TSTP Solution File: SEU030+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU030+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 : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 09:26:46 EDT 2024
% Result : Theorem 0.13s 0.41s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 197
% Syntax : Number of formulae : 623 ( 111 unt; 0 def)
% Number of atoms : 1978 ( 203 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 2415 (1060 ~;1021 |; 145 &)
% ( 143 <=>; 46 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 152 ( 150 usr; 143 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 11 con; 0-2 aty)
% Number of variables : 495 ( 463 !; 32 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1433,plain,
$false,
inference(avatar_sat_refutation,[],[f191,f196,f201,f206,f211,f216,f221,f226,f231,f236,f241,f246,f251,f256,f261,f266,f271,f276,f281,f286,f291,f296,f301,f306,f311,f315,f319,f323,f327,f331,f335,f339,f343,f357,f362,f366,f370,f374,f378,f382,f386,f390,f406,f416,f420,f424,f433,f437,f441,f445,f449,f453,f457,f474,f478,f482,f486,f490,f494,f498,f549,f559,f564,f574,f578,f582,f591,f595,f603,f610,f616,f622,f634,f639,f648,f661,f672,f677,f683,f688,f693,f705,f710,f716,f720,f724,f732,f738,f739,f740,f741,f742,f768,f850,f854,f867,f876,f881,f889,f898,f932,f936,f944,f950,f955,f959,f963,f967,f971,f1020,f1024,f1028,f1032,f1036,f1079,f1086,f1090,f1095,f1104,f1119,f1126,f1130,f1134,f1190,f1205,f1209,f1222,f1228,f1232,f1236,f1271,f1275,f1279,f1335,f1339,f1343,f1347,f1365,f1409,f1414,f1419,f1424,f1432]) ).
fof(f1432,plain,
( ~ spl13_1
| ~ spl13_2
| ~ spl13_52
| spl13_139 ),
inference(avatar_split_clause,[],[f1410,f1406,f447,f193,f188]) ).
fof(f188,plain,
( spl13_1
<=> relation(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_1])]) ).
fof(f193,plain,
( spl13_2
<=> function(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_2])]) ).
fof(f447,plain,
( spl13_52
<=> ! [X0] :
( function(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_52])]) ).
fof(f1406,plain,
( spl13_139
<=> function(function_inverse(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_139])]) ).
fof(f1410,plain,
( ~ function(sK0)
| ~ relation(sK0)
| ~ spl13_52
| spl13_139 ),
inference(resolution,[],[f1408,f448]) ).
fof(f448,plain,
( ! [X0] :
( function(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl13_52 ),
inference(avatar_component_clause,[],[f447]) ).
fof(f1408,plain,
( ~ function(function_inverse(sK0))
| spl13_139 ),
inference(avatar_component_clause,[],[f1406]) ).
fof(f1424,plain,
( spl13_142
| ~ spl13_9
| ~ spl13_81
| ~ spl13_92 ),
inference(avatar_split_clause,[],[f921,f852,f680,f228,f1421]) ).
fof(f1421,plain,
( spl13_142
<=> sK6 = relation_dom(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_142])]) ).
fof(f228,plain,
( spl13_9
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_9])]) ).
fof(f680,plain,
( spl13_81
<=> empty_set = sK6 ),
introduced(avatar_definition,[new_symbols(naming,[spl13_81])]) ).
fof(f852,plain,
( spl13_92
<=> ! [X0] :
( relation_dom(X0) = sK6
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_92])]) ).
fof(f921,plain,
( sK6 = relation_dom(sK6)
| ~ spl13_9
| ~ spl13_81
| ~ spl13_92 ),
inference(forward_demodulation,[],[f914,f682]) ).
fof(f682,plain,
( empty_set = sK6
| ~ spl13_81 ),
inference(avatar_component_clause,[],[f680]) ).
fof(f914,plain,
( sK6 = relation_dom(empty_set)
| ~ spl13_9
| ~ spl13_92 ),
inference(resolution,[],[f853,f230]) ).
fof(f230,plain,
( empty(empty_set)
| ~ spl13_9 ),
inference(avatar_component_clause,[],[f228]) ).
fof(f853,plain,
( ! [X0] :
( ~ empty(X0)
| relation_dom(X0) = sK6 )
| ~ spl13_92 ),
inference(avatar_component_clause,[],[f852]) ).
fof(f1419,plain,
( spl13_141
| ~ spl13_9
| ~ spl13_81
| ~ spl13_91 ),
inference(avatar_split_clause,[],[f908,f848,f680,f228,f1416]) ).
fof(f1416,plain,
( spl13_141
<=> sK6 = relation_rng(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_141])]) ).
fof(f848,plain,
( spl13_91
<=> ! [X0] :
( relation_rng(X0) = sK6
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_91])]) ).
fof(f908,plain,
( sK6 = relation_rng(sK6)
| ~ spl13_9
| ~ spl13_81
| ~ spl13_91 ),
inference(forward_demodulation,[],[f901,f682]) ).
fof(f901,plain,
( sK6 = relation_rng(empty_set)
| ~ spl13_9
| ~ spl13_91 ),
inference(resolution,[],[f849,f230]) ).
fof(f849,plain,
( ! [X0] :
( ~ empty(X0)
| relation_rng(X0) = sK6 )
| ~ spl13_91 ),
inference(avatar_component_clause,[],[f848]) ).
fof(f1414,plain,
( spl13_140
| ~ spl13_41
| ~ spl13_85 ),
inference(avatar_split_clause,[],[f711,f708,f384,f1412]) ).
fof(f1412,plain,
( spl13_140
<=> ! [X0] : element(sK6,powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_140])]) ).
fof(f384,plain,
( spl13_41
<=> ! [X0] : element(sK4(X0),powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_41])]) ).
fof(f708,plain,
( spl13_85
<=> ! [X0] : sK4(X0) = sK6 ),
introduced(avatar_definition,[new_symbols(naming,[spl13_85])]) ).
fof(f711,plain,
( ! [X0] : element(sK6,powerset(X0))
| ~ spl13_41
| ~ spl13_85 ),
inference(superposition,[],[f385,f709]) ).
fof(f709,plain,
( ! [X0] : sK4(X0) = sK6
| ~ spl13_85 ),
inference(avatar_component_clause,[],[f708]) ).
fof(f385,plain,
( ! [X0] : element(sK4(X0),powerset(X0))
| ~ spl13_41 ),
inference(avatar_component_clause,[],[f384]) ).
fof(f1409,plain,
( spl13_6
| ~ spl13_139
| ~ spl13_100
| ~ spl13_76
| ~ spl13_78
| ~ spl13_104 ),
inference(avatar_split_clause,[],[f1081,f942,f658,f636,f891,f1406,f213]) ).
fof(f213,plain,
( spl13_6
<=> function_inverse(sK0) = sK1 ),
introduced(avatar_definition,[new_symbols(naming,[spl13_6])]) ).
fof(f891,plain,
( spl13_100
<=> relation(function_inverse(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_100])]) ).
fof(f636,plain,
( spl13_76
<=> relation_dom(sK0) = relation_rng(function_inverse(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_76])]) ).
fof(f658,plain,
( spl13_78
<=> relation_composition(function_inverse(sK0),sK0) = identity_relation(relation_rng(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_78])]) ).
fof(f942,plain,
( spl13_104
<=> ! [X0] :
( identity_relation(relation_rng(sK0)) != relation_composition(X0,sK0)
| ~ relation(X0)
| ~ function(X0)
| sK1 = X0
| identity_relation(relation_rng(X0)) != identity_relation(relation_dom(sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_104])]) ).
fof(f1081,plain,
( ~ relation(function_inverse(sK0))
| ~ function(function_inverse(sK0))
| function_inverse(sK0) = sK1
| ~ spl13_76
| ~ spl13_78
| ~ spl13_104 ),
inference(trivial_inequality_removal,[],[f1080]) ).
fof(f1080,plain,
( identity_relation(relation_dom(sK0)) != identity_relation(relation_dom(sK0))
| ~ relation(function_inverse(sK0))
| ~ function(function_inverse(sK0))
| function_inverse(sK0) = sK1
| ~ spl13_76
| ~ spl13_78
| ~ spl13_104 ),
inference(forward_demodulation,[],[f946,f638]) ).
fof(f638,plain,
( relation_dom(sK0) = relation_rng(function_inverse(sK0))
| ~ spl13_76 ),
inference(avatar_component_clause,[],[f636]) ).
fof(f946,plain,
( ~ relation(function_inverse(sK0))
| ~ function(function_inverse(sK0))
| function_inverse(sK0) = sK1
| identity_relation(relation_dom(sK0)) != identity_relation(relation_rng(function_inverse(sK0)))
| ~ spl13_78
| ~ spl13_104 ),
inference(trivial_inequality_removal,[],[f945]) ).
fof(f945,plain,
( identity_relation(relation_rng(sK0)) != identity_relation(relation_rng(sK0))
| ~ relation(function_inverse(sK0))
| ~ function(function_inverse(sK0))
| function_inverse(sK0) = sK1
| identity_relation(relation_dom(sK0)) != identity_relation(relation_rng(function_inverse(sK0)))
| ~ spl13_78
| ~ spl13_104 ),
inference(superposition,[],[f943,f660]) ).
fof(f660,plain,
( relation_composition(function_inverse(sK0),sK0) = identity_relation(relation_rng(sK0))
| ~ spl13_78 ),
inference(avatar_component_clause,[],[f658]) ).
fof(f943,plain,
( ! [X0] :
( identity_relation(relation_rng(sK0)) != relation_composition(X0,sK0)
| ~ relation(X0)
| ~ function(X0)
| sK1 = X0
| identity_relation(relation_rng(X0)) != identity_relation(relation_dom(sK0)) )
| ~ spl13_104 ),
inference(avatar_component_clause,[],[f942]) ).
fof(f1365,plain,
( spl13_138
| ~ spl13_9
| ~ spl13_81
| ~ spl13_126 ),
inference(avatar_split_clause,[],[f1289,f1207,f680,f228,f1362]) ).
fof(f1362,plain,
( spl13_138
<=> sK6 = relation_composition(sK0,sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_138])]) ).
fof(f1207,plain,
( spl13_126
<=> ! [X0] :
( sK6 = relation_composition(sK0,X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_126])]) ).
fof(f1289,plain,
( sK6 = relation_composition(sK0,sK6)
| ~ spl13_9
| ~ spl13_81
| ~ spl13_126 ),
inference(forward_demodulation,[],[f1282,f682]) ).
fof(f1282,plain,
( sK6 = relation_composition(sK0,empty_set)
| ~ spl13_9
| ~ spl13_126 ),
inference(resolution,[],[f1208,f230]) ).
fof(f1208,plain,
( ! [X0] :
( ~ empty(X0)
| sK6 = relation_composition(sK0,X0) )
| ~ spl13_126 ),
inference(avatar_component_clause,[],[f1207]) ).
fof(f1347,plain,
( spl13_137
| ~ spl13_3
| ~ spl13_123 ),
inference(avatar_split_clause,[],[f1175,f1132,f198,f1345]) ).
fof(f1345,plain,
( spl13_137
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_composition(X0,sK1) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_137])]) ).
fof(f198,plain,
( spl13_3
<=> relation(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_3])]) ).
fof(f1132,plain,
( spl13_123
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| relation_composition(X1,X0) = X2
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_123])]) ).
fof(f1175,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_composition(X0,sK1) = X1
| ~ empty(X1) )
| ~ spl13_3
| ~ spl13_123 ),
inference(resolution,[],[f1133,f200]) ).
fof(f200,plain,
( relation(sK1)
| ~ spl13_3 ),
inference(avatar_component_clause,[],[f198]) ).
fof(f1133,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| relation_composition(X1,X0) = X2
| ~ empty(X2) )
| ~ spl13_123 ),
inference(avatar_component_clause,[],[f1132]) ).
fof(f1343,plain,
( spl13_136
| ~ spl13_1
| ~ spl13_123 ),
inference(avatar_split_clause,[],[f1174,f1132,f188,f1341]) ).
fof(f1341,plain,
( spl13_136
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_composition(X0,sK0) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_136])]) ).
fof(f1174,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_composition(X0,sK0) = X1
| ~ empty(X1) )
| ~ spl13_1
| ~ spl13_123 ),
inference(resolution,[],[f1133,f190]) ).
fof(f190,plain,
( relation(sK0)
| ~ spl13_1 ),
inference(avatar_component_clause,[],[f188]) ).
fof(f1339,plain,
( spl13_135
| ~ spl13_3
| ~ spl13_122 ),
inference(avatar_split_clause,[],[f1154,f1128,f198,f1337]) ).
fof(f1337,plain,
( spl13_135
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_composition(sK1,X0) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_135])]) ).
fof(f1128,plain,
( spl13_122
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| relation_composition(X0,X1) = X2
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_122])]) ).
fof(f1154,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_composition(sK1,X0) = X1
| ~ empty(X1) )
| ~ spl13_3
| ~ spl13_122 ),
inference(resolution,[],[f1129,f200]) ).
fof(f1129,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| relation_composition(X0,X1) = X2
| ~ empty(X2) )
| ~ spl13_122 ),
inference(avatar_component_clause,[],[f1128]) ).
fof(f1335,plain,
( spl13_134
| ~ spl13_1
| ~ spl13_122 ),
inference(avatar_split_clause,[],[f1153,f1128,f188,f1333]) ).
fof(f1333,plain,
( spl13_134
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_composition(sK0,X0) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_134])]) ).
fof(f1153,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_composition(sK0,X0) = X1
| ~ empty(X1) )
| ~ spl13_1
| ~ spl13_122 ),
inference(resolution,[],[f1129,f190]) ).
fof(f1279,plain,
( spl13_133
| ~ spl13_3
| ~ spl13_113 ),
inference(avatar_split_clause,[],[f1067,f1026,f198,f1277]) ).
fof(f1277,plain,
( spl13_133
<=> ! [X0] :
( sK6 = relation_composition(X0,sK1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_133])]) ).
fof(f1026,plain,
( spl13_113
<=> ! [X0,X1] :
( relation_composition(X1,X0) = sK6
| ~ relation(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_113])]) ).
fof(f1067,plain,
( ! [X0] :
( sK6 = relation_composition(X0,sK1)
| ~ empty(X0) )
| ~ spl13_3
| ~ spl13_113 ),
inference(resolution,[],[f1027,f200]) ).
fof(f1027,plain,
( ! [X0,X1] :
( ~ relation(X0)
| relation_composition(X1,X0) = sK6
| ~ empty(X1) )
| ~ spl13_113 ),
inference(avatar_component_clause,[],[f1026]) ).
fof(f1275,plain,
( spl13_132
| ~ spl13_1
| ~ spl13_113 ),
inference(avatar_split_clause,[],[f1066,f1026,f188,f1273]) ).
fof(f1273,plain,
( spl13_132
<=> ! [X0] :
( sK6 = relation_composition(X0,sK0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_132])]) ).
fof(f1066,plain,
( ! [X0] :
( sK6 = relation_composition(X0,sK0)
| ~ empty(X0) )
| ~ spl13_1
| ~ spl13_113 ),
inference(resolution,[],[f1027,f190]) ).
fof(f1271,plain,
( spl13_131
| ~ spl13_3
| ~ spl13_112 ),
inference(avatar_split_clause,[],[f1047,f1022,f198,f1269]) ).
fof(f1269,plain,
( spl13_131
<=> ! [X0] :
( sK6 = relation_composition(sK1,X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_131])]) ).
fof(f1022,plain,
( spl13_112
<=> ! [X0,X1] :
( relation_composition(X0,X1) = sK6
| ~ relation(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_112])]) ).
fof(f1047,plain,
( ! [X0] :
( sK6 = relation_composition(sK1,X0)
| ~ empty(X0) )
| ~ spl13_3
| ~ spl13_112 ),
inference(resolution,[],[f1023,f200]) ).
fof(f1023,plain,
( ! [X0,X1] :
( ~ relation(X0)
| relation_composition(X0,X1) = sK6
| ~ empty(X1) )
| ~ spl13_112 ),
inference(avatar_component_clause,[],[f1022]) ).
fof(f1236,plain,
( spl13_130
| ~ spl13_55
| ~ spl13_61 ),
inference(avatar_split_clause,[],[f544,f496,f472,f1234]) ).
fof(f1234,plain,
( spl13_130
<=> ! [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,[spl13_130])]) ).
fof(f472,plain,
( spl13_55
<=> ! [X0] :
( one_to_one(X0)
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_55])]) ).
fof(f496,plain,
( spl13_61
<=> ! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_61])]) ).
fof(f544,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ function(relation_composition(X1,X0))
| ~ empty(relation_composition(X1,X0))
| one_to_one(relation_composition(X1,X0)) )
| ~ spl13_55
| ~ spl13_61 ),
inference(resolution,[],[f497,f473]) ).
fof(f473,plain,
( ! [X0] :
( ~ relation(X0)
| ~ function(X0)
| ~ empty(X0)
| one_to_one(X0) )
| ~ spl13_55 ),
inference(avatar_component_clause,[],[f472]) ).
fof(f497,plain,
( ! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl13_61 ),
inference(avatar_component_clause,[],[f496]) ).
fof(f1232,plain,
( spl13_129
| ~ spl13_55
| ~ spl13_60 ),
inference(avatar_split_clause,[],[f542,f492,f472,f1230]) ).
fof(f1230,plain,
( spl13_129
<=> ! [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,[spl13_129])]) ).
fof(f492,plain,
( spl13_60
<=> ! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_60])]) ).
fof(f542,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| ~ function(relation_composition(X1,X0))
| ~ empty(relation_composition(X1,X0))
| one_to_one(relation_composition(X1,X0)) )
| ~ spl13_55
| ~ spl13_60 ),
inference(resolution,[],[f493,f473]) ).
fof(f493,plain,
( ! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) )
| ~ spl13_60 ),
inference(avatar_component_clause,[],[f492]) ).
fof(f1228,plain,
( spl13_128
| ~ spl13_55
| ~ spl13_58 ),
inference(avatar_split_clause,[],[f534,f484,f472,f1226]) ).
fof(f1226,plain,
( spl13_128
<=> ! [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,[spl13_128])]) ).
fof(f484,plain,
( spl13_58
<=> ! [X0,X1] :
( relation(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_58])]) ).
fof(f534,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| ~ function(relation_composition(X0,X1))
| ~ empty(relation_composition(X0,X1))
| one_to_one(relation_composition(X0,X1)) )
| ~ spl13_55
| ~ spl13_58 ),
inference(resolution,[],[f485,f473]) ).
fof(f485,plain,
( ! [X0,X1] :
( relation(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) )
| ~ spl13_58 ),
inference(avatar_component_clause,[],[f484]) ).
fof(f1222,plain,
( spl13_127
| ~ spl13_51
| ~ spl13_55 ),
inference(avatar_split_clause,[],[f500,f472,f443,f1220]) ).
fof(f1220,plain,
( spl13_127
<=> ! [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,[spl13_127])]) ).
fof(f443,plain,
( spl13_51
<=> ! [X0] :
( relation(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_51])]) ).
fof(f500,plain,
( ! [X0] :
( ~ function(function_inverse(X0))
| ~ empty(function_inverse(X0))
| one_to_one(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl13_51
| ~ spl13_55 ),
inference(resolution,[],[f473,f444]) ).
fof(f444,plain,
( ! [X0] :
( relation(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl13_51 ),
inference(avatar_component_clause,[],[f443]) ).
fof(f1209,plain,
( spl13_126
| ~ spl13_1
| ~ spl13_112 ),
inference(avatar_split_clause,[],[f1046,f1022,f188,f1207]) ).
fof(f1046,plain,
( ! [X0] :
( sK6 = relation_composition(sK0,X0)
| ~ empty(X0) )
| ~ spl13_1
| ~ spl13_112 ),
inference(resolution,[],[f1023,f190]) ).
fof(f1205,plain,
( ~ spl13_20
| ~ spl13_21
| spl13_125
| ~ spl13_22
| ~ spl13_69 ),
inference(avatar_split_clause,[],[f599,f593,f293,f1202,f288,f283]) ).
fof(f283,plain,
( spl13_20
<=> relation(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_20])]) ).
fof(f288,plain,
( spl13_21
<=> function(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_21])]) ).
fof(f1202,plain,
( spl13_125
<=> relation_composition(function_inverse(sK11),sK11) = identity_relation(relation_rng(sK11)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_125])]) ).
fof(f293,plain,
( spl13_22
<=> one_to_one(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_22])]) ).
fof(f593,plain,
( spl13_69
<=> ! [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,[spl13_69])]) ).
fof(f599,plain,
( relation_composition(function_inverse(sK11),sK11) = identity_relation(relation_rng(sK11))
| ~ function(sK11)
| ~ relation(sK11)
| ~ spl13_22
| ~ spl13_69 ),
inference(resolution,[],[f594,f295]) ).
fof(f295,plain,
( one_to_one(sK11)
| ~ spl13_22 ),
inference(avatar_component_clause,[],[f293]) ).
fof(f594,plain,
( ! [X0] :
( ~ one_to_one(X0)
| relation_composition(function_inverse(X0),X0) = identity_relation(relation_rng(X0))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl13_69 ),
inference(avatar_component_clause,[],[f593]) ).
fof(f1190,plain,
( ~ spl13_20
| ~ spl13_21
| spl13_124
| ~ spl13_22
| ~ spl13_68 ),
inference(avatar_split_clause,[],[f597,f589,f293,f1187,f288,f283]) ).
fof(f1187,plain,
( spl13_124
<=> relation_composition(sK11,function_inverse(sK11)) = identity_relation(relation_dom(sK11)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_124])]) ).
fof(f589,plain,
( spl13_68
<=> ! [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,[spl13_68])]) ).
fof(f597,plain,
( relation_composition(sK11,function_inverse(sK11)) = identity_relation(relation_dom(sK11))
| ~ function(sK11)
| ~ relation(sK11)
| ~ spl13_22
| ~ spl13_68 ),
inference(resolution,[],[f590,f295]) ).
fof(f590,plain,
( ! [X0] :
( ~ one_to_one(X0)
| relation_composition(X0,function_inverse(X0)) = identity_relation(relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl13_68 ),
inference(avatar_component_clause,[],[f589]) ).
fof(f1134,plain,
( spl13_123
| ~ spl13_54
| ~ spl13_59 ),
inference(avatar_split_clause,[],[f536,f488,f455,f1132]) ).
fof(f455,plain,
( spl13_54
<=> ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_54])]) ).
fof(f488,plain,
( spl13_59
<=> ! [X0,X1] :
( empty(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_59])]) ).
fof(f536,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| relation_composition(X1,X0) = X2
| ~ empty(X2) )
| ~ spl13_54
| ~ spl13_59 ),
inference(resolution,[],[f489,f456]) ).
fof(f456,plain,
( ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) )
| ~ spl13_54 ),
inference(avatar_component_clause,[],[f455]) ).
fof(f489,plain,
( ! [X0,X1] :
( empty(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) )
| ~ spl13_59 ),
inference(avatar_component_clause,[],[f488]) ).
fof(f1130,plain,
( spl13_122
| ~ spl13_54
| ~ spl13_57 ),
inference(avatar_split_clause,[],[f528,f480,f455,f1128]) ).
fof(f480,plain,
( spl13_57
<=> ! [X0,X1] :
( empty(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_57])]) ).
fof(f528,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| relation_composition(X0,X1) = X2
| ~ empty(X2) )
| ~ spl13_54
| ~ spl13_57 ),
inference(resolution,[],[f481,f456]) ).
fof(f481,plain,
( ! [X0,X1] :
( empty(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) )
| ~ spl13_57 ),
inference(avatar_component_clause,[],[f480]) ).
fof(f1126,plain,
( spl13_121
| ~ spl13_38
| ~ spl13_55 ),
inference(avatar_split_clause,[],[f504,f472,f372,f1124]) ).
fof(f1124,plain,
( spl13_121
<=> ! [X0] :
( ~ function(relation_rng(X0))
| ~ empty(relation_rng(X0))
| one_to_one(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_121])]) ).
fof(f372,plain,
( spl13_38
<=> ! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_38])]) ).
fof(f504,plain,
( ! [X0] :
( ~ function(relation_rng(X0))
| ~ empty(relation_rng(X0))
| one_to_one(relation_rng(X0))
| ~ empty(X0) )
| ~ spl13_38
| ~ spl13_55 ),
inference(resolution,[],[f473,f373]) ).
fof(f373,plain,
( ! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) )
| ~ spl13_38 ),
inference(avatar_component_clause,[],[f372]) ).
fof(f1119,plain,
( spl13_120
| ~ spl13_40
| ~ spl13_55 ),
inference(avatar_split_clause,[],[f503,f472,f380,f1117]) ).
fof(f1117,plain,
( spl13_120
<=> ! [X0] :
( ~ function(relation_dom(X0))
| ~ empty(relation_dom(X0))
| one_to_one(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_120])]) ).
fof(f380,plain,
( spl13_40
<=> ! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_40])]) ).
fof(f503,plain,
( ! [X0] :
( ~ function(relation_dom(X0))
| ~ empty(relation_dom(X0))
| one_to_one(relation_dom(X0))
| ~ empty(X0) )
| ~ spl13_40
| ~ spl13_55 ),
inference(resolution,[],[f473,f381]) ).
fof(f381,plain,
( ! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) )
| ~ spl13_40 ),
inference(avatar_component_clause,[],[f380]) ).
fof(f1104,plain,
( ~ spl13_20
| ~ spl13_21
| spl13_119
| ~ spl13_22
| ~ spl13_66 ),
inference(avatar_split_clause,[],[f586,f576,f293,f1101,f288,f283]) ).
fof(f1101,plain,
( spl13_119
<=> relation_dom(sK11) = relation_rng(function_inverse(sK11)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_119])]) ).
fof(f576,plain,
( spl13_66
<=> ! [X0] :
( relation_dom(X0) = relation_rng(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_66])]) ).
fof(f586,plain,
( relation_dom(sK11) = relation_rng(function_inverse(sK11))
| ~ function(sK11)
| ~ relation(sK11)
| ~ spl13_22
| ~ spl13_66 ),
inference(resolution,[],[f577,f295]) ).
fof(f577,plain,
( ! [X0] :
( ~ one_to_one(X0)
| relation_dom(X0) = relation_rng(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl13_66 ),
inference(avatar_component_clause,[],[f576]) ).
fof(f1095,plain,
( ~ spl13_20
| ~ spl13_21
| spl13_118
| ~ spl13_22
| ~ spl13_65 ),
inference(avatar_split_clause,[],[f584,f572,f293,f1092,f288,f283]) ).
fof(f1092,plain,
( spl13_118
<=> relation_rng(sK11) = relation_dom(function_inverse(sK11)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_118])]) ).
fof(f572,plain,
( spl13_65
<=> ! [X0] :
( relation_rng(X0) = relation_dom(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_65])]) ).
fof(f584,plain,
( relation_rng(sK11) = relation_dom(function_inverse(sK11))
| ~ function(sK11)
| ~ relation(sK11)
| ~ spl13_22
| ~ spl13_65 ),
inference(resolution,[],[f573,f295]) ).
fof(f573,plain,
( ! [X0] :
( ~ one_to_one(X0)
| relation_rng(X0) = relation_dom(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) )
| ~ spl13_65 ),
inference(avatar_component_clause,[],[f572]) ).
fof(f1090,plain,
( spl13_117
| ~ spl13_46
| ~ spl13_56 ),
inference(avatar_split_clause,[],[f523,f476,f422,f1088]) ).
fof(f1088,plain,
( spl13_117
<=> ! [X0] :
( empty(powerset(X0))
| in(sK2(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_117])]) ).
fof(f422,plain,
( spl13_46
<=> ! [X0] :
( element(sK2(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_46])]) ).
fof(f476,plain,
( spl13_56
<=> ! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_56])]) ).
fof(f523,plain,
( ! [X0] :
( empty(powerset(X0))
| in(sK2(X0),powerset(X0))
| empty(X0) )
| ~ spl13_46
| ~ spl13_56 ),
inference(resolution,[],[f477,f423]) ).
fof(f423,plain,
( ! [X0] :
( element(sK2(X0),powerset(X0))
| empty(X0) )
| ~ spl13_46 ),
inference(avatar_component_clause,[],[f422]) ).
fof(f477,plain,
( ! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) )
| ~ spl13_56 ),
inference(avatar_component_clause,[],[f476]) ).
fof(f1086,plain,
( spl13_116
| ~ spl13_53
| ~ spl13_56 ),
inference(avatar_split_clause,[],[f522,f476,f451,f1084]) ).
fof(f1084,plain,
( spl13_116
<=> ! [X0,X1] :
( empty(powerset(X0))
| in(X1,powerset(X0))
| ~ subset(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_116])]) ).
fof(f451,plain,
( spl13_53
<=> ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_53])]) ).
fof(f522,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| in(X1,powerset(X0))
| ~ subset(X1,X0) )
| ~ spl13_53
| ~ spl13_56 ),
inference(resolution,[],[f477,f452]) ).
fof(f452,plain,
( ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) )
| ~ spl13_53 ),
inference(avatar_component_clause,[],[f451]) ).
fof(f1079,plain,
( ~ spl13_1
| ~ spl13_2
| ~ spl13_51
| spl13_100 ),
inference(avatar_split_clause,[],[f951,f891,f443,f193,f188]) ).
fof(f951,plain,
( ~ function(sK0)
| ~ relation(sK0)
| ~ spl13_51
| spl13_100 ),
inference(resolution,[],[f893,f444]) ).
fof(f893,plain,
( ~ relation(function_inverse(sK0))
| spl13_100 ),
inference(avatar_component_clause,[],[f891]) ).
fof(f1036,plain,
( spl13_115
| ~ spl13_46
| ~ spl13_63 ),
inference(avatar_split_clause,[],[f566,f557,f422,f1034]) ).
fof(f1034,plain,
( spl13_115
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK2(X1))
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_115])]) ).
fof(f557,plain,
( spl13_63
<=> ! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_63])]) ).
fof(f566,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK2(X1))
| empty(X1) )
| ~ spl13_46
| ~ spl13_63 ),
inference(resolution,[],[f558,f423]) ).
fof(f558,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| element(X0,X2)
| ~ in(X0,X1) )
| ~ spl13_63 ),
inference(avatar_component_clause,[],[f557]) ).
fof(f1032,plain,
( spl13_114
| ~ spl13_53
| ~ spl13_63 ),
inference(avatar_split_clause,[],[f565,f557,f451,f1030]) ).
fof(f1030,plain,
( spl13_114
<=> ! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_114])]) ).
fof(f565,plain,
( ! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,X1) )
| ~ spl13_53
| ~ spl13_63 ),
inference(resolution,[],[f558,f452]) ).
fof(f1028,plain,
( spl13_113
| ~ spl13_12
| ~ spl13_36
| ~ spl13_59 ),
inference(avatar_split_clause,[],[f541,f488,f364,f243,f1026]) ).
fof(f243,plain,
( spl13_12
<=> empty(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_12])]) ).
fof(f364,plain,
( spl13_36
<=> ! [X0] :
( empty_set = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_36])]) ).
fof(f541,plain,
( ! [X0,X1] :
( relation_composition(X1,X0) = sK6
| ~ relation(X0)
| ~ empty(X1) )
| ~ spl13_12
| ~ spl13_36
| ~ spl13_59 ),
inference(forward_demodulation,[],[f537,f393]) ).
fof(f393,plain,
( empty_set = sK6
| ~ spl13_12
| ~ spl13_36 ),
inference(resolution,[],[f365,f245]) ).
fof(f245,plain,
( empty(sK6)
| ~ spl13_12 ),
inference(avatar_component_clause,[],[f243]) ).
fof(f365,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = X0 )
| ~ spl13_36 ),
inference(avatar_component_clause,[],[f364]) ).
fof(f537,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| relation_composition(X1,X0) = empty_set )
| ~ spl13_36
| ~ spl13_59 ),
inference(resolution,[],[f489,f365]) ).
fof(f1024,plain,
( spl13_112
| ~ spl13_12
| ~ spl13_36
| ~ spl13_57 ),
inference(avatar_split_clause,[],[f533,f480,f364,f243,f1022]) ).
fof(f533,plain,
( ! [X0,X1] :
( relation_composition(X0,X1) = sK6
| ~ relation(X0)
| ~ empty(X1) )
| ~ spl13_12
| ~ spl13_36
| ~ spl13_57 ),
inference(forward_demodulation,[],[f529,f393]) ).
fof(f529,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| relation_composition(X0,X1) = empty_set )
| ~ spl13_36
| ~ spl13_57 ),
inference(resolution,[],[f481,f365]) ).
fof(f1020,plain,
( spl13_111
| ~ spl13_27
| ~ spl13_55 ),
inference(avatar_split_clause,[],[f501,f472,f317,f1018]) ).
fof(f1018,plain,
( spl13_111
<=> ! [X0] :
( ~ function(identity_relation(X0))
| ~ empty(identity_relation(X0))
| one_to_one(identity_relation(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_111])]) ).
fof(f317,plain,
( spl13_27
<=> ! [X0] : relation(identity_relation(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_27])]) ).
fof(f501,plain,
( ! [X0] :
( ~ function(identity_relation(X0))
| ~ empty(identity_relation(X0))
| one_to_one(identity_relation(X0)) )
| ~ spl13_27
| ~ spl13_55 ),
inference(resolution,[],[f473,f318]) ).
fof(f318,plain,
( ! [X0] : relation(identity_relation(X0))
| ~ spl13_27 ),
inference(avatar_component_clause,[],[f317]) ).
fof(f971,plain,
( spl13_110
| ~ spl13_33
| ~ spl13_63 ),
inference(avatar_split_clause,[],[f567,f557,f341,f969]) ).
fof(f969,plain,
( spl13_110
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK3(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_110])]) ).
fof(f341,plain,
( spl13_33
<=> ! [X0] : element(sK3(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_33])]) ).
fof(f567,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK3(powerset(X1))) )
| ~ spl13_33
| ~ spl13_63 ),
inference(resolution,[],[f558,f342]) ).
fof(f342,plain,
( ! [X0] : element(sK3(X0),X0)
| ~ spl13_33 ),
inference(avatar_component_clause,[],[f341]) ).
fof(f967,plain,
( spl13_109
| ~ spl13_53
| ~ spl13_62 ),
inference(avatar_split_clause,[],[f550,f547,f451,f965]) ).
fof(f965,plain,
( spl13_109
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,X2)
| ~ subset(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_109])]) ).
fof(f547,plain,
( spl13_62
<=> ! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_62])]) ).
fof(f550,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,X2)
| ~ subset(X2,X0) )
| ~ spl13_53
| ~ spl13_62 ),
inference(resolution,[],[f548,f452]) ).
fof(f548,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X0,X1) )
| ~ spl13_62 ),
inference(avatar_component_clause,[],[f547]) ).
fof(f963,plain,
( spl13_108
| ~ spl13_31
| ~ spl13_59 ),
inference(avatar_split_clause,[],[f539,f488,f333,f961]) ).
fof(f961,plain,
( spl13_108
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| function(relation_composition(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_108])]) ).
fof(f333,plain,
( spl13_31
<=> ! [X0] :
( function(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_31])]) ).
fof(f539,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| function(relation_composition(X1,X0)) )
| ~ spl13_31
| ~ spl13_59 ),
inference(resolution,[],[f489,f334]) ).
fof(f334,plain,
( ! [X0] :
( ~ empty(X0)
| function(X0) )
| ~ spl13_31 ),
inference(avatar_component_clause,[],[f333]) ).
fof(f959,plain,
( spl13_107
| ~ spl13_31
| ~ spl13_57 ),
inference(avatar_split_clause,[],[f531,f480,f333,f957]) ).
fof(f957,plain,
( spl13_107
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| function(relation_composition(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_107])]) ).
fof(f531,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| function(relation_composition(X0,X1)) )
| ~ spl13_31
| ~ spl13_57 ),
inference(resolution,[],[f481,f334]) ).
fof(f955,plain,
( spl13_106
| ~ spl13_37
| ~ spl13_54 ),
inference(avatar_split_clause,[],[f463,f455,f368,f953]) ).
fof(f953,plain,
( spl13_106
<=> ! [X0,X1] :
( relation_rng(X1) = X0
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_106])]) ).
fof(f368,plain,
( spl13_37
<=> ! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_37])]) ).
fof(f463,plain,
( ! [X0,X1] :
( relation_rng(X1) = X0
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl13_37
| ~ spl13_54 ),
inference(resolution,[],[f456,f369]) ).
fof(f369,plain,
( ! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) )
| ~ spl13_37 ),
inference(avatar_component_clause,[],[f368]) ).
fof(f950,plain,
( spl13_105
| ~ spl13_39
| ~ spl13_54 ),
inference(avatar_split_clause,[],[f462,f455,f376,f948]) ).
fof(f948,plain,
( spl13_105
<=> ! [X0,X1] :
( relation_dom(X1) = X0
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_105])]) ).
fof(f376,plain,
( spl13_39
<=> ! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_39])]) ).
fof(f462,plain,
( ! [X0,X1] :
( relation_dom(X1) = X0
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl13_39
| ~ spl13_54 ),
inference(resolution,[],[f456,f377]) ).
fof(f377,plain,
( ! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) )
| ~ spl13_39 ),
inference(avatar_component_clause,[],[f376]) ).
fof(f944,plain,
( ~ spl13_1
| ~ spl13_2
| ~ spl13_3
| ~ spl13_4
| spl13_104
| ~ spl13_7
| ~ spl13_8
| ~ spl13_70 ),
inference(avatar_split_clause,[],[f605,f601,f223,f218,f942,f203,f198,f193,f188]) ).
fof(f203,plain,
( spl13_4
<=> function(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_4])]) ).
fof(f218,plain,
( spl13_7
<=> relation_rng(sK0) = relation_dom(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_7])]) ).
fof(f223,plain,
( spl13_8
<=> identity_relation(relation_dom(sK0)) = relation_composition(sK0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_8])]) ).
fof(f601,plain,
( spl13_70
<=> ! [X2,X1,X3] :
( X1 = X3
| relation_composition(X2,X3) != identity_relation(relation_rng(X1))
| relation_composition(X1,X2) != identity_relation(relation_dom(X3))
| ~ function(X3)
| ~ relation(X3)
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_70])]) ).
fof(f605,plain,
( ! [X0] :
( identity_relation(relation_rng(sK0)) != relation_composition(X0,sK0)
| identity_relation(relation_rng(X0)) != identity_relation(relation_dom(sK0))
| sK1 = X0
| ~ function(sK1)
| ~ relation(sK1)
| ~ function(sK0)
| ~ relation(sK0)
| ~ function(X0)
| ~ relation(X0) )
| ~ spl13_7
| ~ spl13_8
| ~ spl13_70 ),
inference(forward_demodulation,[],[f604,f220]) ).
fof(f220,plain,
( relation_rng(sK0) = relation_dom(sK1)
| ~ spl13_7 ),
inference(avatar_component_clause,[],[f218]) ).
fof(f604,plain,
( ! [X0] :
( identity_relation(relation_rng(X0)) != identity_relation(relation_dom(sK0))
| sK1 = X0
| relation_composition(X0,sK0) != identity_relation(relation_dom(sK1))
| ~ function(sK1)
| ~ relation(sK1)
| ~ function(sK0)
| ~ relation(sK0)
| ~ function(X0)
| ~ relation(X0) )
| ~ spl13_8
| ~ spl13_70 ),
inference(superposition,[],[f602,f225]) ).
fof(f225,plain,
( identity_relation(relation_dom(sK0)) = relation_composition(sK0,sK1)
| ~ spl13_8 ),
inference(avatar_component_clause,[],[f223]) ).
fof(f602,plain,
( ! [X2,X3,X1] :
( relation_composition(X2,X3) != identity_relation(relation_rng(X1))
| X1 = X3
| relation_composition(X1,X2) != identity_relation(relation_dom(X3))
| ~ function(X3)
| ~ relation(X3)
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) )
| ~ spl13_70 ),
inference(avatar_component_clause,[],[f601]) ).
fof(f936,plain,
( spl13_103
| ~ spl13_33
| ~ spl13_62 ),
inference(avatar_split_clause,[],[f552,f547,f341,f934]) ).
fof(f934,plain,
( spl13_103
<=> ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK3(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_103])]) ).
fof(f552,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK3(powerset(X0))) )
| ~ spl13_33
| ~ spl13_62 ),
inference(resolution,[],[f548,f342]) ).
fof(f932,plain,
( spl13_102
| ~ spl13_12
| ~ spl13_29
| ~ spl13_36
| ~ spl13_41
| ~ spl13_56 ),
inference(avatar_split_clause,[],[f527,f476,f384,f364,f325,f243,f930]) ).
fof(f930,plain,
( spl13_102
<=> ! [X0] :
( in(sK6,powerset(X0))
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_102])]) ).
fof(f325,plain,
( spl13_29
<=> ! [X0] : empty(sK4(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_29])]) ).
fof(f527,plain,
( ! [X0] :
( in(sK6,powerset(X0))
| empty(powerset(X0)) )
| ~ spl13_12
| ~ spl13_29
| ~ spl13_36
| ~ spl13_41
| ~ spl13_56 ),
inference(forward_demodulation,[],[f526,f393]) ).
fof(f526,plain,
( ! [X0] :
( in(empty_set,powerset(X0))
| empty(powerset(X0)) )
| ~ spl13_29
| ~ spl13_36
| ~ spl13_41
| ~ spl13_56 ),
inference(forward_demodulation,[],[f525,f392]) ).
fof(f392,plain,
( ! [X0] : empty_set = sK4(X0)
| ~ spl13_29
| ~ spl13_36 ),
inference(resolution,[],[f365,f326]) ).
fof(f326,plain,
( ! [X0] : empty(sK4(X0))
| ~ spl13_29 ),
inference(avatar_component_clause,[],[f325]) ).
fof(f525,plain,
( ! [X0] :
( empty(powerset(X0))
| in(sK4(X0),powerset(X0)) )
| ~ spl13_41
| ~ spl13_56 ),
inference(resolution,[],[f477,f385]) ).
fof(f898,plain,
( spl13_74
| ~ spl13_100
| ~ spl13_101
| ~ spl13_49
| ~ spl13_76 ),
inference(avatar_split_clause,[],[f641,f636,f435,f895,f891,f627]) ).
fof(f627,plain,
( spl13_74
<=> empty(function_inverse(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_74])]) ).
fof(f895,plain,
( spl13_101
<=> empty(relation_dom(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_101])]) ).
fof(f435,plain,
( spl13_49
<=> ! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_49])]) ).
fof(f641,plain,
( ~ empty(relation_dom(sK0))
| ~ relation(function_inverse(sK0))
| empty(function_inverse(sK0))
| ~ spl13_49
| ~ spl13_76 ),
inference(superposition,[],[f436,f638]) ).
fof(f436,plain,
( ! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) )
| ~ spl13_49 ),
inference(avatar_component_clause,[],[f435]) ).
fof(f889,plain,
( spl13_99
| ~ spl13_33
| ~ spl13_56 ),
inference(avatar_split_clause,[],[f524,f476,f341,f887]) ).
fof(f887,plain,
( spl13_99
<=> ! [X0] :
( empty(X0)
| in(sK3(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_99])]) ).
fof(f524,plain,
( ! [X0] :
( empty(X0)
| in(sK3(X0),X0) )
| ~ spl13_33
| ~ spl13_56 ),
inference(resolution,[],[f477,f342]) ).
fof(f881,plain,
( ~ spl13_43
| ~ spl13_12
| spl13_98
| ~ spl13_10
| ~ spl13_12
| ~ spl13_36
| ~ spl13_55 ),
inference(avatar_split_clause,[],[f515,f472,f364,f243,f233,f878,f243,f403]) ).
fof(f403,plain,
( spl13_43
<=> function(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_43])]) ).
fof(f878,plain,
( spl13_98
<=> one_to_one(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_98])]) ).
fof(f233,plain,
( spl13_10
<=> relation(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_10])]) ).
fof(f515,plain,
( one_to_one(sK6)
| ~ empty(sK6)
| ~ function(sK6)
| ~ spl13_10
| ~ spl13_12
| ~ spl13_36
| ~ spl13_55 ),
inference(forward_demodulation,[],[f514,f393]) ).
fof(f514,plain,
( ~ empty(sK6)
| ~ function(sK6)
| one_to_one(empty_set)
| ~ spl13_10
| ~ spl13_12
| ~ spl13_36
| ~ spl13_55 ),
inference(forward_demodulation,[],[f513,f393]) ).
fof(f513,plain,
( ~ function(sK6)
| ~ empty(empty_set)
| one_to_one(empty_set)
| ~ spl13_10
| ~ spl13_12
| ~ spl13_36
| ~ spl13_55 ),
inference(forward_demodulation,[],[f502,f393]) ).
fof(f502,plain,
( ~ function(empty_set)
| ~ empty(empty_set)
| one_to_one(empty_set)
| ~ spl13_10
| ~ spl13_55 ),
inference(resolution,[],[f473,f235]) ).
fof(f235,plain,
( relation(empty_set)
| ~ spl13_10 ),
inference(avatar_component_clause,[],[f233]) ).
fof(f876,plain,
( spl13_96
| ~ spl13_97
| ~ spl13_19
| ~ spl13_18
| ~ spl13_55 ),
inference(avatar_split_clause,[],[f510,f472,f273,f278,f873,f869]) ).
fof(f869,plain,
( spl13_96
<=> one_to_one(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_96])]) ).
fof(f873,plain,
( spl13_97
<=> empty(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_97])]) ).
fof(f278,plain,
( spl13_19
<=> function(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_19])]) ).
fof(f273,plain,
( spl13_18
<=> relation(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_18])]) ).
fof(f510,plain,
( ~ function(sK10)
| ~ empty(sK10)
| one_to_one(sK10)
| ~ spl13_18
| ~ spl13_55 ),
inference(resolution,[],[f473,f275]) ).
fof(f275,plain,
( relation(sK10)
| ~ spl13_18 ),
inference(avatar_component_clause,[],[f273]) ).
fof(f867,plain,
( spl13_93
| ~ spl13_94
| ~ spl13_95
| ~ spl13_17
| ~ spl13_55 ),
inference(avatar_split_clause,[],[f509,f472,f268,f864,f860,f856]) ).
fof(f856,plain,
( spl13_93
<=> one_to_one(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_93])]) ).
fof(f860,plain,
( spl13_94
<=> empty(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_94])]) ).
fof(f864,plain,
( spl13_95
<=> function(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_95])]) ).
fof(f268,plain,
( spl13_17
<=> relation(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_17])]) ).
fof(f509,plain,
( ~ function(sK9)
| ~ empty(sK9)
| one_to_one(sK9)
| ~ spl13_17
| ~ spl13_55 ),
inference(resolution,[],[f473,f270]) ).
fof(f270,plain,
( relation(sK9)
| ~ spl13_17 ),
inference(avatar_component_clause,[],[f268]) ).
fof(f854,plain,
( spl13_92
| ~ spl13_12
| ~ spl13_36
| ~ spl13_39 ),
inference(avatar_split_clause,[],[f411,f376,f364,f243,f852]) ).
fof(f411,plain,
( ! [X0] :
( relation_dom(X0) = sK6
| ~ empty(X0) )
| ~ spl13_12
| ~ spl13_36
| ~ spl13_39 ),
inference(forward_demodulation,[],[f407,f393]) ).
fof(f407,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = relation_dom(X0) )
| ~ spl13_36
| ~ spl13_39 ),
inference(resolution,[],[f377,f365]) ).
fof(f850,plain,
( spl13_91
| ~ spl13_12
| ~ spl13_36
| ~ spl13_37 ),
inference(avatar_split_clause,[],[f401,f368,f364,f243,f848]) ).
fof(f401,plain,
( ! [X0] :
( relation_rng(X0) = sK6
| ~ empty(X0) )
| ~ spl13_12
| ~ spl13_36
| ~ spl13_37 ),
inference(forward_demodulation,[],[f398,f393]) ).
fof(f398,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = relation_rng(X0) )
| ~ spl13_36
| ~ spl13_37 ),
inference(resolution,[],[f369,f365]) ).
fof(f768,plain,
( spl13_88
| ~ spl13_36
| ~ spl13_81 ),
inference(avatar_split_clause,[],[f743,f680,f364,f722]) ).
fof(f722,plain,
( spl13_88
<=> ! [X0] :
( sK6 = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_88])]) ).
fof(f743,plain,
( ! [X0] :
( sK6 = X0
| ~ empty(X0) )
| ~ spl13_36
| ~ spl13_81 ),
inference(forward_demodulation,[],[f365,f682]) ).
fof(f742,plain,
( ~ spl13_9
| ~ spl13_89 ),
inference(avatar_contradiction_clause,[],[f733]) ).
fof(f733,plain,
( $false
| ~ spl13_9
| ~ spl13_89 ),
inference(resolution,[],[f728,f230]) ).
fof(f728,plain,
( ! [X0] : ~ empty(X0)
| ~ spl13_89 ),
inference(avatar_component_clause,[],[f727]) ).
fof(f727,plain,
( spl13_89
<=> ! [X0] : ~ empty(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_89])]) ).
fof(f741,plain,
( ~ spl13_29
| ~ spl13_89 ),
inference(avatar_contradiction_clause,[],[f734]) ).
fof(f734,plain,
( $false
| ~ spl13_29
| ~ spl13_89 ),
inference(resolution,[],[f728,f326]) ).
fof(f740,plain,
( ~ spl13_12
| ~ spl13_89 ),
inference(avatar_contradiction_clause,[],[f735]) ).
fof(f735,plain,
( $false
| ~ spl13_12
| ~ spl13_89 ),
inference(resolution,[],[f728,f245]) ).
fof(f739,plain,
( ~ spl13_15
| ~ spl13_89 ),
inference(avatar_contradiction_clause,[],[f736]) ).
fof(f736,plain,
( $false
| ~ spl13_15
| ~ spl13_89 ),
inference(resolution,[],[f728,f260]) ).
fof(f260,plain,
( empty(sK8)
| ~ spl13_15 ),
inference(avatar_component_clause,[],[f258]) ).
fof(f258,plain,
( spl13_15
<=> empty(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_15])]) ).
fof(f738,plain,
( ~ spl13_24
| ~ spl13_89 ),
inference(avatar_contradiction_clause,[],[f737]) ).
fof(f737,plain,
( $false
| ~ spl13_24
| ~ spl13_89 ),
inference(resolution,[],[f728,f305]) ).
fof(f305,plain,
( empty(sK12)
| ~ spl13_24 ),
inference(avatar_component_clause,[],[f303]) ).
fof(f303,plain,
( spl13_24
<=> empty(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_24])]) ).
fof(f732,plain,
( spl13_89
| spl13_90
| ~ spl13_12
| ~ spl13_29
| ~ spl13_36
| ~ spl13_41
| ~ spl13_62 ),
inference(avatar_split_clause,[],[f555,f547,f384,f364,f325,f243,f730,f727]) ).
fof(f730,plain,
( spl13_90
<=> ! [X1] : ~ in(X1,sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_90])]) ).
fof(f555,plain,
( ! [X0,X1] :
( ~ in(X1,sK6)
| ~ empty(X0) )
| ~ spl13_12
| ~ spl13_29
| ~ spl13_36
| ~ spl13_41
| ~ spl13_62 ),
inference(forward_demodulation,[],[f554,f393]) ).
fof(f554,plain,
( ! [X0,X1] :
( ~ in(X1,empty_set)
| ~ empty(X0) )
| ~ spl13_29
| ~ spl13_36
| ~ spl13_41
| ~ spl13_62 ),
inference(forward_demodulation,[],[f553,f392]) ).
fof(f553,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK4(X0)) )
| ~ spl13_41
| ~ spl13_62 ),
inference(resolution,[],[f548,f385]) ).
fof(f724,plain,
( spl13_88
| ~ spl13_12
| ~ spl13_54 ),
inference(avatar_split_clause,[],[f465,f455,f243,f722]) ).
fof(f465,plain,
( ! [X0] :
( sK6 = X0
| ~ empty(X0) )
| ~ spl13_12
| ~ spl13_54 ),
inference(resolution,[],[f456,f245]) ).
fof(f720,plain,
( spl13_87
| ~ spl13_31
| ~ spl13_39 ),
inference(avatar_split_clause,[],[f409,f376,f333,f718]) ).
fof(f718,plain,
( spl13_87
<=> ! [X0] :
( ~ empty(X0)
| function(relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_87])]) ).
fof(f409,plain,
( ! [X0] :
( ~ empty(X0)
| function(relation_dom(X0)) )
| ~ spl13_31
| ~ spl13_39 ),
inference(resolution,[],[f377,f334]) ).
fof(f716,plain,
( spl13_86
| ~ spl13_31
| ~ spl13_37 ),
inference(avatar_split_clause,[],[f400,f368,f333,f714]) ).
fof(f714,plain,
( spl13_86
<=> ! [X0] :
( ~ empty(X0)
| function(relation_rng(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_86])]) ).
fof(f400,plain,
( ! [X0] :
( ~ empty(X0)
| function(relation_rng(X0)) )
| ~ spl13_31
| ~ spl13_37 ),
inference(resolution,[],[f369,f334]) ).
fof(f710,plain,
( spl13_85
| ~ spl13_81
| ~ spl13_84 ),
inference(avatar_split_clause,[],[f706,f703,f680,f708]) ).
fof(f703,plain,
( spl13_84
<=> ! [X0] : empty_set = sK4(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_84])]) ).
fof(f706,plain,
( ! [X0] : sK4(X0) = sK6
| ~ spl13_81
| ~ spl13_84 ),
inference(forward_demodulation,[],[f704,f682]) ).
fof(f704,plain,
( ! [X0] : empty_set = sK4(X0)
| ~ spl13_84 ),
inference(avatar_component_clause,[],[f703]) ).
fof(f705,plain,
( spl13_84
| ~ spl13_29
| ~ spl13_36 ),
inference(avatar_split_clause,[],[f392,f364,f325,f703]) ).
fof(f693,plain,
( spl13_83
| ~ spl13_12
| ~ spl13_24
| ~ spl13_36 ),
inference(avatar_split_clause,[],[f397,f364,f303,f243,f690]) ).
fof(f690,plain,
( spl13_83
<=> sK6 = sK12 ),
introduced(avatar_definition,[new_symbols(naming,[spl13_83])]) ).
fof(f397,plain,
( sK6 = sK12
| ~ spl13_12
| ~ spl13_24
| ~ spl13_36 ),
inference(forward_demodulation,[],[f395,f393]) ).
fof(f395,plain,
( empty_set = sK12
| ~ spl13_24
| ~ spl13_36 ),
inference(resolution,[],[f365,f305]) ).
fof(f688,plain,
( spl13_82
| ~ spl13_12
| ~ spl13_15
| ~ spl13_36 ),
inference(avatar_split_clause,[],[f396,f364,f258,f243,f685]) ).
fof(f685,plain,
( spl13_82
<=> sK6 = sK8 ),
introduced(avatar_definition,[new_symbols(naming,[spl13_82])]) ).
fof(f396,plain,
( sK6 = sK8
| ~ spl13_12
| ~ spl13_15
| ~ spl13_36 ),
inference(forward_demodulation,[],[f394,f393]) ).
fof(f394,plain,
( empty_set = sK8
| ~ spl13_15
| ~ spl13_36 ),
inference(resolution,[],[f365,f260]) ).
fof(f683,plain,
( spl13_81
| ~ spl13_12
| ~ spl13_36 ),
inference(avatar_split_clause,[],[f393,f364,f243,f680]) ).
fof(f677,plain,
( spl13_80
| ~ spl13_29
| ~ spl13_32 ),
inference(avatar_split_clause,[],[f350,f337,f325,f675]) ).
fof(f675,plain,
( spl13_80
<=> ! [X0] : relation(sK4(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_80])]) ).
fof(f337,plain,
( spl13_32
<=> ! [X0] :
( relation(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_32])]) ).
fof(f350,plain,
( ! [X0] : relation(sK4(X0))
| ~ spl13_29
| ~ spl13_32 ),
inference(resolution,[],[f338,f326]) ).
fof(f338,plain,
( ! [X0] :
( ~ empty(X0)
| relation(X0) )
| ~ spl13_32 ),
inference(avatar_component_clause,[],[f337]) ).
fof(f672,plain,
( spl13_79
| ~ spl13_29
| ~ spl13_31 ),
inference(avatar_split_clause,[],[f345,f333,f325,f670]) ).
fof(f670,plain,
( spl13_79
<=> ! [X0] : function(sK4(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_79])]) ).
fof(f345,plain,
( ! [X0] : function(sK4(X0))
| ~ spl13_29
| ~ spl13_31 ),
inference(resolution,[],[f334,f326]) ).
fof(f661,plain,
( ~ spl13_1
| ~ spl13_2
| spl13_78
| ~ spl13_5
| ~ spl13_69 ),
inference(avatar_split_clause,[],[f598,f593,f208,f658,f193,f188]) ).
fof(f208,plain,
( spl13_5
<=> one_to_one(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_5])]) ).
fof(f598,plain,
( relation_composition(function_inverse(sK0),sK0) = identity_relation(relation_rng(sK0))
| ~ function(sK0)
| ~ relation(sK0)
| ~ spl13_5
| ~ spl13_69 ),
inference(resolution,[],[f594,f210]) ).
fof(f210,plain,
( one_to_one(sK0)
| ~ spl13_5 ),
inference(avatar_component_clause,[],[f208]) ).
fof(f648,plain,
( ~ spl13_1
| ~ spl13_2
| spl13_77
| ~ spl13_5
| ~ spl13_68 ),
inference(avatar_split_clause,[],[f596,f589,f208,f645,f193,f188]) ).
fof(f645,plain,
( spl13_77
<=> identity_relation(relation_dom(sK0)) = relation_composition(sK0,function_inverse(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_77])]) ).
fof(f596,plain,
( identity_relation(relation_dom(sK0)) = relation_composition(sK0,function_inverse(sK0))
| ~ function(sK0)
| ~ relation(sK0)
| ~ spl13_5
| ~ spl13_68 ),
inference(resolution,[],[f590,f210]) ).
fof(f639,plain,
( ~ spl13_1
| ~ spl13_2
| spl13_76
| ~ spl13_5
| ~ spl13_66 ),
inference(avatar_split_clause,[],[f585,f576,f208,f636,f193,f188]) ).
fof(f585,plain,
( relation_dom(sK0) = relation_rng(function_inverse(sK0))
| ~ function(sK0)
| ~ relation(sK0)
| ~ spl13_5
| ~ spl13_66 ),
inference(resolution,[],[f577,f210]) ).
fof(f634,plain,
( ~ spl13_74
| spl13_75
| ~ spl13_40
| ~ spl13_73 ),
inference(avatar_split_clause,[],[f624,f619,f380,f631,f627]) ).
fof(f631,plain,
( spl13_75
<=> relation(relation_rng(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_75])]) ).
fof(f619,plain,
( spl13_73
<=> relation_rng(sK0) = relation_dom(function_inverse(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_73])]) ).
fof(f624,plain,
( relation(relation_rng(sK0))
| ~ empty(function_inverse(sK0))
| ~ spl13_40
| ~ spl13_73 ),
inference(superposition,[],[f381,f621]) ).
fof(f621,plain,
( relation_rng(sK0) = relation_dom(function_inverse(sK0))
| ~ spl13_73 ),
inference(avatar_component_clause,[],[f619]) ).
fof(f622,plain,
( ~ spl13_1
| ~ spl13_2
| spl13_73
| ~ spl13_5
| ~ spl13_65 ),
inference(avatar_split_clause,[],[f583,f572,f208,f619,f193,f188]) ).
fof(f583,plain,
( relation_rng(sK0) = relation_dom(function_inverse(sK0))
| ~ function(sK0)
| ~ relation(sK0)
| ~ spl13_5
| ~ spl13_65 ),
inference(resolution,[],[f573,f210]) ).
fof(f616,plain,
( spl13_72
| ~ spl13_12
| ~ spl13_32 ),
inference(avatar_split_clause,[],[f351,f337,f243,f613]) ).
fof(f613,plain,
( spl13_72
<=> relation(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_72])]) ).
fof(f351,plain,
( relation(sK6)
| ~ spl13_12
| ~ spl13_32 ),
inference(resolution,[],[f338,f245]) ).
fof(f610,plain,
( spl13_71
| ~ spl13_15
| ~ spl13_31 ),
inference(avatar_split_clause,[],[f347,f333,f258,f607]) ).
fof(f607,plain,
( spl13_71
<=> function(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_71])]) ).
fof(f347,plain,
( function(sK8)
| ~ spl13_15
| ~ spl13_31 ),
inference(resolution,[],[f334,f260]) ).
fof(f603,plain,
spl13_70,
inference(avatar_split_clause,[],[f186,f601]) ).
fof(f186,plain,
! [X2,X3,X1] :
( X1 = X3
| relation_composition(X2,X3) != identity_relation(relation_rng(X1))
| relation_composition(X1,X2) != identity_relation(relation_dom(X3))
| ~ function(X3)
| ~ relation(X3)
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(equality_resolution,[],[f164]) ).
fof(f164,plain,
! [X2,X3,X0,X1] :
( X1 = X3
| identity_relation(X0) != relation_composition(X2,X3)
| relation_composition(X1,X2) != identity_relation(relation_dom(X3))
| relation_rng(X1) != X0
| ~ function(X3)
| ~ relation(X3)
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0,X1] :
( ! [X2] :
( ! [X3] :
( X1 = X3
| identity_relation(X0) != relation_composition(X2,X3)
| relation_composition(X1,X2) != identity_relation(relation_dom(X3))
| relation_rng(X1) != X0
| ~ function(X3)
| ~ relation(X3) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f79]) ).
fof(f79,plain,
! [X0,X1] :
( ! [X2] :
( ! [X3] :
( X1 = X3
| identity_relation(X0) != relation_composition(X2,X3)
| relation_composition(X1,X2) != identity_relation(relation_dom(X3))
| relation_rng(X1) != X0
| ~ function(X3)
| ~ relation(X3) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ! [X3] :
( ( function(X3)
& relation(X3) )
=> ( ( identity_relation(X0) = relation_composition(X2,X3)
& relation_composition(X1,X2) = identity_relation(relation_dom(X3))
& relation_rng(X1) = X0 )
=> X1 = X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l72_funct_1) ).
fof(f595,plain,
spl13_69,
inference(avatar_split_clause,[],[f147,f593]) ).
fof(f147,plain,
! [X0] :
( relation_composition(function_inverse(X0),X0) = identity_relation(relation_rng(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,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,[],[f65]) ).
fof(f65,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,[],[f39]) ).
fof(f39,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(f591,plain,
spl13_68,
inference(avatar_split_clause,[],[f146,f589]) ).
fof(f146,plain,
! [X0] :
( relation_composition(X0,function_inverse(X0)) = identity_relation(relation_dom(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f582,plain,
spl13_67,
inference(avatar_split_clause,[],[f163,f580]) ).
fof(f580,plain,
( spl13_67
<=> ! [X0,X1] :
( function(relation_composition(X0,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_67])]) ).
fof(f163,plain,
! [X0,X1] :
( function(relation_composition(X0,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
! [X0,X1] :
( ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) )
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f77]) ).
fof(f77,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(f578,plain,
spl13_66,
inference(avatar_split_clause,[],[f145,f576]) ).
fof(f145,plain,
! [X0] :
( relation_dom(X0) = relation_rng(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f64,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,[],[f63]) ).
fof(f63,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,[],[f37]) ).
fof(f37,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(f574,plain,
spl13_65,
inference(avatar_split_clause,[],[f144,f572]) ).
fof(f144,plain,
! [X0] :
( relation_rng(X0) = relation_dom(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f564,plain,
( ~ spl13_64
| ~ spl13_37
| spl13_48 ),
inference(avatar_split_clause,[],[f499,f430,f368,f561]) ).
fof(f561,plain,
( spl13_64
<=> empty(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_64])]) ).
fof(f430,plain,
( spl13_48
<=> empty(relation_rng(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_48])]) ).
fof(f499,plain,
( ~ empty(sK0)
| ~ spl13_37
| spl13_48 ),
inference(resolution,[],[f431,f369]) ).
fof(f431,plain,
( ~ empty(relation_rng(sK0))
| spl13_48 ),
inference(avatar_component_clause,[],[f430]) ).
fof(f559,plain,
spl13_63,
inference(avatar_split_clause,[],[f169,f557]) ).
fof(f169,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f87]) ).
fof(f87,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f86]) ).
fof(f86,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f549,plain,
spl13_62,
inference(avatar_split_clause,[],[f170,f547]) ).
fof(f170,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f498,plain,
spl13_61,
inference(avatar_split_clause,[],[f165,f496]) ).
fof(f165,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(flattening,[],[f81]) ).
fof(f81,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(f494,plain,
spl13_60,
inference(avatar_split_clause,[],[f161,f492]) ).
fof(f161,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& empty(relation_composition(X0,X1)) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(flattening,[],[f75]) ).
fof(f75,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(f490,plain,
spl13_59,
inference(avatar_split_clause,[],[f160,f488]) ).
fof(f160,plain,
! [X0,X1] :
( empty(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f486,plain,
spl13_58,
inference(avatar_split_clause,[],[f159,f484]) ).
fof(f159,plain,
! [X0,X1] :
( relation(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
! [X0,X1] :
( ( relation(relation_composition(X1,X0))
& empty(relation_composition(X1,X0)) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(flattening,[],[f73]) ).
fof(f73,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(f482,plain,
spl13_57,
inference(avatar_split_clause,[],[f158,f480]) ).
fof(f158,plain,
! [X0,X1] :
( empty(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f478,plain,
spl13_56,
inference(avatar_split_clause,[],[f157,f476]) ).
fof(f157,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f71]) ).
fof(f71,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f474,plain,
spl13_55,
inference(avatar_split_clause,[],[f150,f472]) ).
fof(f150,plain,
! [X0] :
( one_to_one(X0)
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0] :
( ( one_to_one(X0)
& function(X0)
& relation(X0) )
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ),
inference(flattening,[],[f67]) ).
fof(f67,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(f457,plain,
spl13_54,
inference(avatar_split_clause,[],[f167,f455]) ).
fof(f167,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f84,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f44]) ).
fof(f44,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(f453,plain,
spl13_53,
inference(avatar_split_clause,[],[f166,f451]) ).
fof(f166,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0,X1] :
( subset(X0,X1)
=> element(X0,powerset(X1)) ),
inference(unused_predicate_definition_removal,[],[f35]) ).
fof(f35,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f449,plain,
spl13_52,
inference(avatar_split_clause,[],[f143,f447]) ).
fof(f143,plain,
! [X0] :
( function(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0] :
( ( function(function_inverse(X0))
& relation(function_inverse(X0)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f61]) ).
fof(f61,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(f445,plain,
spl13_51,
inference(avatar_split_clause,[],[f142,f443]) ).
fof(f142,plain,
! [X0] :
( relation(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f441,plain,
spl13_50,
inference(avatar_split_clause,[],[f141,f439]) ).
fof(f439,plain,
( spl13_50
<=> ! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_50])]) ).
fof(f141,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(flattening,[],[f59]) ).
fof(f59,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(f437,plain,
spl13_49,
inference(avatar_split_clause,[],[f140,f435]) ).
fof(f140,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(flattening,[],[f57]) ).
fof(f57,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(f433,plain,
( ~ spl13_47
| spl13_48
| ~ spl13_7
| ~ spl13_39 ),
inference(avatar_split_clause,[],[f410,f376,f218,f430,f426]) ).
fof(f426,plain,
( spl13_47
<=> empty(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_47])]) ).
fof(f410,plain,
( empty(relation_rng(sK0))
| ~ empty(sK1)
| ~ spl13_7
| ~ spl13_39 ),
inference(superposition,[],[f377,f220]) ).
fof(f424,plain,
spl13_46,
inference(avatar_split_clause,[],[f131,f422]) ).
fof(f131,plain,
! [X0] :
( element(sK2(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f93,plain,
! [X0] :
( ( ~ empty(sK2(X0))
& element(sK2(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f51,f92]) ).
fof(f92,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( ~ empty(sK2(X0))
& element(sK2(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f51,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f420,plain,
spl13_45,
inference(avatar_split_clause,[],[f156,f418]) ).
fof(f418,plain,
( spl13_45
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_45])]) ).
fof(f156,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f416,plain,
spl13_44,
inference(avatar_split_clause,[],[f155,f414]) ).
fof(f414,plain,
( spl13_44
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_44])]) ).
fof(f155,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,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(f406,plain,
( spl13_43
| ~ spl13_12
| ~ spl13_31 ),
inference(avatar_split_clause,[],[f346,f333,f243,f403]) ).
fof(f346,plain,
( function(sK6)
| ~ spl13_12
| ~ spl13_31 ),
inference(resolution,[],[f334,f245]) ).
fof(f390,plain,
spl13_42,
inference(avatar_split_clause,[],[f168,f388]) ).
fof(f388,plain,
( spl13_42
<=> ! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_42])]) ).
fof(f168,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f43]) ).
fof(f43,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f386,plain,
spl13_41,
inference(avatar_split_clause,[],[f152,f384]) ).
fof(f152,plain,
! [X0] : element(sK4(X0),powerset(X0)),
inference(cnf_transformation,[],[f97]) ).
fof(f97,plain,
! [X0] :
( empty(sK4(X0))
& element(sK4(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f28,f96]) ).
fof(f96,plain,
! [X0] :
( ? [X1] :
( empty(X1)
& element(X1,powerset(X0)) )
=> ( empty(sK4(X0))
& element(sK4(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f28,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f382,plain,
spl13_40,
inference(avatar_split_clause,[],[f139,f380]) ).
fof(f139,plain,
! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f56,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(f378,plain,
spl13_39,
inference(avatar_split_clause,[],[f138,f376]) ).
fof(f138,plain,
! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f374,plain,
spl13_38,
inference(avatar_split_clause,[],[f137,f372]) ).
fof(f137,plain,
! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f55,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(f370,plain,
spl13_37,
inference(avatar_split_clause,[],[f136,f368]) ).
fof(f136,plain,
! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f366,plain,
spl13_36,
inference(avatar_split_clause,[],[f135,f364]) ).
fof(f135,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f362,plain,
( spl13_35
| ~ spl13_9
| ~ spl13_31 ),
inference(avatar_split_clause,[],[f344,f333,f228,f359]) ).
fof(f359,plain,
( spl13_35
<=> function(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_35])]) ).
fof(f344,plain,
( function(empty_set)
| ~ spl13_9
| ~ spl13_31 ),
inference(resolution,[],[f334,f230]) ).
fof(f357,plain,
spl13_34,
inference(avatar_split_clause,[],[f132,f355]) ).
fof(f355,plain,
( spl13_34
<=> ! [X0] :
( ~ empty(sK2(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_34])]) ).
fof(f132,plain,
! [X0] :
( ~ empty(sK2(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f343,plain,
spl13_33,
inference(avatar_split_clause,[],[f151,f341]) ).
fof(f151,plain,
! [X0] : element(sK3(X0),X0),
inference(cnf_transformation,[],[f95]) ).
fof(f95,plain,
! [X0] : element(sK3(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f8,f94]) ).
fof(f94,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK3(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(f339,plain,
spl13_32,
inference(avatar_split_clause,[],[f134,f337]) ).
fof(f134,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f53,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(f335,plain,
spl13_31,
inference(avatar_split_clause,[],[f133,f333]) ).
fof(f133,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,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(f331,plain,
spl13_30,
inference(avatar_split_clause,[],[f154,f329]) ).
fof(f329,plain,
( spl13_30
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_30])]) ).
fof(f154,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f32]) ).
fof(f32,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f327,plain,
spl13_29,
inference(avatar_split_clause,[],[f153,f325]) ).
fof(f153,plain,
! [X0] : empty(sK4(X0)),
inference(cnf_transformation,[],[f97]) ).
fof(f323,plain,
spl13_28,
inference(avatar_split_clause,[],[f130,f321]) ).
fof(f321,plain,
( spl13_28
<=> ! [X0] : function(identity_relation(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_28])]) ).
fof(f130,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(f319,plain,
spl13_27,
inference(avatar_split_clause,[],[f128,f317]) ).
fof(f128,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(f315,plain,
spl13_26,
inference(avatar_split_clause,[],[f127,f313]) ).
fof(f313,plain,
( spl13_26
<=> ! [X0] : ~ empty(powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_26])]) ).
fof(f127,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(f311,plain,
spl13_25,
inference(avatar_split_clause,[],[f185,f308]) ).
fof(f308,plain,
( spl13_25
<=> function(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_25])]) ).
fof(f185,plain,
function(sK12),
inference(cnf_transformation,[],[f113]) ).
fof(f113,plain,
( function(sK12)
& empty(sK12)
& relation(sK12) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f26,f112]) ).
fof(f112,plain,
( ? [X0] :
( function(X0)
& empty(X0)
& relation(X0) )
=> ( function(sK12)
& empty(sK12)
& relation(sK12) ) ),
introduced(choice_axiom,[]) ).
fof(f26,axiom,
? [X0] :
( function(X0)
& empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(f306,plain,
spl13_24,
inference(avatar_split_clause,[],[f184,f303]) ).
fof(f184,plain,
empty(sK12),
inference(cnf_transformation,[],[f113]) ).
fof(f301,plain,
spl13_23,
inference(avatar_split_clause,[],[f183,f298]) ).
fof(f298,plain,
( spl13_23
<=> relation(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_23])]) ).
fof(f183,plain,
relation(sK12),
inference(cnf_transformation,[],[f113]) ).
fof(f296,plain,
spl13_22,
inference(avatar_split_clause,[],[f182,f293]) ).
fof(f182,plain,
one_to_one(sK11),
inference(cnf_transformation,[],[f111]) ).
fof(f111,plain,
( one_to_one(sK11)
& function(sK11)
& relation(sK11) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f30,f110]) ).
fof(f110,plain,
( ? [X0] :
( one_to_one(X0)
& function(X0)
& relation(X0) )
=> ( one_to_one(sK11)
& function(sK11)
& relation(sK11) ) ),
introduced(choice_axiom,[]) ).
fof(f30,axiom,
? [X0] :
( one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
fof(f291,plain,
spl13_21,
inference(avatar_split_clause,[],[f181,f288]) ).
fof(f181,plain,
function(sK11),
inference(cnf_transformation,[],[f111]) ).
fof(f286,plain,
spl13_20,
inference(avatar_split_clause,[],[f180,f283]) ).
fof(f180,plain,
relation(sK11),
inference(cnf_transformation,[],[f111]) ).
fof(f281,plain,
spl13_19,
inference(avatar_split_clause,[],[f179,f278]) ).
fof(f179,plain,
function(sK10),
inference(cnf_transformation,[],[f109]) ).
fof(f109,plain,
( function(sK10)
& relation(sK10) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f22,f108]) ).
fof(f108,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK10)
& relation(sK10) ) ),
introduced(choice_axiom,[]) ).
fof(f22,axiom,
? [X0] :
( function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
fof(f276,plain,
spl13_18,
inference(avatar_split_clause,[],[f178,f273]) ).
fof(f178,plain,
relation(sK10),
inference(cnf_transformation,[],[f109]) ).
fof(f271,plain,
spl13_17,
inference(avatar_split_clause,[],[f177,f268]) ).
fof(f177,plain,
relation(sK9),
inference(cnf_transformation,[],[f107]) ).
fof(f107,plain,
relation(sK9),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f47,f106]) ).
fof(f106,plain,
( ? [X0] : relation(X0)
=> relation(sK9) ),
introduced(choice_axiom,[]) ).
fof(f47,plain,
? [X0] : relation(X0),
inference(pure_predicate_removal,[],[f31]) ).
fof(f31,axiom,
? [X0] :
( relation_empty_yielding(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
fof(f266,plain,
spl13_16,
inference(avatar_split_clause,[],[f176,f263]) ).
fof(f263,plain,
( spl13_16
<=> relation(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_16])]) ).
fof(f176,plain,
relation(sK8),
inference(cnf_transformation,[],[f105]) ).
fof(f105,plain,
( relation(sK8)
& empty(sK8) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f23,f104]) ).
fof(f104,plain,
( ? [X0] :
( relation(X0)
& empty(X0) )
=> ( relation(sK8)
& empty(sK8) ) ),
introduced(choice_axiom,[]) ).
fof(f23,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f261,plain,
spl13_15,
inference(avatar_split_clause,[],[f175,f258]) ).
fof(f175,plain,
empty(sK8),
inference(cnf_transformation,[],[f105]) ).
fof(f256,plain,
spl13_14,
inference(avatar_split_clause,[],[f174,f253]) ).
fof(f253,plain,
( spl13_14
<=> relation(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_14])]) ).
fof(f174,plain,
relation(sK7),
inference(cnf_transformation,[],[f103]) ).
fof(f103,plain,
( relation(sK7)
& ~ empty(sK7) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f27,f102]) ).
fof(f102,plain,
( ? [X0] :
( relation(X0)
& ~ empty(X0) )
=> ( relation(sK7)
& ~ empty(sK7) ) ),
introduced(choice_axiom,[]) ).
fof(f27,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f251,plain,
~ spl13_13,
inference(avatar_split_clause,[],[f173,f248]) ).
fof(f248,plain,
( spl13_13
<=> empty(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_13])]) ).
fof(f173,plain,
~ empty(sK7),
inference(cnf_transformation,[],[f103]) ).
fof(f246,plain,
spl13_12,
inference(avatar_split_clause,[],[f172,f243]) ).
fof(f172,plain,
empty(sK6),
inference(cnf_transformation,[],[f101]) ).
fof(f101,plain,
empty(sK6),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f25,f100]) ).
fof(f100,plain,
( ? [X0] : empty(X0)
=> empty(sK6) ),
introduced(choice_axiom,[]) ).
fof(f25,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f241,plain,
~ spl13_11,
inference(avatar_split_clause,[],[f171,f238]) ).
fof(f238,plain,
( spl13_11
<=> empty(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_11])]) ).
fof(f171,plain,
~ empty(sK5),
inference(cnf_transformation,[],[f99]) ).
fof(f99,plain,
~ empty(sK5),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f29,f98]) ).
fof(f98,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK5) ),
introduced(choice_axiom,[]) ).
fof(f29,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f236,plain,
spl13_10,
inference(avatar_split_clause,[],[f124,f233]) ).
fof(f124,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(f231,plain,
spl13_9,
inference(avatar_split_clause,[],[f122,f228]) ).
fof(f122,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(f226,plain,
spl13_8,
inference(avatar_split_clause,[],[f120,f223]) ).
fof(f120,plain,
identity_relation(relation_dom(sK0)) = relation_composition(sK0,sK1),
inference(cnf_transformation,[],[f91]) ).
fof(f91,plain,
( function_inverse(sK0) != sK1
& identity_relation(relation_dom(sK0)) = relation_composition(sK0,sK1)
& relation_rng(sK0) = relation_dom(sK1)
& one_to_one(sK0)
& function(sK1)
& relation(sK1)
& function(sK0)
& relation(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f50,f90,f89]) ).
fof(f89,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) )
=> ( ? [X1] :
( function_inverse(sK0) != X1
& relation_composition(sK0,X1) = identity_relation(relation_dom(sK0))
& relation_dom(X1) = relation_rng(sK0)
& one_to_one(sK0)
& function(X1)
& relation(X1) )
& function(sK0)
& relation(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f90,plain,
( ? [X1] :
( function_inverse(sK0) != X1
& relation_composition(sK0,X1) = identity_relation(relation_dom(sK0))
& relation_dom(X1) = relation_rng(sK0)
& one_to_one(sK0)
& function(X1)
& relation(X1) )
=> ( function_inverse(sK0) != sK1
& identity_relation(relation_dom(sK0)) = relation_composition(sK0,sK1)
& relation_rng(sK0) = relation_dom(sK1)
& one_to_one(sK0)
& function(sK1)
& relation(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f50,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,[],[f49]) ).
fof(f49,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,[],[f41]) ).
fof(f41,negated_conjecture,
~ ! [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 ) ) ),
inference(negated_conjecture,[],[f40]) ).
fof(f40,conjecture,
! [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(f221,plain,
spl13_7,
inference(avatar_split_clause,[],[f119,f218]) ).
fof(f119,plain,
relation_rng(sK0) = relation_dom(sK1),
inference(cnf_transformation,[],[f91]) ).
fof(f216,plain,
~ spl13_6,
inference(avatar_split_clause,[],[f121,f213]) ).
fof(f121,plain,
function_inverse(sK0) != sK1,
inference(cnf_transformation,[],[f91]) ).
fof(f211,plain,
spl13_5,
inference(avatar_split_clause,[],[f118,f208]) ).
fof(f118,plain,
one_to_one(sK0),
inference(cnf_transformation,[],[f91]) ).
fof(f206,plain,
spl13_4,
inference(avatar_split_clause,[],[f117,f203]) ).
fof(f117,plain,
function(sK1),
inference(cnf_transformation,[],[f91]) ).
fof(f201,plain,
spl13_3,
inference(avatar_split_clause,[],[f116,f198]) ).
fof(f116,plain,
relation(sK1),
inference(cnf_transformation,[],[f91]) ).
fof(f196,plain,
spl13_2,
inference(avatar_split_clause,[],[f115,f193]) ).
fof(f115,plain,
function(sK0),
inference(cnf_transformation,[],[f91]) ).
fof(f191,plain,
spl13_1,
inference(avatar_split_clause,[],[f114,f188]) ).
fof(f114,plain,
relation(sK0),
inference(cnf_transformation,[],[f91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU030+1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35 % Computer : n028.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri May 3 11:18:48 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % (11340)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.37 % (11343)WARNING: value z3 for option sas not known
% 0.13/0.37 % (11342)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.37 % (11341)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.37 % (11344)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.37 % (11343)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)
% 0.13/0.37 % (11345)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)
% 0.13/0.37 % (11346)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 % (11347)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)
% 0.13/0.37 TRYING [1]
% 0.13/0.37 TRYING [2]
% 0.13/0.38 TRYING [3]
% 0.13/0.38 TRYING [1]
% 0.13/0.38 TRYING [2]
% 0.13/0.38 TRYING [4]
% 0.13/0.39 TRYING [1]
% 0.13/0.39 TRYING [2]
% 0.13/0.39 TRYING [3]
% 0.13/0.39 TRYING [3]
% 0.13/0.39 TRYING [5]
% 0.13/0.40 TRYING [4]
% 0.13/0.40 % (11345)First to succeed.
% 0.13/0.41 % (11345)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-11340"
% 0.13/0.41 TRYING [5]
% 0.13/0.41 % (11345)Refutation found. Thanks to Tanya!
% 0.13/0.41 % SZS status Theorem for theBenchmark
% 0.13/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.41 % (11345)------------------------------
% 0.13/0.41 % (11345)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.41 % (11345)Termination reason: Refutation
% 0.13/0.41
% 0.13/0.41 % (11345)Memory used [KB]: 1305
% 0.13/0.41 % (11345)Time elapsed: 0.037 s
% 0.13/0.41 % (11345)Instructions burned: 54 (million)
% 0.13/0.41 % (11340)Success in time 0.056 s
%------------------------------------------------------------------------------