TSTP Solution File: SEU009+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU009+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 : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 15:21:46 EDT 2024
% Result : Theorem 0.12s 0.31s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 199
% Syntax : Number of formulae : 679 ( 83 unt; 0 def)
% Number of atoms : 2186 ( 203 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 2737 (1230 ~;1206 |; 105 &)
% ( 162 <=>; 32 =>; 0 <=; 2 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 162 ( 160 usr; 154 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 10 con; 0-2 aty)
% Number of variables : 614 ( 575 !; 39 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1601,plain,
$false,
inference(avatar_sat_refutation,[],[f167,f172,f177,f182,f187,f192,f197,f202,f207,f212,f217,f222,f227,f236,f241,f245,f249,f253,f257,f261,f265,f269,f273,f285,f289,f293,f297,f301,f305,f315,f326,f330,f338,f342,f347,f351,f355,f367,f371,f375,f379,f384,f388,f408,f419,f423,f433,f438,f442,f447,f454,f460,f464,f470,f475,f480,f485,f491,f496,f507,f513,f524,f529,f535,f540,f544,f550,f556,f561,f569,f574,f591,f593,f595,f603,f607,f614,f619,f620,f621,f622,f642,f669,f680,f684,f704,f708,f716,f721,f725,f729,f733,f737,f758,f763,f767,f771,f775,f809,f813,f823,f827,f859,f863,f871,f875,f880,f889,f901,f911,f913,f921,f925,f949,f954,f958,f979,f1003,f1009,f1015,f1040,f1046,f1051,f1058,f1063,f1082,f1099,f1103,f1108,f1122,f1126,f1130,f1134,f1138,f1142,f1146,f1150,f1155,f1281,f1285,f1315,f1319,f1323,f1327,f1331,f1335,f1340,f1344,f1348,f1352,f1356,f1516,f1520,f1524,f1528,f1532,f1536,f1537,f1543,f1566,f1578,f1584,f1592,f1593,f1598,f1600]) ).
fof(f1600,plain,
( ~ spl13_73
| ~ spl13_74
| ~ spl13_1
| ~ spl13_2
| spl13_15
| ~ spl13_14
| ~ spl13_52 ),
inference(avatar_split_clause,[],[f1586,f452,f229,f233,f169,f164,f584,f580]) ).
fof(f580,plain,
( spl13_73
<=> relation(identity_relation(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_73])]) ).
fof(f584,plain,
( spl13_74
<=> function(identity_relation(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_74])]) ).
fof(f164,plain,
( spl13_1
<=> relation(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_1])]) ).
fof(f169,plain,
( spl13_2
<=> function(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_2])]) ).
fof(f233,plain,
( spl13_15
<=> in(sK1,relation_dom(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_15])]) ).
fof(f229,plain,
( spl13_14
<=> in(sK1,relation_dom(relation_composition(sK2,identity_relation(sK0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_14])]) ).
fof(f452,plain,
( spl13_52
<=> ! [X2,X0,X1] :
( in(X0,relation_dom(X2))
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_52])]) ).
fof(f1586,plain,
( in(sK1,relation_dom(sK2))
| ~ function(sK2)
| ~ relation(sK2)
| ~ function(identity_relation(sK0))
| ~ relation(identity_relation(sK0))
| ~ spl13_14
| ~ spl13_52 ),
inference(resolution,[],[f231,f453]) ).
fof(f453,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_dom(relation_composition(X2,X1)))
| in(X0,relation_dom(X2))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) )
| ~ spl13_52 ),
inference(avatar_component_clause,[],[f452]) ).
fof(f231,plain,
( in(sK1,relation_dom(relation_composition(sK2,identity_relation(sK0))))
| ~ spl13_14 ),
inference(avatar_component_clause,[],[f229]) ).
fof(f1598,plain,
( spl13_60
| ~ spl13_14
| ~ spl13_33 ),
inference(avatar_split_clause,[],[f334,f328,f229,f493]) ).
fof(f493,plain,
( spl13_60
<=> element(sK1,relation_dom(relation_composition(sK2,identity_relation(sK0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_60])]) ).
fof(f328,plain,
( spl13_33
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_33])]) ).
fof(f334,plain,
( element(sK1,relation_dom(relation_composition(sK2,identity_relation(sK0))))
| ~ spl13_14
| ~ spl13_33 ),
inference(resolution,[],[f329,f231]) ).
fof(f329,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) )
| ~ spl13_33 ),
inference(avatar_component_clause,[],[f328]) ).
fof(f1593,plain,
( spl13_16
| ~ spl13_19
| ~ spl13_75
| ~ spl13_90 ),
inference(avatar_split_clause,[],[f917,f735,f588,f251,f238]) ).
fof(f238,plain,
( spl13_16
<=> in(apply(sK2,sK1),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_16])]) ).
fof(f251,plain,
( spl13_19
<=> ! [X0] : function(identity_relation(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_19])]) ).
fof(f588,plain,
( spl13_75
<=> in(apply(sK2,sK1),relation_dom(identity_relation(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_75])]) ).
fof(f735,plain,
( spl13_90
<=> ! [X0] :
( ~ function(identity_relation(X0))
| relation_dom(identity_relation(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_90])]) ).
fof(f917,plain,
( in(apply(sK2,sK1),sK0)
| ~ spl13_19
| ~ spl13_75
| ~ spl13_90 ),
inference(forward_demodulation,[],[f590,f759]) ).
fof(f759,plain,
( ! [X0] : relation_dom(identity_relation(X0)) = X0
| ~ spl13_19
| ~ spl13_90 ),
inference(resolution,[],[f736,f252]) ).
fof(f252,plain,
( ! [X0] : function(identity_relation(X0))
| ~ spl13_19 ),
inference(avatar_component_clause,[],[f251]) ).
fof(f736,plain,
( ! [X0] :
( ~ function(identity_relation(X0))
| relation_dom(identity_relation(X0)) = X0 )
| ~ spl13_90 ),
inference(avatar_component_clause,[],[f735]) ).
fof(f590,plain,
( in(apply(sK2,sK1),relation_dom(identity_relation(sK0)))
| ~ spl13_75 ),
inference(avatar_component_clause,[],[f588]) ).
fof(f1592,plain,
( ~ spl13_14
| ~ spl13_15
| ~ spl13_16 ),
inference(avatar_split_clause,[],[f106,f238,f233,f229]) ).
fof(f106,plain,
( ~ in(apply(sK2,sK1),sK0)
| ~ in(sK1,relation_dom(sK2))
| ~ in(sK1,relation_dom(relation_composition(sK2,identity_relation(sK0)))) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
( ( ~ in(apply(sK2,sK1),sK0)
| ~ in(sK1,relation_dom(sK2))
| ~ in(sK1,relation_dom(relation_composition(sK2,identity_relation(sK0)))) )
& ( ( in(apply(sK2,sK1),sK0)
& in(sK1,relation_dom(sK2)) )
| in(sK1,relation_dom(relation_composition(sK2,identity_relation(sK0)))) )
& function(sK2)
& relation(sK2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f74,f75]) ).
fof(f75,plain,
( ? [X0,X1,X2] :
( ( ~ in(apply(X2,X1),X0)
| ~ in(X1,relation_dom(X2))
| ~ in(X1,relation_dom(relation_composition(X2,identity_relation(X0)))) )
& ( ( in(apply(X2,X1),X0)
& in(X1,relation_dom(X2)) )
| in(X1,relation_dom(relation_composition(X2,identity_relation(X0)))) )
& function(X2)
& relation(X2) )
=> ( ( ~ in(apply(sK2,sK1),sK0)
| ~ in(sK1,relation_dom(sK2))
| ~ in(sK1,relation_dom(relation_composition(sK2,identity_relation(sK0)))) )
& ( ( in(apply(sK2,sK1),sK0)
& in(sK1,relation_dom(sK2)) )
| in(sK1,relation_dom(relation_composition(sK2,identity_relation(sK0)))) )
& function(sK2)
& relation(sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f74,plain,
? [X0,X1,X2] :
( ( ~ in(apply(X2,X1),X0)
| ~ in(X1,relation_dom(X2))
| ~ in(X1,relation_dom(relation_composition(X2,identity_relation(X0)))) )
& ( ( in(apply(X2,X1),X0)
& in(X1,relation_dom(X2)) )
| in(X1,relation_dom(relation_composition(X2,identity_relation(X0)))) )
& function(X2)
& relation(X2) ),
inference(flattening,[],[f73]) ).
fof(f73,plain,
? [X0,X1,X2] :
( ( ~ in(apply(X2,X1),X0)
| ~ in(X1,relation_dom(X2))
| ~ in(X1,relation_dom(relation_composition(X2,identity_relation(X0)))) )
& ( ( in(apply(X2,X1),X0)
& in(X1,relation_dom(X2)) )
| in(X1,relation_dom(relation_composition(X2,identity_relation(X0)))) )
& function(X2)
& relation(X2) ),
inference(nnf_transformation,[],[f43]) ).
fof(f43,plain,
? [X0,X1,X2] :
( ( in(X1,relation_dom(relation_composition(X2,identity_relation(X0))))
<~> ( in(apply(X2,X1),X0)
& in(X1,relation_dom(X2)) ) )
& function(X2)
& relation(X2) ),
inference(flattening,[],[f42]) ).
fof(f42,plain,
? [X0,X1,X2] :
( ( in(X1,relation_dom(relation_composition(X2,identity_relation(X0))))
<~> ( in(apply(X2,X1),X0)
& in(X1,relation_dom(X2)) ) )
& function(X2)
& relation(X2) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,negated_conjecture,
~ ! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X1,relation_dom(relation_composition(X2,identity_relation(X0))))
<=> ( in(apply(X2,X1),X0)
& in(X1,relation_dom(X2)) ) ) ),
inference(negated_conjecture,[],[f31]) ).
fof(f31,conjecture,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X1,relation_dom(relation_composition(X2,identity_relation(X0))))
<=> ( in(apply(X2,X1),X0)
& in(X1,relation_dom(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_funct_1) ).
fof(f1584,plain,
( ~ spl13_79
| ~ spl13_153 ),
inference(avatar_contradiction_clause,[],[f1579]) ).
fof(f1579,plain,
( $false
| ~ spl13_79
| ~ spl13_153 ),
inference(resolution,[],[f1577,f613]) ).
fof(f613,plain,
( ! [X1] : ~ in(X1,sK8)
| ~ spl13_79 ),
inference(avatar_component_clause,[],[f612]) ).
fof(f612,plain,
( spl13_79
<=> ! [X1] : ~ in(X1,sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_79])]) ).
fof(f1577,plain,
( in(sK1,sK8)
| ~ spl13_153 ),
inference(avatar_component_clause,[],[f1575]) ).
fof(f1575,plain,
( spl13_153
<=> in(sK1,sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_153])]) ).
fof(f1578,plain,
( spl13_153
| ~ spl13_3
| ~ spl13_14
| ~ spl13_69
| ~ spl13_116 ),
inference(avatar_split_clause,[],[f1573,f1038,f553,f229,f174,f1575]) ).
fof(f174,plain,
( spl13_3
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_3])]) ).
fof(f553,plain,
( spl13_69
<=> empty_set = sK8 ),
introduced(avatar_definition,[new_symbols(naming,[spl13_69])]) ).
fof(f1038,plain,
( spl13_116
<=> ! [X0] :
( relation_dom(relation_composition(sK2,identity_relation(sK0))) = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_116])]) ).
fof(f1573,plain,
( in(sK1,sK8)
| ~ spl13_3
| ~ spl13_14
| ~ spl13_69
| ~ spl13_116 ),
inference(forward_demodulation,[],[f231,f1561]) ).
fof(f1561,plain,
( relation_dom(relation_composition(sK2,identity_relation(sK0))) = sK8
| ~ spl13_3
| ~ spl13_69
| ~ spl13_116 ),
inference(forward_demodulation,[],[f1555,f555]) ).
fof(f555,plain,
( empty_set = sK8
| ~ spl13_69 ),
inference(avatar_component_clause,[],[f553]) ).
fof(f1555,plain,
( empty_set = relation_dom(relation_composition(sK2,identity_relation(sK0)))
| ~ spl13_3
| ~ spl13_116 ),
inference(resolution,[],[f1039,f176]) ).
fof(f176,plain,
( empty(empty_set)
| ~ spl13_3 ),
inference(avatar_component_clause,[],[f174]) ).
fof(f1039,plain,
( ! [X0] :
( ~ empty(X0)
| relation_dom(relation_composition(sK2,identity_relation(sK0))) = X0 )
| ~ spl13_116 ),
inference(avatar_component_clause,[],[f1038]) ).
fof(f1566,plain,
( ~ spl13_73
| ~ spl13_74
| ~ spl13_1
| ~ spl13_2
| ~ spl13_15
| spl13_14
| ~ spl13_55
| ~ spl13_75 ),
inference(avatar_split_clause,[],[f596,f588,f468,f229,f233,f169,f164,f584,f580]) ).
fof(f468,plain,
( spl13_55
<=> ! [X2,X0,X1] :
( in(X0,relation_dom(relation_composition(X2,X1)))
| ~ in(apply(X2,X0),relation_dom(X1))
| ~ in(X0,relation_dom(X2))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_55])]) ).
fof(f596,plain,
( in(sK1,relation_dom(relation_composition(sK2,identity_relation(sK0))))
| ~ in(sK1,relation_dom(sK2))
| ~ function(sK2)
| ~ relation(sK2)
| ~ function(identity_relation(sK0))
| ~ relation(identity_relation(sK0))
| ~ spl13_55
| ~ spl13_75 ),
inference(resolution,[],[f590,f469]) ).
fof(f469,plain,
( ! [X2,X0,X1] :
( ~ in(apply(X2,X0),relation_dom(X1))
| in(X0,relation_dom(relation_composition(X2,X1)))
| ~ in(X0,relation_dom(X2))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) )
| ~ spl13_55 ),
inference(avatar_component_clause,[],[f468]) ).
fof(f1543,plain,
( ~ spl13_6
| spl13_58
| ~ spl13_115 ),
inference(avatar_split_clause,[],[f1542,f1012,f482,f189]) ).
fof(f189,plain,
( spl13_6
<=> empty(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_6])]) ).
fof(f482,plain,
( spl13_58
<=> empty(relation_dom(relation_composition(sK2,identity_relation(sK0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_58])]) ).
fof(f1012,plain,
( spl13_115
<=> relation_dom(relation_composition(sK2,identity_relation(sK0))) = sK8 ),
introduced(avatar_definition,[new_symbols(naming,[spl13_115])]) ).
fof(f1542,plain,
( ~ empty(sK8)
| spl13_58
| ~ spl13_115 ),
inference(forward_demodulation,[],[f484,f1014]) ).
fof(f1014,plain,
( relation_dom(relation_composition(sK2,identity_relation(sK0))) = sK8
| ~ spl13_115 ),
inference(avatar_component_clause,[],[f1012]) ).
fof(f484,plain,
( ~ empty(relation_dom(relation_composition(sK2,identity_relation(sK0))))
| spl13_58 ),
inference(avatar_component_clause,[],[f482]) ).
fof(f1537,plain,
( ~ spl13_1
| ~ spl13_73
| ~ spl13_44
| spl13_118 ),
inference(avatar_split_clause,[],[f1054,f1048,f386,f580,f164]) ).
fof(f386,plain,
( spl13_44
<=> ! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_44])]) ).
fof(f1048,plain,
( spl13_118
<=> relation(relation_composition(sK2,identity_relation(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_118])]) ).
fof(f1054,plain,
( ~ relation(identity_relation(sK0))
| ~ relation(sK2)
| ~ spl13_44
| spl13_118 ),
inference(resolution,[],[f1050,f387]) ).
fof(f387,plain,
( ! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl13_44 ),
inference(avatar_component_clause,[],[f386]) ).
fof(f1050,plain,
( ~ relation(relation_composition(sK2,identity_relation(sK0)))
| spl13_118 ),
inference(avatar_component_clause,[],[f1048]) ).
fof(f1536,plain,
( spl13_152
| ~ spl13_82
| ~ spl13_95 ),
inference(avatar_split_clause,[],[f805,f773,f682,f1534]) ).
fof(f1534,plain,
( spl13_152
<=> ! [X0] :
( element(sK4(sK3(X0)),X0)
| empty(X0)
| empty(sK3(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_152])]) ).
fof(f682,plain,
( spl13_82
<=> ! [X0] :
( empty(X0)
| in(sK4(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_82])]) ).
fof(f773,plain,
( spl13_95
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK3(X1))
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_95])]) ).
fof(f805,plain,
( ! [X0] :
( element(sK4(sK3(X0)),X0)
| empty(X0)
| empty(sK3(X0)) )
| ~ spl13_82
| ~ spl13_95 ),
inference(resolution,[],[f774,f683]) ).
fof(f683,plain,
( ! [X0] :
( in(sK4(X0),X0)
| empty(X0) )
| ~ spl13_82 ),
inference(avatar_component_clause,[],[f682]) ).
fof(f774,plain,
( ! [X0,X1] :
( ~ in(X0,sK3(X1))
| element(X0,X1)
| empty(X1) )
| ~ spl13_95 ),
inference(avatar_component_clause,[],[f773]) ).
fof(f1532,plain,
( spl13_151
| ~ spl13_28
| ~ spl13_93 ),
inference(avatar_split_clause,[],[f795,f765,f295,f1530]) ).
fof(f1530,plain,
( spl13_151
<=> ! [X0,X1] :
( sK8 = relation_composition(X0,relation_dom(X1))
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_151])]) ).
fof(f295,plain,
( spl13_28
<=> ! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_28])]) ).
fof(f765,plain,
( spl13_93
<=> ! [X0,X1] :
( relation_composition(X1,X0) = sK8
| ~ relation(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_93])]) ).
fof(f795,plain,
( ! [X0,X1] :
( sK8 = relation_composition(X0,relation_dom(X1))
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl13_28
| ~ spl13_93 ),
inference(resolution,[],[f766,f296]) ).
fof(f296,plain,
( ! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) )
| ~ spl13_28 ),
inference(avatar_component_clause,[],[f295]) ).
fof(f766,plain,
( ! [X0,X1] :
( ~ relation(X0)
| relation_composition(X1,X0) = sK8
| ~ empty(X1) )
| ~ spl13_93 ),
inference(avatar_component_clause,[],[f765]) ).
fof(f1528,plain,
( spl13_150
| ~ spl13_28
| ~ spl13_92 ),
inference(avatar_split_clause,[],[f781,f761,f295,f1526]) ).
fof(f1526,plain,
( spl13_150
<=> ! [X0,X1] :
( sK8 = relation_composition(relation_dom(X0),X1)
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_150])]) ).
fof(f761,plain,
( spl13_92
<=> ! [X0,X1] :
( relation_composition(X0,X1) = sK8
| ~ relation(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_92])]) ).
fof(f781,plain,
( ! [X0,X1] :
( sK8 = relation_composition(relation_dom(X0),X1)
| ~ empty(X1)
| ~ empty(X0) )
| ~ spl13_28
| ~ spl13_92 ),
inference(resolution,[],[f762,f296]) ).
fof(f762,plain,
( ! [X0,X1] :
( ~ relation(X0)
| relation_composition(X0,X1) = sK8
| ~ empty(X1) )
| ~ spl13_92 ),
inference(avatar_component_clause,[],[f761]) ).
fof(f1524,plain,
( spl13_149
| ~ spl13_82
| ~ spl13_89 ),
inference(avatar_split_clause,[],[f753,f731,f682,f1522]) ).
fof(f1522,plain,
( spl13_149
<=> ! [X0] :
( element(sK4(sK4(powerset(X0))),X0)
| empty(sK4(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_149])]) ).
fof(f731,plain,
( spl13_89
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK4(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_89])]) ).
fof(f753,plain,
( ! [X0] :
( element(sK4(sK4(powerset(X0))),X0)
| empty(sK4(powerset(X0))) )
| ~ spl13_82
| ~ spl13_89 ),
inference(resolution,[],[f732,f683]) ).
fof(f732,plain,
( ! [X0,X1] :
( ~ in(X0,sK4(powerset(X1)))
| element(X0,X1) )
| ~ spl13_89 ),
inference(avatar_component_clause,[],[f731]) ).
fof(f1520,plain,
( spl13_148
| ~ spl13_40
| ~ spl13_81 ),
inference(avatar_split_clause,[],[f686,f678,f369,f1518]) ).
fof(f1518,plain,
( spl13_148
<=> ! [X0,X1] :
( sK8 = relation_dom(relation_composition(X0,X1))
| ~ relation(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_148])]) ).
fof(f369,plain,
( spl13_40
<=> ! [X0,X1] :
( empty(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_40])]) ).
fof(f678,plain,
( spl13_81
<=> ! [X0] :
( relation_dom(X0) = sK8
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_81])]) ).
fof(f686,plain,
( ! [X0,X1] :
( sK8 = relation_dom(relation_composition(X0,X1))
| ~ relation(X0)
| ~ empty(X1) )
| ~ spl13_40
| ~ spl13_81 ),
inference(resolution,[],[f679,f370]) ).
fof(f370,plain,
( ! [X0,X1] :
( empty(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) )
| ~ spl13_40 ),
inference(avatar_component_clause,[],[f369]) ).
fof(f679,plain,
( ! [X0] :
( ~ empty(X0)
| relation_dom(X0) = sK8 )
| ~ spl13_81 ),
inference(avatar_component_clause,[],[f678]) ).
fof(f1516,plain,
( spl13_147
| ~ spl13_42
| ~ spl13_81 ),
inference(avatar_split_clause,[],[f685,f678,f377,f1514]) ).
fof(f1514,plain,
( spl13_147
<=> ! [X0,X1] :
( sK8 = relation_dom(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_147])]) ).
fof(f377,plain,
( spl13_42
<=> ! [X0,X1] :
( empty(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_42])]) ).
fof(f685,plain,
( ! [X0,X1] :
( sK8 = relation_dom(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) )
| ~ spl13_42
| ~ spl13_81 ),
inference(resolution,[],[f679,f378]) ).
fof(f378,plain,
( ! [X0,X1] :
( empty(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) )
| ~ spl13_42 ),
inference(avatar_component_clause,[],[f377]) ).
fof(f1356,plain,
( spl13_146
| ~ spl13_19
| ~ spl13_100 ),
inference(avatar_split_clause,[],[f864,f857,f251,f1354]) ).
fof(f1354,plain,
( spl13_146
<=> ! [X0,X1] :
( ~ in(X0,X1)
| apply(identity_relation(X1),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_146])]) ).
fof(f857,plain,
( spl13_100
<=> ! [X0,X1] :
( ~ in(X0,X1)
| ~ function(identity_relation(X1))
| apply(identity_relation(X1),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_100])]) ).
fof(f864,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| apply(identity_relation(X1),X0) = X0 )
| ~ spl13_19
| ~ spl13_100 ),
inference(resolution,[],[f858,f252]) ).
fof(f858,plain,
( ! [X0,X1] :
( ~ function(identity_relation(X1))
| ~ in(X0,X1)
| apply(identity_relation(X1),X0) = X0 )
| ~ spl13_100 ),
inference(avatar_component_clause,[],[f857]) ).
fof(f1352,plain,
( spl13_145
| ~ spl13_4
| ~ spl13_69
| ~ spl13_99 ),
inference(avatar_split_clause,[],[f854,f825,f553,f179,f1350]) ).
fof(f1350,plain,
( spl13_145
<=> ! [X0,X1] :
( relation_composition(X0,sK8) = X1
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_145])]) ).
fof(f179,plain,
( spl13_4
<=> relation(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_4])]) ).
fof(f825,plain,
( spl13_99
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| relation_composition(X1,X0) = X2
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_99])]) ).
fof(f854,plain,
( ! [X0,X1] :
( relation_composition(X0,sK8) = X1
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl13_4
| ~ spl13_69
| ~ spl13_99 ),
inference(forward_demodulation,[],[f846,f555]) ).
fof(f846,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_composition(X0,empty_set) = X1
| ~ empty(X1) )
| ~ spl13_4
| ~ spl13_99 ),
inference(resolution,[],[f826,f181]) ).
fof(f181,plain,
( relation(empty_set)
| ~ spl13_4 ),
inference(avatar_component_clause,[],[f179]) ).
fof(f826,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| relation_composition(X1,X0) = X2
| ~ empty(X2) )
| ~ spl13_99 ),
inference(avatar_component_clause,[],[f825]) ).
fof(f1348,plain,
( spl13_144
| ~ spl13_12
| ~ spl13_99 ),
inference(avatar_split_clause,[],[f853,f825,f219,f1346]) ).
fof(f1346,plain,
( spl13_144
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_composition(X0,sK12) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_144])]) ).
fof(f219,plain,
( spl13_12
<=> relation(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_12])]) ).
fof(f853,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_composition(X0,sK12) = X1
| ~ empty(X1) )
| ~ spl13_12
| ~ spl13_99 ),
inference(resolution,[],[f826,f221]) ).
fof(f221,plain,
( relation(sK12)
| ~ spl13_12 ),
inference(avatar_component_clause,[],[f219]) ).
fof(f1344,plain,
( spl13_143
| ~ spl13_11
| ~ spl13_99 ),
inference(avatar_split_clause,[],[f852,f825,f214,f1342]) ).
fof(f1342,plain,
( spl13_143
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_composition(X0,sK11) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_143])]) ).
fof(f214,plain,
( spl13_11
<=> relation(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_11])]) ).
fof(f852,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_composition(X0,sK11) = X1
| ~ empty(X1) )
| ~ spl13_11
| ~ spl13_99 ),
inference(resolution,[],[f826,f216]) ).
fof(f216,plain,
( relation(sK11)
| ~ spl13_11 ),
inference(avatar_component_clause,[],[f214]) ).
fof(f1340,plain,
( spl13_142
| ~ spl13_3
| ~ spl13_69
| ~ spl13_109 ),
inference(avatar_split_clause,[],[f943,f923,f553,f174,f1337]) ).
fof(f1337,plain,
( spl13_142
<=> sK8 = relation_composition(sK8,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_142])]) ).
fof(f923,plain,
( spl13_109
<=> ! [X0] :
( sK8 = relation_composition(X0,sK2)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_109])]) ).
fof(f943,plain,
( sK8 = relation_composition(sK8,sK2)
| ~ spl13_3
| ~ spl13_69
| ~ spl13_109 ),
inference(forward_demodulation,[],[f938,f555]) ).
fof(f938,plain,
( sK8 = relation_composition(empty_set,sK2)
| ~ spl13_3
| ~ spl13_109 ),
inference(resolution,[],[f924,f176]) ).
fof(f924,plain,
( ! [X0] :
( ~ empty(X0)
| sK8 = relation_composition(X0,sK2) )
| ~ spl13_109 ),
inference(avatar_component_clause,[],[f923]) ).
fof(f1335,plain,
( spl13_141
| ~ spl13_8
| ~ spl13_99 ),
inference(avatar_split_clause,[],[f850,f825,f199,f1333]) ).
fof(f1333,plain,
( spl13_141
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_composition(X0,sK9) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_141])]) ).
fof(f199,plain,
( spl13_8
<=> relation(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_8])]) ).
fof(f850,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_composition(X0,sK9) = X1
| ~ empty(X1) )
| ~ spl13_8
| ~ spl13_99 ),
inference(resolution,[],[f826,f201]) ).
fof(f201,plain,
( relation(sK9)
| ~ spl13_8 ),
inference(avatar_component_clause,[],[f199]) ).
fof(f1331,plain,
( spl13_140
| ~ spl13_4
| ~ spl13_69
| ~ spl13_98 ),
inference(avatar_split_clause,[],[f840,f821,f553,f179,f1329]) ).
fof(f1329,plain,
( spl13_140
<=> ! [X0,X1] :
( relation_composition(sK8,X0) = X1
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_140])]) ).
fof(f821,plain,
( spl13_98
<=> ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| relation_composition(X0,X1) = X2
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_98])]) ).
fof(f840,plain,
( ! [X0,X1] :
( relation_composition(sK8,X0) = X1
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl13_4
| ~ spl13_69
| ~ spl13_98 ),
inference(forward_demodulation,[],[f832,f555]) ).
fof(f832,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_composition(empty_set,X0) = X1
| ~ empty(X1) )
| ~ spl13_4
| ~ spl13_98 ),
inference(resolution,[],[f822,f181]) ).
fof(f822,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| relation_composition(X0,X1) = X2
| ~ empty(X2) )
| ~ spl13_98 ),
inference(avatar_component_clause,[],[f821]) ).
fof(f1327,plain,
( spl13_139
| ~ spl13_12
| ~ spl13_98 ),
inference(avatar_split_clause,[],[f839,f821,f219,f1325]) ).
fof(f1325,plain,
( spl13_139
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_composition(sK12,X0) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_139])]) ).
fof(f839,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_composition(sK12,X0) = X1
| ~ empty(X1) )
| ~ spl13_12
| ~ spl13_98 ),
inference(resolution,[],[f822,f221]) ).
fof(f1323,plain,
( spl13_138
| ~ spl13_11
| ~ spl13_98 ),
inference(avatar_split_clause,[],[f838,f821,f214,f1321]) ).
fof(f1321,plain,
( spl13_138
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_composition(sK11,X0) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_138])]) ).
fof(f838,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_composition(sK11,X0) = X1
| ~ empty(X1) )
| ~ spl13_11
| ~ spl13_98 ),
inference(resolution,[],[f822,f216]) ).
fof(f1319,plain,
( spl13_137
| ~ spl13_8
| ~ spl13_98 ),
inference(avatar_split_clause,[],[f836,f821,f199,f1317]) ).
fof(f1317,plain,
( spl13_137
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_composition(sK9,X0) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_137])]) ).
fof(f836,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_composition(sK9,X0) = X1
| ~ empty(X1) )
| ~ spl13_8
| ~ spl13_98 ),
inference(resolution,[],[f822,f201]) ).
fof(f1315,plain,
( spl13_136
| ~ spl13_27
| ~ spl13_85 ),
inference(avatar_split_clause,[],[f741,f714,f291,f1313]) ).
fof(f1313,plain,
( spl13_136
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_dom(relation_dom(X1)) = X0
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_136])]) ).
fof(f291,plain,
( spl13_27
<=> ! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_27])]) ).
fof(f714,plain,
( spl13_85
<=> ! [X0,X1] :
( relation_dom(X1) = X0
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_85])]) ).
fof(f741,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_dom(relation_dom(X1)) = X0
| ~ empty(X1) )
| ~ spl13_27
| ~ spl13_85 ),
inference(resolution,[],[f715,f292]) ).
fof(f292,plain,
( ! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) )
| ~ spl13_27 ),
inference(avatar_component_clause,[],[f291]) ).
fof(f715,plain,
( ! [X0,X1] :
( ~ empty(X1)
| ~ empty(X0)
| relation_dom(X1) = X0 )
| ~ spl13_85 ),
inference(avatar_component_clause,[],[f714]) ).
fof(f1285,plain,
( spl13_135
| ~ spl13_18
| ~ spl13_93 ),
inference(avatar_split_clause,[],[f793,f765,f247,f1283]) ).
fof(f1283,plain,
( spl13_135
<=> ! [X0,X1] :
( sK8 = relation_composition(X0,identity_relation(X1))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_135])]) ).
fof(f247,plain,
( spl13_18
<=> ! [X0] : relation(identity_relation(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_18])]) ).
fof(f793,plain,
( ! [X0,X1] :
( sK8 = relation_composition(X0,identity_relation(X1))
| ~ empty(X0) )
| ~ spl13_18
| ~ spl13_93 ),
inference(resolution,[],[f766,f248]) ).
fof(f248,plain,
( ! [X0] : relation(identity_relation(X0))
| ~ spl13_18 ),
inference(avatar_component_clause,[],[f247]) ).
fof(f1281,plain,
( spl13_134
| ~ spl13_18
| ~ spl13_92 ),
inference(avatar_split_clause,[],[f779,f761,f247,f1279]) ).
fof(f1279,plain,
( spl13_134
<=> ! [X0,X1] :
( sK8 = relation_composition(identity_relation(X0),X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_134])]) ).
fof(f779,plain,
( ! [X0,X1] :
( sK8 = relation_composition(identity_relation(X0),X1)
| ~ empty(X1) )
| ~ spl13_18
| ~ spl13_92 ),
inference(resolution,[],[f762,f248]) ).
fof(f1155,plain,
( spl13_133
| ~ spl13_4
| ~ spl13_69
| ~ spl13_93 ),
inference(avatar_split_clause,[],[f802,f765,f553,f179,f1153]) ).
fof(f1153,plain,
( spl13_133
<=> ! [X0] :
( sK8 = relation_composition(X0,sK8)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_133])]) ).
fof(f802,plain,
( ! [X0] :
( sK8 = relation_composition(X0,sK8)
| ~ empty(X0) )
| ~ spl13_4
| ~ spl13_69
| ~ spl13_93 ),
inference(forward_demodulation,[],[f794,f555]) ).
fof(f794,plain,
( ! [X0] :
( sK8 = relation_composition(X0,empty_set)
| ~ empty(X0) )
| ~ spl13_4
| ~ spl13_93 ),
inference(resolution,[],[f766,f181]) ).
fof(f1150,plain,
( spl13_132
| ~ spl13_12
| ~ spl13_93 ),
inference(avatar_split_clause,[],[f801,f765,f219,f1148]) ).
fof(f1148,plain,
( spl13_132
<=> ! [X0] :
( sK8 = relation_composition(X0,sK12)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_132])]) ).
fof(f801,plain,
( ! [X0] :
( sK8 = relation_composition(X0,sK12)
| ~ empty(X0) )
| ~ spl13_12
| ~ spl13_93 ),
inference(resolution,[],[f766,f221]) ).
fof(f1146,plain,
( spl13_131
| ~ spl13_11
| ~ spl13_93 ),
inference(avatar_split_clause,[],[f800,f765,f214,f1144]) ).
fof(f1144,plain,
( spl13_131
<=> ! [X0] :
( sK8 = relation_composition(X0,sK11)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_131])]) ).
fof(f800,plain,
( ! [X0] :
( sK8 = relation_composition(X0,sK11)
| ~ empty(X0) )
| ~ spl13_11
| ~ spl13_93 ),
inference(resolution,[],[f766,f216]) ).
fof(f1142,plain,
( spl13_130
| ~ spl13_8
| ~ spl13_93 ),
inference(avatar_split_clause,[],[f798,f765,f199,f1140]) ).
fof(f1140,plain,
( spl13_130
<=> ! [X0] :
( sK8 = relation_composition(X0,sK9)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_130])]) ).
fof(f798,plain,
( ! [X0] :
( sK8 = relation_composition(X0,sK9)
| ~ empty(X0) )
| ~ spl13_8
| ~ spl13_93 ),
inference(resolution,[],[f766,f201]) ).
fof(f1138,plain,
( spl13_129
| ~ spl13_4
| ~ spl13_69
| ~ spl13_92 ),
inference(avatar_split_clause,[],[f788,f761,f553,f179,f1136]) ).
fof(f1136,plain,
( spl13_129
<=> ! [X0] :
( sK8 = relation_composition(sK8,X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_129])]) ).
fof(f788,plain,
( ! [X0] :
( sK8 = relation_composition(sK8,X0)
| ~ empty(X0) )
| ~ spl13_4
| ~ spl13_69
| ~ spl13_92 ),
inference(forward_demodulation,[],[f780,f555]) ).
fof(f780,plain,
( ! [X0] :
( sK8 = relation_composition(empty_set,X0)
| ~ empty(X0) )
| ~ spl13_4
| ~ spl13_92 ),
inference(resolution,[],[f762,f181]) ).
fof(f1134,plain,
( spl13_128
| ~ spl13_12
| ~ spl13_92 ),
inference(avatar_split_clause,[],[f787,f761,f219,f1132]) ).
fof(f1132,plain,
( spl13_128
<=> ! [X0] :
( sK8 = relation_composition(sK12,X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_128])]) ).
fof(f787,plain,
( ! [X0] :
( sK8 = relation_composition(sK12,X0)
| ~ empty(X0) )
| ~ spl13_12
| ~ spl13_92 ),
inference(resolution,[],[f762,f221]) ).
fof(f1130,plain,
( spl13_127
| ~ spl13_11
| ~ spl13_92 ),
inference(avatar_split_clause,[],[f786,f761,f214,f1128]) ).
fof(f1128,plain,
( spl13_127
<=> ! [X0] :
( sK8 = relation_composition(sK11,X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_127])]) ).
fof(f786,plain,
( ! [X0] :
( sK8 = relation_composition(sK11,X0)
| ~ empty(X0) )
| ~ spl13_11
| ~ spl13_92 ),
inference(resolution,[],[f762,f216]) ).
fof(f1126,plain,
( spl13_126
| ~ spl13_8
| ~ spl13_92 ),
inference(avatar_split_clause,[],[f784,f761,f199,f1124]) ).
fof(f1124,plain,
( spl13_126
<=> ! [X0] :
( sK8 = relation_composition(sK9,X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_126])]) ).
fof(f784,plain,
( ! [X0] :
( sK8 = relation_composition(sK9,X0)
| ~ empty(X0) )
| ~ spl13_8
| ~ spl13_92 ),
inference(resolution,[],[f762,f201]) ).
fof(f1122,plain,
( spl13_125
| ~ spl13_27
| ~ spl13_81 ),
inference(avatar_split_clause,[],[f688,f678,f291,f1120]) ).
fof(f1120,plain,
( spl13_125
<=> ! [X0] :
( sK8 = relation_dom(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_125])]) ).
fof(f688,plain,
( ! [X0] :
( sK8 = relation_dom(relation_dom(X0))
| ~ empty(X0) )
| ~ spl13_27
| ~ spl13_81 ),
inference(resolution,[],[f679,f292]) ).
fof(f1108,plain,
( ~ spl13_124
| spl13_59
| ~ spl13_115 ),
inference(avatar_split_clause,[],[f1019,f1012,f488,f1105]) ).
fof(f1105,plain,
( spl13_124
<=> in(sK8,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_124])]) ).
fof(f488,plain,
( spl13_59
<=> in(relation_dom(relation_composition(sK2,identity_relation(sK0))),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_59])]) ).
fof(f1019,plain,
( ~ in(sK8,sK1)
| spl13_59
| ~ spl13_115 ),
inference(superposition,[],[f490,f1014]) ).
fof(f490,plain,
( ~ in(relation_dom(relation_composition(sK2,identity_relation(sK0))),sK1)
| spl13_59 ),
inference(avatar_component_clause,[],[f488]) ).
fof(f1103,plain,
( spl13_123
| ~ spl13_82
| ~ spl13_84 ),
inference(avatar_split_clause,[],[f712,f706,f682,f1101]) ).
fof(f1101,plain,
( spl13_123
<=> ! [X0] :
( ~ empty(X0)
| empty(sK4(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_123])]) ).
fof(f706,plain,
( spl13_84
<=> ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK4(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_84])]) ).
fof(f712,plain,
( ! [X0] :
( ~ empty(X0)
| empty(sK4(powerset(X0))) )
| ~ spl13_82
| ~ spl13_84 ),
inference(resolution,[],[f707,f683]) ).
fof(f707,plain,
( ! [X0,X1] :
( ~ in(X1,sK4(powerset(X0)))
| ~ empty(X0) )
| ~ spl13_84 ),
inference(avatar_component_clause,[],[f706]) ).
fof(f1099,plain,
( spl13_122
| ~ spl13_32
| ~ spl13_82 ),
inference(avatar_split_clause,[],[f697,f682,f324,f1097]) ).
fof(f1097,plain,
( spl13_122
<=> ! [X0] :
( empty(X0)
| ~ in(X0,sK4(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_122])]) ).
fof(f324,plain,
( spl13_32
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_32])]) ).
fof(f697,plain,
( ! [X0] :
( empty(X0)
| ~ in(X0,sK4(X0)) )
| ~ spl13_32
| ~ spl13_82 ),
inference(resolution,[],[f683,f325]) ).
fof(f325,plain,
( ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) )
| ~ spl13_32 ),
inference(avatar_component_clause,[],[f324]) ).
fof(f1082,plain,
( spl13_121
| ~ spl13_19
| ~ spl13_90 ),
inference(avatar_split_clause,[],[f759,f735,f251,f1080]) ).
fof(f1080,plain,
( spl13_121
<=> ! [X0] : relation_dom(identity_relation(X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl13_121])]) ).
fof(f1063,plain,
( spl13_120
| ~ spl13_3
| ~ spl13_69
| ~ spl13_81 ),
inference(avatar_split_clause,[],[f692,f678,f553,f174,f1060]) ).
fof(f1060,plain,
( spl13_120
<=> sK8 = relation_dom(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_120])]) ).
fof(f692,plain,
( sK8 = relation_dom(sK8)
| ~ spl13_3
| ~ spl13_69
| ~ spl13_81 ),
inference(forward_demodulation,[],[f687,f555]) ).
fof(f687,plain,
( sK8 = relation_dom(empty_set)
| ~ spl13_3
| ~ spl13_81 ),
inference(resolution,[],[f679,f176]) ).
fof(f1058,plain,
( spl13_119
| ~ spl13_29
| ~ spl13_72 ),
inference(avatar_split_clause,[],[f577,f572,f299,f1056]) ).
fof(f1056,plain,
( spl13_119
<=> ! [X0] : element(sK8,powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_119])]) ).
fof(f299,plain,
( spl13_29
<=> ! [X0] : element(sK5(X0),powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_29])]) ).
fof(f572,plain,
( spl13_72
<=> ! [X0] : sK5(X0) = sK8 ),
introduced(avatar_definition,[new_symbols(naming,[spl13_72])]) ).
fof(f577,plain,
( ! [X0] : element(sK8,powerset(X0))
| ~ spl13_29
| ~ spl13_72 ),
inference(superposition,[],[f300,f573]) ).
fof(f573,plain,
( ! [X0] : sK5(X0) = sK8
| ~ spl13_72 ),
inference(avatar_component_clause,[],[f572]) ).
fof(f300,plain,
( ! [X0] : element(sK5(X0),powerset(X0))
| ~ spl13_29 ),
inference(avatar_component_clause,[],[f299]) ).
fof(f1051,plain,
( spl13_66
| ~ spl13_118
| ~ spl13_35
| ~ spl13_58 ),
inference(avatar_split_clause,[],[f981,f482,f340,f1048,f537]) ).
fof(f537,plain,
( spl13_66
<=> empty(relation_composition(sK2,identity_relation(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_66])]) ).
fof(f340,plain,
( spl13_35
<=> ! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_35])]) ).
fof(f981,plain,
( ~ relation(relation_composition(sK2,identity_relation(sK0)))
| empty(relation_composition(sK2,identity_relation(sK0)))
| ~ spl13_35
| ~ spl13_58 ),
inference(resolution,[],[f483,f341]) ).
fof(f341,plain,
( ! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) )
| ~ spl13_35 ),
inference(avatar_component_clause,[],[f340]) ).
fof(f483,plain,
( empty(relation_dom(relation_composition(sK2,identity_relation(sK0))))
| ~ spl13_58 ),
inference(avatar_component_clause,[],[f482]) ).
fof(f1046,plain,
( spl13_117
| ~ spl13_60
| ~ spl13_115 ),
inference(avatar_split_clause,[],[f1018,f1012,f493,f1043]) ).
fof(f1043,plain,
( spl13_117
<=> element(sK1,sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_117])]) ).
fof(f1018,plain,
( element(sK1,sK8)
| ~ spl13_60
| ~ spl13_115 ),
inference(superposition,[],[f495,f1014]) ).
fof(f495,plain,
( element(sK1,relation_dom(relation_composition(sK2,identity_relation(sK0))))
| ~ spl13_60 ),
inference(avatar_component_clause,[],[f493]) ).
fof(f1040,plain,
( spl13_116
| ~ spl13_38
| ~ spl13_58 ),
inference(avatar_split_clause,[],[f984,f482,f353,f1038]) ).
fof(f353,plain,
( spl13_38
<=> ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_38])]) ).
fof(f984,plain,
( ! [X0] :
( relation_dom(relation_composition(sK2,identity_relation(sK0))) = X0
| ~ empty(X0) )
| ~ spl13_38
| ~ spl13_58 ),
inference(resolution,[],[f483,f354]) ).
fof(f354,plain,
( ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) )
| ~ spl13_38 ),
inference(avatar_component_clause,[],[f353]) ).
fof(f1015,plain,
( spl13_115
| ~ spl13_58
| ~ spl13_77 ),
inference(avatar_split_clause,[],[f985,f605,f482,f1012]) ).
fof(f605,plain,
( spl13_77
<=> ! [X0] :
( sK8 = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_77])]) ).
fof(f985,plain,
( relation_dom(relation_composition(sK2,identity_relation(sK0))) = sK8
| ~ spl13_58
| ~ spl13_77 ),
inference(resolution,[],[f483,f606]) ).
fof(f606,plain,
( ! [X0] :
( ~ empty(X0)
| sK8 = X0 )
| ~ spl13_77 ),
inference(avatar_component_clause,[],[f605]) ).
fof(f1009,plain,
( spl13_114
| ~ spl13_23
| ~ spl13_58 ),
inference(avatar_split_clause,[],[f983,f482,f267,f1006]) ).
fof(f1006,plain,
( spl13_114
<=> relation(relation_dom(relation_composition(sK2,identity_relation(sK0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_114])]) ).
fof(f267,plain,
( spl13_23
<=> ! [X0] :
( relation(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_23])]) ).
fof(f983,plain,
( relation(relation_dom(relation_composition(sK2,identity_relation(sK0))))
| ~ spl13_23
| ~ spl13_58 ),
inference(resolution,[],[f483,f268]) ).
fof(f268,plain,
( ! [X0] :
( ~ empty(X0)
| relation(X0) )
| ~ spl13_23 ),
inference(avatar_component_clause,[],[f267]) ).
fof(f1003,plain,
( spl13_113
| ~ spl13_22
| ~ spl13_58 ),
inference(avatar_split_clause,[],[f982,f482,f263,f1000]) ).
fof(f1000,plain,
( spl13_113
<=> function(relation_dom(relation_composition(sK2,identity_relation(sK0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_113])]) ).
fof(f263,plain,
( spl13_22
<=> ! [X0] :
( function(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_22])]) ).
fof(f982,plain,
( function(relation_dom(relation_composition(sK2,identity_relation(sK0))))
| ~ spl13_22
| ~ spl13_58 ),
inference(resolution,[],[f483,f264]) ).
fof(f264,plain,
( ! [X0] :
( ~ empty(X0)
| function(X0) )
| ~ spl13_22 ),
inference(avatar_component_clause,[],[f263]) ).
fof(f979,plain,
( spl13_14
| spl13_58
| ~ spl13_39
| ~ spl13_60 ),
inference(avatar_split_clause,[],[f519,f493,f365,f482,f229]) ).
fof(f365,plain,
( spl13_39
<=> ! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_39])]) ).
fof(f519,plain,
( empty(relation_dom(relation_composition(sK2,identity_relation(sK0))))
| in(sK1,relation_dom(relation_composition(sK2,identity_relation(sK0))))
| ~ spl13_39
| ~ spl13_60 ),
inference(resolution,[],[f495,f366]) ).
fof(f366,plain,
( ! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) )
| ~ spl13_39 ),
inference(avatar_component_clause,[],[f365]) ).
fof(f958,plain,
( spl13_112
| ~ spl13_1
| ~ spl13_99 ),
inference(avatar_split_clause,[],[f848,f825,f164,f956]) ).
fof(f956,plain,
( spl13_112
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_composition(X0,sK2) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_112])]) ).
fof(f848,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_composition(X0,sK2) = X1
| ~ empty(X1) )
| ~ spl13_1
| ~ spl13_99 ),
inference(resolution,[],[f826,f166]) ).
fof(f166,plain,
( relation(sK2)
| ~ spl13_1 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f954,plain,
( spl13_111
| ~ spl13_3
| ~ spl13_69
| ~ spl13_108 ),
inference(avatar_split_clause,[],[f933,f919,f553,f174,f951]) ).
fof(f951,plain,
( spl13_111
<=> sK8 = relation_composition(sK2,sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_111])]) ).
fof(f919,plain,
( spl13_108
<=> ! [X0] :
( sK8 = relation_composition(sK2,X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_108])]) ).
fof(f933,plain,
( sK8 = relation_composition(sK2,sK8)
| ~ spl13_3
| ~ spl13_69
| ~ spl13_108 ),
inference(forward_demodulation,[],[f928,f555]) ).
fof(f928,plain,
( sK8 = relation_composition(sK2,empty_set)
| ~ spl13_3
| ~ spl13_108 ),
inference(resolution,[],[f920,f176]) ).
fof(f920,plain,
( ! [X0] :
( ~ empty(X0)
| sK8 = relation_composition(sK2,X0) )
| ~ spl13_108 ),
inference(avatar_component_clause,[],[f919]) ).
fof(f949,plain,
( spl13_110
| ~ spl13_1
| ~ spl13_98 ),
inference(avatar_split_clause,[],[f834,f821,f164,f947]) ).
fof(f947,plain,
( spl13_110
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_composition(sK2,X0) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_110])]) ).
fof(f834,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_composition(sK2,X0) = X1
| ~ empty(X1) )
| ~ spl13_1
| ~ spl13_98 ),
inference(resolution,[],[f822,f166]) ).
fof(f925,plain,
( spl13_109
| ~ spl13_1
| ~ spl13_93 ),
inference(avatar_split_clause,[],[f796,f765,f164,f923]) ).
fof(f796,plain,
( ! [X0] :
( sK8 = relation_composition(X0,sK2)
| ~ empty(X0) )
| ~ spl13_1
| ~ spl13_93 ),
inference(resolution,[],[f766,f166]) ).
fof(f921,plain,
( spl13_108
| ~ spl13_1
| ~ spl13_92 ),
inference(avatar_split_clause,[],[f782,f761,f164,f919]) ).
fof(f782,plain,
( ! [X0] :
( sK8 = relation_composition(sK2,X0)
| ~ empty(X0) )
| ~ spl13_1
| ~ spl13_92 ),
inference(resolution,[],[f762,f166]) ).
fof(f913,plain,
( ~ spl13_16
| ~ spl13_19
| spl13_75
| ~ spl13_90 ),
inference(avatar_split_clause,[],[f903,f735,f588,f251,f238]) ).
fof(f903,plain,
( ~ in(apply(sK2,sK1),sK0)
| ~ spl13_19
| spl13_75
| ~ spl13_90 ),
inference(forward_demodulation,[],[f589,f759]) ).
fof(f589,plain,
( ~ in(apply(sK2,sK1),relation_dom(identity_relation(sK0)))
| spl13_75 ),
inference(avatar_component_clause,[],[f588]) ).
fof(f911,plain,
( ~ spl13_107
| ~ spl13_16
| ~ spl13_32 ),
inference(avatar_split_clause,[],[f501,f324,f238,f908]) ).
fof(f908,plain,
( spl13_107
<=> in(sK0,apply(sK2,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_107])]) ).
fof(f501,plain,
( ~ in(sK0,apply(sK2,sK1))
| ~ spl13_16
| ~ spl13_32 ),
inference(resolution,[],[f240,f325]) ).
fof(f240,plain,
( in(apply(sK2,sK1),sK0)
| ~ spl13_16 ),
inference(avatar_component_clause,[],[f238]) ).
fof(f901,plain,
( spl13_106
| ~ spl13_33
| ~ spl13_75 ),
inference(avatar_split_clause,[],[f597,f588,f328,f898]) ).
fof(f898,plain,
( spl13_106
<=> element(apply(sK2,sK1),relation_dom(identity_relation(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_106])]) ).
fof(f597,plain,
( element(apply(sK2,sK1),relation_dom(identity_relation(sK0)))
| ~ spl13_33
| ~ spl13_75 ),
inference(resolution,[],[f590,f329]) ).
fof(f889,plain,
( spl13_105
| ~ spl13_51
| ~ spl13_53 ),
inference(avatar_split_clause,[],[f466,f458,f445,f887]) ).
fof(f887,plain,
( spl13_105
<=> ! [X0,X1] :
( in(apply(X0,sK6(relation_dom(relation_composition(X0,X1)),relation_composition(X0,X1))),relation_dom(X1))
| ~ function(X0)
| ~ relation(X0)
| ~ function(X1)
| ~ relation(X1)
| relation_composition(X0,X1) = identity_relation(relation_dom(relation_composition(X0,X1)))
| ~ function(relation_composition(X0,X1))
| ~ relation(relation_composition(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_105])]) ).
fof(f445,plain,
( spl13_51
<=> ! [X1] :
( identity_relation(relation_dom(X1)) = X1
| in(sK6(relation_dom(X1),X1),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_51])]) ).
fof(f458,plain,
( spl13_53
<=> ! [X2,X0,X1] :
( in(apply(X2,X0),relation_dom(X1))
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_53])]) ).
fof(f466,plain,
( ! [X0,X1] :
( in(apply(X0,sK6(relation_dom(relation_composition(X0,X1)),relation_composition(X0,X1))),relation_dom(X1))
| ~ function(X0)
| ~ relation(X0)
| ~ function(X1)
| ~ relation(X1)
| relation_composition(X0,X1) = identity_relation(relation_dom(relation_composition(X0,X1)))
| ~ function(relation_composition(X0,X1))
| ~ relation(relation_composition(X0,X1)) )
| ~ spl13_51
| ~ spl13_53 ),
inference(resolution,[],[f459,f446]) ).
fof(f446,plain,
( ! [X1] :
( in(sK6(relation_dom(X1),X1),relation_dom(X1))
| identity_relation(relation_dom(X1)) = X1
| ~ function(X1)
| ~ relation(X1) )
| ~ spl13_51 ),
inference(avatar_component_clause,[],[f445]) ).
fof(f459,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_dom(relation_composition(X2,X1)))
| in(apply(X2,X0),relation_dom(X1))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) )
| ~ spl13_53 ),
inference(avatar_component_clause,[],[f458]) ).
fof(f880,plain,
( spl13_104
| ~ spl13_51
| ~ spl13_52 ),
inference(avatar_split_clause,[],[f456,f452,f445,f878]) ).
fof(f878,plain,
( spl13_104
<=> ! [X0,X1] :
( in(sK6(relation_dom(relation_composition(X0,X1)),relation_composition(X0,X1)),relation_dom(X0))
| ~ function(X0)
| ~ relation(X0)
| ~ function(X1)
| ~ relation(X1)
| relation_composition(X0,X1) = identity_relation(relation_dom(relation_composition(X0,X1)))
| ~ function(relation_composition(X0,X1))
| ~ relation(relation_composition(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_104])]) ).
fof(f456,plain,
( ! [X0,X1] :
( in(sK6(relation_dom(relation_composition(X0,X1)),relation_composition(X0,X1)),relation_dom(X0))
| ~ function(X0)
| ~ relation(X0)
| ~ function(X1)
| ~ relation(X1)
| relation_composition(X0,X1) = identity_relation(relation_dom(relation_composition(X0,X1)))
| ~ function(relation_composition(X0,X1))
| ~ relation(relation_composition(X0,X1)) )
| ~ spl13_51
| ~ spl13_52 ),
inference(resolution,[],[f453,f446]) ).
fof(f875,plain,
( spl13_103
| ~ spl13_32
| ~ spl13_51 ),
inference(avatar_split_clause,[],[f449,f445,f324,f873]) ).
fof(f873,plain,
( spl13_103
<=> ! [X0] :
( identity_relation(relation_dom(X0)) = X0
| ~ function(X0)
| ~ relation(X0)
| ~ in(relation_dom(X0),sK6(relation_dom(X0),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_103])]) ).
fof(f449,plain,
( ! [X0] :
( identity_relation(relation_dom(X0)) = X0
| ~ function(X0)
| ~ relation(X0)
| ~ in(relation_dom(X0),sK6(relation_dom(X0),X0)) )
| ~ spl13_32
| ~ spl13_51 ),
inference(resolution,[],[f446,f325]) ).
fof(f871,plain,
( spl13_102
| ~ spl13_33
| ~ spl13_51 ),
inference(avatar_split_clause,[],[f448,f445,f328,f869]) ).
fof(f869,plain,
( spl13_102
<=> ! [X0] :
( identity_relation(relation_dom(X0)) = X0
| ~ function(X0)
| ~ relation(X0)
| element(sK6(relation_dom(X0),X0),relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_102])]) ).
fof(f448,plain,
( ! [X0] :
( identity_relation(relation_dom(X0)) = X0
| ~ function(X0)
| ~ relation(X0)
| element(sK6(relation_dom(X0),X0),relation_dom(X0)) )
| ~ spl13_33
| ~ spl13_51 ),
inference(resolution,[],[f446,f329]) ).
fof(f863,plain,
( spl13_101
| ~ spl13_30
| ~ spl13_51 ),
inference(avatar_split_clause,[],[f450,f445,f303,f861]) ).
fof(f861,plain,
( spl13_101
<=> ! [X0] :
( identity_relation(relation_dom(X0)) = X0
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_101])]) ).
fof(f303,plain,
( spl13_30
<=> ! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_30])]) ).
fof(f450,plain,
( ! [X0] :
( identity_relation(relation_dom(X0)) = X0
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) )
| ~ spl13_30
| ~ spl13_51 ),
inference(resolution,[],[f446,f304]) ).
fof(f304,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) )
| ~ spl13_30 ),
inference(avatar_component_clause,[],[f303]) ).
fof(f859,plain,
( spl13_100
| ~ spl13_18
| ~ spl13_50 ),
inference(avatar_split_clause,[],[f443,f440,f247,f857]) ).
fof(f440,plain,
( spl13_50
<=> ! [X0,X3] :
( apply(identity_relation(X0),X3) = X3
| ~ in(X3,X0)
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_50])]) ).
fof(f443,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| ~ function(identity_relation(X1))
| apply(identity_relation(X1),X0) = X0 )
| ~ spl13_18
| ~ spl13_50 ),
inference(resolution,[],[f441,f248]) ).
fof(f441,plain,
( ! [X3,X0] :
( ~ relation(identity_relation(X0))
| ~ in(X3,X0)
| ~ function(identity_relation(X0))
| apply(identity_relation(X0),X3) = X3 )
| ~ spl13_50 ),
inference(avatar_component_clause,[],[f440]) ).
fof(f827,plain,
( spl13_99
| ~ spl13_38
| ~ spl13_42 ),
inference(avatar_split_clause,[],[f400,f377,f353,f825]) ).
fof(f400,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| relation_composition(X1,X0) = X2
| ~ empty(X2) )
| ~ spl13_38
| ~ spl13_42 ),
inference(resolution,[],[f378,f354]) ).
fof(f823,plain,
( spl13_98
| ~ spl13_38
| ~ spl13_40 ),
inference(avatar_split_clause,[],[f395,f369,f353,f821]) ).
fof(f395,plain,
( ! [X2,X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| relation_composition(X0,X1) = X2
| ~ empty(X2) )
| ~ spl13_38
| ~ spl13_40 ),
inference(resolution,[],[f370,f354]) ).
fof(f813,plain,
( spl13_97
| ~ spl13_34
| ~ spl13_39 ),
inference(avatar_split_clause,[],[f390,f365,f336,f811]) ).
fof(f811,plain,
( spl13_97
<=> ! [X0] :
( empty(powerset(X0))
| in(sK3(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_97])]) ).
fof(f336,plain,
( spl13_34
<=> ! [X0] :
( element(sK3(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_34])]) ).
fof(f390,plain,
( ! [X0] :
( empty(powerset(X0))
| in(sK3(X0),powerset(X0))
| empty(X0) )
| ~ spl13_34
| ~ spl13_39 ),
inference(resolution,[],[f366,f337]) ).
fof(f337,plain,
( ! [X0] :
( element(sK3(X0),powerset(X0))
| empty(X0) )
| ~ spl13_34 ),
inference(avatar_component_clause,[],[f336]) ).
fof(f809,plain,
( spl13_96
| ~ spl13_37
| ~ spl13_39 ),
inference(avatar_split_clause,[],[f389,f365,f349,f807]) ).
fof(f807,plain,
( spl13_96
<=> ! [X0,X1] :
( empty(powerset(X0))
| in(X1,powerset(X0))
| ~ subset(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_96])]) ).
fof(f349,plain,
( spl13_37
<=> ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_37])]) ).
fof(f389,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| in(X1,powerset(X0))
| ~ subset(X1,X0) )
| ~ spl13_37
| ~ spl13_39 ),
inference(resolution,[],[f366,f350]) ).
fof(f350,plain,
( ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) )
| ~ spl13_37 ),
inference(avatar_component_clause,[],[f349]) ).
fof(f775,plain,
( spl13_95
| ~ spl13_34
| ~ spl13_47 ),
inference(avatar_split_clause,[],[f425,f421,f336,f773]) ).
fof(f421,plain,
( spl13_47
<=> ! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_47])]) ).
fof(f425,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK3(X1))
| empty(X1) )
| ~ spl13_34
| ~ spl13_47 ),
inference(resolution,[],[f422,f337]) ).
fof(f422,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| element(X0,X2)
| ~ in(X0,X1) )
| ~ spl13_47 ),
inference(avatar_component_clause,[],[f421]) ).
fof(f771,plain,
( spl13_94
| ~ spl13_37
| ~ spl13_47 ),
inference(avatar_split_clause,[],[f424,f421,f349,f769]) ).
fof(f769,plain,
( spl13_94
<=> ! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_94])]) ).
fof(f424,plain,
( ! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,X1) )
| ~ spl13_37
| ~ spl13_47 ),
inference(resolution,[],[f422,f350]) ).
fof(f767,plain,
( spl13_93
| ~ spl13_6
| ~ spl13_26
| ~ spl13_42 ),
inference(avatar_split_clause,[],[f404,f377,f287,f189,f765]) ).
fof(f287,plain,
( spl13_26
<=> ! [X0] :
( empty_set = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_26])]) ).
fof(f404,plain,
( ! [X0,X1] :
( relation_composition(X1,X0) = sK8
| ~ relation(X0)
| ~ empty(X1) )
| ~ spl13_6
| ~ spl13_26
| ~ spl13_42 ),
inference(forward_demodulation,[],[f401,f308]) ).
fof(f308,plain,
( empty_set = sK8
| ~ spl13_6
| ~ spl13_26 ),
inference(resolution,[],[f288,f191]) ).
fof(f191,plain,
( empty(sK8)
| ~ spl13_6 ),
inference(avatar_component_clause,[],[f189]) ).
fof(f288,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = X0 )
| ~ spl13_26 ),
inference(avatar_component_clause,[],[f287]) ).
fof(f401,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| relation_composition(X1,X0) = empty_set )
| ~ spl13_26
| ~ spl13_42 ),
inference(resolution,[],[f378,f288]) ).
fof(f763,plain,
( spl13_92
| ~ spl13_6
| ~ spl13_26
| ~ spl13_40 ),
inference(avatar_split_clause,[],[f399,f369,f287,f189,f761]) ).
fof(f399,plain,
( ! [X0,X1] :
( relation_composition(X0,X1) = sK8
| ~ relation(X0)
| ~ empty(X1) )
| ~ spl13_6
| ~ spl13_26
| ~ spl13_40 ),
inference(forward_demodulation,[],[f396,f308]) ).
fof(f396,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| relation_composition(X0,X1) = empty_set )
| ~ spl13_26
| ~ spl13_40 ),
inference(resolution,[],[f370,f288]) ).
fof(f758,plain,
( ~ spl13_91
| ~ spl13_27
| spl13_80 ),
inference(avatar_split_clause,[],[f717,f666,f291,f755]) ).
fof(f755,plain,
( spl13_91
<=> empty(identity_relation(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_91])]) ).
fof(f666,plain,
( spl13_80
<=> empty(relation_dom(identity_relation(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_80])]) ).
fof(f717,plain,
( ~ empty(identity_relation(sK0))
| ~ spl13_27
| spl13_80 ),
inference(resolution,[],[f668,f292]) ).
fof(f668,plain,
( ~ empty(relation_dom(identity_relation(sK0)))
| spl13_80 ),
inference(avatar_component_clause,[],[f666]) ).
fof(f737,plain,
( spl13_90
| ~ spl13_18
| ~ spl13_48 ),
inference(avatar_split_clause,[],[f434,f431,f247,f735]) ).
fof(f431,plain,
( spl13_48
<=> ! [X0] :
( relation_dom(identity_relation(X0)) = X0
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_48])]) ).
fof(f434,plain,
( ! [X0] :
( ~ function(identity_relation(X0))
| relation_dom(identity_relation(X0)) = X0 )
| ~ spl13_18
| ~ spl13_48 ),
inference(resolution,[],[f432,f248]) ).
fof(f432,plain,
( ! [X0] :
( ~ relation(identity_relation(X0))
| ~ function(identity_relation(X0))
| relation_dom(identity_relation(X0)) = X0 )
| ~ spl13_48 ),
inference(avatar_component_clause,[],[f431]) ).
fof(f733,plain,
( spl13_89
| ~ spl13_24
| ~ spl13_47 ),
inference(avatar_split_clause,[],[f426,f421,f271,f731]) ).
fof(f271,plain,
( spl13_24
<=> ! [X0] : element(sK4(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_24])]) ).
fof(f426,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK4(powerset(X1))) )
| ~ spl13_24
| ~ spl13_47 ),
inference(resolution,[],[f422,f272]) ).
fof(f272,plain,
( ! [X0] : element(sK4(X0),X0)
| ~ spl13_24 ),
inference(avatar_component_clause,[],[f271]) ).
fof(f729,plain,
( spl13_88
| ~ spl13_37
| ~ spl13_45 ),
inference(avatar_split_clause,[],[f409,f406,f349,f727]) ).
fof(f727,plain,
( spl13_88
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,X2)
| ~ subset(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_88])]) ).
fof(f406,plain,
( spl13_45
<=> ! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_45])]) ).
fof(f409,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,X2)
| ~ subset(X2,X0) )
| ~ spl13_37
| ~ spl13_45 ),
inference(resolution,[],[f407,f350]) ).
fof(f407,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X0,X1) )
| ~ spl13_45 ),
inference(avatar_component_clause,[],[f406]) ).
fof(f725,plain,
( spl13_87
| ~ spl13_22
| ~ spl13_42 ),
inference(avatar_split_clause,[],[f403,f377,f263,f723]) ).
fof(f723,plain,
( spl13_87
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| function(relation_composition(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_87])]) ).
fof(f403,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| function(relation_composition(X1,X0)) )
| ~ spl13_22
| ~ spl13_42 ),
inference(resolution,[],[f378,f264]) ).
fof(f721,plain,
( spl13_86
| ~ spl13_22
| ~ spl13_40 ),
inference(avatar_split_clause,[],[f398,f369,f263,f719]) ).
fof(f719,plain,
( spl13_86
<=> ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| function(relation_composition(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_86])]) ).
fof(f398,plain,
( ! [X0,X1] :
( ~ relation(X0)
| ~ empty(X1)
| function(relation_composition(X0,X1)) )
| ~ spl13_22
| ~ spl13_40 ),
inference(resolution,[],[f370,f264]) ).
fof(f716,plain,
( spl13_85
| ~ spl13_27
| ~ spl13_38 ),
inference(avatar_split_clause,[],[f358,f353,f291,f714]) ).
fof(f358,plain,
( ! [X0,X1] :
( relation_dom(X1) = X0
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl13_27
| ~ spl13_38 ),
inference(resolution,[],[f354,f292]) ).
fof(f708,plain,
( spl13_84
| ~ spl13_24
| ~ spl13_45 ),
inference(avatar_split_clause,[],[f411,f406,f271,f706]) ).
fof(f411,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK4(powerset(X0))) )
| ~ spl13_24
| ~ spl13_45 ),
inference(resolution,[],[f407,f272]) ).
fof(f704,plain,
( spl13_83
| ~ spl13_6
| ~ spl13_20
| ~ spl13_26
| ~ spl13_29
| ~ spl13_39 ),
inference(avatar_split_clause,[],[f394,f365,f299,f287,f255,f189,f702]) ).
fof(f702,plain,
( spl13_83
<=> ! [X0] :
( in(sK8,powerset(X0))
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_83])]) ).
fof(f255,plain,
( spl13_20
<=> ! [X0] : empty(sK5(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_20])]) ).
fof(f394,plain,
( ! [X0] :
( in(sK8,powerset(X0))
| empty(powerset(X0)) )
| ~ spl13_6
| ~ spl13_20
| ~ spl13_26
| ~ spl13_29
| ~ spl13_39 ),
inference(forward_demodulation,[],[f393,f308]) ).
fof(f393,plain,
( ! [X0] :
( in(empty_set,powerset(X0))
| empty(powerset(X0)) )
| ~ spl13_20
| ~ spl13_26
| ~ spl13_29
| ~ spl13_39 ),
inference(forward_demodulation,[],[f392,f307]) ).
fof(f307,plain,
( ! [X0] : empty_set = sK5(X0)
| ~ spl13_20
| ~ spl13_26 ),
inference(resolution,[],[f288,f256]) ).
fof(f256,plain,
( ! [X0] : empty(sK5(X0))
| ~ spl13_20 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f392,plain,
( ! [X0] :
( empty(powerset(X0))
| in(sK5(X0),powerset(X0)) )
| ~ spl13_29
| ~ spl13_39 ),
inference(resolution,[],[f366,f300]) ).
fof(f684,plain,
( spl13_82
| ~ spl13_24
| ~ spl13_39 ),
inference(avatar_split_clause,[],[f391,f365,f271,f682]) ).
fof(f391,plain,
( ! [X0] :
( empty(X0)
| in(sK4(X0),X0) )
| ~ spl13_24
| ~ spl13_39 ),
inference(resolution,[],[f366,f272]) ).
fof(f680,plain,
( spl13_81
| ~ spl13_6
| ~ spl13_26
| ~ spl13_27 ),
inference(avatar_split_clause,[],[f320,f291,f287,f189,f678]) ).
fof(f320,plain,
( ! [X0] :
( relation_dom(X0) = sK8
| ~ empty(X0) )
| ~ spl13_6
| ~ spl13_26
| ~ spl13_27 ),
inference(forward_demodulation,[],[f317,f308]) ).
fof(f317,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = relation_dom(X0) )
| ~ spl13_26
| ~ spl13_27 ),
inference(resolution,[],[f292,f288]) ).
fof(f669,plain,
( ~ spl13_80
| ~ spl13_30
| ~ spl13_75 ),
inference(avatar_split_clause,[],[f599,f588,f303,f666]) ).
fof(f599,plain,
( ~ empty(relation_dom(identity_relation(sK0)))
| ~ spl13_30
| ~ spl13_75 ),
inference(resolution,[],[f590,f304]) ).
fof(f642,plain,
( spl13_77
| ~ spl13_26
| ~ spl13_69 ),
inference(avatar_split_clause,[],[f623,f553,f287,f605]) ).
fof(f623,plain,
( ! [X0] :
( sK8 = X0
| ~ empty(X0) )
| ~ spl13_26
| ~ spl13_69 ),
inference(forward_demodulation,[],[f288,f555]) ).
fof(f622,plain,
( ~ spl13_3
| ~ spl13_78 ),
inference(avatar_contradiction_clause,[],[f615]) ).
fof(f615,plain,
( $false
| ~ spl13_3
| ~ spl13_78 ),
inference(resolution,[],[f610,f176]) ).
fof(f610,plain,
( ! [X0] : ~ empty(X0)
| ~ spl13_78 ),
inference(avatar_component_clause,[],[f609]) ).
fof(f609,plain,
( spl13_78
<=> ! [X0] : ~ empty(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_78])]) ).
fof(f621,plain,
( ~ spl13_20
| ~ spl13_78 ),
inference(avatar_contradiction_clause,[],[f616]) ).
fof(f616,plain,
( $false
| ~ spl13_20
| ~ spl13_78 ),
inference(resolution,[],[f610,f256]) ).
fof(f620,plain,
( ~ spl13_6
| ~ spl13_78 ),
inference(avatar_contradiction_clause,[],[f617]) ).
fof(f617,plain,
( $false
| ~ spl13_6
| ~ spl13_78 ),
inference(resolution,[],[f610,f191]) ).
fof(f619,plain,
( ~ spl13_9
| ~ spl13_78 ),
inference(avatar_contradiction_clause,[],[f618]) ).
fof(f618,plain,
( $false
| ~ spl13_9
| ~ spl13_78 ),
inference(resolution,[],[f610,f206]) ).
fof(f206,plain,
( empty(sK10)
| ~ spl13_9 ),
inference(avatar_component_clause,[],[f204]) ).
fof(f204,plain,
( spl13_9
<=> empty(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_9])]) ).
fof(f614,plain,
( spl13_78
| spl13_79
| ~ spl13_6
| ~ spl13_20
| ~ spl13_26
| ~ spl13_29
| ~ spl13_45 ),
inference(avatar_split_clause,[],[f414,f406,f299,f287,f255,f189,f612,f609]) ).
fof(f414,plain,
( ! [X0,X1] :
( ~ in(X1,sK8)
| ~ empty(X0) )
| ~ spl13_6
| ~ spl13_20
| ~ spl13_26
| ~ spl13_29
| ~ spl13_45 ),
inference(forward_demodulation,[],[f413,f308]) ).
fof(f413,plain,
( ! [X0,X1] :
( ~ in(X1,empty_set)
| ~ empty(X0) )
| ~ spl13_20
| ~ spl13_26
| ~ spl13_29
| ~ spl13_45 ),
inference(forward_demodulation,[],[f412,f307]) ).
fof(f412,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK5(X0)) )
| ~ spl13_29
| ~ spl13_45 ),
inference(resolution,[],[f407,f300]) ).
fof(f607,plain,
( spl13_77
| ~ spl13_6
| ~ spl13_38 ),
inference(avatar_split_clause,[],[f360,f353,f189,f605]) ).
fof(f360,plain,
( ! [X0] :
( sK8 = X0
| ~ empty(X0) )
| ~ spl13_6
| ~ spl13_38 ),
inference(resolution,[],[f354,f191]) ).
fof(f603,plain,
( spl13_76
| ~ spl13_22
| ~ spl13_27 ),
inference(avatar_split_clause,[],[f319,f291,f263,f601]) ).
fof(f601,plain,
( spl13_76
<=> ! [X0] :
( ~ empty(X0)
| function(relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_76])]) ).
fof(f319,plain,
( ! [X0] :
( ~ empty(X0)
| function(relation_dom(X0)) )
| ~ spl13_22
| ~ spl13_27 ),
inference(resolution,[],[f292,f264]) ).
fof(f595,plain,
( ~ spl13_19
| spl13_74 ),
inference(avatar_contradiction_clause,[],[f594]) ).
fof(f594,plain,
( $false
| ~ spl13_19
| spl13_74 ),
inference(resolution,[],[f586,f252]) ).
fof(f586,plain,
( ~ function(identity_relation(sK0))
| spl13_74 ),
inference(avatar_component_clause,[],[f584]) ).
fof(f593,plain,
( ~ spl13_18
| spl13_73 ),
inference(avatar_contradiction_clause,[],[f592]) ).
fof(f592,plain,
( $false
| ~ spl13_18
| spl13_73 ),
inference(resolution,[],[f582,f248]) ).
fof(f582,plain,
( ~ relation(identity_relation(sK0))
| spl13_73 ),
inference(avatar_component_clause,[],[f580]) ).
fof(f591,plain,
( ~ spl13_73
| ~ spl13_74
| ~ spl13_1
| ~ spl13_2
| spl13_75
| ~ spl13_14
| ~ spl13_53 ),
inference(avatar_split_clause,[],[f465,f458,f229,f588,f169,f164,f584,f580]) ).
fof(f465,plain,
( in(apply(sK2,sK1),relation_dom(identity_relation(sK0)))
| ~ function(sK2)
| ~ relation(sK2)
| ~ function(identity_relation(sK0))
| ~ relation(identity_relation(sK0))
| ~ spl13_14
| ~ spl13_53 ),
inference(resolution,[],[f459,f231]) ).
fof(f574,plain,
( spl13_72
| ~ spl13_69
| ~ spl13_71 ),
inference(avatar_split_clause,[],[f570,f567,f553,f572]) ).
fof(f567,plain,
( spl13_71
<=> ! [X0] : empty_set = sK5(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_71])]) ).
fof(f570,plain,
( ! [X0] : sK5(X0) = sK8
| ~ spl13_69
| ~ spl13_71 ),
inference(forward_demodulation,[],[f568,f555]) ).
fof(f568,plain,
( ! [X0] : empty_set = sK5(X0)
| ~ spl13_71 ),
inference(avatar_component_clause,[],[f567]) ).
fof(f569,plain,
( spl13_71
| ~ spl13_20
| ~ spl13_26 ),
inference(avatar_split_clause,[],[f307,f287,f255,f567]) ).
fof(f561,plain,
( spl13_70
| ~ spl13_6
| ~ spl13_9
| ~ spl13_26 ),
inference(avatar_split_clause,[],[f310,f287,f204,f189,f558]) ).
fof(f558,plain,
( spl13_70
<=> sK8 = sK10 ),
introduced(avatar_definition,[new_symbols(naming,[spl13_70])]) ).
fof(f310,plain,
( sK8 = sK10
| ~ spl13_6
| ~ spl13_9
| ~ spl13_26 ),
inference(forward_demodulation,[],[f309,f308]) ).
fof(f309,plain,
( empty_set = sK10
| ~ spl13_9
| ~ spl13_26 ),
inference(resolution,[],[f288,f206]) ).
fof(f556,plain,
( spl13_69
| ~ spl13_6
| ~ spl13_26 ),
inference(avatar_split_clause,[],[f308,f287,f189,f553]) ).
fof(f550,plain,
( spl13_68
| ~ spl13_20
| ~ spl13_23 ),
inference(avatar_split_clause,[],[f279,f267,f255,f548]) ).
fof(f548,plain,
( spl13_68
<=> ! [X0] : relation(sK5(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_68])]) ).
fof(f279,plain,
( ! [X0] : relation(sK5(X0))
| ~ spl13_20
| ~ spl13_23 ),
inference(resolution,[],[f268,f256]) ).
fof(f544,plain,
( spl13_67
| ~ spl13_20
| ~ spl13_22 ),
inference(avatar_split_clause,[],[f275,f263,f255,f542]) ).
fof(f542,plain,
( spl13_67
<=> ! [X0] : function(sK5(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_67])]) ).
fof(f275,plain,
( ! [X0] : function(sK5(X0))
| ~ spl13_20
| ~ spl13_22 ),
inference(resolution,[],[f264,f256]) ).
fof(f540,plain,
( ~ spl13_66
| ~ spl13_27
| spl13_58 ),
inference(avatar_split_clause,[],[f486,f482,f291,f537]) ).
fof(f486,plain,
( ~ empty(relation_composition(sK2,identity_relation(sK0)))
| ~ spl13_27
| spl13_58 ),
inference(resolution,[],[f484,f292]) ).
fof(f535,plain,
( spl13_65
| ~ spl13_6
| ~ spl13_23 ),
inference(avatar_split_clause,[],[f280,f267,f189,f532]) ).
fof(f532,plain,
( spl13_65
<=> relation(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_65])]) ).
fof(f280,plain,
( relation(sK8)
| ~ spl13_6
| ~ spl13_23 ),
inference(resolution,[],[f268,f191]) ).
fof(f529,plain,
( spl13_64
| ~ spl13_9
| ~ spl13_22 ),
inference(avatar_split_clause,[],[f277,f263,f204,f526]) ).
fof(f526,plain,
( spl13_64
<=> function(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_64])]) ).
fof(f277,plain,
( function(sK10)
| ~ spl13_9
| ~ spl13_22 ),
inference(resolution,[],[f264,f206]) ).
fof(f524,plain,
( spl13_63
| ~ spl13_6
| ~ spl13_22 ),
inference(avatar_split_clause,[],[f276,f263,f189,f521]) ).
fof(f521,plain,
( spl13_63
<=> function(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_63])]) ).
fof(f276,plain,
( function(sK8)
| ~ spl13_6
| ~ spl13_22 ),
inference(resolution,[],[f264,f191]) ).
fof(f513,plain,
( spl13_62
| ~ spl13_16
| ~ spl13_33 ),
inference(avatar_split_clause,[],[f500,f328,f238,f510]) ).
fof(f510,plain,
( spl13_62
<=> element(apply(sK2,sK1),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_62])]) ).
fof(f500,plain,
( element(apply(sK2,sK1),sK0)
| ~ spl13_16
| ~ spl13_33 ),
inference(resolution,[],[f240,f329]) ).
fof(f507,plain,
( ~ spl13_61
| ~ spl13_16
| ~ spl13_30 ),
inference(avatar_split_clause,[],[f502,f303,f238,f504]) ).
fof(f504,plain,
( spl13_61
<=> empty(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_61])]) ).
fof(f502,plain,
( ~ empty(sK0)
| ~ spl13_16
| ~ spl13_30 ),
inference(resolution,[],[f240,f304]) ).
fof(f496,plain,
( spl13_60
| ~ spl13_14
| ~ spl13_33 ),
inference(avatar_split_clause,[],[f334,f328,f229,f493]) ).
fof(f491,plain,
( ~ spl13_59
| ~ spl13_14
| ~ spl13_32 ),
inference(avatar_split_clause,[],[f332,f324,f229,f488]) ).
fof(f332,plain,
( ~ in(relation_dom(relation_composition(sK2,identity_relation(sK0))),sK1)
| ~ spl13_14
| ~ spl13_32 ),
inference(resolution,[],[f325,f231]) ).
fof(f485,plain,
( ~ spl13_58
| ~ spl13_14
| ~ spl13_30 ),
inference(avatar_split_clause,[],[f322,f303,f229,f482]) ).
fof(f322,plain,
( ~ empty(relation_dom(relation_composition(sK2,identity_relation(sK0))))
| ~ spl13_14
| ~ spl13_30 ),
inference(resolution,[],[f304,f231]) ).
fof(f480,plain,
( spl13_57
| ~ spl13_15
| ~ spl13_33 ),
inference(avatar_split_clause,[],[f333,f328,f233,f477]) ).
fof(f477,plain,
( spl13_57
<=> element(sK1,relation_dom(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_57])]) ).
fof(f333,plain,
( element(sK1,relation_dom(sK2))
| ~ spl13_15
| ~ spl13_33 ),
inference(resolution,[],[f329,f235]) ).
fof(f235,plain,
( in(sK1,relation_dom(sK2))
| ~ spl13_15 ),
inference(avatar_component_clause,[],[f233]) ).
fof(f475,plain,
( ~ spl13_56
| ~ spl13_15
| ~ spl13_32 ),
inference(avatar_split_clause,[],[f331,f324,f233,f472]) ).
fof(f472,plain,
( spl13_56
<=> in(relation_dom(sK2),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_56])]) ).
fof(f331,plain,
( ~ in(relation_dom(sK2),sK1)
| ~ spl13_15
| ~ spl13_32 ),
inference(resolution,[],[f325,f235]) ).
fof(f470,plain,
spl13_55,
inference(avatar_split_clause,[],[f143,f468]) ).
fof(f143,plain,
! [X2,X0,X1] :
( in(X0,relation_dom(relation_composition(X2,X1)))
| ~ in(apply(X2,X0),relation_dom(X1))
| ~ in(X0,relation_dom(X2))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
! [X0,X1] :
( ! [X2] :
( ( ( in(X0,relation_dom(relation_composition(X2,X1)))
| ~ in(apply(X2,X0),relation_dom(X1))
| ~ in(X0,relation_dom(X2)) )
& ( ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) )
| ~ in(X0,relation_dom(relation_composition(X2,X1))) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f88]) ).
fof(f88,plain,
! [X0,X1] :
( ! [X2] :
( ( ( in(X0,relation_dom(relation_composition(X2,X1)))
| ~ in(apply(X2,X0),relation_dom(X1))
| ~ in(X0,relation_dom(X2)) )
& ( ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) )
| ~ in(X0,relation_dom(relation_composition(X2,X1))) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(nnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0,X1] :
( ! [X2] :
( ( in(X0,relation_dom(relation_composition(X2,X1)))
<=> ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f63]) ).
fof(f63,plain,
! [X0,X1] :
( ! [X2] :
( ( in(X0,relation_dom(relation_composition(X2,X1)))
<=> ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X0,relation_dom(relation_composition(X2,X1)))
<=> ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_funct_1) ).
fof(f464,plain,
spl13_54,
inference(avatar_split_clause,[],[f159,f462]) ).
fof(f462,plain,
( spl13_54
<=> ! [X1] :
( identity_relation(relation_dom(X1)) = X1
| sK6(relation_dom(X1),X1) != apply(X1,sK6(relation_dom(X1),X1))
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_54])]) ).
fof(f159,plain,
! [X1] :
( identity_relation(relation_dom(X1)) = X1
| sK6(relation_dom(X1),X1) != apply(X1,sK6(relation_dom(X1),X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(equality_resolution,[],[f140]) ).
fof(f140,plain,
! [X0,X1] :
( identity_relation(X0) = X1
| sK6(X0,X1) != apply(X1,sK6(X0,X1))
| relation_dom(X1) != X0
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f87]) ).
fof(f87,plain,
! [X0,X1] :
( ( ( identity_relation(X0) = X1
| ( sK6(X0,X1) != apply(X1,sK6(X0,X1))
& in(sK6(X0,X1),X0) )
| relation_dom(X1) != X0 )
& ( ( ! [X3] :
( apply(X1,X3) = X3
| ~ in(X3,X0) )
& relation_dom(X1) = X0 )
| identity_relation(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f85,f86]) ).
fof(f86,plain,
! [X0,X1] :
( ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) )
=> ( sK6(X0,X1) != apply(X1,sK6(X0,X1))
& in(sK6(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f85,plain,
! [X0,X1] :
( ( ( identity_relation(X0) = X1
| ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) )
| relation_dom(X1) != X0 )
& ( ( ! [X3] :
( apply(X1,X3) = X3
| ~ in(X3,X0) )
& relation_dom(X1) = X0 )
| identity_relation(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(rectify,[],[f84]) ).
fof(f84,plain,
! [X0,X1] :
( ( ( identity_relation(X0) = X1
| ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) )
| relation_dom(X1) != X0 )
& ( ( ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) )
& relation_dom(X1) = X0 )
| identity_relation(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f83]) ).
fof(f83,plain,
! [X0,X1] :
( ( ( identity_relation(X0) = X1
| ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) )
| relation_dom(X1) != X0 )
& ( ( ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) )
& relation_dom(X1) = X0 )
| identity_relation(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(nnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0,X1] :
( ( identity_relation(X0) = X1
<=> ( ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) )
& relation_dom(X1) = X0 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f61]) ).
fof(f61,plain,
! [X0,X1] :
( ( identity_relation(X0) = X1
<=> ( ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) )
& relation_dom(X1) = X0 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( identity_relation(X0) = X1
<=> ( ! [X2] :
( in(X2,X0)
=> apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funct_1) ).
fof(f460,plain,
spl13_53,
inference(avatar_split_clause,[],[f142,f458]) ).
fof(f142,plain,
! [X2,X0,X1] :
( in(apply(X2,X0),relation_dom(X1))
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f89]) ).
fof(f454,plain,
spl13_52,
inference(avatar_split_clause,[],[f141,f452]) ).
fof(f141,plain,
! [X2,X0,X1] :
( in(X0,relation_dom(X2))
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f89]) ).
fof(f447,plain,
spl13_51,
inference(avatar_split_clause,[],[f160,f445]) ).
fof(f160,plain,
! [X1] :
( identity_relation(relation_dom(X1)) = X1
| in(sK6(relation_dom(X1),X1),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(equality_resolution,[],[f139]) ).
fof(f139,plain,
! [X0,X1] :
( identity_relation(X0) = X1
| in(sK6(X0,X1),X0)
| relation_dom(X1) != X0
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f87]) ).
fof(f442,plain,
spl13_50,
inference(avatar_split_clause,[],[f161,f440]) ).
fof(f161,plain,
! [X3,X0] :
( apply(identity_relation(X0),X3) = X3
| ~ in(X3,X0)
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(equality_resolution,[],[f138]) ).
fof(f138,plain,
! [X3,X0,X1] :
( apply(X1,X3) = X3
| ~ in(X3,X0)
| identity_relation(X0) != X1
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f87]) ).
fof(f438,plain,
spl13_49,
inference(avatar_split_clause,[],[f136,f436]) ).
fof(f436,plain,
( spl13_49
<=> ! [X0,X1] :
( function(relation_composition(X0,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_49])]) ).
fof(f136,plain,
! [X0,X1] :
( function(relation_composition(X0,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0,X1] :
( ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) )
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f59]) ).
fof(f59,plain,
! [X0,X1] :
( ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) )
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1)
& function(X0)
& relation(X0) )
=> ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_1) ).
fof(f433,plain,
spl13_48,
inference(avatar_split_clause,[],[f162,f431]) ).
fof(f162,plain,
! [X0] :
( relation_dom(identity_relation(X0)) = X0
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(equality_resolution,[],[f137]) ).
fof(f137,plain,
! [X0,X1] :
( relation_dom(X1) = X0
| identity_relation(X0) != X1
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f87]) ).
fof(f423,plain,
spl13_47,
inference(avatar_split_clause,[],[f148,f421]) ).
fof(f148,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f70]) ).
fof(f70,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f419,plain,
( ~ spl13_46
| ~ spl13_27
| spl13_36 ),
inference(avatar_split_clause,[],[f380,f344,f291,f416]) ).
fof(f416,plain,
( spl13_46
<=> empty(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_46])]) ).
fof(f344,plain,
( spl13_36
<=> empty(relation_dom(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_36])]) ).
fof(f380,plain,
( ~ empty(sK2)
| ~ spl13_27
| spl13_36 ),
inference(resolution,[],[f346,f292]) ).
fof(f346,plain,
( ~ empty(relation_dom(sK2))
| spl13_36 ),
inference(avatar_component_clause,[],[f344]) ).
fof(f408,plain,
spl13_45,
inference(avatar_split_clause,[],[f149,f406]) ).
fof(f149,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f388,plain,
spl13_44,
inference(avatar_split_clause,[],[f144,f386]) ).
fof(f144,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(flattening,[],[f65]) ).
fof(f65,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f384,plain,
spl13_43,
inference(avatar_split_clause,[],[f134,f382]) ).
fof(f382,plain,
( spl13_43
<=> ! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_43])]) ).
fof(f134,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& empty(relation_composition(X0,X1)) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(flattening,[],[f57]) ).
fof(f57,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& empty(relation_composition(X0,X1)) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0,X1] :
( ( relation(X1)
& empty(X0) )
=> ( relation(relation_composition(X0,X1))
& empty(relation_composition(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc9_relat_1) ).
fof(f379,plain,
spl13_42,
inference(avatar_split_clause,[],[f133,f377]) ).
fof(f133,plain,
! [X0,X1] :
( empty(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f375,plain,
spl13_41,
inference(avatar_split_clause,[],[f132,f373]) ).
fof(f373,plain,
( spl13_41
<=> ! [X0,X1] :
( relation(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_41])]) ).
fof(f132,plain,
! [X0,X1] :
( relation(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0,X1] :
( ( relation(relation_composition(X1,X0))
& empty(relation_composition(X1,X0)) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(flattening,[],[f55]) ).
fof(f55,plain,
! [X0,X1] :
( ( relation(relation_composition(X1,X0))
& empty(relation_composition(X1,X0)) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] :
( ( relation(X1)
& empty(X0) )
=> ( relation(relation_composition(X1,X0))
& empty(relation_composition(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc10_relat_1) ).
fof(f371,plain,
spl13_40,
inference(avatar_split_clause,[],[f131,f369]) ).
fof(f131,plain,
! [X0,X1] :
( empty(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f367,plain,
spl13_39,
inference(avatar_split_clause,[],[f130,f365]) ).
fof(f130,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f53]) ).
fof(f53,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f355,plain,
spl13_38,
inference(avatar_split_clause,[],[f146,f353]) ).
fof(f146,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(f351,plain,
spl13_37,
inference(avatar_split_clause,[],[f145,f349]) ).
fof(f145,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0,X1] :
( subset(X0,X1)
=> element(X0,powerset(X1)) ),
inference(unused_predicate_definition_removal,[],[f30]) ).
fof(f30,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f347,plain,
( ~ spl13_36
| ~ spl13_15
| ~ spl13_30 ),
inference(avatar_split_clause,[],[f321,f303,f233,f344]) ).
fof(f321,plain,
( ~ empty(relation_dom(sK2))
| ~ spl13_15
| ~ spl13_30 ),
inference(resolution,[],[f304,f235]) ).
fof(f342,plain,
spl13_35,
inference(avatar_split_clause,[],[f123,f340]) ).
fof(f123,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(flattening,[],[f49]) ).
fof(f49,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_dom(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(f338,plain,
spl13_34,
inference(avatar_split_clause,[],[f116,f336]) ).
fof(f116,plain,
! [X0] :
( element(sK3(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
! [X0] :
( ( ~ empty(sK3(X0))
& element(sK3(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f44,f77]) ).
fof(f77,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( ~ empty(sK3(X0))
& element(sK3(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f44,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f330,plain,
spl13_33,
inference(avatar_split_clause,[],[f129,f328]) ).
fof(f129,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(f326,plain,
spl13_32,
inference(avatar_split_clause,[],[f128,f324]) ).
fof(f128,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f315,plain,
( spl13_31
| ~ spl13_3
| ~ spl13_22 ),
inference(avatar_split_clause,[],[f274,f263,f174,f312]) ).
fof(f312,plain,
( spl13_31
<=> function(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_31])]) ).
fof(f274,plain,
( function(empty_set)
| ~ spl13_3
| ~ spl13_22 ),
inference(resolution,[],[f264,f176]) ).
fof(f305,plain,
spl13_30,
inference(avatar_split_clause,[],[f147,f303]) ).
fof(f147,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f301,plain,
spl13_29,
inference(avatar_split_clause,[],[f125,f299]) ).
fof(f125,plain,
! [X0] : element(sK5(X0),powerset(X0)),
inference(cnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0] :
( empty(sK5(X0))
& element(sK5(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f22,f81]) ).
fof(f81,plain,
! [X0] :
( ? [X1] :
( empty(X1)
& element(X1,powerset(X0)) )
=> ( empty(sK5(X0))
& element(sK5(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f22,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f297,plain,
spl13_28,
inference(avatar_split_clause,[],[f122,f295]) ).
fof(f122,plain,
! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0] :
( ( relation(relation_dom(X0))
& empty(relation_dom(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(f293,plain,
spl13_27,
inference(avatar_split_clause,[],[f121,f291]) ).
fof(f121,plain,
! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f289,plain,
spl13_26,
inference(avatar_split_clause,[],[f120,f287]) ).
fof(f120,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f285,plain,
spl13_25,
inference(avatar_split_clause,[],[f117,f283]) ).
fof(f283,plain,
( spl13_25
<=> ! [X0] :
( ~ empty(sK3(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_25])]) ).
fof(f117,plain,
! [X0] :
( ~ empty(sK3(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f273,plain,
spl13_24,
inference(avatar_split_clause,[],[f124,f271]) ).
fof(f124,plain,
! [X0] : element(sK4(X0),X0),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0] : element(sK4(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f6,f79]) ).
fof(f79,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK4(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f6,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f269,plain,
spl13_23,
inference(avatar_split_clause,[],[f119,f267]) ).
fof(f119,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( empty(X0)
=> relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(f265,plain,
spl13_22,
inference(avatar_split_clause,[],[f118,f263]) ).
fof(f118,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( empty(X0)
=> function(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
fof(f261,plain,
spl13_21,
inference(avatar_split_clause,[],[f127,f259]) ).
fof(f259,plain,
( spl13_21
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_21])]) ).
fof(f127,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f38]) ).
fof(f38,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f25]) ).
fof(f25,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f257,plain,
spl13_20,
inference(avatar_split_clause,[],[f126,f255]) ).
fof(f126,plain,
! [X0] : empty(sK5(X0)),
inference(cnf_transformation,[],[f82]) ).
fof(f253,plain,
spl13_19,
inference(avatar_split_clause,[],[f115,f251]) ).
fof(f115,plain,
! [X0] : function(identity_relation(X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0] :
( function(identity_relation(X0))
& relation(identity_relation(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(f249,plain,
spl13_18,
inference(avatar_split_clause,[],[f113,f247]) ).
fof(f113,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] : relation(identity_relation(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(f245,plain,
spl13_17,
inference(avatar_split_clause,[],[f112,f243]) ).
fof(f243,plain,
( spl13_17
<=> ! [X0] : ~ empty(powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_17])]) ).
fof(f112,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f241,plain,
( spl13_14
| spl13_16 ),
inference(avatar_split_clause,[],[f105,f238,f229]) ).
fof(f105,plain,
( in(apply(sK2,sK1),sK0)
| in(sK1,relation_dom(relation_composition(sK2,identity_relation(sK0)))) ),
inference(cnf_transformation,[],[f76]) ).
fof(f236,plain,
( spl13_14
| spl13_15 ),
inference(avatar_split_clause,[],[f104,f233,f229]) ).
fof(f104,plain,
( in(sK1,relation_dom(sK2))
| in(sK1,relation_dom(relation_composition(sK2,identity_relation(sK0)))) ),
inference(cnf_transformation,[],[f76]) ).
fof(f227,plain,
spl13_13,
inference(avatar_split_clause,[],[f158,f224]) ).
fof(f224,plain,
( spl13_13
<=> function(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_13])]) ).
fof(f158,plain,
function(sK12),
inference(cnf_transformation,[],[f101]) ).
fof(f101,plain,
( function(sK12)
& relation(sK12) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f17,f100]) ).
fof(f100,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK12)
& relation(sK12) ) ),
introduced(choice_axiom,[]) ).
fof(f17,axiom,
? [X0] :
( function(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
fof(f222,plain,
spl13_12,
inference(avatar_split_clause,[],[f157,f219]) ).
fof(f157,plain,
relation(sK12),
inference(cnf_transformation,[],[f101]) ).
fof(f217,plain,
spl13_11,
inference(avatar_split_clause,[],[f156,f214]) ).
fof(f156,plain,
relation(sK11),
inference(cnf_transformation,[],[f99]) ).
fof(f99,plain,
relation(sK11),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f41,f98]) ).
fof(f98,plain,
( ? [X0] : relation(X0)
=> relation(sK11) ),
introduced(choice_axiom,[]) ).
fof(f41,plain,
? [X0] : relation(X0),
inference(pure_predicate_removal,[],[f24]) ).
fof(f24,axiom,
? [X0] :
( relation_empty_yielding(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).
fof(f212,plain,
spl13_10,
inference(avatar_split_clause,[],[f155,f209]) ).
fof(f209,plain,
( spl13_10
<=> relation(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_10])]) ).
fof(f155,plain,
relation(sK10),
inference(cnf_transformation,[],[f97]) ).
fof(f97,plain,
( relation(sK10)
& empty(sK10) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f18,f96]) ).
fof(f96,plain,
( ? [X0] :
( relation(X0)
& empty(X0) )
=> ( relation(sK10)
& empty(sK10) ) ),
introduced(choice_axiom,[]) ).
fof(f18,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f207,plain,
spl13_9,
inference(avatar_split_clause,[],[f154,f204]) ).
fof(f154,plain,
empty(sK10),
inference(cnf_transformation,[],[f97]) ).
fof(f202,plain,
spl13_8,
inference(avatar_split_clause,[],[f153,f199]) ).
fof(f153,plain,
relation(sK9),
inference(cnf_transformation,[],[f95]) ).
fof(f95,plain,
( relation(sK9)
& ~ empty(sK9) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f21,f94]) ).
fof(f94,plain,
( ? [X0] :
( relation(X0)
& ~ empty(X0) )
=> ( relation(sK9)
& ~ empty(sK9) ) ),
introduced(choice_axiom,[]) ).
fof(f21,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f197,plain,
~ spl13_7,
inference(avatar_split_clause,[],[f152,f194]) ).
fof(f194,plain,
( spl13_7
<=> empty(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_7])]) ).
fof(f152,plain,
~ empty(sK9),
inference(cnf_transformation,[],[f95]) ).
fof(f192,plain,
spl13_6,
inference(avatar_split_clause,[],[f151,f189]) ).
fof(f151,plain,
empty(sK8),
inference(cnf_transformation,[],[f93]) ).
fof(f93,plain,
empty(sK8),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f20,f92]) ).
fof(f92,plain,
( ? [X0] : empty(X0)
=> empty(sK8) ),
introduced(choice_axiom,[]) ).
fof(f20,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f187,plain,
~ spl13_5,
inference(avatar_split_clause,[],[f150,f184]) ).
fof(f184,plain,
( spl13_5
<=> empty(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_5])]) ).
fof(f150,plain,
~ empty(sK7),
inference(cnf_transformation,[],[f91]) ).
fof(f91,plain,
~ empty(sK7),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f23,f90]) ).
fof(f90,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK7) ),
introduced(choice_axiom,[]) ).
fof(f23,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f182,plain,
spl13_4,
inference(avatar_split_clause,[],[f109,f179]) ).
fof(f109,plain,
relation(empty_set),
inference(cnf_transformation,[],[f13]) ).
fof(f13,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f177,plain,
spl13_3,
inference(avatar_split_clause,[],[f107,f174]) ).
fof(f107,plain,
empty(empty_set),
inference(cnf_transformation,[],[f11]) ).
fof(f11,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f172,plain,
spl13_2,
inference(avatar_split_clause,[],[f103,f169]) ).
fof(f103,plain,
function(sK2),
inference(cnf_transformation,[],[f76]) ).
fof(f167,plain,
spl13_1,
inference(avatar_split_clause,[],[f102,f164]) ).
fof(f102,plain,
relation(sK2),
inference(cnf_transformation,[],[f76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SEU009+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.08 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.07/0.27 % Computer : n026.cluster.edu
% 0.07/0.27 % Model : x86_64 x86_64
% 0.07/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27 % Memory : 8042.1875MB
% 0.07/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27 % CPULimit : 300
% 0.07/0.27 % WCLimit : 300
% 0.07/0.27 % DateTime : Mon Apr 29 20:45:03 EDT 2024
% 0.07/0.27 % CPUTime :
% 0.07/0.27 % (6078)Running in auto input_syntax mode. Trying TPTP
% 0.07/0.28 % (6081)WARNING: value z3 for option sas not known
% 0.07/0.28 % (6083)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)
% 0.07/0.28 % (6082)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.07/0.28 % (6080)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.07/0.28 % (6079)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.07/0.28 % (6084)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)
% 0.07/0.28 % (6085)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)
% 0.07/0.28 % (6081)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)
% 0.07/0.28 TRYING [1]
% 0.07/0.28 TRYING [2]
% 0.12/0.29 TRYING [3]
% 0.12/0.29 TRYING [1]
% 0.12/0.29 TRYING [2]
% 0.12/0.29 TRYING [4]
% 0.12/0.30 TRYING [5]
% 0.12/0.30 TRYING [3]
% 0.12/0.30 % (6083)First to succeed.
% 0.12/0.31 TRYING [6]
% 0.12/0.31 % (6083)Refutation found. Thanks to Tanya!
% 0.12/0.31 % SZS status Theorem for theBenchmark
% 0.12/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.31 % (6083)------------------------------
% 0.12/0.31 % (6083)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.12/0.31 % (6083)Termination reason: Refutation
% 0.12/0.31
% 0.12/0.31 % (6083)Memory used [KB]: 1491
% 0.12/0.31 % (6083)Time elapsed: 0.027 s
% 0.12/0.31 % (6083)Instructions burned: 70 (million)
% 0.12/0.31 % (6083)------------------------------
% 0.12/0.31 % (6083)------------------------------
% 0.12/0.31 % (6078)Success in time 0.037 s
%------------------------------------------------------------------------------