TSTP Solution File: SEU032+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU032+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 : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 15:21:56 EDT 2024
% Result : Theorem 0.13s 0.40s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 221
% Syntax : Number of formulae : 715 ( 104 unt; 0 def)
% Number of atoms : 2316 ( 210 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 2920 (1319 ~;1281 |; 109 &)
% ( 167 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 176 ( 174 usr; 167 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 10 con; 0-2 aty)
% Number of variables : 556 ( 529 !; 27 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1754,plain,
$false,
inference(avatar_sat_refutation,[],[f189,f194,f199,f204,f209,f214,f219,f224,f229,f234,f239,f244,f249,f254,f259,f264,f269,f274,f279,f284,f289,f293,f297,f301,f305,f309,f313,f317,f321,f331,f340,f344,f348,f352,f356,f360,f364,f368,f373,f392,f396,f401,f406,f410,f414,f418,f422,f426,f430,f446,f450,f454,f458,f463,f467,f471,f475,f519,f523,f533,f543,f547,f551,f562,f566,f576,f581,f593,f598,f606,f618,f633,f638,f644,f649,f654,f666,f671,f677,f681,f685,f693,f699,f700,f701,f702,f703,f727,f732,f806,f810,f823,f832,f837,f845,f867,f888,f892,f900,f904,f908,f912,f917,f921,f967,f971,f976,f980,f984,f1029,f1033,f1034,f1039,f1048,f1062,f1066,f1070,f1074,f1130,f1144,f1161,f1167,f1171,f1175,f1179,f1211,f1215,f1225,f1229,f1233,f1270,f1275,f1279,f1284,f1314,f1319,f1324,f1344,f1350,f1354,f1358,f1367,f1384,f1385,f1389,f1393,f1397,f1401,f1405,f1409,f1413,f1417,f1421,f1426,f1430,f1434,f1438,f1442,f1672,f1676,f1692,f1696,f1740,f1744,f1748,f1752,f1753]) ).
fof(f1753,plain,
( ~ spl12_1
| ~ spl12_2
| ~ spl12_3
| ~ spl12_58
| spl12_138 ),
inference(avatar_split_clause,[],[f1346,f1341,f517,f196,f191,f186]) ).
fof(f186,plain,
( spl12_1
<=> relation(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_1])]) ).
fof(f191,plain,
( spl12_2
<=> function(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_2])]) ).
fof(f196,plain,
( spl12_3
<=> one_to_one(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_3])]) ).
fof(f517,plain,
( spl12_58
<=> ! [X0] :
( one_to_one(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_58])]) ).
fof(f1341,plain,
( spl12_138
<=> one_to_one(function_inverse(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_138])]) ).
fof(f1346,plain,
( ~ one_to_one(sK0)
| ~ function(sK0)
| ~ relation(sK0)
| ~ spl12_58
| spl12_138 ),
inference(resolution,[],[f1343,f518]) ).
fof(f518,plain,
( ! [X0] :
( one_to_one(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) )
| ~ spl12_58 ),
inference(avatar_component_clause,[],[f517]) ).
fof(f1343,plain,
( ~ one_to_one(function_inverse(sK0))
| spl12_138 ),
inference(avatar_component_clause,[],[f1341]) ).
fof(f1752,plain,
( spl12_166
| ~ spl12_33
| ~ spl12_100 ),
inference(avatar_split_clause,[],[f944,f902,f346,f1750]) ).
fof(f1750,plain,
( spl12_166
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_rng(relation_rng(X1)) = X0
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_166])]) ).
fof(f346,plain,
( spl12_33
<=> ! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_33])]) ).
fof(f902,plain,
( spl12_100
<=> ! [X0,X1] :
( relation_rng(X1) = X0
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_100])]) ).
fof(f944,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_rng(relation_rng(X1)) = X0
| ~ empty(X1) )
| ~ spl12_33
| ~ spl12_100 ),
inference(resolution,[],[f903,f347]) ).
fof(f347,plain,
( ! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) )
| ~ spl12_33 ),
inference(avatar_component_clause,[],[f346]) ).
fof(f903,plain,
( ! [X0,X1] :
( ~ empty(X1)
| ~ empty(X0)
| relation_rng(X1) = X0 )
| ~ spl12_100 ),
inference(avatar_component_clause,[],[f902]) ).
fof(f1748,plain,
( spl12_165
| ~ spl12_35
| ~ spl12_100 ),
inference(avatar_split_clause,[],[f943,f902,f354,f1746]) ).
fof(f1746,plain,
( spl12_165
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_rng(relation_dom(X1)) = X0
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_165])]) ).
fof(f354,plain,
( spl12_35
<=> ! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_35])]) ).
fof(f943,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_rng(relation_dom(X1)) = X0
| ~ empty(X1) )
| ~ spl12_35
| ~ spl12_100 ),
inference(resolution,[],[f903,f355]) ).
fof(f355,plain,
( ! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) )
| ~ spl12_35 ),
inference(avatar_component_clause,[],[f354]) ).
fof(f1744,plain,
( spl12_164
| ~ spl12_33
| ~ spl12_99 ),
inference(avatar_split_clause,[],[f926,f898,f346,f1742]) ).
fof(f1742,plain,
( spl12_164
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_dom(relation_rng(X1)) = X0
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_164])]) ).
fof(f898,plain,
( spl12_99
<=> ! [X0,X1] :
( relation_dom(X1) = X0
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_99])]) ).
fof(f926,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_dom(relation_rng(X1)) = X0
| ~ empty(X1) )
| ~ spl12_33
| ~ spl12_99 ),
inference(resolution,[],[f899,f347]) ).
fof(f899,plain,
( ! [X0,X1] :
( ~ empty(X1)
| ~ empty(X0)
| relation_dom(X1) = X0 )
| ~ spl12_99 ),
inference(avatar_component_clause,[],[f898]) ).
fof(f1740,plain,
( spl12_163
| ~ spl12_35
| ~ spl12_99 ),
inference(avatar_split_clause,[],[f925,f898,f354,f1738]) ).
fof(f1738,plain,
( spl12_163
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_dom(relation_dom(X1)) = X0
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_163])]) ).
fof(f925,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_dom(relation_dom(X1)) = X0
| ~ empty(X1) )
| ~ spl12_35
| ~ spl12_99 ),
inference(resolution,[],[f899,f355]) ).
fof(f1696,plain,
( spl12_162
| ~ spl12_80
| ~ spl12_115 ),
inference(avatar_split_clause,[],[f1085,f1064,f675,f1694]) ).
fof(f1694,plain,
( spl12_162
<=> ! [X0] :
( ~ empty(relation_rng(X0))
| one_to_one(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_162])]) ).
fof(f675,plain,
( spl12_80
<=> ! [X0] :
( ~ empty(X0)
| function(relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_80])]) ).
fof(f1064,plain,
( spl12_115
<=> ! [X0] :
( ~ function(relation_rng(X0))
| ~ empty(relation_rng(X0))
| one_to_one(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_115])]) ).
fof(f1085,plain,
( ! [X0] :
( ~ empty(relation_rng(X0))
| one_to_one(relation_rng(X0))
| ~ empty(X0) )
| ~ spl12_80
| ~ spl12_115 ),
inference(duplicate_literal_removal,[],[f1082]) ).
fof(f1082,plain,
( ! [X0] :
( ~ empty(relation_rng(X0))
| one_to_one(relation_rng(X0))
| ~ empty(X0)
| ~ empty(X0) )
| ~ spl12_80
| ~ spl12_115 ),
inference(resolution,[],[f1065,f676]) ).
fof(f676,plain,
( ! [X0] :
( function(relation_rng(X0))
| ~ empty(X0) )
| ~ spl12_80 ),
inference(avatar_component_clause,[],[f675]) ).
fof(f1065,plain,
( ! [X0] :
( ~ function(relation_rng(X0))
| ~ empty(relation_rng(X0))
| one_to_one(relation_rng(X0))
| ~ empty(X0) )
| ~ spl12_115 ),
inference(avatar_component_clause,[],[f1064]) ).
fof(f1692,plain,
( spl12_161
| ~ spl12_81
| ~ spl12_114 ),
inference(avatar_split_clause,[],[f1081,f1060,f679,f1690]) ).
fof(f1690,plain,
( spl12_161
<=> ! [X0] :
( ~ empty(relation_dom(X0))
| one_to_one(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_161])]) ).
fof(f679,plain,
( spl12_81
<=> ! [X0] :
( ~ empty(X0)
| function(relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_81])]) ).
fof(f1060,plain,
( spl12_114
<=> ! [X0] :
( ~ function(relation_dom(X0))
| ~ empty(relation_dom(X0))
| one_to_one(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_114])]) ).
fof(f1081,plain,
( ! [X0] :
( ~ empty(relation_dom(X0))
| one_to_one(relation_dom(X0))
| ~ empty(X0) )
| ~ spl12_81
| ~ spl12_114 ),
inference(duplicate_literal_removal,[],[f1078]) ).
fof(f1078,plain,
( ! [X0] :
( ~ empty(relation_dom(X0))
| one_to_one(relation_dom(X0))
| ~ empty(X0)
| ~ empty(X0) )
| ~ spl12_81
| ~ spl12_114 ),
inference(resolution,[],[f1061,f680]) ).
fof(f680,plain,
( ! [X0] :
( function(relation_dom(X0))
| ~ empty(X0) )
| ~ spl12_81 ),
inference(avatar_component_clause,[],[f679]) ).
fof(f1061,plain,
( ! [X0] :
( ~ function(relation_dom(X0))
| ~ empty(relation_dom(X0))
| one_to_one(relation_dom(X0))
| ~ empty(X0) )
| ~ spl12_114 ),
inference(avatar_component_clause,[],[f1060]) ).
fof(f1676,plain,
( spl12_160
| ~ spl12_23
| ~ spl12_107 ),
inference(avatar_split_clause,[],[f1009,f974,f295,f1674]) ).
fof(f1674,plain,
( spl12_160
<=> ! [X0,X1] :
( sK5 = relation_composition(X0,identity_relation(X1))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_160])]) ).
fof(f295,plain,
( spl12_23
<=> ! [X0] : relation(identity_relation(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_23])]) ).
fof(f974,plain,
( spl12_107
<=> ! [X0,X1] :
( relation_composition(X1,X0) = sK5
| ~ relation(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_107])]) ).
fof(f1009,plain,
( ! [X0,X1] :
( sK5 = relation_composition(X0,identity_relation(X1))
| ~ empty(X0) )
| ~ spl12_23
| ~ spl12_107 ),
inference(resolution,[],[f975,f296]) ).
fof(f296,plain,
( ! [X0] : relation(identity_relation(X0))
| ~ spl12_23 ),
inference(avatar_component_clause,[],[f295]) ).
fof(f975,plain,
( ! [X0,X1] :
( ~ relation(X0)
| relation_composition(X1,X0) = sK5
| ~ empty(X1) )
| ~ spl12_107 ),
inference(avatar_component_clause,[],[f974]) ).
fof(f1672,plain,
( spl12_159
| ~ spl12_23
| ~ spl12_106 ),
inference(avatar_split_clause,[],[f990,f969,f295,f1670]) ).
fof(f1670,plain,
( spl12_159
<=> ! [X0,X1] :
( sK5 = relation_composition(identity_relation(X0),X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_159])]) ).
fof(f969,plain,
( spl12_106
<=> ! [X0,X1] :
( relation_composition(X0,X1) = sK5
| ~ relation(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_106])]) ).
fof(f990,plain,
( ! [X0,X1] :
( sK5 = relation_composition(identity_relation(X0),X1)
| ~ empty(X1) )
| ~ spl12_23
| ~ spl12_106 ),
inference(resolution,[],[f970,f296]) ).
fof(f970,plain,
( ! [X0,X1] :
( ~ relation(X0)
| relation_composition(X0,X1) = sK5
| ~ empty(X1) )
| ~ spl12_106 ),
inference(avatar_component_clause,[],[f969]) ).
fof(f1442,plain,
( spl12_158
| ~ spl12_6
| ~ spl12_75
| ~ spl12_107 ),
inference(avatar_split_clause,[],[f1021,f974,f641,f211,f1440]) ).
fof(f1440,plain,
( spl12_158
<=> ! [X0] :
( sK5 = relation_composition(X0,sK5)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_158])]) ).
fof(f211,plain,
( spl12_6
<=> relation(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_6])]) ).
fof(f641,plain,
( spl12_75
<=> empty_set = sK5 ),
introduced(avatar_definition,[new_symbols(naming,[spl12_75])]) ).
fof(f1021,plain,
( ! [X0] :
( sK5 = relation_composition(X0,sK5)
| ~ empty(X0) )
| ~ spl12_6
| ~ spl12_75
| ~ spl12_107 ),
inference(forward_demodulation,[],[f1010,f643]) ).
fof(f643,plain,
( empty_set = sK5
| ~ spl12_75 ),
inference(avatar_component_clause,[],[f641]) ).
fof(f1010,plain,
( ! [X0] :
( sK5 = relation_composition(X0,empty_set)
| ~ empty(X0) )
| ~ spl12_6
| ~ spl12_107 ),
inference(resolution,[],[f975,f213]) ).
fof(f213,plain,
( relation(empty_set)
| ~ spl12_6 ),
inference(avatar_component_clause,[],[f211]) ).
fof(f1438,plain,
( spl12_157
| ~ spl12_16
| ~ spl12_107 ),
inference(avatar_split_clause,[],[f1019,f974,f261,f1436]) ).
fof(f1436,plain,
( spl12_157
<=> ! [X0] :
( sK5 = relation_composition(X0,sK10)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_157])]) ).
fof(f261,plain,
( spl12_16
<=> relation(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_16])]) ).
fof(f1019,plain,
( ! [X0] :
( sK5 = relation_composition(X0,sK10)
| ~ empty(X0) )
| ~ spl12_16
| ~ spl12_107 ),
inference(resolution,[],[f975,f263]) ).
fof(f263,plain,
( relation(sK10)
| ~ spl12_16 ),
inference(avatar_component_clause,[],[f261]) ).
fof(f1434,plain,
( spl12_156
| ~ spl12_14
| ~ spl12_107 ),
inference(avatar_split_clause,[],[f1018,f974,f251,f1432]) ).
fof(f1432,plain,
( spl12_156
<=> ! [X0] :
( sK5 = relation_composition(X0,sK9)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_156])]) ).
fof(f251,plain,
( spl12_14
<=> relation(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_14])]) ).
fof(f1018,plain,
( ! [X0] :
( sK5 = relation_composition(X0,sK9)
| ~ empty(X0) )
| ~ spl12_14
| ~ spl12_107 ),
inference(resolution,[],[f975,f253]) ).
fof(f253,plain,
( relation(sK9)
| ~ spl12_14 ),
inference(avatar_component_clause,[],[f251]) ).
fof(f1430,plain,
( spl12_155
| ~ spl12_13
| ~ spl12_107 ),
inference(avatar_split_clause,[],[f1017,f974,f246,f1428]) ).
fof(f1428,plain,
( spl12_155
<=> ! [X0] :
( sK5 = relation_composition(X0,sK8)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_155])]) ).
fof(f246,plain,
( spl12_13
<=> relation(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_13])]) ).
fof(f1017,plain,
( ! [X0] :
( sK5 = relation_composition(X0,sK8)
| ~ empty(X0) )
| ~ spl12_13
| ~ spl12_107 ),
inference(resolution,[],[f975,f248]) ).
fof(f248,plain,
( relation(sK8)
| ~ spl12_13 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f1426,plain,
( spl12_154
| ~ spl12_5
| ~ spl12_75
| ~ spl12_127 ),
inference(avatar_split_clause,[],[f1262,f1223,f641,f206,f1423]) ).
fof(f1423,plain,
( spl12_154
<=> sK5 = relation_composition(sK5,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_154])]) ).
fof(f206,plain,
( spl12_5
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_5])]) ).
fof(f1223,plain,
( spl12_127
<=> ! [X0] :
( sK5 = relation_composition(X0,sK0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_127])]) ).
fof(f1262,plain,
( sK5 = relation_composition(sK5,sK0)
| ~ spl12_5
| ~ spl12_75
| ~ spl12_127 ),
inference(forward_demodulation,[],[f1255,f643]) ).
fof(f1255,plain,
( sK5 = relation_composition(empty_set,sK0)
| ~ spl12_5
| ~ spl12_127 ),
inference(resolution,[],[f1224,f208]) ).
fof(f208,plain,
( empty(empty_set)
| ~ spl12_5 ),
inference(avatar_component_clause,[],[f206]) ).
fof(f1224,plain,
( ! [X0] :
( ~ empty(X0)
| sK5 = relation_composition(X0,sK0) )
| ~ spl12_127 ),
inference(avatar_component_clause,[],[f1223]) ).
fof(f1421,plain,
( spl12_153
| ~ spl12_10
| ~ spl12_107 ),
inference(avatar_split_clause,[],[f1015,f974,f231,f1419]) ).
fof(f1419,plain,
( spl12_153
<=> ! [X0] :
( sK5 = relation_composition(X0,sK6)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_153])]) ).
fof(f231,plain,
( spl12_10
<=> relation(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_10])]) ).
fof(f1015,plain,
( ! [X0] :
( sK5 = relation_composition(X0,sK6)
| ~ empty(X0) )
| ~ spl12_10
| ~ spl12_107 ),
inference(resolution,[],[f975,f233]) ).
fof(f233,plain,
( relation(sK6)
| ~ spl12_10 ),
inference(avatar_component_clause,[],[f231]) ).
fof(f1417,plain,
( spl12_152
| ~ spl12_6
| ~ spl12_75
| ~ spl12_106 ),
inference(avatar_split_clause,[],[f1002,f969,f641,f211,f1415]) ).
fof(f1415,plain,
( spl12_152
<=> ! [X0] :
( sK5 = relation_composition(sK5,X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_152])]) ).
fof(f1002,plain,
( ! [X0] :
( sK5 = relation_composition(sK5,X0)
| ~ empty(X0) )
| ~ spl12_6
| ~ spl12_75
| ~ spl12_106 ),
inference(forward_demodulation,[],[f991,f643]) ).
fof(f991,plain,
( ! [X0] :
( sK5 = relation_composition(empty_set,X0)
| ~ empty(X0) )
| ~ spl12_6
| ~ spl12_106 ),
inference(resolution,[],[f970,f213]) ).
fof(f1413,plain,
( spl12_151
| ~ spl12_16
| ~ spl12_106 ),
inference(avatar_split_clause,[],[f1000,f969,f261,f1411]) ).
fof(f1411,plain,
( spl12_151
<=> ! [X0] :
( sK5 = relation_composition(sK10,X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_151])]) ).
fof(f1000,plain,
( ! [X0] :
( sK5 = relation_composition(sK10,X0)
| ~ empty(X0) )
| ~ spl12_16
| ~ spl12_106 ),
inference(resolution,[],[f970,f263]) ).
fof(f1409,plain,
( spl12_150
| ~ spl12_14
| ~ spl12_106 ),
inference(avatar_split_clause,[],[f999,f969,f251,f1407]) ).
fof(f1407,plain,
( spl12_150
<=> ! [X0] :
( sK5 = relation_composition(sK9,X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_150])]) ).
fof(f999,plain,
( ! [X0] :
( sK5 = relation_composition(sK9,X0)
| ~ empty(X0) )
| ~ spl12_14
| ~ spl12_106 ),
inference(resolution,[],[f970,f253]) ).
fof(f1405,plain,
( spl12_149
| ~ spl12_13
| ~ spl12_106 ),
inference(avatar_split_clause,[],[f998,f969,f246,f1403]) ).
fof(f1403,plain,
( spl12_149
<=> ! [X0] :
( sK5 = relation_composition(sK8,X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_149])]) ).
fof(f998,plain,
( ! [X0] :
( sK5 = relation_composition(sK8,X0)
| ~ empty(X0) )
| ~ spl12_13
| ~ spl12_106 ),
inference(resolution,[],[f970,f248]) ).
fof(f1401,plain,
( spl12_148
| ~ spl12_10
| ~ spl12_106 ),
inference(avatar_split_clause,[],[f996,f969,f231,f1399]) ).
fof(f1399,plain,
( spl12_148
<=> ! [X0] :
( sK5 = relation_composition(sK6,X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_148])]) ).
fof(f996,plain,
( ! [X0] :
( sK5 = relation_composition(sK6,X0)
| ~ empty(X0) )
| ~ spl12_10
| ~ spl12_106 ),
inference(resolution,[],[f970,f233]) ).
fof(f1397,plain,
( spl12_147
| ~ spl12_33
| ~ spl12_87 ),
inference(avatar_split_clause,[],[f872,f808,f346,f1395]) ).
fof(f1395,plain,
( spl12_147
<=> ! [X0] :
( sK5 = relation_dom(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_147])]) ).
fof(f808,plain,
( spl12_87
<=> ! [X0] :
( relation_dom(X0) = sK5
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_87])]) ).
fof(f872,plain,
( ! [X0] :
( sK5 = relation_dom(relation_rng(X0))
| ~ empty(X0) )
| ~ spl12_33
| ~ spl12_87 ),
inference(resolution,[],[f809,f347]) ).
fof(f809,plain,
( ! [X0] :
( ~ empty(X0)
| relation_dom(X0) = sK5 )
| ~ spl12_87 ),
inference(avatar_component_clause,[],[f808]) ).
fof(f1393,plain,
( spl12_146
| ~ spl12_35
| ~ spl12_87 ),
inference(avatar_split_clause,[],[f871,f808,f354,f1391]) ).
fof(f1391,plain,
( spl12_146
<=> ! [X0] :
( sK5 = relation_dom(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_146])]) ).
fof(f871,plain,
( ! [X0] :
( sK5 = relation_dom(relation_dom(X0))
| ~ empty(X0) )
| ~ spl12_35
| ~ spl12_87 ),
inference(resolution,[],[f809,f355]) ).
fof(f1389,plain,
( spl12_145
| ~ spl12_33
| ~ spl12_86 ),
inference(avatar_split_clause,[],[f850,f804,f346,f1387]) ).
fof(f1387,plain,
( spl12_145
<=> ! [X0] :
( sK5 = relation_rng(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_145])]) ).
fof(f804,plain,
( spl12_86
<=> ! [X0] :
( relation_rng(X0) = sK5
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_86])]) ).
fof(f850,plain,
( ! [X0] :
( sK5 = relation_rng(relation_rng(X0))
| ~ empty(X0) )
| ~ spl12_33
| ~ spl12_86 ),
inference(resolution,[],[f805,f347]) ).
fof(f805,plain,
( ! [X0] :
( ~ empty(X0)
| relation_rng(X0) = sK5 )
| ~ spl12_86 ),
inference(avatar_component_clause,[],[f804]) ).
fof(f1385,plain,
( ~ spl12_1
| ~ spl12_2
| ~ spl12_47
| spl12_137 ),
inference(avatar_split_clause,[],[f1345,f1337,f420,f191,f186]) ).
fof(f420,plain,
( spl12_47
<=> ! [X0] :
( function(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_47])]) ).
fof(f1337,plain,
( spl12_137
<=> function(function_inverse(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_137])]) ).
fof(f1345,plain,
( ~ function(sK0)
| ~ relation(sK0)
| ~ spl12_47
| spl12_137 ),
inference(resolution,[],[f1339,f421]) ).
fof(f421,plain,
( ! [X0] :
( function(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl12_47 ),
inference(avatar_component_clause,[],[f420]) ).
fof(f1339,plain,
( ~ function(function_inverse(sK0))
| spl12_137 ),
inference(avatar_component_clause,[],[f1337]) ).
fof(f1384,plain,
( spl12_144
| ~ spl12_35
| ~ spl12_86 ),
inference(avatar_split_clause,[],[f849,f804,f354,f1382]) ).
fof(f1382,plain,
( spl12_144
<=> ! [X0] :
( sK5 = relation_rng(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_144])]) ).
fof(f849,plain,
( ! [X0] :
( sK5 = relation_rng(relation_dom(X0))
| ~ empty(X0) )
| ~ spl12_35
| ~ spl12_86 ),
inference(resolution,[],[f805,f355]) ).
fof(f1367,plain,
( ~ spl12_142
| spl12_143
| ~ spl12_81
| ~ spl12_112 ),
inference(avatar_split_clause,[],[f1040,f1036,f679,f1364,f1360]) ).
fof(f1360,plain,
( spl12_142
<=> empty(function_inverse(sK10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_142])]) ).
fof(f1364,plain,
( spl12_143
<=> function(relation_rng(sK10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_143])]) ).
fof(f1036,plain,
( spl12_112
<=> relation_rng(sK10) = relation_dom(function_inverse(sK10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_112])]) ).
fof(f1040,plain,
( function(relation_rng(sK10))
| ~ empty(function_inverse(sK10))
| ~ spl12_81
| ~ spl12_112 ),
inference(superposition,[],[f680,f1038]) ).
fof(f1038,plain,
( relation_rng(sK10) = relation_dom(function_inverse(sK10))
| ~ spl12_112 ),
inference(avatar_component_clause,[],[f1036]) ).
fof(f1358,plain,
( spl12_141
| ~ spl12_24
| ~ spl12_105 ),
inference(avatar_split_clause,[],[f985,f965,f299,f1356]) ).
fof(f1356,plain,
( spl12_141
<=> ! [X0] :
( ~ empty(identity_relation(X0))
| one_to_one(identity_relation(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_141])]) ).
fof(f299,plain,
( spl12_24
<=> ! [X0] : function(identity_relation(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_24])]) ).
fof(f965,plain,
( spl12_105
<=> ! [X0] :
( ~ function(identity_relation(X0))
| ~ empty(identity_relation(X0))
| one_to_one(identity_relation(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_105])]) ).
fof(f985,plain,
( ! [X0] :
( ~ empty(identity_relation(X0))
| one_to_one(identity_relation(X0)) )
| ~ spl12_24
| ~ spl12_105 ),
inference(resolution,[],[f966,f300]) ).
fof(f300,plain,
( ! [X0] : function(identity_relation(X0))
| ~ spl12_24 ),
inference(avatar_component_clause,[],[f299]) ).
fof(f966,plain,
( ! [X0] :
( ~ function(identity_relation(X0))
| ~ empty(identity_relation(X0))
| one_to_one(identity_relation(X0)) )
| ~ spl12_105 ),
inference(avatar_component_clause,[],[f965]) ).
fof(f1354,plain,
( spl12_140
| ~ spl12_94
| ~ spl12_98 ),
inference(avatar_split_clause,[],[f896,f890,f843,f1352]) ).
fof(f1352,plain,
( spl12_140
<=> ! [X0] :
( ~ empty(X0)
| empty(sK2(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_140])]) ).
fof(f843,plain,
( spl12_94
<=> ! [X0] :
( empty(X0)
| in(sK2(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_94])]) ).
fof(f890,plain,
( spl12_98
<=> ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK2(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_98])]) ).
fof(f896,plain,
( ! [X0] :
( ~ empty(X0)
| empty(sK2(powerset(X0))) )
| ~ spl12_94
| ~ spl12_98 ),
inference(resolution,[],[f891,f844]) ).
fof(f844,plain,
( ! [X0] :
( in(sK2(X0),X0)
| empty(X0) )
| ~ spl12_94 ),
inference(avatar_component_clause,[],[f843]) ).
fof(f891,plain,
( ! [X0,X1] :
( ~ in(X1,sK2(powerset(X0)))
| ~ empty(X0) )
| ~ spl12_98 ),
inference(avatar_component_clause,[],[f890]) ).
fof(f1350,plain,
( spl12_139
| ~ spl12_40
| ~ spl12_94 ),
inference(avatar_split_clause,[],[f883,f843,f390,f1348]) ).
fof(f1348,plain,
( spl12_139
<=> ! [X0] :
( empty(X0)
| ~ in(X0,sK2(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_139])]) ).
fof(f390,plain,
( spl12_40
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_40])]) ).
fof(f883,plain,
( ! [X0] :
( empty(X0)
| ~ in(X0,sK2(X0)) )
| ~ spl12_40
| ~ spl12_94 ),
inference(resolution,[],[f844,f391]) ).
fof(f391,plain,
( ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) )
| ~ spl12_40 ),
inference(avatar_component_clause,[],[f390]) ).
fof(f1344,plain,
( ~ spl12_95
| ~ spl12_137
| ~ spl12_1
| ~ spl12_2
| ~ spl12_138
| spl12_4
| ~ spl12_66
| ~ spl12_67
| ~ spl12_70
| ~ spl12_72 ),
inference(avatar_split_clause,[],[f629,f615,f595,f578,f574,f201,f1341,f191,f186,f1337,f860]) ).
fof(f860,plain,
( spl12_95
<=> relation(function_inverse(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_95])]) ).
fof(f201,plain,
( spl12_4
<=> sK0 = function_inverse(function_inverse(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_4])]) ).
fof(f574,plain,
( spl12_66
<=> ! [X0,X1] :
( function_inverse(X0) = X1
| relation_composition(X0,X1) != identity_relation(relation_dom(X0))
| relation_rng(X0) != relation_dom(X1)
| ~ one_to_one(X0)
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_66])]) ).
fof(f578,plain,
( spl12_67
<=> relation_rng(sK0) = relation_dom(function_inverse(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_67])]) ).
fof(f595,plain,
( spl12_70
<=> relation_dom(sK0) = relation_rng(function_inverse(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_70])]) ).
fof(f615,plain,
( spl12_72
<=> relation_composition(function_inverse(sK0),sK0) = identity_relation(relation_rng(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_72])]) ).
fof(f629,plain,
( sK0 = function_inverse(function_inverse(sK0))
| ~ one_to_one(function_inverse(sK0))
| ~ function(sK0)
| ~ relation(sK0)
| ~ function(function_inverse(sK0))
| ~ relation(function_inverse(sK0))
| ~ spl12_66
| ~ spl12_67
| ~ spl12_70
| ~ spl12_72 ),
inference(trivial_inequality_removal,[],[f628]) ).
fof(f628,plain,
( relation_dom(sK0) != relation_dom(sK0)
| sK0 = function_inverse(function_inverse(sK0))
| ~ one_to_one(function_inverse(sK0))
| ~ function(sK0)
| ~ relation(sK0)
| ~ function(function_inverse(sK0))
| ~ relation(function_inverse(sK0))
| ~ spl12_66
| ~ spl12_67
| ~ spl12_70
| ~ spl12_72 ),
inference(forward_demodulation,[],[f627,f597]) ).
fof(f597,plain,
( relation_dom(sK0) = relation_rng(function_inverse(sK0))
| ~ spl12_70 ),
inference(avatar_component_clause,[],[f595]) ).
fof(f627,plain,
( sK0 = function_inverse(function_inverse(sK0))
| relation_dom(sK0) != relation_rng(function_inverse(sK0))
| ~ one_to_one(function_inverse(sK0))
| ~ function(sK0)
| ~ relation(sK0)
| ~ function(function_inverse(sK0))
| ~ relation(function_inverse(sK0))
| ~ spl12_66
| ~ spl12_67
| ~ spl12_72 ),
inference(trivial_inequality_removal,[],[f626]) ).
fof(f626,plain,
( identity_relation(relation_rng(sK0)) != identity_relation(relation_rng(sK0))
| sK0 = function_inverse(function_inverse(sK0))
| relation_dom(sK0) != relation_rng(function_inverse(sK0))
| ~ one_to_one(function_inverse(sK0))
| ~ function(sK0)
| ~ relation(sK0)
| ~ function(function_inverse(sK0))
| ~ relation(function_inverse(sK0))
| ~ spl12_66
| ~ spl12_67
| ~ spl12_72 ),
inference(forward_demodulation,[],[f625,f580]) ).
fof(f580,plain,
( relation_rng(sK0) = relation_dom(function_inverse(sK0))
| ~ spl12_67 ),
inference(avatar_component_clause,[],[f578]) ).
fof(f625,plain,
( identity_relation(relation_rng(sK0)) != identity_relation(relation_dom(function_inverse(sK0)))
| sK0 = function_inverse(function_inverse(sK0))
| relation_dom(sK0) != relation_rng(function_inverse(sK0))
| ~ one_to_one(function_inverse(sK0))
| ~ function(sK0)
| ~ relation(sK0)
| ~ function(function_inverse(sK0))
| ~ relation(function_inverse(sK0))
| ~ spl12_66
| ~ spl12_72 ),
inference(superposition,[],[f575,f617]) ).
fof(f617,plain,
( relation_composition(function_inverse(sK0),sK0) = identity_relation(relation_rng(sK0))
| ~ spl12_72 ),
inference(avatar_component_clause,[],[f615]) ).
fof(f575,plain,
( ! [X0,X1] :
( relation_composition(X0,X1) != identity_relation(relation_dom(X0))
| function_inverse(X0) = X1
| relation_rng(X0) != relation_dom(X1)
| ~ one_to_one(X0)
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) )
| ~ spl12_66 ),
inference(avatar_component_clause,[],[f574]) ).
fof(f1324,plain,
( spl12_136
| ~ spl12_5
| ~ spl12_75
| ~ spl12_87 ),
inference(avatar_split_clause,[],[f877,f808,f641,f206,f1321]) ).
fof(f1321,plain,
( spl12_136
<=> sK5 = relation_dom(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_136])]) ).
fof(f877,plain,
( sK5 = relation_dom(sK5)
| ~ spl12_5
| ~ spl12_75
| ~ spl12_87 ),
inference(forward_demodulation,[],[f870,f643]) ).
fof(f870,plain,
( sK5 = relation_dom(empty_set)
| ~ spl12_5
| ~ spl12_87 ),
inference(resolution,[],[f809,f208]) ).
fof(f1319,plain,
( spl12_135
| ~ spl12_5
| ~ spl12_75
| ~ spl12_86 ),
inference(avatar_split_clause,[],[f855,f804,f641,f206,f1316]) ).
fof(f1316,plain,
( spl12_135
<=> sK5 = relation_rng(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_135])]) ).
fof(f855,plain,
( sK5 = relation_rng(sK5)
| ~ spl12_5
| ~ spl12_75
| ~ spl12_86 ),
inference(forward_demodulation,[],[f848,f643]) ).
fof(f848,plain,
( sK5 = relation_rng(empty_set)
| ~ spl12_5
| ~ spl12_86 ),
inference(resolution,[],[f805,f208]) ).
fof(f1314,plain,
( spl12_134
| ~ spl12_37
| ~ spl12_79 ),
inference(avatar_split_clause,[],[f672,f669,f362,f1312]) ).
fof(f1312,plain,
( spl12_134
<=> ! [X0] : element(sK5,powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_134])]) ).
fof(f362,plain,
( spl12_37
<=> ! [X0] : element(sK3(X0),powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_37])]) ).
fof(f669,plain,
( spl12_79
<=> ! [X0] : sK3(X0) = sK5 ),
introduced(avatar_definition,[new_symbols(naming,[spl12_79])]) ).
fof(f672,plain,
( ! [X0] : element(sK5,powerset(X0))
| ~ spl12_37
| ~ spl12_79 ),
inference(superposition,[],[f363,f670]) ).
fof(f670,plain,
( ! [X0] : sK3(X0) = sK5
| ~ spl12_79 ),
inference(avatar_component_clause,[],[f669]) ).
fof(f363,plain,
( ! [X0] : element(sK3(X0),powerset(X0))
| ~ spl12_37 ),
inference(avatar_component_clause,[],[f362]) ).
fof(f1284,plain,
( spl12_133
| ~ spl12_5
| ~ spl12_75
| ~ spl12_121 ),
inference(avatar_split_clause,[],[f1249,f1165,f641,f206,f1281]) ).
fof(f1281,plain,
( spl12_133
<=> sK5 = relation_composition(sK0,sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_133])]) ).
fof(f1165,plain,
( spl12_121
<=> ! [X0] :
( sK5 = relation_composition(sK0,X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_121])]) ).
fof(f1249,plain,
( sK5 = relation_composition(sK0,sK5)
| ~ spl12_5
| ~ spl12_75
| ~ spl12_121 ),
inference(forward_demodulation,[],[f1242,f643]) ).
fof(f1242,plain,
( sK5 = relation_composition(sK0,empty_set)
| ~ spl12_5
| ~ spl12_121 ),
inference(resolution,[],[f1166,f208]) ).
fof(f1166,plain,
( ! [X0] :
( ~ empty(X0)
| sK5 = relation_composition(sK0,X0) )
| ~ spl12_121 ),
inference(avatar_component_clause,[],[f1165]) ).
fof(f1279,plain,
( spl12_132
| ~ spl12_1
| ~ spl12_117 ),
inference(avatar_split_clause,[],[f1115,f1072,f186,f1277]) ).
fof(f1277,plain,
( spl12_132
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_composition(X0,sK0) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_132])]) ).
fof(f1072,plain,
( spl12_117
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| relation_composition(X1,X0) = X2
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_117])]) ).
fof(f1115,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_composition(X0,sK0) = X1
| ~ empty(X1) )
| ~ spl12_1
| ~ spl12_117 ),
inference(resolution,[],[f1073,f188]) ).
fof(f188,plain,
( relation(sK0)
| ~ spl12_1 ),
inference(avatar_component_clause,[],[f186]) ).
fof(f1073,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| relation_composition(X1,X0) = X2
| ~ empty(X2) )
| ~ spl12_117 ),
inference(avatar_component_clause,[],[f1072]) ).
fof(f1275,plain,
( spl12_131
| ~ spl12_1
| ~ spl12_116 ),
inference(avatar_split_clause,[],[f1095,f1068,f186,f1273]) ).
fof(f1273,plain,
( spl12_131
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_composition(sK0,X0) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_131])]) ).
fof(f1068,plain,
( spl12_116
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| relation_composition(X0,X1) = X2
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_116])]) ).
fof(f1095,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_composition(sK0,X0) = X1
| ~ empty(X1) )
| ~ spl12_1
| ~ spl12_116 ),
inference(resolution,[],[f1069,f188]) ).
fof(f1069,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| relation_composition(X0,X1) = X2
| ~ empty(X2) )
| ~ spl12_116 ),
inference(avatar_component_clause,[],[f1068]) ).
fof(f1270,plain,
( spl12_68
| ~ spl12_95
| ~ spl12_130
| ~ spl12_44
| ~ spl12_70 ),
inference(avatar_split_clause,[],[f599,f595,f408,f1267,f860,f586]) ).
fof(f586,plain,
( spl12_68
<=> empty(function_inverse(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_68])]) ).
fof(f1267,plain,
( spl12_130
<=> empty(relation_dom(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_130])]) ).
fof(f408,plain,
( spl12_44
<=> ! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_44])]) ).
fof(f599,plain,
( ~ empty(relation_dom(sK0))
| ~ relation(function_inverse(sK0))
| empty(function_inverse(sK0))
| ~ spl12_44
| ~ spl12_70 ),
inference(superposition,[],[f409,f597]) ).
fof(f409,plain,
( ! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) )
| ~ spl12_44 ),
inference(avatar_component_clause,[],[f408]) ).
fof(f1233,plain,
( spl12_129
| ~ spl12_58
| ~ spl12_65 ),
inference(avatar_split_clause,[],[f572,f564,f517,f1231]) ).
fof(f1231,plain,
( spl12_129
<=> ! [X0] :
( relation_composition(function_inverse(function_inverse(X0)),function_inverse(X0)) = identity_relation(relation_rng(function_inverse(X0)))
| ~ function(function_inverse(X0))
| ~ relation(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_129])]) ).
fof(f564,plain,
( spl12_65
<=> ! [X0] :
( relation_composition(function_inverse(X0),X0) = identity_relation(relation_rng(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_65])]) ).
fof(f572,plain,
( ! [X0] :
( relation_composition(function_inverse(function_inverse(X0)),function_inverse(X0)) = identity_relation(relation_rng(function_inverse(X0)))
| ~ function(function_inverse(X0))
| ~ relation(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) )
| ~ spl12_58
| ~ spl12_65 ),
inference(resolution,[],[f565,f518]) ).
fof(f565,plain,
( ! [X0] :
( ~ one_to_one(X0)
| relation_composition(function_inverse(X0),X0) = identity_relation(relation_rng(X0))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl12_65 ),
inference(avatar_component_clause,[],[f564]) ).
fof(f1229,plain,
( spl12_128
| ~ spl12_58
| ~ spl12_64 ),
inference(avatar_split_clause,[],[f569,f560,f517,f1227]) ).
fof(f1227,plain,
( spl12_128
<=> ! [X0] :
( relation_composition(function_inverse(X0),function_inverse(function_inverse(X0))) = identity_relation(relation_dom(function_inverse(X0)))
| ~ function(function_inverse(X0))
| ~ relation(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_128])]) ).
fof(f560,plain,
( spl12_64
<=> ! [X0] :
( relation_composition(X0,function_inverse(X0)) = identity_relation(relation_dom(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_64])]) ).
fof(f569,plain,
( ! [X0] :
( relation_composition(function_inverse(X0),function_inverse(function_inverse(X0))) = identity_relation(relation_dom(function_inverse(X0)))
| ~ function(function_inverse(X0))
| ~ relation(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) )
| ~ spl12_58
| ~ spl12_64 ),
inference(resolution,[],[f561,f518]) ).
fof(f561,plain,
( ! [X0] :
( ~ one_to_one(X0)
| relation_composition(X0,function_inverse(X0)) = identity_relation(relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl12_64 ),
inference(avatar_component_clause,[],[f560]) ).
fof(f1225,plain,
( spl12_127
| ~ spl12_1
| ~ spl12_107 ),
inference(avatar_split_clause,[],[f1013,f974,f186,f1223]) ).
fof(f1013,plain,
( ! [X0] :
( sK5 = relation_composition(X0,sK0)
| ~ empty(X0) )
| ~ spl12_1
| ~ spl12_107 ),
inference(resolution,[],[f975,f188]) ).
fof(f1215,plain,
( spl12_126
| ~ spl12_58
| ~ spl12_62 ),
inference(avatar_split_clause,[],[f558,f545,f517,f1213]) ).
fof(f1213,plain,
( spl12_126
<=> ! [X0] :
( relation_dom(function_inverse(X0)) = relation_rng(function_inverse(function_inverse(X0)))
| ~ function(function_inverse(X0))
| ~ relation(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_126])]) ).
fof(f545,plain,
( spl12_62
<=> ! [X0] :
( relation_dom(X0) = relation_rng(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_62])]) ).
fof(f558,plain,
( ! [X0] :
( relation_dom(function_inverse(X0)) = relation_rng(function_inverse(function_inverse(X0)))
| ~ function(function_inverse(X0))
| ~ relation(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) )
| ~ spl12_58
| ~ spl12_62 ),
inference(resolution,[],[f546,f518]) ).
fof(f546,plain,
( ! [X0] :
( ~ one_to_one(X0)
| relation_dom(X0) = relation_rng(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl12_62 ),
inference(avatar_component_clause,[],[f545]) ).
fof(f1211,plain,
( spl12_125
| ~ spl12_58
| ~ spl12_61 ),
inference(avatar_split_clause,[],[f554,f541,f517,f1209]) ).
fof(f1209,plain,
( spl12_125
<=> ! [X0] :
( relation_rng(function_inverse(X0)) = relation_dom(function_inverse(function_inverse(X0)))
| ~ function(function_inverse(X0))
| ~ relation(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_125])]) ).
fof(f541,plain,
( spl12_61
<=> ! [X0] :
( relation_rng(X0) = relation_dom(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_61])]) ).
fof(f554,plain,
( ! [X0] :
( relation_rng(function_inverse(X0)) = relation_dom(function_inverse(function_inverse(X0)))
| ~ function(function_inverse(X0))
| ~ relation(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) )
| ~ spl12_58
| ~ spl12_61 ),
inference(resolution,[],[f542,f518]) ).
fof(f542,plain,
( ! [X0] :
( ~ one_to_one(X0)
| relation_rng(X0) = relation_dom(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl12_61 ),
inference(avatar_component_clause,[],[f541]) ).
fof(f1179,plain,
( spl12_124
| ~ spl12_50
| ~ spl12_57 ),
inference(avatar_split_clause,[],[f515,f473,f444,f1177]) ).
fof(f1177,plain,
( spl12_124
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ function(relation_composition(X1,X0))
| ~ empty(relation_composition(X1,X0))
| one_to_one(relation_composition(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_124])]) ).
fof(f444,plain,
( spl12_50
<=> ! [X0] :
( one_to_one(X0)
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_50])]) ).
fof(f473,plain,
( spl12_57
<=> ! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_57])]) ).
fof(f515,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ function(relation_composition(X1,X0))
| ~ empty(relation_composition(X1,X0))
| one_to_one(relation_composition(X1,X0)) )
| ~ spl12_50
| ~ spl12_57 ),
inference(resolution,[],[f474,f445]) ).
fof(f445,plain,
( ! [X0] :
( ~ relation(X0)
| ~ function(X0)
| ~ empty(X0)
| one_to_one(X0) )
| ~ spl12_50 ),
inference(avatar_component_clause,[],[f444]) ).
fof(f474,plain,
( ! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl12_57 ),
inference(avatar_component_clause,[],[f473]) ).
fof(f1175,plain,
( spl12_123
| ~ spl12_50
| ~ spl12_56 ),
inference(avatar_split_clause,[],[f514,f469,f444,f1173]) ).
fof(f1173,plain,
( spl12_123
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| ~ function(relation_composition(X1,X0))
| ~ empty(relation_composition(X1,X0))
| one_to_one(relation_composition(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_123])]) ).
fof(f469,plain,
( spl12_56
<=> ! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_56])]) ).
fof(f514,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| ~ function(relation_composition(X1,X0))
| ~ empty(relation_composition(X1,X0))
| one_to_one(relation_composition(X1,X0)) )
| ~ spl12_50
| ~ spl12_56 ),
inference(resolution,[],[f470,f445]) ).
fof(f470,plain,
( ! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) )
| ~ spl12_56 ),
inference(avatar_component_clause,[],[f469]) ).
fof(f1171,plain,
( spl12_122
| ~ spl12_50
| ~ spl12_53 ),
inference(avatar_split_clause,[],[f508,f456,f444,f1169]) ).
fof(f1169,plain,
( spl12_122
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| ~ function(relation_composition(X0,X1))
| ~ empty(relation_composition(X0,X1))
| one_to_one(relation_composition(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_122])]) ).
fof(f456,plain,
( spl12_53
<=> ! [X0,X1] :
( relation(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_53])]) ).
fof(f508,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| ~ function(relation_composition(X0,X1))
| ~ empty(relation_composition(X0,X1))
| one_to_one(relation_composition(X0,X1)) )
| ~ spl12_50
| ~ spl12_53 ),
inference(resolution,[],[f457,f445]) ).
fof(f457,plain,
( ! [X0,X1] :
( relation(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) )
| ~ spl12_53 ),
inference(avatar_component_clause,[],[f456]) ).
fof(f1167,plain,
( spl12_121
| ~ spl12_1
| ~ spl12_106 ),
inference(avatar_split_clause,[],[f994,f969,f186,f1165]) ).
fof(f994,plain,
( ! [X0] :
( sK5 = relation_composition(sK0,X0)
| ~ empty(X0) )
| ~ spl12_1
| ~ spl12_106 ),
inference(resolution,[],[f970,f188]) ).
fof(f1161,plain,
( spl12_120
| ~ spl12_46
| ~ spl12_50 ),
inference(avatar_split_clause,[],[f476,f444,f416,f1159]) ).
fof(f1159,plain,
( spl12_120
<=> ! [X0] :
( ~ function(function_inverse(X0))
| ~ empty(function_inverse(X0))
| one_to_one(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_120])]) ).
fof(f416,plain,
( spl12_46
<=> ! [X0] :
( relation(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_46])]) ).
fof(f476,plain,
( ! [X0] :
( ~ function(function_inverse(X0))
| ~ empty(function_inverse(X0))
| one_to_one(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl12_46
| ~ spl12_50 ),
inference(resolution,[],[f445,f417]) ).
fof(f417,plain,
( ! [X0] :
( relation(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl12_46 ),
inference(avatar_component_clause,[],[f416]) ).
fof(f1144,plain,
( ~ spl12_16
| ~ spl12_17
| spl12_119
| ~ spl12_18
| ~ spl12_65 ),
inference(avatar_split_clause,[],[f571,f564,f271,f1141,f266,f261]) ).
fof(f266,plain,
( spl12_17
<=> function(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_17])]) ).
fof(f1141,plain,
( spl12_119
<=> relation_composition(function_inverse(sK10),sK10) = identity_relation(relation_rng(sK10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_119])]) ).
fof(f271,plain,
( spl12_18
<=> one_to_one(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_18])]) ).
fof(f571,plain,
( relation_composition(function_inverse(sK10),sK10) = identity_relation(relation_rng(sK10))
| ~ function(sK10)
| ~ relation(sK10)
| ~ spl12_18
| ~ spl12_65 ),
inference(resolution,[],[f565,f273]) ).
fof(f273,plain,
( one_to_one(sK10)
| ~ spl12_18 ),
inference(avatar_component_clause,[],[f271]) ).
fof(f1130,plain,
( ~ spl12_16
| ~ spl12_17
| spl12_118
| ~ spl12_18
| ~ spl12_64 ),
inference(avatar_split_clause,[],[f568,f560,f271,f1127,f266,f261]) ).
fof(f1127,plain,
( spl12_118
<=> relation_composition(sK10,function_inverse(sK10)) = identity_relation(relation_dom(sK10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_118])]) ).
fof(f568,plain,
( relation_composition(sK10,function_inverse(sK10)) = identity_relation(relation_dom(sK10))
| ~ function(sK10)
| ~ relation(sK10)
| ~ spl12_18
| ~ spl12_64 ),
inference(resolution,[],[f561,f273]) ).
fof(f1074,plain,
( spl12_117
| ~ spl12_49
| ~ spl12_55 ),
inference(avatar_split_clause,[],[f509,f465,f428,f1072]) ).
fof(f428,plain,
( spl12_49
<=> ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_49])]) ).
fof(f465,plain,
( spl12_55
<=> ! [X0,X1] :
( empty(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_55])]) ).
fof(f509,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| relation_composition(X1,X0) = X2
| ~ empty(X2) )
| ~ spl12_49
| ~ spl12_55 ),
inference(resolution,[],[f466,f429]) ).
fof(f429,plain,
( ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) )
| ~ spl12_49 ),
inference(avatar_component_clause,[],[f428]) ).
fof(f466,plain,
( ! [X0,X1] :
( empty(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) )
| ~ spl12_55 ),
inference(avatar_component_clause,[],[f465]) ).
fof(f1070,plain,
( spl12_116
| ~ spl12_49
| ~ spl12_52 ),
inference(avatar_split_clause,[],[f503,f452,f428,f1068]) ).
fof(f452,plain,
( spl12_52
<=> ! [X0,X1] :
( empty(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_52])]) ).
fof(f503,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| relation_composition(X0,X1) = X2
| ~ empty(X2) )
| ~ spl12_49
| ~ spl12_52 ),
inference(resolution,[],[f453,f429]) ).
fof(f453,plain,
( ! [X0,X1] :
( empty(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) )
| ~ spl12_52 ),
inference(avatar_component_clause,[],[f452]) ).
fof(f1066,plain,
( spl12_115
| ~ spl12_34
| ~ spl12_50 ),
inference(avatar_split_clause,[],[f480,f444,f350,f1064]) ).
fof(f350,plain,
( spl12_34
<=> ! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_34])]) ).
fof(f480,plain,
( ! [X0] :
( ~ function(relation_rng(X0))
| ~ empty(relation_rng(X0))
| one_to_one(relation_rng(X0))
| ~ empty(X0) )
| ~ spl12_34
| ~ spl12_50 ),
inference(resolution,[],[f445,f351]) ).
fof(f351,plain,
( ! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) )
| ~ spl12_34 ),
inference(avatar_component_clause,[],[f350]) ).
fof(f1062,plain,
( spl12_114
| ~ spl12_36
| ~ spl12_50 ),
inference(avatar_split_clause,[],[f479,f444,f358,f1060]) ).
fof(f358,plain,
( spl12_36
<=> ! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_36])]) ).
fof(f479,plain,
( ! [X0] :
( ~ function(relation_dom(X0))
| ~ empty(relation_dom(X0))
| one_to_one(relation_dom(X0))
| ~ empty(X0) )
| ~ spl12_36
| ~ spl12_50 ),
inference(resolution,[],[f445,f359]) ).
fof(f359,plain,
( ! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) )
| ~ spl12_36 ),
inference(avatar_component_clause,[],[f358]) ).
fof(f1048,plain,
( ~ spl12_16
| ~ spl12_17
| spl12_113
| ~ spl12_18
| ~ spl12_62 ),
inference(avatar_split_clause,[],[f557,f545,f271,f1045,f266,f261]) ).
fof(f1045,plain,
( spl12_113
<=> relation_dom(sK10) = relation_rng(function_inverse(sK10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_113])]) ).
fof(f557,plain,
( relation_dom(sK10) = relation_rng(function_inverse(sK10))
| ~ function(sK10)
| ~ relation(sK10)
| ~ spl12_18
| ~ spl12_62 ),
inference(resolution,[],[f546,f273]) ).
fof(f1039,plain,
( ~ spl12_16
| ~ spl12_17
| spl12_112
| ~ spl12_18
| ~ spl12_61 ),
inference(avatar_split_clause,[],[f553,f541,f271,f1036,f266,f261]) ).
fof(f553,plain,
( relation_rng(sK10) = relation_dom(function_inverse(sK10))
| ~ function(sK10)
| ~ relation(sK10)
| ~ spl12_18
| ~ spl12_61 ),
inference(resolution,[],[f542,f273]) ).
fof(f1034,plain,
( ~ spl12_1
| ~ spl12_2
| ~ spl12_46
| spl12_95 ),
inference(avatar_split_clause,[],[f913,f860,f416,f191,f186]) ).
fof(f913,plain,
( ~ function(sK0)
| ~ relation(sK0)
| ~ spl12_46
| spl12_95 ),
inference(resolution,[],[f862,f417]) ).
fof(f862,plain,
( ~ relation(function_inverse(sK0))
| spl12_95 ),
inference(avatar_component_clause,[],[f860]) ).
fof(f1033,plain,
( spl12_111
| ~ spl12_43
| ~ spl12_51 ),
inference(avatar_split_clause,[],[f498,f448,f404,f1031]) ).
fof(f1031,plain,
( spl12_111
<=> ! [X0] :
( empty(powerset(X0))
| in(sK1(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_111])]) ).
fof(f404,plain,
( spl12_43
<=> ! [X0] :
( element(sK1(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_43])]) ).
fof(f448,plain,
( spl12_51
<=> ! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_51])]) ).
fof(f498,plain,
( ! [X0] :
( empty(powerset(X0))
| in(sK1(X0),powerset(X0))
| empty(X0) )
| ~ spl12_43
| ~ spl12_51 ),
inference(resolution,[],[f449,f405]) ).
fof(f405,plain,
( ! [X0] :
( element(sK1(X0),powerset(X0))
| empty(X0) )
| ~ spl12_43 ),
inference(avatar_component_clause,[],[f404]) ).
fof(f449,plain,
( ! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) )
| ~ spl12_51 ),
inference(avatar_component_clause,[],[f448]) ).
fof(f1029,plain,
( spl12_110
| ~ spl12_48
| ~ spl12_51 ),
inference(avatar_split_clause,[],[f497,f448,f424,f1027]) ).
fof(f1027,plain,
( spl12_110
<=> ! [X0,X1] :
( empty(powerset(X0))
| in(X1,powerset(X0))
| ~ subset(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_110])]) ).
fof(f424,plain,
( spl12_48
<=> ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_48])]) ).
fof(f497,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| in(X1,powerset(X0))
| ~ subset(X1,X0) )
| ~ spl12_48
| ~ spl12_51 ),
inference(resolution,[],[f449,f425]) ).
fof(f425,plain,
( ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) )
| ~ spl12_48 ),
inference(avatar_component_clause,[],[f424]) ).
fof(f984,plain,
( spl12_109
| ~ spl12_43
| ~ spl12_60 ),
inference(avatar_split_clause,[],[f535,f531,f404,f982]) ).
fof(f982,plain,
( spl12_109
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK1(X1))
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_109])]) ).
fof(f531,plain,
( spl12_60
<=> ! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_60])]) ).
fof(f535,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK1(X1))
| empty(X1) )
| ~ spl12_43
| ~ spl12_60 ),
inference(resolution,[],[f532,f405]) ).
fof(f532,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| element(X0,X2)
| ~ in(X0,X1) )
| ~ spl12_60 ),
inference(avatar_component_clause,[],[f531]) ).
fof(f980,plain,
( spl12_108
| ~ spl12_48
| ~ spl12_60 ),
inference(avatar_split_clause,[],[f534,f531,f424,f978]) ).
fof(f978,plain,
( spl12_108
<=> ! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_108])]) ).
fof(f534,plain,
( ! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,X1) )
| ~ spl12_48
| ~ spl12_60 ),
inference(resolution,[],[f532,f425]) ).
fof(f976,plain,
( spl12_107
| ~ spl12_8
| ~ spl12_32
| ~ spl12_55 ),
inference(avatar_split_clause,[],[f513,f465,f342,f221,f974]) ).
fof(f221,plain,
( spl12_8
<=> empty(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_8])]) ).
fof(f342,plain,
( spl12_32
<=> ! [X0] :
( empty_set = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_32])]) ).
fof(f513,plain,
( ! [X0,X1] :
( relation_composition(X1,X0) = sK5
| ~ relation(X0)
| ~ empty(X1) )
| ~ spl12_8
| ~ spl12_32
| ~ spl12_55 ),
inference(forward_demodulation,[],[f510,f376]) ).
fof(f376,plain,
( empty_set = sK5
| ~ spl12_8
| ~ spl12_32 ),
inference(resolution,[],[f343,f223]) ).
fof(f223,plain,
( empty(sK5)
| ~ spl12_8 ),
inference(avatar_component_clause,[],[f221]) ).
fof(f343,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = X0 )
| ~ spl12_32 ),
inference(avatar_component_clause,[],[f342]) ).
fof(f510,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| relation_composition(X1,X0) = empty_set )
| ~ spl12_32
| ~ spl12_55 ),
inference(resolution,[],[f466,f343]) ).
fof(f971,plain,
( spl12_106
| ~ spl12_8
| ~ spl12_32
| ~ spl12_52 ),
inference(avatar_split_clause,[],[f507,f452,f342,f221,f969]) ).
fof(f507,plain,
( ! [X0,X1] :
( relation_composition(X0,X1) = sK5
| ~ relation(X0)
| ~ empty(X1) )
| ~ spl12_8
| ~ spl12_32
| ~ spl12_52 ),
inference(forward_demodulation,[],[f504,f376]) ).
fof(f504,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| relation_composition(X0,X1) = empty_set )
| ~ spl12_32
| ~ spl12_52 ),
inference(resolution,[],[f453,f343]) ).
fof(f967,plain,
( spl12_105
| ~ spl12_23
| ~ spl12_50 ),
inference(avatar_split_clause,[],[f477,f444,f295,f965]) ).
fof(f477,plain,
( ! [X0] :
( ~ function(identity_relation(X0))
| ~ empty(identity_relation(X0))
| one_to_one(identity_relation(X0)) )
| ~ spl12_23
| ~ spl12_50 ),
inference(resolution,[],[f445,f296]) ).
fof(f921,plain,
( spl12_104
| ~ spl12_29
| ~ spl12_60 ),
inference(avatar_split_clause,[],[f536,f531,f319,f919]) ).
fof(f919,plain,
( spl12_104
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK2(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_104])]) ).
fof(f319,plain,
( spl12_29
<=> ! [X0] : element(sK2(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_29])]) ).
fof(f536,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK2(powerset(X1))) )
| ~ spl12_29
| ~ spl12_60 ),
inference(resolution,[],[f532,f320]) ).
fof(f320,plain,
( ! [X0] : element(sK2(X0),X0)
| ~ spl12_29 ),
inference(avatar_component_clause,[],[f319]) ).
fof(f917,plain,
( spl12_103
| ~ spl12_48
| ~ spl12_59 ),
inference(avatar_split_clause,[],[f524,f521,f424,f915]) ).
fof(f915,plain,
( spl12_103
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,X2)
| ~ subset(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_103])]) ).
fof(f521,plain,
( spl12_59
<=> ! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_59])]) ).
fof(f524,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,X2)
| ~ subset(X2,X0) )
| ~ spl12_48
| ~ spl12_59 ),
inference(resolution,[],[f522,f425]) ).
fof(f522,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X0,X1) )
| ~ spl12_59 ),
inference(avatar_component_clause,[],[f521]) ).
fof(f912,plain,
( spl12_102
| ~ spl12_27
| ~ spl12_55 ),
inference(avatar_split_clause,[],[f512,f465,f311,f910]) ).
fof(f910,plain,
( spl12_102
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| function(relation_composition(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_102])]) ).
fof(f311,plain,
( spl12_27
<=> ! [X0] :
( function(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_27])]) ).
fof(f512,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| function(relation_composition(X1,X0)) )
| ~ spl12_27
| ~ spl12_55 ),
inference(resolution,[],[f466,f312]) ).
fof(f312,plain,
( ! [X0] :
( ~ empty(X0)
| function(X0) )
| ~ spl12_27 ),
inference(avatar_component_clause,[],[f311]) ).
fof(f908,plain,
( spl12_101
| ~ spl12_27
| ~ spl12_52 ),
inference(avatar_split_clause,[],[f506,f452,f311,f906]) ).
fof(f906,plain,
( spl12_101
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| function(relation_composition(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_101])]) ).
fof(f506,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| function(relation_composition(X0,X1)) )
| ~ spl12_27
| ~ spl12_52 ),
inference(resolution,[],[f453,f312]) ).
fof(f904,plain,
( spl12_100
| ~ spl12_33
| ~ spl12_49 ),
inference(avatar_split_clause,[],[f435,f428,f346,f902]) ).
fof(f435,plain,
( ! [X0,X1] :
( relation_rng(X1) = X0
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl12_33
| ~ spl12_49 ),
inference(resolution,[],[f429,f347]) ).
fof(f900,plain,
( spl12_99
| ~ spl12_35
| ~ spl12_49 ),
inference(avatar_split_clause,[],[f434,f428,f354,f898]) ).
fof(f434,plain,
( ! [X0,X1] :
( relation_dom(X1) = X0
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl12_35
| ~ spl12_49 ),
inference(resolution,[],[f429,f355]) ).
fof(f892,plain,
( spl12_98
| ~ spl12_29
| ~ spl12_59 ),
inference(avatar_split_clause,[],[f526,f521,f319,f890]) ).
fof(f526,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK2(powerset(X0))) )
| ~ spl12_29
| ~ spl12_59 ),
inference(resolution,[],[f522,f320]) ).
fof(f888,plain,
( spl12_97
| ~ spl12_8
| ~ spl12_25
| ~ spl12_32
| ~ spl12_37
| ~ spl12_51 ),
inference(avatar_split_clause,[],[f502,f448,f362,f342,f303,f221,f886]) ).
fof(f886,plain,
( spl12_97
<=> ! [X0] :
( in(sK5,powerset(X0))
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_97])]) ).
fof(f303,plain,
( spl12_25
<=> ! [X0] : empty(sK3(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_25])]) ).
fof(f502,plain,
( ! [X0] :
( in(sK5,powerset(X0))
| empty(powerset(X0)) )
| ~ spl12_8
| ~ spl12_25
| ~ spl12_32
| ~ spl12_37
| ~ spl12_51 ),
inference(forward_demodulation,[],[f501,f376]) ).
fof(f501,plain,
( ! [X0] :
( in(empty_set,powerset(X0))
| empty(powerset(X0)) )
| ~ spl12_25
| ~ spl12_32
| ~ spl12_37
| ~ spl12_51 ),
inference(forward_demodulation,[],[f500,f375]) ).
fof(f375,plain,
( ! [X0] : empty_set = sK3(X0)
| ~ spl12_25
| ~ spl12_32 ),
inference(resolution,[],[f343,f304]) ).
fof(f304,plain,
( ! [X0] : empty(sK3(X0))
| ~ spl12_25 ),
inference(avatar_component_clause,[],[f303]) ).
fof(f500,plain,
( ! [X0] :
( empty(powerset(X0))
| in(sK3(X0),powerset(X0)) )
| ~ spl12_37
| ~ spl12_51 ),
inference(resolution,[],[f449,f363]) ).
fof(f867,plain,
( spl12_68
| ~ spl12_95
| ~ spl12_96
| ~ spl12_45
| ~ spl12_67 ),
inference(avatar_split_clause,[],[f582,f578,f412,f864,f860,f586]) ).
fof(f864,plain,
( spl12_96
<=> empty(relation_rng(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_96])]) ).
fof(f412,plain,
( spl12_45
<=> ! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_45])]) ).
fof(f582,plain,
( ~ empty(relation_rng(sK0))
| ~ relation(function_inverse(sK0))
| empty(function_inverse(sK0))
| ~ spl12_45
| ~ spl12_67 ),
inference(superposition,[],[f413,f580]) ).
fof(f413,plain,
( ! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) )
| ~ spl12_45 ),
inference(avatar_component_clause,[],[f412]) ).
fof(f845,plain,
( spl12_94
| ~ spl12_29
| ~ spl12_51 ),
inference(avatar_split_clause,[],[f499,f448,f319,f843]) ).
fof(f499,plain,
( ! [X0] :
( empty(X0)
| in(sK2(X0),X0) )
| ~ spl12_29
| ~ spl12_51 ),
inference(resolution,[],[f449,f320]) ).
fof(f837,plain,
( ~ spl12_39
| ~ spl12_8
| spl12_93
| ~ spl12_6
| ~ spl12_8
| ~ spl12_32
| ~ spl12_50 ),
inference(avatar_split_clause,[],[f490,f444,f342,f221,f211,f834,f221,f370]) ).
fof(f370,plain,
( spl12_39
<=> function(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_39])]) ).
fof(f834,plain,
( spl12_93
<=> one_to_one(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_93])]) ).
fof(f490,plain,
( one_to_one(sK5)
| ~ empty(sK5)
| ~ function(sK5)
| ~ spl12_6
| ~ spl12_8
| ~ spl12_32
| ~ spl12_50 ),
inference(forward_demodulation,[],[f489,f376]) ).
fof(f489,plain,
( ~ empty(sK5)
| ~ function(sK5)
| one_to_one(empty_set)
| ~ spl12_6
| ~ spl12_8
| ~ spl12_32
| ~ spl12_50 ),
inference(forward_demodulation,[],[f488,f376]) ).
fof(f488,plain,
( ~ function(sK5)
| ~ empty(empty_set)
| one_to_one(empty_set)
| ~ spl12_6
| ~ spl12_8
| ~ spl12_32
| ~ spl12_50 ),
inference(forward_demodulation,[],[f478,f376]) ).
fof(f478,plain,
( ~ function(empty_set)
| ~ empty(empty_set)
| one_to_one(empty_set)
| ~ spl12_6
| ~ spl12_50 ),
inference(resolution,[],[f445,f213]) ).
fof(f832,plain,
( spl12_91
| ~ spl12_92
| ~ spl12_15
| ~ spl12_14
| ~ spl12_50 ),
inference(avatar_split_clause,[],[f485,f444,f251,f256,f829,f825]) ).
fof(f825,plain,
( spl12_91
<=> one_to_one(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_91])]) ).
fof(f829,plain,
( spl12_92
<=> empty(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_92])]) ).
fof(f256,plain,
( spl12_15
<=> function(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_15])]) ).
fof(f485,plain,
( ~ function(sK9)
| ~ empty(sK9)
| one_to_one(sK9)
| ~ spl12_14
| ~ spl12_50 ),
inference(resolution,[],[f445,f253]) ).
fof(f823,plain,
( spl12_88
| ~ spl12_89
| ~ spl12_90
| ~ spl12_13
| ~ spl12_50 ),
inference(avatar_split_clause,[],[f484,f444,f246,f820,f816,f812]) ).
fof(f812,plain,
( spl12_88
<=> one_to_one(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_88])]) ).
fof(f816,plain,
( spl12_89
<=> empty(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_89])]) ).
fof(f820,plain,
( spl12_90
<=> function(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_90])]) ).
fof(f484,plain,
( ~ function(sK8)
| ~ empty(sK8)
| one_to_one(sK8)
| ~ spl12_13
| ~ spl12_50 ),
inference(resolution,[],[f445,f248]) ).
fof(f810,plain,
( spl12_87
| ~ spl12_8
| ~ spl12_32
| ~ spl12_35 ),
inference(avatar_split_clause,[],[f388,f354,f342,f221,f808]) ).
fof(f388,plain,
( ! [X0] :
( relation_dom(X0) = sK5
| ~ empty(X0) )
| ~ spl12_8
| ~ spl12_32
| ~ spl12_35 ),
inference(forward_demodulation,[],[f385,f376]) ).
fof(f385,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = relation_dom(X0) )
| ~ spl12_32
| ~ spl12_35 ),
inference(resolution,[],[f355,f343]) ).
fof(f806,plain,
( spl12_86
| ~ spl12_8
| ~ spl12_32
| ~ spl12_33 ),
inference(avatar_split_clause,[],[f384,f346,f342,f221,f804]) ).
fof(f384,plain,
( ! [X0] :
( relation_rng(X0) = sK5
| ~ empty(X0) )
| ~ spl12_8
| ~ spl12_32
| ~ spl12_33 ),
inference(forward_demodulation,[],[f381,f376]) ).
fof(f381,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = relation_rng(X0) )
| ~ spl12_32
| ~ spl12_33 ),
inference(resolution,[],[f347,f343]) ).
fof(f732,plain,
( spl12_82
| ~ spl12_32
| ~ spl12_75 ),
inference(avatar_split_clause,[],[f704,f641,f342,f683]) ).
fof(f683,plain,
( spl12_82
<=> ! [X0] :
( sK5 = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_82])]) ).
fof(f704,plain,
( ! [X0] :
( sK5 = X0
| ~ empty(X0) )
| ~ spl12_32
| ~ spl12_75 ),
inference(forward_demodulation,[],[f343,f643]) ).
fof(f727,plain,
( ~ spl12_85
| ~ spl12_34
| spl12_69 ),
inference(avatar_split_clause,[],[f686,f590,f350,f724]) ).
fof(f724,plain,
( spl12_85
<=> empty(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_85])]) ).
fof(f590,plain,
( spl12_69
<=> relation(relation_rng(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_69])]) ).
fof(f686,plain,
( ~ empty(sK0)
| ~ spl12_34
| spl12_69 ),
inference(resolution,[],[f591,f351]) ).
fof(f591,plain,
( ~ relation(relation_rng(sK0))
| spl12_69 ),
inference(avatar_component_clause,[],[f590]) ).
fof(f703,plain,
( ~ spl12_5
| ~ spl12_83 ),
inference(avatar_contradiction_clause,[],[f694]) ).
fof(f694,plain,
( $false
| ~ spl12_5
| ~ spl12_83 ),
inference(resolution,[],[f689,f208]) ).
fof(f689,plain,
( ! [X0] : ~ empty(X0)
| ~ spl12_83 ),
inference(avatar_component_clause,[],[f688]) ).
fof(f688,plain,
( spl12_83
<=> ! [X0] : ~ empty(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_83])]) ).
fof(f702,plain,
( ~ spl12_25
| ~ spl12_83 ),
inference(avatar_contradiction_clause,[],[f695]) ).
fof(f695,plain,
( $false
| ~ spl12_25
| ~ spl12_83 ),
inference(resolution,[],[f689,f304]) ).
fof(f701,plain,
( ~ spl12_8
| ~ spl12_83 ),
inference(avatar_contradiction_clause,[],[f696]) ).
fof(f696,plain,
( $false
| ~ spl12_8
| ~ spl12_83 ),
inference(resolution,[],[f689,f223]) ).
fof(f700,plain,
( ~ spl12_11
| ~ spl12_83 ),
inference(avatar_contradiction_clause,[],[f697]) ).
fof(f697,plain,
( $false
| ~ spl12_11
| ~ spl12_83 ),
inference(resolution,[],[f689,f238]) ).
fof(f238,plain,
( empty(sK7)
| ~ spl12_11 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f236,plain,
( spl12_11
<=> empty(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_11])]) ).
fof(f699,plain,
( ~ spl12_20
| ~ spl12_83 ),
inference(avatar_contradiction_clause,[],[f698]) ).
fof(f698,plain,
( $false
| ~ spl12_20
| ~ spl12_83 ),
inference(resolution,[],[f689,f283]) ).
fof(f283,plain,
( empty(sK11)
| ~ spl12_20 ),
inference(avatar_component_clause,[],[f281]) ).
fof(f281,plain,
( spl12_20
<=> empty(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_20])]) ).
fof(f693,plain,
( spl12_83
| spl12_84
| ~ spl12_8
| ~ spl12_25
| ~ spl12_32
| ~ spl12_37
| ~ spl12_59 ),
inference(avatar_split_clause,[],[f529,f521,f362,f342,f303,f221,f691,f688]) ).
fof(f691,plain,
( spl12_84
<=> ! [X1] : ~ in(X1,sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_84])]) ).
fof(f529,plain,
( ! [X0,X1] :
( ~ in(X1,sK5)
| ~ empty(X0) )
| ~ spl12_8
| ~ spl12_25
| ~ spl12_32
| ~ spl12_37
| ~ spl12_59 ),
inference(forward_demodulation,[],[f528,f376]) ).
fof(f528,plain,
( ! [X0,X1] :
( ~ in(X1,empty_set)
| ~ empty(X0) )
| ~ spl12_25
| ~ spl12_32
| ~ spl12_37
| ~ spl12_59 ),
inference(forward_demodulation,[],[f527,f375]) ).
fof(f527,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK3(X0)) )
| ~ spl12_37
| ~ spl12_59 ),
inference(resolution,[],[f522,f363]) ).
fof(f685,plain,
( spl12_82
| ~ spl12_8
| ~ spl12_49 ),
inference(avatar_split_clause,[],[f437,f428,f221,f683]) ).
fof(f437,plain,
( ! [X0] :
( sK5 = X0
| ~ empty(X0) )
| ~ spl12_8
| ~ spl12_49 ),
inference(resolution,[],[f429,f223]) ).
fof(f681,plain,
( spl12_81
| ~ spl12_27
| ~ spl12_35 ),
inference(avatar_split_clause,[],[f387,f354,f311,f679]) ).
fof(f387,plain,
( ! [X0] :
( ~ empty(X0)
| function(relation_dom(X0)) )
| ~ spl12_27
| ~ spl12_35 ),
inference(resolution,[],[f355,f312]) ).
fof(f677,plain,
( spl12_80
| ~ spl12_27
| ~ spl12_33 ),
inference(avatar_split_clause,[],[f383,f346,f311,f675]) ).
fof(f383,plain,
( ! [X0] :
( ~ empty(X0)
| function(relation_rng(X0)) )
| ~ spl12_27
| ~ spl12_33 ),
inference(resolution,[],[f347,f312]) ).
fof(f671,plain,
( spl12_79
| ~ spl12_75
| ~ spl12_78 ),
inference(avatar_split_clause,[],[f667,f664,f641,f669]) ).
fof(f664,plain,
( spl12_78
<=> ! [X0] : empty_set = sK3(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_78])]) ).
fof(f667,plain,
( ! [X0] : sK3(X0) = sK5
| ~ spl12_75
| ~ spl12_78 ),
inference(forward_demodulation,[],[f665,f643]) ).
fof(f665,plain,
( ! [X0] : empty_set = sK3(X0)
| ~ spl12_78 ),
inference(avatar_component_clause,[],[f664]) ).
fof(f666,plain,
( spl12_78
| ~ spl12_25
| ~ spl12_32 ),
inference(avatar_split_clause,[],[f375,f342,f303,f664]) ).
fof(f654,plain,
( spl12_77
| ~ spl12_8
| ~ spl12_20
| ~ spl12_32 ),
inference(avatar_split_clause,[],[f380,f342,f281,f221,f651]) ).
fof(f651,plain,
( spl12_77
<=> sK5 = sK11 ),
introduced(avatar_definition,[new_symbols(naming,[spl12_77])]) ).
fof(f380,plain,
( sK5 = sK11
| ~ spl12_8
| ~ spl12_20
| ~ spl12_32 ),
inference(forward_demodulation,[],[f378,f376]) ).
fof(f378,plain,
( empty_set = sK11
| ~ spl12_20
| ~ spl12_32 ),
inference(resolution,[],[f343,f283]) ).
fof(f649,plain,
( spl12_76
| ~ spl12_8
| ~ spl12_11
| ~ spl12_32 ),
inference(avatar_split_clause,[],[f379,f342,f236,f221,f646]) ).
fof(f646,plain,
( spl12_76
<=> sK5 = sK7 ),
introduced(avatar_definition,[new_symbols(naming,[spl12_76])]) ).
fof(f379,plain,
( sK5 = sK7
| ~ spl12_8
| ~ spl12_11
| ~ spl12_32 ),
inference(forward_demodulation,[],[f377,f376]) ).
fof(f377,plain,
( empty_set = sK7
| ~ spl12_11
| ~ spl12_32 ),
inference(resolution,[],[f343,f238]) ).
fof(f644,plain,
( spl12_75
| ~ spl12_8
| ~ spl12_32 ),
inference(avatar_split_clause,[],[f376,f342,f221,f641]) ).
fof(f638,plain,
( spl12_74
| ~ spl12_25
| ~ spl12_28 ),
inference(avatar_split_clause,[],[f333,f315,f303,f636]) ).
fof(f636,plain,
( spl12_74
<=> ! [X0] : relation(sK3(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_74])]) ).
fof(f315,plain,
( spl12_28
<=> ! [X0] :
( relation(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_28])]) ).
fof(f333,plain,
( ! [X0] : relation(sK3(X0))
| ~ spl12_25
| ~ spl12_28 ),
inference(resolution,[],[f316,f304]) ).
fof(f316,plain,
( ! [X0] :
( ~ empty(X0)
| relation(X0) )
| ~ spl12_28 ),
inference(avatar_component_clause,[],[f315]) ).
fof(f633,plain,
( spl12_73
| ~ spl12_25
| ~ spl12_27 ),
inference(avatar_split_clause,[],[f323,f311,f303,f631]) ).
fof(f631,plain,
( spl12_73
<=> ! [X0] : function(sK3(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_73])]) ).
fof(f323,plain,
( ! [X0] : function(sK3(X0))
| ~ spl12_25
| ~ spl12_27 ),
inference(resolution,[],[f312,f304]) ).
fof(f618,plain,
( ~ spl12_1
| ~ spl12_2
| spl12_72
| ~ spl12_3
| ~ spl12_65 ),
inference(avatar_split_clause,[],[f570,f564,f196,f615,f191,f186]) ).
fof(f570,plain,
( relation_composition(function_inverse(sK0),sK0) = identity_relation(relation_rng(sK0))
| ~ function(sK0)
| ~ relation(sK0)
| ~ spl12_3
| ~ spl12_65 ),
inference(resolution,[],[f565,f198]) ).
fof(f198,plain,
( one_to_one(sK0)
| ~ spl12_3 ),
inference(avatar_component_clause,[],[f196]) ).
fof(f606,plain,
( ~ spl12_1
| ~ spl12_2
| spl12_71
| ~ spl12_3
| ~ spl12_64 ),
inference(avatar_split_clause,[],[f567,f560,f196,f603,f191,f186]) ).
fof(f603,plain,
( spl12_71
<=> relation_composition(sK0,function_inverse(sK0)) = identity_relation(relation_dom(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_71])]) ).
fof(f567,plain,
( relation_composition(sK0,function_inverse(sK0)) = identity_relation(relation_dom(sK0))
| ~ function(sK0)
| ~ relation(sK0)
| ~ spl12_3
| ~ spl12_64 ),
inference(resolution,[],[f561,f198]) ).
fof(f598,plain,
( ~ spl12_1
| ~ spl12_2
| spl12_70
| ~ spl12_3
| ~ spl12_62 ),
inference(avatar_split_clause,[],[f556,f545,f196,f595,f191,f186]) ).
fof(f556,plain,
( relation_dom(sK0) = relation_rng(function_inverse(sK0))
| ~ function(sK0)
| ~ relation(sK0)
| ~ spl12_3
| ~ spl12_62 ),
inference(resolution,[],[f546,f198]) ).
fof(f593,plain,
( ~ spl12_68
| spl12_69
| ~ spl12_36
| ~ spl12_67 ),
inference(avatar_split_clause,[],[f583,f578,f358,f590,f586]) ).
fof(f583,plain,
( relation(relation_rng(sK0))
| ~ empty(function_inverse(sK0))
| ~ spl12_36
| ~ spl12_67 ),
inference(superposition,[],[f359,f580]) ).
fof(f581,plain,
( ~ spl12_1
| ~ spl12_2
| spl12_67
| ~ spl12_3
| ~ spl12_61 ),
inference(avatar_split_clause,[],[f552,f541,f196,f578,f191,f186]) ).
fof(f552,plain,
( relation_rng(sK0) = relation_dom(function_inverse(sK0))
| ~ function(sK0)
| ~ relation(sK0)
| ~ spl12_3
| ~ spl12_61 ),
inference(resolution,[],[f542,f198]) ).
fof(f576,plain,
spl12_66,
inference(avatar_split_clause,[],[f147,f574]) ).
fof(f147,plain,
! [X0,X1] :
( function_inverse(X0) = X1
| relation_composition(X0,X1) != identity_relation(relation_dom(X0))
| relation_rng(X0) != relation_dom(X1)
| ~ one_to_one(X0)
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0] :
( ! [X1] :
( function_inverse(X0) = X1
| relation_composition(X0,X1) != identity_relation(relation_dom(X0))
| relation_rng(X0) != relation_dom(X1)
| ~ one_to_one(X0)
| ~ function(X1)
| ~ relation(X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f70]) ).
fof(f70,plain,
! [X0] :
( ! [X1] :
( function_inverse(X0) = X1
| relation_composition(X0,X1) != identity_relation(relation_dom(X0))
| relation_rng(X0) != relation_dom(X1)
| ~ one_to_one(X0)
| ~ function(X1)
| ~ relation(X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1] :
( ( function(X1)
& relation(X1) )
=> ( ( relation_composition(X0,X1) = identity_relation(relation_dom(X0))
& relation_rng(X0) = relation_dom(X1)
& one_to_one(X0) )
=> function_inverse(X0) = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_funct_1) ).
fof(f566,plain,
spl12_65,
inference(avatar_split_clause,[],[f146,f564]) ).
fof(f146,plain,
! [X0] :
( relation_composition(function_inverse(X0),X0) = identity_relation(relation_rng(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0] :
( ( relation_composition(function_inverse(X0),X0) = identity_relation(relation_rng(X0))
& relation_composition(X0,function_inverse(X0)) = identity_relation(relation_dom(X0)) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f68]) ).
fof(f68,plain,
! [X0] :
( ( relation_composition(function_inverse(X0),X0) = identity_relation(relation_rng(X0))
& relation_composition(X0,function_inverse(X0)) = identity_relation(relation_dom(X0)) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> ( relation_composition(function_inverse(X0),X0) = identity_relation(relation_rng(X0))
& relation_composition(X0,function_inverse(X0)) = identity_relation(relation_dom(X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_funct_1) ).
fof(f562,plain,
spl12_64,
inference(avatar_split_clause,[],[f145,f560]) ).
fof(f145,plain,
! [X0] :
( relation_composition(X0,function_inverse(X0)) = identity_relation(relation_dom(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f551,plain,
spl12_63,
inference(avatar_split_clause,[],[f163,f549]) ).
fof(f549,plain,
( spl12_63
<=> ! [X0,X1] :
( function(relation_composition(X0,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_63])]) ).
fof(f163,plain,
! [X0,X1] :
( function(relation_composition(X0,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
! [X0,X1] :
( ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) )
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f82]) ).
fof(f82,plain,
! [X0,X1] :
( ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) )
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1)
& function(X0)
& relation(X0) )
=> ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_funct_1) ).
fof(f547,plain,
spl12_62,
inference(avatar_split_clause,[],[f144,f545]) ).
fof(f144,plain,
! [X0] :
( relation_dom(X0) = relation_rng(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0] :
( ( relation_dom(X0) = relation_rng(function_inverse(X0))
& relation_rng(X0) = relation_dom(function_inverse(X0)) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f66]) ).
fof(f66,plain,
! [X0] :
( ( relation_dom(X0) = relation_rng(function_inverse(X0))
& relation_rng(X0) = relation_dom(function_inverse(X0)) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> ( relation_dom(X0) = relation_rng(function_inverse(X0))
& relation_rng(X0) = relation_dom(function_inverse(X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_funct_1) ).
fof(f543,plain,
spl12_61,
inference(avatar_split_clause,[],[f143,f541]) ).
fof(f143,plain,
! [X0] :
( relation_rng(X0) = relation_dom(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f533,plain,
spl12_60,
inference(avatar_split_clause,[],[f168,f531]) ).
fof(f168,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f89]) ).
fof(f89,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f523,plain,
spl12_59,
inference(avatar_split_clause,[],[f169,f521]) ).
fof(f169,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f91]) ).
fof(f91,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f519,plain,
spl12_58,
inference(avatar_split_clause,[],[f142,f517]) ).
fof(f142,plain,
! [X0] :
( one_to_one(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0] :
( one_to_one(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f64]) ).
fof(f64,plain,
! [X0] :
( one_to_one(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f39]) ).
fof(f39,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> one_to_one(function_inverse(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_funct_1) ).
fof(f475,plain,
spl12_57,
inference(avatar_split_clause,[],[f164,f473]) ).
fof(f164,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(flattening,[],[f84]) ).
fof(f84,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f471,plain,
spl12_56,
inference(avatar_split_clause,[],[f161,f469]) ).
fof(f161,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& empty(relation_composition(X0,X1)) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(flattening,[],[f80]) ).
fof(f80,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& empty(relation_composition(X0,X1)) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0,X1] :
( ( relation(X1)
& empty(X0) )
=> ( relation(relation_composition(X0,X1))
& empty(relation_composition(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_relat_1) ).
fof(f467,plain,
spl12_55,
inference(avatar_split_clause,[],[f160,f465]) ).
fof(f160,plain,
! [X0,X1] :
( empty(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f463,plain,
( spl12_54
| ~ spl12_8
| ~ spl12_28 ),
inference(avatar_split_clause,[],[f334,f315,f221,f460]) ).
fof(f460,plain,
( spl12_54
<=> relation(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_54])]) ).
fof(f334,plain,
( relation(sK5)
| ~ spl12_8
| ~ spl12_28 ),
inference(resolution,[],[f316,f223]) ).
fof(f458,plain,
spl12_53,
inference(avatar_split_clause,[],[f159,f456]) ).
fof(f159,plain,
! [X0,X1] :
( relation(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0,X1] :
( ( relation(relation_composition(X1,X0))
& empty(relation_composition(X1,X0)) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(flattening,[],[f78]) ).
fof(f78,plain,
! [X0,X1] :
( ( relation(relation_composition(X1,X0))
& empty(relation_composition(X1,X0)) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1] :
( ( relation(X1)
& empty(X0) )
=> ( relation(relation_composition(X1,X0))
& empty(relation_composition(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_relat_1) ).
fof(f454,plain,
spl12_52,
inference(avatar_split_clause,[],[f158,f452]) ).
fof(f158,plain,
! [X0,X1] :
( empty(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f450,plain,
spl12_51,
inference(avatar_split_clause,[],[f157,f448]) ).
fof(f157,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f76]) ).
fof(f76,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f446,plain,
spl12_50,
inference(avatar_split_clause,[],[f150,f444]) ).
fof(f150,plain,
! [X0] :
( one_to_one(X0)
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f73,plain,
! [X0] :
( ( one_to_one(X0)
& function(X0)
& relation(X0) )
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ),
inference(flattening,[],[f72]) ).
fof(f72,plain,
! [X0] :
( ( one_to_one(X0)
& function(X0)
& relation(X0) )
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( ( function(X0)
& empty(X0)
& relation(X0) )
=> ( one_to_one(X0)
& function(X0)
& relation(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_funct_1) ).
fof(f430,plain,
spl12_49,
inference(avatar_split_clause,[],[f166,f428]) ).
fof(f166,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f87,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(f426,plain,
spl12_48,
inference(avatar_split_clause,[],[f165,f424]) ).
fof(f165,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0,X1] :
( subset(X0,X1)
=> element(X0,powerset(X1)) ),
inference(unused_predicate_definition_removal,[],[f34]) ).
fof(f34,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f422,plain,
spl12_47,
inference(avatar_split_clause,[],[f141,f420]) ).
fof(f141,plain,
! [X0] :
( function(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0] :
( ( function(function_inverse(X0))
& relation(function_inverse(X0)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f62]) ).
fof(f62,plain,
! [X0] :
( ( function(function_inverse(X0))
& relation(function_inverse(X0)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( function(function_inverse(X0))
& relation(function_inverse(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_1) ).
fof(f418,plain,
spl12_46,
inference(avatar_split_clause,[],[f140,f416]) ).
fof(f140,plain,
! [X0] :
( relation(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f414,plain,
spl12_45,
inference(avatar_split_clause,[],[f139,f412]) ).
fof(f139,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(flattening,[],[f60]) ).
fof(f60,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_dom(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(f410,plain,
spl12_44,
inference(avatar_split_clause,[],[f138,f408]) ).
fof(f138,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(flattening,[],[f58]) ).
fof(f58,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_rng(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_relat_1) ).
fof(f406,plain,
spl12_43,
inference(avatar_split_clause,[],[f129,f404]) ).
fof(f129,plain,
! [X0] :
( element(sK1(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f95,plain,
! [X0] :
( ( ~ empty(sK1(X0))
& element(sK1(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f52,f94]) ).
fof(f94,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( ~ empty(sK1(X0))
& element(sK1(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f52,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f401,plain,
( spl12_42
| ~ spl12_11
| ~ spl12_27 ),
inference(avatar_split_clause,[],[f325,f311,f236,f398]) ).
fof(f398,plain,
( spl12_42
<=> function(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_42])]) ).
fof(f325,plain,
( function(sK7)
| ~ spl12_11
| ~ spl12_27 ),
inference(resolution,[],[f312,f238]) ).
fof(f396,plain,
spl12_41,
inference(avatar_split_clause,[],[f156,f394]) ).
fof(f394,plain,
( spl12_41
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_41])]) ).
fof(f156,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f392,plain,
spl12_40,
inference(avatar_split_clause,[],[f155,f390]) ).
fof(f155,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f74]) ).
fof(f74,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(f373,plain,
( spl12_39
| ~ spl12_8
| ~ spl12_27 ),
inference(avatar_split_clause,[],[f324,f311,f221,f370]) ).
fof(f324,plain,
( function(sK5)
| ~ spl12_8
| ~ spl12_27 ),
inference(resolution,[],[f312,f223]) ).
fof(f368,plain,
spl12_38,
inference(avatar_split_clause,[],[f167,f366]) ).
fof(f366,plain,
( spl12_38
<=> ! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_38])]) ).
fof(f167,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f44]) ).
fof(f44,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f364,plain,
spl12_37,
inference(avatar_split_clause,[],[f152,f362]) ).
fof(f152,plain,
! [X0] : element(sK3(X0),powerset(X0)),
inference(cnf_transformation,[],[f99]) ).
fof(f99,plain,
! [X0] :
( empty(sK3(X0))
& element(sK3(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f27,f98]) ).
fof(f98,plain,
! [X0] :
( ? [X1] :
( empty(X1)
& element(X1,powerset(X0)) )
=> ( empty(sK3(X0))
& element(sK3(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(f360,plain,
spl12_36,
inference(avatar_split_clause,[],[f137,f358]) ).
fof(f137,plain,
! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0] :
( ( relation(relation_dom(X0))
& empty(relation_dom(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(f356,plain,
spl12_35,
inference(avatar_split_clause,[],[f136,f354]) ).
fof(f136,plain,
! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f352,plain,
spl12_34,
inference(avatar_split_clause,[],[f135,f350]) ).
fof(f135,plain,
! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0] :
( ( relation(relation_rng(X0))
& empty(relation_rng(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_rng(X0))
& empty(relation_rng(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).
fof(f348,plain,
spl12_33,
inference(avatar_split_clause,[],[f134,f346]) ).
fof(f134,plain,
! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f344,plain,
spl12_32,
inference(avatar_split_clause,[],[f133,f342]) ).
fof(f133,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f43]) ).
fof(f43,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f340,plain,
spl12_31,
inference(avatar_split_clause,[],[f130,f338]) ).
fof(f338,plain,
( spl12_31
<=> ! [X0] :
( ~ empty(sK1(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_31])]) ).
fof(f130,plain,
! [X0] :
( ~ empty(sK1(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f331,plain,
( spl12_30
| ~ spl12_5
| ~ spl12_27 ),
inference(avatar_split_clause,[],[f322,f311,f206,f328]) ).
fof(f328,plain,
( spl12_30
<=> function(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_30])]) ).
fof(f322,plain,
( function(empty_set)
| ~ spl12_5
| ~ spl12_27 ),
inference(resolution,[],[f312,f208]) ).
fof(f321,plain,
spl12_29,
inference(avatar_split_clause,[],[f151,f319]) ).
fof(f151,plain,
! [X0] : element(sK2(X0),X0),
inference(cnf_transformation,[],[f97]) ).
fof(f97,plain,
! [X0] : element(sK2(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f8,f96]) ).
fof(f96,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK2(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f8,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f317,plain,
spl12_28,
inference(avatar_split_clause,[],[f132,f315]) ).
fof(f132,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( empty(X0)
=> relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(f313,plain,
spl12_27,
inference(avatar_split_clause,[],[f131,f311]) ).
fof(f131,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f53,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( empty(X0)
=> function(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
fof(f309,plain,
spl12_26,
inference(avatar_split_clause,[],[f154,f307]) ).
fof(f307,plain,
( spl12_26
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_26])]) ).
fof(f154,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f46]) ).
fof(f46,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(f305,plain,
spl12_25,
inference(avatar_split_clause,[],[f153,f303]) ).
fof(f153,plain,
! [X0] : empty(sK3(X0)),
inference(cnf_transformation,[],[f99]) ).
fof(f301,plain,
spl12_24,
inference(avatar_split_clause,[],[f128,f299]) ).
fof(f128,plain,
! [X0] : function(identity_relation(X0)),
inference(cnf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0] :
( function(identity_relation(X0))
& relation(identity_relation(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(f297,plain,
spl12_23,
inference(avatar_split_clause,[],[f126,f295]) ).
fof(f126,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] : relation(identity_relation(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(f293,plain,
spl12_22,
inference(avatar_split_clause,[],[f125,f291]) ).
fof(f291,plain,
( spl12_22
<=> ! [X0] : ~ empty(powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_22])]) ).
fof(f125,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f289,plain,
spl12_21,
inference(avatar_split_clause,[],[f184,f286]) ).
fof(f286,plain,
( spl12_21
<=> function(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_21])]) ).
fof(f184,plain,
function(sK11),
inference(cnf_transformation,[],[f115]) ).
fof(f115,plain,
( function(sK11)
& empty(sK11)
& relation(sK11) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f25,f114]) ).
fof(f114,plain,
( ? [X0] :
( function(X0)
& empty(X0)
& relation(X0) )
=> ( function(sK11)
& empty(sK11)
& relation(sK11) ) ),
introduced(choice_axiom,[]) ).
fof(f25,axiom,
? [X0] :
( function(X0)
& empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(f284,plain,
spl12_20,
inference(avatar_split_clause,[],[f183,f281]) ).
fof(f183,plain,
empty(sK11),
inference(cnf_transformation,[],[f115]) ).
fof(f279,plain,
spl12_19,
inference(avatar_split_clause,[],[f182,f276]) ).
fof(f276,plain,
( spl12_19
<=> relation(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_19])]) ).
fof(f182,plain,
relation(sK11),
inference(cnf_transformation,[],[f115]) ).
fof(f274,plain,
spl12_18,
inference(avatar_split_clause,[],[f181,f271]) ).
fof(f181,plain,
one_to_one(sK10),
inference(cnf_transformation,[],[f113]) ).
fof(f113,plain,
( one_to_one(sK10)
& function(sK10)
& relation(sK10) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f29,f112]) ).
fof(f112,plain,
( ? [X0] :
( one_to_one(X0)
& function(X0)
& relation(X0) )
=> ( one_to_one(sK10)
& function(sK10)
& relation(sK10) ) ),
introduced(choice_axiom,[]) ).
fof(f29,axiom,
? [X0] :
( one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
fof(f269,plain,
spl12_17,
inference(avatar_split_clause,[],[f180,f266]) ).
fof(f180,plain,
function(sK10),
inference(cnf_transformation,[],[f113]) ).
fof(f264,plain,
spl12_16,
inference(avatar_split_clause,[],[f179,f261]) ).
fof(f179,plain,
relation(sK10),
inference(cnf_transformation,[],[f113]) ).
fof(f259,plain,
spl12_15,
inference(avatar_split_clause,[],[f178,f256]) ).
fof(f178,plain,
function(sK9),
inference(cnf_transformation,[],[f111]) ).
fof(f111,plain,
( function(sK9)
& relation(sK9) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f21,f110]) ).
fof(f110,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK9)
& relation(sK9) ) ),
introduced(choice_axiom,[]) ).
fof(f21,axiom,
? [X0] :
( function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
fof(f254,plain,
spl12_14,
inference(avatar_split_clause,[],[f177,f251]) ).
fof(f177,plain,
relation(sK9),
inference(cnf_transformation,[],[f111]) ).
fof(f249,plain,
spl12_13,
inference(avatar_split_clause,[],[f176,f246]) ).
fof(f176,plain,
relation(sK8),
inference(cnf_transformation,[],[f109]) ).
fof(f109,plain,
relation(sK8),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f49,f108]) ).
fof(f108,plain,
( ? [X0] : relation(X0)
=> relation(sK8) ),
introduced(choice_axiom,[]) ).
fof(f49,plain,
? [X0] : relation(X0),
inference(pure_predicate_removal,[],[f30]) ).
fof(f30,axiom,
? [X0] :
( relation_empty_yielding(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
fof(f244,plain,
spl12_12,
inference(avatar_split_clause,[],[f175,f241]) ).
fof(f241,plain,
( spl12_12
<=> relation(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_12])]) ).
fof(f175,plain,
relation(sK7),
inference(cnf_transformation,[],[f107]) ).
fof(f107,plain,
( relation(sK7)
& empty(sK7) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f22,f106]) ).
fof(f106,plain,
( ? [X0] :
( relation(X0)
& empty(X0) )
=> ( relation(sK7)
& empty(sK7) ) ),
introduced(choice_axiom,[]) ).
fof(f22,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f239,plain,
spl12_11,
inference(avatar_split_clause,[],[f174,f236]) ).
fof(f174,plain,
empty(sK7),
inference(cnf_transformation,[],[f107]) ).
fof(f234,plain,
spl12_10,
inference(avatar_split_clause,[],[f173,f231]) ).
fof(f173,plain,
relation(sK6),
inference(cnf_transformation,[],[f105]) ).
fof(f105,plain,
( relation(sK6)
& ~ empty(sK6) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f26,f104]) ).
fof(f104,plain,
( ? [X0] :
( relation(X0)
& ~ empty(X0) )
=> ( relation(sK6)
& ~ empty(sK6) ) ),
introduced(choice_axiom,[]) ).
fof(f26,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f229,plain,
~ spl12_9,
inference(avatar_split_clause,[],[f172,f226]) ).
fof(f226,plain,
( spl12_9
<=> empty(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_9])]) ).
fof(f172,plain,
~ empty(sK6),
inference(cnf_transformation,[],[f105]) ).
fof(f224,plain,
spl12_8,
inference(avatar_split_clause,[],[f171,f221]) ).
fof(f171,plain,
empty(sK5),
inference(cnf_transformation,[],[f103]) ).
fof(f103,plain,
empty(sK5),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f24,f102]) ).
fof(f102,plain,
( ? [X0] : empty(X0)
=> empty(sK5) ),
introduced(choice_axiom,[]) ).
fof(f24,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f219,plain,
~ spl12_7,
inference(avatar_split_clause,[],[f170,f216]) ).
fof(f216,plain,
( spl12_7
<=> empty(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_7])]) ).
fof(f170,plain,
~ empty(sK4),
inference(cnf_transformation,[],[f101]) ).
fof(f101,plain,
~ empty(sK4),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f28,f100]) ).
fof(f100,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK4) ),
introduced(choice_axiom,[]) ).
fof(f28,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f214,plain,
spl12_6,
inference(avatar_split_clause,[],[f122,f211]) ).
fof(f122,plain,
relation(empty_set),
inference(cnf_transformation,[],[f15]) ).
fof(f15,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f209,plain,
spl12_5,
inference(avatar_split_clause,[],[f120,f206]) ).
fof(f120,plain,
empty(empty_set),
inference(cnf_transformation,[],[f13]) ).
fof(f13,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f204,plain,
~ spl12_4,
inference(avatar_split_clause,[],[f119,f201]) ).
fof(f119,plain,
sK0 != function_inverse(function_inverse(sK0)),
inference(cnf_transformation,[],[f93]) ).
fof(f93,plain,
( sK0 != function_inverse(function_inverse(sK0))
& one_to_one(sK0)
& function(sK0)
& relation(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f51,f92]) ).
fof(f92,plain,
( ? [X0] :
( function_inverse(function_inverse(X0)) != X0
& one_to_one(X0)
& function(X0)
& relation(X0) )
=> ( sK0 != function_inverse(function_inverse(sK0))
& one_to_one(sK0)
& function(sK0)
& relation(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f51,plain,
? [X0] :
( function_inverse(function_inverse(X0)) != X0
& one_to_one(X0)
& function(X0)
& relation(X0) ),
inference(flattening,[],[f50]) ).
fof(f50,plain,
? [X0] :
( function_inverse(function_inverse(X0)) != X0
& one_to_one(X0)
& function(X0)
& relation(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,negated_conjecture,
~ ! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> function_inverse(function_inverse(X0)) = X0 ) ),
inference(negated_conjecture,[],[f41]) ).
fof(f41,conjecture,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> function_inverse(function_inverse(X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_funct_1) ).
fof(f199,plain,
spl12_3,
inference(avatar_split_clause,[],[f118,f196]) ).
fof(f118,plain,
one_to_one(sK0),
inference(cnf_transformation,[],[f93]) ).
fof(f194,plain,
spl12_2,
inference(avatar_split_clause,[],[f117,f191]) ).
fof(f117,plain,
function(sK0),
inference(cnf_transformation,[],[f93]) ).
fof(f189,plain,
spl12_1,
inference(avatar_split_clause,[],[f116,f186]) ).
fof(f116,plain,
relation(sK0),
inference(cnf_transformation,[],[f93]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU032+1 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Apr 29 20:08:58 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % (16296)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.36 % (16299)WARNING: value z3 for option sas not known
% 0.13/0.36 % (16301)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)
% 0.13/0.36 % (16303)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)
% 0.13/0.36 % (16299)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)
% 0.13/0.36 % (16300)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.36 % (16302)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)
% 0.13/0.37 TRYING [1]
% 0.13/0.37 TRYING [2]
% 0.13/0.37 TRYING [3]
% 0.13/0.37 TRYING [4]
% 0.13/0.37 % (16298)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.38 TRYING [5]
% 0.13/0.38 % (16297)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.39 TRYING [6]
% 0.13/0.39 % (16301)First to succeed.
% 0.13/0.40 TRYING [1]
% 0.13/0.40 TRYING [2]
% 0.13/0.40 % (16301)Refutation found. Thanks to Tanya!
% 0.13/0.40 % SZS status Theorem for theBenchmark
% 0.13/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.41 % (16301)------------------------------
% 0.19/0.41 % (16301)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.19/0.41 % (16301)Termination reason: Refutation
% 0.19/0.41
% 0.19/0.41 % (16301)Memory used [KB]: 1518
% 0.19/0.41 % (16301)Time elapsed: 0.042 s
% 0.19/0.41 % (16301)Instructions burned: 68 (million)
% 0.19/0.41 % (16301)------------------------------
% 0.19/0.41 % (16301)------------------------------
% 0.19/0.41 % (16296)Success in time 0.058 s
%------------------------------------------------------------------------------