TSTP Solution File: SEU293+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU293+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n031.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 09:32:37 EDT 2024
% Result : Theorem 0.21s 0.43s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 285
% Syntax : Number of formulae : 950 ( 134 unt; 0 def)
% Number of atoms : 2883 ( 212 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 3356 (1423 ~;1468 |; 178 &)
% ( 240 <=>; 45 =>; 0 <=; 2 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 235 ( 233 usr; 220 prp; 0-3 aty)
% Number of functors : 30 ( 30 usr; 16 con; 0-3 aty)
% Number of variables : 1114 (1044 !; 70 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1925,plain,
$false,
inference(avatar_sat_refutation,[],[f244,f249,f254,f259,f268,f273,f278,f283,f288,f293,f298,f303,f308,f313,f318,f323,f328,f333,f338,f343,f348,f353,f358,f363,f368,f373,f378,f382,f386,f390,f394,f398,f402,f406,f410,f414,f418,f434,f438,f443,f447,f451,f455,f459,f479,f483,f487,f491,f495,f499,f503,f507,f511,f539,f543,f547,f551,f556,f572,f576,f580,f584,f588,f592,f597,f601,f622,f632,f636,f650,f654,f658,f662,f666,f684,f688,f693,f700,f707,f716,f720,f724,f728,f733,f737,f741,f747,f751,f763,f767,f771,f782,f789,f797,f802,f811,f816,f825,f830,f836,f841,f846,f851,f857,f862,f867,f872,f886,f893,f903,f912,f917,f922,f927,f932,f936,f942,f946,f955,f962,f963,f964,f965,f966,f967,f993,f1021,f1032,f1036,f1040,f1044,f1048,f1052,f1056,f1060,f1064,f1103,f1108,f1112,f1116,f1128,f1132,f1136,f1140,f1144,f1149,f1180,f1184,f1188,f1193,f1203,f1207,f1219,f1223,f1227,f1231,f1235,f1258,f1262,f1266,f1271,f1275,f1307,f1311,f1315,f1319,f1323,f1360,f1364,f1368,f1381,f1399,f1408,f1412,f1416,f1420,f1444,f1448,f1452,f1456,f1493,f1498,f1523,f1524,f1529,f1534,f1539,f1541,f1555,f1559,f1565,f1570,f1582,f1587,f1591,f1595,f1599,f1603,f1607,f1616,f1634,f1639,f1643,f1648,f1652,f1656,f1660,f1664,f1687,f1698,f1702,f1729,f1733,f1737,f1775,f1779,f1783,f1787,f1791,f1795,f1831,f1844,f1899,f1903,f1907,f1908,f1913,f1914,f1915,f1917,f1924]) ).
fof(f1924,plain,
( ~ spl26_6
| spl26_158
| ~ spl26_204 ),
inference(avatar_split_clause,[],[f1920,f1684,f1268,f265]) ).
fof(f265,plain,
( spl26_6
<=> in(sK7,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_6])]) ).
fof(f1268,plain,
( spl26_158
<=> in(sK7,relation_dom(sK6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_158])]) ).
fof(f1684,plain,
( spl26_204
<=> sK3 = relation_dom(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_204])]) ).
fof(f1920,plain,
( ~ in(sK7,sK3)
| spl26_158
| ~ spl26_204 ),
inference(forward_demodulation,[],[f1269,f1686]) ).
fof(f1686,plain,
( sK3 = relation_dom(sK6)
| ~ spl26_204 ),
inference(avatar_component_clause,[],[f1684]) ).
fof(f1269,plain,
( ~ in(sK7,relation_dom(sK6))
| spl26_158 ),
inference(avatar_component_clause,[],[f1268]) ).
fof(f1917,plain,
( ~ spl26_147
| spl26_5
| ~ spl26_67
| ~ spl26_183 ),
inference(avatar_split_clause,[],[f1540,f1537,f599,f261,f1190]) ).
fof(f1190,plain,
( spl26_147
<=> sP1(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_147])]) ).
fof(f261,plain,
( spl26_5
<=> in(sK7,relation_inverse_image(sK6,sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_5])]) ).
fof(f599,plain,
( spl26_67
<=> ! [X0,X1] :
( sP0(X1,X0,relation_inverse_image(X0,X1))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_67])]) ).
fof(f1537,plain,
( spl26_183
<=> ! [X0] :
( in(sK7,X0)
| ~ sP0(sK5,sK6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_183])]) ).
fof(f1540,plain,
( in(sK7,relation_inverse_image(sK6,sK5))
| ~ sP1(sK6)
| ~ spl26_67
| ~ spl26_183 ),
inference(resolution,[],[f1538,f600]) ).
fof(f600,plain,
( ! [X0,X1] :
( sP0(X1,X0,relation_inverse_image(X0,X1))
| ~ sP1(X0) )
| ~ spl26_67 ),
inference(avatar_component_clause,[],[f599]) ).
fof(f1538,plain,
( ! [X0] :
( ~ sP0(sK5,sK6,X0)
| in(sK7,X0) )
| ~ spl26_183 ),
inference(avatar_component_clause,[],[f1537]) ).
fof(f1915,plain,
( spl26_66
| ~ spl26_6
| ~ spl26_49 ),
inference(avatar_split_clause,[],[f534,f489,f265,f594]) ).
fof(f594,plain,
( spl26_66
<=> element(sK7,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_66])]) ).
fof(f489,plain,
( spl26_49
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_49])]) ).
fof(f534,plain,
( element(sK7,sK3)
| ~ spl26_6
| ~ spl26_49 ),
inference(resolution,[],[f490,f267]) ).
fof(f267,plain,
( in(sK7,sK3)
| ~ spl26_6 ),
inference(avatar_component_clause,[],[f265]) ).
fof(f490,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) )
| ~ spl26_49 ),
inference(avatar_component_clause,[],[f489]) ).
fof(f1914,plain,
( ~ spl26_46
| ~ spl26_6
| ~ spl26_45 ),
inference(avatar_split_clause,[],[f473,f457,f265,f476]) ).
fof(f476,plain,
( spl26_46
<=> empty(sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_46])]) ).
fof(f457,plain,
( spl26_45
<=> ! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_45])]) ).
fof(f473,plain,
( ~ empty(sK3)
| ~ spl26_6
| ~ spl26_45 ),
inference(resolution,[],[f458,f267]) ).
fof(f458,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) )
| ~ spl26_45 ),
inference(avatar_component_clause,[],[f457]) ).
fof(f1913,plain,
( ~ spl26_10
| spl26_46
| ~ spl26_184 ),
inference(avatar_split_clause,[],[f1909,f1552,f476,f285]) ).
fof(f285,plain,
( spl26_10
<=> empty(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_10])]) ).
fof(f1552,plain,
( spl26_184
<=> sK3 = sK17 ),
introduced(avatar_definition,[new_symbols(naming,[spl26_184])]) ).
fof(f1909,plain,
( ~ empty(sK17)
| spl26_46
| ~ spl26_184 ),
inference(forward_demodulation,[],[f478,f1554]) ).
fof(f1554,plain,
( sK3 = sK17
| ~ spl26_184 ),
inference(avatar_component_clause,[],[f1552]) ).
fof(f478,plain,
( ~ empty(sK3)
| spl26_46 ),
inference(avatar_component_clause,[],[f476]) ).
fof(f1908,plain,
( ~ spl26_46
| spl26_168
| ~ spl26_204 ),
inference(avatar_split_clause,[],[f1743,f1684,f1378,f476]) ).
fof(f1378,plain,
( spl26_168
<=> empty(relation_dom(sK6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_168])]) ).
fof(f1743,plain,
( ~ empty(sK3)
| spl26_168
| ~ spl26_204 ),
inference(superposition,[],[f1380,f1686]) ).
fof(f1380,plain,
( ~ empty(relation_dom(sK6))
| spl26_168 ),
inference(avatar_component_clause,[],[f1378]) ).
fof(f1907,plain,
( spl26_219
| ~ spl26_126
| ~ spl26_146 ),
inference(avatar_split_clause,[],[f1199,f1186,f1034,f1905]) ).
fof(f1905,plain,
( spl26_219
<=> ! [X0] :
( element(sK10(sK8(X0)),X0)
| empty(X0)
| empty(sK8(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_219])]) ).
fof(f1034,plain,
( spl26_126
<=> ! [X0] :
( empty(X0)
| in(sK10(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_126])]) ).
fof(f1186,plain,
( spl26_146
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK8(X1))
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_146])]) ).
fof(f1199,plain,
( ! [X0] :
( element(sK10(sK8(X0)),X0)
| empty(X0)
| empty(sK8(X0)) )
| ~ spl26_126
| ~ spl26_146 ),
inference(resolution,[],[f1187,f1035]) ).
fof(f1035,plain,
( ! [X0] :
( in(sK10(X0),X0)
| empty(X0) )
| ~ spl26_126 ),
inference(avatar_component_clause,[],[f1034]) ).
fof(f1187,plain,
( ! [X0,X1] :
( ~ in(X0,sK8(X1))
| element(X0,X1)
| empty(X1) )
| ~ spl26_146 ),
inference(avatar_component_clause,[],[f1186]) ).
fof(f1903,plain,
( spl26_218
| ~ spl26_126
| ~ spl26_143 ),
inference(avatar_split_clause,[],[f1176,f1147,f1034,f1901]) ).
fof(f1901,plain,
( spl26_218
<=> ! [X0] :
( element(sK10(sK10(powerset(X0))),X0)
| empty(sK10(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_218])]) ).
fof(f1147,plain,
( spl26_143
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK10(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_143])]) ).
fof(f1176,plain,
( ! [X0] :
( element(sK10(sK10(powerset(X0))),X0)
| empty(sK10(powerset(X0))) )
| ~ spl26_126
| ~ spl26_143 ),
inference(resolution,[],[f1148,f1035]) ).
fof(f1148,plain,
( ! [X0,X1] :
( ~ in(X0,sK10(powerset(X1)))
| element(X0,X1) )
| ~ spl26_143 ),
inference(avatar_component_clause,[],[f1147]) ).
fof(f1899,plain,
( spl26_217
| ~ spl26_92
| ~ spl26_123 ),
inference(avatar_split_clause,[],[f1016,f953,f769,f1897]) ).
fof(f1897,plain,
( spl26_217
<=> ! [X0,X1] :
( in(sK9(sK17,X0,X1),X1)
| sP0(sK17,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_217])]) ).
fof(f769,plain,
( spl26_92
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(apply(X1,sK9(X0,X1,X2)),X0)
| in(sK9(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_92])]) ).
fof(f953,plain,
( spl26_123
<=> ! [X1] : ~ in(X1,sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_123])]) ).
fof(f1016,plain,
( ! [X0,X1] :
( in(sK9(sK17,X0,X1),X1)
| sP0(sK17,X0,X1) )
| ~ spl26_92
| ~ spl26_123 ),
inference(resolution,[],[f954,f770]) ).
fof(f770,plain,
( ! [X2,X0,X1] :
( in(apply(X1,sK9(X0,X1,X2)),X0)
| in(sK9(X0,X1,X2),X2)
| sP0(X0,X1,X2) )
| ~ spl26_92 ),
inference(avatar_component_clause,[],[f769]) ).
fof(f954,plain,
( ! [X1] : ~ in(X1,sK17)
| ~ spl26_123 ),
inference(avatar_component_clause,[],[f953]) ).
fof(f1844,plain,
( spl26_216
| ~ spl26_66
| ~ spl26_184 ),
inference(avatar_split_clause,[],[f1832,f1552,f594,f1841]) ).
fof(f1841,plain,
( spl26_216
<=> element(sK7,sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_216])]) ).
fof(f1832,plain,
( element(sK7,sK17)
| ~ spl26_66
| ~ spl26_184 ),
inference(forward_demodulation,[],[f596,f1554]) ).
fof(f596,plain,
( element(sK7,sK3)
| ~ spl26_66 ),
inference(avatar_component_clause,[],[f594]) ).
fof(f1831,plain,
( spl26_66
| ~ spl26_186
| ~ spl26_204 ),
inference(avatar_split_clause,[],[f1742,f1684,f1562,f594]) ).
fof(f1562,plain,
( spl26_186
<=> element(sK7,relation_dom(sK6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_186])]) ).
fof(f1742,plain,
( element(sK7,sK3)
| ~ spl26_186
| ~ spl26_204 ),
inference(superposition,[],[f1564,f1686]) ).
fof(f1564,plain,
( element(sK7,relation_dom(sK6))
| ~ spl26_186 ),
inference(avatar_component_clause,[],[f1562]) ).
fof(f1795,plain,
( spl26_215
| ~ spl26_45
| ~ spl26_162 ),
inference(avatar_split_clause,[],[f1340,f1313,f457,f1793]) ).
fof(f1793,plain,
( spl26_215
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(relation_dom(X1))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_215])]) ).
fof(f1313,plain,
( spl26_162
<=> ! [X2,X0,X1] :
( in(sK9(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| ~ empty(relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_162])]) ).
fof(f1340,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(relation_dom(X1))
| ~ empty(X2) )
| ~ spl26_45
| ~ spl26_162 ),
inference(resolution,[],[f1314,f458]) ).
fof(f1314,plain,
( ! [X2,X0,X1] :
( in(sK9(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| ~ empty(relation_dom(X1)) )
| ~ spl26_162 ),
inference(avatar_component_clause,[],[f1313]) ).
fof(f1791,plain,
( spl26_214
| ~ spl26_132
| ~ spl26_150 ),
inference(avatar_split_clause,[],[f1240,f1217,f1058,f1789]) ).
fof(f1789,plain,
( spl26_214
<=> ! [X2,X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| ~ in(X2,sK15(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_214])]) ).
fof(f1058,plain,
( spl26_132
<=> ! [X0,X1] : relation_of2_as_subset(sK15(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_132])]) ).
fof(f1217,plain,
( spl26_150
<=> ! [X2,X0,X1,X3] :
( ~ relation_of2_as_subset(X0,X1,X2)
| ~ empty(cartesian_product2(X1,X2))
| ~ in(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_150])]) ).
fof(f1240,plain,
( ! [X2,X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| ~ in(X2,sK15(X0,X1)) )
| ~ spl26_132
| ~ spl26_150 ),
inference(resolution,[],[f1218,f1059]) ).
fof(f1059,plain,
( ! [X0,X1] : relation_of2_as_subset(sK15(X0,X1),X0,X1)
| ~ spl26_132 ),
inference(avatar_component_clause,[],[f1058]) ).
fof(f1218,plain,
( ! [X2,X3,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| ~ empty(cartesian_product2(X1,X2))
| ~ in(X3,X0) )
| ~ spl26_150 ),
inference(avatar_component_clause,[],[f1217]) ).
fof(f1787,plain,
( spl26_213
| ~ spl26_131
| ~ spl26_150 ),
inference(avatar_split_clause,[],[f1239,f1217,f1054,f1785]) ).
fof(f1785,plain,
( spl26_213
<=> ! [X2,X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| ~ in(X2,sK14(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_213])]) ).
fof(f1054,plain,
( spl26_131
<=> ! [X0,X1] : relation_of2_as_subset(sK14(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_131])]) ).
fof(f1239,plain,
( ! [X2,X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| ~ in(X2,sK14(X0,X1)) )
| ~ spl26_131
| ~ spl26_150 ),
inference(resolution,[],[f1218,f1055]) ).
fof(f1055,plain,
( ! [X0,X1] : relation_of2_as_subset(sK14(X0,X1),X0,X1)
| ~ spl26_131 ),
inference(avatar_component_clause,[],[f1054]) ).
fof(f1783,plain,
( spl26_212
| ~ spl26_130
| ~ spl26_150 ),
inference(avatar_split_clause,[],[f1238,f1217,f1050,f1781]) ).
fof(f1781,plain,
( spl26_212
<=> ! [X2,X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| ~ in(X2,sK13(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_212])]) ).
fof(f1050,plain,
( spl26_130
<=> ! [X0,X1] : relation_of2_as_subset(sK13(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_130])]) ).
fof(f1238,plain,
( ! [X2,X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| ~ in(X2,sK13(X0,X1)) )
| ~ spl26_130
| ~ spl26_150 ),
inference(resolution,[],[f1218,f1051]) ).
fof(f1051,plain,
( ! [X0,X1] : relation_of2_as_subset(sK13(X0,X1),X0,X1)
| ~ spl26_130 ),
inference(avatar_component_clause,[],[f1050]) ).
fof(f1779,plain,
( spl26_211
| ~ spl26_50
| ~ spl26_150 ),
inference(avatar_split_clause,[],[f1237,f1217,f493,f1777]) ).
fof(f1777,plain,
( spl26_211
<=> ! [X2,X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| ~ in(X2,sK12(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_211])]) ).
fof(f493,plain,
( spl26_50
<=> ! [X0,X1] : relation_of2_as_subset(sK12(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_50])]) ).
fof(f1237,plain,
( ! [X2,X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| ~ in(X2,sK12(X0,X1)) )
| ~ spl26_50
| ~ spl26_150 ),
inference(resolution,[],[f1218,f494]) ).
fof(f494,plain,
( ! [X0,X1] : relation_of2_as_subset(sK12(X0,X1),X0,X1)
| ~ spl26_50 ),
inference(avatar_component_clause,[],[f493]) ).
fof(f1775,plain,
( spl26_210
| ~ spl26_42
| ~ spl26_141 ),
inference(avatar_split_clause,[],[f1154,f1138,f445,f1773]) ).
fof(f1773,plain,
( spl26_210
<=> ! [X0,X1] :
( ~ empty(X0)
| relation_dom(relation_dom(X1)) = X0
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_210])]) ).
fof(f445,plain,
( spl26_42
<=> ! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_42])]) ).
fof(f1138,plain,
( spl26_141
<=> ! [X0,X1] :
( relation_dom(X1) = X0
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_141])]) ).
fof(f1154,plain,
( ! [X0,X1] :
( ~ empty(X0)
| relation_dom(relation_dom(X1)) = X0
| ~ empty(X1) )
| ~ spl26_42
| ~ spl26_141 ),
inference(resolution,[],[f1139,f446]) ).
fof(f446,plain,
( ! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) )
| ~ spl26_42 ),
inference(avatar_component_clause,[],[f445]) ).
fof(f1139,plain,
( ! [X0,X1] :
( ~ empty(X1)
| ~ empty(X0)
| relation_dom(X1) = X0 )
| ~ spl26_141 ),
inference(avatar_component_clause,[],[f1138]) ).
fof(f1737,plain,
( spl26_209
| ~ spl26_132
| ~ spl26_166 ),
inference(avatar_split_clause,[],[f1376,f1362,f1058,f1735]) ).
fof(f1735,plain,
( spl26_209
<=> ! [X0] :
( sK17 = X0
| sK17 = sK15(X0,sK17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_209])]) ).
fof(f1362,plain,
( spl26_166
<=> ! [X0] :
( sK17 = X0
| ~ relation_of2_as_subset(sK15(X0,sK17),X0,sK17)
| sK17 = sK15(X0,sK17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_166])]) ).
fof(f1376,plain,
( ! [X0] :
( sK17 = X0
| sK17 = sK15(X0,sK17) )
| ~ spl26_132
| ~ spl26_166 ),
inference(resolution,[],[f1363,f1059]) ).
fof(f1363,plain,
( ! [X0] :
( ~ relation_of2_as_subset(sK15(X0,sK17),X0,sK17)
| sK17 = X0
| sK17 = sK15(X0,sK17) )
| ~ spl26_166 ),
inference(avatar_component_clause,[],[f1362]) ).
fof(f1733,plain,
( spl26_208
| ~ spl26_45
| ~ spl26_164 ),
inference(avatar_split_clause,[],[f1354,f1321,f457,f1731]) ).
fof(f1731,plain,
( spl26_208
<=> ! [X0,X1] :
( sP0(X0,X1,relation_dom(X1))
| ~ empty(relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_208])]) ).
fof(f1321,plain,
( spl26_164
<=> ! [X0,X1] :
( in(sK9(X0,X1,relation_dom(X1)),relation_dom(X1))
| sP0(X0,X1,relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_164])]) ).
fof(f1354,plain,
( ! [X0,X1] :
( sP0(X0,X1,relation_dom(X1))
| ~ empty(relation_dom(X1)) )
| ~ spl26_45
| ~ spl26_164 ),
inference(resolution,[],[f1322,f458]) ).
fof(f1322,plain,
( ! [X0,X1] :
( in(sK9(X0,X1,relation_dom(X1)),relation_dom(X1))
| sP0(X0,X1,relation_dom(X1)) )
| ~ spl26_164 ),
inference(avatar_component_clause,[],[f1321]) ).
fof(f1729,plain,
( spl26_207
| ~ spl26_45
| ~ spl26_159 ),
inference(avatar_split_clause,[],[f1294,f1273,f457,f1727]) ).
fof(f1727,plain,
( spl26_207
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(X0)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_207])]) ).
fof(f1273,plain,
( spl26_159
<=> ! [X2,X0,X1] :
( in(sK9(X1,X0,X2),X2)
| sP0(X1,X0,X2)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_159])]) ).
fof(f1294,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ empty(X0)
| ~ empty(X2) )
| ~ spl26_45
| ~ spl26_159 ),
inference(resolution,[],[f1274,f458]) ).
fof(f1274,plain,
( ! [X2,X0,X1] :
( in(sK9(X1,X0,X2),X2)
| sP0(X1,X0,X2)
| ~ empty(X1) )
| ~ spl26_159 ),
inference(avatar_component_clause,[],[f1273]) ).
fof(f1702,plain,
( spl26_206
| ~ spl26_123
| ~ spl26_162 ),
inference(avatar_split_clause,[],[f1350,f1313,f953,f1700]) ).
fof(f1700,plain,
( spl26_206
<=> ! [X0,X1] :
( sP0(X0,X1,sK17)
| ~ empty(relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_206])]) ).
fof(f1350,plain,
( ! [X0,X1] :
( sP0(X0,X1,sK17)
| ~ empty(relation_dom(X1)) )
| ~ spl26_123
| ~ spl26_162 ),
inference(resolution,[],[f1314,f954]) ).
fof(f1698,plain,
( spl26_205
| ~ spl26_42
| ~ spl26_125 ),
inference(avatar_split_clause,[],[f1068,f1030,f445,f1696]) ).
fof(f1696,plain,
( spl26_205
<=> ! [X0] :
( sK17 = relation_dom(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_205])]) ).
fof(f1030,plain,
( spl26_125
<=> ! [X0] :
( relation_dom(X0) = sK17
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_125])]) ).
fof(f1068,plain,
( ! [X0] :
( sK17 = relation_dom(relation_dom(X0))
| ~ empty(X0) )
| ~ spl26_42
| ~ spl26_125 ),
inference(resolution,[],[f1031,f446]) ).
fof(f1031,plain,
( ! [X0] :
( ~ empty(X0)
| relation_dom(X0) = sK17 )
| ~ spl26_125 ),
inference(avatar_component_clause,[],[f1030]) ).
fof(f1687,plain,
( spl26_204
| ~ spl26_102
| ~ spl26_187 ),
inference(avatar_split_clause,[],[f1571,f1567,f838,f1684]) ).
fof(f838,plain,
( spl26_102
<=> relation_dom_as_subset(sK3,sK4,sK6) = relation_dom(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_102])]) ).
fof(f1567,plain,
( spl26_187
<=> sK3 = relation_dom_as_subset(sK3,sK4,sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_187])]) ).
fof(f1571,plain,
( sK3 = relation_dom(sK6)
| ~ spl26_102
| ~ spl26_187 ),
inference(superposition,[],[f1569,f840]) ).
fof(f840,plain,
( relation_dom_as_subset(sK3,sK4,sK6) = relation_dom(sK6)
| ~ spl26_102 ),
inference(avatar_component_clause,[],[f838]) ).
fof(f1569,plain,
( sK3 = relation_dom_as_subset(sK3,sK4,sK6)
| ~ spl26_187 ),
inference(avatar_component_clause,[],[f1567]) ).
fof(f1664,plain,
( spl26_203
| ~ spl26_123
| ~ spl26_167 ),
inference(avatar_split_clause,[],[f1394,f1366,f953,f1662]) ).
fof(f1662,plain,
( spl26_203
<=> ! [X0,X1] :
( sP0(sK17,X0,X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_203])]) ).
fof(f1366,plain,
( spl26_167
<=> ! [X2,X0,X1] :
( in(apply(X1,sK9(X0,X1,X2)),X0)
| sP0(X0,X1,X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_167])]) ).
fof(f1394,plain,
( ! [X0,X1] :
( sP0(sK17,X0,X1)
| ~ empty(X1) )
| ~ spl26_123
| ~ spl26_167 ),
inference(resolution,[],[f1367,f954]) ).
fof(f1367,plain,
( ! [X2,X0,X1] :
( in(apply(X1,sK9(X0,X1,X2)),X0)
| sP0(X0,X1,X2)
| ~ empty(X2) )
| ~ spl26_167 ),
inference(avatar_component_clause,[],[f1366]) ).
fof(f1660,plain,
( spl26_202
| ~ spl26_123
| ~ spl26_159 ),
inference(avatar_split_clause,[],[f1303,f1273,f953,f1658]) ).
fof(f1658,plain,
( spl26_202
<=> ! [X0,X1] :
( sP0(X0,X1,sK17)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_202])]) ).
fof(f1303,plain,
( ! [X0,X1] :
( sP0(X0,X1,sK17)
| ~ empty(X0) )
| ~ spl26_123
| ~ spl26_159 ),
inference(resolution,[],[f1274,f954]) ).
fof(f1656,plain,
( spl26_201
| ~ spl26_126
| ~ spl26_137 ),
inference(avatar_split_clause,[],[f1124,f1114,f1034,f1654]) ).
fof(f1654,plain,
( spl26_201
<=> ! [X0] :
( ~ empty(X0)
| empty(sK10(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_201])]) ).
fof(f1114,plain,
( spl26_137
<=> ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK10(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_137])]) ).
fof(f1124,plain,
( ! [X0] :
( ~ empty(X0)
| empty(sK10(powerset(X0))) )
| ~ spl26_126
| ~ spl26_137 ),
inference(resolution,[],[f1115,f1035]) ).
fof(f1115,plain,
( ! [X0,X1] :
( ~ in(X1,sK10(powerset(X0)))
| ~ empty(X0) )
| ~ spl26_137 ),
inference(avatar_component_clause,[],[f1114]) ).
fof(f1652,plain,
( spl26_200
| ~ spl26_62
| ~ spl26_132 ),
inference(avatar_split_clause,[],[f1094,f1058,f578,f1650]) ).
fof(f1650,plain,
( spl26_200
<=> ! [X0,X1] : sP2(X0,sK15(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_200])]) ).
fof(f578,plain,
( spl26_62
<=> ! [X2,X0,X1] :
( sP2(X0,X2,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_62])]) ).
fof(f1094,plain,
( ! [X0,X1] : sP2(X0,sK15(X0,X1),X1)
| ~ spl26_62
| ~ spl26_132 ),
inference(resolution,[],[f1059,f579]) ).
fof(f579,plain,
( ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| sP2(X0,X2,X1) )
| ~ spl26_62 ),
inference(avatar_component_clause,[],[f578]) ).
fof(f1648,plain,
( spl26_199
| ~ spl26_62
| ~ spl26_131 ),
inference(avatar_split_clause,[],[f1092,f1054,f578,f1646]) ).
fof(f1646,plain,
( spl26_199
<=> ! [X0,X1] : sP2(X0,sK14(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_199])]) ).
fof(f1092,plain,
( ! [X0,X1] : sP2(X0,sK14(X0,X1),X1)
| ~ spl26_62
| ~ spl26_131 ),
inference(resolution,[],[f1055,f579]) ).
fof(f1643,plain,
( spl26_198
| ~ spl26_62
| ~ spl26_130 ),
inference(avatar_split_clause,[],[f1090,f1050,f578,f1641]) ).
fof(f1641,plain,
( spl26_198
<=> ! [X0,X1] : sP2(X0,sK13(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_198])]) ).
fof(f1090,plain,
( ! [X0,X1] : sP2(X0,sK13(X0,X1),X1)
| ~ spl26_62
| ~ spl26_130 ),
inference(resolution,[],[f1051,f579]) ).
fof(f1639,plain,
( spl26_197
| ~ spl26_48
| ~ spl26_126 ),
inference(avatar_split_clause,[],[f1082,f1034,f485,f1637]) ).
fof(f1637,plain,
( spl26_197
<=> ! [X0] :
( empty(X0)
| ~ in(X0,sK10(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_197])]) ).
fof(f485,plain,
( spl26_48
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_48])]) ).
fof(f1082,plain,
( ! [X0] :
( empty(X0)
| ~ in(X0,sK10(X0)) )
| ~ spl26_48
| ~ spl26_126 ),
inference(resolution,[],[f1035,f486]) ).
fof(f486,plain,
( ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) )
| ~ spl26_48 ),
inference(avatar_component_clause,[],[f485]) ).
fof(f1634,plain,
( spl26_196
| ~ spl26_120
| ~ spl26_138 ),
inference(avatar_split_clause,[],[f1151,f1126,f940,f1632]) ).
fof(f1632,plain,
( spl26_196
<=> ! [X0] :
( sP1(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_196])]) ).
fof(f940,plain,
( spl26_120
<=> ! [X0] :
( ~ empty(X0)
| function(relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_120])]) ).
fof(f1126,plain,
( spl26_138
<=> ! [X0] :
( ~ function(relation_dom(X0))
| sP1(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_138])]) ).
fof(f1151,plain,
( ! [X0] :
( sP1(relation_dom(X0))
| ~ empty(X0) )
| ~ spl26_120
| ~ spl26_138 ),
inference(duplicate_literal_removal,[],[f1150]) ).
fof(f1150,plain,
( ! [X0] :
( sP1(relation_dom(X0))
| ~ empty(X0)
| ~ empty(X0) )
| ~ spl26_120
| ~ spl26_138 ),
inference(resolution,[],[f1127,f941]) ).
fof(f941,plain,
( ! [X0] :
( function(relation_dom(X0))
| ~ empty(X0) )
| ~ spl26_120 ),
inference(avatar_component_clause,[],[f940]) ).
fof(f1127,plain,
( ! [X0] :
( ~ function(relation_dom(X0))
| sP1(relation_dom(X0))
| ~ empty(X0) )
| ~ spl26_138 ),
inference(avatar_component_clause,[],[f1126]) ).
fof(f1616,plain,
( ~ spl26_195
| ~ spl26_48
| ~ spl26_158 ),
inference(avatar_split_clause,[],[f1326,f1268,f485,f1613]) ).
fof(f1613,plain,
( spl26_195
<=> in(relation_dom(sK6),sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_195])]) ).
fof(f1326,plain,
( ~ in(relation_dom(sK6),sK7)
| ~ spl26_48
| ~ spl26_158 ),
inference(resolution,[],[f1270,f486]) ).
fof(f1270,plain,
( in(sK7,relation_dom(sK6))
| ~ spl26_158 ),
inference(avatar_component_clause,[],[f1268]) ).
fof(f1607,plain,
( spl26_194
| ~ spl26_38
| ~ spl26_140 ),
inference(avatar_split_clause,[],[f1153,f1134,f416,f1605]) ).
fof(f1605,plain,
( spl26_194
<=> ! [X0,X1] : sP1(sK15(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_194])]) ).
fof(f416,plain,
( spl26_38
<=> ! [X0,X1] : function(sK15(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_38])]) ).
fof(f1134,plain,
( spl26_140
<=> ! [X0,X1] :
( ~ function(sK15(X0,X1))
| sP1(sK15(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_140])]) ).
fof(f1153,plain,
( ! [X0,X1] : sP1(sK15(X0,X1))
| ~ spl26_38
| ~ spl26_140 ),
inference(resolution,[],[f1135,f417]) ).
fof(f417,plain,
( ! [X0,X1] : function(sK15(X0,X1))
| ~ spl26_38 ),
inference(avatar_component_clause,[],[f416]) ).
fof(f1135,plain,
( ! [X0,X1] :
( ~ function(sK15(X0,X1))
| sP1(sK15(X0,X1)) )
| ~ spl26_140 ),
inference(avatar_component_clause,[],[f1134]) ).
fof(f1603,plain,
( spl26_193
| ~ spl26_36
| ~ spl26_139 ),
inference(avatar_split_clause,[],[f1152,f1130,f408,f1601]) ).
fof(f1601,plain,
( spl26_193
<=> ! [X0,X1] : sP1(sK14(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_193])]) ).
fof(f408,plain,
( spl26_36
<=> ! [X0,X1] : function(sK14(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_36])]) ).
fof(f1130,plain,
( spl26_139
<=> ! [X0,X1] :
( ~ function(sK14(X0,X1))
| sP1(sK14(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_139])]) ).
fof(f1152,plain,
( ! [X0,X1] : sP1(sK14(X0,X1))
| ~ spl26_36
| ~ spl26_139 ),
inference(resolution,[],[f1131,f409]) ).
fof(f409,plain,
( ! [X0,X1] : function(sK14(X0,X1))
| ~ spl26_36 ),
inference(avatar_component_clause,[],[f408]) ).
fof(f1131,plain,
( ! [X0,X1] :
( ~ function(sK14(X0,X1))
| sP1(sK14(X0,X1)) )
| ~ spl26_139 ),
inference(avatar_component_clause,[],[f1130]) ).
fof(f1599,plain,
( spl26_192
| ~ spl26_31
| ~ spl26_136 ),
inference(avatar_split_clause,[],[f1120,f1110,f388,f1597]) ).
fof(f1597,plain,
( spl26_192
<=> ! [X0,X1] : relation(cartesian_product2(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_192])]) ).
fof(f388,plain,
( spl26_31
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_31])]) ).
fof(f1110,plain,
( spl26_136
<=> ! [X2,X0,X1] :
( relation(X0)
| ~ subset(X0,cartesian_product2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_136])]) ).
fof(f1120,plain,
( ! [X0,X1] : relation(cartesian_product2(X0,X1))
| ~ spl26_31
| ~ spl26_136 ),
inference(resolution,[],[f1111,f389]) ).
fof(f389,plain,
( ! [X0] : subset(X0,X0)
| ~ spl26_31 ),
inference(avatar_component_clause,[],[f388]) ).
fof(f1111,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,cartesian_product2(X1,X2))
| relation(X0) )
| ~ spl26_136 ),
inference(avatar_component_clause,[],[f1110]) ).
fof(f1595,plain,
( spl26_191
| ~ spl26_130
| ~ spl26_133 ),
inference(avatar_split_clause,[],[f1097,f1062,f1050,f1593]) ).
fof(f1593,plain,
( spl26_191
<=> ! [X0,X1] : relation(sK13(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_191])]) ).
fof(f1062,plain,
( spl26_133
<=> ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_133])]) ).
fof(f1097,plain,
( ! [X0,X1] : relation(sK13(X0,X1))
| ~ spl26_130
| ~ spl26_133 ),
inference(resolution,[],[f1063,f1051]) ).
fof(f1063,plain,
( ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| relation(X0) )
| ~ spl26_133 ),
inference(avatar_component_clause,[],[f1062]) ).
fof(f1591,plain,
( spl26_190
| ~ spl26_50
| ~ spl26_133 ),
inference(avatar_split_clause,[],[f1096,f1062,f493,f1589]) ).
fof(f1589,plain,
( spl26_190
<=> ! [X0,X1] : relation(sK12(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_190])]) ).
fof(f1096,plain,
( ! [X0,X1] : relation(sK12(X0,X1))
| ~ spl26_50
| ~ spl26_133 ),
inference(resolution,[],[f1063,f494]) ).
fof(f1587,plain,
( spl26_189
| ~ spl26_7
| ~ spl26_105
| ~ spl26_125 ),
inference(avatar_split_clause,[],[f1075,f1030,f854,f270,f1584]) ).
fof(f1584,plain,
( spl26_189
<=> sK17 = relation_dom(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_189])]) ).
fof(f270,plain,
( spl26_7
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_7])]) ).
fof(f854,plain,
( spl26_105
<=> empty_set = sK17 ),
introduced(avatar_definition,[new_symbols(naming,[spl26_105])]) ).
fof(f1075,plain,
( sK17 = relation_dom(sK17)
| ~ spl26_7
| ~ spl26_105
| ~ spl26_125 ),
inference(forward_demodulation,[],[f1069,f856]) ).
fof(f856,plain,
( empty_set = sK17
| ~ spl26_105 ),
inference(avatar_component_clause,[],[f854]) ).
fof(f1069,plain,
( sK17 = relation_dom(empty_set)
| ~ spl26_7
| ~ spl26_125 ),
inference(resolution,[],[f1031,f272]) ).
fof(f272,plain,
( empty(empty_set)
| ~ spl26_7 ),
inference(avatar_component_clause,[],[f270]) ).
fof(f1582,plain,
( spl26_188
| ~ spl26_44
| ~ spl26_119 ),
inference(avatar_split_clause,[],[f937,f934,f453,f1580]) ).
fof(f1580,plain,
( spl26_188
<=> ! [X0] : element(sK17,powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_188])]) ).
fof(f453,plain,
( spl26_44
<=> ! [X0] : element(sK11(X0),powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_44])]) ).
fof(f934,plain,
( spl26_119
<=> ! [X0] : sK11(X0) = sK17 ),
introduced(avatar_definition,[new_symbols(naming,[spl26_119])]) ).
fof(f937,plain,
( ! [X0] : element(sK17,powerset(X0))
| ~ spl26_44
| ~ spl26_119 ),
inference(superposition,[],[f454,f935]) ).
fof(f935,plain,
( ! [X0] : sK11(X0) = sK17
| ~ spl26_119 ),
inference(avatar_component_clause,[],[f934]) ).
fof(f454,plain,
( ! [X0] : element(sK11(X0),powerset(X0))
| ~ spl26_44 ),
inference(avatar_component_clause,[],[f453]) ).
fof(f1570,plain,
( spl26_109
| ~ spl26_3
| spl26_187
| ~ spl26_88
| ~ spl26_90 ),
inference(avatar_split_clause,[],[f790,f761,f744,f1567,f251,f883]) ).
fof(f883,plain,
( spl26_109
<=> sK4 = sK17 ),
introduced(avatar_definition,[new_symbols(naming,[spl26_109])]) ).
fof(f251,plain,
( spl26_3
<=> quasi_total(sK6,sK3,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_3])]) ).
fof(f744,plain,
( spl26_88
<=> sP2(sK3,sK6,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_88])]) ).
fof(f761,plain,
( spl26_90
<=> ! [X2,X0,X1] :
( sK17 = X2
| relation_dom_as_subset(X0,X2,X1) = X0
| ~ quasi_total(X1,X0,X2)
| ~ sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_90])]) ).
fof(f790,plain,
( sK3 = relation_dom_as_subset(sK3,sK4,sK6)
| ~ quasi_total(sK6,sK3,sK4)
| sK4 = sK17
| ~ spl26_88
| ~ spl26_90 ),
inference(resolution,[],[f746,f762]) ).
fof(f762,plain,
( ! [X2,X0,X1] :
( ~ sP2(X0,X1,X2)
| relation_dom_as_subset(X0,X2,X1) = X0
| ~ quasi_total(X1,X0,X2)
| sK17 = X2 )
| ~ spl26_90 ),
inference(avatar_component_clause,[],[f761]) ).
fof(f746,plain,
( sP2(sK3,sK6,sK4)
| ~ spl26_88 ),
inference(avatar_component_clause,[],[f744]) ).
fof(f1565,plain,
( spl26_186
| ~ spl26_49
| ~ spl26_158 ),
inference(avatar_split_clause,[],[f1325,f1268,f489,f1562]) ).
fof(f1325,plain,
( element(sK7,relation_dom(sK6))
| ~ spl26_49
| ~ spl26_158 ),
inference(resolution,[],[f1270,f490]) ).
fof(f1559,plain,
( spl26_185
| ~ spl26_4
| ~ spl26_155 ),
inference(avatar_split_clause,[],[f1276,f1256,f256,f1557]) ).
fof(f1557,plain,
( spl26_185
<=> ! [X0] :
( ~ in(X0,sK6)
| element(X0,cartesian_product2(sK3,sK4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_185])]) ).
fof(f256,plain,
( spl26_4
<=> relation_of2_as_subset(sK6,sK3,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_4])]) ).
fof(f1256,plain,
( spl26_155
<=> ! [X0,X3,X2,X1] :
( element(X0,cartesian_product2(X1,X2))
| ~ in(X0,X3)
| ~ relation_of2_as_subset(X3,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_155])]) ).
fof(f1276,plain,
( ! [X0] :
( ~ in(X0,sK6)
| element(X0,cartesian_product2(sK3,sK4)) )
| ~ spl26_4
| ~ spl26_155 ),
inference(resolution,[],[f1257,f258]) ).
fof(f258,plain,
( relation_of2_as_subset(sK6,sK3,sK4)
| ~ spl26_4 ),
inference(avatar_component_clause,[],[f256]) ).
fof(f1257,plain,
( ! [X2,X3,X0,X1] :
( ~ relation_of2_as_subset(X3,X1,X2)
| ~ in(X0,X3)
| element(X0,cartesian_product2(X1,X2)) )
| ~ spl26_155 ),
inference(avatar_component_clause,[],[f1256]) ).
fof(f1555,plain,
( spl26_184
| ~ spl26_46
| ~ spl26_121 ),
inference(avatar_split_clause,[],[f1544,f944,f476,f1552]) ).
fof(f944,plain,
( spl26_121
<=> ! [X0] :
( sK17 = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_121])]) ).
fof(f1544,plain,
( sK3 = sK17
| ~ spl26_46
| ~ spl26_121 ),
inference(resolution,[],[f477,f945]) ).
fof(f945,plain,
( ! [X0] :
( ~ empty(X0)
| sK17 = X0 )
| ~ spl26_121 ),
inference(avatar_component_clause,[],[f944]) ).
fof(f477,plain,
( empty(sK3)
| ~ spl26_46 ),
inference(avatar_component_clause,[],[f476]) ).
fof(f1541,plain,
( spl26_6
| spl26_46
| ~ spl26_60
| ~ spl26_66 ),
inference(avatar_split_clause,[],[f672,f594,f570,f476,f265]) ).
fof(f570,plain,
( spl26_60
<=> ! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_60])]) ).
fof(f672,plain,
( empty(sK3)
| in(sK7,sK3)
| ~ spl26_60
| ~ spl26_66 ),
inference(resolution,[],[f596,f571]) ).
fof(f571,plain,
( ! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) )
| ~ spl26_60 ),
inference(avatar_component_clause,[],[f570]) ).
fof(f1539,plain,
( ~ spl26_158
| spl26_183
| ~ spl26_28
| ~ spl26_85 ),
inference(avatar_split_clause,[],[f803,f731,f375,f1537,f1268]) ).
fof(f375,plain,
( spl26_28
<=> in(apply(sK6,sK7),sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_28])]) ).
fof(f731,plain,
( spl26_85
<=> ! [X4,X0,X2,X1] :
( in(X4,X2)
| ~ in(apply(X1,X4),X0)
| ~ in(X4,relation_dom(X1))
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_85])]) ).
fof(f803,plain,
( ! [X0] :
( in(sK7,X0)
| ~ in(sK7,relation_dom(sK6))
| ~ sP0(sK5,sK6,X0) )
| ~ spl26_28
| ~ spl26_85 ),
inference(resolution,[],[f377,f732]) ).
fof(f732,plain,
( ! [X2,X0,X1,X4] :
( ~ in(apply(X1,X4),X0)
| in(X4,X2)
| ~ in(X4,relation_dom(X1))
| ~ sP0(X0,X1,X2) )
| ~ spl26_85 ),
inference(avatar_component_clause,[],[f731]) ).
fof(f377,plain,
( in(apply(sK6,sK7),sK5)
| ~ spl26_28 ),
inference(avatar_component_clause,[],[f375]) ).
fof(f1534,plain,
( ~ spl26_182
| ~ spl26_28
| ~ spl26_48 ),
inference(avatar_split_clause,[],[f805,f485,f375,f1531]) ).
fof(f1531,plain,
( spl26_182
<=> in(sK5,apply(sK6,sK7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_182])]) ).
fof(f805,plain,
( ~ in(sK5,apply(sK6,sK7))
| ~ spl26_28
| ~ spl26_48 ),
inference(resolution,[],[f377,f486]) ).
fof(f1529,plain,
( ~ spl26_5
| ~ spl26_6
| ~ spl26_28 ),
inference(avatar_split_clause,[],[f154,f375,f265,f261]) ).
fof(f154,plain,
( ~ in(apply(sK6,sK7),sK5)
| ~ in(sK7,sK3)
| ~ in(sK7,relation_inverse_image(sK6,sK5)) ),
inference(cnf_transformation,[],[f103]) ).
fof(f103,plain,
( ( ~ in(apply(sK6,sK7),sK5)
| ~ in(sK7,sK3)
| ~ in(sK7,relation_inverse_image(sK6,sK5)) )
& ( ( in(apply(sK6,sK7),sK5)
& in(sK7,sK3) )
| in(sK7,relation_inverse_image(sK6,sK5)) )
& empty_set != sK4
& relation_of2_as_subset(sK6,sK3,sK4)
& quasi_total(sK6,sK3,sK4)
& function(sK6) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6,sK7])],[f100,f102,f101]) ).
fof(f101,plain,
( ? [X0,X1,X2,X3] :
( ? [X4] :
( ( ~ in(apply(X3,X4),X2)
| ~ in(X4,X0)
| ~ in(X4,relation_inverse_image(X3,X2)) )
& ( ( in(apply(X3,X4),X2)
& in(X4,X0) )
| in(X4,relation_inverse_image(X3,X2)) ) )
& empty_set != X1
& relation_of2_as_subset(X3,X0,X1)
& quasi_total(X3,X0,X1)
& function(X3) )
=> ( ? [X4] :
( ( ~ in(apply(sK6,X4),sK5)
| ~ in(X4,sK3)
| ~ in(X4,relation_inverse_image(sK6,sK5)) )
& ( ( in(apply(sK6,X4),sK5)
& in(X4,sK3) )
| in(X4,relation_inverse_image(sK6,sK5)) ) )
& empty_set != sK4
& relation_of2_as_subset(sK6,sK3,sK4)
& quasi_total(sK6,sK3,sK4)
& function(sK6) ) ),
introduced(choice_axiom,[]) ).
fof(f102,plain,
( ? [X4] :
( ( ~ in(apply(sK6,X4),sK5)
| ~ in(X4,sK3)
| ~ in(X4,relation_inverse_image(sK6,sK5)) )
& ( ( in(apply(sK6,X4),sK5)
& in(X4,sK3) )
| in(X4,relation_inverse_image(sK6,sK5)) ) )
=> ( ( ~ in(apply(sK6,sK7),sK5)
| ~ in(sK7,sK3)
| ~ in(sK7,relation_inverse_image(sK6,sK5)) )
& ( ( in(apply(sK6,sK7),sK5)
& in(sK7,sK3) )
| in(sK7,relation_inverse_image(sK6,sK5)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f100,plain,
? [X0,X1,X2,X3] :
( ? [X4] :
( ( ~ in(apply(X3,X4),X2)
| ~ in(X4,X0)
| ~ in(X4,relation_inverse_image(X3,X2)) )
& ( ( in(apply(X3,X4),X2)
& in(X4,X0) )
| in(X4,relation_inverse_image(X3,X2)) ) )
& empty_set != X1
& relation_of2_as_subset(X3,X0,X1)
& quasi_total(X3,X0,X1)
& function(X3) ),
inference(flattening,[],[f99]) ).
fof(f99,plain,
? [X0,X1,X2,X3] :
( ? [X4] :
( ( ~ in(apply(X3,X4),X2)
| ~ in(X4,X0)
| ~ in(X4,relation_inverse_image(X3,X2)) )
& ( ( in(apply(X3,X4),X2)
& in(X4,X0) )
| in(X4,relation_inverse_image(X3,X2)) ) )
& empty_set != X1
& relation_of2_as_subset(X3,X0,X1)
& quasi_total(X3,X0,X1)
& function(X3) ),
inference(nnf_transformation,[],[f64]) ).
fof(f64,plain,
? [X0,X1,X2,X3] :
( ? [X4] :
( in(X4,relation_inverse_image(X3,X2))
<~> ( in(apply(X3,X4),X2)
& in(X4,X0) ) )
& empty_set != X1
& relation_of2_as_subset(X3,X0,X1)
& quasi_total(X3,X0,X1)
& function(X3) ),
inference(flattening,[],[f63]) ).
fof(f63,plain,
? [X0,X1,X2,X3] :
( ? [X4] :
( in(X4,relation_inverse_image(X3,X2))
<~> ( in(apply(X3,X4),X2)
& in(X4,X0) ) )
& empty_set != X1
& relation_of2_as_subset(X3,X0,X1)
& quasi_total(X3,X0,X1)
& function(X3) ),
inference(ennf_transformation,[],[f49]) ).
fof(f49,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( relation_of2_as_subset(X3,X0,X1)
& quasi_total(X3,X0,X1)
& function(X3) )
=> ( empty_set != X1
=> ! [X4] :
( in(X4,relation_inverse_image(X3,X2))
<=> ( in(apply(X3,X4),X2)
& in(X4,X0) ) ) ) ),
inference(negated_conjecture,[],[f48]) ).
fof(f48,conjecture,
! [X0,X1,X2,X3] :
( ( relation_of2_as_subset(X3,X0,X1)
& quasi_total(X3,X0,X1)
& function(X3) )
=> ( empty_set != X1
=> ! [X4] :
( in(X4,relation_inverse_image(X3,X2))
<=> ( in(apply(X3,X4),X2)
& in(X4,X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_funct_2) ).
fof(f1524,plain,
( ~ spl26_147
| spl26_28
| ~ spl26_5
| ~ spl26_157 ),
inference(avatar_split_clause,[],[f1290,f1264,f261,f375,f1190]) ).
fof(f1264,plain,
( spl26_157
<=> ! [X2,X0,X1] :
( ~ in(X0,relation_inverse_image(X1,X2))
| in(apply(X1,X0),X2)
| ~ sP1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_157])]) ).
fof(f1290,plain,
( in(apply(sK6,sK7),sK5)
| ~ sP1(sK6)
| ~ spl26_5
| ~ spl26_157 ),
inference(resolution,[],[f1265,f263]) ).
fof(f263,plain,
( in(sK7,relation_inverse_image(sK6,sK5))
| ~ spl26_5 ),
inference(avatar_component_clause,[],[f261]) ).
fof(f1265,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_inverse_image(X1,X2))
| in(apply(X1,X0),X2)
| ~ sP1(X1) )
| ~ spl26_157 ),
inference(avatar_component_clause,[],[f1264]) ).
fof(f1523,plain,
( spl26_180
| ~ spl26_181
| ~ spl26_4
| ~ spl26_150 ),
inference(avatar_split_clause,[],[f1236,f1217,f256,f1520,f1517]) ).
fof(f1517,plain,
( spl26_180
<=> ! [X0] : ~ in(X0,sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_180])]) ).
fof(f1520,plain,
( spl26_181
<=> empty(cartesian_product2(sK3,sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_181])]) ).
fof(f1236,plain,
( ! [X0] :
( ~ empty(cartesian_product2(sK3,sK4))
| ~ in(X0,sK6) )
| ~ spl26_4
| ~ spl26_150 ),
inference(resolution,[],[f1218,f258]) ).
fof(f1498,plain,
( ~ spl26_179
| ~ spl26_42
| spl26_168 ),
inference(avatar_split_clause,[],[f1440,f1378,f445,f1495]) ).
fof(f1495,plain,
( spl26_179
<=> empty(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_179])]) ).
fof(f1440,plain,
( ~ empty(sK6)
| ~ spl26_42
| spl26_168 ),
inference(resolution,[],[f1380,f446]) ).
fof(f1493,plain,
( spl26_178
| ~ spl26_85
| ~ spl26_92 ),
inference(avatar_split_clause,[],[f772,f769,f731,f1491]) ).
fof(f1491,plain,
( spl26_178
<=> ! [X0,X3,X2,X1] :
( in(sK9(X1,X0,X2),X2)
| sP0(X1,X0,X2)
| in(sK9(X1,X0,X2),X3)
| ~ in(sK9(X1,X0,X2),relation_dom(X0))
| ~ sP0(X1,X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_178])]) ).
fof(f772,plain,
( ! [X2,X3,X0,X1] :
( in(sK9(X1,X0,X2),X2)
| sP0(X1,X0,X2)
| in(sK9(X1,X0,X2),X3)
| ~ in(sK9(X1,X0,X2),relation_dom(X0))
| ~ sP0(X1,X0,X3) )
| ~ spl26_85
| ~ spl26_92 ),
inference(resolution,[],[f770,f732]) ).
fof(f1456,plain,
( spl26_177
| ~ spl26_48
| ~ spl26_92 ),
inference(avatar_split_clause,[],[f777,f769,f485,f1454]) ).
fof(f1454,plain,
( spl26_177
<=> ! [X2,X0,X1] :
( in(apply(X1,sK9(X0,X1,X2)),X0)
| sP0(X0,X1,X2)
| ~ in(X2,sK9(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_177])]) ).
fof(f777,plain,
( ! [X2,X0,X1] :
( in(apply(X1,sK9(X0,X1,X2)),X0)
| sP0(X0,X1,X2)
| ~ in(X2,sK9(X0,X1,X2)) )
| ~ spl26_48
| ~ spl26_92 ),
inference(resolution,[],[f770,f486]) ).
fof(f1452,plain,
( spl26_176
| ~ spl26_49
| ~ spl26_92 ),
inference(avatar_split_clause,[],[f776,f769,f489,f1450]) ).
fof(f1450,plain,
( spl26_176
<=> ! [X2,X0,X1] :
( in(apply(X1,sK9(X0,X1,X2)),X0)
| sP0(X0,X1,X2)
| element(sK9(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_176])]) ).
fof(f776,plain,
( ! [X2,X0,X1] :
( in(apply(X1,sK9(X0,X1,X2)),X0)
| sP0(X0,X1,X2)
| element(sK9(X0,X1,X2),X2) )
| ~ spl26_49
| ~ spl26_92 ),
inference(resolution,[],[f770,f490]) ).
fof(f1448,plain,
( spl26_175
| ~ spl26_48
| ~ spl26_92 ),
inference(avatar_split_clause,[],[f774,f769,f485,f1446]) ).
fof(f1446,plain,
( spl26_175
<=> ! [X2,X0,X1] :
( in(sK9(X1,X0,X2),X2)
| sP0(X1,X0,X2)
| ~ in(X1,apply(X0,sK9(X1,X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_175])]) ).
fof(f774,plain,
( ! [X2,X0,X1] :
( in(sK9(X1,X0,X2),X2)
| sP0(X1,X0,X2)
| ~ in(X1,apply(X0,sK9(X1,X0,X2))) )
| ~ spl26_48
| ~ spl26_92 ),
inference(resolution,[],[f770,f486]) ).
fof(f1444,plain,
( spl26_174
| ~ spl26_49
| ~ spl26_92 ),
inference(avatar_split_clause,[],[f773,f769,f489,f1442]) ).
fof(f1442,plain,
( spl26_174
<=> ! [X2,X0,X1] :
( in(sK9(X1,X0,X2),X2)
| sP0(X1,X0,X2)
| element(apply(X0,sK9(X1,X0,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_174])]) ).
fof(f773,plain,
( ! [X2,X0,X1] :
( in(sK9(X1,X0,X2),X2)
| sP0(X1,X0,X2)
| element(apply(X0,sK9(X1,X0,X2)),X1) )
| ~ spl26_49
| ~ spl26_92 ),
inference(resolution,[],[f770,f490]) ).
fof(f1420,plain,
( spl26_173
| ~ spl26_48
| ~ spl26_86 ),
inference(avatar_split_clause,[],[f757,f735,f485,f1418]) ).
fof(f1418,plain,
( spl26_173
<=> ! [X2,X0,X1] :
( in(sK9(X0,X1,X2),relation_dom(X1))
| sP0(X0,X1,X2)
| ~ in(X2,sK9(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_173])]) ).
fof(f735,plain,
( spl26_86
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(sK9(X0,X1,X2),relation_dom(X1))
| in(sK9(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_86])]) ).
fof(f757,plain,
( ! [X2,X0,X1] :
( in(sK9(X0,X1,X2),relation_dom(X1))
| sP0(X0,X1,X2)
| ~ in(X2,sK9(X0,X1,X2)) )
| ~ spl26_48
| ~ spl26_86 ),
inference(resolution,[],[f736,f486]) ).
fof(f736,plain,
( ! [X2,X0,X1] :
( in(sK9(X0,X1,X2),relation_dom(X1))
| in(sK9(X0,X1,X2),X2)
| sP0(X0,X1,X2) )
| ~ spl26_86 ),
inference(avatar_component_clause,[],[f735]) ).
fof(f1416,plain,
( spl26_172
| ~ spl26_49
| ~ spl26_86 ),
inference(avatar_split_clause,[],[f756,f735,f489,f1414]) ).
fof(f1414,plain,
( spl26_172
<=> ! [X2,X0,X1] :
( in(sK9(X0,X1,X2),relation_dom(X1))
| sP0(X0,X1,X2)
| element(sK9(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_172])]) ).
fof(f756,plain,
( ! [X2,X0,X1] :
( in(sK9(X0,X1,X2),relation_dom(X1))
| sP0(X0,X1,X2)
| element(sK9(X0,X1,X2),X2) )
| ~ spl26_49
| ~ spl26_86 ),
inference(resolution,[],[f736,f490]) ).
fof(f1412,plain,
( spl26_171
| ~ spl26_48
| ~ spl26_86 ),
inference(avatar_split_clause,[],[f754,f735,f485,f1410]) ).
fof(f1410,plain,
( spl26_171
<=> ! [X2,X0,X1] :
( in(sK9(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| ~ in(relation_dom(X1),sK9(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_171])]) ).
fof(f754,plain,
( ! [X2,X0,X1] :
( in(sK9(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| ~ in(relation_dom(X1),sK9(X0,X1,X2)) )
| ~ spl26_48
| ~ spl26_86 ),
inference(resolution,[],[f736,f486]) ).
fof(f1408,plain,
( spl26_170
| ~ spl26_49
| ~ spl26_86 ),
inference(avatar_split_clause,[],[f753,f735,f489,f1406]) ).
fof(f1406,plain,
( spl26_170
<=> ! [X2,X0,X1] :
( in(sK9(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| element(sK9(X0,X1,X2),relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_170])]) ).
fof(f753,plain,
( ! [X2,X0,X1] :
( in(sK9(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| element(sK9(X0,X1,X2),relation_dom(X1)) )
| ~ spl26_49
| ~ spl26_86 ),
inference(resolution,[],[f736,f490]) ).
fof(f1399,plain,
( spl26_169
| ~ spl26_60
| ~ spl26_69 ),
inference(avatar_split_clause,[],[f639,f630,f570,f1397]) ).
fof(f1397,plain,
( spl26_169
<=> ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| empty(powerset(cartesian_product2(X1,X2)))
| in(X0,powerset(cartesian_product2(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_169])]) ).
fof(f630,plain,
( spl26_69
<=> ! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_69])]) ).
fof(f639,plain,
( ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| empty(powerset(cartesian_product2(X1,X2)))
| in(X0,powerset(cartesian_product2(X1,X2))) )
| ~ spl26_60
| ~ spl26_69 ),
inference(resolution,[],[f631,f571]) ).
fof(f631,plain,
( ! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) )
| ~ spl26_69 ),
inference(avatar_component_clause,[],[f630]) ).
fof(f1381,plain,
( ~ spl26_168
| ~ spl26_45
| ~ spl26_158 ),
inference(avatar_split_clause,[],[f1324,f1268,f457,f1378]) ).
fof(f1324,plain,
( ~ empty(relation_dom(sK6))
| ~ spl26_45
| ~ spl26_158 ),
inference(resolution,[],[f1270,f458]) ).
fof(f1368,plain,
( spl26_167
| ~ spl26_45
| ~ spl26_92 ),
inference(avatar_split_clause,[],[f778,f769,f457,f1366]) ).
fof(f778,plain,
( ! [X2,X0,X1] :
( in(apply(X1,sK9(X0,X1,X2)),X0)
| sP0(X0,X1,X2)
| ~ empty(X2) )
| ~ spl26_45
| ~ spl26_92 ),
inference(resolution,[],[f770,f458]) ).
fof(f1364,plain,
( spl26_166
| ~ spl26_54
| ~ spl26_84 ),
inference(avatar_split_clause,[],[f729,f726,f509,f1362]) ).
fof(f509,plain,
( spl26_54
<=> ! [X0,X1] : quasi_total(sK15(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_54])]) ).
fof(f726,plain,
( spl26_84
<=> ! [X2,X0] :
( ~ relation_of2_as_subset(X2,X0,sK17)
| sK17 = X0
| ~ quasi_total(X2,X0,sK17)
| sK17 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_84])]) ).
fof(f729,plain,
( ! [X0] :
( sK17 = X0
| ~ relation_of2_as_subset(sK15(X0,sK17),X0,sK17)
| sK17 = sK15(X0,sK17) )
| ~ spl26_54
| ~ spl26_84 ),
inference(resolution,[],[f727,f510]) ).
fof(f510,plain,
( ! [X0,X1] : quasi_total(sK15(X0,X1),X0,X1)
| ~ spl26_54 ),
inference(avatar_component_clause,[],[f509]) ).
fof(f727,plain,
( ! [X2,X0] :
( ~ quasi_total(X2,X0,sK17)
| sK17 = X0
| ~ relation_of2_as_subset(X2,X0,sK17)
| sK17 = X2 )
| ~ spl26_84 ),
inference(avatar_component_clause,[],[f726]) ).
fof(f1360,plain,
( spl26_165
| ~ spl26_60
| ~ spl26_74 ),
inference(avatar_split_clause,[],[f680,f660,f570,f1358]) ).
fof(f1358,plain,
( spl26_165
<=> ! [X2,X0,X1] :
( ~ relation_of2(X0,X1,X2)
| empty(powerset(X1))
| in(relation_dom_as_subset(X1,X2,X0),powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_165])]) ).
fof(f660,plain,
( spl26_74
<=> ! [X2,X0,X1] :
( element(relation_dom_as_subset(X0,X1,X2),powerset(X0))
| ~ relation_of2(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_74])]) ).
fof(f680,plain,
( ! [X2,X0,X1] :
( ~ relation_of2(X0,X1,X2)
| empty(powerset(X1))
| in(relation_dom_as_subset(X1,X2,X0),powerset(X1)) )
| ~ spl26_60
| ~ spl26_74 ),
inference(resolution,[],[f661,f571]) ).
fof(f661,plain,
( ! [X2,X0,X1] :
( element(relation_dom_as_subset(X0,X1,X2),powerset(X0))
| ~ relation_of2(X2,X0,X1) )
| ~ spl26_74 ),
inference(avatar_component_clause,[],[f660]) ).
fof(f1323,plain,
( spl26_164
| ~ spl26_86 ),
inference(avatar_split_clause,[],[f759,f735,f1321]) ).
fof(f759,plain,
( ! [X0,X1] :
( in(sK9(X0,X1,relation_dom(X1)),relation_dom(X1))
| sP0(X0,X1,relation_dom(X1)) )
| ~ spl26_86 ),
inference(factoring,[],[f736]) ).
fof(f1319,plain,
( spl26_163
| ~ spl26_45
| ~ spl26_86 ),
inference(avatar_split_clause,[],[f758,f735,f457,f1317]) ).
fof(f1317,plain,
( spl26_163
<=> ! [X2,X0,X1] :
( in(sK9(X0,X1,X2),relation_dom(X1))
| sP0(X0,X1,X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_163])]) ).
fof(f758,plain,
( ! [X2,X0,X1] :
( in(sK9(X0,X1,X2),relation_dom(X1))
| sP0(X0,X1,X2)
| ~ empty(X2) )
| ~ spl26_45
| ~ spl26_86 ),
inference(resolution,[],[f736,f458]) ).
fof(f1315,plain,
( spl26_162
| ~ spl26_45
| ~ spl26_86 ),
inference(avatar_split_clause,[],[f755,f735,f457,f1313]) ).
fof(f755,plain,
( ! [X2,X0,X1] :
( in(sK9(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| ~ empty(relation_dom(X1)) )
| ~ spl26_45
| ~ spl26_86 ),
inference(resolution,[],[f736,f458]) ).
fof(f1311,plain,
( spl26_161
| ~ spl26_70
| ~ spl26_74 ),
inference(avatar_split_clause,[],[f678,f660,f634,f1309]) ).
fof(f1309,plain,
( spl26_161
<=> ! [X0,X3,X2,X1] :
( ~ relation_of2(X0,X1,X2)
| element(X3,X1)
| ~ in(X3,relation_dom_as_subset(X1,X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_161])]) ).
fof(f634,plain,
( spl26_70
<=> ! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_70])]) ).
fof(f678,plain,
( ! [X2,X3,X0,X1] :
( ~ relation_of2(X0,X1,X2)
| element(X3,X1)
| ~ in(X3,relation_dom_as_subset(X1,X2,X0)) )
| ~ spl26_70
| ~ spl26_74 ),
inference(resolution,[],[f661,f635]) ).
fof(f635,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| element(X0,X2)
| ~ in(X0,X1) )
| ~ spl26_70 ),
inference(avatar_component_clause,[],[f634]) ).
fof(f1307,plain,
( spl26_160
| ~ spl26_63
| ~ spl26_74 ),
inference(avatar_split_clause,[],[f677,f660,f582,f1305]) ).
fof(f1305,plain,
( spl26_160
<=> ! [X0,X3,X2,X1] :
( ~ relation_of2(X0,cartesian_product2(X1,X2),X3)
| relation(relation_dom_as_subset(cartesian_product2(X1,X2),X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_160])]) ).
fof(f582,plain,
( spl26_63
<=> ! [X2,X0,X1] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_63])]) ).
fof(f677,plain,
( ! [X2,X3,X0,X1] :
( ~ relation_of2(X0,cartesian_product2(X1,X2),X3)
| relation(relation_dom_as_subset(cartesian_product2(X1,X2),X3,X0)) )
| ~ spl26_63
| ~ spl26_74 ),
inference(resolution,[],[f661,f583]) ).
fof(f583,plain,
( ! [X2,X0,X1] :
( ~ element(X2,powerset(cartesian_product2(X0,X1)))
| relation(X2) )
| ~ spl26_63 ),
inference(avatar_component_clause,[],[f582]) ).
fof(f1275,plain,
( spl26_159
| ~ spl26_45
| ~ spl26_92 ),
inference(avatar_split_clause,[],[f775,f769,f457,f1273]) ).
fof(f775,plain,
( ! [X2,X0,X1] :
( in(sK9(X1,X0,X2),X2)
| sP0(X1,X0,X2)
| ~ empty(X1) )
| ~ spl26_45
| ~ spl26_92 ),
inference(resolution,[],[f770,f458]) ).
fof(f1271,plain,
( ~ spl26_147
| spl26_158
| ~ spl26_5
| ~ spl26_151 ),
inference(avatar_split_clause,[],[f1242,f1221,f261,f1268,f1190]) ).
fof(f1221,plain,
( spl26_151
<=> ! [X2,X0,X1] :
( ~ in(X0,relation_inverse_image(X1,X2))
| in(X0,relation_dom(X1))
| ~ sP1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_151])]) ).
fof(f1242,plain,
( in(sK7,relation_dom(sK6))
| ~ sP1(sK6)
| ~ spl26_5
| ~ spl26_151 ),
inference(resolution,[],[f1222,f263]) ).
fof(f1222,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_inverse_image(X1,X2))
| in(X0,relation_dom(X1))
| ~ sP1(X1) )
| ~ spl26_151 ),
inference(avatar_component_clause,[],[f1221]) ).
fof(f1266,plain,
( spl26_157
| ~ spl26_67
| ~ spl26_77 ),
inference(avatar_split_clause,[],[f689,f686,f599,f1264]) ).
fof(f686,plain,
( spl26_77
<=> ! [X2,X4,X0,X1] :
( in(apply(X1,X4),X0)
| ~ in(X4,X2)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_77])]) ).
fof(f689,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_inverse_image(X1,X2))
| in(apply(X1,X0),X2)
| ~ sP1(X1) )
| ~ spl26_67
| ~ spl26_77 ),
inference(resolution,[],[f687,f600]) ).
fof(f687,plain,
( ! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| ~ in(X4,X2)
| in(apply(X1,X4),X0) )
| ~ spl26_77 ),
inference(avatar_component_clause,[],[f686]) ).
fof(f1262,plain,
( spl26_156
| ~ spl26_68
| ~ spl26_74 ),
inference(avatar_split_clause,[],[f679,f660,f620,f1260]) ).
fof(f1260,plain,
( spl26_156
<=> ! [X2,X0,X1,X3] :
( ~ relation_of2(X0,X1,X2)
| ~ empty(X1)
| ~ in(X3,relation_dom_as_subset(X1,X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_156])]) ).
fof(f620,plain,
( spl26_68
<=> ! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_68])]) ).
fof(f679,plain,
( ! [X2,X3,X0,X1] :
( ~ relation_of2(X0,X1,X2)
| ~ empty(X1)
| ~ in(X3,relation_dom_as_subset(X1,X2,X0)) )
| ~ spl26_68
| ~ spl26_74 ),
inference(resolution,[],[f661,f621]) ).
fof(f621,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X0,X1) )
| ~ spl26_68 ),
inference(avatar_component_clause,[],[f620]) ).
fof(f1258,plain,
( spl26_155
| ~ spl26_69
| ~ spl26_70 ),
inference(avatar_split_clause,[],[f641,f634,f630,f1256]) ).
fof(f641,plain,
( ! [X2,X3,X0,X1] :
( element(X0,cartesian_product2(X1,X2))
| ~ in(X0,X3)
| ~ relation_of2_as_subset(X3,X1,X2) )
| ~ spl26_69
| ~ spl26_70 ),
inference(resolution,[],[f635,f631]) ).
fof(f1235,plain,
( spl26_154
| ~ spl26_53
| ~ spl26_73 ),
inference(avatar_split_clause,[],[f676,f656,f505,f1233]) ).
fof(f1233,plain,
( spl26_154
<=> ! [X0,X1] : relation_dom_as_subset(X0,X1,sK15(X0,X1)) = relation_dom(sK15(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_154])]) ).
fof(f505,plain,
( spl26_53
<=> ! [X0,X1] : relation_of2(sK15(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_53])]) ).
fof(f656,plain,
( spl26_73
<=> ! [X2,X0,X1] :
( relation_dom_as_subset(X0,X1,X2) = relation_dom(X2)
| ~ relation_of2(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_73])]) ).
fof(f676,plain,
( ! [X0,X1] : relation_dom_as_subset(X0,X1,sK15(X0,X1)) = relation_dom(sK15(X0,X1))
| ~ spl26_53
| ~ spl26_73 ),
inference(resolution,[],[f657,f506]) ).
fof(f506,plain,
( ! [X0,X1] : relation_of2(sK15(X0,X1),X0,X1)
| ~ spl26_53 ),
inference(avatar_component_clause,[],[f505]) ).
fof(f657,plain,
( ! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| relation_dom_as_subset(X0,X1,X2) = relation_dom(X2) )
| ~ spl26_73 ),
inference(avatar_component_clause,[],[f656]) ).
fof(f1231,plain,
( spl26_153
| ~ spl26_52
| ~ spl26_73 ),
inference(avatar_split_clause,[],[f675,f656,f501,f1229]) ).
fof(f1229,plain,
( spl26_153
<=> ! [X0,X1] : relation_dom_as_subset(X0,X1,sK14(X0,X1)) = relation_dom(sK14(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_153])]) ).
fof(f501,plain,
( spl26_52
<=> ! [X0,X1] : relation_of2(sK14(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_52])]) ).
fof(f675,plain,
( ! [X0,X1] : relation_dom_as_subset(X0,X1,sK14(X0,X1)) = relation_dom(sK14(X0,X1))
| ~ spl26_52
| ~ spl26_73 ),
inference(resolution,[],[f657,f502]) ).
fof(f502,plain,
( ! [X0,X1] : relation_of2(sK14(X0,X1),X0,X1)
| ~ spl26_52 ),
inference(avatar_component_clause,[],[f501]) ).
fof(f1227,plain,
( spl26_152
| ~ spl26_51
| ~ spl26_73 ),
inference(avatar_split_clause,[],[f674,f656,f497,f1225]) ).
fof(f1225,plain,
( spl26_152
<=> ! [X0,X1] : relation_dom_as_subset(X0,X1,sK13(X0,X1)) = relation_dom(sK13(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_152])]) ).
fof(f497,plain,
( spl26_51
<=> ! [X0,X1] : relation_of2(sK13(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_51])]) ).
fof(f674,plain,
( ! [X0,X1] : relation_dom_as_subset(X0,X1,sK13(X0,X1)) = relation_dom(sK13(X0,X1))
| ~ spl26_51
| ~ spl26_73 ),
inference(resolution,[],[f657,f498]) ).
fof(f498,plain,
( ! [X0,X1] : relation_of2(sK13(X0,X1),X0,X1)
| ~ spl26_51 ),
inference(avatar_component_clause,[],[f497]) ).
fof(f1223,plain,
( spl26_151
| ~ spl26_67
| ~ spl26_72 ),
inference(avatar_split_clause,[],[f673,f652,f599,f1221]) ).
fof(f652,plain,
( spl26_72
<=> ! [X4,X0,X1,X2] :
( in(X4,relation_dom(X1))
| ~ in(X4,X2)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_72])]) ).
fof(f673,plain,
( ! [X2,X0,X1] :
( ~ in(X0,relation_inverse_image(X1,X2))
| in(X0,relation_dom(X1))
| ~ sP1(X1) )
| ~ spl26_67
| ~ spl26_72 ),
inference(resolution,[],[f653,f600]) ).
fof(f653,plain,
( ! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| ~ in(X4,X2)
| in(X4,relation_dom(X1)) )
| ~ spl26_72 ),
inference(avatar_component_clause,[],[f652]) ).
fof(f1219,plain,
( spl26_150
| ~ spl26_68
| ~ spl26_69 ),
inference(avatar_split_clause,[],[f638,f630,f620,f1217]) ).
fof(f638,plain,
( ! [X2,X3,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| ~ empty(cartesian_product2(X1,X2))
| ~ in(X3,X0) )
| ~ spl26_68
| ~ spl26_69 ),
inference(resolution,[],[f631,f621]) ).
fof(f1207,plain,
( spl26_149
| ~ spl26_55
| ~ spl26_60 ),
inference(avatar_split_clause,[],[f603,f570,f537,f1205]) ).
fof(f1205,plain,
( spl26_149
<=> ! [X0] :
( empty(powerset(X0))
| in(sK8(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_149])]) ).
fof(f537,plain,
( spl26_55
<=> ! [X0] :
( element(sK8(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_55])]) ).
fof(f603,plain,
( ! [X0] :
( empty(powerset(X0))
| in(sK8(X0),powerset(X0))
| empty(X0) )
| ~ spl26_55
| ~ spl26_60 ),
inference(resolution,[],[f571,f538]) ).
fof(f538,plain,
( ! [X0] :
( element(sK8(X0),powerset(X0))
| empty(X0) )
| ~ spl26_55 ),
inference(avatar_component_clause,[],[f537]) ).
fof(f1203,plain,
( spl26_148
| ~ spl26_57
| ~ spl26_60 ),
inference(avatar_split_clause,[],[f602,f570,f545,f1201]) ).
fof(f1201,plain,
( spl26_148
<=> ! [X0,X1] :
( empty(powerset(X0))
| in(X1,powerset(X0))
| ~ subset(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_148])]) ).
fof(f545,plain,
( spl26_57
<=> ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_57])]) ).
fof(f602,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| in(X1,powerset(X0))
| ~ subset(X1,X0) )
| ~ spl26_57
| ~ spl26_60 ),
inference(resolution,[],[f571,f546]) ).
fof(f546,plain,
( ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) )
| ~ spl26_57 ),
inference(avatar_component_clause,[],[f545]) ).
fof(f1193,plain,
( spl26_147
| ~ spl26_1
| ~ spl26_47
| ~ spl26_135 ),
inference(avatar_split_clause,[],[f1145,f1105,f481,f241,f1190]) ).
fof(f241,plain,
( spl26_1
<=> function(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_1])]) ).
fof(f481,plain,
( spl26_47
<=> ! [X0] :
( sP1(X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_47])]) ).
fof(f1105,plain,
( spl26_135
<=> relation(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_135])]) ).
fof(f1145,plain,
( ~ function(sK6)
| sP1(sK6)
| ~ spl26_47
| ~ spl26_135 ),
inference(resolution,[],[f1107,f482]) ).
fof(f482,plain,
( ! [X0] :
( ~ relation(X0)
| ~ function(X0)
| sP1(X0) )
| ~ spl26_47 ),
inference(avatar_component_clause,[],[f481]) ).
fof(f1107,plain,
( relation(sK6)
| ~ spl26_135 ),
inference(avatar_component_clause,[],[f1105]) ).
fof(f1188,plain,
( spl26_146
| ~ spl26_55
| ~ spl26_70 ),
inference(avatar_split_clause,[],[f642,f634,f537,f1186]) ).
fof(f642,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK8(X1))
| empty(X1) )
| ~ spl26_55
| ~ spl26_70 ),
inference(resolution,[],[f635,f538]) ).
fof(f1184,plain,
( spl26_145
| ~ spl26_57
| ~ spl26_70 ),
inference(avatar_split_clause,[],[f640,f634,f545,f1182]) ).
fof(f1182,plain,
( spl26_145
<=> ! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_145])]) ).
fof(f640,plain,
( ! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,X1) )
| ~ spl26_57
| ~ spl26_70 ),
inference(resolution,[],[f635,f546]) ).
fof(f1180,plain,
( spl26_144
| ~ spl26_55
| ~ spl26_63 ),
inference(avatar_split_clause,[],[f611,f582,f537,f1178]) ).
fof(f1178,plain,
( spl26_144
<=> ! [X0,X1] :
( relation(sK8(cartesian_product2(X0,X1)))
| empty(cartesian_product2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_144])]) ).
fof(f611,plain,
( ! [X0,X1] :
( relation(sK8(cartesian_product2(X0,X1)))
| empty(cartesian_product2(X0,X1)) )
| ~ spl26_55
| ~ spl26_63 ),
inference(resolution,[],[f583,f538]) ).
fof(f1149,plain,
( spl26_143
| ~ spl26_34
| ~ spl26_70 ),
inference(avatar_split_clause,[],[f643,f634,f400,f1147]) ).
fof(f400,plain,
( spl26_34
<=> ! [X0] : element(sK10(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_34])]) ).
fof(f643,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK10(powerset(X1))) )
| ~ spl26_34
| ~ spl26_70 ),
inference(resolution,[],[f635,f401]) ).
fof(f401,plain,
( ! [X0] : element(sK10(X0),X0)
| ~ spl26_34 ),
inference(avatar_component_clause,[],[f400]) ).
fof(f1144,plain,
( spl26_142
| ~ spl26_57
| ~ spl26_68 ),
inference(avatar_split_clause,[],[f623,f620,f545,f1142]) ).
fof(f1142,plain,
( spl26_142
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,X2)
| ~ subset(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_142])]) ).
fof(f623,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,X2)
| ~ subset(X2,X0) )
| ~ spl26_57
| ~ spl26_68 ),
inference(resolution,[],[f621,f546]) ).
fof(f1140,plain,
( spl26_141
| ~ spl26_42
| ~ spl26_58 ),
inference(avatar_split_clause,[],[f558,f549,f445,f1138]) ).
fof(f549,plain,
( spl26_58
<=> ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_58])]) ).
fof(f558,plain,
( ! [X0,X1] :
( relation_dom(X1) = X0
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl26_42
| ~ spl26_58 ),
inference(resolution,[],[f550,f446]) ).
fof(f550,plain,
( ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) )
| ~ spl26_58 ),
inference(avatar_component_clause,[],[f549]) ).
fof(f1136,plain,
( spl26_140
| ~ spl26_37
| ~ spl26_47 ),
inference(avatar_split_clause,[],[f515,f481,f412,f1134]) ).
fof(f412,plain,
( spl26_37
<=> ! [X0,X1] : relation(sK15(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_37])]) ).
fof(f515,plain,
( ! [X0,X1] :
( ~ function(sK15(X0,X1))
| sP1(sK15(X0,X1)) )
| ~ spl26_37
| ~ spl26_47 ),
inference(resolution,[],[f482,f413]) ).
fof(f413,plain,
( ! [X0,X1] : relation(sK15(X0,X1))
| ~ spl26_37 ),
inference(avatar_component_clause,[],[f412]) ).
fof(f1132,plain,
( spl26_139
| ~ spl26_35
| ~ spl26_47 ),
inference(avatar_split_clause,[],[f514,f481,f404,f1130]) ).
fof(f404,plain,
( spl26_35
<=> ! [X0,X1] : relation(sK14(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_35])]) ).
fof(f514,plain,
( ! [X0,X1] :
( ~ function(sK14(X0,X1))
| sP1(sK14(X0,X1)) )
| ~ spl26_35
| ~ spl26_47 ),
inference(resolution,[],[f482,f405]) ).
fof(f405,plain,
( ! [X0,X1] : relation(sK14(X0,X1))
| ~ spl26_35 ),
inference(avatar_component_clause,[],[f404]) ).
fof(f1128,plain,
( spl26_138
| ~ spl26_43
| ~ spl26_47 ),
inference(avatar_split_clause,[],[f512,f481,f449,f1126]) ).
fof(f449,plain,
( spl26_43
<=> ! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_43])]) ).
fof(f512,plain,
( ! [X0] :
( ~ function(relation_dom(X0))
| sP1(relation_dom(X0))
| ~ empty(X0) )
| ~ spl26_43
| ~ spl26_47 ),
inference(resolution,[],[f482,f450]) ).
fof(f450,plain,
( ! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) )
| ~ spl26_43 ),
inference(avatar_component_clause,[],[f449]) ).
fof(f1116,plain,
( spl26_137
| ~ spl26_34
| ~ spl26_68 ),
inference(avatar_split_clause,[],[f625,f620,f400,f1114]) ).
fof(f625,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK10(powerset(X0))) )
| ~ spl26_34
| ~ spl26_68 ),
inference(resolution,[],[f621,f401]) ).
fof(f1112,plain,
( spl26_136
| ~ spl26_57
| ~ spl26_63 ),
inference(avatar_split_clause,[],[f610,f582,f545,f1110]) ).
fof(f610,plain,
( ! [X2,X0,X1] :
( relation(X0)
| ~ subset(X0,cartesian_product2(X1,X2)) )
| ~ spl26_57
| ~ spl26_63 ),
inference(resolution,[],[f583,f546]) ).
fof(f1108,plain,
( spl26_135
| ~ spl26_4
| ~ spl26_133 ),
inference(avatar_split_clause,[],[f1095,f1062,f256,f1105]) ).
fof(f1095,plain,
( relation(sK6)
| ~ spl26_4
| ~ spl26_133 ),
inference(resolution,[],[f1063,f258]) ).
fof(f1103,plain,
( spl26_134
| ~ spl26_10
| ~ spl26_30
| ~ spl26_40
| ~ spl26_44
| ~ spl26_60 ),
inference(avatar_split_clause,[],[f607,f570,f453,f436,f384,f285,f1101]) ).
fof(f1101,plain,
( spl26_134
<=> ! [X0] :
( in(sK17,powerset(X0))
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_134])]) ).
fof(f384,plain,
( spl26_30
<=> ! [X0] : empty(sK11(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_30])]) ).
fof(f436,plain,
( spl26_40
<=> ! [X0] :
( empty_set = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_40])]) ).
fof(f607,plain,
( ! [X0] :
( in(sK17,powerset(X0))
| empty(powerset(X0)) )
| ~ spl26_10
| ~ spl26_30
| ~ spl26_40
| ~ spl26_44
| ~ spl26_60 ),
inference(forward_demodulation,[],[f606,f462]) ).
fof(f462,plain,
( empty_set = sK17
| ~ spl26_10
| ~ spl26_40 ),
inference(resolution,[],[f437,f287]) ).
fof(f287,plain,
( empty(sK17)
| ~ spl26_10 ),
inference(avatar_component_clause,[],[f285]) ).
fof(f437,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = X0 )
| ~ spl26_40 ),
inference(avatar_component_clause,[],[f436]) ).
fof(f606,plain,
( ! [X0] :
( in(empty_set,powerset(X0))
| empty(powerset(X0)) )
| ~ spl26_30
| ~ spl26_40
| ~ spl26_44
| ~ spl26_60 ),
inference(forward_demodulation,[],[f605,f461]) ).
fof(f461,plain,
( ! [X0] : empty_set = sK11(X0)
| ~ spl26_30
| ~ spl26_40 ),
inference(resolution,[],[f437,f385]) ).
fof(f385,plain,
( ! [X0] : empty(sK11(X0))
| ~ spl26_30 ),
inference(avatar_component_clause,[],[f384]) ).
fof(f605,plain,
( ! [X0] :
( empty(powerset(X0))
| in(sK11(X0),powerset(X0)) )
| ~ spl26_44
| ~ spl26_60 ),
inference(resolution,[],[f571,f454]) ).
fof(f1064,plain,
( spl26_133
| ~ spl26_63
| ~ spl26_69 ),
inference(avatar_split_clause,[],[f637,f630,f582,f1062]) ).
fof(f637,plain,
( ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| relation(X0) )
| ~ spl26_63
| ~ spl26_69 ),
inference(resolution,[],[f631,f583]) ).
fof(f1060,plain,
( spl26_132
| ~ spl26_53
| ~ spl26_65 ),
inference(avatar_split_clause,[],[f618,f590,f505,f1058]) ).
fof(f590,plain,
( spl26_65
<=> ! [X2,X0,X1] :
( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_65])]) ).
fof(f618,plain,
( ! [X0,X1] : relation_of2_as_subset(sK15(X0,X1),X0,X1)
| ~ spl26_53
| ~ spl26_65 ),
inference(resolution,[],[f591,f506]) ).
fof(f591,plain,
( ! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| relation_of2_as_subset(X2,X0,X1) )
| ~ spl26_65 ),
inference(avatar_component_clause,[],[f590]) ).
fof(f1056,plain,
( spl26_131
| ~ spl26_52
| ~ spl26_65 ),
inference(avatar_split_clause,[],[f617,f590,f501,f1054]) ).
fof(f617,plain,
( ! [X0,X1] : relation_of2_as_subset(sK14(X0,X1),X0,X1)
| ~ spl26_52
| ~ spl26_65 ),
inference(resolution,[],[f591,f502]) ).
fof(f1052,plain,
( spl26_130
| ~ spl26_51
| ~ spl26_65 ),
inference(avatar_split_clause,[],[f616,f590,f497,f1050]) ).
fof(f616,plain,
( ! [X0,X1] : relation_of2_as_subset(sK13(X0,X1),X0,X1)
| ~ spl26_51
| ~ spl26_65 ),
inference(resolution,[],[f591,f498]) ).
fof(f1048,plain,
( spl26_129
| ~ spl26_50
| ~ spl26_64 ),
inference(avatar_split_clause,[],[f615,f586,f493,f1046]) ).
fof(f1046,plain,
( spl26_129
<=> ! [X0,X1] : relation_of2(sK12(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_129])]) ).
fof(f586,plain,
( spl26_64
<=> ! [X2,X0,X1] :
( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_64])]) ).
fof(f615,plain,
( ! [X0,X1] : relation_of2(sK12(X0,X1),X0,X1)
| ~ spl26_50
| ~ spl26_64 ),
inference(resolution,[],[f587,f494]) ).
fof(f587,plain,
( ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| relation_of2(X2,X0,X1) )
| ~ spl26_64 ),
inference(avatar_component_clause,[],[f586]) ).
fof(f1044,plain,
( spl26_128
| ~ spl26_34
| ~ spl26_63 ),
inference(avatar_split_clause,[],[f612,f582,f400,f1042]) ).
fof(f1042,plain,
( spl26_128
<=> ! [X0,X1] : relation(sK10(powerset(cartesian_product2(X0,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_128])]) ).
fof(f612,plain,
( ! [X0,X1] : relation(sK10(powerset(cartesian_product2(X0,X1))))
| ~ spl26_34
| ~ spl26_63 ),
inference(resolution,[],[f583,f401]) ).
fof(f1040,plain,
( spl26_127
| ~ spl26_50
| ~ spl26_62 ),
inference(avatar_split_clause,[],[f609,f578,f493,f1038]) ).
fof(f1038,plain,
( spl26_127
<=> ! [X0,X1] : sP2(X0,sK12(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_127])]) ).
fof(f609,plain,
( ! [X0,X1] : sP2(X0,sK12(X0,X1),X1)
| ~ spl26_50
| ~ spl26_62 ),
inference(resolution,[],[f579,f494]) ).
fof(f1036,plain,
( spl26_126
| ~ spl26_34
| ~ spl26_60 ),
inference(avatar_split_clause,[],[f604,f570,f400,f1034]) ).
fof(f604,plain,
( ! [X0] :
( empty(X0)
| in(sK10(X0),X0) )
| ~ spl26_34
| ~ spl26_60 ),
inference(resolution,[],[f571,f401]) ).
fof(f1032,plain,
( spl26_125
| ~ spl26_10
| ~ spl26_40
| ~ spl26_42 ),
inference(avatar_split_clause,[],[f472,f445,f436,f285,f1030]) ).
fof(f472,plain,
( ! [X0] :
( relation_dom(X0) = sK17
| ~ empty(X0) )
| ~ spl26_10
| ~ spl26_40
| ~ spl26_42 ),
inference(forward_demodulation,[],[f469,f462]) ).
fof(f469,plain,
( ! [X0] :
( ~ empty(X0)
| relation_dom(X0) = empty_set )
| ~ spl26_40
| ~ spl26_42 ),
inference(resolution,[],[f446,f437]) ).
fof(f1021,plain,
( ~ spl26_94
| spl26_124
| ~ spl26_74
| ~ spl26_102 ),
inference(avatar_split_clause,[],[f948,f838,f660,f1018,f786]) ).
fof(f786,plain,
( spl26_94
<=> relation_of2(sK6,sK3,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_94])]) ).
fof(f1018,plain,
( spl26_124
<=> element(relation_dom(sK6),powerset(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_124])]) ).
fof(f948,plain,
( element(relation_dom(sK6),powerset(sK3))
| ~ relation_of2(sK6,sK3,sK4)
| ~ spl26_74
| ~ spl26_102 ),
inference(superposition,[],[f661,f840]) ).
fof(f993,plain,
( spl26_121
| ~ spl26_40
| ~ spl26_105 ),
inference(avatar_split_clause,[],[f968,f854,f436,f944]) ).
fof(f968,plain,
( ! [X0] :
( sK17 = X0
| ~ empty(X0) )
| ~ spl26_40
| ~ spl26_105 ),
inference(forward_demodulation,[],[f437,f856]) ).
fof(f967,plain,
( ~ spl26_7
| ~ spl26_122 ),
inference(avatar_contradiction_clause,[],[f956]) ).
fof(f956,plain,
( $false
| ~ spl26_7
| ~ spl26_122 ),
inference(resolution,[],[f951,f272]) ).
fof(f951,plain,
( ! [X0] : ~ empty(X0)
| ~ spl26_122 ),
inference(avatar_component_clause,[],[f950]) ).
fof(f950,plain,
( spl26_122
<=> ! [X0] : ~ empty(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_122])]) ).
fof(f966,plain,
( ~ spl26_30
| ~ spl26_122 ),
inference(avatar_contradiction_clause,[],[f957]) ).
fof(f957,plain,
( $false
| ~ spl26_30
| ~ spl26_122 ),
inference(resolution,[],[f951,f385]) ).
fof(f965,plain,
( ~ spl26_10
| ~ spl26_122 ),
inference(avatar_contradiction_clause,[],[f958]) ).
fof(f958,plain,
( $false
| ~ spl26_10
| ~ spl26_122 ),
inference(resolution,[],[f951,f287]) ).
fof(f964,plain,
( ~ spl26_13
| ~ spl26_122 ),
inference(avatar_contradiction_clause,[],[f959]) ).
fof(f959,plain,
( $false
| ~ spl26_13
| ~ spl26_122 ),
inference(resolution,[],[f951,f302]) ).
fof(f302,plain,
( empty(sK19)
| ~ spl26_13 ),
inference(avatar_component_clause,[],[f300]) ).
fof(f300,plain,
( spl26_13
<=> empty(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_13])]) ).
fof(f963,plain,
( ~ spl26_24
| ~ spl26_122 ),
inference(avatar_contradiction_clause,[],[f960]) ).
fof(f960,plain,
( $false
| ~ spl26_24
| ~ spl26_122 ),
inference(resolution,[],[f951,f357]) ).
fof(f357,plain,
( empty(sK24)
| ~ spl26_24 ),
inference(avatar_component_clause,[],[f355]) ).
fof(f355,plain,
( spl26_24
<=> empty(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_24])]) ).
fof(f962,plain,
( ~ spl26_26
| ~ spl26_122 ),
inference(avatar_contradiction_clause,[],[f961]) ).
fof(f961,plain,
( $false
| ~ spl26_26
| ~ spl26_122 ),
inference(resolution,[],[f951,f367]) ).
fof(f367,plain,
( empty(sK25)
| ~ spl26_26 ),
inference(avatar_component_clause,[],[f365]) ).
fof(f365,plain,
( spl26_26
<=> empty(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_26])]) ).
fof(f955,plain,
( spl26_122
| spl26_123
| ~ spl26_10
| ~ spl26_30
| ~ spl26_40
| ~ spl26_44
| ~ spl26_68 ),
inference(avatar_split_clause,[],[f628,f620,f453,f436,f384,f285,f953,f950]) ).
fof(f628,plain,
( ! [X0,X1] :
( ~ in(X1,sK17)
| ~ empty(X0) )
| ~ spl26_10
| ~ spl26_30
| ~ spl26_40
| ~ spl26_44
| ~ spl26_68 ),
inference(forward_demodulation,[],[f627,f462]) ).
fof(f627,plain,
( ! [X0,X1] :
( ~ in(X1,empty_set)
| ~ empty(X0) )
| ~ spl26_30
| ~ spl26_40
| ~ spl26_44
| ~ spl26_68 ),
inference(forward_demodulation,[],[f626,f461]) ).
fof(f626,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK11(X0)) )
| ~ spl26_44
| ~ spl26_68 ),
inference(resolution,[],[f621,f454]) ).
fof(f946,plain,
( spl26_121
| ~ spl26_10
| ~ spl26_58 ),
inference(avatar_split_clause,[],[f561,f549,f285,f944]) ).
fof(f561,plain,
( ! [X0] :
( sK17 = X0
| ~ empty(X0) )
| ~ spl26_10
| ~ spl26_58 ),
inference(resolution,[],[f550,f287]) ).
fof(f942,plain,
( spl26_120
| ~ spl26_32
| ~ spl26_42 ),
inference(avatar_split_clause,[],[f471,f445,f392,f940]) ).
fof(f392,plain,
( spl26_32
<=> ! [X0] :
( function(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_32])]) ).
fof(f471,plain,
( ! [X0] :
( ~ empty(X0)
| function(relation_dom(X0)) )
| ~ spl26_32
| ~ spl26_42 ),
inference(resolution,[],[f446,f393]) ).
fof(f393,plain,
( ! [X0] :
( ~ empty(X0)
| function(X0) )
| ~ spl26_32 ),
inference(avatar_component_clause,[],[f392]) ).
fof(f936,plain,
( spl26_119
| ~ spl26_105
| ~ spl26_110 ),
inference(avatar_split_clause,[],[f894,f891,f854,f934]) ).
fof(f891,plain,
( spl26_110
<=> ! [X0] : empty_set = sK11(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_110])]) ).
fof(f894,plain,
( ! [X0] : sK11(X0) = sK17
| ~ spl26_105
| ~ spl26_110 ),
inference(forward_demodulation,[],[f892,f856]) ).
fof(f892,plain,
( ! [X0] : empty_set = sK11(X0)
| ~ spl26_110 ),
inference(avatar_component_clause,[],[f891]) ).
fof(f932,plain,
( ~ spl26_99
| spl26_118
| ~ spl26_8
| ~ spl26_10
| ~ spl26_40
| ~ spl26_47 ),
inference(avatar_split_clause,[],[f525,f481,f436,f285,f275,f929,f822]) ).
fof(f822,plain,
( spl26_99
<=> function(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_99])]) ).
fof(f929,plain,
( spl26_118
<=> sP1(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_118])]) ).
fof(f275,plain,
( spl26_8
<=> relation(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_8])]) ).
fof(f525,plain,
( sP1(sK17)
| ~ function(sK17)
| ~ spl26_8
| ~ spl26_10
| ~ spl26_40
| ~ spl26_47 ),
inference(forward_demodulation,[],[f524,f462]) ).
fof(f524,plain,
( ~ function(sK17)
| sP1(empty_set)
| ~ spl26_8
| ~ spl26_10
| ~ spl26_40
| ~ spl26_47 ),
inference(forward_demodulation,[],[f513,f462]) ).
fof(f513,plain,
( ~ function(empty_set)
| sP1(empty_set)
| ~ spl26_8
| ~ spl26_47 ),
inference(resolution,[],[f482,f277]) ).
fof(f277,plain,
( relation(empty_set)
| ~ spl26_8 ),
inference(avatar_component_clause,[],[f275]) ).
fof(f927,plain,
( spl26_117
| ~ spl26_21
| ~ spl26_20
| ~ spl26_47 ),
inference(avatar_split_clause,[],[f521,f481,f335,f340,f924]) ).
fof(f924,plain,
( spl26_117
<=> sP1(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_117])]) ).
fof(f340,plain,
( spl26_21
<=> function(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_21])]) ).
fof(f335,plain,
( spl26_20
<=> relation(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_20])]) ).
fof(f521,plain,
( ~ function(sK23)
| sP1(sK23)
| ~ spl26_20
| ~ spl26_47 ),
inference(resolution,[],[f482,f337]) ).
fof(f337,plain,
( relation(sK23)
| ~ spl26_20 ),
inference(avatar_component_clause,[],[f335]) ).
fof(f922,plain,
( spl26_116
| ~ spl26_19
| ~ spl26_18
| ~ spl26_47 ),
inference(avatar_split_clause,[],[f520,f481,f325,f330,f919]) ).
fof(f919,plain,
( spl26_116
<=> sP1(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_116])]) ).
fof(f330,plain,
( spl26_19
<=> function(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_19])]) ).
fof(f325,plain,
( spl26_18
<=> relation(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_18])]) ).
fof(f520,plain,
( ~ function(sK22)
| sP1(sK22)
| ~ spl26_18
| ~ spl26_47 ),
inference(resolution,[],[f482,f327]) ).
fof(f327,plain,
( relation(sK22)
| ~ spl26_18 ),
inference(avatar_component_clause,[],[f325]) ).
fof(f917,plain,
( spl26_115
| ~ spl26_17
| ~ spl26_16
| ~ spl26_47 ),
inference(avatar_split_clause,[],[f519,f481,f315,f320,f914]) ).
fof(f914,plain,
( spl26_115
<=> sP1(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_115])]) ).
fof(f320,plain,
( spl26_17
<=> function(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_17])]) ).
fof(f315,plain,
( spl26_16
<=> relation(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_16])]) ).
fof(f519,plain,
( ~ function(sK21)
| sP1(sK21)
| ~ spl26_16
| ~ spl26_47 ),
inference(resolution,[],[f482,f317]) ).
fof(f317,plain,
( relation(sK21)
| ~ spl26_16 ),
inference(avatar_component_clause,[],[f315]) ).
fof(f912,plain,
( spl26_113
| ~ spl26_114
| ~ spl26_15
| ~ spl26_47 ),
inference(avatar_split_clause,[],[f518,f481,f310,f909,f905]) ).
fof(f905,plain,
( spl26_113
<=> sP1(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_113])]) ).
fof(f909,plain,
( spl26_114
<=> function(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_114])]) ).
fof(f310,plain,
( spl26_15
<=> relation(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_15])]) ).
fof(f518,plain,
( ~ function(sK20)
| sP1(sK20)
| ~ spl26_15
| ~ spl26_47 ),
inference(resolution,[],[f482,f312]) ).
fof(f312,plain,
( relation(sK20)
| ~ spl26_15 ),
inference(avatar_component_clause,[],[f310]) ).
fof(f903,plain,
( spl26_111
| ~ spl26_112
| ~ spl26_12
| ~ spl26_47 ),
inference(avatar_split_clause,[],[f516,f481,f295,f900,f896]) ).
fof(f896,plain,
( spl26_111
<=> sP1(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_111])]) ).
fof(f900,plain,
( spl26_112
<=> function(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_112])]) ).
fof(f295,plain,
( spl26_12
<=> relation(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_12])]) ).
fof(f516,plain,
( ~ function(sK18)
| sP1(sK18)
| ~ spl26_12
| ~ spl26_47 ),
inference(resolution,[],[f482,f297]) ).
fof(f297,plain,
( relation(sK18)
| ~ spl26_12 ),
inference(avatar_component_clause,[],[f295]) ).
fof(f893,plain,
( spl26_110
| ~ spl26_30
| ~ spl26_40 ),
inference(avatar_split_clause,[],[f461,f436,f384,f891]) ).
fof(f886,plain,
( ~ spl26_109
| spl26_2
| ~ spl26_105 ),
inference(avatar_split_clause,[],[f876,f854,f246,f883]) ).
fof(f246,plain,
( spl26_2
<=> empty_set = sK4 ),
introduced(avatar_definition,[new_symbols(naming,[spl26_2])]) ).
fof(f876,plain,
( sK4 != sK17
| spl26_2
| ~ spl26_105 ),
inference(superposition,[],[f248,f856]) ).
fof(f248,plain,
( empty_set != sK4
| spl26_2 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f872,plain,
( spl26_108
| ~ spl26_10
| ~ spl26_26
| ~ spl26_40 ),
inference(avatar_split_clause,[],[f468,f436,f365,f285,f869]) ).
fof(f869,plain,
( spl26_108
<=> sK17 = sK25 ),
introduced(avatar_definition,[new_symbols(naming,[spl26_108])]) ).
fof(f468,plain,
( sK17 = sK25
| ~ spl26_10
| ~ spl26_26
| ~ spl26_40 ),
inference(forward_demodulation,[],[f465,f462]) ).
fof(f465,plain,
( empty_set = sK25
| ~ spl26_26
| ~ spl26_40 ),
inference(resolution,[],[f437,f367]) ).
fof(f867,plain,
( spl26_107
| ~ spl26_10
| ~ spl26_24
| ~ spl26_40 ),
inference(avatar_split_clause,[],[f467,f436,f355,f285,f864]) ).
fof(f864,plain,
( spl26_107
<=> sK17 = sK24 ),
introduced(avatar_definition,[new_symbols(naming,[spl26_107])]) ).
fof(f467,plain,
( sK17 = sK24
| ~ spl26_10
| ~ spl26_24
| ~ spl26_40 ),
inference(forward_demodulation,[],[f464,f462]) ).
fof(f464,plain,
( empty_set = sK24
| ~ spl26_24
| ~ spl26_40 ),
inference(resolution,[],[f437,f357]) ).
fof(f862,plain,
( spl26_106
| ~ spl26_10
| ~ spl26_13
| ~ spl26_40 ),
inference(avatar_split_clause,[],[f466,f436,f300,f285,f859]) ).
fof(f859,plain,
( spl26_106
<=> sK17 = sK19 ),
introduced(avatar_definition,[new_symbols(naming,[spl26_106])]) ).
fof(f466,plain,
( sK17 = sK19
| ~ spl26_10
| ~ spl26_13
| ~ spl26_40 ),
inference(forward_demodulation,[],[f463,f462]) ).
fof(f463,plain,
( empty_set = sK19
| ~ spl26_13
| ~ spl26_40 ),
inference(resolution,[],[f437,f302]) ).
fof(f857,plain,
( spl26_105
| ~ spl26_10
| ~ spl26_40 ),
inference(avatar_split_clause,[],[f462,f436,f285,f854]) ).
fof(f851,plain,
( spl26_104
| ~ spl26_30
| ~ spl26_33 ),
inference(avatar_split_clause,[],[f426,f396,f384,f849]) ).
fof(f849,plain,
( spl26_104
<=> ! [X0] : relation(sK11(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_104])]) ).
fof(f396,plain,
( spl26_33
<=> ! [X0] :
( relation(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_33])]) ).
fof(f426,plain,
( ! [X0] : relation(sK11(X0))
| ~ spl26_30
| ~ spl26_33 ),
inference(resolution,[],[f397,f385]) ).
fof(f397,plain,
( ! [X0] :
( ~ empty(X0)
| relation(X0) )
| ~ spl26_33 ),
inference(avatar_component_clause,[],[f396]) ).
fof(f846,plain,
( spl26_103
| ~ spl26_30
| ~ spl26_32 ),
inference(avatar_split_clause,[],[f420,f392,f384,f844]) ).
fof(f844,plain,
( spl26_103
<=> ! [X0] : function(sK11(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_103])]) ).
fof(f420,plain,
( ! [X0] : function(sK11(X0))
| ~ spl26_30
| ~ spl26_32 ),
inference(resolution,[],[f393,f385]) ).
fof(f841,plain,
( spl26_102
| ~ spl26_73
| ~ spl26_94 ),
inference(avatar_split_clause,[],[f791,f786,f656,f838]) ).
fof(f791,plain,
( relation_dom_as_subset(sK3,sK4,sK6) = relation_dom(sK6)
| ~ spl26_73
| ~ spl26_94 ),
inference(resolution,[],[f788,f657]) ).
fof(f788,plain,
( relation_of2(sK6,sK3,sK4)
| ~ spl26_94 ),
inference(avatar_component_clause,[],[f786]) ).
fof(f836,plain,
( spl26_101
| ~ spl26_10
| ~ spl26_33 ),
inference(avatar_split_clause,[],[f427,f396,f285,f833]) ).
fof(f833,plain,
( spl26_101
<=> relation(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_101])]) ).
fof(f427,plain,
( relation(sK17)
| ~ spl26_10
| ~ spl26_33 ),
inference(resolution,[],[f397,f287]) ).
fof(f830,plain,
( spl26_100
| ~ spl26_13
| ~ spl26_32 ),
inference(avatar_split_clause,[],[f422,f392,f300,f827]) ).
fof(f827,plain,
( spl26_100
<=> function(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_100])]) ).
fof(f422,plain,
( function(sK19)
| ~ spl26_13
| ~ spl26_32 ),
inference(resolution,[],[f393,f302]) ).
fof(f825,plain,
( spl26_99
| ~ spl26_10
| ~ spl26_32 ),
inference(avatar_split_clause,[],[f421,f392,f285,f822]) ).
fof(f421,plain,
( function(sK17)
| ~ spl26_10
| ~ spl26_32 ),
inference(resolution,[],[f393,f287]) ).
fof(f816,plain,
( spl26_98
| ~ spl26_28
| ~ spl26_49 ),
inference(avatar_split_clause,[],[f804,f489,f375,f813]) ).
fof(f813,plain,
( spl26_98
<=> element(apply(sK6,sK7),sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_98])]) ).
fof(f804,plain,
( element(apply(sK6,sK7),sK5)
| ~ spl26_28
| ~ spl26_49 ),
inference(resolution,[],[f377,f490]) ).
fof(f811,plain,
( ~ spl26_97
| ~ spl26_28
| ~ spl26_45 ),
inference(avatar_split_clause,[],[f806,f457,f375,f808]) ).
fof(f808,plain,
( spl26_97
<=> empty(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_97])]) ).
fof(f806,plain,
( ~ empty(sK5)
| ~ spl26_28
| ~ spl26_45 ),
inference(resolution,[],[f377,f458]) ).
fof(f802,plain,
( spl26_96
| ~ spl26_5
| ~ spl26_49 ),
inference(avatar_split_clause,[],[f535,f489,f261,f799]) ).
fof(f799,plain,
( spl26_96
<=> element(sK7,relation_inverse_image(sK6,sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_96])]) ).
fof(f535,plain,
( element(sK7,relation_inverse_image(sK6,sK5))
| ~ spl26_5
| ~ spl26_49 ),
inference(resolution,[],[f490,f263]) ).
fof(f797,plain,
( ~ spl26_95
| ~ spl26_5
| ~ spl26_48 ),
inference(avatar_split_clause,[],[f533,f485,f261,f794]) ).
fof(f794,plain,
( spl26_95
<=> in(relation_inverse_image(sK6,sK5),sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_95])]) ).
fof(f533,plain,
( ~ in(relation_inverse_image(sK6,sK5),sK7)
| ~ spl26_5
| ~ spl26_48 ),
inference(resolution,[],[f486,f263]) ).
fof(f789,plain,
( spl26_94
| ~ spl26_4
| ~ spl26_64 ),
inference(avatar_split_clause,[],[f614,f586,f256,f786]) ).
fof(f614,plain,
( relation_of2(sK6,sK3,sK4)
| ~ spl26_4
| ~ spl26_64 ),
inference(resolution,[],[f587,f258]) ).
fof(f782,plain,
spl26_93,
inference(avatar_split_clause,[],[f176,f780]) ).
fof(f780,plain,
( spl26_93
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ in(apply(X1,sK9(X0,X1,X2)),X0)
| ~ in(sK9(X0,X1,X2),relation_dom(X1))
| ~ in(sK9(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_93])]) ).
fof(f176,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ in(apply(X1,sK9(X0,X1,X2)),X0)
| ~ in(sK9(X0,X1,X2),relation_dom(X1))
| ~ in(sK9(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f111]) ).
fof(f111,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ( ( ~ in(apply(X1,sK9(X0,X1,X2)),X0)
| ~ in(sK9(X0,X1,X2),relation_dom(X1))
| ~ in(sK9(X0,X1,X2),X2) )
& ( ( in(apply(X1,sK9(X0,X1,X2)),X0)
& in(sK9(X0,X1,X2),relation_dom(X1)) )
| in(sK9(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(apply(X1,X4),X0)
| ~ in(X4,relation_dom(X1)) )
& ( ( in(apply(X1,X4),X0)
& in(X4,relation_dom(X1)) )
| ~ in(X4,X2) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f109,f110]) ).
fof(f110,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(apply(X1,X3),X0)
| ~ in(X3,relation_dom(X1))
| ~ in(X3,X2) )
& ( ( in(apply(X1,X3),X0)
& in(X3,relation_dom(X1)) )
| in(X3,X2) ) )
=> ( ( ~ in(apply(X1,sK9(X0,X1,X2)),X0)
| ~ in(sK9(X0,X1,X2),relation_dom(X1))
| ~ in(sK9(X0,X1,X2),X2) )
& ( ( in(apply(X1,sK9(X0,X1,X2)),X0)
& in(sK9(X0,X1,X2),relation_dom(X1)) )
| in(sK9(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f109,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ? [X3] :
( ( ~ in(apply(X1,X3),X0)
| ~ in(X3,relation_dom(X1))
| ~ in(X3,X2) )
& ( ( in(apply(X1,X3),X0)
& in(X3,relation_dom(X1)) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(apply(X1,X4),X0)
| ~ in(X4,relation_dom(X1)) )
& ( ( in(apply(X1,X4),X0)
& in(X4,relation_dom(X1)) )
| ~ in(X4,X2) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f108]) ).
fof(f108,plain,
! [X1,X0,X2] :
( ( sP0(X1,X0,X2)
| ? [X3] :
( ( ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0))
| ~ in(X3,X2) )
& ( ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0)) )
& ( ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) )
| ~ in(X3,X2) ) )
| ~ sP0(X1,X0,X2) ) ),
inference(flattening,[],[f107]) ).
fof(f107,plain,
! [X1,X0,X2] :
( ( sP0(X1,X0,X2)
| ? [X3] :
( ( ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0))
| ~ in(X3,X2) )
& ( ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0)) )
& ( ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) )
| ~ in(X3,X2) ) )
| ~ sP0(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f94]) ).
fof(f94,plain,
! [X1,X0,X2] :
( sP0(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f771,plain,
spl26_92,
inference(avatar_split_clause,[],[f175,f769]) ).
fof(f175,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(apply(X1,sK9(X0,X1,X2)),X0)
| in(sK9(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f111]) ).
fof(f767,plain,
( spl26_91
| ~ spl26_10
| ~ spl26_40
| ~ spl26_89 ),
inference(avatar_split_clause,[],[f752,f749,f436,f285,f765]) ).
fof(f765,plain,
( spl26_91
<=> ! [X2,X0,X1] :
( sK17 = X2
| quasi_total(X1,X0,X2)
| relation_dom_as_subset(X0,X2,X1) != X0
| ~ sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_91])]) ).
fof(f749,plain,
( spl26_89
<=> ! [X2,X0,X1] :
( quasi_total(X1,X0,X2)
| relation_dom_as_subset(X0,X2,X1) != X0
| empty_set = X2
| ~ sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_89])]) ).
fof(f752,plain,
( ! [X2,X0,X1] :
( sK17 = X2
| quasi_total(X1,X0,X2)
| relation_dom_as_subset(X0,X2,X1) != X0
| ~ sP2(X0,X1,X2) )
| ~ spl26_10
| ~ spl26_40
| ~ spl26_89 ),
inference(forward_demodulation,[],[f750,f462]) ).
fof(f750,plain,
( ! [X2,X0,X1] :
( quasi_total(X1,X0,X2)
| relation_dom_as_subset(X0,X2,X1) != X0
| empty_set = X2
| ~ sP2(X0,X1,X2) )
| ~ spl26_89 ),
inference(avatar_component_clause,[],[f749]) ).
fof(f763,plain,
( spl26_90
| ~ spl26_10
| ~ spl26_40
| ~ spl26_87 ),
inference(avatar_split_clause,[],[f742,f739,f436,f285,f761]) ).
fof(f739,plain,
( spl26_87
<=> ! [X2,X0,X1] :
( relation_dom_as_subset(X0,X2,X1) = X0
| ~ quasi_total(X1,X0,X2)
| empty_set = X2
| ~ sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_87])]) ).
fof(f742,plain,
( ! [X2,X0,X1] :
( sK17 = X2
| relation_dom_as_subset(X0,X2,X1) = X0
| ~ quasi_total(X1,X0,X2)
| ~ sP2(X0,X1,X2) )
| ~ spl26_10
| ~ spl26_40
| ~ spl26_87 ),
inference(forward_demodulation,[],[f740,f462]) ).
fof(f740,plain,
( ! [X2,X0,X1] :
( relation_dom_as_subset(X0,X2,X1) = X0
| ~ quasi_total(X1,X0,X2)
| empty_set = X2
| ~ sP2(X0,X1,X2) )
| ~ spl26_87 ),
inference(avatar_component_clause,[],[f739]) ).
fof(f751,plain,
spl26_89,
inference(avatar_split_clause,[],[f203,f749]) ).
fof(f203,plain,
! [X2,X0,X1] :
( quasi_total(X1,X0,X2)
| relation_dom_as_subset(X0,X2,X1) != X0
| empty_set = X2
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f125]) ).
fof(f125,plain,
! [X0,X1,X2] :
( ( ( quasi_total(X1,X0,X2)
| relation_dom_as_subset(X0,X2,X1) != X0 )
& ( relation_dom_as_subset(X0,X2,X1) = X0
| ~ quasi_total(X1,X0,X2) ) )
| ( empty_set != X0
& empty_set = X2 )
| ~ sP2(X0,X1,X2) ),
inference(rectify,[],[f124]) ).
fof(f124,plain,
! [X0,X2,X1] :
( ( ( quasi_total(X2,X0,X1)
| relation_dom_as_subset(X0,X1,X2) != X0 )
& ( relation_dom_as_subset(X0,X1,X2) = X0
| ~ quasi_total(X2,X0,X1) ) )
| ( empty_set != X0
& empty_set = X1 )
| ~ sP2(X0,X2,X1) ),
inference(nnf_transformation,[],[f97]) ).
fof(f97,plain,
! [X0,X2,X1] :
( ( quasi_total(X2,X0,X1)
<=> relation_dom_as_subset(X0,X1,X2) = X0 )
| ( empty_set != X0
& empty_set = X1 )
| ~ sP2(X0,X2,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f747,plain,
( spl26_88
| ~ spl26_4
| ~ spl26_62 ),
inference(avatar_split_clause,[],[f608,f578,f256,f744]) ).
fof(f608,plain,
( sP2(sK3,sK6,sK4)
| ~ spl26_4
| ~ spl26_62 ),
inference(resolution,[],[f579,f258]) ).
fof(f741,plain,
spl26_87,
inference(avatar_split_clause,[],[f201,f739]) ).
fof(f201,plain,
! [X2,X0,X1] :
( relation_dom_as_subset(X0,X2,X1) = X0
| ~ quasi_total(X1,X0,X2)
| empty_set = X2
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f125]) ).
fof(f737,plain,
spl26_86,
inference(avatar_split_clause,[],[f174,f735]) ).
fof(f174,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(sK9(X0,X1,X2),relation_dom(X1))
| in(sK9(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f111]) ).
fof(f733,plain,
spl26_85,
inference(avatar_split_clause,[],[f173,f731]) ).
fof(f173,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(apply(X1,X4),X0)
| ~ in(X4,relation_dom(X1))
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f111]) ).
fof(f728,plain,
( spl26_84
| ~ spl26_10
| ~ spl26_40
| ~ spl26_80 ),
inference(avatar_split_clause,[],[f711,f705,f436,f285,f726]) ).
fof(f705,plain,
( spl26_80
<=> ! [X2,X0] :
( empty_set = X2
| ~ quasi_total(X2,X0,empty_set)
| empty_set = X0
| ~ relation_of2_as_subset(X2,X0,empty_set) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_80])]) ).
fof(f711,plain,
( ! [X2,X0] :
( ~ relation_of2_as_subset(X2,X0,sK17)
| sK17 = X0
| ~ quasi_total(X2,X0,sK17)
| sK17 = X2 )
| ~ spl26_10
| ~ spl26_40
| ~ spl26_80 ),
inference(forward_demodulation,[],[f710,f462]) ).
fof(f710,plain,
( ! [X2,X0] :
( sK17 = X0
| ~ quasi_total(X2,X0,sK17)
| sK17 = X2
| ~ relation_of2_as_subset(X2,X0,empty_set) )
| ~ spl26_10
| ~ spl26_40
| ~ spl26_80 ),
inference(forward_demodulation,[],[f709,f462]) ).
fof(f709,plain,
( ! [X2,X0] :
( ~ quasi_total(X2,X0,sK17)
| sK17 = X2
| empty_set = X0
| ~ relation_of2_as_subset(X2,X0,empty_set) )
| ~ spl26_10
| ~ spl26_40
| ~ spl26_80 ),
inference(forward_demodulation,[],[f708,f462]) ).
fof(f708,plain,
( ! [X2,X0] :
( sK17 = X2
| ~ quasi_total(X2,X0,empty_set)
| empty_set = X0
| ~ relation_of2_as_subset(X2,X0,empty_set) )
| ~ spl26_10
| ~ spl26_40
| ~ spl26_80 ),
inference(forward_demodulation,[],[f706,f462]) ).
fof(f706,plain,
( ! [X2,X0] :
( empty_set = X2
| ~ quasi_total(X2,X0,empty_set)
| empty_set = X0
| ~ relation_of2_as_subset(X2,X0,empty_set) )
| ~ spl26_80 ),
inference(avatar_component_clause,[],[f705]) ).
fof(f724,plain,
( spl26_83
| ~ spl26_10
| ~ spl26_40
| ~ spl26_79 ),
inference(avatar_split_clause,[],[f703,f698,f436,f285,f722]) ).
fof(f722,plain,
( spl26_83
<=> ! [X2,X1] :
( ~ sP2(sK17,X1,X2)
| ~ quasi_total(X1,sK17,X2)
| sK17 = relation_dom_as_subset(sK17,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_83])]) ).
fof(f698,plain,
( spl26_79
<=> ! [X2,X1] :
( empty_set = relation_dom_as_subset(empty_set,X2,X1)
| ~ quasi_total(X1,empty_set,X2)
| ~ sP2(empty_set,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_79])]) ).
fof(f703,plain,
( ! [X2,X1] :
( ~ sP2(sK17,X1,X2)
| ~ quasi_total(X1,sK17,X2)
| sK17 = relation_dom_as_subset(sK17,X2,X1) )
| ~ spl26_10
| ~ spl26_40
| ~ spl26_79 ),
inference(forward_demodulation,[],[f702,f462]) ).
fof(f702,plain,
( ! [X2,X1] :
( ~ quasi_total(X1,sK17,X2)
| sK17 = relation_dom_as_subset(sK17,X2,X1)
| ~ sP2(empty_set,X1,X2) )
| ~ spl26_10
| ~ spl26_40
| ~ spl26_79 ),
inference(forward_demodulation,[],[f701,f462]) ).
fof(f701,plain,
( ! [X2,X1] :
( sK17 = relation_dom_as_subset(sK17,X2,X1)
| ~ quasi_total(X1,empty_set,X2)
| ~ sP2(empty_set,X1,X2) )
| ~ spl26_10
| ~ spl26_40
| ~ spl26_79 ),
inference(forward_demodulation,[],[f699,f462]) ).
fof(f699,plain,
( ! [X2,X1] :
( empty_set = relation_dom_as_subset(empty_set,X2,X1)
| ~ quasi_total(X1,empty_set,X2)
| ~ sP2(empty_set,X1,X2) )
| ~ spl26_79 ),
inference(avatar_component_clause,[],[f698]) ).
fof(f720,plain,
( spl26_82
| ~ spl26_10
| ~ spl26_40
| ~ spl26_78 ),
inference(avatar_split_clause,[],[f696,f691,f436,f285,f718]) ).
fof(f718,plain,
( spl26_82
<=> ! [X2,X1] :
( ~ sP2(sK17,X1,X2)
| sK17 != relation_dom_as_subset(sK17,X2,X1)
| quasi_total(X1,sK17,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_82])]) ).
fof(f691,plain,
( spl26_78
<=> ! [X2,X1] :
( quasi_total(X1,empty_set,X2)
| empty_set != relation_dom_as_subset(empty_set,X2,X1)
| ~ sP2(empty_set,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_78])]) ).
fof(f696,plain,
( ! [X2,X1] :
( ~ sP2(sK17,X1,X2)
| sK17 != relation_dom_as_subset(sK17,X2,X1)
| quasi_total(X1,sK17,X2) )
| ~ spl26_10
| ~ spl26_40
| ~ spl26_78 ),
inference(forward_demodulation,[],[f695,f462]) ).
fof(f695,plain,
( ! [X2,X1] :
( sK17 != relation_dom_as_subset(sK17,X2,X1)
| quasi_total(X1,sK17,X2)
| ~ sP2(empty_set,X1,X2) )
| ~ spl26_10
| ~ spl26_40
| ~ spl26_78 ),
inference(forward_demodulation,[],[f694,f462]) ).
fof(f694,plain,
( ! [X2,X1] :
( quasi_total(X1,sK17,X2)
| empty_set != relation_dom_as_subset(empty_set,X2,X1)
| ~ sP2(empty_set,X1,X2) )
| ~ spl26_10
| ~ spl26_40
| ~ spl26_78 ),
inference(forward_demodulation,[],[f692,f462]) ).
fof(f692,plain,
( ! [X2,X1] :
( quasi_total(X1,empty_set,X2)
| empty_set != relation_dom_as_subset(empty_set,X2,X1)
| ~ sP2(empty_set,X1,X2) )
| ~ spl26_78 ),
inference(avatar_component_clause,[],[f691]) ).
fof(f716,plain,
( ~ spl26_81
| ~ spl26_5
| ~ spl26_45 ),
inference(avatar_split_clause,[],[f474,f457,f261,f713]) ).
fof(f713,plain,
( spl26_81
<=> empty(relation_inverse_image(sK6,sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_81])]) ).
fof(f474,plain,
( ~ empty(relation_inverse_image(sK6,sK5))
| ~ spl26_5
| ~ spl26_45 ),
inference(resolution,[],[f458,f263]) ).
fof(f707,plain,
spl26_80,
inference(avatar_split_clause,[],[f239,f705]) ).
fof(f239,plain,
! [X2,X0] :
( empty_set = X2
| ~ quasi_total(X2,X0,empty_set)
| empty_set = X0
| ~ relation_of2_as_subset(X2,X0,empty_set) ),
inference(equality_resolution,[],[f206]) ).
fof(f206,plain,
! [X2,X0,X1] :
( empty_set = X2
| ~ quasi_total(X2,X0,X1)
| empty_set = X0
| empty_set != X1
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f126]) ).
fof(f126,plain,
! [X0,X1,X2] :
( ( ( ( ( quasi_total(X2,X0,X1)
| empty_set != X2 )
& ( empty_set = X2
| ~ quasi_total(X2,X0,X1) ) )
| empty_set = X0
| empty_set != X1 )
& sP2(X0,X2,X1) )
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(nnf_transformation,[],[f98]) ).
fof(f98,plain,
! [X0,X1,X2] :
( ( ( ( quasi_total(X2,X0,X1)
<=> empty_set = X2 )
| empty_set = X0
| empty_set != X1 )
& sP2(X0,X2,X1) )
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(definition_folding,[],[f87,f97]) ).
fof(f87,plain,
! [X0,X1,X2] :
( ( ( ( quasi_total(X2,X0,X1)
<=> empty_set = X2 )
| empty_set = X0
| empty_set != X1 )
& ( ( quasi_total(X2,X0,X1)
<=> relation_dom_as_subset(X0,X1,X2) = X0 )
| ( empty_set != X0
& empty_set = X1 ) ) )
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(flattening,[],[f86]) ).
fof(f86,plain,
! [X0,X1,X2] :
( ( ( ( quasi_total(X2,X0,X1)
<=> empty_set = X2 )
| empty_set = X0
| empty_set != X1 )
& ( ( quasi_total(X2,X0,X1)
<=> relation_dom_as_subset(X0,X1,X2) = X0 )
| ( empty_set != X0
& empty_set = X1 ) ) )
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> ( ( empty_set = X1
=> ( ( quasi_total(X2,X0,X1)
<=> empty_set = X2 )
| empty_set = X0 ) )
& ( ( empty_set = X1
=> empty_set = X0 )
=> ( quasi_total(X2,X0,X1)
<=> relation_dom_as_subset(X0,X1,X2) = X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_funct_2) ).
fof(f700,plain,
spl26_79,
inference(avatar_split_clause,[],[f236,f698]) ).
fof(f236,plain,
! [X2,X1] :
( empty_set = relation_dom_as_subset(empty_set,X2,X1)
| ~ quasi_total(X1,empty_set,X2)
| ~ sP2(empty_set,X1,X2) ),
inference(equality_resolution,[],[f202]) ).
fof(f202,plain,
! [X2,X0,X1] :
( relation_dom_as_subset(X0,X2,X1) = X0
| ~ quasi_total(X1,X0,X2)
| empty_set != X0
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f125]) ).
fof(f693,plain,
spl26_78,
inference(avatar_split_clause,[],[f235,f691]) ).
fof(f235,plain,
! [X2,X1] :
( quasi_total(X1,empty_set,X2)
| empty_set != relation_dom_as_subset(empty_set,X2,X1)
| ~ sP2(empty_set,X1,X2) ),
inference(equality_resolution,[],[f204]) ).
fof(f204,plain,
! [X2,X0,X1] :
( quasi_total(X1,X0,X2)
| relation_dom_as_subset(X0,X2,X1) != X0
| empty_set != X0
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f125]) ).
fof(f688,plain,
spl26_77,
inference(avatar_split_clause,[],[f172,f686]) ).
fof(f172,plain,
! [X2,X0,X1,X4] :
( in(apply(X1,X4),X0)
| ~ in(X4,X2)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f111]) ).
fof(f684,plain,
( spl26_76
| ~ spl26_10
| ~ spl26_40
| ~ spl26_75 ),
inference(avatar_split_clause,[],[f669,f664,f436,f285,f682]) ).
fof(f682,plain,
( spl26_76
<=> ! [X0] :
( ~ relation_of2_as_subset(sK17,X0,sK17)
| sK17 = X0
| quasi_total(sK17,X0,sK17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_76])]) ).
fof(f664,plain,
( spl26_75
<=> ! [X0] :
( quasi_total(empty_set,X0,empty_set)
| empty_set = X0
| ~ relation_of2_as_subset(empty_set,X0,empty_set) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_75])]) ).
fof(f669,plain,
( ! [X0] :
( ~ relation_of2_as_subset(sK17,X0,sK17)
| sK17 = X0
| quasi_total(sK17,X0,sK17) )
| ~ spl26_10
| ~ spl26_40
| ~ spl26_75 ),
inference(forward_demodulation,[],[f668,f462]) ).
fof(f668,plain,
( ! [X0] :
( sK17 = X0
| quasi_total(sK17,X0,sK17)
| ~ relation_of2_as_subset(empty_set,X0,empty_set) )
| ~ spl26_10
| ~ spl26_40
| ~ spl26_75 ),
inference(forward_demodulation,[],[f667,f462]) ).
fof(f667,plain,
( ! [X0] :
( quasi_total(sK17,X0,sK17)
| empty_set = X0
| ~ relation_of2_as_subset(empty_set,X0,empty_set) )
| ~ spl26_10
| ~ spl26_40
| ~ spl26_75 ),
inference(forward_demodulation,[],[f665,f462]) ).
fof(f665,plain,
( ! [X0] :
( quasi_total(empty_set,X0,empty_set)
| empty_set = X0
| ~ relation_of2_as_subset(empty_set,X0,empty_set) )
| ~ spl26_75 ),
inference(avatar_component_clause,[],[f664]) ).
fof(f666,plain,
spl26_75,
inference(avatar_split_clause,[],[f238,f664]) ).
fof(f238,plain,
! [X0] :
( quasi_total(empty_set,X0,empty_set)
| empty_set = X0
| ~ relation_of2_as_subset(empty_set,X0,empty_set) ),
inference(equality_resolution,[],[f237]) ).
fof(f237,plain,
! [X0,X1] :
( quasi_total(empty_set,X0,X1)
| empty_set = X0
| empty_set != X1
| ~ relation_of2_as_subset(empty_set,X0,X1) ),
inference(equality_resolution,[],[f207]) ).
fof(f207,plain,
! [X2,X0,X1] :
( quasi_total(X2,X0,X1)
| empty_set != X2
| empty_set = X0
| empty_set != X1
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f126]) ).
fof(f662,plain,
spl26_74,
inference(avatar_split_clause,[],[f209,f660]) ).
fof(f209,plain,
! [X2,X0,X1] :
( element(relation_dom_as_subset(X0,X1,X2),powerset(X0))
| ~ relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
! [X0,X1,X2] :
( element(relation_dom_as_subset(X0,X1,X2),powerset(X0))
| ~ relation_of2(X2,X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0,X1,X2] :
( relation_of2(X2,X0,X1)
=> element(relation_dom_as_subset(X0,X1,X2),powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relset_1) ).
fof(f658,plain,
spl26_73,
inference(avatar_split_clause,[],[f208,f656]) ).
fof(f208,plain,
! [X2,X0,X1] :
( relation_dom_as_subset(X0,X1,X2) = relation_dom(X2)
| ~ relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0,X1,X2] :
( relation_dom_as_subset(X0,X1,X2) = relation_dom(X2)
| ~ relation_of2(X2,X0,X1) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0,X1,X2] :
( relation_of2(X2,X0,X1)
=> relation_dom_as_subset(X0,X1,X2) = relation_dom(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_relset_1) ).
fof(f654,plain,
spl26_72,
inference(avatar_split_clause,[],[f171,f652]) ).
fof(f171,plain,
! [X2,X0,X1,X4] :
( in(X4,relation_dom(X1))
| ~ in(X4,X2)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f111]) ).
fof(f650,plain,
spl26_71,
inference(avatar_split_clause,[],[f170,f648]) ).
fof(f648,plain,
( spl26_71
<=> ! [X2,X0,X1] :
( relation_inverse_image(X0,X1) = X2
| ~ sP0(X1,X0,X2)
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_71])]) ).
fof(f170,plain,
! [X2,X0,X1] :
( relation_inverse_image(X0,X1) = X2
| ~ sP0(X1,X0,X2)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f106,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_inverse_image(X0,X1) = X2
| ~ sP0(X1,X0,X2) )
& ( sP0(X1,X0,X2)
| relation_inverse_image(X0,X1) != X2 ) )
| ~ sP1(X0) ),
inference(nnf_transformation,[],[f95]) ).
fof(f95,plain,
! [X0] :
( ! [X1,X2] :
( relation_inverse_image(X0,X1) = X2
<=> sP0(X1,X0,X2) )
| ~ sP1(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f636,plain,
spl26_70,
inference(avatar_split_clause,[],[f211,f634]) ).
fof(f211,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f92]) ).
fof(f92,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f91]) ).
fof(f91,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f50]) ).
fof(f50,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f632,plain,
spl26_69,
inference(avatar_split_clause,[],[f200,f630]) ).
fof(f200,plain,
! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> element(X2,powerset(cartesian_product2(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(f622,plain,
spl26_68,
inference(avatar_split_clause,[],[f214,f620]) ).
fof(f214,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f93]) ).
fof(f93,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f51]) ).
fof(f51,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f601,plain,
spl26_67,
inference(avatar_split_clause,[],[f234,f599]) ).
fof(f234,plain,
! [X0,X1] :
( sP0(X1,X0,relation_inverse_image(X0,X1))
| ~ sP1(X0) ),
inference(equality_resolution,[],[f169]) ).
fof(f169,plain,
! [X2,X0,X1] :
( sP0(X1,X0,X2)
| relation_inverse_image(X0,X1) != X2
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f597,plain,
( spl26_66
| ~ spl26_6
| ~ spl26_49 ),
inference(avatar_split_clause,[],[f534,f489,f265,f594]) ).
fof(f592,plain,
spl26_65,
inference(avatar_split_clause,[],[f213,f590]) ).
fof(f213,plain,
! [X2,X0,X1] :
( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f127]) ).
fof(f127,plain,
! [X0,X1,X2] :
( ( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) )
& ( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f43]) ).
fof(f43,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
<=> relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f588,plain,
spl26_64,
inference(avatar_split_clause,[],[f212,f586]) ).
fof(f212,plain,
! [X2,X0,X1] :
( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f127]) ).
fof(f584,plain,
spl26_63,
inference(avatar_split_clause,[],[f210,f582]) ).
fof(f210,plain,
! [X2,X0,X1] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0,X1,X2] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
=> relation(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f580,plain,
spl26_62,
inference(avatar_split_clause,[],[f205,f578]) ).
fof(f205,plain,
! [X2,X0,X1] :
( sP2(X0,X2,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f126]) ).
fof(f576,plain,
spl26_61,
inference(avatar_split_clause,[],[f187,f574]) ).
fof(f574,plain,
( spl26_61
<=> ! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_61])]) ).
fof(f187,plain,
! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ),
inference(flattening,[],[f80]) ).
fof(f80,plain,
! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0,X1] :
( ( ~ empty(X1)
& ~ empty(X0) )
=> ~ empty(cartesian_product2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_subset_1) ).
fof(f572,plain,
spl26_60,
inference(avatar_split_clause,[],[f186,f570]) ).
fof(f186,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f78]) ).
fof(f78,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f46]) ).
fof(f46,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f556,plain,
( ~ spl26_59
| ~ spl26_6
| ~ spl26_48 ),
inference(avatar_split_clause,[],[f532,f485,f265,f553]) ).
fof(f553,plain,
( spl26_59
<=> in(sK3,sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_59])]) ).
fof(f532,plain,
( ~ in(sK3,sK7)
| ~ spl26_6
| ~ spl26_48 ),
inference(resolution,[],[f486,f267]) ).
fof(f551,plain,
spl26_58,
inference(avatar_split_clause,[],[f189,f549]) ).
fof(f189,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f54]) ).
fof(f54,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(f547,plain,
spl26_57,
inference(avatar_split_clause,[],[f188,f545]) ).
fof(f188,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0,X1] :
( subset(X0,X1)
=> element(X0,powerset(X1)) ),
inference(unused_predicate_definition_removal,[],[f47]) ).
fof(f47,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f543,plain,
spl26_56,
inference(avatar_split_clause,[],[f168,f541]) ).
fof(f541,plain,
( spl26_56
<=> ! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_56])]) ).
fof(f168,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(flattening,[],[f70]) ).
fof(f70,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_dom(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(f539,plain,
spl26_55,
inference(avatar_split_clause,[],[f161,f537]) ).
fof(f161,plain,
! [X0] :
( element(sK8(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f105,plain,
! [X0] :
( ( ~ empty(sK8(X0))
& element(sK8(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f65,f104]) ).
fof(f104,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( ~ empty(sK8(X0))
& element(sK8(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f65,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f511,plain,
spl26_54,
inference(avatar_split_clause,[],[f199,f509]) ).
fof(f199,plain,
! [X0,X1] : quasi_total(sK15(X0,X1),X0,X1),
inference(cnf_transformation,[],[f123]) ).
fof(f123,plain,
! [X0,X1] :
( quasi_total(sK15(X0,X1),X0,X1)
& function(sK15(X0,X1))
& relation(sK15(X0,X1))
& relation_of2(sK15(X0,X1),X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f29,f122]) ).
fof(f122,plain,
! [X0,X1] :
( ? [X2] :
( quasi_total(X2,X0,X1)
& function(X2)
& relation(X2)
& relation_of2(X2,X0,X1) )
=> ( quasi_total(sK15(X0,X1),X0,X1)
& function(sK15(X0,X1))
& relation(sK15(X0,X1))
& relation_of2(sK15(X0,X1),X0,X1) ) ),
introduced(choice_axiom,[]) ).
fof(f29,axiom,
! [X0,X1] :
? [X2] :
( quasi_total(X2,X0,X1)
& function(X2)
& relation(X2)
& relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_2) ).
fof(f507,plain,
spl26_53,
inference(avatar_split_clause,[],[f196,f505]) ).
fof(f196,plain,
! [X0,X1] : relation_of2(sK15(X0,X1),X0,X1),
inference(cnf_transformation,[],[f123]) ).
fof(f503,plain,
spl26_52,
inference(avatar_split_clause,[],[f193,f501]) ).
fof(f193,plain,
! [X0,X1] : relation_of2(sK14(X0,X1),X0,X1),
inference(cnf_transformation,[],[f121]) ).
fof(f121,plain,
! [X0,X1] :
( function(sK14(X0,X1))
& relation(sK14(X0,X1))
& relation_of2(sK14(X0,X1),X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f35,f120]) ).
fof(f120,plain,
! [X0,X1] :
( ? [X2] :
( function(X2)
& relation(X2)
& relation_of2(X2,X0,X1) )
=> ( function(sK14(X0,X1))
& relation(sK14(X0,X1))
& relation_of2(sK14(X0,X1),X0,X1) ) ),
introduced(choice_axiom,[]) ).
fof(f35,axiom,
! [X0,X1] :
? [X2] :
( function(X2)
& relation(X2)
& relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_partfun1) ).
fof(f499,plain,
spl26_51,
inference(avatar_split_clause,[],[f192,f497]) ).
fof(f192,plain,
! [X0,X1] : relation_of2(sK13(X0,X1),X0,X1),
inference(cnf_transformation,[],[f119]) ).
fof(f119,plain,
! [X0,X1] : relation_of2(sK13(X0,X1),X0,X1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f18,f118]) ).
fof(f118,plain,
! [X0,X1] :
( ? [X2] : relation_of2(X2,X0,X1)
=> relation_of2(sK13(X0,X1),X0,X1) ),
introduced(choice_axiom,[]) ).
fof(f18,axiom,
! [X0,X1] :
? [X2] : relation_of2(X2,X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_relset_1) ).
fof(f495,plain,
spl26_50,
inference(avatar_split_clause,[],[f191,f493]) ).
fof(f191,plain,
! [X0,X1] : relation_of2_as_subset(sK12(X0,X1),X0,X1),
inference(cnf_transformation,[],[f117]) ).
fof(f117,plain,
! [X0,X1] : relation_of2_as_subset(sK12(X0,X1),X0,X1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f20,f116]) ).
fof(f116,plain,
! [X0,X1] :
( ? [X2] : relation_of2_as_subset(X2,X0,X1)
=> relation_of2_as_subset(sK12(X0,X1),X0,X1) ),
introduced(choice_axiom,[]) ).
fof(f20,axiom,
! [X0,X1] :
? [X2] : relation_of2_as_subset(X2,X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_relset_1) ).
fof(f491,plain,
spl26_49,
inference(avatar_split_clause,[],[f185,f489]) ).
fof(f185,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f487,plain,
spl26_48,
inference(avatar_split_clause,[],[f184,f485]) ).
fof(f184,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f483,plain,
spl26_47,
inference(avatar_split_clause,[],[f177,f481]) ).
fof(f177,plain,
! [X0] :
( sP1(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f96]) ).
fof(f96,plain,
! [X0] :
( sP1(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f73,f95,f94]) ).
fof(f73,plain,
! [X0] :
( ! [X1,X2] :
( relation_inverse_image(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f72]) ).
fof(f72,plain,
! [X0] :
( ! [X1,X2] :
( relation_inverse_image(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1,X2] :
( relation_inverse_image(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_funct_1) ).
fof(f479,plain,
( ~ spl26_46
| ~ spl26_6
| ~ spl26_45 ),
inference(avatar_split_clause,[],[f473,f457,f265,f476]) ).
fof(f459,plain,
spl26_45,
inference(avatar_split_clause,[],[f190,f457]) ).
fof(f190,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f84,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f53]) ).
fof(f53,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f455,plain,
spl26_44,
inference(avatar_split_clause,[],[f181,f453]) ).
fof(f181,plain,
! [X0] : element(sK11(X0),powerset(X0)),
inference(cnf_transformation,[],[f115]) ).
fof(f115,plain,
! [X0] :
( empty(sK11(X0))
& element(sK11(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f37,f114]) ).
fof(f114,plain,
! [X0] :
( ? [X1] :
( empty(X1)
& element(X1,powerset(X0)) )
=> ( empty(sK11(X0))
& element(sK11(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f37,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f451,plain,
spl26_43,
inference(avatar_split_clause,[],[f167,f449]) ).
fof(f167,plain,
! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0] :
( ( relation(relation_dom(X0))
& empty(relation_dom(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(f447,plain,
spl26_42,
inference(avatar_split_clause,[],[f166,f445]) ).
fof(f166,plain,
! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f443,plain,
( spl26_41
| ~ spl26_7
| ~ spl26_32 ),
inference(avatar_split_clause,[],[f419,f392,f270,f440]) ).
fof(f440,plain,
( spl26_41
<=> function(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_41])]) ).
fof(f419,plain,
( function(empty_set)
| ~ spl26_7
| ~ spl26_32 ),
inference(resolution,[],[f393,f272]) ).
fof(f438,plain,
spl26_40,
inference(avatar_split_clause,[],[f165,f436]) ).
fof(f165,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f52]) ).
fof(f52,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f434,plain,
spl26_39,
inference(avatar_split_clause,[],[f162,f432]) ).
fof(f432,plain,
( spl26_39
<=> ! [X0] :
( ~ empty(sK8(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_39])]) ).
fof(f162,plain,
! [X0] :
( ~ empty(sK8(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f418,plain,
spl26_38,
inference(avatar_split_clause,[],[f198,f416]) ).
fof(f198,plain,
! [X0,X1] : function(sK15(X0,X1)),
inference(cnf_transformation,[],[f123]) ).
fof(f414,plain,
spl26_37,
inference(avatar_split_clause,[],[f197,f412]) ).
fof(f197,plain,
! [X0,X1] : relation(sK15(X0,X1)),
inference(cnf_transformation,[],[f123]) ).
fof(f410,plain,
spl26_36,
inference(avatar_split_clause,[],[f195,f408]) ).
fof(f195,plain,
! [X0,X1] : function(sK14(X0,X1)),
inference(cnf_transformation,[],[f121]) ).
fof(f406,plain,
spl26_35,
inference(avatar_split_clause,[],[f194,f404]) ).
fof(f194,plain,
! [X0,X1] : relation(sK14(X0,X1)),
inference(cnf_transformation,[],[f121]) ).
fof(f402,plain,
spl26_34,
inference(avatar_split_clause,[],[f180,f400]) ).
fof(f180,plain,
! [X0] : element(sK10(X0),X0),
inference(cnf_transformation,[],[f113]) ).
fof(f113,plain,
! [X0] : element(sK10(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f19,f112]) ).
fof(f112,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK10(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f19,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f398,plain,
spl26_33,
inference(avatar_split_clause,[],[f164,f396]) ).
fof(f164,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( empty(X0)
=> relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(f394,plain,
spl26_32,
inference(avatar_split_clause,[],[f163,f392]) ).
fof(f163,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( empty(X0)
=> function(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
fof(f390,plain,
spl26_31,
inference(avatar_split_clause,[],[f183,f388]) ).
fof(f183,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f44]) ).
fof(f44,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f386,plain,
spl26_30,
inference(avatar_split_clause,[],[f182,f384]) ).
fof(f182,plain,
! [X0] : empty(sK11(X0)),
inference(cnf_transformation,[],[f115]) ).
fof(f382,plain,
spl26_29,
inference(avatar_split_clause,[],[f160,f380]) ).
fof(f380,plain,
( spl26_29
<=> ! [X0] : ~ empty(powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_29])]) ).
fof(f160,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f378,plain,
( spl26_5
| spl26_28 ),
inference(avatar_split_clause,[],[f153,f375,f261]) ).
fof(f153,plain,
( in(apply(sK6,sK7),sK5)
| in(sK7,relation_inverse_image(sK6,sK5)) ),
inference(cnf_transformation,[],[f103]) ).
fof(f373,plain,
spl26_27,
inference(avatar_split_clause,[],[f233,f370]) ).
fof(f370,plain,
( spl26_27
<=> function(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_27])]) ).
fof(f233,plain,
function(sK25),
inference(cnf_transformation,[],[f147]) ).
fof(f147,plain,
( function(sK25)
& empty(sK25)
& relation(sK25) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f34,f146]) ).
fof(f146,plain,
( ? [X0] :
( function(X0)
& empty(X0)
& relation(X0) )
=> ( function(sK25)
& empty(sK25)
& relation(sK25) ) ),
introduced(choice_axiom,[]) ).
fof(f34,axiom,
? [X0] :
( function(X0)
& empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(f368,plain,
spl26_26,
inference(avatar_split_clause,[],[f232,f365]) ).
fof(f232,plain,
empty(sK25),
inference(cnf_transformation,[],[f147]) ).
fof(f363,plain,
spl26_25,
inference(avatar_split_clause,[],[f231,f360]) ).
fof(f360,plain,
( spl26_25
<=> relation(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_25])]) ).
fof(f231,plain,
relation(sK25),
inference(cnf_transformation,[],[f147]) ).
fof(f358,plain,
spl26_24,
inference(avatar_split_clause,[],[f230,f355]) ).
fof(f230,plain,
empty(sK24),
inference(cnf_transformation,[],[f145]) ).
fof(f145,plain,
( empty(sK24)
& function(sK24)
& relation(sK24) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f62,f144]) ).
fof(f144,plain,
( ? [X0] :
( empty(X0)
& function(X0)
& relation(X0) )
=> ( empty(sK24)
& function(sK24)
& relation(sK24) ) ),
introduced(choice_axiom,[]) ).
fof(f62,plain,
? [X0] :
( empty(X0)
& function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f30]) ).
fof(f30,axiom,
? [X0] :
( empty(X0)
& one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_partfun1) ).
fof(f353,plain,
spl26_23,
inference(avatar_split_clause,[],[f229,f350]) ).
fof(f350,plain,
( spl26_23
<=> function(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_23])]) ).
fof(f229,plain,
function(sK24),
inference(cnf_transformation,[],[f145]) ).
fof(f348,plain,
spl26_22,
inference(avatar_split_clause,[],[f228,f345]) ).
fof(f345,plain,
( spl26_22
<=> relation(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_22])]) ).
fof(f228,plain,
relation(sK24),
inference(cnf_transformation,[],[f145]) ).
fof(f343,plain,
spl26_21,
inference(avatar_split_clause,[],[f227,f340]) ).
fof(f227,plain,
function(sK23),
inference(cnf_transformation,[],[f143]) ).
fof(f143,plain,
( function(sK23)
& relation(sK23) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f60,f142]) ).
fof(f142,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK23)
& relation(sK23) ) ),
introduced(choice_axiom,[]) ).
fof(f60,plain,
? [X0] :
( function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f39]) ).
fof(f39,axiom,
? [X0] :
( one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
fof(f338,plain,
spl26_20,
inference(avatar_split_clause,[],[f226,f335]) ).
fof(f226,plain,
relation(sK23),
inference(cnf_transformation,[],[f143]) ).
fof(f333,plain,
spl26_19,
inference(avatar_split_clause,[],[f225,f330]) ).
fof(f225,plain,
function(sK22),
inference(cnf_transformation,[],[f141]) ).
fof(f141,plain,
( function(sK22)
& relation(sK22) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22])],[f28,f140]) ).
fof(f140,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK22)
& relation(sK22) ) ),
introduced(choice_axiom,[]) ).
fof(f28,axiom,
? [X0] :
( function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
fof(f328,plain,
spl26_18,
inference(avatar_split_clause,[],[f224,f325]) ).
fof(f224,plain,
relation(sK22),
inference(cnf_transformation,[],[f141]) ).
fof(f323,plain,
spl26_17,
inference(avatar_split_clause,[],[f223,f320]) ).
fof(f223,plain,
function(sK21),
inference(cnf_transformation,[],[f139]) ).
fof(f139,plain,
( function(sK21)
& relation(sK21) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f59,f138]) ).
fof(f138,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK21)
& relation(sK21) ) ),
introduced(choice_axiom,[]) ).
fof(f59,plain,
? [X0] :
( function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f41]) ).
fof(f41,axiom,
? [X0] :
( function(X0)
& relation_empty_yielding(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_funct_1) ).
fof(f318,plain,
spl26_16,
inference(avatar_split_clause,[],[f222,f315]) ).
fof(f222,plain,
relation(sK21),
inference(cnf_transformation,[],[f139]) ).
fof(f313,plain,
spl26_15,
inference(avatar_split_clause,[],[f221,f310]) ).
fof(f221,plain,
relation(sK20),
inference(cnf_transformation,[],[f137]) ).
fof(f137,plain,
relation(sK20),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f57,f136]) ).
fof(f136,plain,
( ? [X0] : relation(X0)
=> relation(sK20) ),
introduced(choice_axiom,[]) ).
fof(f57,plain,
? [X0] : relation(X0),
inference(pure_predicate_removal,[],[f40]) ).
fof(f40,axiom,
? [X0] :
( relation_empty_yielding(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
fof(f308,plain,
spl26_14,
inference(avatar_split_clause,[],[f220,f305]) ).
fof(f305,plain,
( spl26_14
<=> relation(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_14])]) ).
fof(f220,plain,
relation(sK19),
inference(cnf_transformation,[],[f135]) ).
fof(f135,plain,
( relation(sK19)
& empty(sK19) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f31,f134]) ).
fof(f134,plain,
( ? [X0] :
( relation(X0)
& empty(X0) )
=> ( relation(sK19)
& empty(sK19) ) ),
introduced(choice_axiom,[]) ).
fof(f31,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f303,plain,
spl26_13,
inference(avatar_split_clause,[],[f219,f300]) ).
fof(f219,plain,
empty(sK19),
inference(cnf_transformation,[],[f135]) ).
fof(f298,plain,
spl26_12,
inference(avatar_split_clause,[],[f218,f295]) ).
fof(f218,plain,
relation(sK18),
inference(cnf_transformation,[],[f133]) ).
fof(f133,plain,
( relation(sK18)
& ~ empty(sK18) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f36,f132]) ).
fof(f132,plain,
( ? [X0] :
( relation(X0)
& ~ empty(X0) )
=> ( relation(sK18)
& ~ empty(sK18) ) ),
introduced(choice_axiom,[]) ).
fof(f36,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f293,plain,
~ spl26_11,
inference(avatar_split_clause,[],[f217,f290]) ).
fof(f290,plain,
( spl26_11
<=> empty(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_11])]) ).
fof(f217,plain,
~ empty(sK18),
inference(cnf_transformation,[],[f133]) ).
fof(f288,plain,
spl26_10,
inference(avatar_split_clause,[],[f216,f285]) ).
fof(f216,plain,
empty(sK17),
inference(cnf_transformation,[],[f131]) ).
fof(f131,plain,
empty(sK17),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f33,f130]) ).
fof(f130,plain,
( ? [X0] : empty(X0)
=> empty(sK17) ),
introduced(choice_axiom,[]) ).
fof(f33,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f283,plain,
~ spl26_9,
inference(avatar_split_clause,[],[f215,f280]) ).
fof(f280,plain,
( spl26_9
<=> empty(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_9])]) ).
fof(f215,plain,
~ empty(sK16),
inference(cnf_transformation,[],[f129]) ).
fof(f129,plain,
~ empty(sK16),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f38,f128]) ).
fof(f128,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK16) ),
introduced(choice_axiom,[]) ).
fof(f38,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f278,plain,
spl26_8,
inference(avatar_split_clause,[],[f157,f275]) ).
fof(f157,plain,
relation(empty_set),
inference(cnf_transformation,[],[f24]) ).
fof(f24,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f273,plain,
spl26_7,
inference(avatar_split_clause,[],[f155,f270]) ).
fof(f155,plain,
empty(empty_set),
inference(cnf_transformation,[],[f23]) ).
fof(f23,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f268,plain,
( spl26_5
| spl26_6 ),
inference(avatar_split_clause,[],[f152,f265,f261]) ).
fof(f152,plain,
( in(sK7,sK3)
| in(sK7,relation_inverse_image(sK6,sK5)) ),
inference(cnf_transformation,[],[f103]) ).
fof(f259,plain,
spl26_4,
inference(avatar_split_clause,[],[f150,f256]) ).
fof(f150,plain,
relation_of2_as_subset(sK6,sK3,sK4),
inference(cnf_transformation,[],[f103]) ).
fof(f254,plain,
spl26_3,
inference(avatar_split_clause,[],[f149,f251]) ).
fof(f149,plain,
quasi_total(sK6,sK3,sK4),
inference(cnf_transformation,[],[f103]) ).
fof(f249,plain,
~ spl26_2,
inference(avatar_split_clause,[],[f151,f246]) ).
fof(f151,plain,
empty_set != sK4,
inference(cnf_transformation,[],[f103]) ).
fof(f244,plain,
spl26_1,
inference(avatar_split_clause,[],[f148,f241]) ).
fof(f148,plain,
function(sK6),
inference(cnf_transformation,[],[f103]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU293+1 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.34 % Computer : n031.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 3 12:23:17 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (13088)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.36 % (13096)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.37 % (13093)WARNING: value z3 for option sas not known
% 0.14/0.37 % (13091)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.37 % (13092)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.37 % (13094)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.37 % (13095)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.37 % (13097)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.37 % (13093)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.37 TRYING [1]
% 0.14/0.37 TRYING [2]
% 0.21/0.38 TRYING [3]
% 0.21/0.39 TRYING [1]
% 0.21/0.39 TRYING [1]
% 0.21/0.39 TRYING [2]
% 0.21/0.39 TRYING [3]
% 0.21/0.39 TRYING [2]
% 0.21/0.40 TRYING [4]
% 0.21/0.41 TRYING [4]
% 0.21/0.42 % (13095)First to succeed.
% 0.21/0.43 % (13095)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-13088"
% 0.21/0.43 % (13095)Refutation found. Thanks to Tanya!
% 0.21/0.43 % SZS status Theorem for theBenchmark
% 0.21/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.44 % (13095)------------------------------
% 0.21/0.44 % (13095)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.44 % (13095)Termination reason: Refutation
% 0.21/0.44
% 0.21/0.44 % (13095)Memory used [KB]: 1609
% 0.21/0.44 % (13095)Time elapsed: 0.067 s
% 0.21/0.44 % (13095)Instructions burned: 76 (million)
% 0.21/0.44 % (13088)Success in time 0.089 s
%------------------------------------------------------------------------------