TSTP Solution File: SEU290+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU290+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n017.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 : Sat Sep 2 00:12:21 EDT 2023
% Result : Theorem 0.15s 0.37s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 291
% Syntax : Number of formulae : 922 ( 151 unt; 0 def)
% Number of atoms : 2764 ( 272 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 3189 (1347 ~;1377 |; 178 &)
% ( 239 <=>; 48 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 236 ( 234 usr; 221 prp; 0-3 aty)
% Number of functors : 31 ( 31 usr; 15 con; 0-3 aty)
% Number of variables : 1033 (; 971 !; 62 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1793,plain,
$false,
inference(avatar_sat_refutation,[],[f243,f248,f253,f258,f263,f268,f273,f278,f283,f288,f293,f298,f303,f308,f313,f318,f323,f328,f333,f338,f343,f348,f353,f358,f363,f368,f373,f378,f383,f388,f393,f398,f402,f406,f410,f414,f418,f422,f426,f430,f434,f438,f449,f459,f463,f467,f471,f476,f480,f484,f488,f492,f514,f520,f524,f528,f532,f536,f540,f544,f548,f553,f580,f584,f588,f592,f596,f600,f625,f629,f633,f637,f641,f645,f649,f653,f686,f701,f705,f709,f720,f724,f739,f743,f755,f760,f764,f774,f779,f783,f788,f793,f799,f803,f808,f815,f825,f829,f833,f837,f841,f845,f850,f857,f865,f870,f876,f881,f887,f892,f897,f902,f909,f927,f937,f942,f951,f956,f961,f966,f971,f975,f981,f985,f989,f993,f1000,f1007,f1008,f1009,f1010,f1011,f1012,f1043,f1044,f1096,f1108,f1112,f1116,f1125,f1134,f1138,f1142,f1146,f1150,f1154,f1158,f1162,f1166,f1170,f1224,f1228,f1232,f1246,f1250,f1254,f1259,f1263,f1267,f1271,f1275,f1279,f1336,f1340,f1344,f1348,f1362,f1369,f1373,f1377,f1391,f1395,f1399,f1403,f1407,f1411,f1415,f1419,f1445,f1463,f1467,f1471,f1475,f1479,f1507,f1511,f1529,f1533,f1537,f1541,f1545,f1549,f1553,f1557,f1561,f1594,f1606,f1613,f1617,f1627,f1636,f1644,f1659,f1664,f1665,f1674,f1678,f1682,f1686,f1690,f1694,f1719,f1729,f1733,f1739,f1754,f1758,f1762,f1766,f1770,f1792]) ).
fof(f1792,plain,
( ~ spl27_2
| spl27_202
| ~ spl27_212 ),
inference(avatar_split_clause,[],[f1740,f1716,f1633,f245]) ).
fof(f245,plain,
( spl27_2
<=> in(sK5,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_2])]) ).
fof(f1633,plain,
( spl27_202
<=> in(sK5,relation_dom(sK6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_202])]) ).
fof(f1716,plain,
( spl27_212
<=> sK3 = relation_dom(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_212])]) ).
fof(f1740,plain,
( ~ in(sK5,sK3)
| spl27_202
| ~ spl27_212 ),
inference(superposition,[],[f1635,f1718]) ).
fof(f1718,plain,
( sK3 = relation_dom(sK6)
| ~ spl27_212 ),
inference(avatar_component_clause,[],[f1716]) ).
fof(f1635,plain,
( ~ in(sK5,relation_dom(sK6))
| spl27_202 ),
inference(avatar_component_clause,[],[f1633]) ).
fof(f1770,plain,
( spl27_220
| ~ spl27_130
| ~ spl27_175 ),
inference(avatar_split_clause,[],[f1456,f1413,f998,f1768]) ).
fof(f1768,plain,
( spl27_220
<=> ! [X12] :
( sP0(X12,sK18)
| ~ empty(relation_dom(X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_220])]) ).
fof(f998,plain,
( spl27_130
<=> ! [X8] : ~ in(X8,sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_130])]) ).
fof(f1413,plain,
( spl27_175
<=> ! [X4,X5] :
( in(sK8(X4,X5),X5)
| sP0(X4,X5)
| ~ empty(relation_dom(X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_175])]) ).
fof(f1456,plain,
( ! [X12] :
( sP0(X12,sK18)
| ~ empty(relation_dom(X12)) )
| ~ spl27_130
| ~ spl27_175 ),
inference(resolution,[],[f1414,f999]) ).
fof(f999,plain,
( ! [X8] : ~ in(X8,sK18)
| ~ spl27_130 ),
inference(avatar_component_clause,[],[f998]) ).
fof(f1414,plain,
( ! [X4,X5] :
( in(sK8(X4,X5),X5)
| sP0(X4,X5)
| ~ empty(relation_dom(X4)) )
| ~ spl27_175 ),
inference(avatar_component_clause,[],[f1413]) ).
fof(f1766,plain,
( spl27_219
| ~ spl27_140
| ~ spl27_151 ),
inference(avatar_split_clause,[],[f1242,f1230,f1136,f1764]) ).
fof(f1764,plain,
( spl27_219
<=> ! [X4] :
( ~ empty(X4)
| empty(sK11(powerset(X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_219])]) ).
fof(f1136,plain,
( spl27_140
<=> ! [X3] :
( empty(X3)
| in(sK11(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_140])]) ).
fof(f1230,plain,
( spl27_151
<=> ! [X6,X5] :
( ~ empty(X5)
| ~ in(X6,sK11(powerset(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_151])]) ).
fof(f1242,plain,
( ! [X4] :
( ~ empty(X4)
| empty(sK11(powerset(X4))) )
| ~ spl27_140
| ~ spl27_151 ),
inference(resolution,[],[f1231,f1137]) ).
fof(f1137,plain,
( ! [X3] :
( in(sK11(X3),X3)
| empty(X3) )
| ~ spl27_140 ),
inference(avatar_component_clause,[],[f1136]) ).
fof(f1231,plain,
( ! [X6,X5] :
( ~ in(X6,sK11(powerset(X5)))
| ~ empty(X5) )
| ~ spl27_151 ),
inference(avatar_component_clause,[],[f1230]) ).
fof(f1762,plain,
( spl27_218
| ~ spl27_73
| ~ spl27_146 ),
inference(avatar_split_clause,[],[f1211,f1160,f639,f1760]) ).
fof(f1760,plain,
( spl27_218
<=> ! [X2,X3] : sP2(X2,sK16(X2,X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_218])]) ).
fof(f639,plain,
( spl27_73
<=> ! [X2,X0,X1] :
( sP2(X0,X2,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_73])]) ).
fof(f1160,plain,
( spl27_146
<=> ! [X4,X5] : relation_of2_as_subset(sK16(X4,X5),X4,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_146])]) ).
fof(f1211,plain,
( ! [X2,X3] : sP2(X2,sK16(X2,X3),X3)
| ~ spl27_73
| ~ spl27_146 ),
inference(resolution,[],[f1161,f640]) ).
fof(f640,plain,
( ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| sP2(X0,X2,X1) )
| ~ spl27_73 ),
inference(avatar_component_clause,[],[f639]) ).
fof(f1161,plain,
( ! [X4,X5] : relation_of2_as_subset(sK16(X4,X5),X4,X5)
| ~ spl27_146 ),
inference(avatar_component_clause,[],[f1160]) ).
fof(f1758,plain,
( spl27_217
| ~ spl27_73
| ~ spl27_145 ),
inference(avatar_split_clause,[],[f1209,f1156,f639,f1756]) ).
fof(f1756,plain,
( spl27_217
<=> ! [X2,X3] : sP2(X2,sK15(X2,X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_217])]) ).
fof(f1156,plain,
( spl27_145
<=> ! [X2,X3] : relation_of2_as_subset(sK15(X2,X3),X2,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_145])]) ).
fof(f1209,plain,
( ! [X2,X3] : sP2(X2,sK15(X2,X3),X3)
| ~ spl27_73
| ~ spl27_145 ),
inference(resolution,[],[f1157,f640]) ).
fof(f1157,plain,
( ! [X2,X3] : relation_of2_as_subset(sK15(X2,X3),X2,X3)
| ~ spl27_145 ),
inference(avatar_component_clause,[],[f1156]) ).
fof(f1754,plain,
( spl27_216
| ~ spl27_73
| ~ spl27_144 ),
inference(avatar_split_clause,[],[f1207,f1152,f639,f1752]) ).
fof(f1752,plain,
( spl27_216
<=> ! [X2,X3] : sP2(X2,sK14(X2,X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_216])]) ).
fof(f1152,plain,
( spl27_144
<=> ! [X0,X1] : relation_of2_as_subset(sK14(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_144])]) ).
fof(f1207,plain,
( ! [X2,X3] : sP2(X2,sK14(X2,X3),X3)
| ~ spl27_73
| ~ spl27_144 ),
inference(resolution,[],[f1153,f640]) ).
fof(f1153,plain,
( ! [X0,X1] : relation_of2_as_subset(sK14(X0,X1),X0,X1)
| ~ spl27_144 ),
inference(avatar_component_clause,[],[f1152]) ).
fof(f1739,plain,
( spl27_215
| ~ spl27_55
| ~ spl27_140 ),
inference(avatar_split_clause,[],[f1199,f1136,f522,f1737]) ).
fof(f1737,plain,
( spl27_215
<=> ! [X2] :
( empty(X2)
| ~ in(X2,sK11(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_215])]) ).
fof(f522,plain,
( spl27_55
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_55])]) ).
fof(f1199,plain,
( ! [X2] :
( empty(X2)
| ~ in(X2,sK11(X2)) )
| ~ spl27_55
| ~ spl27_140 ),
inference(resolution,[],[f1137,f523]) ).
fof(f523,plain,
( ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) )
| ~ spl27_55 ),
inference(avatar_component_clause,[],[f522]) ).
fof(f1733,plain,
( spl27_214
| ~ spl27_126
| ~ spl27_153 ),
inference(avatar_split_clause,[],[f1283,f1248,f983,f1731]) ).
fof(f1731,plain,
( spl27_214
<=> ! [X0] :
( sP1(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_214])]) ).
fof(f983,plain,
( spl27_126
<=> ! [X2] :
( ~ empty(X2)
| function(relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_126])]) ).
fof(f1248,plain,
( spl27_153
<=> ! [X1] :
( ~ function(relation_dom(X1))
| sP1(relation_dom(X1))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_153])]) ).
fof(f1283,plain,
( ! [X0] :
( sP1(relation_dom(X0))
| ~ empty(X0) )
| ~ spl27_126
| ~ spl27_153 ),
inference(duplicate_literal_removal,[],[f1282]) ).
fof(f1282,plain,
( ! [X0] :
( sP1(relation_dom(X0))
| ~ empty(X0)
| ~ empty(X0) )
| ~ spl27_126
| ~ spl27_153 ),
inference(resolution,[],[f1249,f984]) ).
fof(f984,plain,
( ! [X2] :
( function(relation_dom(X2))
| ~ empty(X2) )
| ~ spl27_126 ),
inference(avatar_component_clause,[],[f983]) ).
fof(f1249,plain,
( ! [X1] :
( ~ function(relation_dom(X1))
| sP1(relation_dom(X1))
| ~ empty(X1) )
| ~ spl27_153 ),
inference(avatar_component_clause,[],[f1248]) ).
fof(f1729,plain,
( spl27_213
| ~ spl27_125
| ~ spl27_152 ),
inference(avatar_split_clause,[],[f1281,f1244,f979,f1727]) ).
fof(f1727,plain,
( spl27_213
<=> ! [X0] :
( sP1(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_213])]) ).
fof(f979,plain,
( spl27_125
<=> ! [X2] :
( ~ empty(X2)
| function(relation_rng(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_125])]) ).
fof(f1244,plain,
( spl27_152
<=> ! [X0] :
( ~ function(relation_rng(X0))
| sP1(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_152])]) ).
fof(f1281,plain,
( ! [X0] :
( sP1(relation_rng(X0))
| ~ empty(X0) )
| ~ spl27_125
| ~ spl27_152 ),
inference(duplicate_literal_removal,[],[f1280]) ).
fof(f1280,plain,
( ! [X0] :
( sP1(relation_rng(X0))
| ~ empty(X0)
| ~ empty(X0) )
| ~ spl27_125
| ~ spl27_152 ),
inference(resolution,[],[f1245,f980]) ).
fof(f980,plain,
( ! [X2] :
( function(relation_rng(X2))
| ~ empty(X2) )
| ~ spl27_125 ),
inference(avatar_component_clause,[],[f979]) ).
fof(f1245,plain,
( ! [X0] :
( ~ function(relation_rng(X0))
| sP1(relation_rng(X0))
| ~ empty(X0) )
| ~ spl27_152 ),
inference(avatar_component_clause,[],[f1244]) ).
fof(f1719,plain,
( spl27_212
| ~ spl27_105
| ~ spl27_203 ),
inference(avatar_split_clause,[],[f1645,f1641,f862,f1716]) ).
fof(f862,plain,
( spl27_105
<=> relation_dom_as_subset(sK3,sK4,sK6) = relation_dom(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_105])]) ).
fof(f1641,plain,
( spl27_203
<=> sK3 = relation_dom_as_subset(sK3,sK4,sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_203])]) ).
fof(f1645,plain,
( sK3 = relation_dom(sK6)
| ~ spl27_105
| ~ spl27_203 ),
inference(superposition,[],[f1643,f864]) ).
fof(f864,plain,
( relation_dom_as_subset(sK3,sK4,sK6) = relation_dom(sK6)
| ~ spl27_105 ),
inference(avatar_component_clause,[],[f862]) ).
fof(f1643,plain,
( sK3 = relation_dom_as_subset(sK3,sK4,sK6)
| ~ spl27_203 ),
inference(avatar_component_clause,[],[f1641]) ).
fof(f1694,plain,
( spl27_211
| ~ spl27_42
| ~ spl27_156 ),
inference(avatar_split_clause,[],[f1285,f1261,f436,f1692]) ).
fof(f1692,plain,
( spl27_211
<=> ! [X0,X1] : sP1(sK16(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_211])]) ).
fof(f436,plain,
( spl27_42
<=> ! [X0,X1] : function(sK16(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_42])]) ).
fof(f1261,plain,
( spl27_156
<=> ! [X4,X5] :
( ~ function(sK16(X4,X5))
| sP1(sK16(X4,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_156])]) ).
fof(f1285,plain,
( ! [X0,X1] : sP1(sK16(X0,X1))
| ~ spl27_42
| ~ spl27_156 ),
inference(resolution,[],[f1262,f437]) ).
fof(f437,plain,
( ! [X0,X1] : function(sK16(X0,X1))
| ~ spl27_42 ),
inference(avatar_component_clause,[],[f436]) ).
fof(f1262,plain,
( ! [X4,X5] :
( ~ function(sK16(X4,X5))
| sP1(sK16(X4,X5)) )
| ~ spl27_156 ),
inference(avatar_component_clause,[],[f1261]) ).
fof(f1690,plain,
( spl27_210
| ~ spl27_40
| ~ spl27_154 ),
inference(avatar_split_clause,[],[f1284,f1252,f428,f1688]) ).
fof(f1688,plain,
( spl27_210
<=> ! [X0,X1] : sP1(sK15(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_210])]) ).
fof(f428,plain,
( spl27_40
<=> ! [X0,X1] : function(sK15(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_40])]) ).
fof(f1252,plain,
( spl27_154
<=> ! [X2,X3] :
( ~ function(sK15(X2,X3))
| sP1(sK15(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_154])]) ).
fof(f1284,plain,
( ! [X0,X1] : sP1(sK15(X0,X1))
| ~ spl27_40
| ~ spl27_154 ),
inference(resolution,[],[f1253,f429]) ).
fof(f429,plain,
( ! [X0,X1] : function(sK15(X0,X1))
| ~ spl27_40 ),
inference(avatar_component_clause,[],[f428]) ).
fof(f1253,plain,
( ! [X2,X3] :
( ~ function(sK15(X2,X3))
| sP1(sK15(X2,X3)) )
| ~ spl27_154 ),
inference(avatar_component_clause,[],[f1252]) ).
fof(f1686,plain,
( spl27_209
| ~ spl27_35
| ~ spl27_150 ),
inference(avatar_split_clause,[],[f1236,f1226,f408,f1684]) ).
fof(f1684,plain,
( spl27_209
<=> ! [X0,X1] : relation(cartesian_product2(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_209])]) ).
fof(f408,plain,
( spl27_35
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_35])]) ).
fof(f1226,plain,
( spl27_150
<=> ! [X2,X0,X1] :
( relation(X0)
| ~ subset(X0,cartesian_product2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_150])]) ).
fof(f1236,plain,
( ! [X0,X1] : relation(cartesian_product2(X0,X1))
| ~ spl27_35
| ~ spl27_150 ),
inference(resolution,[],[f1227,f409]) ).
fof(f409,plain,
( ! [X0] : subset(X0,X0)
| ~ spl27_35 ),
inference(avatar_component_clause,[],[f408]) ).
fof(f1227,plain,
( ! [X2,X0,X1] :
( ~ subset(X0,cartesian_product2(X1,X2))
| relation(X0) )
| ~ spl27_150 ),
inference(avatar_component_clause,[],[f1226]) ).
fof(f1682,plain,
( spl27_208
| ~ spl27_144
| ~ spl27_148 ),
inference(avatar_split_clause,[],[f1218,f1168,f1152,f1680]) ).
fof(f1680,plain,
( spl27_208
<=> ! [X2,X3] : relation(sK14(X2,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_208])]) ).
fof(f1168,plain,
( spl27_148
<=> ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_148])]) ).
fof(f1218,plain,
( ! [X2,X3] : relation(sK14(X2,X3))
| ~ spl27_144
| ~ spl27_148 ),
inference(resolution,[],[f1169,f1153]) ).
fof(f1169,plain,
( ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| relation(X0) )
| ~ spl27_148 ),
inference(avatar_component_clause,[],[f1168]) ).
fof(f1678,plain,
( spl27_207
| ~ spl27_57
| ~ spl27_148 ),
inference(avatar_split_clause,[],[f1217,f1168,f530,f1676]) ).
fof(f1676,plain,
( spl27_207
<=> ! [X0,X1] : relation(sK13(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_207])]) ).
fof(f530,plain,
( spl27_57
<=> ! [X0,X1] : relation_of2_as_subset(sK13(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_57])]) ).
fof(f1217,plain,
( ! [X0,X1] : relation(sK13(X0,X1))
| ~ spl27_57
| ~ spl27_148 ),
inference(resolution,[],[f1169,f531]) ).
fof(f531,plain,
( ! [X0,X1] : relation_of2_as_subset(sK13(X0,X1),X0,X1)
| ~ spl27_57 ),
inference(avatar_component_clause,[],[f530]) ).
fof(f1674,plain,
( spl27_206
| ~ spl27_7
| ~ spl27_109
| ~ spl27_134 ),
inference(avatar_split_clause,[],[f1192,f1110,f884,f270,f1671]) ).
fof(f1671,plain,
( spl27_206
<=> sK18 = relation_dom(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_206])]) ).
fof(f270,plain,
( spl27_7
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_7])]) ).
fof(f884,plain,
( spl27_109
<=> empty_set = sK18 ),
introduced(avatar_definition,[new_symbols(naming,[spl27_109])]) ).
fof(f1110,plain,
( spl27_134
<=> ! [X0] :
( relation_dom(X0) = sK18
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_134])]) ).
fof(f1192,plain,
( sK18 = relation_dom(sK18)
| ~ spl27_7
| ~ spl27_109
| ~ spl27_134 ),
inference(forward_demodulation,[],[f1184,f886]) ).
fof(f886,plain,
( empty_set = sK18
| ~ spl27_109 ),
inference(avatar_component_clause,[],[f884]) ).
fof(f1184,plain,
( sK18 = relation_dom(empty_set)
| ~ spl27_7
| ~ spl27_134 ),
inference(resolution,[],[f1111,f272]) ).
fof(f272,plain,
( empty(empty_set)
| ~ spl27_7 ),
inference(avatar_component_clause,[],[f270]) ).
fof(f1111,plain,
( ! [X0] :
( ~ empty(X0)
| relation_dom(X0) = sK18 )
| ~ spl27_134 ),
inference(avatar_component_clause,[],[f1110]) ).
fof(f1665,plain,
( ~ spl27_165
| ~ spl27_147
| spl27_201 ),
inference(avatar_split_clause,[],[f1637,f1629,f1164,f1359]) ).
fof(f1359,plain,
( spl27_165
<=> sP1(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_165])]) ).
fof(f1164,plain,
( spl27_147
<=> ! [X0] :
( sP0(X0,relation_rng(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_147])]) ).
fof(f1629,plain,
( spl27_201
<=> sP0(sK6,relation_rng(sK6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_201])]) ).
fof(f1637,plain,
( ~ sP1(sK6)
| ~ spl27_147
| spl27_201 ),
inference(resolution,[],[f1631,f1165]) ).
fof(f1165,plain,
( ! [X0] :
( sP0(X0,relation_rng(X0))
| ~ sP1(X0) )
| ~ spl27_147 ),
inference(avatar_component_clause,[],[f1164]) ).
fof(f1631,plain,
( ~ sP0(sK6,relation_rng(sK6))
| spl27_201 ),
inference(avatar_component_clause,[],[f1629]) ).
fof(f1664,plain,
( spl27_205
| ~ spl27_7
| ~ spl27_109
| ~ spl27_133 ),
inference(avatar_split_clause,[],[f1179,f1106,f884,f270,f1661]) ).
fof(f1661,plain,
( spl27_205
<=> sK18 = relation_rng(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_205])]) ).
fof(f1106,plain,
( spl27_133
<=> ! [X0] :
( relation_rng(X0) = sK18
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_133])]) ).
fof(f1179,plain,
( sK18 = relation_rng(sK18)
| ~ spl27_7
| ~ spl27_109
| ~ spl27_133 ),
inference(forward_demodulation,[],[f1171,f886]) ).
fof(f1171,plain,
( sK18 = relation_rng(empty_set)
| ~ spl27_7
| ~ spl27_133 ),
inference(resolution,[],[f1107,f272]) ).
fof(f1107,plain,
( ! [X0] :
( ~ empty(X0)
| relation_rng(X0) = sK18 )
| ~ spl27_133 ),
inference(avatar_component_clause,[],[f1106]) ).
fof(f1659,plain,
( spl27_204
| ~ spl27_51
| ~ spl27_124 ),
inference(avatar_split_clause,[],[f976,f973,f486,f1657]) ).
fof(f1657,plain,
( spl27_204
<=> ! [X0] : element(sK18,powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_204])]) ).
fof(f486,plain,
( spl27_51
<=> ! [X0] : element(sK12(X0),powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_51])]) ).
fof(f973,plain,
( spl27_124
<=> ! [X0] : sK12(X0) = sK18 ),
introduced(avatar_definition,[new_symbols(naming,[spl27_124])]) ).
fof(f976,plain,
( ! [X0] : element(sK18,powerset(X0))
| ~ spl27_51
| ~ spl27_124 ),
inference(superposition,[],[f487,f974]) ).
fof(f974,plain,
( ! [X0] : sK12(X0) = sK18
| ~ spl27_124 ),
inference(avatar_component_clause,[],[f973]) ).
fof(f487,plain,
( ! [X0] : element(sK12(X0),powerset(X0))
| ~ spl27_51 ),
inference(avatar_component_clause,[],[f486]) ).
fof(f1644,plain,
( spl27_117
| ~ spl27_4
| spl27_203
| ~ spl27_93
| ~ spl27_97 ),
inference(avatar_split_clause,[],[f858,f823,f796,f1641,f255,f939]) ).
fof(f939,plain,
( spl27_117
<=> sK4 = sK18 ),
introduced(avatar_definition,[new_symbols(naming,[spl27_117])]) ).
fof(f255,plain,
( spl27_4
<=> quasi_total(sK6,sK3,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_4])]) ).
fof(f796,plain,
( spl27_93
<=> sP2(sK3,sK6,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_93])]) ).
fof(f823,plain,
( spl27_97
<=> ! [X2,X0,X1] :
( sK18 = X2
| relation_dom_as_subset(X0,X2,X1) = X0
| ~ quasi_total(X1,X0,X2)
| ~ sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_97])]) ).
fof(f858,plain,
( sK3 = relation_dom_as_subset(sK3,sK4,sK6)
| ~ quasi_total(sK6,sK3,sK4)
| sK4 = sK18
| ~ spl27_93
| ~ spl27_97 ),
inference(resolution,[],[f798,f824]) ).
fof(f824,plain,
( ! [X2,X0,X1] :
( ~ sP2(X0,X1,X2)
| relation_dom_as_subset(X0,X2,X1) = X0
| ~ quasi_total(X1,X0,X2)
| sK18 = X2 )
| ~ spl27_97 ),
inference(avatar_component_clause,[],[f823]) ).
fof(f798,plain,
( sP2(sK3,sK6,sK4)
| ~ spl27_93 ),
inference(avatar_component_clause,[],[f796]) ).
fof(f1636,plain,
( ~ spl27_201
| ~ spl27_202
| spl27_6
| ~ spl27_183 ),
inference(avatar_split_clause,[],[f1495,f1477,f265,f1633,f1629]) ).
fof(f265,plain,
( spl27_6
<=> in(apply(sK6,sK5),relation_rng(sK6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_6])]) ).
fof(f1477,plain,
( spl27_183
<=> ! [X2,X0,X1] :
( in(apply(X0,X1),X2)
| ~ in(X1,relation_dom(X0))
| ~ sP0(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_183])]) ).
fof(f1495,plain,
( ~ in(sK5,relation_dom(sK6))
| ~ sP0(sK6,relation_rng(sK6))
| spl27_6
| ~ spl27_183 ),
inference(resolution,[],[f1478,f267]) ).
fof(f267,plain,
( ~ in(apply(sK6,sK5),relation_rng(sK6))
| spl27_6 ),
inference(avatar_component_clause,[],[f265]) ).
fof(f1478,plain,
( ! [X2,X0,X1] :
( in(apply(X0,X1),X2)
| ~ in(X1,relation_dom(X0))
| ~ sP0(X0,X2) )
| ~ spl27_183 ),
inference(avatar_component_clause,[],[f1477]) ).
fof(f1627,plain,
( spl27_200
| ~ spl27_5
| ~ spl27_181 ),
inference(avatar_split_clause,[],[f1482,f1469,f260,f1625]) ).
fof(f1625,plain,
( spl27_200
<=> ! [X0] :
( ~ in(X0,sK6)
| element(X0,cartesian_product2(sK3,sK4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_200])]) ).
fof(f260,plain,
( spl27_5
<=> relation_of2_as_subset(sK6,sK3,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_5])]) ).
fof(f1469,plain,
( spl27_181
<=> ! [X5,X4,X6,X3] :
( element(X3,cartesian_product2(X4,X5))
| ~ in(X3,X6)
| ~ relation_of2_as_subset(X6,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_181])]) ).
fof(f1482,plain,
( ! [X0] :
( ~ in(X0,sK6)
| element(X0,cartesian_product2(sK3,sK4)) )
| ~ spl27_5
| ~ spl27_181 ),
inference(resolution,[],[f1470,f262]) ).
fof(f262,plain,
( relation_of2_as_subset(sK6,sK3,sK4)
| ~ spl27_5 ),
inference(avatar_component_clause,[],[f260]) ).
fof(f1470,plain,
( ! [X3,X6,X4,X5] :
( ~ relation_of2_as_subset(X6,X4,X5)
| ~ in(X3,X6)
| element(X3,cartesian_product2(X4,X5)) )
| ~ spl27_181 ),
inference(avatar_component_clause,[],[f1469]) ).
fof(f1617,plain,
( spl27_199
| ~ spl27_55
| ~ spl27_89 ),
inference(avatar_split_clause,[],[f820,f777,f522,f1615]) ).
fof(f1615,plain,
( spl27_199
<=> ! [X2,X3] :
( sK8(X2,X3) = apply(X2,sK9(X2,X3))
| sP0(X2,X3)
| ~ in(X3,sK8(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_199])]) ).
fof(f777,plain,
( spl27_89
<=> ! [X0,X1] :
( sP0(X0,X1)
| sK8(X0,X1) = apply(X0,sK9(X0,X1))
| in(sK8(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_89])]) ).
fof(f820,plain,
( ! [X2,X3] :
( sK8(X2,X3) = apply(X2,sK9(X2,X3))
| sP0(X2,X3)
| ~ in(X3,sK8(X2,X3)) )
| ~ spl27_55
| ~ spl27_89 ),
inference(resolution,[],[f778,f523]) ).
fof(f778,plain,
( ! [X0,X1] :
( in(sK8(X0,X1),X1)
| sK8(X0,X1) = apply(X0,sK9(X0,X1))
| sP0(X0,X1) )
| ~ spl27_89 ),
inference(avatar_component_clause,[],[f777]) ).
fof(f1613,plain,
( spl27_198
| ~ spl27_56
| ~ spl27_89 ),
inference(avatar_split_clause,[],[f819,f777,f526,f1611]) ).
fof(f1611,plain,
( spl27_198
<=> ! [X0,X1] :
( sK8(X0,X1) = apply(X0,sK9(X0,X1))
| sP0(X0,X1)
| element(sK8(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_198])]) ).
fof(f526,plain,
( spl27_56
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_56])]) ).
fof(f819,plain,
( ! [X0,X1] :
( sK8(X0,X1) = apply(X0,sK9(X0,X1))
| sP0(X0,X1)
| element(sK8(X0,X1),X1) )
| ~ spl27_56
| ~ spl27_89 ),
inference(resolution,[],[f778,f527]) ).
fof(f527,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) )
| ~ spl27_56 ),
inference(avatar_component_clause,[],[f526]) ).
fof(f1606,plain,
( spl27_197
| ~ spl27_71
| ~ spl27_81 ),
inference(avatar_split_clause,[],[f728,f718,f631,f1604]) ).
fof(f1604,plain,
( spl27_197
<=> ! [X11,X12,X10] :
( ~ relation_of2_as_subset(X10,X11,X12)
| empty(powerset(cartesian_product2(X11,X12)))
| in(X10,powerset(cartesian_product2(X11,X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_197])]) ).
fof(f631,plain,
( spl27_71
<=> ! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_71])]) ).
fof(f718,plain,
( spl27_81
<=> ! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_81])]) ).
fof(f728,plain,
( ! [X10,X11,X12] :
( ~ relation_of2_as_subset(X10,X11,X12)
| empty(powerset(cartesian_product2(X11,X12)))
| in(X10,powerset(cartesian_product2(X11,X12))) )
| ~ spl27_71
| ~ spl27_81 ),
inference(resolution,[],[f719,f632]) ).
fof(f632,plain,
( ! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) )
| ~ spl27_71 ),
inference(avatar_component_clause,[],[f631]) ).
fof(f719,plain,
( ! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) )
| ~ spl27_81 ),
inference(avatar_component_clause,[],[f718]) ).
fof(f1594,plain,
( spl27_195
| ~ spl27_196
| ~ spl27_5
| ~ spl27_171 ),
inference(avatar_split_clause,[],[f1424,f1397,f260,f1591,f1588]) ).
fof(f1588,plain,
( spl27_195
<=> ! [X0] : ~ in(X0,sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_195])]) ).
fof(f1591,plain,
( spl27_196
<=> empty(cartesian_product2(sK3,sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_196])]) ).
fof(f1397,plain,
( spl27_171
<=> ! [X6,X4,X5,X3] :
( ~ relation_of2_as_subset(X3,X4,X5)
| ~ empty(cartesian_product2(X4,X5))
| ~ in(X6,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_171])]) ).
fof(f1424,plain,
( ! [X0] :
( ~ empty(cartesian_product2(sK3,sK4))
| ~ in(X0,sK6) )
| ~ spl27_5
| ~ spl27_171 ),
inference(resolution,[],[f1398,f262]) ).
fof(f1398,plain,
( ! [X3,X6,X4,X5] :
( ~ relation_of2_as_subset(X3,X4,X5)
| ~ empty(cartesian_product2(X4,X5))
| ~ in(X6,X3) )
| ~ spl27_171 ),
inference(avatar_component_clause,[],[f1397]) ).
fof(f1561,plain,
( spl27_194
| ~ spl27_102 ),
inference(avatar_split_clause,[],[f853,f843,f1559]) ).
fof(f1559,plain,
( spl27_194
<=> ! [X0,X1] :
( sK18 = X0
| sK18 != X1
| quasi_total(sK18,X0,X1)
| ~ relation_of2_as_subset(sK18,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_194])]) ).
fof(f843,plain,
( spl27_102
<=> ! [X2,X0,X1] :
( sK18 != X1
| sK18 = X0
| sK18 != X2
| quasi_total(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_102])]) ).
fof(f853,plain,
( ! [X0,X1] :
( sK18 = X0
| sK18 != X1
| quasi_total(sK18,X0,X1)
| ~ relation_of2_as_subset(sK18,X0,X1) )
| ~ spl27_102 ),
inference(equality_resolution,[],[f844]) ).
fof(f844,plain,
( ! [X2,X0,X1] :
( sK18 != X2
| sK18 = X0
| sK18 != X1
| quasi_total(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) )
| ~ spl27_102 ),
inference(avatar_component_clause,[],[f843]) ).
fof(f1557,plain,
( spl27_193
| ~ spl27_101 ),
inference(avatar_split_clause,[],[f852,f839,f1555]) ).
fof(f1555,plain,
( spl27_193
<=> ! [X0,X1] :
( sK18 = X0
| sK18 = X1
| ~ quasi_total(X1,X0,sK18)
| ~ relation_of2_as_subset(X1,X0,sK18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_193])]) ).
fof(f839,plain,
( spl27_101
<=> ! [X2,X0,X1] :
( sK18 != X1
| sK18 = X0
| sK18 = X2
| ~ quasi_total(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_101])]) ).
fof(f852,plain,
( ! [X0,X1] :
( sK18 = X0
| sK18 = X1
| ~ quasi_total(X1,X0,sK18)
| ~ relation_of2_as_subset(X1,X0,sK18) )
| ~ spl27_101 ),
inference(equality_resolution,[],[f840]) ).
fof(f840,plain,
( ! [X2,X0,X1] :
( sK18 != X1
| sK18 = X0
| sK18 = X2
| ~ quasi_total(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) )
| ~ spl27_101 ),
inference(avatar_component_clause,[],[f839]) ).
fof(f1553,plain,
( spl27_192
| ~ spl27_98 ),
inference(avatar_split_clause,[],[f851,f827,f1551]) ).
fof(f1551,plain,
( spl27_192
<=> ! [X0,X1] :
( sK18 = relation_dom_as_subset(sK18,X0,X1)
| ~ quasi_total(X1,sK18,X0)
| ~ sP2(sK18,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_192])]) ).
fof(f827,plain,
( spl27_98
<=> ! [X2,X0,X1] :
( sK18 != X0
| relation_dom_as_subset(X0,X2,X1) = X0
| ~ quasi_total(X1,X0,X2)
| ~ sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_98])]) ).
fof(f851,plain,
( ! [X0,X1] :
( sK18 = relation_dom_as_subset(sK18,X0,X1)
| ~ quasi_total(X1,sK18,X0)
| ~ sP2(sK18,X1,X0) )
| ~ spl27_98 ),
inference(equality_resolution,[],[f828]) ).
fof(f828,plain,
( ! [X2,X0,X1] :
( sK18 != X0
| relation_dom_as_subset(X0,X2,X1) = X0
| ~ quasi_total(X1,X0,X2)
| ~ sP2(X0,X1,X2) )
| ~ spl27_98 ),
inference(avatar_component_clause,[],[f827]) ).
fof(f1549,plain,
( spl27_191
| ~ spl27_52
| ~ spl27_89 ),
inference(avatar_split_clause,[],[f821,f777,f490,f1547]) ).
fof(f1547,plain,
( spl27_191
<=> ! [X4,X5] :
( sK8(X4,X5) = apply(X4,sK9(X4,X5))
| sP0(X4,X5)
| ~ empty(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_191])]) ).
fof(f490,plain,
( spl27_52
<=> ! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_52])]) ).
fof(f821,plain,
( ! [X4,X5] :
( sK8(X4,X5) = apply(X4,sK9(X4,X5))
| sP0(X4,X5)
| ~ empty(X5) )
| ~ spl27_52
| ~ spl27_89 ),
inference(resolution,[],[f778,f491]) ).
fof(f491,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) )
| ~ spl27_52 ),
inference(avatar_component_clause,[],[f490]) ).
fof(f1545,plain,
( spl27_190
| ~ spl27_55
| ~ spl27_87 ),
inference(avatar_split_clause,[],[f769,f762,f522,f1543]) ).
fof(f1543,plain,
( spl27_190
<=> ! [X2,X3] :
( in(sK9(X2,X3),relation_dom(X2))
| sP0(X2,X3)
| ~ in(X3,sK8(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_190])]) ).
fof(f762,plain,
( spl27_87
<=> ! [X0,X1] :
( sP0(X0,X1)
| in(sK9(X0,X1),relation_dom(X0))
| in(sK8(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_87])]) ).
fof(f769,plain,
( ! [X2,X3] :
( in(sK9(X2,X3),relation_dom(X2))
| sP0(X2,X3)
| ~ in(X3,sK8(X2,X3)) )
| ~ spl27_55
| ~ spl27_87 ),
inference(resolution,[],[f763,f523]) ).
fof(f763,plain,
( ! [X0,X1] :
( in(sK9(X0,X1),relation_dom(X0))
| in(sK8(X0,X1),X1)
| sP0(X0,X1) )
| ~ spl27_87 ),
inference(avatar_component_clause,[],[f762]) ).
fof(f1541,plain,
( spl27_189
| ~ spl27_56
| ~ spl27_87 ),
inference(avatar_split_clause,[],[f768,f762,f526,f1539]) ).
fof(f1539,plain,
( spl27_189
<=> ! [X0,X1] :
( in(sK9(X0,X1),relation_dom(X0))
| sP0(X0,X1)
| element(sK8(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_189])]) ).
fof(f768,plain,
( ! [X0,X1] :
( in(sK9(X0,X1),relation_dom(X0))
| sP0(X0,X1)
| element(sK8(X0,X1),X1) )
| ~ spl27_56
| ~ spl27_87 ),
inference(resolution,[],[f763,f527]) ).
fof(f1537,plain,
( spl27_188
| ~ spl27_55
| ~ spl27_87 ),
inference(avatar_split_clause,[],[f766,f762,f522,f1535]) ).
fof(f1535,plain,
( spl27_188
<=> ! [X2,X3] :
( in(sK8(X2,X3),X3)
| sP0(X2,X3)
| ~ in(relation_dom(X2),sK9(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_188])]) ).
fof(f766,plain,
( ! [X2,X3] :
( in(sK8(X2,X3),X3)
| sP0(X2,X3)
| ~ in(relation_dom(X2),sK9(X2,X3)) )
| ~ spl27_55
| ~ spl27_87 ),
inference(resolution,[],[f763,f523]) ).
fof(f1533,plain,
( spl27_187
| ~ spl27_56
| ~ spl27_87 ),
inference(avatar_split_clause,[],[f765,f762,f526,f1531]) ).
fof(f1531,plain,
( spl27_187
<=> ! [X0,X1] :
( in(sK8(X0,X1),X1)
| sP0(X0,X1)
| element(sK9(X0,X1),relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_187])]) ).
fof(f765,plain,
( ! [X0,X1] :
( in(sK8(X0,X1),X1)
| sP0(X0,X1)
| element(sK9(X0,X1),relation_dom(X0)) )
| ~ spl27_56
| ~ spl27_87 ),
inference(resolution,[],[f763,f527]) ).
fof(f1529,plain,
( spl27_186
| ~ spl27_71
| ~ spl27_84 ),
inference(avatar_split_clause,[],[f751,f741,f631,f1527]) ).
fof(f1527,plain,
( spl27_186
<=> ! [X16,X17,X15] :
( ~ relation_of2(X15,X16,X17)
| empty(powerset(X16))
| in(relation_dom_as_subset(X16,X17,X15),powerset(X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_186])]) ).
fof(f741,plain,
( spl27_84
<=> ! [X2,X0,X1] :
( element(relation_dom_as_subset(X0,X1,X2),powerset(X0))
| ~ relation_of2(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_84])]) ).
fof(f751,plain,
( ! [X16,X17,X15] :
( ~ relation_of2(X15,X16,X17)
| empty(powerset(X16))
| in(relation_dom_as_subset(X16,X17,X15),powerset(X16)) )
| ~ spl27_71
| ~ spl27_84 ),
inference(resolution,[],[f742,f632]) ).
fof(f742,plain,
( ! [X2,X0,X1] :
( element(relation_dom_as_subset(X0,X1,X2),powerset(X0))
| ~ relation_of2(X2,X0,X1) )
| ~ spl27_84 ),
inference(avatar_component_clause,[],[f741]) ).
fof(f1511,plain,
( spl27_185
| ~ spl27_74
| ~ spl27_84 ),
inference(avatar_split_clause,[],[f750,f741,f643,f1509]) ).
fof(f1509,plain,
( spl27_185
<=> ! [X11,X13,X14,X12] :
( ~ relation_of2(X11,cartesian_product2(X12,X13),X14)
| relation(relation_dom_as_subset(cartesian_product2(X12,X13),X14,X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_185])]) ).
fof(f643,plain,
( spl27_74
<=> ! [X2,X0,X1] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_74])]) ).
fof(f750,plain,
( ! [X11,X14,X12,X13] :
( ~ relation_of2(X11,cartesian_product2(X12,X13),X14)
| relation(relation_dom_as_subset(cartesian_product2(X12,X13),X14,X11)) )
| ~ spl27_74
| ~ spl27_84 ),
inference(resolution,[],[f742,f644]) ).
fof(f644,plain,
( ! [X2,X0,X1] :
( ~ element(X2,powerset(cartesian_product2(X0,X1)))
| relation(X2) )
| ~ spl27_74 ),
inference(avatar_component_clause,[],[f643]) ).
fof(f1507,plain,
( spl27_184
| ~ spl27_82
| ~ spl27_84 ),
inference(avatar_split_clause,[],[f747,f741,f722,f1505]) ).
fof(f1505,plain,
( spl27_184
<=> ! [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,[spl27_184])]) ).
fof(f722,plain,
( spl27_82
<=> ! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_82])]) ).
fof(f747,plain,
( ! [X2,X3,X0,X1] :
( ~ relation_of2(X0,X1,X2)
| element(X3,X1)
| ~ in(X3,relation_dom_as_subset(X1,X2,X0)) )
| ~ spl27_82
| ~ spl27_84 ),
inference(resolution,[],[f742,f723]) ).
fof(f723,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| element(X0,X2)
| ~ in(X0,X1) )
| ~ spl27_82 ),
inference(avatar_component_clause,[],[f722]) ).
fof(f1479,plain,
( spl27_183
| ~ spl27_88 ),
inference(avatar_split_clause,[],[f775,f772,f1477]) ).
fof(f772,plain,
( spl27_88
<=> ! [X5,X0,X6,X1] :
( in(X5,X1)
| apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0))
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_88])]) ).
fof(f775,plain,
( ! [X2,X0,X1] :
( in(apply(X0,X1),X2)
| ~ in(X1,relation_dom(X0))
| ~ sP0(X0,X2) )
| ~ spl27_88 ),
inference(equality_resolution,[],[f773]) ).
fof(f773,plain,
( ! [X0,X1,X6,X5] :
( apply(X0,X6) != X5
| in(X5,X1)
| ~ in(X6,relation_dom(X0))
| ~ sP0(X0,X1) )
| ~ spl27_88 ),
inference(avatar_component_clause,[],[f772]) ).
fof(f1475,plain,
( spl27_182
| ~ spl27_80
| ~ spl27_84 ),
inference(avatar_split_clause,[],[f748,f741,f707,f1473]) ).
fof(f1473,plain,
( spl27_182
<=> ! [X6,X4,X5,X7] :
( ~ relation_of2(X4,X5,X6)
| ~ empty(X5)
| ~ in(X7,relation_dom_as_subset(X5,X6,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_182])]) ).
fof(f707,plain,
( spl27_80
<=> ! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_80])]) ).
fof(f748,plain,
( ! [X6,X7,X4,X5] :
( ~ relation_of2(X4,X5,X6)
| ~ empty(X5)
| ~ in(X7,relation_dom_as_subset(X5,X6,X4)) )
| ~ spl27_80
| ~ spl27_84 ),
inference(resolution,[],[f742,f708]) ).
fof(f708,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X0,X1) )
| ~ spl27_80 ),
inference(avatar_component_clause,[],[f707]) ).
fof(f1471,plain,
( spl27_181
| ~ spl27_81
| ~ spl27_82 ),
inference(avatar_split_clause,[],[f730,f722,f718,f1469]) ).
fof(f730,plain,
( ! [X3,X6,X4,X5] :
( element(X3,cartesian_product2(X4,X5))
| ~ in(X3,X6)
| ~ relation_of2_as_subset(X6,X4,X5) )
| ~ spl27_81
| ~ spl27_82 ),
inference(resolution,[],[f723,f719]) ).
fof(f1467,plain,
( spl27_180
| ~ spl27_41
| ~ spl27_70 ),
inference(avatar_split_clause,[],[f658,f627,f432,f1465]) ).
fof(f1465,plain,
( spl27_180
<=> ! [X4,X5] :
( ~ function(sK16(X4,X5))
| ~ empty(sK16(X4,X5))
| one_to_one(sK16(X4,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_180])]) ).
fof(f432,plain,
( spl27_41
<=> ! [X0,X1] : relation(sK16(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_41])]) ).
fof(f627,plain,
( spl27_70
<=> ! [X0] :
( one_to_one(X0)
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_70])]) ).
fof(f658,plain,
( ! [X4,X5] :
( ~ function(sK16(X4,X5))
| ~ empty(sK16(X4,X5))
| one_to_one(sK16(X4,X5)) )
| ~ spl27_41
| ~ spl27_70 ),
inference(resolution,[],[f628,f433]) ).
fof(f433,plain,
( ! [X0,X1] : relation(sK16(X0,X1))
| ~ spl27_41 ),
inference(avatar_component_clause,[],[f432]) ).
fof(f628,plain,
( ! [X0] :
( ~ relation(X0)
| ~ function(X0)
| ~ empty(X0)
| one_to_one(X0) )
| ~ spl27_70 ),
inference(avatar_component_clause,[],[f627]) ).
fof(f1463,plain,
( spl27_179
| ~ spl27_39
| ~ spl27_70 ),
inference(avatar_split_clause,[],[f657,f627,f424,f1461]) ).
fof(f1461,plain,
( spl27_179
<=> ! [X2,X3] :
( ~ function(sK15(X2,X3))
| ~ empty(sK15(X2,X3))
| one_to_one(sK15(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_179])]) ).
fof(f424,plain,
( spl27_39
<=> ! [X0,X1] : relation(sK15(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_39])]) ).
fof(f657,plain,
( ! [X2,X3] :
( ~ function(sK15(X2,X3))
| ~ empty(sK15(X2,X3))
| one_to_one(sK15(X2,X3)) )
| ~ spl27_39
| ~ spl27_70 ),
inference(resolution,[],[f628,f425]) ).
fof(f425,plain,
( ! [X0,X1] : relation(sK15(X0,X1))
| ~ spl27_39 ),
inference(avatar_component_clause,[],[f424]) ).
fof(f1445,plain,
( spl27_177
| ~ spl27_178
| ~ spl27_1
| ~ spl27_70
| ~ spl27_155 ),
inference(avatar_split_clause,[],[f1305,f1256,f627,f240,f1442,f1438]) ).
fof(f1438,plain,
( spl27_177
<=> one_to_one(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_177])]) ).
fof(f1442,plain,
( spl27_178
<=> empty(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_178])]) ).
fof(f240,plain,
( spl27_1
<=> function(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_1])]) ).
fof(f1256,plain,
( spl27_155
<=> relation(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_155])]) ).
fof(f1305,plain,
( ~ function(sK6)
| ~ empty(sK6)
| one_to_one(sK6)
| ~ spl27_70
| ~ spl27_155 ),
inference(resolution,[],[f1258,f628]) ).
fof(f1258,plain,
( relation(sK6)
| ~ spl27_155 ),
inference(avatar_component_clause,[],[f1256]) ).
fof(f1419,plain,
( spl27_176
| ~ spl27_52
| ~ spl27_87 ),
inference(avatar_split_clause,[],[f770,f762,f490,f1417]) ).
fof(f1417,plain,
( spl27_176
<=> ! [X4,X5] :
( in(sK9(X4,X5),relation_dom(X4))
| sP0(X4,X5)
| ~ empty(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_176])]) ).
fof(f770,plain,
( ! [X4,X5] :
( in(sK9(X4,X5),relation_dom(X4))
| sP0(X4,X5)
| ~ empty(X5) )
| ~ spl27_52
| ~ spl27_87 ),
inference(resolution,[],[f763,f491]) ).
fof(f1415,plain,
( spl27_175
| ~ spl27_52
| ~ spl27_87 ),
inference(avatar_split_clause,[],[f767,f762,f490,f1413]) ).
fof(f767,plain,
( ! [X4,X5] :
( in(sK8(X4,X5),X5)
| sP0(X4,X5)
| ~ empty(relation_dom(X4)) )
| ~ spl27_52
| ~ spl27_87 ),
inference(resolution,[],[f763,f491]) ).
fof(f1411,plain,
( spl27_174
| ~ spl27_60
| ~ spl27_83 ),
inference(avatar_split_clause,[],[f746,f737,f542,f1409]) ).
fof(f1409,plain,
( spl27_174
<=> ! [X4,X5] : relation_dom_as_subset(X4,X5,sK16(X4,X5)) = relation_dom(sK16(X4,X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_174])]) ).
fof(f542,plain,
( spl27_60
<=> ! [X0,X1] : relation_of2(sK16(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_60])]) ).
fof(f737,plain,
( spl27_83
<=> ! [X2,X0,X1] :
( relation_dom_as_subset(X0,X1,X2) = relation_dom(X2)
| ~ relation_of2(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_83])]) ).
fof(f746,plain,
( ! [X4,X5] : relation_dom_as_subset(X4,X5,sK16(X4,X5)) = relation_dom(sK16(X4,X5))
| ~ spl27_60
| ~ spl27_83 ),
inference(resolution,[],[f738,f543]) ).
fof(f543,plain,
( ! [X0,X1] : relation_of2(sK16(X0,X1),X0,X1)
| ~ spl27_60 ),
inference(avatar_component_clause,[],[f542]) ).
fof(f738,plain,
( ! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| relation_dom_as_subset(X0,X1,X2) = relation_dom(X2) )
| ~ spl27_83 ),
inference(avatar_component_clause,[],[f737]) ).
fof(f1407,plain,
( spl27_173
| ~ spl27_59
| ~ spl27_83 ),
inference(avatar_split_clause,[],[f745,f737,f538,f1405]) ).
fof(f1405,plain,
( spl27_173
<=> ! [X2,X3] : relation_dom_as_subset(X2,X3,sK15(X2,X3)) = relation_dom(sK15(X2,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_173])]) ).
fof(f538,plain,
( spl27_59
<=> ! [X0,X1] : relation_of2(sK15(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_59])]) ).
fof(f745,plain,
( ! [X2,X3] : relation_dom_as_subset(X2,X3,sK15(X2,X3)) = relation_dom(sK15(X2,X3))
| ~ spl27_59
| ~ spl27_83 ),
inference(resolution,[],[f738,f539]) ).
fof(f539,plain,
( ! [X0,X1] : relation_of2(sK15(X0,X1),X0,X1)
| ~ spl27_59 ),
inference(avatar_component_clause,[],[f538]) ).
fof(f1403,plain,
( spl27_172
| ~ spl27_58
| ~ spl27_83 ),
inference(avatar_split_clause,[],[f744,f737,f534,f1401]) ).
fof(f1401,plain,
( spl27_172
<=> ! [X0,X1] : relation_dom_as_subset(X0,X1,sK14(X0,X1)) = relation_dom(sK14(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_172])]) ).
fof(f534,plain,
( spl27_58
<=> ! [X0,X1] : relation_of2(sK14(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_58])]) ).
fof(f744,plain,
( ! [X0,X1] : relation_dom_as_subset(X0,X1,sK14(X0,X1)) = relation_dom(sK14(X0,X1))
| ~ spl27_58
| ~ spl27_83 ),
inference(resolution,[],[f738,f535]) ).
fof(f535,plain,
( ! [X0,X1] : relation_of2(sK14(X0,X1),X0,X1)
| ~ spl27_58 ),
inference(avatar_component_clause,[],[f534]) ).
fof(f1399,plain,
( spl27_171
| ~ spl27_80
| ~ spl27_81 ),
inference(avatar_split_clause,[],[f726,f718,f707,f1397]) ).
fof(f726,plain,
( ! [X3,X6,X4,X5] :
( ~ relation_of2_as_subset(X3,X4,X5)
| ~ empty(cartesian_product2(X4,X5))
| ~ in(X6,X3) )
| ~ spl27_80
| ~ spl27_81 ),
inference(resolution,[],[f719,f708]) ).
fof(f1395,plain,
( spl27_170
| ~ spl27_50
| ~ spl27_70 ),
inference(avatar_split_clause,[],[f656,f627,f482,f1393]) ).
fof(f1393,plain,
( spl27_170
<=> ! [X1] :
( ~ function(relation_dom(X1))
| ~ empty(relation_dom(X1))
| one_to_one(relation_dom(X1))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_170])]) ).
fof(f482,plain,
( spl27_50
<=> ! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_50])]) ).
fof(f656,plain,
( ! [X1] :
( ~ function(relation_dom(X1))
| ~ empty(relation_dom(X1))
| one_to_one(relation_dom(X1))
| ~ empty(X1) )
| ~ spl27_50
| ~ spl27_70 ),
inference(resolution,[],[f628,f483]) ).
fof(f483,plain,
( ! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) )
| ~ spl27_50 ),
inference(avatar_component_clause,[],[f482]) ).
fof(f1391,plain,
( spl27_169
| ~ spl27_47
| ~ spl27_70 ),
inference(avatar_split_clause,[],[f655,f627,f469,f1389]) ).
fof(f1389,plain,
( spl27_169
<=> ! [X0] :
( ~ function(relation_rng(X0))
| ~ empty(relation_rng(X0))
| one_to_one(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_169])]) ).
fof(f469,plain,
( spl27_47
<=> ! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_47])]) ).
fof(f655,plain,
( ! [X0] :
( ~ function(relation_rng(X0))
| ~ empty(relation_rng(X0))
| one_to_one(relation_rng(X0))
| ~ empty(X0) )
| ~ spl27_47
| ~ spl27_70 ),
inference(resolution,[],[f628,f470]) ).
fof(f470,plain,
( ! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) )
| ~ spl27_47 ),
inference(avatar_component_clause,[],[f469]) ).
fof(f1377,plain,
( spl27_168
| ~ spl27_66
| ~ spl27_84 ),
inference(avatar_split_clause,[],[f749,f741,f590,f1375]) ).
fof(f1375,plain,
( spl27_168
<=> ! [X9,X8,X10] :
( ~ relation_of2(X8,X9,X10)
| subset(relation_dom_as_subset(X9,X10,X8),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_168])]) ).
fof(f590,plain,
( spl27_66
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_66])]) ).
fof(f749,plain,
( ! [X10,X8,X9] :
( ~ relation_of2(X8,X9,X10)
| subset(relation_dom_as_subset(X9,X10,X8),X9) )
| ~ spl27_66
| ~ spl27_84 ),
inference(resolution,[],[f742,f591]) ).
fof(f591,plain,
( ! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) )
| ~ spl27_66 ),
inference(avatar_component_clause,[],[f590]) ).
fof(f1373,plain,
( spl27_167
| ~ spl27_63
| ~ spl27_71 ),
inference(avatar_split_clause,[],[f677,f631,f578,f1371]) ).
fof(f1371,plain,
( spl27_167
<=> ! [X2] :
( empty(powerset(X2))
| in(sK7(X2),powerset(X2))
| empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_167])]) ).
fof(f578,plain,
( spl27_63
<=> ! [X0] :
( element(sK7(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_63])]) ).
fof(f677,plain,
( ! [X2] :
( empty(powerset(X2))
| in(sK7(X2),powerset(X2))
| empty(X2) )
| ~ spl27_63
| ~ spl27_71 ),
inference(resolution,[],[f632,f579]) ).
fof(f579,plain,
( ! [X0] :
( element(sK7(X0),powerset(X0))
| empty(X0) )
| ~ spl27_63 ),
inference(avatar_component_clause,[],[f578]) ).
fof(f1369,plain,
( spl27_166
| ~ spl27_67
| ~ spl27_71 ),
inference(avatar_split_clause,[],[f676,f631,f594,f1367]) ).
fof(f1367,plain,
( spl27_166
<=> ! [X0,X1] :
( empty(powerset(X0))
| in(X1,powerset(X0))
| ~ subset(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_166])]) ).
fof(f594,plain,
( spl27_67
<=> ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_67])]) ).
fof(f676,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| in(X1,powerset(X0))
| ~ subset(X1,X0) )
| ~ spl27_67
| ~ spl27_71 ),
inference(resolution,[],[f632,f595]) ).
fof(f595,plain,
( ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) )
| ~ spl27_67 ),
inference(avatar_component_clause,[],[f594]) ).
fof(f1362,plain,
( spl27_165
| ~ spl27_1
| ~ spl27_54
| ~ spl27_155 ),
inference(avatar_split_clause,[],[f1306,f1256,f518,f240,f1359]) ).
fof(f518,plain,
( spl27_54
<=> ! [X0] :
( sP1(X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_54])]) ).
fof(f1306,plain,
( ~ function(sK6)
| sP1(sK6)
| ~ spl27_54
| ~ spl27_155 ),
inference(resolution,[],[f1258,f519]) ).
fof(f519,plain,
( ! [X0] :
( ~ relation(X0)
| ~ function(X0)
| sP1(X0) )
| ~ spl27_54 ),
inference(avatar_component_clause,[],[f518]) ).
fof(f1348,plain,
( spl27_164
| ~ spl27_63
| ~ spl27_82 ),
inference(avatar_split_clause,[],[f731,f722,f578,f1346]) ).
fof(f1346,plain,
( spl27_164
<=> ! [X8,X7] :
( element(X7,X8)
| ~ in(X7,sK7(X8))
| empty(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_164])]) ).
fof(f731,plain,
( ! [X8,X7] :
( element(X7,X8)
| ~ in(X7,sK7(X8))
| empty(X8) )
| ~ spl27_63
| ~ spl27_82 ),
inference(resolution,[],[f723,f579]) ).
fof(f1344,plain,
( spl27_163
| ~ spl27_67
| ~ spl27_82 ),
inference(avatar_split_clause,[],[f729,f722,f594,f1342]) ).
fof(f1342,plain,
( spl27_163
<=> ! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_163])]) ).
fof(f729,plain,
( ! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,X1) )
| ~ spl27_67
| ~ spl27_82 ),
inference(resolution,[],[f723,f595]) ).
fof(f1340,plain,
( spl27_162
| ~ spl27_66
| ~ spl27_81 ),
inference(avatar_split_clause,[],[f727,f718,f590,f1338]) ).
fof(f1338,plain,
( spl27_162
<=> ! [X9,X8,X7] :
( ~ relation_of2_as_subset(X7,X8,X9)
| subset(X7,cartesian_product2(X8,X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_162])]) ).
fof(f727,plain,
( ! [X8,X9,X7] :
( ~ relation_of2_as_subset(X7,X8,X9)
| subset(X7,cartesian_product2(X8,X9)) )
| ~ spl27_66
| ~ spl27_81 ),
inference(resolution,[],[f719,f591]) ).
fof(f1336,plain,
( spl27_161
| ~ spl27_63
| ~ spl27_74 ),
inference(avatar_split_clause,[],[f690,f643,f578,f1334]) ).
fof(f1334,plain,
( spl27_161
<=> ! [X4,X3] :
( relation(sK7(cartesian_product2(X3,X4)))
| empty(cartesian_product2(X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_161])]) ).
fof(f690,plain,
( ! [X3,X4] :
( relation(sK7(cartesian_product2(X3,X4)))
| empty(cartesian_product2(X3,X4)) )
| ~ spl27_63
| ~ spl27_74 ),
inference(resolution,[],[f644,f579]) ).
fof(f1279,plain,
( spl27_160
| ~ spl27_38
| ~ spl27_82 ),
inference(avatar_split_clause,[],[f732,f722,f420,f1277]) ).
fof(f1277,plain,
( spl27_160
<=> ! [X9,X10] :
( element(X9,X10)
| ~ in(X9,sK11(powerset(X10))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_160])]) ).
fof(f420,plain,
( spl27_38
<=> ! [X0] : element(sK11(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_38])]) ).
fof(f732,plain,
( ! [X10,X9] :
( element(X9,X10)
| ~ in(X9,sK11(powerset(X10))) )
| ~ spl27_38
| ~ spl27_82 ),
inference(resolution,[],[f723,f421]) ).
fof(f421,plain,
( ! [X0] : element(sK11(X0),X0)
| ~ spl27_38 ),
inference(avatar_component_clause,[],[f420]) ).
fof(f1275,plain,
( spl27_159
| ~ spl27_67
| ~ spl27_80 ),
inference(avatar_split_clause,[],[f711,f707,f594,f1273]) ).
fof(f1273,plain,
( spl27_159
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,X2)
| ~ subset(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_159])]) ).
fof(f711,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,X2)
| ~ subset(X2,X0) )
| ~ spl27_67
| ~ spl27_80 ),
inference(resolution,[],[f708,f595]) ).
fof(f1271,plain,
( spl27_158
| ~ spl27_49
| ~ spl27_68 ),
inference(avatar_split_clause,[],[f611,f598,f478,f1269]) ).
fof(f1269,plain,
( spl27_158
<=> ! [X4,X3] :
( relation_dom(X4) = X3
| ~ empty(X3)
| ~ empty(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_158])]) ).
fof(f478,plain,
( spl27_49
<=> ! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_49])]) ).
fof(f598,plain,
( spl27_68
<=> ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_68])]) ).
fof(f611,plain,
( ! [X3,X4] :
( relation_dom(X4) = X3
| ~ empty(X3)
| ~ empty(X4) )
| ~ spl27_49
| ~ spl27_68 ),
inference(resolution,[],[f599,f479]) ).
fof(f479,plain,
( ! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) )
| ~ spl27_49 ),
inference(avatar_component_clause,[],[f478]) ).
fof(f599,plain,
( ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) )
| ~ spl27_68 ),
inference(avatar_component_clause,[],[f598]) ).
fof(f1267,plain,
( spl27_157
| ~ spl27_46
| ~ spl27_68 ),
inference(avatar_split_clause,[],[f610,f598,f465,f1265]) ).
fof(f1265,plain,
( spl27_157
<=> ! [X2,X1] :
( relation_rng(X2) = X1
| ~ empty(X1)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_157])]) ).
fof(f465,plain,
( spl27_46
<=> ! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_46])]) ).
fof(f610,plain,
( ! [X2,X1] :
( relation_rng(X2) = X1
| ~ empty(X1)
| ~ empty(X2) )
| ~ spl27_46
| ~ spl27_68 ),
inference(resolution,[],[f599,f466]) ).
fof(f466,plain,
( ! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) )
| ~ spl27_46 ),
inference(avatar_component_clause,[],[f465]) ).
fof(f1263,plain,
( spl27_156
| ~ spl27_41
| ~ spl27_54 ),
inference(avatar_split_clause,[],[f558,f518,f432,f1261]) ).
fof(f558,plain,
( ! [X4,X5] :
( ~ function(sK16(X4,X5))
| sP1(sK16(X4,X5)) )
| ~ spl27_41
| ~ spl27_54 ),
inference(resolution,[],[f519,f433]) ).
fof(f1259,plain,
( spl27_155
| ~ spl27_5
| ~ spl27_148 ),
inference(avatar_split_clause,[],[f1216,f1168,f260,f1256]) ).
fof(f1216,plain,
( relation(sK6)
| ~ spl27_5
| ~ spl27_148 ),
inference(resolution,[],[f1169,f262]) ).
fof(f1254,plain,
( spl27_154
| ~ spl27_39
| ~ spl27_54 ),
inference(avatar_split_clause,[],[f557,f518,f424,f1252]) ).
fof(f557,plain,
( ! [X2,X3] :
( ~ function(sK15(X2,X3))
| sP1(sK15(X2,X3)) )
| ~ spl27_39
| ~ spl27_54 ),
inference(resolution,[],[f519,f425]) ).
fof(f1250,plain,
( spl27_153
| ~ spl27_50
| ~ spl27_54 ),
inference(avatar_split_clause,[],[f556,f518,f482,f1248]) ).
fof(f556,plain,
( ! [X1] :
( ~ function(relation_dom(X1))
| sP1(relation_dom(X1))
| ~ empty(X1) )
| ~ spl27_50
| ~ spl27_54 ),
inference(resolution,[],[f519,f483]) ).
fof(f1246,plain,
( spl27_152
| ~ spl27_47
| ~ spl27_54 ),
inference(avatar_split_clause,[],[f555,f518,f469,f1244]) ).
fof(f555,plain,
( ! [X0] :
( ~ function(relation_rng(X0))
| sP1(relation_rng(X0))
| ~ empty(X0) )
| ~ spl27_47
| ~ spl27_54 ),
inference(resolution,[],[f519,f470]) ).
fof(f1232,plain,
( spl27_151
| ~ spl27_38
| ~ spl27_80 ),
inference(avatar_split_clause,[],[f713,f707,f420,f1230]) ).
fof(f713,plain,
( ! [X6,X5] :
( ~ empty(X5)
| ~ in(X6,sK11(powerset(X5))) )
| ~ spl27_38
| ~ spl27_80 ),
inference(resolution,[],[f708,f421]) ).
fof(f1228,plain,
( spl27_150
| ~ spl27_67
| ~ spl27_74 ),
inference(avatar_split_clause,[],[f689,f643,f594,f1226]) ).
fof(f689,plain,
( ! [X2,X0,X1] :
( relation(X0)
| ~ subset(X0,cartesian_product2(X1,X2)) )
| ~ spl27_67
| ~ spl27_74 ),
inference(resolution,[],[f644,f595]) ).
fof(f1224,plain,
( spl27_149
| ~ spl27_11
| ~ spl27_34
| ~ spl27_45
| ~ spl27_51
| ~ spl27_71 ),
inference(avatar_split_clause,[],[f681,f631,f486,f461,f404,f290,f1222]) ).
fof(f1222,plain,
( spl27_149
<=> ! [X4] :
( in(sK18,powerset(X4))
| empty(powerset(X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_149])]) ).
fof(f290,plain,
( spl27_11
<=> empty(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_11])]) ).
fof(f404,plain,
( spl27_34
<=> ! [X0] : empty(sK12(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_34])]) ).
fof(f461,plain,
( spl27_45
<=> ! [X0] :
( empty_set = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_45])]) ).
fof(f681,plain,
( ! [X4] :
( in(sK18,powerset(X4))
| empty(powerset(X4)) )
| ~ spl27_11
| ~ spl27_34
| ~ spl27_45
| ~ spl27_51
| ~ spl27_71 ),
inference(forward_demodulation,[],[f680,f495]) ).
fof(f495,plain,
( empty_set = sK18
| ~ spl27_11
| ~ spl27_45 ),
inference(resolution,[],[f462,f292]) ).
fof(f292,plain,
( empty(sK18)
| ~ spl27_11 ),
inference(avatar_component_clause,[],[f290]) ).
fof(f462,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = X0 )
| ~ spl27_45 ),
inference(avatar_component_clause,[],[f461]) ).
fof(f680,plain,
( ! [X4] :
( in(empty_set,powerset(X4))
| empty(powerset(X4)) )
| ~ spl27_34
| ~ spl27_45
| ~ spl27_51
| ~ spl27_71 ),
inference(forward_demodulation,[],[f679,f494]) ).
fof(f494,plain,
( ! [X0] : empty_set = sK12(X0)
| ~ spl27_34
| ~ spl27_45 ),
inference(resolution,[],[f462,f405]) ).
fof(f405,plain,
( ! [X0] : empty(sK12(X0))
| ~ spl27_34 ),
inference(avatar_component_clause,[],[f404]) ).
fof(f679,plain,
( ! [X4] :
( empty(powerset(X4))
| in(sK12(X4),powerset(X4)) )
| ~ spl27_51
| ~ spl27_71 ),
inference(resolution,[],[f632,f487]) ).
fof(f1170,plain,
( spl27_148
| ~ spl27_74
| ~ spl27_81 ),
inference(avatar_split_clause,[],[f725,f718,f643,f1168]) ).
fof(f725,plain,
( ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| relation(X0) )
| ~ spl27_74
| ~ spl27_81 ),
inference(resolution,[],[f719,f644]) ).
fof(f1166,plain,
( spl27_147
| ~ spl27_78 ),
inference(avatar_split_clause,[],[f710,f699,f1164]) ).
fof(f699,plain,
( spl27_78
<=> ! [X0,X1] :
( sP0(X0,X1)
| relation_rng(X0) != X1
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_78])]) ).
fof(f710,plain,
( ! [X0] :
( sP0(X0,relation_rng(X0))
| ~ sP1(X0) )
| ~ spl27_78 ),
inference(equality_resolution,[],[f700]) ).
fof(f700,plain,
( ! [X0,X1] :
( relation_rng(X0) != X1
| sP0(X0,X1)
| ~ sP1(X0) )
| ~ spl27_78 ),
inference(avatar_component_clause,[],[f699]) ).
fof(f1162,plain,
( spl27_146
| ~ spl27_60
| ~ spl27_76 ),
inference(avatar_split_clause,[],[f697,f651,f542,f1160]) ).
fof(f651,plain,
( spl27_76
<=> ! [X2,X0,X1] :
( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_76])]) ).
fof(f697,plain,
( ! [X4,X5] : relation_of2_as_subset(sK16(X4,X5),X4,X5)
| ~ spl27_60
| ~ spl27_76 ),
inference(resolution,[],[f652,f543]) ).
fof(f652,plain,
( ! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| relation_of2_as_subset(X2,X0,X1) )
| ~ spl27_76 ),
inference(avatar_component_clause,[],[f651]) ).
fof(f1158,plain,
( spl27_145
| ~ spl27_59
| ~ spl27_76 ),
inference(avatar_split_clause,[],[f696,f651,f538,f1156]) ).
fof(f696,plain,
( ! [X2,X3] : relation_of2_as_subset(sK15(X2,X3),X2,X3)
| ~ spl27_59
| ~ spl27_76 ),
inference(resolution,[],[f652,f539]) ).
fof(f1154,plain,
( spl27_144
| ~ spl27_58
| ~ spl27_76 ),
inference(avatar_split_clause,[],[f695,f651,f534,f1152]) ).
fof(f695,plain,
( ! [X0,X1] : relation_of2_as_subset(sK14(X0,X1),X0,X1)
| ~ spl27_58
| ~ spl27_76 ),
inference(resolution,[],[f652,f535]) ).
fof(f1150,plain,
( spl27_143
| ~ spl27_57
| ~ spl27_75 ),
inference(avatar_split_clause,[],[f694,f647,f530,f1148]) ).
fof(f1148,plain,
( spl27_143
<=> ! [X0,X1] : relation_of2(sK13(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_143])]) ).
fof(f647,plain,
( spl27_75
<=> ! [X2,X0,X1] :
( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_75])]) ).
fof(f694,plain,
( ! [X0,X1] : relation_of2(sK13(X0,X1),X0,X1)
| ~ spl27_57
| ~ spl27_75 ),
inference(resolution,[],[f648,f531]) ).
fof(f648,plain,
( ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| relation_of2(X2,X0,X1) )
| ~ spl27_75 ),
inference(avatar_component_clause,[],[f647]) ).
fof(f1146,plain,
( spl27_142
| ~ spl27_38
| ~ spl27_74 ),
inference(avatar_split_clause,[],[f691,f643,f420,f1144]) ).
fof(f1144,plain,
( spl27_142
<=> ! [X6,X5] : relation(sK11(powerset(cartesian_product2(X5,X6)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_142])]) ).
fof(f691,plain,
( ! [X6,X5] : relation(sK11(powerset(cartesian_product2(X5,X6))))
| ~ spl27_38
| ~ spl27_74 ),
inference(resolution,[],[f644,f421]) ).
fof(f1142,plain,
( spl27_141
| ~ spl27_57
| ~ spl27_73 ),
inference(avatar_split_clause,[],[f688,f639,f530,f1140]) ).
fof(f1140,plain,
( spl27_141
<=> ! [X0,X1] : sP2(X0,sK13(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_141])]) ).
fof(f688,plain,
( ! [X0,X1] : sP2(X0,sK13(X0,X1),X1)
| ~ spl27_57
| ~ spl27_73 ),
inference(resolution,[],[f640,f531]) ).
fof(f1138,plain,
( spl27_140
| ~ spl27_38
| ~ spl27_71 ),
inference(avatar_split_clause,[],[f678,f631,f420,f1136]) ).
fof(f678,plain,
( ! [X3] :
( empty(X3)
| in(sK11(X3),X3) )
| ~ spl27_38
| ~ spl27_71 ),
inference(resolution,[],[f632,f421]) ).
fof(f1134,plain,
( spl27_138
| ~ spl27_139
| ~ spl27_22
| ~ spl27_21
| ~ spl27_70 ),
inference(avatar_split_clause,[],[f663,f627,f340,f345,f1131,f1127]) ).
fof(f1127,plain,
( spl27_138
<=> one_to_one(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_138])]) ).
fof(f1131,plain,
( spl27_139
<=> empty(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_139])]) ).
fof(f345,plain,
( spl27_22
<=> function(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_22])]) ).
fof(f340,plain,
( spl27_21
<=> relation(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_21])]) ).
fof(f663,plain,
( ~ function(sK23)
| ~ empty(sK23)
| one_to_one(sK23)
| ~ spl27_21
| ~ spl27_70 ),
inference(resolution,[],[f628,f342]) ).
fof(f342,plain,
( relation(sK23)
| ~ spl27_21 ),
inference(avatar_component_clause,[],[f340]) ).
fof(f1125,plain,
( spl27_136
| ~ spl27_137
| ~ spl27_20
| ~ spl27_18
| ~ spl27_70 ),
inference(avatar_split_clause,[],[f662,f627,f325,f335,f1122,f1118]) ).
fof(f1118,plain,
( spl27_136
<=> one_to_one(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_136])]) ).
fof(f1122,plain,
( spl27_137
<=> empty(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_137])]) ).
fof(f335,plain,
( spl27_20
<=> function(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_20])]) ).
fof(f325,plain,
( spl27_18
<=> relation(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_18])]) ).
fof(f662,plain,
( ~ function(sK22)
| ~ empty(sK22)
| one_to_one(sK22)
| ~ spl27_18
| ~ spl27_70 ),
inference(resolution,[],[f628,f327]) ).
fof(f327,plain,
( relation(sK22)
| ~ spl27_18 ),
inference(avatar_component_clause,[],[f325]) ).
fof(f1116,plain,
( spl27_135
| ~ spl27_63
| ~ spl27_66 ),
inference(avatar_split_clause,[],[f605,f590,f578,f1114]) ).
fof(f1114,plain,
( spl27_135
<=> ! [X2] :
( subset(sK7(X2),X2)
| empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_135])]) ).
fof(f605,plain,
( ! [X2] :
( subset(sK7(X2),X2)
| empty(X2) )
| ~ spl27_63
| ~ spl27_66 ),
inference(resolution,[],[f591,f579]) ).
fof(f1112,plain,
( spl27_134
| ~ spl27_11
| ~ spl27_45
| ~ spl27_49 ),
inference(avatar_split_clause,[],[f509,f478,f461,f290,f1110]) ).
fof(f509,plain,
( ! [X0] :
( relation_dom(X0) = sK18
| ~ empty(X0) )
| ~ spl27_11
| ~ spl27_45
| ~ spl27_49 ),
inference(forward_demodulation,[],[f506,f495]) ).
fof(f506,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = relation_dom(X0) )
| ~ spl27_45
| ~ spl27_49 ),
inference(resolution,[],[f479,f462]) ).
fof(f1108,plain,
( spl27_133
| ~ spl27_11
| ~ spl27_45
| ~ spl27_46 ),
inference(avatar_split_clause,[],[f505,f465,f461,f290,f1106]) ).
fof(f505,plain,
( ! [X0] :
( relation_rng(X0) = sK18
| ~ empty(X0) )
| ~ spl27_11
| ~ spl27_45
| ~ spl27_46 ),
inference(forward_demodulation,[],[f502,f495]) ).
fof(f502,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = relation_rng(X0) )
| ~ spl27_45
| ~ spl27_46 ),
inference(resolution,[],[f466,f462]) ).
fof(f1096,plain,
( spl27_132
| ~ spl27_28
| ~ spl27_111 ),
inference(avatar_split_clause,[],[f918,f894,f375,f1093]) ).
fof(f1093,plain,
( spl27_132
<=> one_to_one(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_132])]) ).
fof(f375,plain,
( spl27_28
<=> one_to_one(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_28])]) ).
fof(f894,plain,
( spl27_111
<=> sK18 = sK25 ),
introduced(avatar_definition,[new_symbols(naming,[spl27_111])]) ).
fof(f918,plain,
( one_to_one(sK18)
| ~ spl27_28
| ~ spl27_111 ),
inference(superposition,[],[f377,f896]) ).
fof(f896,plain,
( sK18 = sK25
| ~ spl27_111 ),
inference(avatar_component_clause,[],[f894]) ).
fof(f377,plain,
( one_to_one(sK25)
| ~ spl27_28 ),
inference(avatar_component_clause,[],[f375]) ).
fof(f1044,plain,
( spl27_128
| ~ spl27_45
| ~ spl27_109 ),
inference(avatar_split_clause,[],[f1013,f884,f461,f991]) ).
fof(f991,plain,
( spl27_128
<=> ! [X7] :
( sK18 = X7
| ~ empty(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_128])]) ).
fof(f1013,plain,
( ! [X0] :
( sK18 = X0
| ~ empty(X0) )
| ~ spl27_45
| ~ spl27_109 ),
inference(forward_demodulation,[],[f462,f886]) ).
fof(f1043,plain,
( spl27_131
| ~ spl27_9
| ~ spl27_109 ),
inference(avatar_split_clause,[],[f911,f884,f280,f1040]) ).
fof(f1040,plain,
( spl27_131
<=> relation_empty_yielding(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_131])]) ).
fof(f280,plain,
( spl27_9
<=> relation_empty_yielding(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_9])]) ).
fof(f911,plain,
( relation_empty_yielding(sK18)
| ~ spl27_9
| ~ spl27_109 ),
inference(superposition,[],[f282,f886]) ).
fof(f282,plain,
( relation_empty_yielding(empty_set)
| ~ spl27_9 ),
inference(avatar_component_clause,[],[f280]) ).
fof(f1012,plain,
( ~ spl27_7
| ~ spl27_129 ),
inference(avatar_contradiction_clause,[],[f1001]) ).
fof(f1001,plain,
( $false
| ~ spl27_7
| ~ spl27_129 ),
inference(resolution,[],[f996,f272]) ).
fof(f996,plain,
( ! [X7] : ~ empty(X7)
| ~ spl27_129 ),
inference(avatar_component_clause,[],[f995]) ).
fof(f995,plain,
( spl27_129
<=> ! [X7] : ~ empty(X7) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_129])]) ).
fof(f1011,plain,
( ~ spl27_34
| ~ spl27_129 ),
inference(avatar_contradiction_clause,[],[f1002]) ).
fof(f1002,plain,
( $false
| ~ spl27_34
| ~ spl27_129 ),
inference(resolution,[],[f996,f405]) ).
fof(f1010,plain,
( ~ spl27_11
| ~ spl27_129 ),
inference(avatar_contradiction_clause,[],[f1003]) ).
fof(f1003,plain,
( $false
| ~ spl27_11
| ~ spl27_129 ),
inference(resolution,[],[f996,f292]) ).
fof(f1009,plain,
( ~ spl27_14
| ~ spl27_129 ),
inference(avatar_contradiction_clause,[],[f1004]) ).
fof(f1004,plain,
( $false
| ~ spl27_14
| ~ spl27_129 ),
inference(resolution,[],[f996,f307]) ).
fof(f307,plain,
( empty(sK20)
| ~ spl27_14 ),
inference(avatar_component_clause,[],[f305]) ).
fof(f305,plain,
( spl27_14
<=> empty(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_14])]) ).
fof(f1008,plain,
( ~ spl27_29
| ~ spl27_129 ),
inference(avatar_contradiction_clause,[],[f1005]) ).
fof(f1005,plain,
( $false
| ~ spl27_29
| ~ spl27_129 ),
inference(resolution,[],[f996,f382]) ).
fof(f382,plain,
( empty(sK25)
| ~ spl27_29 ),
inference(avatar_component_clause,[],[f380]) ).
fof(f380,plain,
( spl27_29
<=> empty(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_29])]) ).
fof(f1007,plain,
( ~ spl27_31
| ~ spl27_129 ),
inference(avatar_contradiction_clause,[],[f1006]) ).
fof(f1006,plain,
( $false
| ~ spl27_31
| ~ spl27_129 ),
inference(resolution,[],[f996,f392]) ).
fof(f392,plain,
( empty(sK26)
| ~ spl27_31 ),
inference(avatar_component_clause,[],[f390]) ).
fof(f390,plain,
( spl27_31
<=> empty(sK26) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_31])]) ).
fof(f1000,plain,
( spl27_129
| spl27_130
| ~ spl27_11
| ~ spl27_34
| ~ spl27_45
| ~ spl27_51
| ~ spl27_80 ),
inference(avatar_split_clause,[],[f716,f707,f486,f461,f404,f290,f998,f995]) ).
fof(f716,plain,
( ! [X8,X7] :
( ~ in(X8,sK18)
| ~ empty(X7) )
| ~ spl27_11
| ~ spl27_34
| ~ spl27_45
| ~ spl27_51
| ~ spl27_80 ),
inference(forward_demodulation,[],[f715,f495]) ).
fof(f715,plain,
( ! [X8,X7] :
( ~ in(X8,empty_set)
| ~ empty(X7) )
| ~ spl27_34
| ~ spl27_45
| ~ spl27_51
| ~ spl27_80 ),
inference(forward_demodulation,[],[f714,f494]) ).
fof(f714,plain,
( ! [X8,X7] :
( ~ empty(X7)
| ~ in(X8,sK12(X7)) )
| ~ spl27_51
| ~ spl27_80 ),
inference(resolution,[],[f708,f487]) ).
fof(f993,plain,
( spl27_128
| ~ spl27_11
| ~ spl27_68 ),
inference(avatar_split_clause,[],[f613,f598,f290,f991]) ).
fof(f613,plain,
( ! [X7] :
( sK18 = X7
| ~ empty(X7) )
| ~ spl27_11
| ~ spl27_68 ),
inference(resolution,[],[f599,f292]) ).
fof(f989,plain,
( spl27_127
| ~ spl27_38
| ~ spl27_66 ),
inference(avatar_split_clause,[],[f603,f590,f420,f987]) ).
fof(f987,plain,
( spl27_127
<=> ! [X0] : subset(sK11(powerset(X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_127])]) ).
fof(f603,plain,
( ! [X0] : subset(sK11(powerset(X0)),X0)
| ~ spl27_38
| ~ spl27_66 ),
inference(resolution,[],[f591,f421]) ).
fof(f985,plain,
( spl27_126
| ~ spl27_36
| ~ spl27_49 ),
inference(avatar_split_clause,[],[f508,f478,f412,f983]) ).
fof(f412,plain,
( spl27_36
<=> ! [X0] :
( function(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_36])]) ).
fof(f508,plain,
( ! [X2] :
( ~ empty(X2)
| function(relation_dom(X2)) )
| ~ spl27_36
| ~ spl27_49 ),
inference(resolution,[],[f479,f413]) ).
fof(f413,plain,
( ! [X0] :
( ~ empty(X0)
| function(X0) )
| ~ spl27_36 ),
inference(avatar_component_clause,[],[f412]) ).
fof(f981,plain,
( spl27_125
| ~ spl27_36
| ~ spl27_46 ),
inference(avatar_split_clause,[],[f504,f465,f412,f979]) ).
fof(f504,plain,
( ! [X2] :
( ~ empty(X2)
| function(relation_rng(X2)) )
| ~ spl27_36
| ~ spl27_46 ),
inference(resolution,[],[f466,f413]) ).
fof(f975,plain,
( spl27_124
| ~ spl27_109
| ~ spl27_114 ),
inference(avatar_split_clause,[],[f928,f925,f884,f973]) ).
fof(f925,plain,
( spl27_114
<=> ! [X0] : empty_set = sK12(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_114])]) ).
fof(f928,plain,
( ! [X0] : sK12(X0) = sK18
| ~ spl27_109
| ~ spl27_114 ),
inference(forward_demodulation,[],[f926,f886]) ).
fof(f926,plain,
( ! [X0] : empty_set = sK12(X0)
| ~ spl27_114 ),
inference(avatar_component_clause,[],[f925]) ).
fof(f971,plain,
( ~ spl27_48
| spl27_123
| ~ spl27_8
| ~ spl27_11
| ~ spl27_45
| ~ spl27_54 ),
inference(avatar_split_clause,[],[f568,f518,f461,f290,f275,f968,f473]) ).
fof(f473,plain,
( spl27_48
<=> function(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_48])]) ).
fof(f968,plain,
( spl27_123
<=> sP1(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_123])]) ).
fof(f275,plain,
( spl27_8
<=> relation(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_8])]) ).
fof(f568,plain,
( sP1(sK18)
| ~ function(sK18)
| ~ spl27_8
| ~ spl27_11
| ~ spl27_45
| ~ spl27_54 ),
inference(forward_demodulation,[],[f567,f495]) ).
fof(f567,plain,
( ~ function(sK18)
| sP1(empty_set)
| ~ spl27_8
| ~ spl27_11
| ~ spl27_45
| ~ spl27_54 ),
inference(forward_demodulation,[],[f554,f495]) ).
fof(f554,plain,
( ~ function(empty_set)
| sP1(empty_set)
| ~ spl27_8
| ~ spl27_54 ),
inference(resolution,[],[f519,f277]) ).
fof(f277,plain,
( relation(empty_set)
| ~ spl27_8 ),
inference(avatar_component_clause,[],[f275]) ).
fof(f966,plain,
( spl27_122
| ~ spl27_24
| ~ spl27_23
| ~ spl27_54 ),
inference(avatar_split_clause,[],[f564,f518,f350,f355,f963]) ).
fof(f963,plain,
( spl27_122
<=> sP1(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_122])]) ).
fof(f355,plain,
( spl27_24
<=> function(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_24])]) ).
fof(f350,plain,
( spl27_23
<=> relation(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_23])]) ).
fof(f564,plain,
( ~ function(sK24)
| sP1(sK24)
| ~ spl27_23
| ~ spl27_54 ),
inference(resolution,[],[f519,f352]) ).
fof(f352,plain,
( relation(sK24)
| ~ spl27_23 ),
inference(avatar_component_clause,[],[f350]) ).
fof(f961,plain,
( spl27_121
| ~ spl27_22
| ~ spl27_21
| ~ spl27_54 ),
inference(avatar_split_clause,[],[f563,f518,f340,f345,f958]) ).
fof(f958,plain,
( spl27_121
<=> sP1(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_121])]) ).
fof(f563,plain,
( ~ function(sK23)
| sP1(sK23)
| ~ spl27_21
| ~ spl27_54 ),
inference(resolution,[],[f519,f342]) ).
fof(f956,plain,
( spl27_120
| ~ spl27_20
| ~ spl27_18
| ~ spl27_54 ),
inference(avatar_split_clause,[],[f562,f518,f325,f335,f953]) ).
fof(f953,plain,
( spl27_120
<=> sP1(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_120])]) ).
fof(f562,plain,
( ~ function(sK22)
| sP1(sK22)
| ~ spl27_18
| ~ spl27_54 ),
inference(resolution,[],[f519,f327]) ).
fof(f951,plain,
( spl27_118
| ~ spl27_119
| ~ spl27_16
| ~ spl27_54 ),
inference(avatar_split_clause,[],[f561,f518,f315,f948,f944]) ).
fof(f944,plain,
( spl27_118
<=> sP1(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_118])]) ).
fof(f948,plain,
( spl27_119
<=> function(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_119])]) ).
fof(f315,plain,
( spl27_16
<=> relation(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_16])]) ).
fof(f561,plain,
( ~ function(sK21)
| sP1(sK21)
| ~ spl27_16
| ~ spl27_54 ),
inference(resolution,[],[f519,f317]) ).
fof(f317,plain,
( relation(sK21)
| ~ spl27_16 ),
inference(avatar_component_clause,[],[f315]) ).
fof(f942,plain,
( ~ spl27_117
| spl27_3
| ~ spl27_109 ),
inference(avatar_split_clause,[],[f914,f884,f250,f939]) ).
fof(f250,plain,
( spl27_3
<=> empty_set = sK4 ),
introduced(avatar_definition,[new_symbols(naming,[spl27_3])]) ).
fof(f914,plain,
( sK4 != sK18
| spl27_3
| ~ spl27_109 ),
inference(superposition,[],[f252,f886]) ).
fof(f252,plain,
( empty_set != sK4
| spl27_3 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f937,plain,
( spl27_115
| ~ spl27_116
| ~ spl27_13
| ~ spl27_54 ),
inference(avatar_split_clause,[],[f559,f518,f300,f934,f930]) ).
fof(f930,plain,
( spl27_115
<=> sP1(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_115])]) ).
fof(f934,plain,
( spl27_116
<=> function(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_116])]) ).
fof(f300,plain,
( spl27_13
<=> relation(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_13])]) ).
fof(f559,plain,
( ~ function(sK19)
| sP1(sK19)
| ~ spl27_13
| ~ spl27_54 ),
inference(resolution,[],[f519,f302]) ).
fof(f302,plain,
( relation(sK19)
| ~ spl27_13 ),
inference(avatar_component_clause,[],[f300]) ).
fof(f927,plain,
( spl27_114
| ~ spl27_34
| ~ spl27_45 ),
inference(avatar_split_clause,[],[f494,f461,f404,f925]) ).
fof(f909,plain,
( spl27_113
| ~ spl27_11
| ~ spl27_34
| ~ spl27_45
| ~ spl27_51
| ~ spl27_66 ),
inference(avatar_split_clause,[],[f607,f590,f486,f461,f404,f290,f907]) ).
fof(f907,plain,
( spl27_113
<=> ! [X1] : subset(sK18,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_113])]) ).
fof(f607,plain,
( ! [X1] : subset(sK18,X1)
| ~ spl27_11
| ~ spl27_34
| ~ spl27_45
| ~ spl27_51
| ~ spl27_66 ),
inference(forward_demodulation,[],[f606,f495]) ).
fof(f606,plain,
( ! [X1] : subset(empty_set,X1)
| ~ spl27_34
| ~ spl27_45
| ~ spl27_51
| ~ spl27_66 ),
inference(forward_demodulation,[],[f604,f494]) ).
fof(f604,plain,
( ! [X1] : subset(sK12(X1),X1)
| ~ spl27_51
| ~ spl27_66 ),
inference(resolution,[],[f591,f487]) ).
fof(f902,plain,
( spl27_112
| ~ spl27_11
| ~ spl27_31
| ~ spl27_45 ),
inference(avatar_split_clause,[],[f501,f461,f390,f290,f899]) ).
fof(f899,plain,
( spl27_112
<=> sK18 = sK26 ),
introduced(avatar_definition,[new_symbols(naming,[spl27_112])]) ).
fof(f501,plain,
( sK18 = sK26
| ~ spl27_11
| ~ spl27_31
| ~ spl27_45 ),
inference(forward_demodulation,[],[f498,f495]) ).
fof(f498,plain,
( empty_set = sK26
| ~ spl27_31
| ~ spl27_45 ),
inference(resolution,[],[f462,f392]) ).
fof(f897,plain,
( spl27_111
| ~ spl27_11
| ~ spl27_29
| ~ spl27_45 ),
inference(avatar_split_clause,[],[f500,f461,f380,f290,f894]) ).
fof(f500,plain,
( sK18 = sK25
| ~ spl27_11
| ~ spl27_29
| ~ spl27_45 ),
inference(forward_demodulation,[],[f497,f495]) ).
fof(f497,plain,
( empty_set = sK25
| ~ spl27_29
| ~ spl27_45 ),
inference(resolution,[],[f462,f382]) ).
fof(f892,plain,
( spl27_110
| ~ spl27_11
| ~ spl27_14
| ~ spl27_45 ),
inference(avatar_split_clause,[],[f499,f461,f305,f290,f889]) ).
fof(f889,plain,
( spl27_110
<=> sK18 = sK20 ),
introduced(avatar_definition,[new_symbols(naming,[spl27_110])]) ).
fof(f499,plain,
( sK18 = sK20
| ~ spl27_11
| ~ spl27_14
| ~ spl27_45 ),
inference(forward_demodulation,[],[f496,f495]) ).
fof(f496,plain,
( empty_set = sK20
| ~ spl27_14
| ~ spl27_45 ),
inference(resolution,[],[f462,f307]) ).
fof(f887,plain,
( spl27_109
| ~ spl27_11
| ~ spl27_45 ),
inference(avatar_split_clause,[],[f495,f461,f290,f884]) ).
fof(f881,plain,
( spl27_108
| ~ spl27_34
| ~ spl27_37 ),
inference(avatar_split_clause,[],[f451,f416,f404,f879]) ).
fof(f879,plain,
( spl27_108
<=> ! [X0] : relation(sK12(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_108])]) ).
fof(f416,plain,
( spl27_37
<=> ! [X0] :
( relation(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_37])]) ).
fof(f451,plain,
( ! [X0] : relation(sK12(X0))
| ~ spl27_34
| ~ spl27_37 ),
inference(resolution,[],[f417,f405]) ).
fof(f417,plain,
( ! [X0] :
( ~ empty(X0)
| relation(X0) )
| ~ spl27_37 ),
inference(avatar_component_clause,[],[f416]) ).
fof(f876,plain,
( spl27_107
| ~ spl27_34
| ~ spl27_36 ),
inference(avatar_split_clause,[],[f440,f412,f404,f874]) ).
fof(f874,plain,
( spl27_107
<=> ! [X0] : function(sK12(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_107])]) ).
fof(f440,plain,
( ! [X0] : function(sK12(X0))
| ~ spl27_34
| ~ spl27_36 ),
inference(resolution,[],[f413,f405]) ).
fof(f870,plain,
( spl27_106
| ~ spl27_11
| ~ spl27_37 ),
inference(avatar_split_clause,[],[f452,f416,f290,f867]) ).
fof(f867,plain,
( spl27_106
<=> relation(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_106])]) ).
fof(f452,plain,
( relation(sK18)
| ~ spl27_11
| ~ spl27_37 ),
inference(resolution,[],[f417,f292]) ).
fof(f865,plain,
( spl27_105
| ~ spl27_83
| ~ spl27_103 ),
inference(avatar_split_clause,[],[f859,f847,f737,f862]) ).
fof(f847,plain,
( spl27_103
<=> relation_of2(sK6,sK3,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_103])]) ).
fof(f859,plain,
( relation_dom_as_subset(sK3,sK4,sK6) = relation_dom(sK6)
| ~ spl27_83
| ~ spl27_103 ),
inference(resolution,[],[f849,f738]) ).
fof(f849,plain,
( relation_of2(sK6,sK3,sK4)
| ~ spl27_103 ),
inference(avatar_component_clause,[],[f847]) ).
fof(f857,plain,
spl27_104,
inference(avatar_split_clause,[],[f175,f855]) ).
fof(f855,plain,
( spl27_104
<=> ! [X0,X1,X3] :
( sP0(X0,X1)
| apply(X0,X3) != sK8(X0,X1)
| ~ in(X3,relation_dom(X0))
| ~ in(sK8(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_104])]) ).
fof(f175,plain,
! [X3,X0,X1] :
( sP0(X0,X1)
| apply(X0,X3) != sK8(X0,X1)
| ~ in(X3,relation_dom(X0))
| ~ in(sK8(X0,X1),X1) ),
inference(cnf_transformation,[],[f106]) ).
fof(f106,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( ( ! [X3] :
( apply(X0,X3) != sK8(X0,X1)
| ~ in(X3,relation_dom(X0)) )
| ~ in(sK8(X0,X1),X1) )
& ( ( sK8(X0,X1) = apply(X0,sK9(X0,X1))
& in(sK9(X0,X1),relation_dom(X0)) )
| in(sK8(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0)) ) )
& ( ( apply(X0,sK10(X0,X5)) = X5
& in(sK10(X0,X5),relation_dom(X0)) )
| ~ in(X5,X1) ) )
| ~ sP0(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10])],[f102,f105,f104,f103]) ).
fof(f103,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
| ~ in(X2,X1) )
& ( ? [X4] :
( apply(X0,X4) = X2
& in(X4,relation_dom(X0)) )
| in(X2,X1) ) )
=> ( ( ! [X3] :
( apply(X0,X3) != sK8(X0,X1)
| ~ in(X3,relation_dom(X0)) )
| ~ in(sK8(X0,X1),X1) )
& ( ? [X4] :
( apply(X0,X4) = sK8(X0,X1)
& in(X4,relation_dom(X0)) )
| in(sK8(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f104,plain,
! [X0,X1] :
( ? [X4] :
( apply(X0,X4) = sK8(X0,X1)
& in(X4,relation_dom(X0)) )
=> ( sK8(X0,X1) = apply(X0,sK9(X0,X1))
& in(sK9(X0,X1),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f105,plain,
! [X0,X5] :
( ? [X7] :
( apply(X0,X7) = X5
& in(X7,relation_dom(X0)) )
=> ( apply(X0,sK10(X0,X5)) = X5
& in(sK10(X0,X5),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f102,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( ( ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
| ~ in(X2,X1) )
& ( ? [X4] :
( apply(X0,X4) = X2
& in(X4,relation_dom(X0)) )
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0)) ) )
& ( ? [X7] :
( apply(X0,X7) = X5
& in(X7,relation_dom(X0)) )
| ~ in(X5,X1) ) )
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f101]) ).
fof(f101,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( ( ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
| ~ in(X2,X1) )
& ( ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) )
& ( ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| ~ in(X2,X1) ) )
| ~ sP0(X0,X1) ) ),
inference(nnf_transformation,[],[f91]) ).
fof(f91,plain,
! [X0,X1] :
( sP0(X0,X1)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f850,plain,
( spl27_103
| ~ spl27_5
| ~ spl27_75 ),
inference(avatar_split_clause,[],[f693,f647,f260,f847]) ).
fof(f693,plain,
( relation_of2(sK6,sK3,sK4)
| ~ spl27_5
| ~ spl27_75 ),
inference(resolution,[],[f648,f262]) ).
fof(f845,plain,
( spl27_102
| ~ spl27_11
| ~ spl27_45
| ~ spl27_96 ),
inference(avatar_split_clause,[],[f818,f813,f461,f290,f843]) ).
fof(f813,plain,
( spl27_96
<=> ! [X2,X0,X1] :
( quasi_total(X2,X0,X1)
| empty_set != X2
| empty_set = X0
| empty_set != X1
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_96])]) ).
fof(f818,plain,
( ! [X2,X0,X1] :
( sK18 != X1
| sK18 = X0
| sK18 != X2
| quasi_total(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) )
| ~ spl27_11
| ~ spl27_45
| ~ spl27_96 ),
inference(forward_demodulation,[],[f817,f495]) ).
fof(f817,plain,
( ! [X2,X0,X1] :
( sK18 = X0
| sK18 != X2
| quasi_total(X2,X0,X1)
| empty_set != X1
| ~ relation_of2_as_subset(X2,X0,X1) )
| ~ spl27_11
| ~ spl27_45
| ~ spl27_96 ),
inference(forward_demodulation,[],[f816,f495]) ).
fof(f816,plain,
( ! [X2,X0,X1] :
( sK18 != X2
| quasi_total(X2,X0,X1)
| empty_set = X0
| empty_set != X1
| ~ relation_of2_as_subset(X2,X0,X1) )
| ~ spl27_11
| ~ spl27_45
| ~ spl27_96 ),
inference(forward_demodulation,[],[f814,f495]) ).
fof(f814,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) )
| ~ spl27_96 ),
inference(avatar_component_clause,[],[f813]) ).
fof(f841,plain,
( spl27_101
| ~ spl27_11
| ~ spl27_45
| ~ spl27_95 ),
inference(avatar_split_clause,[],[f811,f806,f461,f290,f839]) ).
fof(f806,plain,
( spl27_95
<=> ! [X2,X0,X1] :
( empty_set = X2
| ~ quasi_total(X2,X0,X1)
| empty_set = X0
| empty_set != X1
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_95])]) ).
fof(f811,plain,
( ! [X2,X0,X1] :
( sK18 != X1
| sK18 = X0
| sK18 = X2
| ~ quasi_total(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) )
| ~ spl27_11
| ~ spl27_45
| ~ spl27_95 ),
inference(forward_demodulation,[],[f810,f495]) ).
fof(f810,plain,
( ! [X2,X0,X1] :
( sK18 = X0
| sK18 = X2
| ~ quasi_total(X2,X0,X1)
| empty_set != X1
| ~ relation_of2_as_subset(X2,X0,X1) )
| ~ spl27_11
| ~ spl27_45
| ~ spl27_95 ),
inference(forward_demodulation,[],[f809,f495]) ).
fof(f809,plain,
( ! [X2,X0,X1] :
( sK18 = X2
| ~ quasi_total(X2,X0,X1)
| empty_set = X0
| empty_set != X1
| ~ relation_of2_as_subset(X2,X0,X1) )
| ~ spl27_11
| ~ spl27_45
| ~ spl27_95 ),
inference(forward_demodulation,[],[f807,f495]) ).
fof(f807,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) )
| ~ spl27_95 ),
inference(avatar_component_clause,[],[f806]) ).
fof(f837,plain,
( spl27_100
| ~ spl27_11
| ~ spl27_45
| ~ spl27_94 ),
inference(avatar_split_clause,[],[f804,f801,f461,f290,f835]) ).
fof(f835,plain,
( spl27_100
<=> ! [X2,X0,X1] :
( sK18 != X0
| quasi_total(X1,X0,X2)
| relation_dom_as_subset(X0,X2,X1) != X0
| ~ sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_100])]) ).
fof(f801,plain,
( spl27_94
<=> ! [X2,X0,X1] :
( quasi_total(X1,X0,X2)
| relation_dom_as_subset(X0,X2,X1) != X0
| empty_set != X0
| ~ sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_94])]) ).
fof(f804,plain,
( ! [X2,X0,X1] :
( sK18 != X0
| quasi_total(X1,X0,X2)
| relation_dom_as_subset(X0,X2,X1) != X0
| ~ sP2(X0,X1,X2) )
| ~ spl27_11
| ~ spl27_45
| ~ spl27_94 ),
inference(forward_demodulation,[],[f802,f495]) ).
fof(f802,plain,
( ! [X2,X0,X1] :
( quasi_total(X1,X0,X2)
| relation_dom_as_subset(X0,X2,X1) != X0
| empty_set != X0
| ~ sP2(X0,X1,X2) )
| ~ spl27_94 ),
inference(avatar_component_clause,[],[f801]) ).
fof(f833,plain,
( spl27_99
| ~ spl27_11
| ~ spl27_45
| ~ spl27_92 ),
inference(avatar_split_clause,[],[f794,f791,f461,f290,f831]) ).
fof(f831,plain,
( spl27_99
<=> ! [X2,X0,X1] :
( sK18 = X2
| quasi_total(X1,X0,X2)
| relation_dom_as_subset(X0,X2,X1) != X0
| ~ sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_99])]) ).
fof(f791,plain,
( spl27_92
<=> ! [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,[spl27_92])]) ).
fof(f794,plain,
( ! [X2,X0,X1] :
( sK18 = X2
| quasi_total(X1,X0,X2)
| relation_dom_as_subset(X0,X2,X1) != X0
| ~ sP2(X0,X1,X2) )
| ~ spl27_11
| ~ spl27_45
| ~ spl27_92 ),
inference(forward_demodulation,[],[f792,f495]) ).
fof(f792,plain,
( ! [X2,X0,X1] :
( quasi_total(X1,X0,X2)
| relation_dom_as_subset(X0,X2,X1) != X0
| empty_set = X2
| ~ sP2(X0,X1,X2) )
| ~ spl27_92 ),
inference(avatar_component_clause,[],[f791]) ).
fof(f829,plain,
( spl27_98
| ~ spl27_11
| ~ spl27_45
| ~ spl27_91 ),
inference(avatar_split_clause,[],[f789,f786,f461,f290,f827]) ).
fof(f786,plain,
( spl27_91
<=> ! [X2,X0,X1] :
( relation_dom_as_subset(X0,X2,X1) = X0
| ~ quasi_total(X1,X0,X2)
| empty_set != X0
| ~ sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_91])]) ).
fof(f789,plain,
( ! [X2,X0,X1] :
( sK18 != X0
| relation_dom_as_subset(X0,X2,X1) = X0
| ~ quasi_total(X1,X0,X2)
| ~ sP2(X0,X1,X2) )
| ~ spl27_11
| ~ spl27_45
| ~ spl27_91 ),
inference(forward_demodulation,[],[f787,f495]) ).
fof(f787,plain,
( ! [X2,X0,X1] :
( relation_dom_as_subset(X0,X2,X1) = X0
| ~ quasi_total(X1,X0,X2)
| empty_set != X0
| ~ sP2(X0,X1,X2) )
| ~ spl27_91 ),
inference(avatar_component_clause,[],[f786]) ).
fof(f825,plain,
( spl27_97
| ~ spl27_11
| ~ spl27_45
| ~ spl27_90 ),
inference(avatar_split_clause,[],[f784,f781,f461,f290,f823]) ).
fof(f781,plain,
( spl27_90
<=> ! [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,[spl27_90])]) ).
fof(f784,plain,
( ! [X2,X0,X1] :
( sK18 = X2
| relation_dom_as_subset(X0,X2,X1) = X0
| ~ quasi_total(X1,X0,X2)
| ~ sP2(X0,X1,X2) )
| ~ spl27_11
| ~ spl27_45
| ~ spl27_90 ),
inference(forward_demodulation,[],[f782,f495]) ).
fof(f782,plain,
( ! [X2,X0,X1] :
( relation_dom_as_subset(X0,X2,X1) = X0
| ~ quasi_total(X1,X0,X2)
| empty_set = X2
| ~ sP2(X0,X1,X2) )
| ~ spl27_90 ),
inference(avatar_component_clause,[],[f781]) ).
fof(f815,plain,
spl27_96,
inference(avatar_split_clause,[],[f208,f813]) ).
fof(f208,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,[],[f122]) ).
fof(f122,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,[],[f95]) ).
fof(f95,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,[],[f84,f94]) ).
fof(f94,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(f84,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,[],[f83]) ).
fof(f83,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,[],[f6]) ).
fof(f6,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/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',d1_funct_2) ).
fof(f808,plain,
spl27_95,
inference(avatar_split_clause,[],[f207,f806]) ).
fof(f207,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,[],[f122]) ).
fof(f803,plain,
spl27_94,
inference(avatar_split_clause,[],[f205,f801]) ).
fof(f205,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,[],[f121]) ).
fof(f121,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,[],[f120]) ).
fof(f120,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,[],[f94]) ).
fof(f799,plain,
( spl27_93
| ~ spl27_5
| ~ spl27_73 ),
inference(avatar_split_clause,[],[f687,f639,f260,f796]) ).
fof(f687,plain,
( sP2(sK3,sK6,sK4)
| ~ spl27_5
| ~ spl27_73 ),
inference(resolution,[],[f640,f262]) ).
fof(f793,plain,
spl27_92,
inference(avatar_split_clause,[],[f204,f791]) ).
fof(f204,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,[],[f121]) ).
fof(f788,plain,
spl27_91,
inference(avatar_split_clause,[],[f203,f786]) ).
fof(f203,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,[],[f121]) ).
fof(f783,plain,
spl27_90,
inference(avatar_split_clause,[],[f202,f781]) ).
fof(f202,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,[],[f121]) ).
fof(f779,plain,
spl27_89,
inference(avatar_split_clause,[],[f174,f777]) ).
fof(f174,plain,
! [X0,X1] :
( sP0(X0,X1)
| sK8(X0,X1) = apply(X0,sK9(X0,X1))
| in(sK8(X0,X1),X1) ),
inference(cnf_transformation,[],[f106]) ).
fof(f774,plain,
spl27_88,
inference(avatar_split_clause,[],[f172,f772]) ).
fof(f172,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f106]) ).
fof(f764,plain,
spl27_87,
inference(avatar_split_clause,[],[f173,f762]) ).
fof(f173,plain,
! [X0,X1] :
( sP0(X0,X1)
| in(sK9(X0,X1),relation_dom(X0))
| in(sK8(X0,X1),X1) ),
inference(cnf_transformation,[],[f106]) ).
fof(f760,plain,
spl27_86,
inference(avatar_split_clause,[],[f171,f758]) ).
fof(f758,plain,
( spl27_86
<=> ! [X5,X0,X1] :
( apply(X0,sK10(X0,X5)) = X5
| ~ in(X5,X1)
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_86])]) ).
fof(f171,plain,
! [X0,X1,X5] :
( apply(X0,sK10(X0,X5)) = X5
| ~ in(X5,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f106]) ).
fof(f755,plain,
spl27_85,
inference(avatar_split_clause,[],[f170,f753]) ).
fof(f753,plain,
( spl27_85
<=> ! [X5,X0,X1] :
( in(sK10(X0,X5),relation_dom(X0))
| ~ in(X5,X1)
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_85])]) ).
fof(f170,plain,
! [X0,X1,X5] :
( in(sK10(X0,X5),relation_dom(X0))
| ~ in(X5,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f106]) ).
fof(f743,plain,
spl27_84,
inference(avatar_split_clause,[],[f210,f741]) ).
fof(f210,plain,
! [X2,X0,X1] :
( element(relation_dom_as_subset(X0,X1,X2),powerset(X0))
| ~ relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f86]) ).
fof(f86,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/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',dt_k4_relset_1) ).
fof(f739,plain,
spl27_83,
inference(avatar_split_clause,[],[f209,f737]) ).
fof(f209,plain,
! [X2,X0,X1] :
( relation_dom_as_subset(X0,X1,X2) = relation_dom(X2)
| ~ relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
! [X0,X1,X2] :
( relation_dom_as_subset(X0,X1,X2) = relation_dom(X2)
| ~ relation_of2(X2,X0,X1) ),
inference(ennf_transformation,[],[f44]) ).
fof(f44,axiom,
! [X0,X1,X2] :
( relation_of2(X2,X0,X1)
=> relation_dom_as_subset(X0,X1,X2) = relation_dom(X2) ),
file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',redefinition_k4_relset_1) ).
fof(f724,plain,
spl27_82,
inference(avatar_split_clause,[],[f212,f722]) ).
fof(f212,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f88]) ).
fof(f88,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/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',t4_subset) ).
fof(f720,plain,
spl27_81,
inference(avatar_split_clause,[],[f201,f718]) ).
fof(f201,plain,
! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f82]) ).
fof(f82,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/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',dt_m2_relset_1) ).
fof(f709,plain,
spl27_80,
inference(avatar_split_clause,[],[f215,f707]) ).
fof(f215,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,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/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',t5_subset) ).
fof(f705,plain,
spl27_79,
inference(avatar_split_clause,[],[f169,f703]) ).
fof(f703,plain,
( spl27_79
<=> ! [X0,X1] :
( relation_rng(X0) = X1
| ~ sP0(X0,X1)
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_79])]) ).
fof(f169,plain,
! [X0,X1] :
( relation_rng(X0) = X1
| ~ sP0(X0,X1)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f100,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ~ sP0(X0,X1) )
& ( sP0(X0,X1)
| relation_rng(X0) != X1 ) )
| ~ sP1(X0) ),
inference(nnf_transformation,[],[f92]) ).
fof(f92,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> sP0(X0,X1) )
| ~ sP1(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f701,plain,
spl27_78,
inference(avatar_split_clause,[],[f168,f699]) ).
fof(f168,plain,
! [X0,X1] :
( sP0(X0,X1)
| relation_rng(X0) != X1
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f686,plain,
( spl27_77
| ~ spl27_2
| ~ spl27_56 ),
inference(avatar_split_clause,[],[f576,f526,f245,f683]) ).
fof(f683,plain,
( spl27_77
<=> element(sK5,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_77])]) ).
fof(f576,plain,
( element(sK5,sK3)
| ~ spl27_2
| ~ spl27_56 ),
inference(resolution,[],[f527,f247]) ).
fof(f247,plain,
( in(sK5,sK3)
| ~ spl27_2 ),
inference(avatar_component_clause,[],[f245]) ).
fof(f653,plain,
spl27_76,
inference(avatar_split_clause,[],[f214,f651]) ).
fof(f214,plain,
! [X2,X0,X1] :
( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f123]) ).
fof(f123,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,[],[f45]) ).
fof(f45,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
<=> relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',redefinition_m2_relset_1) ).
fof(f649,plain,
spl27_75,
inference(avatar_split_clause,[],[f213,f647]) ).
fof(f213,plain,
! [X2,X0,X1] :
( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f123]) ).
fof(f645,plain,
spl27_74,
inference(avatar_split_clause,[],[f211,f643]) ).
fof(f211,plain,
! [X2,X0,X1] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(cnf_transformation,[],[f87]) ).
fof(f87,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/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',cc1_relset_1) ).
fof(f641,plain,
spl27_73,
inference(avatar_split_clause,[],[f206,f639]) ).
fof(f206,plain,
! [X2,X0,X1] :
( sP2(X0,X2,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f122]) ).
fof(f637,plain,
spl27_72,
inference(avatar_split_clause,[],[f187,f635]) ).
fof(f635,plain,
( spl27_72
<=> ! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_72])]) ).
fof(f187,plain,
! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ),
inference(flattening,[],[f78]) ).
fof(f78,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/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',fc4_subset_1) ).
fof(f633,plain,
spl27_71,
inference(avatar_split_clause,[],[f186,f631]) ).
fof(f186,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f76]) ).
fof(f76,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f48]) ).
fof(f48,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',t2_subset) ).
fof(f629,plain,
spl27_70,
inference(avatar_split_clause,[],[f179,f627]) ).
fof(f179,plain,
! [X0] :
( one_to_one(X0)
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f73,plain,
! [X0] :
( ( one_to_one(X0)
& function(X0)
& relation(X0) )
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ),
inference(flattening,[],[f72]) ).
fof(f72,plain,
! [X0] :
( ( one_to_one(X0)
& function(X0)
& relation(X0) )
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( ( function(X0)
& empty(X0)
& relation(X0) )
=> ( one_to_one(X0)
& function(X0)
& relation(X0) ) ),
file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',cc2_funct_1) ).
fof(f625,plain,
( ~ spl27_69
| ~ spl27_2
| ~ spl27_55 ),
inference(avatar_split_clause,[],[f575,f522,f245,f622]) ).
fof(f622,plain,
( spl27_69
<=> in(sK3,sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_69])]) ).
fof(f575,plain,
( ~ in(sK3,sK5)
| ~ spl27_2
| ~ spl27_55 ),
inference(resolution,[],[f523,f247]) ).
fof(f600,plain,
spl27_68,
inference(avatar_split_clause,[],[f190,f598]) ).
fof(f190,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f56]) ).
fof(f56,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',t8_boole) ).
fof(f596,plain,
spl27_67,
inference(avatar_split_clause,[],[f189,f594]) ).
fof(f189,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f111]) ).
fof(f111,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f49]) ).
fof(f49,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',t3_subset) ).
fof(f592,plain,
spl27_66,
inference(avatar_split_clause,[],[f188,f590]) ).
fof(f188,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f111]) ).
fof(f588,plain,
spl27_65,
inference(avatar_split_clause,[],[f167,f586]) ).
fof(f586,plain,
( spl27_65
<=> ! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_65])]) ).
fof(f167,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(flattening,[],[f68]) ).
fof(f68,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/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',fc5_relat_1) ).
fof(f584,plain,
spl27_64,
inference(avatar_split_clause,[],[f166,f582]) ).
fof(f582,plain,
( spl27_64
<=> ! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_64])]) ).
fof(f166,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(flattening,[],[f66]) ).
fof(f66,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_rng(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',fc6_relat_1) ).
fof(f580,plain,
spl27_63,
inference(avatar_split_clause,[],[f157,f578]) ).
fof(f157,plain,
! [X0] :
( element(sK7(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f99,plain,
! [X0] :
( ( ~ empty(sK7(X0))
& element(sK7(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f60,f98]) ).
fof(f98,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( ~ empty(sK7(X0))
& element(sK7(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f60,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',rc1_subset_1) ).
fof(f553,plain,
( ~ spl27_62
| ~ spl27_2
| ~ spl27_52 ),
inference(avatar_split_clause,[],[f516,f490,f245,f550]) ).
fof(f550,plain,
( spl27_62
<=> empty(sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_62])]) ).
fof(f516,plain,
( ~ empty(sK3)
| ~ spl27_2
| ~ spl27_52 ),
inference(resolution,[],[f491,f247]) ).
fof(f548,plain,
spl27_61,
inference(avatar_split_clause,[],[f200,f546]) ).
fof(f546,plain,
( spl27_61
<=> ! [X0,X1] : quasi_total(sK16(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_61])]) ).
fof(f200,plain,
! [X0,X1] : quasi_total(sK16(X0,X1),X0,X1),
inference(cnf_transformation,[],[f119]) ).
fof(f119,plain,
! [X0,X1] :
( quasi_total(sK16(X0,X1),X0,X1)
& function(sK16(X0,X1))
& relation(sK16(X0,X1))
& relation_of2(sK16(X0,X1),X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f31,f118]) ).
fof(f118,plain,
! [X0,X1] :
( ? [X2] :
( quasi_total(X2,X0,X1)
& function(X2)
& relation(X2)
& relation_of2(X2,X0,X1) )
=> ( quasi_total(sK16(X0,X1),X0,X1)
& function(sK16(X0,X1))
& relation(sK16(X0,X1))
& relation_of2(sK16(X0,X1),X0,X1) ) ),
introduced(choice_axiom,[]) ).
fof(f31,axiom,
! [X0,X1] :
? [X2] :
( quasi_total(X2,X0,X1)
& function(X2)
& relation(X2)
& relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',rc1_funct_2) ).
fof(f544,plain,
spl27_60,
inference(avatar_split_clause,[],[f197,f542]) ).
fof(f197,plain,
! [X0,X1] : relation_of2(sK16(X0,X1),X0,X1),
inference(cnf_transformation,[],[f119]) ).
fof(f540,plain,
spl27_59,
inference(avatar_split_clause,[],[f194,f538]) ).
fof(f194,plain,
! [X0,X1] : relation_of2(sK15(X0,X1),X0,X1),
inference(cnf_transformation,[],[f117]) ).
fof(f117,plain,
! [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])],[f37,f116]) ).
fof(f116,plain,
! [X0,X1] :
( ? [X2] :
( function(X2)
& relation(X2)
& relation_of2(X2,X0,X1) )
=> ( function(sK15(X0,X1))
& relation(sK15(X0,X1))
& relation_of2(sK15(X0,X1),X0,X1) ) ),
introduced(choice_axiom,[]) ).
fof(f37,axiom,
! [X0,X1] :
? [X2] :
( function(X2)
& relation(X2)
& relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',rc2_partfun1) ).
fof(f536,plain,
spl27_58,
inference(avatar_split_clause,[],[f193,f534]) ).
fof(f193,plain,
! [X0,X1] : relation_of2(sK14(X0,X1),X0,X1),
inference(cnf_transformation,[],[f115]) ).
fof(f115,plain,
! [X0,X1] : relation_of2(sK14(X0,X1),X0,X1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f18,f114]) ).
fof(f114,plain,
! [X0,X1] :
( ? [X2] : relation_of2(X2,X0,X1)
=> relation_of2(sK14(X0,X1),X0,X1) ),
introduced(choice_axiom,[]) ).
fof(f18,axiom,
! [X0,X1] :
? [X2] : relation_of2(X2,X0,X1),
file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',existence_m1_relset_1) ).
fof(f532,plain,
spl27_57,
inference(avatar_split_clause,[],[f192,f530]) ).
fof(f192,plain,
! [X0,X1] : relation_of2_as_subset(sK13(X0,X1),X0,X1),
inference(cnf_transformation,[],[f113]) ).
fof(f113,plain,
! [X0,X1] : relation_of2_as_subset(sK13(X0,X1),X0,X1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f20,f112]) ).
fof(f112,plain,
! [X0,X1] :
( ? [X2] : relation_of2_as_subset(X2,X0,X1)
=> relation_of2_as_subset(sK13(X0,X1),X0,X1) ),
introduced(choice_axiom,[]) ).
fof(f20,axiom,
! [X0,X1] :
? [X2] : relation_of2_as_subset(X2,X0,X1),
file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',existence_m2_relset_1) ).
fof(f528,plain,
spl27_56,
inference(avatar_split_clause,[],[f185,f526]) ).
fof(f185,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f47]) ).
fof(f47,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',t1_subset) ).
fof(f524,plain,
spl27_55,
inference(avatar_split_clause,[],[f184,f522]) ).
fof(f184,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',antisymmetry_r2_hidden) ).
fof(f520,plain,
spl27_54,
inference(avatar_split_clause,[],[f176,f518]) ).
fof(f176,plain,
! [X0] :
( sP1(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f93,plain,
! [X0] :
( sP1(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f71,f92,f91]) ).
fof(f71,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f70]) ).
fof(f70,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',d5_funct_1) ).
fof(f514,plain,
( spl27_53
| ~ spl27_14
| ~ spl27_36 ),
inference(avatar_split_clause,[],[f442,f412,f305,f511]) ).
fof(f511,plain,
( spl27_53
<=> function(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_53])]) ).
fof(f442,plain,
( function(sK20)
| ~ spl27_14
| ~ spl27_36 ),
inference(resolution,[],[f413,f307]) ).
fof(f492,plain,
spl27_52,
inference(avatar_split_clause,[],[f191,f490]) ).
fof(f191,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f55]) ).
fof(f55,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',t7_boole) ).
fof(f488,plain,
spl27_51,
inference(avatar_split_clause,[],[f181,f486]) ).
fof(f181,plain,
! [X0] : element(sK12(X0),powerset(X0)),
inference(cnf_transformation,[],[f110]) ).
fof(f110,plain,
! [X0] :
( empty(sK12(X0))
& element(sK12(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f39,f109]) ).
fof(f109,plain,
! [X0] :
( ? [X1] :
( empty(X1)
& element(X1,powerset(X0)) )
=> ( empty(sK12(X0))
& element(sK12(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f39,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',rc2_subset_1) ).
fof(f484,plain,
spl27_50,
inference(avatar_split_clause,[],[f165,f482]) ).
fof(f165,plain,
! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0] :
( ( relation(relation_dom(X0))
& empty(relation_dom(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',fc7_relat_1) ).
fof(f480,plain,
spl27_49,
inference(avatar_split_clause,[],[f164,f478]) ).
fof(f164,plain,
! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f476,plain,
( spl27_48
| ~ spl27_11
| ~ spl27_36 ),
inference(avatar_split_clause,[],[f441,f412,f290,f473]) ).
fof(f441,plain,
( function(sK18)
| ~ spl27_11
| ~ spl27_36 ),
inference(resolution,[],[f413,f292]) ).
fof(f471,plain,
spl27_47,
inference(avatar_split_clause,[],[f163,f469]) ).
fof(f163,plain,
! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0] :
( ( relation(relation_rng(X0))
& empty(relation_rng(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_rng(X0))
& empty(relation_rng(X0)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',fc8_relat_1) ).
fof(f467,plain,
spl27_46,
inference(avatar_split_clause,[],[f162,f465]) ).
fof(f162,plain,
! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f463,plain,
spl27_45,
inference(avatar_split_clause,[],[f161,f461]) ).
fof(f161,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f52]) ).
fof(f52,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',t6_boole) ).
fof(f459,plain,
spl27_44,
inference(avatar_split_clause,[],[f158,f457]) ).
fof(f457,plain,
( spl27_44
<=> ! [X0] :
( ~ empty(sK7(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_44])]) ).
fof(f158,plain,
! [X0] :
( ~ empty(sK7(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f449,plain,
( spl27_43
| ~ spl27_7
| ~ spl27_36 ),
inference(avatar_split_clause,[],[f439,f412,f270,f446]) ).
fof(f446,plain,
( spl27_43
<=> function(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_43])]) ).
fof(f439,plain,
( function(empty_set)
| ~ spl27_7
| ~ spl27_36 ),
inference(resolution,[],[f413,f272]) ).
fof(f438,plain,
spl27_42,
inference(avatar_split_clause,[],[f199,f436]) ).
fof(f199,plain,
! [X0,X1] : function(sK16(X0,X1)),
inference(cnf_transformation,[],[f119]) ).
fof(f434,plain,
spl27_41,
inference(avatar_split_clause,[],[f198,f432]) ).
fof(f198,plain,
! [X0,X1] : relation(sK16(X0,X1)),
inference(cnf_transformation,[],[f119]) ).
fof(f430,plain,
spl27_40,
inference(avatar_split_clause,[],[f196,f428]) ).
fof(f196,plain,
! [X0,X1] : function(sK15(X0,X1)),
inference(cnf_transformation,[],[f117]) ).
fof(f426,plain,
spl27_39,
inference(avatar_split_clause,[],[f195,f424]) ).
fof(f195,plain,
! [X0,X1] : relation(sK15(X0,X1)),
inference(cnf_transformation,[],[f117]) ).
fof(f422,plain,
spl27_38,
inference(avatar_split_clause,[],[f180,f420]) ).
fof(f180,plain,
! [X0] : element(sK11(X0),X0),
inference(cnf_transformation,[],[f108]) ).
fof(f108,plain,
! [X0] : element(sK11(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f19,f107]) ).
fof(f107,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK11(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f19,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',existence_m1_subset_1) ).
fof(f418,plain,
spl27_37,
inference(avatar_split_clause,[],[f160,f416]) ).
fof(f160,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( empty(X0)
=> relation(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',cc1_relat_1) ).
fof(f414,plain,
spl27_36,
inference(avatar_split_clause,[],[f159,f412]) ).
fof(f159,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( empty(X0)
=> function(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',cc1_funct_1) ).
fof(f410,plain,
spl27_35,
inference(avatar_split_clause,[],[f183,f408]) ).
fof(f183,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f46]) ).
fof(f46,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',reflexivity_r1_tarski) ).
fof(f406,plain,
spl27_34,
inference(avatar_split_clause,[],[f182,f404]) ).
fof(f182,plain,
! [X0] : empty(sK12(X0)),
inference(cnf_transformation,[],[f110]) ).
fof(f402,plain,
spl27_33,
inference(avatar_split_clause,[],[f156,f400]) ).
fof(f400,plain,
( spl27_33
<=> ! [X0] : ~ empty(powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_33])]) ).
fof(f156,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',fc1_subset_1) ).
fof(f398,plain,
spl27_32,
inference(avatar_split_clause,[],[f238,f395]) ).
fof(f395,plain,
( spl27_32
<=> function(sK26) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_32])]) ).
fof(f238,plain,
function(sK26),
inference(cnf_transformation,[],[f143]) ).
fof(f143,plain,
( function(sK26)
& empty(sK26)
& relation(sK26) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f36,f142]) ).
fof(f142,plain,
( ? [X0] :
( function(X0)
& empty(X0)
& relation(X0) )
=> ( function(sK26)
& empty(sK26)
& relation(sK26) ) ),
introduced(choice_axiom,[]) ).
fof(f36,axiom,
? [X0] :
( function(X0)
& empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',rc2_funct_1) ).
fof(f393,plain,
spl27_31,
inference(avatar_split_clause,[],[f237,f390]) ).
fof(f237,plain,
empty(sK26),
inference(cnf_transformation,[],[f143]) ).
fof(f388,plain,
spl27_30,
inference(avatar_split_clause,[],[f236,f385]) ).
fof(f385,plain,
( spl27_30
<=> relation(sK26) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_30])]) ).
fof(f236,plain,
relation(sK26),
inference(cnf_transformation,[],[f143]) ).
fof(f383,plain,
spl27_29,
inference(avatar_split_clause,[],[f235,f380]) ).
fof(f235,plain,
empty(sK25),
inference(cnf_transformation,[],[f141]) ).
fof(f141,plain,
( empty(sK25)
& one_to_one(sK25)
& function(sK25)
& relation(sK25) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f32,f140]) ).
fof(f140,plain,
( ? [X0] :
( empty(X0)
& one_to_one(X0)
& function(X0)
& relation(X0) )
=> ( empty(sK25)
& one_to_one(sK25)
& function(sK25)
& relation(sK25) ) ),
introduced(choice_axiom,[]) ).
fof(f32,axiom,
? [X0] :
( empty(X0)
& one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',rc1_partfun1) ).
fof(f378,plain,
spl27_28,
inference(avatar_split_clause,[],[f234,f375]) ).
fof(f234,plain,
one_to_one(sK25),
inference(cnf_transformation,[],[f141]) ).
fof(f373,plain,
spl27_27,
inference(avatar_split_clause,[],[f233,f370]) ).
fof(f370,plain,
( spl27_27
<=> function(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_27])]) ).
fof(f233,plain,
function(sK25),
inference(cnf_transformation,[],[f141]) ).
fof(f368,plain,
spl27_26,
inference(avatar_split_clause,[],[f232,f365]) ).
fof(f365,plain,
( spl27_26
<=> relation(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_26])]) ).
fof(f232,plain,
relation(sK25),
inference(cnf_transformation,[],[f141]) ).
fof(f363,plain,
spl27_25,
inference(avatar_split_clause,[],[f231,f360]) ).
fof(f360,plain,
( spl27_25
<=> one_to_one(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_25])]) ).
fof(f231,plain,
one_to_one(sK24),
inference(cnf_transformation,[],[f139]) ).
fof(f139,plain,
( one_to_one(sK24)
& function(sK24)
& relation(sK24) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f41,f138]) ).
fof(f138,plain,
( ? [X0] :
( one_to_one(X0)
& function(X0)
& relation(X0) )
=> ( one_to_one(sK24)
& function(sK24)
& relation(sK24) ) ),
introduced(choice_axiom,[]) ).
fof(f41,axiom,
? [X0] :
( one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',rc3_funct_1) ).
fof(f358,plain,
spl27_24,
inference(avatar_split_clause,[],[f230,f355]) ).
fof(f230,plain,
function(sK24),
inference(cnf_transformation,[],[f139]) ).
fof(f353,plain,
spl27_23,
inference(avatar_split_clause,[],[f229,f350]) ).
fof(f229,plain,
relation(sK24),
inference(cnf_transformation,[],[f139]) ).
fof(f348,plain,
spl27_22,
inference(avatar_split_clause,[],[f228,f345]) ).
fof(f228,plain,
function(sK23),
inference(cnf_transformation,[],[f137]) ).
fof(f137,plain,
( function(sK23)
& relation(sK23) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f30,f136]) ).
fof(f136,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK23)
& relation(sK23) ) ),
introduced(choice_axiom,[]) ).
fof(f30,axiom,
? [X0] :
( function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',rc1_funct_1) ).
fof(f343,plain,
spl27_21,
inference(avatar_split_clause,[],[f227,f340]) ).
fof(f227,plain,
relation(sK23),
inference(cnf_transformation,[],[f137]) ).
fof(f338,plain,
spl27_20,
inference(avatar_split_clause,[],[f226,f335]) ).
fof(f226,plain,
function(sK22),
inference(cnf_transformation,[],[f135]) ).
fof(f135,plain,
( function(sK22)
& relation_empty_yielding(sK22)
& relation(sK22) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22])],[f43,f134]) ).
fof(f134,plain,
( ? [X0] :
( function(X0)
& relation_empty_yielding(X0)
& relation(X0) )
=> ( function(sK22)
& relation_empty_yielding(sK22)
& relation(sK22) ) ),
introduced(choice_axiom,[]) ).
fof(f43,axiom,
? [X0] :
( function(X0)
& relation_empty_yielding(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',rc4_funct_1) ).
fof(f333,plain,
spl27_19,
inference(avatar_split_clause,[],[f225,f330]) ).
fof(f330,plain,
( spl27_19
<=> relation_empty_yielding(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_19])]) ).
fof(f225,plain,
relation_empty_yielding(sK22),
inference(cnf_transformation,[],[f135]) ).
fof(f328,plain,
spl27_18,
inference(avatar_split_clause,[],[f224,f325]) ).
fof(f224,plain,
relation(sK22),
inference(cnf_transformation,[],[f135]) ).
fof(f323,plain,
spl27_17,
inference(avatar_split_clause,[],[f223,f320]) ).
fof(f320,plain,
( spl27_17
<=> relation_empty_yielding(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_17])]) ).
fof(f223,plain,
relation_empty_yielding(sK21),
inference(cnf_transformation,[],[f133]) ).
fof(f133,plain,
( relation_empty_yielding(sK21)
& relation(sK21) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f42,f132]) ).
fof(f132,plain,
( ? [X0] :
( relation_empty_yielding(X0)
& relation(X0) )
=> ( relation_empty_yielding(sK21)
& relation(sK21) ) ),
introduced(choice_axiom,[]) ).
fof(f42,axiom,
? [X0] :
( relation_empty_yielding(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',rc3_relat_1) ).
fof(f318,plain,
spl27_16,
inference(avatar_split_clause,[],[f222,f315]) ).
fof(f222,plain,
relation(sK21),
inference(cnf_transformation,[],[f133]) ).
fof(f313,plain,
spl27_15,
inference(avatar_split_clause,[],[f221,f310]) ).
fof(f310,plain,
( spl27_15
<=> relation(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_15])]) ).
fof(f221,plain,
relation(sK20),
inference(cnf_transformation,[],[f131]) ).
fof(f131,plain,
( relation(sK20)
& empty(sK20) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f33,f130]) ).
fof(f130,plain,
( ? [X0] :
( relation(X0)
& empty(X0) )
=> ( relation(sK20)
& empty(sK20) ) ),
introduced(choice_axiom,[]) ).
fof(f33,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',rc1_relat_1) ).
fof(f308,plain,
spl27_14,
inference(avatar_split_clause,[],[f220,f305]) ).
fof(f220,plain,
empty(sK20),
inference(cnf_transformation,[],[f131]) ).
fof(f303,plain,
spl27_13,
inference(avatar_split_clause,[],[f219,f300]) ).
fof(f219,plain,
relation(sK19),
inference(cnf_transformation,[],[f129]) ).
fof(f129,plain,
( relation(sK19)
& ~ empty(sK19) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f38,f128]) ).
fof(f128,plain,
( ? [X0] :
( relation(X0)
& ~ empty(X0) )
=> ( relation(sK19)
& ~ empty(sK19) ) ),
introduced(choice_axiom,[]) ).
fof(f38,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',rc2_relat_1) ).
fof(f298,plain,
~ spl27_12,
inference(avatar_split_clause,[],[f218,f295]) ).
fof(f295,plain,
( spl27_12
<=> empty(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_12])]) ).
fof(f218,plain,
~ empty(sK19),
inference(cnf_transformation,[],[f129]) ).
fof(f293,plain,
spl27_11,
inference(avatar_split_clause,[],[f217,f290]) ).
fof(f217,plain,
empty(sK18),
inference(cnf_transformation,[],[f127]) ).
fof(f127,plain,
empty(sK18),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f35,f126]) ).
fof(f126,plain,
( ? [X0] : empty(X0)
=> empty(sK18) ),
introduced(choice_axiom,[]) ).
fof(f35,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',rc1_xboole_0) ).
fof(f288,plain,
~ spl27_10,
inference(avatar_split_clause,[],[f216,f285]) ).
fof(f285,plain,
( spl27_10
<=> empty(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_10])]) ).
fof(f216,plain,
~ empty(sK17),
inference(cnf_transformation,[],[f125]) ).
fof(f125,plain,
~ empty(sK17),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f40,f124]) ).
fof(f124,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK17) ),
introduced(choice_axiom,[]) ).
fof(f40,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',rc2_xboole_0) ).
fof(f283,plain,
spl27_9,
inference(avatar_split_clause,[],[f155,f280]) ).
fof(f155,plain,
relation_empty_yielding(empty_set),
inference(cnf_transformation,[],[f21]) ).
fof(f21,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',fc12_relat_1) ).
fof(f278,plain,
spl27_8,
inference(avatar_split_clause,[],[f152,f275]) ).
fof(f152,plain,
relation(empty_set),
inference(cnf_transformation,[],[f24]) ).
fof(f24,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',fc4_relat_1) ).
fof(f273,plain,
spl27_7,
inference(avatar_split_clause,[],[f150,f270]) ).
fof(f150,plain,
empty(empty_set),
inference(cnf_transformation,[],[f23]) ).
fof(f23,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',fc1_xboole_0) ).
fof(f268,plain,
~ spl27_6,
inference(avatar_split_clause,[],[f149,f265]) ).
fof(f149,plain,
~ in(apply(sK6,sK5),relation_rng(sK6)),
inference(cnf_transformation,[],[f97]) ).
fof(f97,plain,
( ~ in(apply(sK6,sK5),relation_rng(sK6))
& empty_set != sK4
& in(sK5,sK3)
& 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])],[f59,f96]) ).
fof(f96,plain,
( ? [X0,X1,X2,X3] :
( ~ in(apply(X3,X2),relation_rng(X3))
& empty_set != X1
& in(X2,X0)
& relation_of2_as_subset(X3,X0,X1)
& quasi_total(X3,X0,X1)
& function(X3) )
=> ( ~ in(apply(sK6,sK5),relation_rng(sK6))
& empty_set != sK4
& in(sK5,sK3)
& relation_of2_as_subset(sK6,sK3,sK4)
& quasi_total(sK6,sK3,sK4)
& function(sK6) ) ),
introduced(choice_axiom,[]) ).
fof(f59,plain,
? [X0,X1,X2,X3] :
( ~ in(apply(X3,X2),relation_rng(X3))
& empty_set != X1
& in(X2,X0)
& relation_of2_as_subset(X3,X0,X1)
& quasi_total(X3,X0,X1)
& function(X3) ),
inference(flattening,[],[f58]) ).
fof(f58,plain,
? [X0,X1,X2,X3] :
( ~ in(apply(X3,X2),relation_rng(X3))
& empty_set != X1
& in(X2,X0)
& relation_of2_as_subset(X3,X0,X1)
& quasi_total(X3,X0,X1)
& function(X3) ),
inference(ennf_transformation,[],[f54]) ).
fof(f54,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( relation_of2_as_subset(X3,X0,X1)
& quasi_total(X3,X0,X1)
& function(X3) )
=> ( in(X2,X0)
=> ( in(apply(X3,X2),relation_rng(X3))
| empty_set = X1 ) ) ),
inference(negated_conjecture,[],[f53]) ).
fof(f53,conjecture,
! [X0,X1,X2,X3] :
( ( relation_of2_as_subset(X3,X0,X1)
& quasi_total(X3,X0,X1)
& function(X3) )
=> ( in(X2,X0)
=> ( in(apply(X3,X2),relation_rng(X3))
| empty_set = X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.zGF3ohbVjv/Vampire---4.8_6571',t6_funct_2) ).
fof(f263,plain,
spl27_5,
inference(avatar_split_clause,[],[f146,f260]) ).
fof(f146,plain,
relation_of2_as_subset(sK6,sK3,sK4),
inference(cnf_transformation,[],[f97]) ).
fof(f258,plain,
spl27_4,
inference(avatar_split_clause,[],[f145,f255]) ).
fof(f145,plain,
quasi_total(sK6,sK3,sK4),
inference(cnf_transformation,[],[f97]) ).
fof(f253,plain,
~ spl27_3,
inference(avatar_split_clause,[],[f148,f250]) ).
fof(f148,plain,
empty_set != sK4,
inference(cnf_transformation,[],[f97]) ).
fof(f248,plain,
spl27_2,
inference(avatar_split_clause,[],[f147,f245]) ).
fof(f147,plain,
in(sK5,sK3),
inference(cnf_transformation,[],[f97]) ).
fof(f243,plain,
spl27_1,
inference(avatar_split_clause,[],[f144,f240]) ).
fof(f144,plain,
function(sK6),
inference(cnf_transformation,[],[f97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : SEU290+1 : TPTP v8.1.2. Released v3.3.0.
% 0.05/0.10 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.09/0.29 % Computer : n017.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.30 % DateTime : Wed Aug 30 13:23:44 EDT 2023
% 0.09/0.30 % CPUTime :
% 0.15/0.33 % (7858)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.33 % (7967)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.15/0.33 % (7965)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.15/0.33 % (7964)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.15/0.33 % (7966)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 Vampire---4 for (569ds/0Mi)
% 0.15/0.33 % (7969)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 Vampire---4 for (522ds/0Mi)
% 0.15/0.33 % (7968)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 Vampire---4 for (531ds/0Mi)
% 0.15/0.33 % (7970)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 Vampire---4 for (497ds/0Mi)
% 0.15/0.33 TRYING [1]
% 0.15/0.33 TRYING [2]
% 0.15/0.33 TRYING [3]
% 0.15/0.34 TRYING [4]
% 0.15/0.34 TRYING [1]
% 0.15/0.34 TRYING [2]
% 0.15/0.35 TRYING [5]
% 0.15/0.36 % (7968)First to succeed.
% 0.15/0.37 TRYING [3]
% 0.15/0.37 % (7968)Refutation found. Thanks to Tanya!
% 0.15/0.37 % SZS status Theorem for Vampire---4
% 0.15/0.37 % SZS output start Proof for Vampire---4
% See solution above
% 0.15/0.37 % (7968)------------------------------
% 0.15/0.37 % (7968)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.15/0.37 % (7968)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.15/0.37 % (7968)Termination reason: Refutation
% 0.15/0.37
% 0.15/0.37 % (7968)Memory used [KB]: 6524
% 0.15/0.37 % (7968)Time elapsed: 0.036 s
% 0.15/0.37 % (7968)------------------------------
% 0.15/0.37 % (7968)------------------------------
% 0.15/0.37 % (7858)Success in time 0.075 s
% 0.15/0.37 % Vampire---4.8 exiting
%------------------------------------------------------------------------------