference(avatar_split_clause,[],[f1136,f1130,f270,f1118,f1146]) ).
fof(f1146,plain,
( spl14_108
<=> element(sK5(sK1),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_108])]) ).
fof(f1118,plain,
( spl14_102
<=> element(set_intersection2(sK6(sK1),sK5(sK1)),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_102])]) ).
fof(f270,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(f1130,plain,
( spl14_105
<=> in(symmetric_difference(sK5(sK1),set_intersection2(sK6(sK1),sK5(sK1))),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_105])]) ).
fof(f1136,plain,
( ~ element(set_intersection2(sK6(sK1),sK5(sK1)),sK1)
| ~ element(sK5(sK1),sK1)
| ~ spl14_12
| spl14_105 ),
inference(resolution,[],[f1132,f271]) ).
fof(f271,plain,
( ! [X2,X1] :
( in(symmetric_difference(X1,X2),sK1)
| ~ element(X2,sK1)
| ~ element(X1,sK1) )
| ~ spl14_12 ),
inference(avatar_component_clause,[],[f270]) ).
fof(f1132,plain,
( ~ in(symmetric_difference(sK5(sK1),set_intersection2(sK6(sK1),sK5(sK1))),sK1)
| spl14_105 ),
inference(avatar_component_clause,[],[f1130]) ).
fof(f5505,plain,
( spl14_165
| ~ spl14_42
| ~ spl14_108 ),
inference(avatar_split_clause,[],[f2018,f1146,f409,f5502]) ).
fof(f5502,plain,
( spl14_165
<=> in(sK5(sK1),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_165])]) ).
fof(f409,plain,
( spl14_42
<=> ! [X0] :
( in(X0,sK1)
| ~ element(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_42])]) ).
fof(f2018,plain,
( in(sK5(sK1),sK1)
| ~ spl14_42
| ~ spl14_108 ),
inference(resolution,[],[f1147,f410]) ).
fof(f410,plain,
( ! [X0] :
( ~ element(X0,sK1)
| in(X0,sK1) )
| ~ spl14_42 ),
inference(avatar_component_clause,[],[f409]) ).
fof(f1147,plain,
( element(sK5(sK1),sK1)
| ~ spl14_108 ),
inference(avatar_component_clause,[],[f1146]) ).
fof(f5497,plain,
( spl14_164
| ~ spl14_42
| ~ spl14_103 ),
inference(avatar_split_clause,[],[f5491,f1122,f409,f5494]) ).
fof(f5494,plain,
( spl14_164
<=> in(symmetric_difference(sK6(sK1),sK5(sK1)),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_164])]) ).
fof(f1122,plain,
( spl14_103
<=> element(symmetric_difference(sK6(sK1),sK5(sK1)),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_103])]) ).
fof(f5491,plain,
( in(symmetric_difference(sK6(sK1),sK5(sK1)),sK1)
| ~ spl14_42
| ~ spl14_103 ),
inference(resolution,[],[f1123,f410]) ).
fof(f1123,plain,
( element(symmetric_difference(sK6(sK1),sK5(sK1)),sK1)
| ~ spl14_103 ),
inference(avatar_component_clause,[],[f1122]) ).
fof(f5489,plain,
( ~ spl14_107
| ~ spl14_108
| ~ spl14_78
| spl14_103 ),
inference(avatar_split_clause,[],[f1135,f1122,f827,f1146,f1142]) ).
fof(f1142,plain,
( spl14_107
<=> element(sK6(sK1),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_107])]) ).
fof(f827,plain,
( spl14_78
<=> ! [X0,X1] :
( element(symmetric_difference(X0,X1),sK1)
| ~ element(X1,sK1)
| ~ element(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_78])]) ).
fof(f1135,plain,
( ~ element(sK5(sK1),sK1)
| ~ element(sK6(sK1),sK1)
| ~ spl14_78
| spl14_103 ),
inference(resolution,[],[f1124,f828]) ).
fof(f828,plain,
( ! [X0,X1] :
( element(symmetric_difference(X0,X1),sK1)
| ~ element(X1,sK1)
| ~ element(X0,sK1) )
| ~ spl14_78 ),
inference(avatar_component_clause,[],[f827]) ).
fof(f1124,plain,
( ~ element(symmetric_difference(sK6(sK1),sK5(sK1)),sK1)
| spl14_103 ),
inference(avatar_component_clause,[],[f1122]) ).
fof(f5485,plain,
( spl14_163
| ~ spl14_42
| ~ spl14_102 ),
inference(avatar_split_clause,[],[f1691,f1118,f409,f5482]) ).
fof(f5482,plain,
( spl14_163
<=> in(set_intersection2(sK6(sK1),sK5(sK1)),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_163])]) ).
fof(f1691,plain,
( in(set_intersection2(sK6(sK1),sK5(sK1)),sK1)
| ~ spl14_42
| ~ spl14_102 ),
inference(resolution,[],[f1119,f410]) ).
fof(f1119,plain,
( element(set_intersection2(sK6(sK1),sK5(sK1)),sK1)
| ~ spl14_102 ),
inference(avatar_component_clause,[],[f1118]) ).
fof(f5180,plain,
( spl14_162
| ~ spl14_50
| ~ spl14_51
| ~ spl14_71
| ~ spl14_74 ),
inference(avatar_split_clause,[],[f811,f755,f719,f461,f457,f5178]) ).
fof(f5178,plain,
( spl14_162
<=> ! [X2,X0,X1] :
( in(symmetric_difference(symmetric_difference(X0,X1),set_intersection2(set_intersection2(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))),symmetric_difference(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))))),X2)
| ~ in(symmetric_difference(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))),X2)
| ~ in(set_intersection2(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))),X2)
| ~ sP0(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_162])]) ).
fof(f457,plain,
( spl14_50
<=> ! [X0,X1] : symmetric_difference(X0,X1) = symmetric_difference(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_50])]) ).
fof(f461,plain,
( spl14_51
<=> ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_51])]) ).
fof(f719,plain,
( spl14_71
<=> ! [X4,X0,X3] :
( in(symmetric_difference(set_intersection2(X4,X3),symmetric_difference(X4,X3)),X0)
| ~ in(X4,X0)
| ~ in(X3,X0)
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_71])]) ).
fof(f755,plain,
( spl14_74
<=> ! [X0,X1] : symmetric_difference(X0,X1) = symmetric_difference(symmetric_difference(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))),set_intersection2(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_74])]) ).
fof(f811,plain,
( ! [X2,X0,X1] :
( in(symmetric_difference(symmetric_difference(X0,X1),set_intersection2(set_intersection2(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))),symmetric_difference(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))))),X2)
| ~ in(symmetric_difference(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))),X2)
| ~ in(set_intersection2(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))),X2)
| ~ sP0(X2) )
| ~ spl14_50
| ~ spl14_51
| ~ spl14_71
| ~ spl14_74 ),
inference(forward_demodulation,[],[f810,f462]) ).
fof(f462,plain,
( ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0)
| ~ spl14_51 ),
inference(avatar_component_clause,[],[f461]) ).
fof(f810,plain,
( ! [X2,X0,X1] :
( in(symmetric_difference(symmetric_difference(X0,X1),set_intersection2(symmetric_difference(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))),set_intersection2(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))))),X2)
| ~ in(symmetric_difference(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))),X2)
| ~ in(set_intersection2(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))),X2)
| ~ sP0(X2) )
| ~ spl14_50
| ~ spl14_71
| ~ spl14_74 ),
inference(forward_demodulation,[],[f783,f458]) ).
fof(f458,plain,
( ! [X0,X1] : symmetric_difference(X0,X1) = symmetric_difference(X1,X0)
| ~ spl14_50 ),
inference(avatar_component_clause,[],[f457]) ).
fof(f783,plain,
( ! [X2,X0,X1] :
( in(symmetric_difference(set_intersection2(symmetric_difference(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))),set_intersection2(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0)))),symmetric_difference(X0,X1)),X2)
| ~ in(symmetric_difference(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))),X2)
| ~ in(set_intersection2(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))),X2)
| ~ sP0(X2) )
| ~ spl14_71
| ~ spl14_74 ),
inference(superposition,[],[f720,f756]) ).
fof(f756,plain,
( ! [X0,X1] : symmetric_difference(X0,X1) = symmetric_difference(symmetric_difference(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))),set_intersection2(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))))
| ~ spl14_74 ),
inference(avatar_component_clause,[],[f755]) ).
fof(f720,plain,
( ! [X3,X0,X4] :
( in(symmetric_difference(set_intersection2(X4,X3),symmetric_difference(X4,X3)),X0)
| ~ in(X4,X0)
| ~ in(X3,X0)
| ~ sP0(X0) )
| ~ spl14_71 ),
inference(avatar_component_clause,[],[f719]) ).
fof(f4955,plain,
( spl14_161
| ~ spl14_51
| ~ spl14_69
| ~ spl14_74 ),
inference(avatar_split_clause,[],[f809,f755,f668,f461,f4953]) ).
fof(f4953,plain,
( spl14_161
<=> ! [X0,X1] : symmetric_difference(symmetric_difference(X0,X1),set_intersection2(set_intersection2(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))),symmetric_difference(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))))) = symmetric_difference(set_intersection2(set_intersection2(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))),symmetric_difference(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0)))),symmetric_difference(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_161])]) ).
fof(f668,plain,
( spl14_69
<=> ! [X0,X1] : symmetric_difference(symmetric_difference(X0,X1),set_intersection2(X0,X1)) = symmetric_difference(set_intersection2(X1,X0),symmetric_difference(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_69])]) ).
fof(f809,plain,
( ! [X0,X1] : symmetric_difference(symmetric_difference(X0,X1),set_intersection2(set_intersection2(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))),symmetric_difference(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))))) = symmetric_difference(set_intersection2(set_intersection2(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))),symmetric_difference(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0)))),symmetric_difference(X1,X0))
| ~ spl14_51
| ~ spl14_69
| ~ spl14_74 ),
inference(forward_demodulation,[],[f808,f771]) ).
fof(f771,plain,
( ! [X0,X1] : symmetric_difference(X0,X1) = symmetric_difference(set_intersection2(symmetric_difference(X1,set_intersection2(X1,X0)),symmetric_difference(X0,set_intersection2(X0,X1))),symmetric_difference(symmetric_difference(X1,set_intersection2(X1,X0)),symmetric_difference(X0,set_intersection2(X0,X1))))
| ~ spl14_69
| ~ spl14_74 ),
inference(superposition,[],[f756,f669]) ).
fof(f669,plain,
( ! [X0,X1] : symmetric_difference(symmetric_difference(X0,X1),set_intersection2(X0,X1)) = symmetric_difference(set_intersection2(X1,X0),symmetric_difference(X1,X0))
| ~ spl14_69 ),
inference(avatar_component_clause,[],[f668]) ).
fof(f808,plain,
( ! [X0,X1] : symmetric_difference(set_intersection2(set_intersection2(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))),symmetric_difference(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0)))),symmetric_difference(set_intersection2(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))),symmetric_difference(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))))) = symmetric_difference(symmetric_difference(X0,X1),set_intersection2(set_intersection2(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))),symmetric_difference(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0)))))
| ~ spl14_51
| ~ spl14_69
| ~ spl14_74 ),
inference(forward_demodulation,[],[f782,f462]) ).
fof(f782,plain,
( ! [X0,X1] : symmetric_difference(set_intersection2(set_intersection2(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))),symmetric_difference(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0)))),symmetric_difference(set_intersection2(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))),symmetric_difference(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))))) = symmetric_difference(symmetric_difference(X0,X1),set_intersection2(symmetric_difference(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))),set_intersection2(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0)))))
| ~ spl14_69
| ~ spl14_74 ),
inference(superposition,[],[f669,f756]) ).
fof(f4951,plain,
( ~ spl14_160
| ~ spl14_81
| ~ spl14_108 ),
inference(avatar_split_clause,[],[f2017,f1146,f869,f4948]) ).
fof(f4948,plain,
( spl14_160
<=> in(sK1,sK5(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_160])]) ).
fof(f869,plain,
( spl14_81
<=> ! [X0] :
( ~ in(sK1,X0)
| ~ element(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_81])]) ).
fof(f2017,plain,
( ~ in(sK1,sK5(sK1))
| ~ spl14_81
| ~ spl14_108 ),
inference(resolution,[],[f1147,f870]) ).
fof(f870,plain,
( ! [X0] :
( ~ element(X0,sK1)
| ~ in(sK1,X0) )
| ~ spl14_81 ),
inference(avatar_component_clause,[],[f869]) ).
fof(f4676,plain,
( spl14_159
| ~ spl14_50
| ~ spl14_51
| ~ spl14_67
| ~ spl14_74 ),
inference(avatar_split_clause,[],[f807,f755,f647,f461,f457,f4674]) ).
fof(f4674,plain,
( spl14_159
<=> ! [X0,X1] :
( finite(symmetric_difference(symmetric_difference(X0,X1),set_intersection2(set_intersection2(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))),symmetric_difference(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))))))
| ~ finite(symmetric_difference(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))))
| ~ finite(set_intersection2(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_159])]) ).
fof(f647,plain,
( spl14_67
<=> ! [X0,X1] :
( finite(symmetric_difference(set_intersection2(X1,X0),symmetric_difference(X1,X0)))
| ~ finite(X1)
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_67])]) ).
fof(f807,plain,
( ! [X0,X1] :
( finite(symmetric_difference(symmetric_difference(X0,X1),set_intersection2(set_intersection2(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))),symmetric_difference(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))))))
| ~ finite(symmetric_difference(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))))
| ~ finite(set_intersection2(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0)))) )
| ~ spl14_50
| ~ spl14_51
| ~ spl14_67
| ~ spl14_74 ),
inference(forward_demodulation,[],[f806,f462]) ).
fof(f806,plain,
( ! [X0,X1] :
( finite(symmetric_difference(symmetric_difference(X0,X1),set_intersection2(symmetric_difference(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))),set_intersection2(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))))))
| ~ finite(symmetric_difference(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))))
| ~ finite(set_intersection2(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0)))) )
| ~ spl14_50
| ~ spl14_67
| ~ spl14_74 ),
inference(forward_demodulation,[],[f781,f458]) ).
fof(f781,plain,
( ! [X0,X1] :
( finite(symmetric_difference(set_intersection2(symmetric_difference(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))),set_intersection2(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0)))),symmetric_difference(X0,X1)))
| ~ finite(symmetric_difference(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))))
| ~ finite(set_intersection2(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0)))) )
| ~ spl14_67
| ~ spl14_74 ),
inference(superposition,[],[f648,f756]) ).
fof(f648,plain,
( ! [X0,X1] :
( finite(symmetric_difference(set_intersection2(X1,X0),symmetric_difference(X1,X0)))
| ~ finite(X1)
| ~ finite(X0) )
| ~ spl14_67 ),
inference(avatar_component_clause,[],[f647]) ).
fof(f4168,plain,
( spl14_158
| ~ spl14_50
| ~ spl14_51
| ~ spl14_66
| ~ spl14_74 ),
inference(avatar_split_clause,[],[f805,f755,f604,f461,f457,f4166]) ).
fof(f4166,plain,
( spl14_158
<=> ! [X0,X1] :
( ~ empty(symmetric_difference(symmetric_difference(X0,X1),set_intersection2(set_intersection2(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))),symmetric_difference(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))))))
| empty(set_intersection2(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_158])]) ).
fof(f604,plain,
( spl14_66
<=> ! [X0,X1] :
( ~ empty(symmetric_difference(set_intersection2(X1,X0),symmetric_difference(X1,X0)))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_66])]) ).
fof(f805,plain,
( ! [X0,X1] :
( ~ empty(symmetric_difference(symmetric_difference(X0,X1),set_intersection2(set_intersection2(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))),symmetric_difference(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))))))
| empty(set_intersection2(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0)))) )
| ~ spl14_50
| ~ spl14_51
| ~ spl14_66
| ~ spl14_74 ),
inference(forward_demodulation,[],[f804,f462]) ).
fof(f804,plain,
( ! [X0,X1] :
( ~ empty(symmetric_difference(symmetric_difference(X0,X1),set_intersection2(symmetric_difference(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))),set_intersection2(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))))))
| empty(set_intersection2(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0)))) )
| ~ spl14_50
| ~ spl14_66
| ~ spl14_74 ),
inference(forward_demodulation,[],[f780,f458]) ).
fof(f780,plain,
( ! [X0,X1] :
( ~ empty(symmetric_difference(set_intersection2(symmetric_difference(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))),set_intersection2(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0)))),symmetric_difference(X0,X1)))
| empty(set_intersection2(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0)))) )
| ~ spl14_66
| ~ spl14_74 ),
inference(superposition,[],[f605,f756]) ).
fof(f605,plain,
( ! [X0,X1] :
( ~ empty(symmetric_difference(set_intersection2(X1,X0),symmetric_difference(X1,X0)))
| empty(X0) )
| ~ spl14_66 ),
inference(avatar_component_clause,[],[f604]) ).
fof(f4164,plain,
( spl14_157
| ~ spl14_50
| ~ spl14_51
| ~ spl14_65
| ~ spl14_74 ),
inference(avatar_split_clause,[],[f803,f755,f600,f461,f457,f4162]) ).
fof(f4162,plain,
( spl14_157
<=> ! [X0,X1] :
( ~ empty(symmetric_difference(symmetric_difference(X0,X1),set_intersection2(set_intersection2(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))),symmetric_difference(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))))))
| empty(symmetric_difference(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_157])]) ).
fof(f600,plain,
( spl14_65
<=> ! [X0,X1] :
( ~ empty(symmetric_difference(set_intersection2(X0,X1),symmetric_difference(X0,X1)))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_65])]) ).
fof(f803,plain,
( ! [X0,X1] :
( ~ empty(symmetric_difference(symmetric_difference(X0,X1),set_intersection2(set_intersection2(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))),symmetric_difference(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))))))
| empty(symmetric_difference(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0)))) )
| ~ spl14_50
| ~ spl14_51
| ~ spl14_65
| ~ spl14_74 ),
inference(forward_demodulation,[],[f802,f462]) ).
fof(f802,plain,
( ! [X0,X1] :
( ~ empty(symmetric_difference(symmetric_difference(X0,X1),set_intersection2(symmetric_difference(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))),set_intersection2(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))))))
| empty(symmetric_difference(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0)))) )
| ~ spl14_50
| ~ spl14_65
| ~ spl14_74 ),
inference(forward_demodulation,[],[f779,f458]) ).
fof(f779,plain,
( ! [X0,X1] :
( ~ empty(symmetric_difference(set_intersection2(symmetric_difference(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))),set_intersection2(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0)))),symmetric_difference(X0,X1)))
| empty(symmetric_difference(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0)))) )
| ~ spl14_65
| ~ spl14_74 ),
inference(superposition,[],[f601,f756]) ).
fof(f601,plain,
( ! [X0,X1] :
( ~ empty(symmetric_difference(set_intersection2(X0,X1),symmetric_difference(X0,X1)))
| empty(X0) )
| ~ spl14_65 ),
inference(avatar_component_clause,[],[f600]) ).
fof(f3890,plain,
( spl14_156
| ~ spl14_51
| ~ spl14_69 ),
inference(avatar_split_clause,[],[f704,f668,f461,f3888]) ).
fof(f3888,plain,
( spl14_156
<=> ! [X0,X1] : symmetric_difference(set_intersection2(set_intersection2(X0,X1),symmetric_difference(X0,X1)),symmetric_difference(set_intersection2(X0,X1),symmetric_difference(X0,X1))) = symmetric_difference(symmetric_difference(set_intersection2(X1,X0),symmetric_difference(X1,X0)),set_intersection2(set_intersection2(X0,X1),symmetric_difference(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_156])]) ).
fof(f704,plain,
( ! [X0,X1] : symmetric_difference(set_intersection2(set_intersection2(X0,X1),symmetric_difference(X0,X1)),symmetric_difference(set_intersection2(X0,X1),symmetric_difference(X0,X1))) = symmetric_difference(symmetric_difference(set_intersection2(X1,X0),symmetric_difference(X1,X0)),set_intersection2(set_intersection2(X0,X1),symmetric_difference(X0,X1)))
| ~ spl14_51
| ~ spl14_69 ),
inference(forward_demodulation,[],[f684,f462]) ).
fof(f684,plain,
( ! [X0,X1] : symmetric_difference(set_intersection2(set_intersection2(X0,X1),symmetric_difference(X0,X1)),symmetric_difference(set_intersection2(X0,X1),symmetric_difference(X0,X1))) = symmetric_difference(symmetric_difference(set_intersection2(X1,X0),symmetric_difference(X1,X0)),set_intersection2(symmetric_difference(X0,X1),set_intersection2(X0,X1)))
| ~ spl14_69 ),
inference(superposition,[],[f669,f669]) ).
fof(f3602,plain,
( spl14_155
| ~ spl14_51
| ~ spl14_69
| ~ spl14_71 ),
inference(avatar_split_clause,[],[f741,f719,f668,f461,f3600]) ).
fof(f3600,plain,
( spl14_155
<=> ! [X2,X0,X1] :
( in(symmetric_difference(set_intersection2(set_intersection2(X0,X1),symmetric_difference(X0,X1)),symmetric_difference(set_intersection2(X1,X0),symmetric_difference(X1,X0))),X2)
| ~ in(symmetric_difference(X0,X1),X2)
| ~ in(set_intersection2(X0,X1),X2)
| ~ sP0(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_155])]) ).
fof(f741,plain,
( ! [X2,X0,X1] :
( in(symmetric_difference(set_intersection2(set_intersection2(X0,X1),symmetric_difference(X0,X1)),symmetric_difference(set_intersection2(X1,X0),symmetric_difference(X1,X0))),X2)
| ~ in(symmetric_difference(X0,X1),X2)
| ~ in(set_intersection2(X0,X1),X2)
| ~ sP0(X2) )
| ~ spl14_51
| ~ spl14_69
| ~ spl14_71 ),
inference(forward_demodulation,[],[f733,f462]) ).
fof(f733,plain,
( ! [X2,X0,X1] :
( in(symmetric_difference(set_intersection2(symmetric_difference(X0,X1),set_intersection2(X0,X1)),symmetric_difference(set_intersection2(X1,X0),symmetric_difference(X1,X0))),X2)
| ~ in(symmetric_difference(X0,X1),X2)
| ~ in(set_intersection2(X0,X1),X2)
| ~ sP0(X2) )
| ~ spl14_69
| ~ spl14_71 ),
inference(superposition,[],[f720,f669]) ).
fof(f3598,plain,
( spl14_154
| ~ spl14_42
| ~ spl14_107 ),
inference(avatar_split_clause,[],[f1393,f1142,f409,f3595]) ).
fof(f3595,plain,
( spl14_154
<=> in(sK6(sK1),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_154])]) ).
fof(f1393,plain,
( in(sK6(sK1),sK1)
| ~ spl14_42
| ~ spl14_107 ),
inference(resolution,[],[f1143,f410]) ).
fof(f1143,plain,
( element(sK6(sK1),sK1)
| ~ spl14_107 ),
inference(avatar_component_clause,[],[f1142]) ).
fof(f3512,plain,
( spl14_153
| ~ spl14_60
| ~ spl14_74 ),
inference(avatar_split_clause,[],[f778,f755,f541,f3510]) ).
fof(f3510,plain,
( spl14_153
<=> ! [X0,X1] :
( finite(symmetric_difference(X0,X1))
| ~ finite(set_intersection2(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))))
| ~ finite(symmetric_difference(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_153])]) ).
fof(f541,plain,
( spl14_60
<=> ! [X0,X1] :
( finite(symmetric_difference(X0,X1))
| ~ finite(X1)
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_60])]) ).
fof(f778,plain,
( ! [X0,X1] :
( finite(symmetric_difference(X0,X1))
| ~ finite(set_intersection2(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))))
| ~ finite(symmetric_difference(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0)))) )
| ~ spl14_60
| ~ spl14_74 ),
inference(superposition,[],[f542,f756]) ).
fof(f542,plain,
( ! [X0,X1] :
( finite(symmetric_difference(X0,X1))
| ~ finite(X1)
| ~ finite(X0) )
| ~ spl14_60 ),
inference(avatar_component_clause,[],[f541]) ).
fof(f2556,plain,
( spl14_152
| ~ spl14_50
| ~ spl14_74 ),
inference(avatar_split_clause,[],[f772,f755,f457,f2554]) ).
fof(f2554,plain,
( spl14_152
<=> ! [X0,X1] : symmetric_difference(X0,X1) = symmetric_difference(set_intersection2(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))),symmetric_difference(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_152])]) ).
fof(f772,plain,
( ! [X0,X1] : symmetric_difference(X0,X1) = symmetric_difference(set_intersection2(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))),symmetric_difference(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))))
| ~ spl14_50
| ~ spl14_74 ),
inference(superposition,[],[f756,f458]) ).
fof(f2552,plain,
( spl14_151
| ~ spl14_69
| ~ spl14_74 ),
inference(avatar_split_clause,[],[f771,f755,f668,f2550]) ).
fof(f2550,plain,
( spl14_151
<=> ! [X0,X1] : symmetric_difference(X0,X1) = symmetric_difference(set_intersection2(symmetric_difference(X1,set_intersection2(X1,X0)),symmetric_difference(X0,set_intersection2(X0,X1))),symmetric_difference(symmetric_difference(X1,set_intersection2(X1,X0)),symmetric_difference(X0,set_intersection2(X0,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_151])]) ).
fof(f2548,plain,
( ~ spl14_150
| ~ spl14_81
| ~ spl14_107 ),
inference(avatar_split_clause,[],[f1392,f1142,f869,f2545]) ).
fof(f2545,plain,
( spl14_150
<=> in(sK1,sK6(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_150])]) ).
fof(f1392,plain,
( ~ in(sK1,sK6(sK1))
| ~ spl14_81
| ~ spl14_107 ),
inference(resolution,[],[f1143,f870]) ).
fof(f2543,plain,
( spl14_149
| ~ spl14_51
| ~ spl14_74 ),
inference(avatar_split_clause,[],[f769,f755,f461,f2541]) ).
fof(f2541,plain,
( spl14_149
<=> ! [X0,X1] : symmetric_difference(X0,X1) = symmetric_difference(symmetric_difference(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))),set_intersection2(symmetric_difference(X1,set_intersection2(X1,X0)),symmetric_difference(X0,set_intersection2(X0,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_149])]) ).
fof(f769,plain,
( ! [X0,X1] : symmetric_difference(X0,X1) = symmetric_difference(symmetric_difference(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))),set_intersection2(symmetric_difference(X1,set_intersection2(X1,X0)),symmetric_difference(X0,set_intersection2(X0,X1))))
| ~ spl14_51
| ~ spl14_74 ),
inference(superposition,[],[f756,f462]) ).
fof(f2539,plain,
( spl14_148
| ~ spl14_51
| ~ spl14_74 ),
inference(avatar_split_clause,[],[f766,f755,f461,f2537]) ).
fof(f2537,plain,
( spl14_148
<=> ! [X0,X1] : symmetric_difference(X1,X0) = symmetric_difference(symmetric_difference(symmetric_difference(X1,set_intersection2(X1,X0)),symmetric_difference(X0,set_intersection2(X1,X0))),set_intersection2(symmetric_difference(X1,set_intersection2(X1,X0)),symmetric_difference(X0,set_intersection2(X1,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_148])]) ).
fof(f766,plain,
( ! [X0,X1] : symmetric_difference(X1,X0) = symmetric_difference(symmetric_difference(symmetric_difference(X1,set_intersection2(X1,X0)),symmetric_difference(X0,set_intersection2(X1,X0))),set_intersection2(symmetric_difference(X1,set_intersection2(X1,X0)),symmetric_difference(X0,set_intersection2(X1,X0))))
| ~ spl14_51
| ~ spl14_74 ),
inference(superposition,[],[f756,f462]) ).
fof(f2535,plain,
( spl14_147
| ~ spl14_51
| ~ spl14_74 ),
inference(avatar_split_clause,[],[f762,f755,f461,f2533]) ).
fof(f2533,plain,
( spl14_147
<=> ! [X0,X1] : symmetric_difference(X0,X1) = symmetric_difference(symmetric_difference(symmetric_difference(X0,set_intersection2(X1,X0)),symmetric_difference(X1,set_intersection2(X1,X0))),set_intersection2(symmetric_difference(X0,set_intersection2(X1,X0)),symmetric_difference(X1,set_intersection2(X1,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_147])]) ).
fof(f762,plain,
( ! [X0,X1] : symmetric_difference(X0,X1) = symmetric_difference(symmetric_difference(symmetric_difference(X0,set_intersection2(X1,X0)),symmetric_difference(X1,set_intersection2(X1,X0))),set_intersection2(symmetric_difference(X0,set_intersection2(X1,X0)),symmetric_difference(X1,set_intersection2(X1,X0))))
| ~ spl14_51
| ~ spl14_74 ),
inference(superposition,[],[f756,f462]) ).
fof(f2531,plain,
( spl14_146
| ~ spl14_50
| ~ spl14_74 ),
inference(avatar_split_clause,[],[f758,f755,f457,f2529]) ).
fof(f2529,plain,
( spl14_146
<=> ! [X0,X1] : symmetric_difference(X0,X1) = symmetric_difference(symmetric_difference(symmetric_difference(X1,set_intersection2(X1,X0)),symmetric_difference(X0,set_intersection2(X0,X1))),set_intersection2(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_146])]) ).
fof(f758,plain,
( ! [X0,X1] : symmetric_difference(X0,X1) = symmetric_difference(symmetric_difference(symmetric_difference(X1,set_intersection2(X1,X0)),symmetric_difference(X0,set_intersection2(X0,X1))),set_intersection2(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))))
| ~ spl14_50
| ~ spl14_74 ),
inference(superposition,[],[f756,f458]) ).
fof(f2358,plain,
( spl14_145
| ~ spl14_51
| ~ spl14_67
| ~ spl14_69 ),
inference(avatar_split_clause,[],[f712,f668,f647,f461,f2356]) ).
fof(f2356,plain,
( spl14_145
<=> ! [X0,X1] :
( finite(symmetric_difference(set_intersection2(set_intersection2(X0,X1),symmetric_difference(X0,X1)),symmetric_difference(set_intersection2(X1,X0),symmetric_difference(X1,X0))))
| ~ finite(symmetric_difference(X0,X1))
| ~ finite(set_intersection2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_145])]) ).
fof(f712,plain,
( ! [X0,X1] :
( finite(symmetric_difference(set_intersection2(set_intersection2(X0,X1),symmetric_difference(X0,X1)),symmetric_difference(set_intersection2(X1,X0),symmetric_difference(X1,X0))))
| ~ finite(symmetric_difference(X0,X1))
| ~ finite(set_intersection2(X0,X1)) )
| ~ spl14_51
| ~ spl14_67
| ~ spl14_69 ),
inference(forward_demodulation,[],[f697,f462]) ).
fof(f697,plain,
( ! [X0,X1] :
( finite(symmetric_difference(set_intersection2(symmetric_difference(X0,X1),set_intersection2(X0,X1)),symmetric_difference(set_intersection2(X1,X0),symmetric_difference(X1,X0))))
| ~ finite(symmetric_difference(X0,X1))
| ~ finite(set_intersection2(X0,X1)) )
| ~ spl14_67
| ~ spl14_69 ),
inference(superposition,[],[f648,f669]) ).
fof(f2027,plain,
( spl14_144
| ~ spl14_51
| ~ spl14_66
| ~ spl14_69 ),
inference(avatar_split_clause,[],[f711,f668,f604,f461,f2025]) ).
fof(f2025,plain,
( spl14_144
<=> ! [X0,X1] :
( ~ empty(symmetric_difference(set_intersection2(set_intersection2(X0,X1),symmetric_difference(X0,X1)),symmetric_difference(set_intersection2(X1,X0),symmetric_difference(X1,X0))))
| empty(set_intersection2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_144])]) ).
fof(f711,plain,
( ! [X0,X1] :
( ~ empty(symmetric_difference(set_intersection2(set_intersection2(X0,X1),symmetric_difference(X0,X1)),symmetric_difference(set_intersection2(X1,X0),symmetric_difference(X1,X0))))
| empty(set_intersection2(X0,X1)) )
| ~ spl14_51
| ~ spl14_66
| ~ spl14_69 ),
inference(forward_demodulation,[],[f696,f462]) ).
fof(f696,plain,
( ! [X0,X1] :
( ~ empty(symmetric_difference(set_intersection2(symmetric_difference(X0,X1),set_intersection2(X0,X1)),symmetric_difference(set_intersection2(X1,X0),symmetric_difference(X1,X0))))
| empty(set_intersection2(X0,X1)) )
| ~ spl14_66
| ~ spl14_69 ),
inference(superposition,[],[f605,f669]) ).
fof(f2023,plain,
( spl14_143
| ~ spl14_51
| ~ spl14_65
| ~ spl14_69 ),
inference(avatar_split_clause,[],[f710,f668,f600,f461,f2021]) ).
fof(f2021,plain,
( spl14_143
<=> ! [X0,X1] :
( ~ empty(symmetric_difference(set_intersection2(set_intersection2(X0,X1),symmetric_difference(X0,X1)),symmetric_difference(set_intersection2(X1,X0),symmetric_difference(X1,X0))))
| empty(symmetric_difference(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_143])]) ).
fof(f710,plain,
( ! [X0,X1] :
( ~ empty(symmetric_difference(set_intersection2(set_intersection2(X0,X1),symmetric_difference(X0,X1)),symmetric_difference(set_intersection2(X1,X0),symmetric_difference(X1,X0))))
| empty(symmetric_difference(X0,X1)) )
| ~ spl14_51
| ~ spl14_65
| ~ spl14_69 ),
inference(forward_demodulation,[],[f695,f462]) ).
fof(f695,plain,
( ! [X0,X1] :
( ~ empty(symmetric_difference(set_intersection2(symmetric_difference(X0,X1),set_intersection2(X0,X1)),symmetric_difference(set_intersection2(X1,X0),symmetric_difference(X1,X0))))
| empty(symmetric_difference(X0,X1)) )
| ~ spl14_65
| ~ spl14_69 ),
inference(superposition,[],[f601,f669]) ).
fof(f1889,plain,
( spl14_142
| ~ spl14_51
| ~ spl14_71 ),
inference(avatar_split_clause,[],[f727,f719,f461,f1887]) ).
fof(f1887,plain,
( spl14_142
<=> ! [X2,X0,X1] :
( in(symmetric_difference(set_intersection2(X1,X0),symmetric_difference(X0,X1)),X2)
| ~ in(X0,X2)
| ~ in(X1,X2)
| ~ sP0(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_142])]) ).
fof(f727,plain,
( ! [X2,X0,X1] :
( in(symmetric_difference(set_intersection2(X1,X0),symmetric_difference(X0,X1)),X2)
| ~ in(X0,X2)
| ~ in(X1,X2)
| ~ sP0(X2) )
| ~ spl14_51
| ~ spl14_71 ),
inference(superposition,[],[f720,f462]) ).
fof(f1885,plain,
( spl14_141
| ~ spl14_45
| ~ spl14_71 ),
inference(avatar_split_clause,[],[f723,f719,f421,f1883]) ).
fof(f1883,plain,
( spl14_141
<=> ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(X2,X1)
| ~ sP0(X1)
| ~ in(X1,symmetric_difference(set_intersection2(X0,X2),symmetric_difference(X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_141])]) ).
fof(f421,plain,
( spl14_45
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_45])]) ).
fof(f723,plain,
( ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(X2,X1)
| ~ sP0(X1)
| ~ in(X1,symmetric_difference(set_intersection2(X0,X2),symmetric_difference(X0,X2))) )
| ~ spl14_45
| ~ spl14_71 ),
inference(resolution,[],[f720,f422]) ).
fof(f422,plain,
( ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) )
| ~ spl14_45 ),
inference(avatar_component_clause,[],[f421]) ).
fof(f1881,plain,
( spl14_140
| ~ spl14_46
| ~ spl14_71 ),
inference(avatar_split_clause,[],[f722,f719,f425,f1879]) ).
fof(f1879,plain,
( spl14_140
<=> ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(X2,X1)
| ~ sP0(X1)
| element(symmetric_difference(set_intersection2(X0,X2),symmetric_difference(X0,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_140])]) ).
fof(f425,plain,
( spl14_46
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_46])]) ).
fof(f722,plain,
( ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(X2,X1)
| ~ sP0(X1)
| element(symmetric_difference(set_intersection2(X0,X2),symmetric_difference(X0,X2)),X1) )
| ~ spl14_46
| ~ spl14_71 ),
inference(resolution,[],[f720,f426]) ).
fof(f426,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) )
| ~ spl14_46 ),
inference(avatar_component_clause,[],[f425]) ).
fof(f1828,plain,
( spl14_139
| ~ spl14_60
| ~ spl14_69 ),
inference(avatar_split_clause,[],[f694,f668,f541,f1826]) ).
fof(f1826,plain,
( spl14_139
<=> ! [X0,X1] :
( finite(symmetric_difference(set_intersection2(X1,X0),symmetric_difference(X1,X0)))
| ~ finite(set_intersection2(X0,X1))
| ~ finite(symmetric_difference(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_139])]) ).
fof(f694,plain,
( ! [X0,X1] :
( finite(symmetric_difference(set_intersection2(X1,X0),symmetric_difference(X1,X0)))
| ~ finite(set_intersection2(X0,X1))
| ~ finite(symmetric_difference(X0,X1)) )
| ~ spl14_60
| ~ spl14_69 ),
inference(superposition,[],[f542,f669]) ).
fof(f1689,plain,
( spl14_104
| ~ spl14_97
| spl14_108 ),
inference(avatar_split_clause,[],[f1505,f1146,f1075,f1126]) ).
fof(f1126,plain,
( spl14_104
<=> sP0(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_104])]) ).
fof(f1075,plain,
( spl14_97
<=> ! [X0] :
( element(sK5(X0),X0)
| sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_97])]) ).
fof(f1505,plain,
( sP0(sK1)
| ~ spl14_97
| spl14_108 ),
inference(resolution,[],[f1148,f1076]) ).
fof(f1076,plain,
( ! [X0] :
( element(sK5(X0),X0)
| sP0(X0) )
| ~ spl14_97 ),
inference(avatar_component_clause,[],[f1075]) ).
fof(f1148,plain,
( ~ element(sK5(sK1),sK1)
| spl14_108 ),
inference(avatar_component_clause,[],[f1146]) ).
fof(f1525,plain,
( spl14_138
| ~ spl14_50
| ~ spl14_69 ),
inference(avatar_split_clause,[],[f689,f668,f457,f1523]) ).
fof(f1523,plain,
( spl14_138
<=> ! [X0,X1] : symmetric_difference(set_intersection2(X1,X0),symmetric_difference(X1,X0)) = symmetric_difference(set_intersection2(X0,X1),symmetric_difference(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_138])]) ).
fof(f689,plain,
( ! [X0,X1] : symmetric_difference(set_intersection2(X1,X0),symmetric_difference(X1,X0)) = symmetric_difference(set_intersection2(X0,X1),symmetric_difference(X0,X1))
| ~ spl14_50
| ~ spl14_69 ),
inference(superposition,[],[f669,f458]) ).
fof(f1521,plain,
( spl14_137
| ~ spl14_51
| ~ spl14_69 ),
inference(avatar_split_clause,[],[f687,f668,f461,f1519]) ).
fof(f1519,plain,
( spl14_137
<=> ! [X0,X1] : symmetric_difference(set_intersection2(X1,X0),symmetric_difference(X1,X0)) = symmetric_difference(symmetric_difference(X0,X1),set_intersection2(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_137])]) ).
fof(f687,plain,
( ! [X0,X1] : symmetric_difference(set_intersection2(X1,X0),symmetric_difference(X1,X0)) = symmetric_difference(symmetric_difference(X0,X1),set_intersection2(X1,X0))
| ~ spl14_51
| ~ spl14_69 ),
inference(superposition,[],[f669,f462]) ).
fof(f1517,plain,
( spl14_136
| ~ spl14_50
| ~ spl14_69 ),
inference(avatar_split_clause,[],[f681,f668,f457,f1515]) ).
fof(f1515,plain,
( spl14_136
<=> ! [X0,X1] : symmetric_difference(set_intersection2(X1,X0),symmetric_difference(X1,X0)) = symmetric_difference(symmetric_difference(X1,X0),set_intersection2(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_136])]) ).
fof(f681,plain,
( ! [X0,X1] : symmetric_difference(set_intersection2(X1,X0),symmetric_difference(X1,X0)) = symmetric_difference(symmetric_difference(X1,X0),set_intersection2(X0,X1))
| ~ spl14_50
| ~ spl14_69 ),
inference(superposition,[],[f669,f458]) ).
fof(f1513,plain,
( spl14_135
| ~ spl14_51
| ~ spl14_68 ),
inference(avatar_split_clause,[],[f676,f664,f461,f1511]) ).
fof(f1511,plain,
( spl14_135
<=> ! [X2,X0,X1] :
( in(symmetric_difference(X0,set_intersection2(X1,X0)),X2)
| ~ in(X1,X2)
| ~ in(X0,X2)
| ~ sP0(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_135])]) ).
fof(f664,plain,
( spl14_68
<=> ! [X4,X0,X3] :
( in(symmetric_difference(X3,set_intersection2(X3,X4)),X0)
| ~ in(X4,X0)
| ~ in(X3,X0)
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_68])]) ).
fof(f676,plain,
( ! [X2,X0,X1] :
( in(symmetric_difference(X0,set_intersection2(X1,X0)),X2)
| ~ in(X1,X2)
| ~ in(X0,X2)
| ~ sP0(X2) )
| ~ spl14_51
| ~ spl14_68 ),
inference(superposition,[],[f665,f462]) ).
fof(f665,plain,
( ! [X3,X0,X4] :
( in(symmetric_difference(X3,set_intersection2(X3,X4)),X0)
| ~ in(X4,X0)
| ~ in(X3,X0)
| ~ sP0(X0) )
| ~ spl14_68 ),
inference(avatar_component_clause,[],[f664]) ).
fof(f1509,plain,
( spl14_134
| ~ spl14_45
| ~ spl14_68 ),
inference(avatar_split_clause,[],[f672,f664,f421,f1507]) ).
fof(f1507,plain,
( spl14_134
<=> ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(X2,X1)
| ~ sP0(X1)
| ~ in(X1,symmetric_difference(X2,set_intersection2(X2,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_134])]) ).
fof(f672,plain,
( ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(X2,X1)
| ~ sP0(X1)
| ~ in(X1,symmetric_difference(X2,set_intersection2(X2,X0))) )
| ~ spl14_45
| ~ spl14_68 ),
inference(resolution,[],[f665,f422]) ).
fof(f1504,plain,
( spl14_133
| ~ spl14_46
| ~ spl14_68 ),
inference(avatar_split_clause,[],[f671,f664,f425,f1502]) ).
fof(f1502,plain,
( spl14_133
<=> ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(X2,X1)
| ~ sP0(X1)
| element(symmetric_difference(X2,set_intersection2(X2,X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_133])]) ).
fof(f671,plain,
( ! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(X2,X1)
| ~ sP0(X1)
| element(symmetric_difference(X2,set_intersection2(X2,X0)),X1) )
| ~ spl14_46
| ~ spl14_68 ),
inference(resolution,[],[f665,f426]) ).
fof(f1470,plain,
( spl14_132
| ~ spl14_51
| ~ spl14_67 ),
inference(avatar_split_clause,[],[f652,f647,f461,f1468]) ).
fof(f1468,plain,
( spl14_132
<=> ! [X0,X1] :
( finite(symmetric_difference(set_intersection2(X1,X0),symmetric_difference(X0,X1)))
| ~ finite(X0)
| ~ finite(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_132])]) ).
fof(f652,plain,
( ! [X0,X1] :
( finite(symmetric_difference(set_intersection2(X1,X0),symmetric_difference(X0,X1)))
| ~ finite(X0)
| ~ finite(X1) )
| ~ spl14_51
| ~ spl14_67 ),
inference(superposition,[],[f648,f462]) ).
fof(f1466,plain,
( spl14_131
| ~ spl14_50
| ~ spl14_51
| ~ spl14_55
| ~ spl14_65 ),
inference(avatar_split_clause,[],[f634,f600,f478,f461,f457,f1464]) ).
fof(f1464,plain,
( spl14_131
<=> ! [X0] :
( ~ empty(symmetric_difference(X0,set_intersection2(X0,symmetric_difference(X0,X0))))
| empty(symmetric_difference(X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_131])]) ).
fof(f478,plain,
( spl14_55
<=> ! [X0] : symmetric_difference(symmetric_difference(X0,X0),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl14_55])]) ).
fof(f634,plain,
( ! [X0] :
( ~ empty(symmetric_difference(X0,set_intersection2(X0,symmetric_difference(X0,X0))))
| empty(symmetric_difference(X0,X0)) )
| ~ spl14_50
| ~ spl14_51
| ~ spl14_55
| ~ spl14_65 ),
inference(forward_demodulation,[],[f633,f462]) ).
fof(f633,plain,
( ! [X0] :
( ~ empty(symmetric_difference(X0,set_intersection2(symmetric_difference(X0,X0),X0)))
| empty(symmetric_difference(X0,X0)) )
| ~ spl14_50
| ~ spl14_55
| ~ spl14_65 ),
inference(forward_demodulation,[],[f625,f458]) ).
fof(f625,plain,
( ! [X0] :
( ~ empty(symmetric_difference(set_intersection2(symmetric_difference(X0,X0),X0),X0))
| empty(symmetric_difference(X0,X0)) )
| ~ spl14_55
| ~ spl14_65 ),
inference(superposition,[],[f601,f479]) ).
fof(f479,plain,
( ! [X0] : symmetric_difference(symmetric_difference(X0,X0),X0) = X0
| ~ spl14_55 ),
inference(avatar_component_clause,[],[f478]) ).
fof(f1381,plain,
( spl14_130
| ~ spl14_36
| ~ spl14_68 ),
inference(avatar_split_clause,[],[f678,f664,f375,f1379]) ).
fof(f1379,plain,
( spl14_130
<=> ! [X0,X1] :
( in(symmetric_difference(X0,X0),X1)
| ~ in(X0,X1)
| ~ sP0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_130])]) ).
fof(f375,plain,
( spl14_36
<=> ! [X0] : set_intersection2(X0,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl14_36])]) ).
fof(f678,plain,
( ! [X0,X1] :
( in(symmetric_difference(X0,X0),X1)
| ~ in(X0,X1)
| ~ sP0(X1) )
| ~ spl14_36
| ~ spl14_68 ),
inference(duplicate_literal_removal,[],[f675]) ).
fof(f675,plain,
( ! [X0,X1] :
( in(symmetric_difference(X0,X0),X1)
| ~ in(X0,X1)
| ~ in(X0,X1)
| ~ sP0(X1) )
| ~ spl14_36
| ~ spl14_68 ),
inference(superposition,[],[f665,f376]) ).
fof(f376,plain,
( ! [X0] : set_intersection2(X0,X0) = X0
| ~ spl14_36 ),
inference(avatar_component_clause,[],[f375]) ).
fof(f1377,plain,
( spl14_129
| ~ spl14_50
| ~ spl14_51
| ~ spl14_55
| ~ spl14_66 ),
inference(avatar_split_clause,[],[f645,f604,f478,f461,f457,f1375]) ).
fof(f1375,plain,
( spl14_129
<=> ! [X0] :
( ~ empty(symmetric_difference(X0,set_intersection2(X0,symmetric_difference(X0,X0))))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_129])]) ).
fof(f645,plain,
( ! [X0] :
( ~ empty(symmetric_difference(X0,set_intersection2(X0,symmetric_difference(X0,X0))))
| empty(X0) )
| ~ spl14_50
| ~ spl14_51
| ~ spl14_55
| ~ spl14_66 ),
inference(forward_demodulation,[],[f644,f462]) ).
fof(f644,plain,
( ! [X0] :
( ~ empty(symmetric_difference(X0,set_intersection2(symmetric_difference(X0,X0),X0)))
| empty(X0) )
| ~ spl14_50
| ~ spl14_55
| ~ spl14_66 ),
inference(forward_demodulation,[],[f642,f458]) ).
fof(f642,plain,
( ! [X0] :
( ~ empty(symmetric_difference(set_intersection2(symmetric_difference(X0,X0),X0),X0))
| empty(X0) )
| ~ spl14_55
| ~ spl14_66 ),
inference(superposition,[],[f605,f479]) ).
fof(f1373,plain,
( spl14_128
| ~ spl14_50
| ~ spl14_65 ),
inference(avatar_split_clause,[],[f623,f600,f457,f1371]) ).
fof(f1371,plain,
( spl14_128
<=> ! [X0,X1] :
( ~ empty(symmetric_difference(set_intersection2(X0,X1),symmetric_difference(X1,X0)))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_128])]) ).
fof(f623,plain,
( ! [X0,X1] :
( ~ empty(symmetric_difference(set_intersection2(X0,X1),symmetric_difference(X1,X0)))
| empty(X0) )
| ~ spl14_50
| ~ spl14_65 ),
inference(superposition,[],[f601,f458]) ).
fof(f1369,plain,
( spl14_127
| ~ spl14_51
| ~ spl14_65 ),
inference(avatar_split_clause,[],[f620,f600,f461,f1367]) ).
fof(f1367,plain,
( spl14_127
<=> ! [X0,X1] :
( ~ empty(symmetric_difference(set_intersection2(X1,X0),symmetric_difference(X0,X1)))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_127])]) ).
fof(f620,plain,
( ! [X0,X1] :
( ~ empty(symmetric_difference(set_intersection2(X1,X0),symmetric_difference(X0,X1)))
| empty(X0) )
| ~ spl14_51
| ~ spl14_65 ),
inference(superposition,[],[f601,f462]) ).
fof(f1365,plain,
( spl14_126
| ~ spl14_49
| ~ spl14_59 ),
inference(avatar_split_clause,[],[f558,f537,f453,f1363]) ).
fof(f1363,plain,
( spl14_126
<=> ! [X0] :
( empty(powerset(X0))
| in(sK4(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_126])]) ).
fof(f453,plain,
( spl14_49
<=> ! [X0] :
( element(sK4(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_49])]) ).
fof(f537,plain,
( spl14_59
<=> ! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_59])]) ).
fof(f558,plain,
( ! [X0] :
( empty(powerset(X0))
| in(sK4(X0),powerset(X0))
| empty(X0) )
| ~ spl14_49
| ~ spl14_59 ),
inference(resolution,[],[f538,f454]) ).
fof(f454,plain,
( ! [X0] :
( element(sK4(X0),powerset(X0))
| empty(X0) )
| ~ spl14_49 ),
inference(avatar_component_clause,[],[f453]) ).
fof(f538,plain,
( ! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) )
| ~ spl14_59 ),
inference(avatar_component_clause,[],[f537]) ).
fof(f1361,plain,
( spl14_125
| ~ spl14_48
| ~ spl14_59 ),
inference(avatar_split_clause,[],[f557,f537,f449,f1359]) ).
fof(f1359,plain,
( spl14_125
<=> ! [X0] :
( empty(powerset(X0))
| in(sK3(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_125])]) ).
fof(f449,plain,
( spl14_48
<=> ! [X0] :
( element(sK3(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_48])]) ).
fof(f557,plain,
( ! [X0] :
( empty(powerset(X0))
| in(sK3(X0),powerset(X0))
| empty(X0) )
| ~ spl14_48
| ~ spl14_59 ),
inference(resolution,[],[f538,f450]) ).
fof(f450,plain,
( ! [X0] :
( element(sK3(X0),powerset(X0))
| empty(X0) )
| ~ spl14_48 ),
inference(avatar_component_clause,[],[f449]) ).
fof(f1357,plain,
( spl14_2
| ~ spl14_23
| ~ spl14_104 ),
inference(avatar_split_clause,[],[f1320,f1126,f314,f220]) ).
fof(f220,plain,
( spl14_2
<=> preboolean(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_2])]) ).
fof(f314,plain,
( spl14_23
<=> ! [X0] :
( preboolean(X0)
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_23])]) ).
fof(f1320,plain,
( preboolean(sK1)
| ~ spl14_23
| ~ spl14_104 ),
inference(resolution,[],[f1128,f315]) ).
fof(f315,plain,
( ! [X0] :
( ~ sP0(X0)
| preboolean(X0) )
| ~ spl14_23 ),
inference(avatar_component_clause,[],[f314]) ).
fof(f1128,plain,
( sP0(sK1)
| ~ spl14_104 ),
inference(avatar_component_clause,[],[f1126]) ).
fof(f1356,plain,
( spl14_124
| ~ spl14_47
| ~ spl14_59 ),
inference(avatar_split_clause,[],[f556,f537,f445,f1354]) ).
fof(f1354,plain,
( spl14_124
<=> ! [X0] :
( empty(powerset(X0))
| in(sK2(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_124])]) ).
fof(f445,plain,
( spl14_47
<=> ! [X0] :
( element(sK2(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_47])]) ).
fof(f556,plain,
( ! [X0] :
( empty(powerset(X0))
| in(sK2(X0),powerset(X0))
| empty(X0) )
| ~ spl14_47
| ~ spl14_59 ),
inference(resolution,[],[f538,f446]) ).
fof(f446,plain,
( ! [X0] :
( element(sK2(X0),powerset(X0))
| empty(X0) )
| ~ spl14_47 ),
inference(avatar_component_clause,[],[f445]) ).
fof(f1352,plain,
( spl14_123
| ~ spl14_52
| ~ spl14_59 ),
inference(avatar_split_clause,[],[f555,f537,f465,f1350]) ).
fof(f1350,plain,
( spl14_123
<=> ! [X0,X1] :
( empty(powerset(X0))
| in(X1,powerset(X0))
| ~ subset(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_123])]) ).
fof(f465,plain,
( spl14_52
<=> ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_52])]) ).
fof(f555,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| in(X1,powerset(X0))
| ~ subset(X1,X0) )
| ~ spl14_52
| ~ spl14_59 ),
inference(resolution,[],[f538,f466]) ).
fof(f466,plain,
( ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) )
| ~ spl14_52 ),
inference(avatar_component_clause,[],[f465]) ).
fof(f1332,plain,
( spl14_122
| ~ spl14_49
| ~ spl14_63 ),
inference(avatar_split_clause,[],[f610,f591,f453,f1330]) ).
fof(f1330,plain,
( spl14_122
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK4(X1))
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_122])]) ).
fof(f591,plain,
( spl14_63
<=> ! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_63])]) ).
fof(f610,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK4(X1))
| empty(X1) )
| ~ spl14_49
| ~ spl14_63 ),
inference(resolution,[],[f592,f454]) ).
fof(f592,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| element(X0,X2)
| ~ in(X0,X1) )
| ~ spl14_63 ),
inference(avatar_component_clause,[],[f591]) ).
fof(f1328,plain,
( spl14_121
| ~ spl14_48
| ~ spl14_63 ),
inference(avatar_split_clause,[],[f609,f591,f449,f1326]) ).
fof(f1326,plain,
( spl14_121
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK3(X1))
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_121])]) ).
fof(f609,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK3(X1))
| empty(X1) )
| ~ spl14_48
| ~ spl14_63 ),
inference(resolution,[],[f592,f450]) ).
fof(f1324,plain,
( spl14_120
| ~ spl14_47
| ~ spl14_63 ),
inference(avatar_split_clause,[],[f608,f591,f445,f1322]) ).
fof(f1322,plain,
( spl14_120
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK2(X1))
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_120])]) ).
fof(f608,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK2(X1))
| empty(X1) )
| ~ spl14_47
| ~ spl14_63 ),
inference(resolution,[],[f592,f446]) ).
fof(f1319,plain,
( spl14_104
| ~ spl14_98
| spl14_107 ),
inference(avatar_split_clause,[],[f1203,f1142,f1079,f1126]) ).
fof(f1079,plain,
( spl14_98
<=> ! [X0] :
( element(sK6(X0),X0)
| sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_98])]) ).
fof(f1203,plain,
( sP0(sK1)
| ~ spl14_98
| spl14_107 ),
inference(resolution,[],[f1144,f1080]) ).
fof(f1080,plain,
( ! [X0] :
( element(sK6(X0),X0)
| sP0(X0) )
| ~ spl14_98 ),
inference(avatar_component_clause,[],[f1079]) ).
fof(f1144,plain,
( ~ element(sK6(sK1),sK1)
| spl14_107 ),
inference(avatar_component_clause,[],[f1142]) ).
fof(f1318,plain,
( spl14_119
| ~ spl14_52
| ~ spl14_63 ),
inference(avatar_split_clause,[],[f607,f591,f465,f1316]) ).
fof(f1316,plain,
( spl14_119
<=> ! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_119])]) ).
fof(f607,plain,
( ! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,X1) )
| ~ spl14_52
| ~ spl14_63 ),
inference(resolution,[],[f592,f466]) ).
fof(f1301,plain,
( spl14_118
| ~ spl14_24
| ~ spl14_63 ),
inference(avatar_split_clause,[],[f611,f591,f318,f1299]) ).
fof(f1299,plain,
( spl14_118
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK7(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_118])]) ).
fof(f318,plain,
( spl14_24
<=> ! [X0] : element(sK7(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_24])]) ).
fof(f611,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK7(powerset(X1))) )
| ~ spl14_24
| ~ spl14_63 ),
inference(resolution,[],[f592,f319]) ).
fof(f319,plain,
( ! [X0] : element(sK7(X0),X0)
| ~ spl14_24 ),
inference(avatar_component_clause,[],[f318]) ).
fof(f1297,plain,
( spl14_117
| ~ spl14_52
| ~ spl14_62 ),
inference(avatar_split_clause,[],[f579,f576,f465,f1295]) ).
fof(f1295,plain,
( spl14_117
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,X2)
| ~ subset(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_117])]) ).
fof(f576,plain,
( spl14_62
<=> ! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_62])]) ).
fof(f579,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,X2)
| ~ subset(X2,X0) )
| ~ spl14_52
| ~ spl14_62 ),
inference(resolution,[],[f577,f466]) ).
fof(f577,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X0,X1) )
| ~ spl14_62 ),
inference(avatar_component_clause,[],[f576]) ).
fof(f1293,plain,
( spl14_116
| ~ spl14_51
| ~ spl14_61 ),
inference(avatar_split_clause,[],[f572,f545,f461,f1291]) ).
fof(f1291,plain,
( spl14_116
<=> ! [X0,X1] :
( finite(symmetric_difference(X0,set_intersection2(X1,X0)))
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_116])]) ).
fof(f545,plain,
( spl14_61
<=> ! [X0,X1] :
( finite(symmetric_difference(X0,set_intersection2(X0,X1)))
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_61])]) ).
fof(f572,plain,
( ! [X0,X1] :
( finite(symmetric_difference(X0,set_intersection2(X1,X0)))
| ~ finite(X0) )
| ~ spl14_51
| ~ spl14_61 ),
inference(superposition,[],[f546,f462]) ).
fof(f546,plain,
( ! [X0,X1] :
( finite(symmetric_difference(X0,set_intersection2(X0,X1)))
| ~ finite(X0) )
| ~ spl14_61 ),
inference(avatar_component_clause,[],[f545]) ).
fof(f1212,plain,
( spl14_115
| ~ spl14_12
| ~ spl14_74 ),
inference(avatar_split_clause,[],[f775,f755,f270,f1210]) ).
fof(f1210,plain,
( spl14_115
<=> ! [X0,X1] :
( in(symmetric_difference(X0,X1),sK1)
| ~ element(set_intersection2(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))),sK1)
| ~ element(symmetric_difference(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))),sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_115])]) ).
fof(f775,plain,
( ! [X0,X1] :
( in(symmetric_difference(X0,X1),sK1)
| ~ element(set_intersection2(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))),sK1)
| ~ element(symmetric_difference(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))),sK1) )
| ~ spl14_12
| ~ spl14_74 ),
inference(superposition,[],[f271,f756]) ).
fof(f1174,plain,
( spl14_114
| ~ spl14_5
| ~ spl14_26
| ~ spl14_32
| ~ spl14_38
| ~ spl14_50
| ~ spl14_51
| ~ spl14_74 ),
inference(avatar_split_clause,[],[f799,f755,f461,f457,f383,f358,f334,f235,f1172]) ).
fof(f1172,plain,
( spl14_114
<=> ! [X0] : symmetric_difference(symmetric_difference(X0,sK11),sK11) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl14_114])]) ).
fof(f235,plain,
( spl14_5
<=> empty(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_5])]) ).
fof(f334,plain,
( spl14_26
<=> ! [X0] : empty_set = set_intersection2(X0,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_26])]) ).
fof(f358,plain,
( spl14_32
<=> ! [X0] :
( empty_set = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_32])]) ).
fof(f383,plain,
( spl14_38
<=> ! [X0] : symmetric_difference(X0,empty_set) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl14_38])]) ).
fof(f799,plain,
( ! [X0] : symmetric_difference(symmetric_difference(X0,sK11),sK11) = X0
| ~ spl14_5
| ~ spl14_26
| ~ spl14_32
| ~ spl14_38
| ~ spl14_50
| ~ spl14_51
| ~ spl14_74 ),
inference(forward_demodulation,[],[f798,f492]) ).
fof(f492,plain,
( ! [X0] : symmetric_difference(sK11,X0) = X0
| ~ spl14_5
| ~ spl14_32
| ~ spl14_38
| ~ spl14_50 ),
inference(forward_demodulation,[],[f486,f390]) ).
fof(f390,plain,
( empty_set = sK11
| ~ spl14_5
| ~ spl14_32 ),
inference(resolution,[],[f359,f237]) ).
fof(f237,plain,
( empty(sK11)
| ~ spl14_5 ),
inference(avatar_component_clause,[],[f235]) ).
fof(f359,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = X0 )
| ~ spl14_32 ),
inference(avatar_component_clause,[],[f358]) ).
fof(f486,plain,
( ! [X0] : symmetric_difference(empty_set,X0) = X0
| ~ spl14_38
| ~ spl14_50 ),
inference(superposition,[],[f458,f384]) ).
fof(f384,plain,
( ! [X0] : symmetric_difference(X0,empty_set) = X0
| ~ spl14_38 ),
inference(avatar_component_clause,[],[f383]) ).
fof(f798,plain,
( ! [X0] : symmetric_difference(sK11,X0) = symmetric_difference(symmetric_difference(X0,sK11),sK11)
| ~ spl14_5
| ~ spl14_26
| ~ spl14_32
| ~ spl14_38
| ~ spl14_50
| ~ spl14_51
| ~ spl14_74 ),
inference(forward_demodulation,[],[f797,f492]) ).
fof(f797,plain,
( ! [X0] : symmetric_difference(sK11,X0) = symmetric_difference(symmetric_difference(sK11,symmetric_difference(X0,sK11)),sK11)
| ~ spl14_5
| ~ spl14_26
| ~ spl14_32
| ~ spl14_38
| ~ spl14_50
| ~ spl14_51
| ~ spl14_74 ),
inference(forward_demodulation,[],[f796,f506]) ).
fof(f506,plain,
( ! [X0] : sK11 = set_intersection2(sK11,X0)
| ~ spl14_5
| ~ spl14_26
| ~ spl14_32
| ~ spl14_51 ),
inference(forward_demodulation,[],[f496,f390]) ).
fof(f496,plain,
( ! [X0] : empty_set = set_intersection2(empty_set,X0)
| ~ spl14_26
| ~ spl14_51 ),
inference(superposition,[],[f462,f335]) ).
fof(f335,plain,
( ! [X0] : empty_set = set_intersection2(X0,empty_set)
| ~ spl14_26 ),
inference(avatar_component_clause,[],[f334]) ).
fof(f796,plain,
( ! [X0] : symmetric_difference(sK11,X0) = symmetric_difference(symmetric_difference(sK11,symmetric_difference(X0,sK11)),set_intersection2(sK11,symmetric_difference(X0,sK11)))
| ~ spl14_5
| ~ spl14_26
| ~ spl14_32
| ~ spl14_38
| ~ spl14_50
| ~ spl14_51
| ~ spl14_74 ),
inference(forward_demodulation,[],[f795,f506]) ).
fof(f795,plain,
( ! [X0] : symmetric_difference(sK11,X0) = symmetric_difference(symmetric_difference(set_intersection2(sK11,X0),symmetric_difference(X0,sK11)),set_intersection2(set_intersection2(sK11,X0),symmetric_difference(X0,sK11)))
| ~ spl14_5
| ~ spl14_26
| ~ spl14_32
| ~ spl14_38
| ~ spl14_50
| ~ spl14_51
| ~ spl14_74 ),
inference(forward_demodulation,[],[f794,f462]) ).
fof(f794,plain,
( ! [X0] : symmetric_difference(sK11,X0) = symmetric_difference(symmetric_difference(set_intersection2(sK11,X0),symmetric_difference(X0,sK11)),set_intersection2(symmetric_difference(X0,sK11),set_intersection2(sK11,X0)))
| ~ spl14_5
| ~ spl14_26
| ~ spl14_32
| ~ spl14_38
| ~ spl14_50
| ~ spl14_51
| ~ spl14_74 ),
inference(forward_demodulation,[],[f793,f492]) ).
fof(f793,plain,
( ! [X0] : symmetric_difference(sK11,X0) = symmetric_difference(symmetric_difference(symmetric_difference(sK11,set_intersection2(sK11,X0)),symmetric_difference(X0,sK11)),set_intersection2(symmetric_difference(X0,sK11),symmetric_difference(sK11,set_intersection2(sK11,X0))))
| ~ spl14_5
| ~ spl14_26
| ~ spl14_32
| ~ spl14_51
| ~ spl14_74 ),
inference(forward_demodulation,[],[f792,f390]) ).
fof(f792,plain,
( ! [X0] : symmetric_difference(empty_set,X0) = symmetric_difference(symmetric_difference(symmetric_difference(empty_set,set_intersection2(empty_set,X0)),symmetric_difference(X0,empty_set)),set_intersection2(symmetric_difference(X0,empty_set),symmetric_difference(empty_set,set_intersection2(empty_set,X0))))
| ~ spl14_26
| ~ spl14_51
| ~ spl14_74 ),
inference(forward_demodulation,[],[f764,f462]) ).
fof(f764,plain,
( ! [X0] : symmetric_difference(empty_set,X0) = symmetric_difference(symmetric_difference(symmetric_difference(empty_set,set_intersection2(empty_set,X0)),symmetric_difference(X0,empty_set)),set_intersection2(symmetric_difference(empty_set,set_intersection2(empty_set,X0)),symmetric_difference(X0,empty_set)))
| ~ spl14_26
| ~ spl14_74 ),
inference(superposition,[],[f756,f335]) ).
fof(f1169,plain,
( spl14_113
| ~ spl14_5
| ~ spl14_26
| ~ spl14_32
| ~ spl14_38
| ~ spl14_50
| ~ spl14_51
| ~ spl14_69 ),
inference(avatar_split_clause,[],[f701,f668,f461,f457,f383,f358,f334,f235,f1167]) ).
fof(f1167,plain,
( spl14_113
<=> ! [X0] : symmetric_difference(X0,set_intersection2(X0,sK11)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl14_113])]) ).
fof(f701,plain,
( ! [X0] : symmetric_difference(X0,set_intersection2(X0,sK11)) = X0
| ~ spl14_5
| ~ spl14_26
| ~ spl14_32
| ~ spl14_38
| ~ spl14_50
| ~ spl14_51
| ~ spl14_69 ),
inference(forward_demodulation,[],[f700,f492]) ).
fof(f700,plain,
( ! [X0] : symmetric_difference(sK11,X0) = symmetric_difference(X0,set_intersection2(X0,sK11))
| ~ spl14_5
| ~ spl14_26
| ~ spl14_32
| ~ spl14_38
| ~ spl14_50
| ~ spl14_51
| ~ spl14_69 ),
inference(forward_demodulation,[],[f699,f506]) ).
fof(f699,plain,
( ! [X0] : symmetric_difference(X0,set_intersection2(X0,sK11)) = symmetric_difference(set_intersection2(sK11,X0),X0)
| ~ spl14_5
| ~ spl14_32
| ~ spl14_38
| ~ spl14_50
| ~ spl14_69 ),
inference(forward_demodulation,[],[f698,f492]) ).
fof(f698,plain,
( ! [X0] : symmetric_difference(X0,set_intersection2(X0,sK11)) = symmetric_difference(set_intersection2(sK11,X0),symmetric_difference(sK11,X0))
| ~ spl14_5
| ~ spl14_32
| ~ spl14_38
| ~ spl14_69 ),
inference(forward_demodulation,[],[f680,f390]) ).
fof(f680,plain,
( ! [X0] : symmetric_difference(X0,set_intersection2(X0,empty_set)) = symmetric_difference(set_intersection2(empty_set,X0),symmetric_difference(empty_set,X0))
| ~ spl14_38
| ~ spl14_69 ),
inference(superposition,[],[f669,f384]) ).
fof(f1165,plain,
( spl14_112
| ~ spl14_24
| ~ spl14_62 ),
inference(avatar_split_clause,[],[f583,f576,f318,f1163]) ).
fof(f1163,plain,
( spl14_112
<=> ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK7(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_112])]) ).
fof(f583,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK7(powerset(X0))) )
| ~ spl14_24
| ~ spl14_62 ),
inference(resolution,[],[f577,f319]) ).
fof(f1161,plain,
( spl14_111
| ~ spl14_5
| ~ spl14_15
| ~ spl14_32
| ~ spl14_34
| ~ spl14_59 ),
inference(avatar_split_clause,[],[f563,f537,f367,f358,f282,f235,f1159]) ).
fof(f1159,plain,
( spl14_111
<=> ! [X0] :
( in(sK11,powerset(X0))
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_111])]) ).
fof(f282,plain,
( spl14_15
<=> ! [X0] : empty(sK8(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_15])]) ).
fof(f367,plain,
( spl14_34
<=> ! [X0] : element(sK8(X0),powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_34])]) ).
fof(f563,plain,
( ! [X0] :
( in(sK11,powerset(X0))
| empty(powerset(X0)) )
| ~ spl14_5
| ~ spl14_15
| ~ spl14_32
| ~ spl14_34
| ~ spl14_59 ),
inference(forward_demodulation,[],[f562,f390]) ).
fof(f562,plain,
( ! [X0] :
( in(empty_set,powerset(X0))
| empty(powerset(X0)) )
| ~ spl14_15
| ~ spl14_32
| ~ spl14_34
| ~ spl14_59 ),
inference(forward_demodulation,[],[f560,f388]) ).
fof(f388,plain,
( ! [X0] : empty_set = sK8(X0)
| ~ spl14_15
| ~ spl14_32 ),
inference(resolution,[],[f359,f283]) ).
fof(f283,plain,
( ! [X0] : empty(sK8(X0))
| ~ spl14_15 ),
inference(avatar_component_clause,[],[f282]) ).
fof(f560,plain,
( ! [X0] :
( empty(powerset(X0))
| in(sK8(X0),powerset(X0)) )
| ~ spl14_34
| ~ spl14_59 ),
inference(resolution,[],[f538,f368]) ).
fof(f368,plain,
( ! [X0] : element(sK8(X0),powerset(X0))
| ~ spl14_34 ),
inference(avatar_component_clause,[],[f367]) ).
fof(f1157,plain,
( spl14_110
| ~ spl14_47
| ~ spl14_58 ),
inference(avatar_split_clause,[],[f549,f530,f445,f1155]) ).
fof(f1155,plain,
( spl14_110
<=> ! [X0] :
( finite(sK2(X0))
| ~ finite(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_110])]) ).
fof(f530,plain,
( spl14_58
<=> ! [X0,X1] :
( finite(X1)
| ~ element(X1,powerset(X0))
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_58])]) ).
fof(f549,plain,
( ! [X0] :
( finite(sK2(X0))
| ~ finite(X0)
| empty(X0) )
| ~ spl14_47
| ~ spl14_58 ),
inference(resolution,[],[f531,f446]) ).
fof(f531,plain,
( ! [X0,X1] :
( ~ element(X1,powerset(X0))
| finite(X1)
| ~ finite(X0) )
| ~ spl14_58 ),
inference(avatar_component_clause,[],[f530]) ).
fof(f1153,plain,
( spl14_109
| ~ spl14_52
| ~ spl14_58 ),
inference(avatar_split_clause,[],[f548,f530,f465,f1151]) ).
fof(f1151,plain,
( spl14_109
<=> ! [X0,X1] :
( finite(X0)
| ~ finite(X1)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_109])]) ).
fof(f548,plain,
( ! [X0,X1] :
( finite(X0)
| ~ finite(X1)
| ~ subset(X0,X1) )
| ~ spl14_52
| ~ spl14_58 ),
inference(resolution,[],[f531,f466]) ).
fof(f1149,plain,
( ~ spl14_107
| ~ spl14_108
| ~ spl14_79
| spl14_102 ),
inference(avatar_split_clause,[],[f1134,f1118,f831,f1146,f1142]) ).
fof(f831,plain,
( spl14_79
<=> ! [X0,X1] :
( element(set_intersection2(X0,X1),sK1)
| ~ element(X1,sK1)
| ~ element(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_79])]) ).
fof(f1134,plain,
( ~ element(sK5(sK1),sK1)
| ~ element(sK6(sK1),sK1)
| ~ spl14_79
| spl14_102 ),
inference(resolution,[],[f1120,f832]) ).
fof(f832,plain,
( ! [X0,X1] :
( element(set_intersection2(X0,X1),sK1)
| ~ element(X1,sK1)
| ~ element(X0,sK1) )
| ~ spl14_79 ),
inference(avatar_component_clause,[],[f831]) ).
fof(f1120,plain,
( ~ element(set_intersection2(sK6(sK1),sK5(sK1)),sK1)
| spl14_102 ),
inference(avatar_component_clause,[],[f1118]) ).
fof(f1140,plain,
( spl14_106
| ~ spl14_50
| ~ spl14_55 ),
inference(avatar_split_clause,[],[f523,f478,f457,f1138]) ).
fof(f1138,plain,
( spl14_106
<=> ! [X0] : symmetric_difference(X0,symmetric_difference(X0,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl14_106])]) ).
fof(f523,plain,
( ! [X0] : symmetric_difference(X0,symmetric_difference(X0,X0)) = X0
| ~ spl14_50
| ~ spl14_55 ),
inference(superposition,[],[f479,f458]) ).
fof(f1133,plain,
( ~ spl14_102
| ~ spl14_103
| spl14_104
| ~ spl14_105
| ~ spl14_12
| ~ spl14_73 ),
inference(avatar_split_clause,[],[f752,f749,f270,f1130,f1126,f1122,f1118]) ).
fof(f749,plain,
( spl14_73
<=> ! [X0] :
( ~ in(symmetric_difference(set_intersection2(sK6(X0),sK5(X0)),symmetric_difference(sK6(X0),sK5(X0))),X0)
| ~ in(symmetric_difference(sK5(X0),set_intersection2(sK6(X0),sK5(X0))),X0)
| sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_73])]) ).
fof(f752,plain,
( ~ in(symmetric_difference(sK5(sK1),set_intersection2(sK6(sK1),sK5(sK1))),sK1)
| sP0(sK1)
| ~ element(symmetric_difference(sK6(sK1),sK5(sK1)),sK1)
| ~ element(set_intersection2(sK6(sK1),sK5(sK1)),sK1)
| ~ spl14_12
| ~ spl14_73 ),
inference(resolution,[],[f750,f271]) ).
fof(f750,plain,
( ! [X0] :
( ~ in(symmetric_difference(set_intersection2(sK6(X0),sK5(X0)),symmetric_difference(sK6(X0),sK5(X0))),X0)
| ~ in(symmetric_difference(sK5(X0),set_intersection2(sK6(X0),sK5(X0))),X0)
| sP0(X0) )
| ~ spl14_73 ),
inference(avatar_component_clause,[],[f749]) ).
fof(f1093,plain,
( spl14_101
| ~ spl14_36
| ~ spl14_61 ),
inference(avatar_split_clause,[],[f571,f545,f375,f1091]) ).
fof(f1091,plain,
( spl14_101
<=> ! [X0] :
( finite(symmetric_difference(X0,X0))
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_101])]) ).
fof(f571,plain,
( ! [X0] :
( finite(symmetric_difference(X0,X0))
| ~ finite(X0) )
| ~ spl14_36
| ~ spl14_61 ),
inference(superposition,[],[f546,f376]) ).
fof(f1089,plain,
( spl14_100
| ~ spl14_24
| ~ spl14_59 ),
inference(avatar_split_clause,[],[f559,f537,f318,f1087]) ).
fof(f1087,plain,
( spl14_100
<=> ! [X0] :
( empty(X0)
| in(sK7(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_100])]) ).
fof(f559,plain,
( ! [X0] :
( empty(X0)
| in(sK7(X0),X0) )
| ~ spl14_24
| ~ spl14_59 ),
inference(resolution,[],[f538,f319]) ).
fof(f1085,plain,
( spl14_99
| ~ spl14_24
| ~ spl14_58 ),
inference(avatar_split_clause,[],[f552,f530,f318,f1083]) ).
fof(f1083,plain,
( spl14_99
<=> ! [X0] :
( finite(sK7(powerset(X0)))
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_99])]) ).
fof(f552,plain,
( ! [X0] :
( finite(sK7(powerset(X0)))
| ~ finite(X0) )
| ~ spl14_24
| ~ spl14_58 ),
inference(resolution,[],[f531,f319]) ).
fof(f1081,plain,
( spl14_98
| ~ spl14_41
| ~ spl14_46 ),
inference(avatar_split_clause,[],[f443,f425,f405,f1079]) ).
fof(f405,plain,
( spl14_41
<=> ! [X0] :
( sP0(X0)
| in(sK6(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_41])]) ).
fof(f443,plain,
( ! [X0] :
( element(sK6(X0),X0)
| sP0(X0) )
| ~ spl14_41
| ~ spl14_46 ),
inference(resolution,[],[f426,f406]) ).
fof(f406,plain,
( ! [X0] :
( in(sK6(X0),X0)
| sP0(X0) )
| ~ spl14_41 ),
inference(avatar_component_clause,[],[f405]) ).
fof(f1077,plain,
( spl14_97
| ~ spl14_40
| ~ spl14_46 ),
inference(avatar_split_clause,[],[f442,f425,f401,f1075]) ).
fof(f401,plain,
( spl14_40
<=> ! [X0] :
( sP0(X0)
| in(sK5(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_40])]) ).
fof(f442,plain,
( ! [X0] :
( element(sK5(X0),X0)
| sP0(X0) )
| ~ spl14_40
| ~ spl14_46 ),
inference(resolution,[],[f426,f402]) ).
fof(f402,plain,
( ! [X0] :
( in(sK5(X0),X0)
| sP0(X0) )
| ~ spl14_40 ),
inference(avatar_component_clause,[],[f401]) ).
fof(f1073,plain,
( spl14_96
| ~ spl14_41
| ~ spl14_45 ),
inference(avatar_split_clause,[],[f438,f421,f405,f1071]) ).
fof(f1071,plain,
( spl14_96
<=> ! [X0] :
( ~ in(X0,sK6(X0))
| sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_96])]) ).
fof(f438,plain,
( ! [X0] :
( ~ in(X0,sK6(X0))
| sP0(X0) )
| ~ spl14_41
| ~ spl14_45 ),
inference(resolution,[],[f422,f406]) ).
fof(f1069,plain,
( spl14_95
| ~ spl14_40
| ~ spl14_45 ),
inference(avatar_split_clause,[],[f437,f421,f401,f1067]) ).
fof(f1067,plain,
( spl14_95
<=> ! [X0] :
( ~ in(X0,sK5(X0))
| sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_95])]) ).
fof(f437,plain,
( ! [X0] :
( ~ in(X0,sK5(X0))
| sP0(X0) )
| ~ spl14_40
| ~ spl14_45 ),
inference(resolution,[],[f422,f402]) ).
fof(f1065,plain,
( spl14_94
| ~ spl14_3
| ~ spl14_82
| ~ spl14_85 ),
inference(avatar_split_clause,[],[f907,f892,f873,f225,f1062]) ).
fof(f1062,plain,
( spl14_94
<=> sP0(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_94])]) ).
fof(f225,plain,
( spl14_3
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_3])]) ).
fof(f873,plain,
( spl14_82
<=> empty_set = sK11 ),
introduced(avatar_definition,[new_symbols(naming,[spl14_82])]) ).
fof(f892,plain,
( spl14_85
<=> ! [X0] :
( sP0(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_85])]) ).
fof(f907,plain,
( sP0(sK11)
| ~ spl14_3
| ~ spl14_82
| ~ spl14_85 ),
inference(forward_demodulation,[],[f903,f875]) ).
fof(f875,plain,
( empty_set = sK11
| ~ spl14_82 ),
inference(avatar_component_clause,[],[f873]) ).
fof(f903,plain,
( sP0(empty_set)
| ~ spl14_3
| ~ spl14_85 ),
inference(resolution,[],[f893,f227]) ).
fof(f227,plain,
( empty(empty_set)
| ~ spl14_3 ),
inference(avatar_component_clause,[],[f225]) ).
fof(f893,plain,
( ! [X0] :
( ~ empty(X0)
| sP0(X0) )
| ~ spl14_85 ),
inference(avatar_component_clause,[],[f892]) ).
fof(f971,plain,
( spl14_92
| spl14_93
| ~ spl14_5
| ~ spl14_15
| ~ spl14_32
| ~ spl14_34
| ~ spl14_62 ),
inference(avatar_split_clause,[],[f587,f576,f367,f358,f282,f235,f969,f966]) ).
fof(f966,plain,
( spl14_92
<=> ! [X0] : ~ empty(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_92])]) ).
fof(f969,plain,
( spl14_93
<=> ! [X1] : ~ in(X1,sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_93])]) ).
fof(f587,plain,
( ! [X0,X1] :
( ~ in(X1,sK11)
| ~ empty(X0) )
| ~ spl14_5
| ~ spl14_15
| ~ spl14_32
| ~ spl14_34
| ~ spl14_62 ),
inference(forward_demodulation,[],[f586,f390]) ).
fof(f586,plain,
( ! [X0,X1] :
( ~ in(X1,empty_set)
| ~ empty(X0) )
| ~ spl14_15
| ~ spl14_32
| ~ spl14_34
| ~ spl14_62 ),
inference(forward_demodulation,[],[f584,f388]) ).
fof(f584,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK8(X0)) )
| ~ spl14_34
| ~ spl14_62 ),
inference(resolution,[],[f577,f368]) ).
fof(f964,plain,
( spl14_91
| ~ spl14_5
| ~ spl14_53 ),
inference(avatar_split_clause,[],[f513,f469,f235,f962]) ).
fof(f962,plain,
( spl14_91
<=> ! [X0] :
( sK11 = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_91])]) ).
fof(f469,plain,
( spl14_53
<=> ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_53])]) ).
fof(f513,plain,
( ! [X0] :
( sK11 = X0
| ~ empty(X0) )
| ~ spl14_5
| ~ spl14_53 ),
inference(resolution,[],[f470,f237]) ).
fof(f470,plain,
( ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) )
| ~ spl14_53 ),
inference(avatar_component_clause,[],[f469]) ).
fof(f960,plain,
( spl14_90
| ~ spl14_5
| ~ spl14_26
| ~ spl14_32
| ~ spl14_51 ),
inference(avatar_split_clause,[],[f506,f461,f358,f334,f235,f958]) ).
fof(f958,plain,
( spl14_90
<=> ! [X0] : sK11 = set_intersection2(sK11,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_90])]) ).
fof(f956,plain,
( spl14_89
| ~ spl14_5
| ~ spl14_32
| ~ spl14_38
| ~ spl14_50 ),
inference(avatar_split_clause,[],[f492,f457,f383,f358,f235,f954]) ).
fof(f954,plain,
( spl14_89
<=> ! [X0] : symmetric_difference(sK11,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl14_89])]) ).
fof(f921,plain,
( spl14_88
| ~ spl14_12
| ~ spl14_69 ),
inference(avatar_split_clause,[],[f691,f668,f270,f919]) ).
fof(f919,plain,
( spl14_88
<=> ! [X0,X1] :
( in(symmetric_difference(set_intersection2(X1,X0),symmetric_difference(X1,X0)),sK1)
| ~ element(set_intersection2(X0,X1),sK1)
| ~ element(symmetric_difference(X0,X1),sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_88])]) ).
fof(f691,plain,
( ! [X0,X1] :
( in(symmetric_difference(set_intersection2(X1,X0),symmetric_difference(X1,X0)),sK1)
| ~ element(set_intersection2(X0,X1),sK1)
| ~ element(symmetric_difference(X0,X1),sK1) )
| ~ spl14_12
| ~ spl14_69 ),
inference(superposition,[],[f271,f669]) ).
fof(f902,plain,
( spl14_87
| ~ spl14_82
| ~ spl14_84 ),
inference(avatar_split_clause,[],[f890,f887,f873,f900]) ).
fof(f900,plain,
( spl14_87
<=> ! [X0] : sK9(X0) = sK11 ),
introduced(avatar_definition,[new_symbols(naming,[spl14_87])]) ).
fof(f887,plain,
( spl14_84
<=> ! [X0] : empty_set = sK9(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_84])]) ).
fof(f890,plain,
( ! [X0] : sK9(X0) = sK11
| ~ spl14_82
| ~ spl14_84 ),
inference(forward_demodulation,[],[f888,f875]) ).
fof(f888,plain,
( ! [X0] : empty_set = sK9(X0)
| ~ spl14_84 ),
inference(avatar_component_clause,[],[f887]) ).
fof(f898,plain,
( spl14_86
| ~ spl14_82
| ~ spl14_83 ),
inference(avatar_split_clause,[],[f885,f882,f873,f896]) ).
fof(f896,plain,
( spl14_86
<=> ! [X0] : sK8(X0) = sK11 ),
introduced(avatar_definition,[new_symbols(naming,[spl14_86])]) ).
fof(f882,plain,
( spl14_83
<=> ! [X0] : empty_set = sK8(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_83])]) ).
fof(f885,plain,
( ! [X0] : sK8(X0) = sK11
| ~ spl14_82
| ~ spl14_83 ),
inference(forward_demodulation,[],[f883,f875]) ).
fof(f883,plain,
( ! [X0] : empty_set = sK8(X0)
| ~ spl14_83 ),
inference(avatar_component_clause,[],[f882]) ).
fof(f894,plain,
( spl14_85
| ~ spl14_37
| ~ spl14_40 ),
inference(avatar_split_clause,[],[f429,f401,f379,f892]) ).
fof(f379,plain,
( spl14_37
<=> ! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_37])]) ).
fof(f429,plain,
( ! [X0] :
( sP0(X0)
| ~ empty(X0) )
| ~ spl14_37
| ~ spl14_40 ),
inference(resolution,[],[f402,f380]) ).
fof(f380,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) )
| ~ spl14_37 ),
inference(avatar_component_clause,[],[f379]) ).
fof(f889,plain,
( spl14_84
| ~ spl14_16
| ~ spl14_32 ),
inference(avatar_split_clause,[],[f389,f358,f286,f887]) ).
fof(f286,plain,
( spl14_16
<=> ! [X0] : empty(sK9(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_16])]) ).
fof(f389,plain,
( ! [X0] : empty_set = sK9(X0)
| ~ spl14_16
| ~ spl14_32 ),
inference(resolution,[],[f359,f287]) ).
fof(f287,plain,
( ! [X0] : empty(sK9(X0))
| ~ spl14_16 ),
inference(avatar_component_clause,[],[f286]) ).
fof(f884,plain,
( spl14_83
| ~ spl14_15
| ~ spl14_32 ),
inference(avatar_split_clause,[],[f388,f358,f282,f882]) ).
fof(f876,plain,
( spl14_82
| ~ spl14_5
| ~ spl14_32 ),
inference(avatar_split_clause,[],[f390,f358,f235,f873]) ).
fof(f871,plain,
( spl14_81
| ~ spl14_36
| ~ spl14_77 ),
inference(avatar_split_clause,[],[f845,f823,f375,f869]) ).
fof(f823,plain,
( spl14_77
<=> ! [X0,X1] :
( ~ in(sK1,set_intersection2(X0,X1))
| ~ element(X1,sK1)
| ~ element(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_77])]) ).
fof(f845,plain,
( ! [X0] :
( ~ in(sK1,X0)
| ~ element(X0,sK1) )
| ~ spl14_36
| ~ spl14_77 ),
inference(duplicate_literal_removal,[],[f842]) ).
fof(f842,plain,
( ! [X0] :
( ~ in(sK1,X0)
| ~ element(X0,sK1)
| ~ element(X0,sK1) )
| ~ spl14_36
| ~ spl14_77 ),
inference(superposition,[],[f824,f376]) ).
fof(f824,plain,
( ! [X0,X1] :
( ~ in(sK1,set_intersection2(X0,X1))
| ~ element(X1,sK1)
| ~ element(X0,sK1) )
| ~ spl14_77 ),
inference(avatar_component_clause,[],[f823]) ).
fof(f866,plain,
( spl14_80
| ~ spl14_15
| ~ spl14_21 ),
inference(avatar_split_clause,[],[f324,f306,f282,f864]) ).
fof(f864,plain,
( spl14_80
<=> ! [X0] : finite(sK8(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_80])]) ).
fof(f306,plain,
( spl14_21
<=> ! [X0] :
( finite(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_21])]) ).
fof(f324,plain,
( ! [X0] : finite(sK8(X0))
| ~ spl14_15
| ~ spl14_21 ),
inference(resolution,[],[f307,f283]) ).
fof(f307,plain,
( ! [X0] :
( ~ empty(X0)
| finite(X0) )
| ~ spl14_21 ),
inference(avatar_component_clause,[],[f306]) ).
fof(f833,plain,
( spl14_79
| ~ spl14_13
| ~ spl14_46 ),
inference(avatar_split_clause,[],[f441,f425,f274,f831]) ).
fof(f274,plain,
( spl14_13
<=> ! [X2,X1] :
( in(set_intersection2(X1,X2),sK1)
| ~ element(X2,sK1)
| ~ element(X1,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_13])]) ).
fof(f441,plain,
( ! [X0,X1] :
( element(set_intersection2(X0,X1),sK1)
| ~ element(X1,sK1)
| ~ element(X0,sK1) )
| ~ spl14_13
| ~ spl14_46 ),
inference(resolution,[],[f426,f275]) ).
fof(f275,plain,
( ! [X2,X1] :
( in(set_intersection2(X1,X2),sK1)
| ~ element(X2,sK1)
| ~ element(X1,sK1) )
| ~ spl14_13 ),
inference(avatar_component_clause,[],[f274]) ).
fof(f829,plain,
( spl14_78
| ~ spl14_12
| ~ spl14_46 ),
inference(avatar_split_clause,[],[f440,f425,f270,f827]) ).
fof(f440,plain,
( ! [X0,X1] :
( element(symmetric_difference(X0,X1),sK1)
| ~ element(X1,sK1)
| ~ element(X0,sK1) )
| ~ spl14_12
| ~ spl14_46 ),
inference(resolution,[],[f426,f271]) ).
fof(f825,plain,
( spl14_77
| ~ spl14_13
| ~ spl14_45 ),
inference(avatar_split_clause,[],[f436,f421,f274,f823]) ).
fof(f436,plain,
( ! [X0,X1] :
( ~ in(sK1,set_intersection2(X0,X1))
| ~ element(X1,sK1)
| ~ element(X0,sK1) )
| ~ spl14_13
| ~ spl14_45 ),
inference(resolution,[],[f422,f275]) ).
fof(f821,plain,
( spl14_76
| ~ spl14_12
| ~ spl14_45 ),
inference(avatar_split_clause,[],[f435,f421,f270,f819]) ).
fof(f819,plain,
( spl14_76
<=> ! [X0,X1] :
( ~ in(sK1,symmetric_difference(X0,X1))
| ~ element(X1,sK1)
| ~ element(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_76])]) ).
fof(f435,plain,
( ! [X0,X1] :
( ~ in(sK1,symmetric_difference(X0,X1))
| ~ element(X1,sK1)
| ~ element(X0,sK1) )
| ~ spl14_12
| ~ spl14_45 ),
inference(resolution,[],[f422,f271]) ).
fof(f816,plain,
( spl14_75
| ~ spl14_9
| ~ spl14_22 ),
inference(avatar_split_clause,[],[f332,f310,f255,f813]) ).
fof(f813,plain,
( spl14_75
<=> sP0(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_75])]) ).
fof(f255,plain,
( spl14_9
<=> preboolean(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_9])]) ).
fof(f310,plain,
( spl14_22
<=> ! [X0] :
( sP0(X0)
| ~ preboolean(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_22])]) ).
fof(f332,plain,
( sP0(sK12)
| ~ spl14_9
| ~ spl14_22 ),
inference(resolution,[],[f311,f257]) ).
fof(f257,plain,
( preboolean(sK12)
| ~ spl14_9 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f311,plain,
( ! [X0] :
( ~ preboolean(X0)
| sP0(X0) )
| ~ spl14_22 ),
inference(avatar_component_clause,[],[f310]) ).
fof(f757,plain,
spl14_74,
inference(avatar_split_clause,[],[f193,f755]) ).
fof(f193,plain,
! [X0,X1] : symmetric_difference(X0,X1) = symmetric_difference(symmetric_difference(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0))),set_intersection2(symmetric_difference(X0,set_intersection2(X0,X1)),symmetric_difference(X1,set_intersection2(X1,X0)))),
inference(definition_unfolding,[],[f168,f169,f167,f167]) ).
fof(f167,plain,
! [X0,X1] : set_difference(X0,X1) = symmetric_difference(X0,set_intersection2(X0,X1)),
inference(cnf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0,X1] : set_difference(X0,X1) = symmetric_difference(X0,set_intersection2(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t100_xboole_1) ).
fof(f169,plain,
! [X0,X1] : set_union2(X0,X1) = symmetric_difference(symmetric_difference(X0,X1),set_intersection2(X0,X1)),
inference(cnf_transformation,[],[f49]) ).
fof(f49,axiom,
! [X0,X1] : set_union2(X0,X1) = symmetric_difference(symmetric_difference(X0,X1),set_intersection2(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t94_xboole_1) ).
fof(f168,plain,
! [X0,X1] : symmetric_difference(X0,X1) = set_union2(set_difference(X0,X1),set_difference(X1,X0)),
inference(cnf_transformation,[],[f9]) ).
fof(f9,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(f751,plain,
( spl14_73
| ~ spl14_51
| ~ spl14_69
| ~ spl14_72 ),
inference(avatar_split_clause,[],[f747,f743,f668,f461,f749]) ).
fof(f743,plain,
( spl14_72
<=> ! [X0] :
( sP0(X0)
| ~ in(symmetric_difference(sK5(X0),set_intersection2(sK5(X0),sK6(X0))),X0)
| ~ in(symmetric_difference(symmetric_difference(sK5(X0),sK6(X0)),set_intersection2(sK5(X0),sK6(X0))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_72])]) ).
fof(f747,plain,
( ! [X0] :
( ~ in(symmetric_difference(set_intersection2(sK6(X0),sK5(X0)),symmetric_difference(sK6(X0),sK5(X0))),X0)
| ~ in(symmetric_difference(sK5(X0),set_intersection2(sK6(X0),sK5(X0))),X0)
| sP0(X0) )
| ~ spl14_51
| ~ spl14_69
| ~ spl14_72 ),
inference(forward_demodulation,[],[f746,f669]) ).
fof(f746,plain,
( ! [X0] :
( ~ in(symmetric_difference(sK5(X0),set_intersection2(sK6(X0),sK5(X0))),X0)
| sP0(X0)
| ~ in(symmetric_difference(symmetric_difference(sK5(X0),sK6(X0)),set_intersection2(sK5(X0),sK6(X0))),X0) )
| ~ spl14_51
| ~ spl14_72 ),
inference(forward_demodulation,[],[f744,f462]) ).
fof(f744,plain,
( ! [X0] :
( sP0(X0)
| ~ in(symmetric_difference(sK5(X0),set_intersection2(sK5(X0),sK6(X0))),X0)
| ~ in(symmetric_difference(symmetric_difference(sK5(X0),sK6(X0)),set_intersection2(sK5(X0),sK6(X0))),X0) )
| ~ spl14_72 ),
inference(avatar_component_clause,[],[f743]) ).
fof(f745,plain,
spl14_72,
inference(avatar_split_clause,[],[f197,f743]) ).
fof(f197,plain,
! [X0] :
( sP0(X0)
| ~ in(symmetric_difference(sK5(X0),set_intersection2(sK5(X0),sK6(X0))),X0)
| ~ in(symmetric_difference(symmetric_difference(sK5(X0),sK6(X0)),set_intersection2(sK5(X0),sK6(X0))),X0) ),
inference(definition_unfolding,[],[f152,f167,f169]) ).
fof(f152,plain,
! [X0] :
( sP0(X0)
| ~ in(set_difference(sK5(X0),sK6(X0)),X0)
| ~ in(set_union2(sK5(X0),sK6(X0)),X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f107,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])],[f105,f106]) ).
fof(f106,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(f105,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,[],[f104]) ).
fof(f104,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,[],[f94]) ).
fof(f94,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(f721,plain,
( spl14_71
| ~ spl14_69
| ~ spl14_70 ),
inference(avatar_split_clause,[],[f717,f714,f668,f719]) ).
fof(f714,plain,
( spl14_70
<=> ! [X4,X0,X3] :
( in(symmetric_difference(symmetric_difference(X3,X4),set_intersection2(X3,X4)),X0)
| ~ in(X4,X0)
| ~ in(X3,X0)
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_70])]) ).
fof(f717,plain,
( ! [X3,X0,X4] :
( in(symmetric_difference(set_intersection2(X4,X3),symmetric_difference(X4,X3)),X0)
| ~ in(X4,X0)
| ~ in(X3,X0)
| ~ sP0(X0) )
| ~ spl14_69
| ~ spl14_70 ),
inference(forward_demodulation,[],[f715,f669]) ).
fof(f715,plain,
( ! [X3,X0,X4] :
( in(symmetric_difference(symmetric_difference(X3,X4),set_intersection2(X3,X4)),X0)
| ~ in(X4,X0)
| ~ in(X3,X0)
| ~ sP0(X0) )
| ~ spl14_70 ),
inference(avatar_component_clause,[],[f714]) ).
fof(f716,plain,
spl14_70,
inference(avatar_split_clause,[],[f199,f714]) ).
fof(f199,plain,
! [X3,X0,X4] :
( in(symmetric_difference(symmetric_difference(X3,X4),set_intersection2(X3,X4)),X0)
| ~ in(X4,X0)
| ~ in(X3,X0)
| ~ sP0(X0) ),
inference(definition_unfolding,[],[f148,f169]) ).
fof(f148,plain,
! [X3,X0,X4] :
( in(set_union2(X3,X4),X0)
| ~ in(X4,X0)
| ~ in(X3,X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f670,plain,
spl14_69,
inference(avatar_split_clause,[],[f210,f668]) ).
fof(f210,plain,
! [X0,X1] : symmetric_difference(symmetric_difference(X0,X1),set_intersection2(X0,X1)) = symmetric_difference(set_intersection2(X1,X0),symmetric_difference(X1,X0)),
inference(forward_demodulation,[],[f201,f164]) ).
fof(f164,plain,
! [X0,X1] : symmetric_difference(X0,X1) = symmetric_difference(X1,X0),
inference(cnf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1] : symmetric_difference(X0,X1) = symmetric_difference(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k5_xboole_0) ).
fof(f201,plain,
! [X0,X1] : symmetric_difference(symmetric_difference(X0,X1),set_intersection2(X0,X1)) = symmetric_difference(symmetric_difference(X1,X0),set_intersection2(X1,X0)),
inference(definition_unfolding,[],[f166,f169,f169]) ).
fof(f166,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(f666,plain,
spl14_68,
inference(avatar_split_clause,[],[f198,f664]) ).
fof(f198,plain,
! [X3,X0,X4] :
( in(symmetric_difference(X3,set_intersection2(X3,X4)),X0)
| ~ in(X4,X0)
| ~ in(X3,X0)
| ~ sP0(X0) ),
inference(definition_unfolding,[],[f149,f167]) ).
fof(f149,plain,
! [X3,X0,X4] :
( in(set_difference(X3,X4),X0)
| ~ in(X4,X0)
| ~ in(X3,X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f649,plain,
spl14_67,
inference(avatar_split_clause,[],[f213,f647]) ).
fof(f213,plain,
! [X0,X1] :
( finite(symmetric_difference(set_intersection2(X1,X0),symmetric_difference(X1,X0)))
| ~ finite(X1)
| ~ finite(X0) ),
inference(forward_demodulation,[],[f205,f210]) ).
fof(f205,plain,
! [X0,X1] :
( finite(symmetric_difference(symmetric_difference(X0,X1),set_intersection2(X0,X1)))
| ~ finite(X1)
| ~ finite(X0) ),
inference(definition_unfolding,[],[f179,f169]) ).
fof(f179,plain,
! [X0,X1] :
( finite(set_union2(X0,X1))
| ~ finite(X1)
| ~ finite(X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f87,plain,
! [X0,X1] :
( finite(set_union2(X0,X1))
| ~ finite(X1)
| ~ finite(X0) ),
inference(flattening,[],[f86]) ).
fof(f86,plain,
! [X0,X1] :
( finite(set_union2(X0,X1))
| ~ finite(X1)
| ~ finite(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0,X1] :
( ( finite(X1)
& finite(X0) )
=> finite(set_union2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_finset_1) ).
fof(f606,plain,
spl14_66,
inference(avatar_split_clause,[],[f212,f604]) ).
fof(f212,plain,
! [X0,X1] :
( ~ empty(symmetric_difference(set_intersection2(X1,X0),symmetric_difference(X1,X0)))
| empty(X0) ),
inference(forward_demodulation,[],[f203,f210]) ).
fof(f203,plain,
! [X0,X1] :
( ~ empty(symmetric_difference(symmetric_difference(X0,X1),set_intersection2(X0,X1)))
| empty(X0) ),
inference(definition_unfolding,[],[f171,f169]) ).
fof(f171,plain,
! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
fof(f602,plain,
spl14_65,
inference(avatar_split_clause,[],[f211,f600]) ).
fof(f211,plain,
! [X0,X1] :
( ~ empty(symmetric_difference(set_intersection2(X0,X1),symmetric_difference(X0,X1)))
| empty(X0) ),
inference(forward_demodulation,[],[f202,f210]) ).
fof(f202,plain,
! [X0,X1] :
( ~ empty(symmetric_difference(symmetric_difference(X1,X0),set_intersection2(X1,X0)))
| empty(X0) ),
inference(definition_unfolding,[],[f170,f169]) ).
fof(f170,plain,
! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
fof(f598,plain,
( ~ spl14_64
| ~ spl14_45
| ~ spl14_56 ),
inference(avatar_split_clause,[],[f534,f482,f421,f595]) ).
fof(f595,plain,
( spl14_64
<=> in(sK1,sK7(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_64])]) ).
fof(f482,plain,
( spl14_56
<=> in(sK7(sK1),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_56])]) ).
fof(f534,plain,
( ~ in(sK1,sK7(sK1))
| ~ spl14_45
| ~ spl14_56 ),
inference(resolution,[],[f484,f422]) ).
fof(f484,plain,
( in(sK7(sK1),sK1)
| ~ spl14_56 ),
inference(avatar_component_clause,[],[f482]) ).
fof(f593,plain,
spl14_63,
inference(avatar_split_clause,[],[f183,f591]) ).
fof(f183,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f92]) ).
fof(f92,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f91]) ).
fof(f91,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f43]) ).
fof(f43,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f578,plain,
spl14_62,
inference(avatar_split_clause,[],[f184,f576]) ).
fof(f184,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f93]) ).
fof(f93,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f547,plain,
spl14_61,
inference(avatar_split_clause,[],[f204,f545]) ).
fof(f204,plain,
! [X0,X1] :
( finite(symmetric_difference(X0,set_intersection2(X0,X1)))
| ~ finite(X0) ),
inference(definition_unfolding,[],[f172,f167]) ).
fof(f172,plain,
! [X0,X1] :
( finite(set_difference(X0,X1))
| ~ finite(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0,X1] :
( finite(set_difference(X0,X1))
| ~ finite(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0,X1] :
( finite(X0)
=> finite(set_difference(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_finset_1) ).
fof(f543,plain,
spl14_60,
inference(avatar_split_clause,[],[f178,f541]) ).
fof(f178,plain,
! [X0,X1] :
( finite(symmetric_difference(X0,X1))
| ~ finite(X1)
| ~ finite(X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
! [X0,X1] :
( finite(symmetric_difference(X0,X1))
| ~ finite(X1)
| ~ finite(X0) ),
inference(flattening,[],[f84]) ).
fof(f84,plain,
! [X0,X1] :
( finite(symmetric_difference(X0,X1))
| ~ finite(X1)
| ~ finite(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0,X1] :
( ( finite(X1)
& finite(X0) )
=> finite(symmetric_difference(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc17_finset_1) ).
fof(f539,plain,
spl14_59,
inference(avatar_split_clause,[],[f177,f537]) ).
fof(f177,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f82]) ).
fof(f82,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f39,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f532,plain,
spl14_58,
inference(avatar_split_clause,[],[f146,f530]) ).
fof(f146,plain,
! [X0,X1] :
( finite(X1)
| ~ element(X1,powerset(X0))
| ~ finite(X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f70,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(f519,plain,
( spl14_57
| ~ spl14_5
| ~ spl14_32
| ~ spl14_54 ),
inference(avatar_split_clause,[],[f476,f473,f358,f235,f517]) ).
fof(f517,plain,
( spl14_57
<=> ! [X0] : sK11 = symmetric_difference(sK11,set_intersection2(sK11,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_57])]) ).
fof(f473,plain,
( spl14_54
<=> ! [X0] : empty_set = symmetric_difference(empty_set,set_intersection2(empty_set,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_54])]) ).
fof(f476,plain,
( ! [X0] : sK11 = symmetric_difference(sK11,set_intersection2(sK11,X0))
| ~ spl14_5
| ~ spl14_32
| ~ spl14_54 ),
inference(forward_demodulation,[],[f474,f390]) ).
fof(f474,plain,
( ! [X0] : empty_set = symmetric_difference(empty_set,set_intersection2(empty_set,X0))
| ~ spl14_54 ),
inference(avatar_component_clause,[],[f473]) ).
fof(f485,plain,
( spl14_56
| ~ spl14_24
| ~ spl14_42 ),
inference(avatar_split_clause,[],[f439,f409,f318,f482]) ).
fof(f439,plain,
( in(sK7(sK1),sK1)
| ~ spl14_24
| ~ spl14_42 ),
inference(resolution,[],[f410,f319]) ).
fof(f480,plain,
spl14_55,
inference(avatar_split_clause,[],[f209,f478]) ).
fof(f209,plain,
! [X0] : symmetric_difference(symmetric_difference(X0,X0),X0) = X0,
inference(forward_demodulation,[],[f200,f162]) ).
fof(f162,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(cnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(rectify,[],[f21]) ).
fof(f21,axiom,
! [X0,X1] : set_intersection2(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
fof(f200,plain,
! [X0] : symmetric_difference(symmetric_difference(X0,X0),set_intersection2(X0,X0)) = X0,
inference(definition_unfolding,[],[f163,f169]) ).
fof(f163,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(rectify,[],[f20]) ).
fof(f20,axiom,
! [X0,X1] : set_union2(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(f475,plain,
spl14_54,
inference(avatar_split_clause,[],[f194,f473]) ).
fof(f194,plain,
! [X0] : empty_set = symmetric_difference(empty_set,set_intersection2(empty_set,X0)),
inference(definition_unfolding,[],[f129,f167]) ).
fof(f129,plain,
! [X0] : empty_set = set_difference(empty_set,X0),
inference(cnf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0] : empty_set = set_difference(empty_set,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
fof(f471,plain,
spl14_53,
inference(avatar_split_clause,[],[f181,f469]) ).
fof(f181,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f48]) ).
fof(f48,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(f467,plain,
spl14_52,
inference(avatar_split_clause,[],[f180,f465]) ).
fof(f180,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f53]) ).
fof(f53,plain,
! [X0,X1] :
( subset(X0,X1)
=> element(X0,powerset(X1)) ),
inference(unused_predicate_definition_removal,[],[f41]) ).
fof(f41,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f463,plain,
spl14_51,
inference(avatar_split_clause,[],[f165,f461]) ).
fof(f165,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f459,plain,
spl14_50,
inference(avatar_split_clause,[],[f164,f457]) ).
fof(f455,plain,
spl14_49,
inference(avatar_split_clause,[],[f139,f453]) ).
fof(f139,plain,
! [X0] :
( element(sK4(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f103,plain,
! [X0] :
( ( finite(sK4(X0))
& ~ empty(sK4(X0))
& element(sK4(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f66,f102]) ).
fof(f102,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(f66,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_finset_1) ).
fof(f451,plain,
spl14_48,
inference(avatar_split_clause,[],[f136,f449]) ).
fof(f136,plain,
! [X0] :
( element(sK3(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f101,plain,
! [X0] :
( ( finite(sK3(X0))
& ~ empty(sK3(X0))
& element(sK3(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f65,f100]) ).
fof(f100,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(f65,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_finset_1) ).
fof(f447,plain,
spl14_47,
inference(avatar_split_clause,[],[f134,f445]) ).
fof(f134,plain,
! [X0] :
( element(sK2(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f99,plain,
! [X0] :
( ( ~ empty(sK2(X0))
& element(sK2(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f64,f98]) ).
fof(f98,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( ~ empty(sK2(X0))
& element(sK2(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f64,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f427,plain,
spl14_46,
inference(avatar_split_clause,[],[f176,f425]) ).
fof(f176,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f423,plain,
spl14_45,
inference(avatar_split_clause,[],[f175,f421]) ).
fof(f175,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,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(f419,plain,
spl14_44,
inference(avatar_split_clause,[],[f174,f417]) ).
fof(f417,plain,
( spl14_44
<=> ! [X0,X1] :
( finite(set_intersection2(X0,X1))
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_44])]) ).
fof(f174,plain,
! [X0,X1] :
( finite(set_intersection2(X0,X1))
| ~ finite(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0,X1] :
( finite(set_intersection2(X0,X1))
| ~ finite(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0,X1] :
( finite(X0)
=> finite(set_intersection2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc11_finset_1) ).
fof(f415,plain,
spl14_43,
inference(avatar_split_clause,[],[f173,f413]) ).
fof(f413,plain,
( spl14_43
<=> ! [X0,X1] :
( finite(set_intersection2(X0,X1))
| ~ finite(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_43])]) ).
fof(f173,plain,
! [X0,X1] :
( finite(set_intersection2(X0,X1))
| ~ finite(X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
! [X0,X1] :
( finite(set_intersection2(X0,X1))
| ~ finite(X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0,X1] :
( finite(X1)
=> finite(set_intersection2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_finset_1) ).
fof(f411,plain,
( spl14_42
| ~ spl14_13
| ~ spl14_36 ),
inference(avatar_split_clause,[],[f392,f375,f274,f409]) ).
fof(f392,plain,
( ! [X0] :
( in(X0,sK1)
| ~ element(X0,sK1) )
| ~ spl14_13
| ~ spl14_36 ),
inference(duplicate_literal_removal,[],[f391]) ).
fof(f391,plain,
( ! [X0] :
( in(X0,sK1)
| ~ element(X0,sK1)
| ~ element(X0,sK1) )
| ~ spl14_13
| ~ spl14_36 ),
inference(superposition,[],[f275,f376]) ).
fof(f407,plain,
spl14_41,
inference(avatar_split_clause,[],[f151,f405]) ).
fof(f151,plain,
! [X0] :
( sP0(X0)
| in(sK6(X0),X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f403,plain,
spl14_40,
inference(avatar_split_clause,[],[f150,f401]) ).
fof(f150,plain,
! [X0] :
( sP0(X0)
| in(sK5(X0),X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f399,plain,
spl14_39,
inference(avatar_split_clause,[],[f147,f397]) ).
fof(f397,plain,
( spl14_39
<=> ! [X0] :
( preboolean(X0)
| ~ diff_closed(X0)
| ~ cup_closed(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_39])]) ).
fof(f147,plain,
! [X0] :
( preboolean(X0)
| ~ diff_closed(X0)
| ~ cup_closed(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0] :
( preboolean(X0)
| ~ diff_closed(X0)
| ~ cup_closed(X0) ),
inference(flattening,[],[f71]) ).
fof(f71,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(f385,plain,
spl14_38,
inference(avatar_split_clause,[],[f206,f383]) ).
fof(f206,plain,
! [X0] : symmetric_difference(X0,empty_set) = X0,
inference(forward_demodulation,[],[f195,f130]) ).
fof(f130,plain,
! [X0] : empty_set = set_intersection2(X0,empty_set),
inference(cnf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0] : empty_set = set_intersection2(X0,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
fof(f195,plain,
! [X0] : symmetric_difference(X0,set_intersection2(X0,empty_set)) = X0,
inference(definition_unfolding,[],[f131,f167]) ).
fof(f131,plain,
! [X0] : set_difference(X0,empty_set) = X0,
inference(cnf_transformation,[],[f40]) ).
fof(f40,axiom,
! [X0] : set_difference(X0,empty_set) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
fof(f381,plain,
spl14_37,
inference(avatar_split_clause,[],[f182,f379]) ).
fof(f182,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f47]) ).
fof(f47,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f377,plain,
spl14_36,
inference(avatar_split_clause,[],[f162,f375]) ).
fof(f373,plain,
spl14_35,
inference(avatar_split_clause,[],[f158,f371]) ).
fof(f371,plain,
( spl14_35
<=> ! [X0] : element(sK9(X0),powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_35])]) ).
fof(f158,plain,
! [X0] : element(sK9(X0),powerset(X0)),
inference(cnf_transformation,[],[f114]) ).
fof(f114,plain,
! [X0] :
( finite(sK9(X0))
& empty(sK9(X0))
& element(sK9(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f60,f113]) ).
fof(f113,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(f60,plain,
! [X0] :
? [X1] :
( finite(X1)
& empty(X1)
& element(X1,powerset(X0)) ),
inference(pure_predicate_removal,[],[f59]) ).
fof(f59,plain,
! [X0] :
? [X1] :
( finite(X1)
& relation(X1)
& empty(X1)
& element(X1,powerset(X0)) ),
inference(pure_predicate_removal,[],[f58]) ).
fof(f58,plain,
! [X0] :
? [X1] :
( finite(X1)
& function(X1)
& relation(X1)
& empty(X1)
& element(X1,powerset(X0)) ),
inference(pure_predicate_removal,[],[f57]) ).
fof(f57,plain,
! [X0] :
? [X1] :
( finite(X1)
& one_to_one(X1)
& function(X1)
& relation(X1)
& empty(X1)
& element(X1,powerset(X0)) ),
inference(pure_predicate_removal,[],[f56]) ).
fof(f56,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,[],[f55]) ).
fof(f55,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,[],[f54]) ).
fof(f54,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,[],[f26]) ).
fof(f26,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(f369,plain,
spl14_34,
inference(avatar_split_clause,[],[f156,f367]) ).
fof(f156,plain,
! [X0] : element(sK8(X0),powerset(X0)),
inference(cnf_transformation,[],[f112]) ).
fof(f112,plain,
! [X0] :
( empty(sK8(X0))
& element(sK8(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f27,f111]) ).
fof(f111,plain,
! [X0] :
( ? [X1] :
( empty(X1)
& element(X1,powerset(X0)) )
=> ( empty(sK8(X0))
& element(sK8(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f27,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f365,plain,
( spl14_33
| ~ spl14_5
| ~ spl14_21 ),
inference(avatar_split_clause,[],[f326,f306,f235,f362]) ).
fof(f362,plain,
( spl14_33
<=> finite(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_33])]) ).
fof(f326,plain,
( finite(sK11)
| ~ spl14_5
| ~ spl14_21 ),
inference(resolution,[],[f307,f237]) ).
fof(f360,plain,
spl14_32,
inference(avatar_split_clause,[],[f145,f358]) ).
fof(f145,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f46]) ).
fof(f46,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f356,plain,
spl14_31,
inference(avatar_split_clause,[],[f141,f354]) ).
fof(f354,plain,
( spl14_31
<=> ! [X0] :
( finite(sK4(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_31])]) ).
fof(f141,plain,
! [X0] :
( finite(sK4(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f352,plain,
spl14_30,
inference(avatar_split_clause,[],[f140,f350]) ).
fof(f350,plain,
( spl14_30
<=> ! [X0] :
( ~ empty(sK4(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_30])]) ).
fof(f140,plain,
! [X0] :
( ~ empty(sK4(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f348,plain,
spl14_29,
inference(avatar_split_clause,[],[f138,f346]) ).
fof(f346,plain,
( spl14_29
<=> ! [X0] :
( finite(sK3(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_29])]) ).
fof(f138,plain,
! [X0] :
( finite(sK3(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f344,plain,
spl14_28,
inference(avatar_split_clause,[],[f137,f342]) ).
fof(f342,plain,
( spl14_28
<=> ! [X0] :
( ~ empty(sK3(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_28])]) ).
fof(f137,plain,
! [X0] :
( ~ empty(sK3(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f340,plain,
spl14_27,
inference(avatar_split_clause,[],[f135,f338]) ).
fof(f338,plain,
( spl14_27
<=> ! [X0] :
( ~ empty(sK2(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_27])]) ).
fof(f135,plain,
! [X0] :
( ~ empty(sK2(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f336,plain,
spl14_26,
inference(avatar_split_clause,[],[f130,f334]) ).
fof(f331,plain,
( spl14_25
| ~ spl14_3
| ~ spl14_21 ),
inference(avatar_split_clause,[],[f323,f306,f225,f328]) ).
fof(f328,plain,
( spl14_25
<=> finite(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_25])]) ).
fof(f323,plain,
( finite(empty_set)
| ~ spl14_3
| ~ spl14_21 ),
inference(resolution,[],[f307,f227]) ).
fof(f320,plain,
spl14_24,
inference(avatar_split_clause,[],[f155,f318]) ).
fof(f155,plain,
! [X0] : element(sK7(X0),X0),
inference(cnf_transformation,[],[f110]) ).
fof(f110,plain,
! [X0] : element(sK7(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f10,f109]) ).
fof(f109,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK7(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f10,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f316,plain,
spl14_23,
inference(avatar_split_clause,[],[f154,f314]) ).
fof(f154,plain,
! [X0] :
( preboolean(X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f108,plain,
! [X0] :
( ( preboolean(X0)
| ~ sP0(X0) )
& ( sP0(X0)
| ~ preboolean(X0) ) ),
inference(nnf_transformation,[],[f95]) ).
fof(f95,plain,
! [X0] :
( preboolean(X0)
<=> sP0(X0) ),
inference(definition_folding,[],[f74,f94]) ).
fof(f74,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,[],[f73]) ).
fof(f73,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,[],[f33]) ).
fof(f33,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(f312,plain,
spl14_22,
inference(avatar_split_clause,[],[f153,f310]) ).
fof(f153,plain,
! [X0] :
( sP0(X0)
| ~ preboolean(X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f308,plain,
spl14_21,
inference(avatar_split_clause,[],[f144,f306]) ).
fof(f144,plain,
! [X0] :
( finite(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,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(f304,plain,
spl14_20,
inference(avatar_split_clause,[],[f143,f302]) ).
fof(f302,plain,
( spl14_20
<=> ! [X0] :
( diff_closed(X0)
| ~ preboolean(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_20])]) ).
fof(f143,plain,
! [X0] :
( diff_closed(X0)
| ~ preboolean(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,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(f300,plain,
spl14_19,
inference(avatar_split_clause,[],[f142,f298]) ).
fof(f298,plain,
( spl14_19
<=> ! [X0] :
( cup_closed(X0)
| ~ preboolean(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_19])]) ).
fof(f142,plain,
! [X0] :
( cup_closed(X0)
| ~ preboolean(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f296,plain,
spl14_18,
inference(avatar_split_clause,[],[f161,f294]) ).
fof(f294,plain,
( spl14_18
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_18])]) ).
fof(f161,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f31]) ).
fof(f31,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f292,plain,
spl14_17,
inference(avatar_split_clause,[],[f160,f290]) ).
fof(f290,plain,
( spl14_17
<=> ! [X0] : finite(sK9(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_17])]) ).
fof(f160,plain,
! [X0] : finite(sK9(X0)),
inference(cnf_transformation,[],[f114]) ).
fof(f288,plain,
spl14_16,
inference(avatar_split_clause,[],[f159,f286]) ).
fof(f159,plain,
! [X0] : empty(sK9(X0)),
inference(cnf_transformation,[],[f114]) ).
fof(f284,plain,
spl14_15,
inference(avatar_split_clause,[],[f157,f282]) ).
fof(f157,plain,
! [X0] : empty(sK8(X0)),
inference(cnf_transformation,[],[f112]) ).
fof(f280,plain,
spl14_14,
inference(avatar_split_clause,[],[f128,f278]) ).
fof(f278,plain,
( spl14_14
<=> ! [X0] : ~ empty(powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_14])]) ).
fof(f128,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f276,plain,
spl14_13,
inference(avatar_split_clause,[],[f125,f274]) ).
fof(f125,plain,
! [X2,X1] :
( in(set_intersection2(X1,X2),sK1)
| ~ element(X2,sK1)
| ~ element(X1,sK1) ),
inference(cnf_transformation,[],[f97]) ).
fof(f97,plain,
( ~ preboolean(sK1)
& ! [X1] :
( ! [X2] :
( ( in(set_intersection2(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])],[f63,f96]) ).
fof(f96,plain,
( ? [X0] :
( ~ preboolean(X0)
& ! [X1] :
( ! [X2] :
( ( in(set_intersection2(X1,X2),X0)
& in(symmetric_difference(X1,X2),X0) )
| ~ element(X2,X0) )
| ~ element(X1,X0) )
& ~ empty(X0) )
=> ( ~ preboolean(sK1)
& ! [X1] :
( ! [X2] :
( ( in(set_intersection2(X1,X2),sK1)
& in(symmetric_difference(X1,X2),sK1) )
| ~ element(X2,sK1) )
| ~ element(X1,sK1) )
& ~ empty(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f63,plain,
? [X0] :
( ~ preboolean(X0)
& ! [X1] :
( ! [X2] :
( ( in(set_intersection2(X1,X2),X0)
& in(symmetric_difference(X1,X2),X0) )
| ~ element(X2,X0) )
| ~ element(X1,X0) )
& ~ empty(X0) ),
inference(flattening,[],[f62]) ).
fof(f62,plain,
? [X0] :
( ~ preboolean(X0)
& ! [X1] :
( ! [X2] :
( ( in(set_intersection2(X1,X2),X0)
& in(symmetric_difference(X1,X2),X0) )
| ~ element(X2,X0) )
| ~ element(X1,X0) )
& ~ empty(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,negated_conjecture,
~ ! [X0] :
( ~ empty(X0)
=> ( ! [X1] :
( element(X1,X0)
=> ! [X2] :
( element(X2,X0)
=> ( in(set_intersection2(X1,X2),X0)
& in(symmetric_difference(X1,X2),X0) ) ) )
=> preboolean(X0) ) ),
inference(negated_conjecture,[],[f34]) ).
fof(f34,conjecture,
! [X0] :
( ~ empty(X0)
=> ( ! [X1] :
( element(X1,X0)
=> ! [X2] :
( element(X2,X0)
=> ( in(set_intersection2(X1,X2),X0)
& in(symmetric_difference(X1,X2),X0) ) ) )
=> preboolean(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_finsub_1) ).
fof(f272,plain,
spl14_12,
inference(avatar_split_clause,[],[f124,f270]) ).
fof(f124,plain,
! [X2,X1] :
( in(symmetric_difference(X1,X2),sK1)
| ~ element(X2,sK1)
| ~ element(X1,sK1) ),
inference(cnf_transformation,[],[f97]) ).
fof(f268,plain,
spl14_11,
inference(avatar_split_clause,[],[f192,f265]) ).
fof(f265,plain,
( spl14_11
<=> finite(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_11])]) ).
fof(f192,plain,
finite(sK13),
inference(cnf_transformation,[],[f122]) ).
fof(f122,plain,
( finite(sK13)
& ~ empty(sK13) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f22,f121]) ).
fof(f121,plain,
( ? [X0] :
( finite(X0)
& ~ empty(X0) )
=> ( finite(sK13)
& ~ empty(sK13) ) ),
introduced(choice_axiom,[]) ).
fof(f22,axiom,
? [X0] :
( finite(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
fof(f263,plain,
~ spl14_10,
inference(avatar_split_clause,[],[f191,f260]) ).
fof(f260,plain,
( spl14_10
<=> empty(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_10])]) ).
fof(f191,plain,
~ empty(sK13),
inference(cnf_transformation,[],[f122]) ).
fof(f258,plain,
spl14_9,
inference(avatar_split_clause,[],[f190,f255]) ).
fof(f190,plain,
preboolean(sK12),
inference(cnf_transformation,[],[f120]) ).
fof(f120,plain,
( preboolean(sK12)
& diff_closed(sK12)
& cup_closed(sK12)
& ~ empty(sK12) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f61,f119]) ).
fof(f119,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(f61,plain,
? [X0] :
( preboolean(X0)
& diff_closed(X0)
& cup_closed(X0)
& ~ empty(X0) ),
inference(pure_predicate_removal,[],[f23]) ).
fof(f23,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(f253,plain,
spl14_8,
inference(avatar_split_clause,[],[f189,f250]) ).
fof(f250,plain,
( spl14_8
<=> diff_closed(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_8])]) ).
fof(f189,plain,
diff_closed(sK12),
inference(cnf_transformation,[],[f120]) ).
fof(f248,plain,
spl14_7,
inference(avatar_split_clause,[],[f188,f245]) ).
fof(f245,plain,
( spl14_7
<=> cup_closed(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_7])]) ).
fof(f188,plain,
cup_closed(sK12),
inference(cnf_transformation,[],[f120]) ).
fof(f243,plain,
~ spl14_6,
inference(avatar_split_clause,[],[f187,f240]) ).
fof(f240,plain,
( spl14_6
<=> empty(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_6])]) ).
fof(f187,plain,
~ empty(sK12),
inference(cnf_transformation,[],[f120]) ).
fof(f238,plain,
spl14_5,
inference(avatar_split_clause,[],[f186,f235]) ).
fof(f186,plain,
empty(sK11),
inference(cnf_transformation,[],[f118]) ).
fof(f118,plain,
empty(sK11),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f25,f117]) ).
fof(f117,plain,
( ? [X0] : empty(X0)
=> empty(sK11) ),
introduced(choice_axiom,[]) ).
fof(f25,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f233,plain,
~ spl14_4,
inference(avatar_split_clause,[],[f185,f230]) ).
fof(f230,plain,
( spl14_4
<=> empty(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_4])]) ).
fof(f185,plain,
~ empty(sK10),
inference(cnf_transformation,[],[f116]) ).
fof(f116,plain,
~ empty(sK10),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f28,f115]) ).
fof(f115,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK10) ),
introduced(choice_axiom,[]) ).
fof(f28,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f228,plain,
spl14_3,
inference(avatar_split_clause,[],[f127,f225]) ).
fof(f127,plain,
empty(empty_set),
inference(cnf_transformation,[],[f16]) ).
fof(f16,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f223,plain,
~ spl14_2,
inference(avatar_split_clause,[],[f126,f220]) ).
fof(f126,plain,
~ preboolean(sK1),
inference(cnf_transformation,[],[f97]) ).
fof(f218,plain,
~ spl14_1,
inference(avatar_split_clause,[],[f123,f215]) ).
fof(f215,plain,
( spl14_1
<=> empty(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_1])]) ).
fof(f123,plain,
~ empty(sK1),
inference(cnf_transformation,[],[f97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU105+1 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n019.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % 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 : Fri May 3 11:00:59 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (11302)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37 % (11305)WARNING: value z3 for option sas not known
% 0.14/0.37 % (11304)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 % (11306)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.37 % (11305)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 % (11303)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.37 % (11309)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 % (11307)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)
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [2]
% 0.14/0.38 TRYING [3]
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [2]
% 0.14/0.38 % (11308)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)
% 0.14/0.39 TRYING [3]
% 0.14/0.39 TRYING [4]
% 0.21/0.41 TRYING [1]
% 0.21/0.41 TRYING [2]
% 0.21/0.41 TRYING [3]
% 0.21/0.42 TRYING [4]
% 0.21/0.43 TRYING [4]
% 0.21/0.44 TRYING [5]
% 0.21/0.44 TRYING [5]
% 0.21/0.49 TRYING [6]
% 0.21/0.49 % (11307)First to succeed.
% 0.21/0.50 % (11307)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-11302"
% 0.21/0.50 % (11307)Refutation found. Thanks to Tanya!
% 0.21/0.50 % SZS status Theorem for theBenchmark
% 0.21/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.51 % (11307)------------------------------
% 0.21/0.51 % (11307)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.51 % (11307)Termination reason: Refutation
% 0.21/0.51
% 0.21/0.51 % (11307)Memory used [KB]: 2993
% 0.21/0.51 % (11307)Time elapsed: 0.127 s
% 0.21/0.51 % (11307)Instructions burned: 421 (million)
% 0.21/0.51 % (11302)Success in time 0.138 s
%------------------------------------------------------------------------------