TSTP Solution File: SEU387+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU387+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 15:33:48 EDT 2024
% Result : Theorem 0.12s 0.31s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 410
% Syntax : Number of formulae : 1259 ( 336 unt; 0 def)
% Number of atoms : 4042 ( 71 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 4411 (1628 ~;1507 |; 871 &)
% ( 310 <=>; 95 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 346 ( 344 usr; 306 prp; 0-3 aty)
% Number of functors : 37 ( 37 usr; 18 con; 0-2 aty)
% Number of variables : 827 ( 739 !; 88 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2233,plain,
$false,
inference(avatar_sat_refutation,[],[f525,f530,f535,f540,f545,f550,f555,f560,f565,f570,f575,f580,f585,f590,f595,f600,f605,f610,f615,f620,f625,f630,f635,f640,f645,f650,f655,f660,f665,f670,f675,f680,f685,f690,f695,f700,f705,f710,f715,f720,f725,f730,f735,f740,f745,f750,f755,f760,f765,f770,f775,f780,f785,f790,f795,f800,f805,f810,f815,f820,f825,f830,f835,f840,f845,f850,f855,f860,f865,f870,f875,f880,f885,f890,f895,f900,f905,f910,f915,f920,f925,f930,f935,f940,f945,f950,f955,f960,f965,f969,f973,f977,f981,f985,f989,f993,f997,f1001,f1005,f1009,f1013,f1017,f1021,f1025,f1029,f1033,f1037,f1041,f1045,f1049,f1053,f1057,f1061,f1065,f1069,f1073,f1077,f1081,f1085,f1089,f1093,f1097,f1101,f1105,f1109,f1113,f1117,f1121,f1125,f1129,f1133,f1137,f1158,f1163,f1172,f1176,f1180,f1184,f1188,f1192,f1196,f1200,f1204,f1208,f1212,f1216,f1220,f1228,f1241,f1245,f1249,f1253,f1257,f1261,f1265,f1269,f1273,f1277,f1281,f1294,f1315,f1320,f1324,f1328,f1332,f1336,f1340,f1344,f1348,f1353,f1369,f1373,f1377,f1381,f1385,f1390,f1394,f1398,f1402,f1406,f1410,f1414,f1418,f1422,f1426,f1481,f1485,f1489,f1508,f1513,f1517,f1521,f1525,f1529,f1533,f1537,f1551,f1587,f1591,f1603,f1610,f1614,f1626,f1630,f1634,f1638,f1646,f1657,f1665,f1675,f1679,f1687,f1705,f1712,f1726,f1730,f1734,f1742,f1750,f1756,f1761,f1766,f1771,f1776,f1786,f1791,f1796,f1801,f1806,f1811,f1816,f1822,f1827,f1830,f1831,f1842,f1849,f1853,f1857,f1861,f1867,f1871,f1876,f1880,f1884,f1888,f1892,f1896,f1901,f1905,f1910,f1917,f1922,f1929,f1936,f1944,f1949,f1953,f1957,f1961,f1965,f1979,f1983,f1987,f1991,f1995,f1999,f2003,f2020,f2024,f2028,f2032,f2037,f2047,f2052,f2057,f2062,f2067,f2073,f2079,f2084,f2089,f2094,f2098,f2108,f2112,f2116,f2120,f2124,f2128,f2133,f2142,f2151,f2156,f2165,f2174,f2183,f2220,f2222,f2224,f2226,f2228,f2230,f2232]) ).
fof(f2232,plain,
( ~ spl34_91
| ~ spl34_300 ),
inference(avatar_contradiction_clause,[],[f2231]) ).
fof(f2231,plain,
( $false
| ~ spl34_91
| ~ spl34_300 ),
inference(resolution,[],[f2199,f972]) ).
fof(f972,plain,
( ! [X0] : ~ empty_carrier(boole_POSet(X0))
| ~ spl34_91 ),
inference(avatar_component_clause,[],[f971]) ).
fof(f971,plain,
( spl34_91
<=> ! [X0] : ~ empty_carrier(boole_POSet(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_91])]) ).
fof(f2199,plain,
( empty_carrier(boole_POSet(sK5))
| ~ spl34_300 ),
inference(avatar_component_clause,[],[f2197]) ).
fof(f2197,plain,
( spl34_300
<=> empty_carrier(boole_POSet(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_300])]) ).
fof(f2230,plain,
( ~ spl34_104
| spl34_305 ),
inference(avatar_contradiction_clause,[],[f2229]) ).
fof(f2229,plain,
( $false
| ~ spl34_104
| spl34_305 ),
inference(resolution,[],[f2219,f1024]) ).
fof(f1024,plain,
( ! [X0] : rel_str(boole_POSet(X0))
| ~ spl34_104 ),
inference(avatar_component_clause,[],[f1023]) ).
fof(f1023,plain,
( spl34_104
<=> ! [X0] : rel_str(boole_POSet(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_104])]) ).
fof(f2219,plain,
( ~ rel_str(boole_POSet(sK5))
| spl34_305 ),
inference(avatar_component_clause,[],[f2217]) ).
fof(f2217,plain,
( spl34_305
<=> rel_str(boole_POSet(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_305])]) ).
fof(f2228,plain,
( ~ spl34_96
| spl34_304 ),
inference(avatar_contradiction_clause,[],[f2227]) ).
fof(f2227,plain,
( $false
| ~ spl34_96
| spl34_304 ),
inference(resolution,[],[f2215,f992]) ).
fof(f992,plain,
( ! [X0] : lower_bounded_relstr(boole_POSet(X0))
| ~ spl34_96 ),
inference(avatar_component_clause,[],[f991]) ).
fof(f991,plain,
( spl34_96
<=> ! [X0] : lower_bounded_relstr(boole_POSet(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_96])]) ).
fof(f2215,plain,
( ~ lower_bounded_relstr(boole_POSet(sK5))
| spl34_304 ),
inference(avatar_component_clause,[],[f2213]) ).
fof(f2213,plain,
( spl34_304
<=> lower_bounded_relstr(boole_POSet(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_304])]) ).
fof(f2226,plain,
( ~ spl34_95
| spl34_303 ),
inference(avatar_contradiction_clause,[],[f2225]) ).
fof(f2225,plain,
( $false
| ~ spl34_95
| spl34_303 ),
inference(resolution,[],[f2211,f988]) ).
fof(f988,plain,
( ! [X0] : antisymmetric_relstr(boole_POSet(X0))
| ~ spl34_95 ),
inference(avatar_component_clause,[],[f987]) ).
fof(f987,plain,
( spl34_95
<=> ! [X0] : antisymmetric_relstr(boole_POSet(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_95])]) ).
fof(f2211,plain,
( ~ antisymmetric_relstr(boole_POSet(sK5))
| spl34_303 ),
inference(avatar_component_clause,[],[f2209]) ).
fof(f2209,plain,
( spl34_303
<=> antisymmetric_relstr(boole_POSet(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_303])]) ).
fof(f2224,plain,
( ~ spl34_94
| spl34_302 ),
inference(avatar_contradiction_clause,[],[f2223]) ).
fof(f2223,plain,
( $false
| ~ spl34_94
| spl34_302 ),
inference(resolution,[],[f2207,f984]) ).
fof(f984,plain,
( ! [X0] : transitive_relstr(boole_POSet(X0))
| ~ spl34_94 ),
inference(avatar_component_clause,[],[f983]) ).
fof(f983,plain,
( spl34_94
<=> ! [X0] : transitive_relstr(boole_POSet(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_94])]) ).
fof(f2207,plain,
( ~ transitive_relstr(boole_POSet(sK5))
| spl34_302 ),
inference(avatar_component_clause,[],[f2205]) ).
fof(f2205,plain,
( spl34_302
<=> transitive_relstr(boole_POSet(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_302])]) ).
fof(f2222,plain,
( ~ spl34_93
| spl34_301 ),
inference(avatar_contradiction_clause,[],[f2221]) ).
fof(f2221,plain,
( $false
| ~ spl34_93
| spl34_301 ),
inference(resolution,[],[f2203,f980]) ).
fof(f980,plain,
( ! [X0] : reflexive_relstr(boole_POSet(X0))
| ~ spl34_93 ),
inference(avatar_component_clause,[],[f979]) ).
fof(f979,plain,
( spl34_93
<=> ! [X0] : reflexive_relstr(boole_POSet(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_93])]) ).
fof(f2203,plain,
( ~ reflexive_relstr(boole_POSet(sK5))
| spl34_301 ),
inference(avatar_component_clause,[],[f2201]) ).
fof(f2201,plain,
( spl34_301
<=> reflexive_relstr(boole_POSet(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_301])]) ).
fof(f2220,plain,
( spl34_300
| ~ spl34_301
| ~ spl34_302
| ~ spl34_303
| ~ spl34_304
| ~ spl34_305
| spl34_2
| ~ spl34_5
| ~ spl34_6
| ~ spl34_8
| ~ spl34_197
| ~ spl34_7
| ~ spl34_89
| ~ spl34_135
| ~ spl34_144
| ~ spl34_210 ),
inference(avatar_split_clause,[],[f1683,f1673,f1206,f1170,f962,f552,f1548,f557,f547,f542,f527,f2217,f2213,f2209,f2205,f2201,f2197]) ).
fof(f527,plain,
( spl34_2
<=> empty(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_2])]) ).
fof(f542,plain,
( spl34_5
<=> filtered_subset(sK6,boole_POSet(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_5])]) ).
fof(f547,plain,
( spl34_6
<=> upper_relstr_subset(sK6,boole_POSet(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_6])]) ).
fof(f557,plain,
( spl34_8
<=> element(sK6,powerset(the_carrier(boole_POSet(sK5)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_8])]) ).
fof(f1548,plain,
( spl34_197
<=> in(sK33,sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_197])]) ).
fof(f552,plain,
( spl34_7
<=> proper_element(sK6,powerset(the_carrier(boole_POSet(sK5)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_7])]) ).
fof(f962,plain,
( spl34_89
<=> empty(sK33) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_89])]) ).
fof(f1170,plain,
( spl34_135
<=> ! [X0] : empty_set = bottom_of_relstr(boole_POSet(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_135])]) ).
fof(f1206,plain,
( spl34_144
<=> ! [X0] :
( empty_set = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_144])]) ).
fof(f1673,plain,
( spl34_210
<=> ! [X0,X1] :
( ~ in(bottom_of_relstr(X0),X1)
| ~ proper_element(X1,powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ upper_relstr_subset(X1,X0)
| ~ filtered_subset(X1,X0)
| empty(X1)
| ~ rel_str(X0)
| ~ lower_bounded_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_210])]) ).
fof(f1683,plain,
( ~ in(sK33,sK6)
| ~ element(sK6,powerset(the_carrier(boole_POSet(sK5))))
| ~ upper_relstr_subset(sK6,boole_POSet(sK5))
| ~ filtered_subset(sK6,boole_POSet(sK5))
| empty(sK6)
| ~ rel_str(boole_POSet(sK5))
| ~ lower_bounded_relstr(boole_POSet(sK5))
| ~ antisymmetric_relstr(boole_POSet(sK5))
| ~ transitive_relstr(boole_POSet(sK5))
| ~ reflexive_relstr(boole_POSet(sK5))
| empty_carrier(boole_POSet(sK5))
| ~ spl34_7
| ~ spl34_89
| ~ spl34_135
| ~ spl34_144
| ~ spl34_210 ),
inference(forward_demodulation,[],[f1682,f1234]) ).
fof(f1234,plain,
( empty_set = sK33
| ~ spl34_89
| ~ spl34_144 ),
inference(resolution,[],[f1207,f964]) ).
fof(f964,plain,
( empty(sK33)
| ~ spl34_89 ),
inference(avatar_component_clause,[],[f962]) ).
fof(f1207,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = X0 )
| ~ spl34_144 ),
inference(avatar_component_clause,[],[f1206]) ).
fof(f1682,plain,
( ~ in(empty_set,sK6)
| ~ element(sK6,powerset(the_carrier(boole_POSet(sK5))))
| ~ upper_relstr_subset(sK6,boole_POSet(sK5))
| ~ filtered_subset(sK6,boole_POSet(sK5))
| empty(sK6)
| ~ rel_str(boole_POSet(sK5))
| ~ lower_bounded_relstr(boole_POSet(sK5))
| ~ antisymmetric_relstr(boole_POSet(sK5))
| ~ transitive_relstr(boole_POSet(sK5))
| ~ reflexive_relstr(boole_POSet(sK5))
| empty_carrier(boole_POSet(sK5))
| ~ spl34_7
| ~ spl34_135
| ~ spl34_210 ),
inference(forward_demodulation,[],[f1680,f1171]) ).
fof(f1171,plain,
( ! [X0] : empty_set = bottom_of_relstr(boole_POSet(X0))
| ~ spl34_135 ),
inference(avatar_component_clause,[],[f1170]) ).
fof(f1680,plain,
( ~ in(bottom_of_relstr(boole_POSet(sK5)),sK6)
| ~ element(sK6,powerset(the_carrier(boole_POSet(sK5))))
| ~ upper_relstr_subset(sK6,boole_POSet(sK5))
| ~ filtered_subset(sK6,boole_POSet(sK5))
| empty(sK6)
| ~ rel_str(boole_POSet(sK5))
| ~ lower_bounded_relstr(boole_POSet(sK5))
| ~ antisymmetric_relstr(boole_POSet(sK5))
| ~ transitive_relstr(boole_POSet(sK5))
| ~ reflexive_relstr(boole_POSet(sK5))
| empty_carrier(boole_POSet(sK5))
| ~ spl34_7
| ~ spl34_210 ),
inference(resolution,[],[f1674,f554]) ).
fof(f554,plain,
( proper_element(sK6,powerset(the_carrier(boole_POSet(sK5))))
| ~ spl34_7 ),
inference(avatar_component_clause,[],[f552]) ).
fof(f1674,plain,
( ! [X0,X1] :
( ~ proper_element(X1,powerset(the_carrier(X0)))
| ~ in(bottom_of_relstr(X0),X1)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ upper_relstr_subset(X1,X0)
| ~ filtered_subset(X1,X0)
| empty(X1)
| ~ rel_str(X0)
| ~ lower_bounded_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) )
| ~ spl34_210 ),
inference(avatar_component_clause,[],[f1673]) ).
fof(f2183,plain,
( ~ spl34_59
| spl34_299
| ~ spl34_61
| ~ spl34_198 ),
inference(avatar_split_clause,[],[f1598,f1585,f822,f2180,f812]) ).
fof(f812,plain,
( spl34_59
<=> rel_str(sK30) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_59])]) ).
fof(f2180,plain,
( spl34_299
<=> sK30 = rel_str_of(the_carrier(sK30),the_InternalRel(sK30)) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_299])]) ).
fof(f822,plain,
( spl34_61
<=> strict_rel_str(sK30) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_61])]) ).
fof(f1585,plain,
( spl34_198
<=> ! [X0] :
( rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0
| ~ strict_rel_str(X0)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_198])]) ).
fof(f1598,plain,
( sK30 = rel_str_of(the_carrier(sK30),the_InternalRel(sK30))
| ~ rel_str(sK30)
| ~ spl34_61
| ~ spl34_198 ),
inference(resolution,[],[f1586,f824]) ).
fof(f824,plain,
( strict_rel_str(sK30)
| ~ spl34_61 ),
inference(avatar_component_clause,[],[f822]) ).
fof(f1586,plain,
( ! [X0] :
( ~ strict_rel_str(X0)
| rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0
| ~ rel_str(X0) )
| ~ spl34_198 ),
inference(avatar_component_clause,[],[f1585]) ).
fof(f2174,plain,
( ~ spl34_49
| spl34_298
| ~ spl34_51
| ~ spl34_198 ),
inference(avatar_split_clause,[],[f1597,f1585,f772,f2171,f762]) ).
fof(f762,plain,
( spl34_49
<=> rel_str(sK29) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_49])]) ).
fof(f2171,plain,
( spl34_298
<=> sK29 = rel_str_of(the_carrier(sK29),the_InternalRel(sK29)) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_298])]) ).
fof(f772,plain,
( spl34_51
<=> strict_rel_str(sK29) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_51])]) ).
fof(f1597,plain,
( sK29 = rel_str_of(the_carrier(sK29),the_InternalRel(sK29))
| ~ rel_str(sK29)
| ~ spl34_51
| ~ spl34_198 ),
inference(resolution,[],[f1586,f774]) ).
fof(f774,plain,
( strict_rel_str(sK29)
| ~ spl34_51 ),
inference(avatar_component_clause,[],[f772]) ).
fof(f2165,plain,
( ~ spl34_40
| spl34_297
| ~ spl34_42
| ~ spl34_198 ),
inference(avatar_split_clause,[],[f1596,f1585,f727,f2162,f717]) ).
fof(f717,plain,
( spl34_40
<=> rel_str(sK28) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_40])]) ).
fof(f2162,plain,
( spl34_297
<=> sK28 = rel_str_of(the_carrier(sK28),the_InternalRel(sK28)) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_297])]) ).
fof(f727,plain,
( spl34_42
<=> strict_rel_str(sK28) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_42])]) ).
fof(f1596,plain,
( sK28 = rel_str_of(the_carrier(sK28),the_InternalRel(sK28))
| ~ rel_str(sK28)
| ~ spl34_42
| ~ spl34_198 ),
inference(resolution,[],[f1586,f729]) ).
fof(f729,plain,
( strict_rel_str(sK28)
| ~ spl34_42 ),
inference(avatar_component_clause,[],[f727]) ).
fof(f2156,plain,
( ~ spl34_33
| spl34_296
| ~ spl34_35
| ~ spl34_198 ),
inference(avatar_split_clause,[],[f1595,f1585,f692,f2153,f682]) ).
fof(f682,plain,
( spl34_33
<=> rel_str(sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_33])]) ).
fof(f2153,plain,
( spl34_296
<=> sK27 = rel_str_of(the_carrier(sK27),the_InternalRel(sK27)) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_296])]) ).
fof(f692,plain,
( spl34_35
<=> strict_rel_str(sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_35])]) ).
fof(f1595,plain,
( sK27 = rel_str_of(the_carrier(sK27),the_InternalRel(sK27))
| ~ rel_str(sK27)
| ~ spl34_35
| ~ spl34_198 ),
inference(resolution,[],[f1586,f694]) ).
fof(f694,plain,
( strict_rel_str(sK27)
| ~ spl34_35 ),
inference(avatar_component_clause,[],[f692]) ).
fof(f2151,plain,
( ~ spl34_295
| ~ spl34_265
| ~ spl34_283 ),
inference(avatar_split_clause,[],[f2104,f2082,f1981,f2148]) ).
fof(f2148,plain,
( spl34_295
<=> in(the_carrier(boole_POSet(sK5)),sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_295])]) ).
fof(f1981,plain,
( spl34_265
<=> ! [X0] :
( ~ in(X0,sK6)
| in(X0,the_carrier(boole_POSet(sK5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_265])]) ).
fof(f2082,plain,
( spl34_283
<=> ! [X0] :
( ~ in(X0,sK6)
| ~ in(the_carrier(boole_POSet(sK5)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_283])]) ).
fof(f2104,plain,
( ~ in(the_carrier(boole_POSet(sK5)),sK6)
| ~ spl34_265
| ~ spl34_283 ),
inference(duplicate_literal_removal,[],[f2103]) ).
fof(f2103,plain,
( ~ in(the_carrier(boole_POSet(sK5)),sK6)
| ~ in(the_carrier(boole_POSet(sK5)),sK6)
| ~ spl34_265
| ~ spl34_283 ),
inference(resolution,[],[f2083,f1982]) ).
fof(f1982,plain,
( ! [X0] :
( in(X0,the_carrier(boole_POSet(sK5)))
| ~ in(X0,sK6) )
| ~ spl34_265 ),
inference(avatar_component_clause,[],[f1981]) ).
fof(f2083,plain,
( ! [X0] :
( ~ in(the_carrier(boole_POSet(sK5)),X0)
| ~ in(X0,sK6) )
| ~ spl34_283 ),
inference(avatar_component_clause,[],[f2082]) ).
fof(f2142,plain,
( ~ spl34_29
| spl34_294
| ~ spl34_31
| ~ spl34_198 ),
inference(avatar_split_clause,[],[f1594,f1585,f672,f2139,f662]) ).
fof(f662,plain,
( spl34_29
<=> rel_str(sK26) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_29])]) ).
fof(f2139,plain,
( spl34_294
<=> sK26 = rel_str_of(the_carrier(sK26),the_InternalRel(sK26)) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_294])]) ).
fof(f672,plain,
( spl34_31
<=> strict_rel_str(sK26) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_31])]) ).
fof(f1594,plain,
( sK26 = rel_str_of(the_carrier(sK26),the_InternalRel(sK26))
| ~ rel_str(sK26)
| ~ spl34_31
| ~ spl34_198 ),
inference(resolution,[],[f1586,f674]) ).
fof(f674,plain,
( strict_rel_str(sK26)
| ~ spl34_31 ),
inference(avatar_component_clause,[],[f672]) ).
fof(f2133,plain,
( ~ spl34_17
| spl34_293
| ~ spl34_20
| ~ spl34_198 ),
inference(avatar_split_clause,[],[f1593,f1585,f617,f2130,f602]) ).
fof(f602,plain,
( spl34_17
<=> rel_str(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_17])]) ).
fof(f2130,plain,
( spl34_293
<=> sK25 = rel_str_of(the_carrier(sK25),the_InternalRel(sK25)) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_293])]) ).
fof(f617,plain,
( spl34_20
<=> strict_rel_str(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_20])]) ).
fof(f1593,plain,
( sK25 = rel_str_of(the_carrier(sK25),the_InternalRel(sK25))
| ~ rel_str(sK25)
| ~ spl34_20
| ~ spl34_198 ),
inference(resolution,[],[f1586,f619]) ).
fof(f619,plain,
( strict_rel_str(sK25)
| ~ spl34_20 ),
inference(avatar_component_clause,[],[f617]) ).
fof(f2128,plain,
( spl34_292
| ~ spl34_164
| ~ spl34_196 ),
inference(avatar_split_clause,[],[f1575,f1535,f1326,f2126]) ).
fof(f2126,plain,
( spl34_292
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK10(X1))
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_292])]) ).
fof(f1326,plain,
( spl34_164
<=> ! [X0] :
( element(sK10(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_164])]) ).
fof(f1535,plain,
( spl34_196
<=> ! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_196])]) ).
fof(f1575,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK10(X1))
| empty(X1) )
| ~ spl34_164
| ~ spl34_196 ),
inference(resolution,[],[f1536,f1327]) ).
fof(f1327,plain,
( ! [X0] :
( element(sK10(X0),powerset(X0))
| empty(X0) )
| ~ spl34_164 ),
inference(avatar_component_clause,[],[f1326]) ).
fof(f1536,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| element(X0,X2)
| ~ in(X0,X1) )
| ~ spl34_196 ),
inference(avatar_component_clause,[],[f1535]) ).
fof(f2124,plain,
( spl34_291
| ~ spl34_163
| ~ spl34_196 ),
inference(avatar_split_clause,[],[f1574,f1535,f1322,f2122]) ).
fof(f2122,plain,
( spl34_291
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK9(X1))
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_291])]) ).
fof(f1322,plain,
( spl34_163
<=> ! [X0] :
( element(sK9(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_163])]) ).
fof(f1574,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK9(X1))
| empty(X1) )
| ~ spl34_163
| ~ spl34_196 ),
inference(resolution,[],[f1536,f1323]) ).
fof(f1323,plain,
( ! [X0] :
( element(sK9(X0),powerset(X0))
| empty(X0) )
| ~ spl34_163 ),
inference(avatar_component_clause,[],[f1322]) ).
fof(f2120,plain,
( spl34_290
| ~ spl34_161
| ~ spl34_196 ),
inference(avatar_split_clause,[],[f1573,f1535,f1313,f2118]) ).
fof(f2118,plain,
( spl34_290
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK8(X1))
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_290])]) ).
fof(f1313,plain,
( spl34_161
<=> ! [X0] :
( element(sK8(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_161])]) ).
fof(f1573,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK8(X1))
| empty(X1) )
| ~ spl34_161
| ~ spl34_196 ),
inference(resolution,[],[f1536,f1314]) ).
fof(f1314,plain,
( ! [X0] :
( element(sK8(X0),powerset(X0))
| empty(X0) )
| ~ spl34_161 ),
inference(avatar_component_clause,[],[f1313]) ).
fof(f2116,plain,
( spl34_289
| ~ spl34_168
| ~ spl34_196 ),
inference(avatar_split_clause,[],[f1570,f1535,f1342,f2114]) ).
fof(f2114,plain,
( spl34_289
<=> ! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_289])]) ).
fof(f1342,plain,
( spl34_168
<=> ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_168])]) ).
fof(f1570,plain,
( ! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,X1) )
| ~ spl34_168
| ~ spl34_196 ),
inference(resolution,[],[f1536,f1343]) ).
fof(f1343,plain,
( ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) )
| ~ spl34_168 ),
inference(avatar_component_clause,[],[f1342]) ).
fof(f2112,plain,
( spl34_288
| ~ spl34_177
| ~ spl34_188 ),
inference(avatar_split_clause,[],[f1499,f1487,f1392,f2110]) ).
fof(f2110,plain,
( spl34_288
<=> ! [X0,X1] :
( ~ empty(the_carrier(X0))
| ~ in(X1,sK12(X0))
| ~ sP4(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_288])]) ).
fof(f1392,plain,
( spl34_177
<=> ! [X0] :
( element(sK12(X0),powerset(the_carrier(X0)))
| ~ sP4(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_177])]) ).
fof(f1487,plain,
( spl34_188
<=> ! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_188])]) ).
fof(f1499,plain,
( ! [X0,X1] :
( ~ empty(the_carrier(X0))
| ~ in(X1,sK12(X0))
| ~ sP4(X0) )
| ~ spl34_177
| ~ spl34_188 ),
inference(resolution,[],[f1488,f1393]) ).
fof(f1393,plain,
( ! [X0] :
( element(sK12(X0),powerset(the_carrier(X0)))
| ~ sP4(X0) )
| ~ spl34_177 ),
inference(avatar_component_clause,[],[f1392]) ).
fof(f1488,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X0,X1) )
| ~ spl34_188 ),
inference(avatar_component_clause,[],[f1487]) ).
fof(f2108,plain,
( spl34_287
| ~ spl34_184
| ~ spl34_187 ),
inference(avatar_split_clause,[],[f1492,f1483,f1420,f2106]) ).
fof(f2106,plain,
( spl34_287
<=> ! [X0] :
( ~ rel_str(X0)
| relation_of2(the_InternalRel(X0),the_carrier(X0),the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_287])]) ).
fof(f1420,plain,
( spl34_184
<=> ! [X2,X0,X1] :
( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_184])]) ).
fof(f1483,plain,
( spl34_187
<=> ! [X0] :
( relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_187])]) ).
fof(f1492,plain,
( ! [X0] :
( ~ rel_str(X0)
| relation_of2(the_InternalRel(X0),the_carrier(X0),the_carrier(X0)) )
| ~ spl34_184
| ~ spl34_187 ),
inference(resolution,[],[f1484,f1421]) ).
fof(f1421,plain,
( ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| relation_of2(X2,X0,X1) )
| ~ spl34_184 ),
inference(avatar_component_clause,[],[f1420]) ).
fof(f1484,plain,
( ! [X0] :
( relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0) )
| ~ spl34_187 ),
inference(avatar_component_clause,[],[f1483]) ).
fof(f2098,plain,
( spl34_286
| ~ spl34_155
| ~ spl34_196 ),
inference(avatar_split_clause,[],[f1581,f1535,f1263,f2096]) ).
fof(f2096,plain,
( spl34_286
<=> ! [X0,X1] :
( element(X0,powerset(X1))
| ~ in(X0,sK17(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_286])]) ).
fof(f1263,plain,
( spl34_155
<=> ! [X0] : element(sK17(X0),powerset(powerset(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_155])]) ).
fof(f1581,plain,
( ! [X0,X1] :
( element(X0,powerset(X1))
| ~ in(X0,sK17(X1)) )
| ~ spl34_155
| ~ spl34_196 ),
inference(resolution,[],[f1536,f1264]) ).
fof(f1264,plain,
( ! [X0] : element(sK17(X0),powerset(powerset(X0)))
| ~ spl34_155 ),
inference(avatar_component_clause,[],[f1263]) ).
fof(f2094,plain,
( spl34_285
| ~ spl34_132
| ~ spl34_196 ),
inference(avatar_split_clause,[],[f1579,f1535,f1135,f2092]) ).
fof(f2092,plain,
( spl34_285
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK15(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_285])]) ).
fof(f1135,plain,
( spl34_132
<=> ! [X0] : element(sK15(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_132])]) ).
fof(f1579,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK15(powerset(X1))) )
| ~ spl34_132
| ~ spl34_196 ),
inference(resolution,[],[f1536,f1136]) ).
fof(f1136,plain,
( ! [X0] : element(sK15(X0),X0)
| ~ spl34_132 ),
inference(avatar_component_clause,[],[f1135]) ).
fof(f2089,plain,
( ~ spl34_78
| spl34_79
| ~ spl34_80
| spl34_284
| ~ spl34_85
| ~ spl34_192 ),
inference(avatar_split_clause,[],[f1557,f1519,f942,f2086,f917,f912,f907]) ).
fof(f907,plain,
( spl34_78
<=> rel_str(sK32) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_78])]) ).
fof(f912,plain,
( spl34_79
<=> empty_carrier(sK32) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_79])]) ).
fof(f917,plain,
( spl34_80
<=> reflexive_relstr(sK32) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_80])]) ).
fof(f2086,plain,
( spl34_284
<=> join_complete_relstr(sK32) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_284])]) ).
fof(f942,plain,
( spl34_85
<=> complete_relstr(sK32) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_85])]) ).
fof(f1519,plain,
( spl34_192
<=> ! [X0] :
( join_complete_relstr(X0)
| ~ complete_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_192])]) ).
fof(f1557,plain,
( join_complete_relstr(sK32)
| ~ reflexive_relstr(sK32)
| empty_carrier(sK32)
| ~ rel_str(sK32)
| ~ spl34_85
| ~ spl34_192 ),
inference(resolution,[],[f1520,f944]) ).
fof(f944,plain,
( complete_relstr(sK32)
| ~ spl34_85 ),
inference(avatar_component_clause,[],[f942]) ).
fof(f1520,plain,
( ! [X0] :
( ~ complete_relstr(X0)
| join_complete_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) )
| ~ spl34_192 ),
inference(avatar_component_clause,[],[f1519]) ).
fof(f2084,plain,
( spl34_283
| ~ spl34_156
| ~ spl34_265 ),
inference(avatar_split_clause,[],[f2014,f1981,f1267,f2082]) ).
fof(f1267,plain,
( spl34_156
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_156])]) ).
fof(f2014,plain,
( ! [X0] :
( ~ in(X0,sK6)
| ~ in(the_carrier(boole_POSet(sK5)),X0) )
| ~ spl34_156
| ~ spl34_265 ),
inference(resolution,[],[f1982,f1268]) ).
fof(f1268,plain,
( ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) )
| ~ spl34_156 ),
inference(avatar_component_clause,[],[f1267]) ).
fof(f2079,plain,
( ~ spl34_49
| spl34_50
| ~ spl34_52
| spl34_282
| ~ spl34_57
| ~ spl34_192 ),
inference(avatar_split_clause,[],[f1555,f1519,f802,f2076,f777,f767,f762]) ).
fof(f767,plain,
( spl34_50
<=> empty_carrier(sK29) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_50])]) ).
fof(f777,plain,
( spl34_52
<=> reflexive_relstr(sK29) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_52])]) ).
fof(f2076,plain,
( spl34_282
<=> join_complete_relstr(sK29) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_282])]) ).
fof(f802,plain,
( spl34_57
<=> complete_relstr(sK29) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_57])]) ).
fof(f1555,plain,
( join_complete_relstr(sK29)
| ~ reflexive_relstr(sK29)
| empty_carrier(sK29)
| ~ rel_str(sK29)
| ~ spl34_57
| ~ spl34_192 ),
inference(resolution,[],[f1520,f804]) ).
fof(f804,plain,
( complete_relstr(sK29)
| ~ spl34_57 ),
inference(avatar_component_clause,[],[f802]) ).
fof(f2073,plain,
( ~ spl34_40
| spl34_41
| ~ spl34_43
| spl34_281
| ~ spl34_48
| ~ spl34_192 ),
inference(avatar_split_clause,[],[f1554,f1519,f757,f2070,f732,f722,f717]) ).
fof(f722,plain,
( spl34_41
<=> empty_carrier(sK28) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_41])]) ).
fof(f732,plain,
( spl34_43
<=> reflexive_relstr(sK28) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_43])]) ).
fof(f2070,plain,
( spl34_281
<=> join_complete_relstr(sK28) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_281])]) ).
fof(f757,plain,
( spl34_48
<=> complete_relstr(sK28) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_48])]) ).
fof(f1554,plain,
( join_complete_relstr(sK28)
| ~ reflexive_relstr(sK28)
| empty_carrier(sK28)
| ~ rel_str(sK28)
| ~ spl34_48
| ~ spl34_192 ),
inference(resolution,[],[f1520,f759]) ).
fof(f759,plain,
( complete_relstr(sK28)
| ~ spl34_48 ),
inference(avatar_component_clause,[],[f757]) ).
fof(f2067,plain,
( ~ spl34_33
| spl34_34
| ~ spl34_36
| spl34_280
| ~ spl34_39
| ~ spl34_192 ),
inference(avatar_split_clause,[],[f1553,f1519,f712,f2064,f697,f687,f682]) ).
fof(f687,plain,
( spl34_34
<=> empty_carrier(sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_34])]) ).
fof(f697,plain,
( spl34_36
<=> reflexive_relstr(sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_36])]) ).
fof(f2064,plain,
( spl34_280
<=> join_complete_relstr(sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_280])]) ).
fof(f712,plain,
( spl34_39
<=> complete_relstr(sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_39])]) ).
fof(f1553,plain,
( join_complete_relstr(sK27)
| ~ reflexive_relstr(sK27)
| empty_carrier(sK27)
| ~ rel_str(sK27)
| ~ spl34_39
| ~ spl34_192 ),
inference(resolution,[],[f1520,f714]) ).
fof(f714,plain,
( complete_relstr(sK27)
| ~ spl34_39 ),
inference(avatar_component_clause,[],[f712]) ).
fof(f2062,plain,
( ~ spl34_78
| spl34_79
| ~ spl34_80
| spl34_279
| ~ spl34_85
| ~ spl34_191 ),
inference(avatar_split_clause,[],[f1546,f1515,f942,f2059,f917,f912,f907]) ).
fof(f2059,plain,
( spl34_279
<=> up_complete_relstr(sK32) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_279])]) ).
fof(f1515,plain,
( spl34_191
<=> ! [X0] :
( up_complete_relstr(X0)
| ~ complete_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_191])]) ).
fof(f1546,plain,
( up_complete_relstr(sK32)
| ~ reflexive_relstr(sK32)
| empty_carrier(sK32)
| ~ rel_str(sK32)
| ~ spl34_85
| ~ spl34_191 ),
inference(resolution,[],[f1516,f944]) ).
fof(f1516,plain,
( ! [X0] :
( ~ complete_relstr(X0)
| up_complete_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) )
| ~ spl34_191 ),
inference(avatar_component_clause,[],[f1515]) ).
fof(f2057,plain,
( ~ spl34_49
| spl34_50
| ~ spl34_52
| spl34_278
| ~ spl34_57
| ~ spl34_191 ),
inference(avatar_split_clause,[],[f1544,f1515,f802,f2054,f777,f767,f762]) ).
fof(f2054,plain,
( spl34_278
<=> up_complete_relstr(sK29) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_278])]) ).
fof(f1544,plain,
( up_complete_relstr(sK29)
| ~ reflexive_relstr(sK29)
| empty_carrier(sK29)
| ~ rel_str(sK29)
| ~ spl34_57
| ~ spl34_191 ),
inference(resolution,[],[f1516,f804]) ).
fof(f2052,plain,
( ~ spl34_40
| spl34_41
| ~ spl34_43
| spl34_277
| ~ spl34_48
| ~ spl34_191 ),
inference(avatar_split_clause,[],[f1543,f1515,f757,f2049,f732,f722,f717]) ).
fof(f2049,plain,
( spl34_277
<=> up_complete_relstr(sK28) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_277])]) ).
fof(f1543,plain,
( up_complete_relstr(sK28)
| ~ reflexive_relstr(sK28)
| empty_carrier(sK28)
| ~ rel_str(sK28)
| ~ spl34_48
| ~ spl34_191 ),
inference(resolution,[],[f1516,f759]) ).
fof(f2047,plain,
( ~ spl34_33
| spl34_34
| ~ spl34_36
| spl34_276
| ~ spl34_39
| ~ spl34_191 ),
inference(avatar_split_clause,[],[f1542,f1515,f712,f2044,f697,f687,f682]) ).
fof(f2044,plain,
( spl34_276
<=> up_complete_relstr(sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_276])]) ).
fof(f1542,plain,
( up_complete_relstr(sK27)
| ~ reflexive_relstr(sK27)
| empty_carrier(sK27)
| ~ rel_str(sK27)
| ~ spl34_39
| ~ spl34_191 ),
inference(resolution,[],[f1516,f714]) ).
fof(f2037,plain,
( ~ spl34_49
| spl34_50
| ~ spl34_52
| spl34_275
| ~ spl34_58
| ~ spl34_189 ),
inference(avatar_split_clause,[],[f1538,f1506,f807,f2034,f777,f767,f762]) ).
fof(f2034,plain,
( spl34_275
<=> sP1(sK29) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_275])]) ).
fof(f807,plain,
( spl34_58
<=> trivial_carrier(sK29) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_58])]) ).
fof(f1506,plain,
( spl34_189
<=> ! [X0] :
( sP1(X0)
| ~ trivial_carrier(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_189])]) ).
fof(f1538,plain,
( sP1(sK29)
| ~ reflexive_relstr(sK29)
| empty_carrier(sK29)
| ~ rel_str(sK29)
| ~ spl34_58
| ~ spl34_189 ),
inference(resolution,[],[f1507,f809]) ).
fof(f809,plain,
( trivial_carrier(sK29)
| ~ spl34_58 ),
inference(avatar_component_clause,[],[f807]) ).
fof(f1507,plain,
( ! [X0] :
( ~ trivial_carrier(X0)
| sP1(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) )
| ~ spl34_189 ),
inference(avatar_component_clause,[],[f1506]) ).
fof(f2032,plain,
( spl34_274
| ~ spl34_168
| ~ spl34_188 ),
inference(avatar_split_clause,[],[f1493,f1487,f1342,f2030]) ).
fof(f2030,plain,
( spl34_274
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,X2)
| ~ subset(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_274])]) ).
fof(f1493,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,X2)
| ~ subset(X2,X0) )
| ~ spl34_168
| ~ spl34_188 ),
inference(resolution,[],[f1488,f1343]) ).
fof(f2028,plain,
( spl34_273
| ~ spl34_109
| ~ spl34_182 ),
inference(avatar_split_clause,[],[f1475,f1412,f1043,f2026]) ).
fof(f2026,plain,
( spl34_273
<=> ! [X0,X1] :
( empty(X0)
| empty(X1)
| sP0(cartesian_product2(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_273])]) ).
fof(f1043,plain,
( spl34_109
<=> ! [X0] :
( sP0(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_109])]) ).
fof(f1412,plain,
( spl34_182
<=> ! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_182])]) ).
fof(f1475,plain,
( ! [X0,X1] :
( empty(X0)
| empty(X1)
| sP0(cartesian_product2(X1,X0)) )
| ~ spl34_109
| ~ spl34_182 ),
inference(resolution,[],[f1413,f1044]) ).
fof(f1044,plain,
( ! [X0] :
( empty(X0)
| sP0(X0) )
| ~ spl34_109 ),
inference(avatar_component_clause,[],[f1043]) ).
fof(f1413,plain,
( ! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) )
| ~ spl34_182 ),
inference(avatar_component_clause,[],[f1412]) ).
fof(f2024,plain,
( spl34_272
| ~ spl34_171
| ~ spl34_177 ),
inference(avatar_split_clause,[],[f1460,f1392,f1367,f2022]) ).
fof(f2022,plain,
( spl34_272
<=> ! [X0] :
( ~ sP4(X0)
| finite(sK12(X0))
| ~ finite(the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_272])]) ).
fof(f1367,plain,
( spl34_171
<=> ! [X0,X1] :
( finite(X1)
| ~ element(X1,powerset(X0))
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_171])]) ).
fof(f1460,plain,
( ! [X0] :
( ~ sP4(X0)
| finite(sK12(X0))
| ~ finite(the_carrier(X0)) )
| ~ spl34_171
| ~ spl34_177 ),
inference(resolution,[],[f1393,f1368]) ).
fof(f1368,plain,
( ! [X0,X1] :
( ~ element(X1,powerset(X0))
| finite(X1)
| ~ finite(X0) )
| ~ spl34_171 ),
inference(avatar_component_clause,[],[f1367]) ).
fof(f2020,plain,
( spl34_271
| ~ spl34_89
| ~ spl34_135
| ~ spl34_144
| ~ spl34_165 ),
inference(avatar_split_clause,[],[f1355,f1330,f1206,f1170,f962,f2018]) ).
fof(f2018,plain,
( spl34_271
<=> ! [X0] :
( element(sK33,the_carrier(boole_POSet(X0)))
| ~ rel_str(boole_POSet(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_271])]) ).
fof(f1330,plain,
( spl34_165
<=> ! [X0] :
( element(bottom_of_relstr(X0),the_carrier(X0))
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_165])]) ).
fof(f1355,plain,
( ! [X0] :
( element(sK33,the_carrier(boole_POSet(X0)))
| ~ rel_str(boole_POSet(X0)) )
| ~ spl34_89
| ~ spl34_135
| ~ spl34_144
| ~ spl34_165 ),
inference(forward_demodulation,[],[f1354,f1234]) ).
fof(f1354,plain,
( ! [X0] :
( element(empty_set,the_carrier(boole_POSet(X0)))
| ~ rel_str(boole_POSet(X0)) )
| ~ spl34_135
| ~ spl34_165 ),
inference(superposition,[],[f1331,f1171]) ).
fof(f1331,plain,
( ! [X0] :
( element(bottom_of_relstr(X0),the_carrier(X0))
| ~ rel_str(X0) )
| ~ spl34_165 ),
inference(avatar_component_clause,[],[f1330]) ).
fof(f2003,plain,
( spl34_270
| ~ spl34_132
| ~ spl34_188 ),
inference(avatar_split_clause,[],[f1500,f1487,f1135,f2001]) ).
fof(f2001,plain,
( spl34_270
<=> ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK15(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_270])]) ).
fof(f1500,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK15(powerset(X0))) )
| ~ spl34_132
| ~ spl34_188 ),
inference(resolution,[],[f1488,f1136]) ).
fof(f1999,plain,
( spl34_269
| ~ spl34_161
| ~ spl34_171 ),
inference(avatar_split_clause,[],[f1429,f1367,f1313,f1997]) ).
fof(f1997,plain,
( spl34_269
<=> ! [X0] :
( finite(sK8(X0))
| ~ finite(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_269])]) ).
fof(f1429,plain,
( ! [X0] :
( finite(sK8(X0))
| ~ finite(X0)
| empty(X0) )
| ~ spl34_161
| ~ spl34_171 ),
inference(resolution,[],[f1368,f1314]) ).
fof(f1995,plain,
( spl34_268
| ~ spl34_168
| ~ spl34_171 ),
inference(avatar_split_clause,[],[f1427,f1367,f1342,f1993]) ).
fof(f1993,plain,
( spl34_268
<=> ! [X0,X1] :
( finite(X0)
| ~ finite(X1)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_268])]) ).
fof(f1427,plain,
( ! [X0,X1] :
( finite(X0)
| ~ finite(X1)
| ~ subset(X0,X1) )
| ~ spl34_168
| ~ spl34_171 ),
inference(resolution,[],[f1368,f1343]) ).
fof(f1991,plain,
( spl34_267
| ~ spl34_109
| ~ spl34_169 ),
inference(avatar_split_clause,[],[f1358,f1346,f1043,f1989]) ).
fof(f1989,plain,
( spl34_267
<=> ! [X0,X1] :
( X0 = X1
| ~ empty(X0)
| sP0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_267])]) ).
fof(f1346,plain,
( spl34_169
<=> ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_169])]) ).
fof(f1358,plain,
( ! [X0,X1] :
( X0 = X1
| ~ empty(X0)
| sP0(X1) )
| ~ spl34_109
| ~ spl34_169 ),
inference(resolution,[],[f1347,f1044]) ).
fof(f1347,plain,
( ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) )
| ~ spl34_169 ),
inference(avatar_component_clause,[],[f1346]) ).
fof(f1987,plain,
( spl34_266
| ~ spl34_109
| ~ spl34_167 ),
inference(avatar_split_clause,[],[f1357,f1338,f1043,f1985]) ).
fof(f1985,plain,
( spl34_266
<=> ! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| sP0(sK13(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_266])]) ).
fof(f1338,plain,
( spl34_167
<=> ! [X0] :
( ~ empty(sK13(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_167])]) ).
fof(f1357,plain,
( ! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| sP0(sK13(X0)) )
| ~ spl34_109
| ~ spl34_167 ),
inference(resolution,[],[f1339,f1044]) ).
fof(f1339,plain,
( ! [X0] :
( ~ empty(sK13(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) )
| ~ spl34_167 ),
inference(avatar_component_clause,[],[f1338]) ).
fof(f1983,plain,
( spl34_221
| spl34_265
| ~ spl34_179
| ~ spl34_222 ),
inference(avatar_split_clause,[],[f1751,f1748,f1400,f1981,f1739]) ).
fof(f1739,plain,
( spl34_221
<=> empty(the_carrier(boole_POSet(sK5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_221])]) ).
fof(f1400,plain,
( spl34_179
<=> ! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_179])]) ).
fof(f1748,plain,
( spl34_222
<=> ! [X0] :
( element(X0,the_carrier(boole_POSet(sK5)))
| ~ in(X0,sK6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_222])]) ).
fof(f1751,plain,
( ! [X0] :
( ~ in(X0,sK6)
| empty(the_carrier(boole_POSet(sK5)))
| in(X0,the_carrier(boole_POSet(sK5))) )
| ~ spl34_179
| ~ spl34_222 ),
inference(resolution,[],[f1749,f1401]) ).
fof(f1401,plain,
( ! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) )
| ~ spl34_179 ),
inference(avatar_component_clause,[],[f1400]) ).
fof(f1749,plain,
( ! [X0] :
( element(X0,the_carrier(boole_POSet(sK5)))
| ~ in(X0,sK6) )
| ~ spl34_222 ),
inference(avatar_component_clause,[],[f1748]) ).
fof(f1979,plain,
( spl34_264
| ~ spl34_109
| ~ spl34_166 ),
inference(avatar_split_clause,[],[f1356,f1334,f1043,f1977]) ).
fof(f1977,plain,
( spl34_264
<=> ! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| sP0(the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_264])]) ).
fof(f1334,plain,
( spl34_166
<=> ! [X0] :
( ~ empty(the_carrier(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_166])]) ).
fof(f1356,plain,
( ! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| sP0(the_carrier(X0)) )
| ~ spl34_109
| ~ spl34_166 ),
inference(resolution,[],[f1335,f1044]) ).
fof(f1335,plain,
( ! [X0] :
( ~ empty(the_carrier(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) )
| ~ spl34_166 ),
inference(avatar_component_clause,[],[f1334]) ).
fof(f1965,plain,
( spl34_263
| ~ spl34_158
| ~ spl34_185 ),
inference(avatar_split_clause,[],[f1477,f1424,f1275,f1963]) ).
fof(f1963,plain,
( spl34_263
<=> ! [X0,X1] : relation_of2_as_subset(sK18(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_263])]) ).
fof(f1275,plain,
( spl34_158
<=> ! [X0,X1] : relation_of2(sK18(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_158])]) ).
fof(f1424,plain,
( spl34_185
<=> ! [X2,X0,X1] :
( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_185])]) ).
fof(f1477,plain,
( ! [X0,X1] : relation_of2_as_subset(sK18(X0,X1),X0,X1)
| ~ spl34_158
| ~ spl34_185 ),
inference(resolution,[],[f1425,f1276]) ).
fof(f1276,plain,
( ! [X0,X1] : relation_of2(sK18(X0,X1),X0,X1)
| ~ spl34_158 ),
inference(avatar_component_clause,[],[f1275]) ).
fof(f1425,plain,
( ! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| relation_of2_as_subset(X2,X0,X1) )
| ~ spl34_185 ),
inference(avatar_component_clause,[],[f1424]) ).
fof(f1961,plain,
( spl34_262
| ~ spl34_159
| ~ spl34_184 ),
inference(avatar_split_clause,[],[f1476,f1420,f1279,f1959]) ).
fof(f1959,plain,
( spl34_262
<=> ! [X0,X1] : relation_of2(sK19(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_262])]) ).
fof(f1279,plain,
( spl34_159
<=> ! [X0,X1] : relation_of2_as_subset(sK19(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_159])]) ).
fof(f1476,plain,
( ! [X0,X1] : relation_of2(sK19(X0,X1),X0,X1)
| ~ spl34_159
| ~ spl34_184 ),
inference(resolution,[],[f1421,f1280]) ).
fof(f1280,plain,
( ! [X0,X1] : relation_of2_as_subset(sK19(X0,X1),X0,X1)
| ~ spl34_159 ),
inference(avatar_component_clause,[],[f1279]) ).
fof(f1957,plain,
( spl34_261
| ~ spl34_158
| ~ spl34_181 ),
inference(avatar_split_clause,[],[f1474,f1408,f1275,f1955]) ).
fof(f1955,plain,
( spl34_261
<=> ! [X0] : rel_str(rel_str_of(X0,sK18(X0,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_261])]) ).
fof(f1408,plain,
( spl34_181
<=> ! [X0,X1] :
( rel_str(rel_str_of(X0,X1))
| ~ relation_of2(X1,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_181])]) ).
fof(f1474,plain,
( ! [X0] : rel_str(rel_str_of(X0,sK18(X0,X0)))
| ~ spl34_158
| ~ spl34_181 ),
inference(resolution,[],[f1409,f1276]) ).
fof(f1409,plain,
( ! [X0,X1] :
( ~ relation_of2(X1,X0,X0)
| rel_str(rel_str_of(X0,X1)) )
| ~ spl34_181 ),
inference(avatar_component_clause,[],[f1408]) ).
fof(f1953,plain,
( spl34_260
| ~ spl34_158
| ~ spl34_180 ),
inference(avatar_split_clause,[],[f1473,f1404,f1275,f1951]) ).
fof(f1951,plain,
( spl34_260
<=> ! [X0] : strict_rel_str(rel_str_of(X0,sK18(X0,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_260])]) ).
fof(f1404,plain,
( spl34_180
<=> ! [X0,X1] :
( strict_rel_str(rel_str_of(X0,X1))
| ~ relation_of2(X1,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_180])]) ).
fof(f1473,plain,
( ! [X0] : strict_rel_str(rel_str_of(X0,sK18(X0,X0)))
| ~ spl34_158
| ~ spl34_180 ),
inference(resolution,[],[f1405,f1276]) ).
fof(f1405,plain,
( ! [X0,X1] :
( ~ relation_of2(X1,X0,X0)
| strict_rel_str(rel_str_of(X0,X1)) )
| ~ spl34_180 ),
inference(avatar_component_clause,[],[f1404]) ).
fof(f1949,plain,
( spl34_259
| ~ spl34_132
| ~ spl34_179 ),
inference(avatar_split_clause,[],[f1468,f1400,f1135,f1947]) ).
fof(f1947,plain,
( spl34_259
<=> ! [X0] :
( empty(X0)
| in(sK15(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_259])]) ).
fof(f1468,plain,
( ! [X0] :
( empty(X0)
| in(sK15(X0),X0) )
| ~ spl34_132
| ~ spl34_179 ),
inference(resolution,[],[f1401,f1136]) ).
fof(f1944,plain,
( ~ spl34_33
| spl34_34
| spl34_258
| ~ spl34_39
| ~ spl34_174 ),
inference(avatar_split_clause,[],[f1451,f1379,f712,f1941,f687,f682]) ).
fof(f1941,plain,
( spl34_258
<=> with_infima_relstr(sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_258])]) ).
fof(f1379,plain,
( spl34_174
<=> ! [X0] :
( with_infima_relstr(X0)
| ~ complete_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_174])]) ).
fof(f1451,plain,
( with_infima_relstr(sK27)
| empty_carrier(sK27)
| ~ rel_str(sK27)
| ~ spl34_39
| ~ spl34_174 ),
inference(resolution,[],[f1380,f714]) ).
fof(f1380,plain,
( ! [X0] :
( ~ complete_relstr(X0)
| with_infima_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) )
| ~ spl34_174 ),
inference(avatar_component_clause,[],[f1379]) ).
fof(f1936,plain,
( ~ spl34_33
| spl34_34
| spl34_257
| ~ spl34_39
| ~ spl34_173 ),
inference(avatar_split_clause,[],[f1445,f1375,f712,f1933,f687,f682]) ).
fof(f1933,plain,
( spl34_257
<=> with_suprema_relstr(sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_257])]) ).
fof(f1375,plain,
( spl34_173
<=> ! [X0] :
( with_suprema_relstr(X0)
| ~ complete_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_173])]) ).
fof(f1445,plain,
( with_suprema_relstr(sK27)
| empty_carrier(sK27)
| ~ rel_str(sK27)
| ~ spl34_39
| ~ spl34_173 ),
inference(resolution,[],[f1376,f714]) ).
fof(f1376,plain,
( ! [X0] :
( ~ complete_relstr(X0)
| with_suprema_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) )
| ~ spl34_173 ),
inference(avatar_component_clause,[],[f1375]) ).
fof(f1929,plain,
( ~ spl34_49
| spl34_50
| spl34_256
| ~ spl34_57
| ~ spl34_172 ),
inference(avatar_split_clause,[],[f1441,f1371,f802,f1926,f767,f762]) ).
fof(f1926,plain,
( spl34_256
<=> bounded_relstr(sK29) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_256])]) ).
fof(f1371,plain,
( spl34_172
<=> ! [X0] :
( bounded_relstr(X0)
| ~ complete_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_172])]) ).
fof(f1441,plain,
( bounded_relstr(sK29)
| empty_carrier(sK29)
| ~ rel_str(sK29)
| ~ spl34_57
| ~ spl34_172 ),
inference(resolution,[],[f1372,f804]) ).
fof(f1372,plain,
( ! [X0] :
( ~ complete_relstr(X0)
| bounded_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) )
| ~ spl34_172 ),
inference(avatar_component_clause,[],[f1371]) ).
fof(f1922,plain,
( ~ spl34_40
| spl34_41
| spl34_255
| ~ spl34_48
| ~ spl34_172 ),
inference(avatar_split_clause,[],[f1440,f1371,f757,f1919,f722,f717]) ).
fof(f1919,plain,
( spl34_255
<=> bounded_relstr(sK28) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_255])]) ).
fof(f1440,plain,
( bounded_relstr(sK28)
| empty_carrier(sK28)
| ~ rel_str(sK28)
| ~ spl34_48
| ~ spl34_172 ),
inference(resolution,[],[f1372,f759]) ).
fof(f1917,plain,
( ~ spl34_254
| ~ spl34_156
| ~ spl34_237 ),
inference(avatar_split_clause,[],[f1844,f1835,f1267,f1914]) ).
fof(f1914,plain,
( spl34_254
<=> in(powerset(the_carrier(boole_POSet(sK5))),sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_254])]) ).
fof(f1835,plain,
( spl34_237
<=> in(sK6,powerset(the_carrier(boole_POSet(sK5)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_237])]) ).
fof(f1844,plain,
( ~ in(powerset(the_carrier(boole_POSet(sK5))),sK6)
| ~ spl34_156
| ~ spl34_237 ),
inference(resolution,[],[f1837,f1268]) ).
fof(f1837,plain,
( in(sK6,powerset(the_carrier(boole_POSet(sK5))))
| ~ spl34_237 ),
inference(avatar_component_clause,[],[f1835]) ).
fof(f1910,plain,
( ~ spl34_33
| spl34_34
| spl34_253
| ~ spl34_39
| ~ spl34_172 ),
inference(avatar_split_clause,[],[f1439,f1371,f712,f1907,f687,f682]) ).
fof(f1907,plain,
( spl34_253
<=> bounded_relstr(sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_253])]) ).
fof(f1439,plain,
( bounded_relstr(sK27)
| empty_carrier(sK27)
| ~ rel_str(sK27)
| ~ spl34_39
| ~ spl34_172 ),
inference(resolution,[],[f1372,f714]) ).
fof(f1905,plain,
( spl34_252
| ~ spl34_132
| ~ spl34_171 ),
inference(avatar_split_clause,[],[f1432,f1367,f1135,f1903]) ).
fof(f1903,plain,
( spl34_252
<=> ! [X0] :
( finite(sK15(powerset(X0)))
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_252])]) ).
fof(f1432,plain,
( ! [X0] :
( finite(sK15(powerset(X0)))
| ~ finite(X0) )
| ~ spl34_132
| ~ spl34_171 ),
inference(resolution,[],[f1368,f1136]) ).
fof(f1901,plain,
( spl34_251
| ~ spl34_109
| ~ spl34_145 ),
inference(avatar_split_clause,[],[f1236,f1210,f1043,f1899]) ).
fof(f1899,plain,
( spl34_251
<=> ! [X0] :
( ~ sP4(X0)
| sP0(sK12(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_251])]) ).
fof(f1210,plain,
( spl34_145
<=> ! [X0] :
( ~ empty(sK12(X0))
| ~ sP4(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_145])]) ).
fof(f1236,plain,
( ! [X0] :
( ~ sP4(X0)
| sP0(sK12(X0)) )
| ~ spl34_109
| ~ spl34_145 ),
inference(resolution,[],[f1211,f1044]) ).
fof(f1211,plain,
( ! [X0] :
( ~ empty(sK12(X0))
| ~ sP4(X0) )
| ~ spl34_145 ),
inference(avatar_component_clause,[],[f1210]) ).
fof(f1896,plain,
( spl34_250
| ~ spl34_109
| ~ spl34_144 ),
inference(avatar_split_clause,[],[f1230,f1206,f1043,f1894]) ).
fof(f1894,plain,
( spl34_250
<=> ! [X0] :
( empty_set = X0
| sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_250])]) ).
fof(f1230,plain,
( ! [X0] :
( empty_set = X0
| sP0(X0) )
| ~ spl34_109
| ~ spl34_144 ),
inference(resolution,[],[f1207,f1044]) ).
fof(f1892,plain,
( spl34_249
| ~ spl34_109
| ~ spl34_142 ),
inference(avatar_split_clause,[],[f1229,f1198,f1043,f1890]) ).
fof(f1890,plain,
( spl34_249
<=> ! [X0] :
( ~ one_sorted_str(X0)
| sP0(sK11(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_249])]) ).
fof(f1198,plain,
( spl34_142
<=> ! [X0] :
( ~ empty(sK11(X0))
| ~ one_sorted_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_142])]) ).
fof(f1229,plain,
( ! [X0] :
( ~ one_sorted_str(X0)
| sP0(sK11(X0)) )
| ~ spl34_109
| ~ spl34_142 ),
inference(resolution,[],[f1199,f1044]) ).
fof(f1199,plain,
( ! [X0] :
( ~ empty(sK11(X0))
| ~ one_sorted_str(X0) )
| ~ spl34_142 ),
inference(avatar_component_clause,[],[f1198]) ).
fof(f1888,plain,
( spl34_248
| ~ spl34_109
| ~ spl34_140 ),
inference(avatar_split_clause,[],[f1223,f1190,f1043,f1886]) ).
fof(f1886,plain,
( spl34_248
<=> ! [X0] :
( empty(X0)
| sP0(sK10(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_248])]) ).
fof(f1190,plain,
( spl34_140
<=> ! [X0] :
( ~ empty(sK10(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_140])]) ).
fof(f1223,plain,
( ! [X0] :
( empty(X0)
| sP0(sK10(X0)) )
| ~ spl34_109
| ~ spl34_140 ),
inference(resolution,[],[f1191,f1044]) ).
fof(f1191,plain,
( ! [X0] :
( ~ empty(sK10(X0))
| empty(X0) )
| ~ spl34_140 ),
inference(avatar_component_clause,[],[f1190]) ).
fof(f1884,plain,
( spl34_247
| ~ spl34_109
| ~ spl34_138 ),
inference(avatar_split_clause,[],[f1222,f1182,f1043,f1882]) ).
fof(f1882,plain,
( spl34_247
<=> ! [X0] :
( empty(X0)
| sP0(sK9(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_247])]) ).
fof(f1182,plain,
( spl34_138
<=> ! [X0] :
( ~ empty(sK9(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_138])]) ).
fof(f1222,plain,
( ! [X0] :
( empty(X0)
| sP0(sK9(X0)) )
| ~ spl34_109
| ~ spl34_138 ),
inference(resolution,[],[f1183,f1044]) ).
fof(f1183,plain,
( ! [X0] :
( ~ empty(sK9(X0))
| empty(X0) )
| ~ spl34_138 ),
inference(avatar_component_clause,[],[f1182]) ).
fof(f1880,plain,
( spl34_246
| ~ spl34_109
| ~ spl34_137 ),
inference(avatar_split_clause,[],[f1221,f1178,f1043,f1878]) ).
fof(f1878,plain,
( spl34_246
<=> ! [X0] :
( empty(X0)
| sP0(sK8(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_246])]) ).
fof(f1178,plain,
( spl34_137
<=> ! [X0] :
( ~ empty(sK8(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_137])]) ).
fof(f1221,plain,
( ! [X0] :
( empty(X0)
| sP0(sK8(X0)) )
| ~ spl34_109
| ~ spl34_137 ),
inference(resolution,[],[f1179,f1044]) ).
fof(f1179,plain,
( ! [X0] :
( ~ empty(sK8(X0))
| empty(X0) )
| ~ spl34_137 ),
inference(avatar_component_clause,[],[f1178]) ).
fof(f1876,plain,
( spl34_245
| ~ spl34_109
| ~ spl34_131 ),
inference(avatar_split_clause,[],[f1164,f1131,f1043,f1874]) ).
fof(f1874,plain,
( spl34_245
<=> ! [X0] :
( finite(X0)
| sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_245])]) ).
fof(f1131,plain,
( spl34_131
<=> ! [X0] :
( finite(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_131])]) ).
fof(f1164,plain,
( ! [X0] :
( finite(X0)
| sP0(X0) )
| ~ spl34_109
| ~ spl34_131 ),
inference(resolution,[],[f1132,f1044]) ).
fof(f1132,plain,
( ! [X0] :
( ~ empty(X0)
| finite(X0) )
| ~ spl34_131 ),
inference(avatar_component_clause,[],[f1131]) ).
fof(f1871,plain,
( spl34_244
| ~ spl34_109
| ~ spl34_213 ),
inference(avatar_split_clause,[],[f1713,f1703,f1043,f1869]) ).
fof(f1869,plain,
( spl34_244
<=> ! [X0] :
( sK33 = X0
| sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_244])]) ).
fof(f1703,plain,
( spl34_213
<=> ! [X0] :
( sK33 = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_213])]) ).
fof(f1713,plain,
( ! [X0] :
( sK33 = X0
| sP0(X0) )
| ~ spl34_109
| ~ spl34_213 ),
inference(resolution,[],[f1704,f1044]) ).
fof(f1704,plain,
( ! [X0] :
( ~ empty(X0)
| sK33 = X0 )
| ~ spl34_213 ),
inference(avatar_component_clause,[],[f1703]) ).
fof(f1867,plain,
( spl34_243
| ~ spl34_89
| ~ spl34_144 ),
inference(avatar_split_clause,[],[f1234,f1206,f962,f1864]) ).
fof(f1864,plain,
( spl34_243
<=> empty_set = sK33 ),
introduced(avatar_definition,[new_symbols(naming,[spl34_243])]) ).
fof(f1861,plain,
( spl34_242
| ~ spl34_105
| ~ spl34_131 ),
inference(avatar_split_clause,[],[f1167,f1131,f1027,f1859]) ).
fof(f1859,plain,
( spl34_242
<=> ! [X0] : finite(sK16(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_242])]) ).
fof(f1027,plain,
( spl34_105
<=> ! [X0] : empty(sK16(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_105])]) ).
fof(f1167,plain,
( ! [X0] : finite(sK16(X0))
| ~ spl34_105
| ~ spl34_131 ),
inference(resolution,[],[f1132,f1028]) ).
fof(f1028,plain,
( ! [X0] : empty(sK16(X0))
| ~ spl34_105 ),
inference(avatar_component_clause,[],[f1027]) ).
fof(f1857,plain,
( spl34_241
| ~ spl34_104
| ~ spl34_110 ),
inference(avatar_split_clause,[],[f1144,f1047,f1023,f1855]) ).
fof(f1855,plain,
( spl34_241
<=> ! [X0] : one_sorted_str(boole_POSet(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_241])]) ).
fof(f1047,plain,
( spl34_110
<=> ! [X0] :
( one_sorted_str(X0)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_110])]) ).
fof(f1144,plain,
( ! [X0] : one_sorted_str(boole_POSet(X0))
| ~ spl34_104
| ~ spl34_110 ),
inference(resolution,[],[f1048,f1024]) ).
fof(f1048,plain,
( ! [X0] :
( ~ rel_str(X0)
| one_sorted_str(X0) )
| ~ spl34_110 ),
inference(avatar_component_clause,[],[f1047]) ).
fof(f1853,plain,
( spl34_240
| ~ spl34_106
| ~ spl34_109 ),
inference(avatar_split_clause,[],[f1141,f1043,f1031,f1851]) ).
fof(f1851,plain,
( spl34_240
<=> ! [X0] : sP0(sK17(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_240])]) ).
fof(f1031,plain,
( spl34_106
<=> ! [X0] : ~ empty(sK17(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_106])]) ).
fof(f1141,plain,
( ! [X0] : sP0(sK17(X0))
| ~ spl34_106
| ~ spl34_109 ),
inference(resolution,[],[f1044,f1032]) ).
fof(f1032,plain,
( ! [X0] : ~ empty(sK17(X0))
| ~ spl34_106 ),
inference(avatar_component_clause,[],[f1031]) ).
fof(f1849,plain,
( spl34_239
| ~ spl34_90
| ~ spl34_109 ),
inference(avatar_split_clause,[],[f1138,f1043,f967,f1847]) ).
fof(f1847,plain,
( spl34_239
<=> ! [X0] : sP0(powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_239])]) ).
fof(f967,plain,
( spl34_90
<=> ! [X0] : ~ empty(powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_90])]) ).
fof(f1138,plain,
( ! [X0] : sP0(powerset(X0))
| ~ spl34_90
| ~ spl34_109 ),
inference(resolution,[],[f1044,f968]) ).
fof(f968,plain,
( ! [X0] : ~ empty(powerset(X0))
| ~ spl34_90 ),
inference(avatar_component_clause,[],[f967]) ).
fof(f1842,plain,
( spl34_237
| spl34_238
| ~ spl34_8
| ~ spl34_179 ),
inference(avatar_split_clause,[],[f1463,f1400,f557,f1839,f1835]) ).
fof(f1839,plain,
( spl34_238
<=> empty(powerset(the_carrier(boole_POSet(sK5)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_238])]) ).
fof(f1463,plain,
( empty(powerset(the_carrier(boole_POSet(sK5))))
| in(sK6,powerset(the_carrier(boole_POSet(sK5))))
| ~ spl34_8
| ~ spl34_179 ),
inference(resolution,[],[f1401,f559]) ).
fof(f559,plain,
( element(sK6,powerset(the_carrier(boole_POSet(sK5))))
| ~ spl34_8 ),
inference(avatar_component_clause,[],[f557]) ).
fof(f1831,plain,
( ~ spl34_4
| ~ spl34_220 ),
inference(avatar_contradiction_clause,[],[f1828]) ).
fof(f1828,plain,
( $false
| ~ spl34_4
| ~ spl34_220 ),
inference(resolution,[],[f1737,f539]) ).
fof(f539,plain,
( in(sK7,sK6)
| ~ spl34_4 ),
inference(avatar_component_clause,[],[f537]) ).
fof(f537,plain,
( spl34_4
<=> in(sK7,sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_4])]) ).
fof(f1737,plain,
( ! [X0] : ~ in(X0,sK6)
| ~ spl34_220 ),
inference(avatar_component_clause,[],[f1736]) ).
fof(f1736,plain,
( spl34_220
<=> ! [X0] : ~ in(X0,sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_220])]) ).
fof(f1830,plain,
( ~ spl34_197
| ~ spl34_220 ),
inference(avatar_contradiction_clause,[],[f1829]) ).
fof(f1829,plain,
( $false
| ~ spl34_197
| ~ spl34_220 ),
inference(resolution,[],[f1737,f1550]) ).
fof(f1550,plain,
( in(sK33,sK6)
| ~ spl34_197 ),
inference(avatar_component_clause,[],[f1548]) ).
fof(f1827,plain,
( spl34_236
| ~ spl34_109
| spl34_221 ),
inference(avatar_split_clause,[],[f1743,f1739,f1043,f1824]) ).
fof(f1824,plain,
( spl34_236
<=> sP0(the_carrier(boole_POSet(sK5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_236])]) ).
fof(f1743,plain,
( sP0(the_carrier(boole_POSet(sK5)))
| ~ spl34_109
| spl34_221 ),
inference(resolution,[],[f1741,f1044]) ).
fof(f1741,plain,
( ~ empty(the_carrier(boole_POSet(sK5)))
| spl34_221 ),
inference(avatar_component_clause,[],[f1739]) ).
fof(f1822,plain,
( spl34_235
| ~ spl34_89
| ~ spl34_131 ),
inference(avatar_split_clause,[],[f1168,f1131,f962,f1819]) ).
fof(f1819,plain,
( spl34_235
<=> finite(sK33) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_235])]) ).
fof(f1168,plain,
( finite(sK33)
| ~ spl34_89
| ~ spl34_131 ),
inference(resolution,[],[f1132,f964]) ).
fof(f1816,plain,
( spl34_234
| ~ spl34_9
| ~ spl34_131 ),
inference(avatar_split_clause,[],[f1165,f1131,f562,f1813]) ).
fof(f1813,plain,
( spl34_234
<=> finite(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_234])]) ).
fof(f562,plain,
( spl34_9
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_9])]) ).
fof(f1165,plain,
( finite(empty_set)
| ~ spl34_9
| ~ spl34_131 ),
inference(resolution,[],[f1132,f564]) ).
fof(f564,plain,
( empty(empty_set)
| ~ spl34_9 ),
inference(avatar_component_clause,[],[f562]) ).
fof(f1811,plain,
( spl34_233
| ~ spl34_78
| ~ spl34_110 ),
inference(avatar_split_clause,[],[f1153,f1047,f907,f1808]) ).
fof(f1808,plain,
( spl34_233
<=> one_sorted_str(sK32) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_233])]) ).
fof(f1153,plain,
( one_sorted_str(sK32)
| ~ spl34_78
| ~ spl34_110 ),
inference(resolution,[],[f1048,f909]) ).
fof(f909,plain,
( rel_str(sK32)
| ~ spl34_78 ),
inference(avatar_component_clause,[],[f907]) ).
fof(f1806,plain,
( spl34_232
| ~ spl34_73
| ~ spl34_110 ),
inference(avatar_split_clause,[],[f1152,f1047,f882,f1803]) ).
fof(f1803,plain,
( spl34_232
<=> one_sorted_str(sK31) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_232])]) ).
fof(f882,plain,
( spl34_73
<=> rel_str(sK31) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_73])]) ).
fof(f1152,plain,
( one_sorted_str(sK31)
| ~ spl34_73
| ~ spl34_110 ),
inference(resolution,[],[f1048,f884]) ).
fof(f884,plain,
( rel_str(sK31)
| ~ spl34_73 ),
inference(avatar_component_clause,[],[f882]) ).
fof(f1801,plain,
( spl34_231
| ~ spl34_59
| ~ spl34_110 ),
inference(avatar_split_clause,[],[f1151,f1047,f812,f1798]) ).
fof(f1798,plain,
( spl34_231
<=> one_sorted_str(sK30) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_231])]) ).
fof(f1151,plain,
( one_sorted_str(sK30)
| ~ spl34_59
| ~ spl34_110 ),
inference(resolution,[],[f1048,f814]) ).
fof(f814,plain,
( rel_str(sK30)
| ~ spl34_59 ),
inference(avatar_component_clause,[],[f812]) ).
fof(f1796,plain,
( spl34_230
| ~ spl34_49
| ~ spl34_110 ),
inference(avatar_split_clause,[],[f1150,f1047,f762,f1793]) ).
fof(f1793,plain,
( spl34_230
<=> one_sorted_str(sK29) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_230])]) ).
fof(f1150,plain,
( one_sorted_str(sK29)
| ~ spl34_49
| ~ spl34_110 ),
inference(resolution,[],[f1048,f764]) ).
fof(f764,plain,
( rel_str(sK29)
| ~ spl34_49 ),
inference(avatar_component_clause,[],[f762]) ).
fof(f1791,plain,
( spl34_229
| ~ spl34_40
| ~ spl34_110 ),
inference(avatar_split_clause,[],[f1149,f1047,f717,f1788]) ).
fof(f1788,plain,
( spl34_229
<=> one_sorted_str(sK28) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_229])]) ).
fof(f1149,plain,
( one_sorted_str(sK28)
| ~ spl34_40
| ~ spl34_110 ),
inference(resolution,[],[f1048,f719]) ).
fof(f719,plain,
( rel_str(sK28)
| ~ spl34_40 ),
inference(avatar_component_clause,[],[f717]) ).
fof(f1786,plain,
( spl34_228
| ~ spl34_33
| ~ spl34_110 ),
inference(avatar_split_clause,[],[f1148,f1047,f682,f1783]) ).
fof(f1783,plain,
( spl34_228
<=> one_sorted_str(sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_228])]) ).
fof(f1148,plain,
( one_sorted_str(sK27)
| ~ spl34_33
| ~ spl34_110 ),
inference(resolution,[],[f1048,f684]) ).
fof(f684,plain,
( rel_str(sK27)
| ~ spl34_33 ),
inference(avatar_component_clause,[],[f682]) ).
fof(f1776,plain,
( spl34_227
| ~ spl34_29
| ~ spl34_110 ),
inference(avatar_split_clause,[],[f1147,f1047,f662,f1773]) ).
fof(f1773,plain,
( spl34_227
<=> one_sorted_str(sK26) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_227])]) ).
fof(f1147,plain,
( one_sorted_str(sK26)
| ~ spl34_29
| ~ spl34_110 ),
inference(resolution,[],[f1048,f664]) ).
fof(f664,plain,
( rel_str(sK26)
| ~ spl34_29 ),
inference(avatar_component_clause,[],[f662]) ).
fof(f1771,plain,
( spl34_226
| ~ spl34_17
| ~ spl34_110 ),
inference(avatar_split_clause,[],[f1146,f1047,f602,f1768]) ).
fof(f1768,plain,
( spl34_226
<=> one_sorted_str(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_226])]) ).
fof(f1146,plain,
( one_sorted_str(sK25)
| ~ spl34_17
| ~ spl34_110 ),
inference(resolution,[],[f1048,f604]) ).
fof(f604,plain,
( rel_str(sK25)
| ~ spl34_17 ),
inference(avatar_component_clause,[],[f602]) ).
fof(f1766,plain,
( spl34_225
| ~ spl34_11
| ~ spl34_110 ),
inference(avatar_split_clause,[],[f1145,f1047,f572,f1763]) ).
fof(f1763,plain,
( spl34_225
<=> one_sorted_str(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_225])]) ).
fof(f572,plain,
( spl34_11
<=> rel_str(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_11])]) ).
fof(f1145,plain,
( one_sorted_str(sK21)
| ~ spl34_11
| ~ spl34_110 ),
inference(resolution,[],[f1048,f574]) ).
fof(f574,plain,
( rel_str(sK21)
| ~ spl34_11 ),
inference(avatar_component_clause,[],[f572]) ).
fof(f1761,plain,
( spl34_224
| spl34_13
| ~ spl34_109 ),
inference(avatar_split_clause,[],[f1143,f1043,f582,f1758]) ).
fof(f1758,plain,
( spl34_224
<=> sP0(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_224])]) ).
fof(f582,plain,
( spl34_13
<=> empty(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_13])]) ).
fof(f1143,plain,
( sP0(sK23)
| spl34_13
| ~ spl34_109 ),
inference(resolution,[],[f1044,f584]) ).
fof(f584,plain,
( ~ empty(sK23)
| spl34_13 ),
inference(avatar_component_clause,[],[f582]) ).
fof(f1756,plain,
( spl34_223
| spl34_12
| ~ spl34_109 ),
inference(avatar_split_clause,[],[f1142,f1043,f577,f1753]) ).
fof(f1753,plain,
( spl34_223
<=> sP0(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_223])]) ).
fof(f577,plain,
( spl34_12
<=> empty(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_12])]) ).
fof(f1142,plain,
( sP0(sK22)
| spl34_12
| ~ spl34_109 ),
inference(resolution,[],[f1044,f579]) ).
fof(f579,plain,
( ~ empty(sK22)
| spl34_12 ),
inference(avatar_component_clause,[],[f577]) ).
fof(f1750,plain,
( spl34_222
| ~ spl34_8
| ~ spl34_196 ),
inference(avatar_split_clause,[],[f1572,f1535,f557,f1748]) ).
fof(f1572,plain,
( ! [X0] :
( element(X0,the_carrier(boole_POSet(sK5)))
| ~ in(X0,sK6) )
| ~ spl34_8
| ~ spl34_196 ),
inference(resolution,[],[f1536,f559]) ).
fof(f1742,plain,
( spl34_220
| ~ spl34_221
| ~ spl34_8
| ~ spl34_188 ),
inference(avatar_split_clause,[],[f1494,f1487,f557,f1739,f1736]) ).
fof(f1494,plain,
( ! [X0] :
( ~ empty(the_carrier(boole_POSet(sK5)))
| ~ in(X0,sK6) )
| ~ spl34_8
| ~ spl34_188 ),
inference(resolution,[],[f1488,f559]) ).
fof(f1734,plain,
( spl34_219
| ~ spl34_146
| ~ spl34_212 ),
inference(avatar_split_clause,[],[f1700,f1685,f1214,f1732]) ).
fof(f1732,plain,
( spl34_219
<=> ! [X0] : element(sK33,powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_219])]) ).
fof(f1214,plain,
( spl34_146
<=> ! [X0] : element(sK16(X0),powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_146])]) ).
fof(f1685,plain,
( spl34_212
<=> ! [X0] : sK16(X0) = sK33 ),
introduced(avatar_definition,[new_symbols(naming,[spl34_212])]) ).
fof(f1700,plain,
( ! [X0] : element(sK33,powerset(X0))
| ~ spl34_146
| ~ spl34_212 ),
inference(superposition,[],[f1215,f1686]) ).
fof(f1686,plain,
( ! [X0] : sK16(X0) = sK33
| ~ spl34_212 ),
inference(avatar_component_clause,[],[f1685]) ).
fof(f1215,plain,
( ! [X0] : element(sK16(X0),powerset(X0))
| ~ spl34_146 ),
inference(avatar_component_clause,[],[f1214]) ).
fof(f1730,plain,
( spl34_218
| ~ spl34_3
| ~ spl34_105
| ~ spl34_144
| ~ spl34_146
| ~ spl34_162
| ~ spl34_179 ),
inference(avatar_split_clause,[],[f1472,f1400,f1317,f1214,f1206,f1027,f532,f1728]) ).
fof(f1728,plain,
( spl34_218
<=> ! [X0] :
( in(sK33,powerset(X0))
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_218])]) ).
fof(f532,plain,
( spl34_3
<=> empty(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_3])]) ).
fof(f1317,plain,
( spl34_162
<=> sK7 = sK33 ),
introduced(avatar_definition,[new_symbols(naming,[spl34_162])]) ).
fof(f1472,plain,
( ! [X0] :
( in(sK33,powerset(X0))
| empty(powerset(X0)) )
| ~ spl34_3
| ~ spl34_105
| ~ spl34_144
| ~ spl34_146
| ~ spl34_162
| ~ spl34_179 ),
inference(forward_demodulation,[],[f1471,f1319]) ).
fof(f1319,plain,
( sK7 = sK33
| ~ spl34_162 ),
inference(avatar_component_clause,[],[f1317]) ).
fof(f1471,plain,
( ! [X0] :
( in(sK7,powerset(X0))
| empty(powerset(X0)) )
| ~ spl34_3
| ~ spl34_105
| ~ spl34_144
| ~ spl34_146
| ~ spl34_179 ),
inference(forward_demodulation,[],[f1469,f1235]) ).
fof(f1235,plain,
( ! [X0] : sK7 = sK16(X0)
| ~ spl34_3
| ~ spl34_105
| ~ spl34_144 ),
inference(forward_demodulation,[],[f1233,f1232]) ).
fof(f1232,plain,
( empty_set = sK7
| ~ spl34_3
| ~ spl34_144 ),
inference(resolution,[],[f1207,f534]) ).
fof(f534,plain,
( empty(sK7)
| ~ spl34_3 ),
inference(avatar_component_clause,[],[f532]) ).
fof(f1233,plain,
( ! [X0] : empty_set = sK16(X0)
| ~ spl34_105
| ~ spl34_144 ),
inference(resolution,[],[f1207,f1028]) ).
fof(f1469,plain,
( ! [X0] :
( empty(powerset(X0))
| in(sK16(X0),powerset(X0)) )
| ~ spl34_146
| ~ spl34_179 ),
inference(resolution,[],[f1401,f1215]) ).
fof(f1726,plain,
( ~ spl34_216
| spl34_217
| ~ spl34_8
| ~ spl34_171 ),
inference(avatar_split_clause,[],[f1428,f1367,f557,f1723,f1719]) ).
fof(f1719,plain,
( spl34_216
<=> finite(the_carrier(boole_POSet(sK5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_216])]) ).
fof(f1723,plain,
( spl34_217
<=> finite(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_217])]) ).
fof(f1428,plain,
( finite(sK6)
| ~ finite(the_carrier(boole_POSet(sK5)))
| ~ spl34_8
| ~ spl34_171 ),
inference(resolution,[],[f1368,f559]) ).
fof(f1712,plain,
( spl34_214
| spl34_215
| ~ spl34_3
| ~ spl34_105
| ~ spl34_144
| ~ spl34_146
| ~ spl34_162
| ~ spl34_188 ),
inference(avatar_split_clause,[],[f1504,f1487,f1317,f1214,f1206,f1027,f532,f1710,f1707]) ).
fof(f1707,plain,
( spl34_214
<=> ! [X0] : ~ empty(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_214])]) ).
fof(f1710,plain,
( spl34_215
<=> ! [X1] : ~ in(X1,sK33) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_215])]) ).
fof(f1504,plain,
( ! [X0,X1] :
( ~ in(X1,sK33)
| ~ empty(X0) )
| ~ spl34_3
| ~ spl34_105
| ~ spl34_144
| ~ spl34_146
| ~ spl34_162
| ~ spl34_188 ),
inference(forward_demodulation,[],[f1503,f1319]) ).
fof(f1503,plain,
( ! [X0,X1] :
( ~ in(X1,sK7)
| ~ empty(X0) )
| ~ spl34_3
| ~ spl34_105
| ~ spl34_144
| ~ spl34_146
| ~ spl34_188 ),
inference(forward_demodulation,[],[f1501,f1235]) ).
fof(f1501,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK16(X0)) )
| ~ spl34_146
| ~ spl34_188 ),
inference(resolution,[],[f1488,f1215]) ).
fof(f1705,plain,
( spl34_213
| ~ spl34_3
| ~ spl34_162
| ~ spl34_169 ),
inference(avatar_split_clause,[],[f1363,f1346,f1317,f532,f1703]) ).
fof(f1363,plain,
( ! [X0] :
( sK33 = X0
| ~ empty(X0) )
| ~ spl34_3
| ~ spl34_162
| ~ spl34_169 ),
inference(forward_demodulation,[],[f1360,f1319]) ).
fof(f1360,plain,
( ! [X0] :
( sK7 = X0
| ~ empty(X0) )
| ~ spl34_3
| ~ spl34_169 ),
inference(resolution,[],[f1347,f534]) ).
fof(f1687,plain,
( spl34_212
| ~ spl34_162
| ~ spl34_207 ),
inference(avatar_split_clause,[],[f1647,f1644,f1317,f1685]) ).
fof(f1644,plain,
( spl34_207
<=> ! [X0] : sK7 = sK16(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_207])]) ).
fof(f1647,plain,
( ! [X0] : sK16(X0) = sK33
| ~ spl34_162
| ~ spl34_207 ),
inference(forward_demodulation,[],[f1645,f1319]) ).
fof(f1645,plain,
( ! [X0] : sK7 = sK16(X0)
| ~ spl34_207 ),
inference(avatar_component_clause,[],[f1644]) ).
fof(f1679,plain,
spl34_211,
inference(avatar_split_clause,[],[f414,f1677]) ).
fof(f1677,plain,
( spl34_211
<=> ! [X0,X1] :
( proper_element(X1,powerset(the_carrier(X0)))
| in(bottom_of_relstr(X0),X1)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ upper_relstr_subset(X1,X0)
| ~ filtered_subset(X1,X0)
| empty(X1)
| ~ rel_str(X0)
| ~ lower_bounded_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_211])]) ).
fof(f414,plain,
! [X0,X1] :
( proper_element(X1,powerset(the_carrier(X0)))
| in(bottom_of_relstr(X0),X1)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ upper_relstr_subset(X1,X0)
| ~ filtered_subset(X1,X0)
| empty(X1)
| ~ rel_str(X0)
| ~ lower_bounded_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f221]) ).
fof(f221,plain,
! [X0] :
( ! [X1] :
( ( ( proper_element(X1,powerset(the_carrier(X0)))
| in(bottom_of_relstr(X0),X1) )
& ( ~ in(bottom_of_relstr(X0),X1)
| ~ proper_element(X1,powerset(the_carrier(X0))) ) )
| ~ element(X1,powerset(the_carrier(X0)))
| ~ upper_relstr_subset(X1,X0)
| ~ filtered_subset(X1,X0)
| empty(X1) )
| ~ rel_str(X0)
| ~ lower_bounded_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(nnf_transformation,[],[f170]) ).
fof(f170,plain,
! [X0] :
( ! [X1] :
( ( proper_element(X1,powerset(the_carrier(X0)))
<=> ~ in(bottom_of_relstr(X0),X1) )
| ~ element(X1,powerset(the_carrier(X0)))
| ~ upper_relstr_subset(X1,X0)
| ~ filtered_subset(X1,X0)
| empty(X1) )
| ~ rel_str(X0)
| ~ lower_bounded_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f169]) ).
fof(f169,plain,
! [X0] :
( ! [X1] :
( ( proper_element(X1,powerset(the_carrier(X0)))
<=> ~ in(bottom_of_relstr(X0),X1) )
| ~ element(X1,powerset(the_carrier(X0)))
| ~ upper_relstr_subset(X1,X0)
| ~ filtered_subset(X1,X0)
| empty(X1) )
| ~ rel_str(X0)
| ~ lower_bounded_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f86]) ).
fof(f86,axiom,
! [X0] :
( ( rel_str(X0)
& lower_bounded_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( ( element(X1,powerset(the_carrier(X0)))
& upper_relstr_subset(X1,X0)
& filtered_subset(X1,X0)
& ~ empty(X1) )
=> ( proper_element(X1,powerset(the_carrier(X0)))
<=> ~ in(bottom_of_relstr(X0),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_waybel_7) ).
fof(f1675,plain,
spl34_210,
inference(avatar_split_clause,[],[f413,f1673]) ).
fof(f413,plain,
! [X0,X1] :
( ~ in(bottom_of_relstr(X0),X1)
| ~ proper_element(X1,powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ upper_relstr_subset(X1,X0)
| ~ filtered_subset(X1,X0)
| empty(X1)
| ~ rel_str(X0)
| ~ lower_bounded_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f221]) ).
fof(f1665,plain,
spl34_209,
inference(avatar_split_clause,[],[f382,f1663]) ).
fof(f1663,plain,
( spl34_209
<=> ! [X0] :
( sP2(X0)
| ~ up_complete_relstr(X0)
| ~ lower_bounded_relstr(X0)
| ~ with_suprema_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_209])]) ).
fof(f382,plain,
! [X0] :
( sP2(X0)
| ~ up_complete_relstr(X0)
| ~ lower_bounded_relstr(X0)
| ~ with_suprema_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f193]) ).
fof(f193,plain,
! [X0] :
( sP2(X0)
| ~ up_complete_relstr(X0)
| ~ lower_bounded_relstr(X0)
| ~ with_suprema_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(definition_folding,[],[f150,f192]) ).
fof(f192,plain,
! [X0] :
( ( bounded_relstr(X0)
& upper_bounded_relstr(X0)
& lower_bounded_relstr(X0)
& complete_relstr(X0)
& with_infima_relstr(X0)
& with_suprema_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ sP2(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f150,plain,
! [X0] :
( ( bounded_relstr(X0)
& upper_bounded_relstr(X0)
& lower_bounded_relstr(X0)
& complete_relstr(X0)
& with_infima_relstr(X0)
& with_suprema_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ up_complete_relstr(X0)
| ~ lower_bounded_relstr(X0)
| ~ with_suprema_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f149]) ).
fof(f149,plain,
! [X0] :
( ( bounded_relstr(X0)
& upper_bounded_relstr(X0)
& lower_bounded_relstr(X0)
& complete_relstr(X0)
& with_infima_relstr(X0)
& with_suprema_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ up_complete_relstr(X0)
| ~ lower_bounded_relstr(X0)
| ~ with_suprema_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( rel_str(X0)
=> ( ( up_complete_relstr(X0)
& lower_bounded_relstr(X0)
& with_suprema_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
=> ( bounded_relstr(X0)
& upper_bounded_relstr(X0)
& lower_bounded_relstr(X0)
& complete_relstr(X0)
& with_infima_relstr(X0)
& with_suprema_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc12_waybel_0) ).
fof(f1657,plain,
spl34_208,
inference(avatar_split_clause,[],[f405,f1655]) ).
fof(f1655,plain,
( spl34_208
<=> ! [X0] :
( sP4(X0)
| ~ rel_str(X0)
| ~ upper_bounded_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| trivial_carrier(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_208])]) ).
fof(f405,plain,
! [X0] :
( sP4(X0)
| ~ rel_str(X0)
| ~ upper_bounded_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| trivial_carrier(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f197]) ).
fof(f197,plain,
! [X0] :
( sP4(X0)
| ~ rel_str(X0)
| ~ upper_bounded_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| trivial_carrier(X0)
| empty_carrier(X0) ),
inference(definition_folding,[],[f162,f196]) ).
fof(f196,plain,
! [X0] :
( ? [X1] :
( upper_relstr_subset(X1,X0)
& filtered_subset(X1,X0)
& proper_element(X1,powerset(the_carrier(X0)))
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ sP4(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f162,plain,
! [X0] :
( ? [X1] :
( upper_relstr_subset(X1,X0)
& filtered_subset(X1,X0)
& proper_element(X1,powerset(the_carrier(X0)))
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ rel_str(X0)
| ~ upper_bounded_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| trivial_carrier(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f161]) ).
fof(f161,plain,
! [X0] :
( ? [X1] :
( upper_relstr_subset(X1,X0)
& filtered_subset(X1,X0)
& proper_element(X1,powerset(the_carrier(X0)))
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ rel_str(X0)
| ~ upper_bounded_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| trivial_carrier(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f70]) ).
fof(f70,axiom,
! [X0] :
( ( rel_str(X0)
& upper_bounded_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ trivial_carrier(X0)
& ~ empty_carrier(X0) )
=> ? [X1] :
( upper_relstr_subset(X1,X0)
& filtered_subset(X1,X0)
& proper_element(X1,powerset(the_carrier(X0)))
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_waybel_7) ).
fof(f1646,plain,
( spl34_207
| ~ spl34_3
| ~ spl34_105
| ~ spl34_144 ),
inference(avatar_split_clause,[],[f1235,f1206,f1027,f532,f1644]) ).
fof(f1638,plain,
spl34_206,
inference(avatar_split_clause,[],[f428,f1636]) ).
fof(f1636,plain,
( spl34_206
<=> ! [X0,X3,X2,X1] :
( X1 = X3
| rel_str_of(X0,X1) != rel_str_of(X2,X3)
| ~ relation_of2(X1,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_206])]) ).
fof(f428,plain,
! [X2,X3,X0,X1] :
( X1 = X3
| rel_str_of(X0,X1) != rel_str_of(X2,X3)
| ~ relation_of2(X1,X0,X0) ),
inference(cnf_transformation,[],[f176]) ).
fof(f176,plain,
! [X0,X1] :
( ! [X2,X3] :
( ( X1 = X3
& X0 = X2 )
| rel_str_of(X0,X1) != rel_str_of(X2,X3) )
| ~ relation_of2(X1,X0,X0) ),
inference(ennf_transformation,[],[f50]) ).
fof(f50,axiom,
! [X0,X1] :
( relation_of2(X1,X0,X0)
=> ! [X2,X3] :
( rel_str_of(X0,X1) = rel_str_of(X2,X3)
=> ( X1 = X3
& X0 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g1_orders_2) ).
fof(f1634,plain,
spl34_205,
inference(avatar_split_clause,[],[f427,f1632]) ).
fof(f1632,plain,
( spl34_205
<=> ! [X0,X3,X2,X1] :
( X0 = X2
| rel_str_of(X0,X1) != rel_str_of(X2,X3)
| ~ relation_of2(X1,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_205])]) ).
fof(f427,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| rel_str_of(X0,X1) != rel_str_of(X2,X3)
| ~ relation_of2(X1,X0,X0) ),
inference(cnf_transformation,[],[f176]) ).
fof(f1630,plain,
spl34_204,
inference(avatar_split_clause,[],[f409,f1628]) ).
fof(f1628,plain,
( spl34_204
<=> ! [X0] :
( element(sK14(X0),powerset(the_carrier(X0)))
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_204])]) ).
fof(f409,plain,
! [X0] :
( element(sK14(X0),powerset(the_carrier(X0)))
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f220]) ).
fof(f220,plain,
! [X0] :
( ( upper_relstr_subset(sK14(X0),X0)
& filtered_subset(sK14(X0),X0)
& ~ empty(sK14(X0))
& element(sK14(X0),powerset(the_carrier(X0))) )
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f168,f219]) ).
fof(f219,plain,
! [X0] :
( ? [X1] :
( upper_relstr_subset(X1,X0)
& filtered_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
=> ( upper_relstr_subset(sK14(X0),X0)
& filtered_subset(sK14(X0),X0)
& ~ empty(sK14(X0))
& element(sK14(X0),powerset(the_carrier(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f168,plain,
! [X0] :
( ? [X1] :
( upper_relstr_subset(X1,X0)
& filtered_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f167]) ).
fof(f167,plain,
! [X0] :
( ? [X1] :
( upper_relstr_subset(X1,X0)
& filtered_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f51]) ).
fof(f51,axiom,
! [X0] :
( ( rel_str(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
=> ? [X1] :
( upper_relstr_subset(X1,X0)
& filtered_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc10_waybel_0) ).
fof(f1626,plain,
spl34_203,
inference(avatar_split_clause,[],[f392,f1624]) ).
fof(f1624,plain,
( spl34_203
<=> ! [X0] :
( sP3(X0)
| ~ join_complete_relstr(X0)
| ~ upper_bounded_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_203])]) ).
fof(f392,plain,
! [X0] :
( sP3(X0)
| ~ join_complete_relstr(X0)
| ~ upper_bounded_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f195]) ).
fof(f195,plain,
! [X0] :
( sP3(X0)
| ~ join_complete_relstr(X0)
| ~ upper_bounded_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(definition_folding,[],[f154,f194]) ).
fof(f194,plain,
! [X0] :
( ( upper_bounded_relstr(X0)
& with_suprema_relstr(X0)
& antisymmetric_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ sP3(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f154,plain,
! [X0] :
( ( upper_bounded_relstr(X0)
& with_suprema_relstr(X0)
& antisymmetric_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ join_complete_relstr(X0)
| ~ upper_bounded_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f153]) ).
fof(f153,plain,
! [X0] :
( ( upper_bounded_relstr(X0)
& with_suprema_relstr(X0)
& antisymmetric_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ join_complete_relstr(X0)
| ~ upper_bounded_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] :
( rel_str(X0)
=> ( ( join_complete_relstr(X0)
& upper_bounded_relstr(X0)
& antisymmetric_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
=> ( upper_bounded_relstr(X0)
& with_suprema_relstr(X0)
& antisymmetric_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc14_waybel_0) ).
fof(f1614,plain,
spl34_202,
inference(avatar_split_clause,[],[f412,f1612]) ).
fof(f1612,plain,
( spl34_202
<=> ! [X0] :
( upper_relstr_subset(sK14(X0),X0)
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_202])]) ).
fof(f412,plain,
! [X0] :
( upper_relstr_subset(sK14(X0),X0)
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f220]) ).
fof(f1610,plain,
spl34_201,
inference(avatar_split_clause,[],[f411,f1608]) ).
fof(f1608,plain,
( spl34_201
<=> ! [X0] :
( filtered_subset(sK14(X0),X0)
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_201])]) ).
fof(f411,plain,
! [X0] :
( filtered_subset(sK14(X0),X0)
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f220]) ).
fof(f1603,plain,
spl34_200,
inference(avatar_split_clause,[],[f386,f1601]) ).
fof(f1601,plain,
( spl34_200
<=> ! [X0] :
( with_infima_relstr(X0)
| ~ join_complete_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_200])]) ).
fof(f386,plain,
! [X0] :
( with_infima_relstr(X0)
| ~ join_complete_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f152]) ).
fof(f152,plain,
! [X0] :
( ( with_infima_relstr(X0)
& antisymmetric_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ join_complete_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f151]) ).
fof(f151,plain,
! [X0] :
( ( with_infima_relstr(X0)
& antisymmetric_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ join_complete_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( rel_str(X0)
=> ( ( join_complete_relstr(X0)
& antisymmetric_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
=> ( with_infima_relstr(X0)
& antisymmetric_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc13_waybel_0) ).
fof(f1591,plain,
spl34_199,
inference(avatar_split_clause,[],[f410,f1589]) ).
fof(f1589,plain,
( spl34_199
<=> ! [X0] :
( ~ empty(sK14(X0))
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_199])]) ).
fof(f410,plain,
! [X0] :
( ~ empty(sK14(X0))
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f220]) ).
fof(f1587,plain,
spl34_198,
inference(avatar_split_clause,[],[f350,f1585]) ).
fof(f350,plain,
! [X0] :
( rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0
| ~ strict_rel_str(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f134,plain,
! [X0] :
( rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0
| ~ strict_rel_str(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f133]) ).
fof(f133,plain,
! [X0] :
( rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0
| ~ strict_rel_str(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0] :
( rel_str(X0)
=> ( strict_rel_str(X0)
=> rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v1_orders_2) ).
fof(f1551,plain,
( spl34_197
| ~ spl34_4
| ~ spl34_162 ),
inference(avatar_split_clause,[],[f1436,f1317,f537,f1548]) ).
fof(f1436,plain,
( in(sK33,sK6)
| ~ spl34_4
| ~ spl34_162 ),
inference(superposition,[],[f539,f1319]) ).
fof(f1537,plain,
spl34_196,
inference(avatar_split_clause,[],[f437,f1535]) ).
fof(f437,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f186]) ).
fof(f186,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f185]) ).
fof(f185,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f81]) ).
fof(f81,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f1533,plain,
spl34_195,
inference(avatar_split_clause,[],[f436,f1531]) ).
fof(f1531,plain,
( spl34_195
<=> ! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_195])]) ).
fof(f436,plain,
! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f184]) ).
fof(f184,plain,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> element(X2,powerset(cartesian_product2(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(f1529,plain,
spl34_194,
inference(avatar_split_clause,[],[f407,f1527]) ).
fof(f1527,plain,
( spl34_194
<=> ! [X0] :
( element(sK13(X0),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_194])]) ).
fof(f407,plain,
! [X0] :
( element(sK13(X0),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f218]) ).
fof(f218,plain,
! [X0] :
( ( ~ empty(sK13(X0))
& element(sK13(X0),powerset(the_carrier(X0))) )
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f166,f217]) ).
fof(f217,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
=> ( ~ empty(sK13(X0))
& element(sK13(X0),powerset(the_carrier(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f166,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f165]) ).
fof(f165,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f72]) ).
fof(f72,axiom,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_struct_0) ).
fof(f1525,plain,
spl34_193,
inference(avatar_split_clause,[],[f397,f1523]) ).
fof(f1523,plain,
( spl34_193
<=> ! [X0] :
( upper_bounded_relstr(X0)
| ~ up_complete_relstr(X0)
| ~ with_suprema_relstr(X0)
| ~ reflexive_relstr(X0)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_193])]) ).
fof(f397,plain,
! [X0] :
( upper_bounded_relstr(X0)
| ~ up_complete_relstr(X0)
| ~ with_suprema_relstr(X0)
| ~ reflexive_relstr(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f158]) ).
fof(f158,plain,
! [X0] :
( ( upper_bounded_relstr(X0)
& with_suprema_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ up_complete_relstr(X0)
| ~ with_suprema_relstr(X0)
| ~ reflexive_relstr(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f157]) ).
fof(f157,plain,
! [X0] :
( ( upper_bounded_relstr(X0)
& with_suprema_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ up_complete_relstr(X0)
| ~ with_suprema_relstr(X0)
| ~ reflexive_relstr(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0] :
( rel_str(X0)
=> ( ( up_complete_relstr(X0)
& with_suprema_relstr(X0)
& reflexive_relstr(X0) )
=> ( upper_bounded_relstr(X0)
& with_suprema_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc9_waybel_0) ).
fof(f1521,plain,
spl34_192,
inference(avatar_split_clause,[],[f371,f1519]) ).
fof(f371,plain,
! [X0] :
( join_complete_relstr(X0)
| ~ complete_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f148,plain,
! [X0] :
( ( join_complete_relstr(X0)
& up_complete_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ complete_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f147]) ).
fof(f147,plain,
! [X0] :
( ( join_complete_relstr(X0)
& up_complete_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ complete_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( rel_str(X0)
=> ( ( complete_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
=> ( join_complete_relstr(X0)
& up_complete_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc10_waybel_0) ).
fof(f1517,plain,
spl34_191,
inference(avatar_split_clause,[],[f370,f1515]) ).
fof(f370,plain,
! [X0] :
( up_complete_relstr(X0)
| ~ complete_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f1513,plain,
spl34_190,
inference(avatar_split_clause,[],[f367,f1511]) ).
fof(f1511,plain,
( spl34_190
<=> ! [X0] :
( lower_bounded_relstr(X0)
| ~ join_complete_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_190])]) ).
fof(f367,plain,
! [X0] :
( lower_bounded_relstr(X0)
| ~ join_complete_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f146]) ).
fof(f146,plain,
! [X0] :
( ( lower_bounded_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ join_complete_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f145]) ).
fof(f145,plain,
! [X0] :
( ( lower_bounded_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ join_complete_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( rel_str(X0)
=> ( ( join_complete_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
=> ( lower_bounded_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc11_waybel_0) ).
fof(f1508,plain,
spl34_189,
inference(avatar_split_clause,[],[f364,f1506]) ).
fof(f364,plain,
! [X0] :
( sP1(X0)
| ~ trivial_carrier(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f191]) ).
fof(f191,plain,
! [X0] :
( sP1(X0)
| ~ trivial_carrier(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(definition_folding,[],[f144,f190]) ).
fof(f190,plain,
! [X0] :
( ( complete_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ sP1(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f144,plain,
! [X0] :
( ( complete_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ trivial_carrier(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f143]) ).
fof(f143,plain,
! [X0] :
( ( complete_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ trivial_carrier(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] :
( rel_str(X0)
=> ( ( trivial_carrier(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
=> ( complete_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_yellow_0) ).
fof(f1489,plain,
spl34_188,
inference(avatar_split_clause,[],[f440,f1487]) ).
fof(f440,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f187]) ).
fof(f187,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f82]) ).
fof(f82,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f1485,plain,
spl34_187,
inference(avatar_split_clause,[],[f346,f1483]) ).
fof(f346,plain,
! [X0] :
( relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f128,plain,
! [X0] :
( relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0] :
( rel_str(X0)
=> relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_orders_2) ).
fof(f1481,plain,
spl34_186,
inference(avatar_split_clause,[],[f340,f1479]) ).
fof(f1479,plain,
( spl34_186
<=> ! [X0] :
( element(sK11(X0),powerset(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_186])]) ).
fof(f340,plain,
! [X0] :
( element(sK11(X0),powerset(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f210]) ).
fof(f210,plain,
! [X0] :
( ( finite(sK11(X0))
& ~ empty(sK11(X0))
& element(sK11(X0),powerset(powerset(the_carrier(X0)))) )
| ~ one_sorted_str(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f124,f209]) ).
fof(f209,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(powerset(the_carrier(X0)))) )
=> ( finite(sK11(X0))
& ~ empty(sK11(X0))
& element(sK11(X0),powerset(powerset(the_carrier(X0)))) ) ),
introduced(choice_axiom,[]) ).
fof(f124,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(powerset(the_carrier(X0)))) )
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f68]) ).
fof(f68,axiom,
! [X0] :
( one_sorted_str(X0)
=> ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(powerset(the_carrier(X0)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_waybel_7) ).
fof(f1426,plain,
spl34_185,
inference(avatar_split_clause,[],[f439,f1424]) ).
fof(f439,plain,
! [X2,X0,X1] :
( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f232]) ).
fof(f232,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,[],[f73]) ).
fof(f73,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
<=> relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f1422,plain,
spl34_184,
inference(avatar_split_clause,[],[f438,f1420]) ).
fof(f438,plain,
! [X2,X0,X1] :
( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f232]) ).
fof(f1418,plain,
spl34_183,
inference(avatar_split_clause,[],[f430,f1416]) ).
fof(f1416,plain,
( spl34_183
<=> ! [X0,X1] :
( finite(cartesian_product2(X0,X1))
| ~ finite(X1)
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_183])]) ).
fof(f430,plain,
! [X0,X1] :
( finite(cartesian_product2(X0,X1))
| ~ finite(X1)
| ~ finite(X0) ),
inference(cnf_transformation,[],[f180]) ).
fof(f180,plain,
! [X0,X1] :
( finite(cartesian_product2(X0,X1))
| ~ finite(X1)
| ~ finite(X0) ),
inference(flattening,[],[f179]) ).
fof(f179,plain,
! [X0,X1] :
( finite(cartesian_product2(X0,X1))
| ~ finite(X1)
| ~ finite(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,axiom,
! [X0,X1] :
( ( finite(X1)
& finite(X0) )
=> finite(cartesian_product2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc14_finset_1) ).
fof(f1414,plain,
spl34_182,
inference(avatar_split_clause,[],[f429,f1412]) ).
fof(f429,plain,
! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ),
inference(cnf_transformation,[],[f178]) ).
fof(f178,plain,
! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ),
inference(flattening,[],[f177]) ).
fof(f177,plain,
! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ),
inference(ennf_transformation,[],[f46]) ).
fof(f46,axiom,
! [X0,X1] :
( ( ~ empty(X1)
& ~ empty(X0) )
=> ~ empty(cartesian_product2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_subset_1) ).
fof(f1410,plain,
spl34_181,
inference(avatar_split_clause,[],[f426,f1408]) ).
fof(f426,plain,
! [X0,X1] :
( rel_str(rel_str_of(X0,X1))
| ~ relation_of2(X1,X0,X0) ),
inference(cnf_transformation,[],[f175]) ).
fof(f175,plain,
! [X0,X1] :
( ( rel_str(rel_str_of(X0,X1))
& strict_rel_str(rel_str_of(X0,X1)) )
| ~ relation_of2(X1,X0,X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0,X1] :
( relation_of2(X1,X0,X0)
=> ( rel_str(rel_str_of(X0,X1))
& strict_rel_str(rel_str_of(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_g1_orders_2) ).
fof(f1406,plain,
spl34_180,
inference(avatar_split_clause,[],[f425,f1404]) ).
fof(f425,plain,
! [X0,X1] :
( strict_rel_str(rel_str_of(X0,X1))
| ~ relation_of2(X1,X0,X0) ),
inference(cnf_transformation,[],[f175]) ).
fof(f1402,plain,
spl34_179,
inference(avatar_split_clause,[],[f424,f1400]) ).
fof(f424,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f174]) ).
fof(f174,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f173]) ).
fof(f173,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f77]) ).
fof(f77,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f1398,plain,
spl34_178,
inference(avatar_split_clause,[],[f402,f1396]) ).
fof(f1396,plain,
( spl34_178
<=> ! [X0] :
( proper_element(sK12(X0),powerset(the_carrier(X0)))
| ~ sP4(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_178])]) ).
fof(f402,plain,
! [X0] :
( proper_element(sK12(X0),powerset(the_carrier(X0)))
| ~ sP4(X0) ),
inference(cnf_transformation,[],[f216]) ).
fof(f216,plain,
! [X0] :
( ( upper_relstr_subset(sK12(X0),X0)
& filtered_subset(sK12(X0),X0)
& proper_element(sK12(X0),powerset(the_carrier(X0)))
& ~ empty(sK12(X0))
& element(sK12(X0),powerset(the_carrier(X0))) )
| ~ sP4(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f214,f215]) ).
fof(f215,plain,
! [X0] :
( ? [X1] :
( upper_relstr_subset(X1,X0)
& filtered_subset(X1,X0)
& proper_element(X1,powerset(the_carrier(X0)))
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
=> ( upper_relstr_subset(sK12(X0),X0)
& filtered_subset(sK12(X0),X0)
& proper_element(sK12(X0),powerset(the_carrier(X0)))
& ~ empty(sK12(X0))
& element(sK12(X0),powerset(the_carrier(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f214,plain,
! [X0] :
( ? [X1] :
( upper_relstr_subset(X1,X0)
& filtered_subset(X1,X0)
& proper_element(X1,powerset(the_carrier(X0)))
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ sP4(X0) ),
inference(nnf_transformation,[],[f196]) ).
fof(f1394,plain,
spl34_177,
inference(avatar_split_clause,[],[f400,f1392]) ).
fof(f400,plain,
! [X0] :
( element(sK12(X0),powerset(the_carrier(X0)))
| ~ sP4(X0) ),
inference(cnf_transformation,[],[f216]) ).
fof(f1390,plain,
( spl34_176
| ~ spl34_4
| ~ spl34_89
| ~ spl34_144
| ~ spl34_157
| ~ spl34_160 ),
inference(avatar_split_clause,[],[f1311,f1291,f1271,f1206,f962,f537,f1387]) ).
fof(f1387,plain,
( spl34_176
<=> element(sK33,sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_176])]) ).
fof(f1271,plain,
( spl34_157
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_157])]) ).
fof(f1291,plain,
( spl34_160
<=> empty_set = sK7 ),
introduced(avatar_definition,[new_symbols(naming,[spl34_160])]) ).
fof(f1311,plain,
( element(sK33,sK6)
| ~ spl34_4
| ~ spl34_89
| ~ spl34_144
| ~ spl34_157
| ~ spl34_160 ),
inference(forward_demodulation,[],[f1310,f1295]) ).
fof(f1295,plain,
( sK7 = sK33
| ~ spl34_89
| ~ spl34_144
| ~ spl34_160 ),
inference(forward_demodulation,[],[f1293,f1234]) ).
fof(f1293,plain,
( empty_set = sK7
| ~ spl34_160 ),
inference(avatar_component_clause,[],[f1291]) ).
fof(f1310,plain,
( element(sK7,sK6)
| ~ spl34_4
| ~ spl34_157 ),
inference(resolution,[],[f1272,f539]) ).
fof(f1272,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) )
| ~ spl34_157 ),
inference(avatar_component_clause,[],[f1271]) ).
fof(f1385,plain,
spl34_175,
inference(avatar_split_clause,[],[f393,f1383]) ).
fof(f1383,plain,
( spl34_175
<=> ! [X0] :
( bounded_relstr(X0)
| ~ upper_bounded_relstr(X0)
| ~ lower_bounded_relstr(X0)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_175])]) ).
fof(f393,plain,
! [X0] :
( bounded_relstr(X0)
| ~ upper_bounded_relstr(X0)
| ~ lower_bounded_relstr(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f156]) ).
fof(f156,plain,
! [X0] :
( bounded_relstr(X0)
| ~ upper_bounded_relstr(X0)
| ~ lower_bounded_relstr(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f155]) ).
fof(f155,plain,
! [X0] :
( bounded_relstr(X0)
| ~ upper_bounded_relstr(X0)
| ~ lower_bounded_relstr(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0] :
( rel_str(X0)
=> ( ( upper_bounded_relstr(X0)
& lower_bounded_relstr(X0) )
=> bounded_relstr(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc5_yellow_0) ).
fof(f1381,plain,
spl34_174,
inference(avatar_split_clause,[],[f356,f1379]) ).
fof(f356,plain,
! [X0] :
( with_infima_relstr(X0)
| ~ complete_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f140]) ).
fof(f140,plain,
! [X0] :
( ( with_infima_relstr(X0)
& with_suprema_relstr(X0)
& ~ empty_carrier(X0) )
| ~ complete_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f139]) ).
fof(f139,plain,
! [X0] :
( ( with_infima_relstr(X0)
& with_suprema_relstr(X0)
& ~ empty_carrier(X0) )
| ~ complete_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0] :
( rel_str(X0)
=> ( ( complete_relstr(X0)
& ~ empty_carrier(X0) )
=> ( with_infima_relstr(X0)
& with_suprema_relstr(X0)
& ~ empty_carrier(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_yellow_0) ).
fof(f1377,plain,
spl34_173,
inference(avatar_split_clause,[],[f355,f1375]) ).
fof(f355,plain,
! [X0] :
( with_suprema_relstr(X0)
| ~ complete_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f140]) ).
fof(f1373,plain,
spl34_172,
inference(avatar_split_clause,[],[f353,f1371]) ).
fof(f353,plain,
! [X0] :
( bounded_relstr(X0)
| ~ complete_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f138]) ).
fof(f138,plain,
! [X0] :
( ( bounded_relstr(X0)
& ~ empty_carrier(X0) )
| ~ complete_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f137]) ).
fof(f137,plain,
! [X0] :
( ( bounded_relstr(X0)
& ~ empty_carrier(X0) )
| ~ complete_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0] :
( rel_str(X0)
=> ( ( complete_relstr(X0)
& ~ empty_carrier(X0) )
=> ( bounded_relstr(X0)
& ~ empty_carrier(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_yellow_0) ).
fof(f1369,plain,
spl34_171,
inference(avatar_split_clause,[],[f343,f1367]) ).
fof(f343,plain,
! [X0,X1] :
( finite(X1)
| ~ element(X1,powerset(X0))
| ~ finite(X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f125,plain,
! [X0] :
( ! [X1] :
( finite(X1)
| ~ element(X1,powerset(X0)) )
| ~ finite(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0] :
( finite(X0)
=> ! [X1] :
( element(X1,powerset(X0))
=> finite(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
fof(f1353,plain,
( ~ spl34_170
| ~ spl34_4
| ~ spl34_89
| ~ spl34_144
| ~ spl34_156
| ~ spl34_160 ),
inference(avatar_split_clause,[],[f1309,f1291,f1267,f1206,f962,f537,f1350]) ).
fof(f1350,plain,
( spl34_170
<=> in(sK6,sK33) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_170])]) ).
fof(f1309,plain,
( ~ in(sK6,sK33)
| ~ spl34_4
| ~ spl34_89
| ~ spl34_144
| ~ spl34_156
| ~ spl34_160 ),
inference(forward_demodulation,[],[f1308,f1295]) ).
fof(f1308,plain,
( ~ in(sK6,sK7)
| ~ spl34_4
| ~ spl34_156 ),
inference(resolution,[],[f1268,f539]) ).
fof(f1348,plain,
spl34_169,
inference(avatar_split_clause,[],[f432,f1346]) ).
fof(f432,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f182]) ).
fof(f182,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f85]) ).
fof(f85,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(f1344,plain,
spl34_168,
inference(avatar_split_clause,[],[f431,f1342]) ).
fof(f431,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f181]) ).
fof(f181,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0,X1] :
( subset(X0,X1)
=> element(X0,powerset(X1)) ),
inference(unused_predicate_definition_removal,[],[f80]) ).
fof(f80,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f1340,plain,
spl34_167,
inference(avatar_split_clause,[],[f408,f1338]) ).
fof(f408,plain,
! [X0] :
( ~ empty(sK13(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f218]) ).
fof(f1336,plain,
spl34_166,
inference(avatar_split_clause,[],[f406,f1334]) ).
fof(f406,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f164]) ).
fof(f164,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f163]) ).
fof(f163,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f41,axiom,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ~ empty(the_carrier(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(f1332,plain,
spl34_165,
inference(avatar_split_clause,[],[f345,f1330]) ).
fof(f345,plain,
! [X0] :
( element(bottom_of_relstr(X0),the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f127,plain,
! [X0] :
( element(bottom_of_relstr(X0),the_carrier(X0))
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0] :
( rel_str(X0)
=> element(bottom_of_relstr(X0),the_carrier(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_yellow_0) ).
fof(f1328,plain,
spl34_164,
inference(avatar_split_clause,[],[f337,f1326]) ).
fof(f337,plain,
! [X0] :
( element(sK10(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f208]) ).
fof(f208,plain,
! [X0] :
( ( finite(sK10(X0))
& ~ empty(sK10(X0))
& element(sK10(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f123,f207]) ).
fof(f207,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( finite(sK10(X0))
& ~ empty(sK10(X0))
& element(sK10(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f123,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f65]) ).
fof(f65,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_finset_1) ).
fof(f1324,plain,
spl34_163,
inference(avatar_split_clause,[],[f334,f1322]) ).
fof(f334,plain,
! [X0] :
( element(sK9(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f206]) ).
fof(f206,plain,
! [X0] :
( ( finite(sK9(X0))
& ~ empty(sK9(X0))
& element(sK9(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f122,f205]) ).
fof(f205,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( finite(sK9(X0))
& ~ empty(sK9(X0))
& element(sK9(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f122,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f69]) ).
fof(f69,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_finset_1) ).
fof(f1320,plain,
( spl34_162
| ~ spl34_89
| ~ spl34_144
| ~ spl34_160 ),
inference(avatar_split_clause,[],[f1295,f1291,f1206,f962,f1317]) ).
fof(f1315,plain,
spl34_161,
inference(avatar_split_clause,[],[f332,f1313]) ).
fof(f332,plain,
! [X0] :
( element(sK8(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f204]) ).
fof(f204,plain,
! [X0] :
( ( ~ empty(sK8(X0))
& element(sK8(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f121,f203]) ).
fof(f203,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( ~ empty(sK8(X0))
& element(sK8(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f121,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f57,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f1294,plain,
( spl34_160
| ~ spl34_3
| ~ spl34_144 ),
inference(avatar_split_clause,[],[f1232,f1206,f532,f1291]) ).
fof(f1281,plain,
spl34_159,
inference(avatar_split_clause,[],[f435,f1279]) ).
fof(f435,plain,
! [X0,X1] : relation_of2_as_subset(sK19(X0,X1),X0,X1),
inference(cnf_transformation,[],[f231]) ).
fof(f231,plain,
! [X0,X1] : relation_of2_as_subset(sK19(X0,X1),X0,X1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f38,f230]) ).
fof(f230,plain,
! [X0,X1] :
( ? [X2] : relation_of2_as_subset(X2,X0,X1)
=> relation_of2_as_subset(sK19(X0,X1),X0,X1) ),
introduced(choice_axiom,[]) ).
fof(f38,axiom,
! [X0,X1] :
? [X2] : relation_of2_as_subset(X2,X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_relset_1) ).
fof(f1277,plain,
spl34_158,
inference(avatar_split_clause,[],[f434,f1275]) ).
fof(f434,plain,
! [X0,X1] : relation_of2(sK18(X0,X1),X0,X1),
inference(cnf_transformation,[],[f229]) ).
fof(f229,plain,
! [X0,X1] : relation_of2(sK18(X0,X1),X0,X1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f36,f228]) ).
fof(f228,plain,
! [X0,X1] :
( ? [X2] : relation_of2(X2,X0,X1)
=> relation_of2(sK18(X0,X1),X0,X1) ),
introduced(choice_axiom,[]) ).
fof(f36,axiom,
! [X0,X1] :
? [X2] : relation_of2(X2,X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_relset_1) ).
fof(f1273,plain,
spl34_157,
inference(avatar_split_clause,[],[f423,f1271]) ).
fof(f423,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f172]) ).
fof(f172,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f76]) ).
fof(f76,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f1269,plain,
spl34_156,
inference(avatar_split_clause,[],[f422,f1267]) ).
fof(f422,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f171]) ).
fof(f171,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f1265,plain,
spl34_155,
inference(avatar_split_clause,[],[f418,f1263]) ).
fof(f418,plain,
! [X0] : element(sK17(X0),powerset(powerset(X0))),
inference(cnf_transformation,[],[f227]) ).
fof(f227,plain,
! [X0] :
( finite(sK17(X0))
& ~ empty(sK17(X0))
& element(sK17(X0),powerset(powerset(X0))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f63,f226]) ).
fof(f226,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(powerset(X0))) )
=> ( finite(sK17(X0))
& ~ empty(sK17(X0))
& element(sK17(X0),powerset(powerset(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f63,axiom,
! [X0] :
? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(powerset(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_waybel_7) ).
fof(f1261,plain,
spl34_154,
inference(avatar_split_clause,[],[f404,f1259]) ).
fof(f1259,plain,
( spl34_154
<=> ! [X0] :
( upper_relstr_subset(sK12(X0),X0)
| ~ sP4(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_154])]) ).
fof(f404,plain,
! [X0] :
( upper_relstr_subset(sK12(X0),X0)
| ~ sP4(X0) ),
inference(cnf_transformation,[],[f216]) ).
fof(f1257,plain,
spl34_153,
inference(avatar_split_clause,[],[f403,f1255]) ).
fof(f1255,plain,
( spl34_153
<=> ! [X0] :
( filtered_subset(sK12(X0),X0)
| ~ sP4(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_153])]) ).
fof(f403,plain,
! [X0] :
( filtered_subset(sK12(X0),X0)
| ~ sP4(X0) ),
inference(cnf_transformation,[],[f216]) ).
fof(f1253,plain,
spl34_152,
inference(avatar_split_clause,[],[f351,f1251]) ).
fof(f1251,plain,
( spl34_152
<=> ! [X0] :
( ~ empty_carrier(X0)
| ~ with_suprema_relstr(X0)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_152])]) ).
fof(f351,plain,
! [X0] :
( ~ empty_carrier(X0)
| ~ with_suprema_relstr(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f136]) ).
fof(f136,plain,
! [X0] :
( ~ empty_carrier(X0)
| ~ with_suprema_relstr(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f135]) ).
fof(f135,plain,
! [X0] :
( ~ empty_carrier(X0)
| ~ with_suprema_relstr(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0] :
( rel_str(X0)
=> ( with_suprema_relstr(X0)
=> ~ empty_carrier(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_lattice3) ).
fof(f1249,plain,
spl34_151,
inference(avatar_split_clause,[],[f349,f1247]) ).
fof(f1247,plain,
( spl34_151
<=> ! [X0] :
( ~ empty_carrier(X0)
| ~ with_infima_relstr(X0)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_151])]) ).
fof(f349,plain,
! [X0] :
( ~ empty_carrier(X0)
| ~ with_infima_relstr(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f132,plain,
! [X0] :
( ~ empty_carrier(X0)
| ~ with_infima_relstr(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f131]) ).
fof(f131,plain,
! [X0] :
( ~ empty_carrier(X0)
| ~ with_infima_relstr(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0] :
( rel_str(X0)
=> ( with_infima_relstr(X0)
=> ~ empty_carrier(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_lattice3) ).
fof(f1245,plain,
spl34_150,
inference(avatar_split_clause,[],[f348,f1243]) ).
fof(f1243,plain,
( spl34_150
<=> ! [X0] :
( upper_bounded_relstr(X0)
| ~ bounded_relstr(X0)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_150])]) ).
fof(f348,plain,
! [X0] :
( upper_bounded_relstr(X0)
| ~ bounded_relstr(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f130,plain,
! [X0] :
( ( upper_bounded_relstr(X0)
& lower_bounded_relstr(X0) )
| ~ bounded_relstr(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f129]) ).
fof(f129,plain,
! [X0] :
( ( upper_bounded_relstr(X0)
& lower_bounded_relstr(X0) )
| ~ bounded_relstr(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0] :
( rel_str(X0)
=> ( bounded_relstr(X0)
=> ( upper_bounded_relstr(X0)
& lower_bounded_relstr(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_yellow_0) ).
fof(f1241,plain,
spl34_149,
inference(avatar_split_clause,[],[f347,f1239]) ).
fof(f1239,plain,
( spl34_149
<=> ! [X0] :
( lower_bounded_relstr(X0)
| ~ bounded_relstr(X0)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_149])]) ).
fof(f347,plain,
! [X0] :
( lower_bounded_relstr(X0)
| ~ bounded_relstr(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f1228,plain,
( spl34_148
| ~ spl34_3
| ~ spl34_131 ),
inference(avatar_split_clause,[],[f1166,f1131,f532,f1225]) ).
fof(f1225,plain,
( spl34_148
<=> finite(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_148])]) ).
fof(f1166,plain,
( finite(sK7)
| ~ spl34_3
| ~ spl34_131 ),
inference(resolution,[],[f1132,f534]) ).
fof(f1220,plain,
spl34_147,
inference(avatar_split_clause,[],[f433,f1218]) ).
fof(f1218,plain,
( spl34_147
<=> ! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_147])]) ).
fof(f433,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f183]) ).
fof(f183,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f84]) ).
fof(f84,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f1216,plain,
spl34_146,
inference(avatar_split_clause,[],[f416,f1214]) ).
fof(f416,plain,
! [X0] : element(sK16(X0),powerset(X0)),
inference(cnf_transformation,[],[f225]) ).
fof(f225,plain,
! [X0] :
( empty(sK16(X0))
& element(sK16(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f62,f224]) ).
fof(f224,plain,
! [X0] :
( ? [X1] :
( empty(X1)
& element(X1,powerset(X0)) )
=> ( empty(sK16(X0))
& element(sK16(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f62,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f1212,plain,
spl34_145,
inference(avatar_split_clause,[],[f401,f1210]) ).
fof(f401,plain,
! [X0] :
( ~ empty(sK12(X0))
| ~ sP4(X0) ),
inference(cnf_transformation,[],[f216]) ).
fof(f1208,plain,
spl34_144,
inference(avatar_split_clause,[],[f399,f1206]) ).
fof(f399,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f160]) ).
fof(f160,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f83]) ).
fof(f83,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f1204,plain,
spl34_143,
inference(avatar_split_clause,[],[f342,f1202]) ).
fof(f1202,plain,
( spl34_143
<=> ! [X0] :
( finite(sK11(X0))
| ~ one_sorted_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_143])]) ).
fof(f342,plain,
! [X0] :
( finite(sK11(X0))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f210]) ).
fof(f1200,plain,
spl34_142,
inference(avatar_split_clause,[],[f341,f1198]) ).
fof(f341,plain,
! [X0] :
( ~ empty(sK11(X0))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f210]) ).
fof(f1196,plain,
spl34_141,
inference(avatar_split_clause,[],[f339,f1194]) ).
fof(f1194,plain,
( spl34_141
<=> ! [X0] :
( finite(sK10(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_141])]) ).
fof(f339,plain,
! [X0] :
( finite(sK10(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f208]) ).
fof(f1192,plain,
spl34_140,
inference(avatar_split_clause,[],[f338,f1190]) ).
fof(f338,plain,
! [X0] :
( ~ empty(sK10(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f208]) ).
fof(f1188,plain,
spl34_139,
inference(avatar_split_clause,[],[f336,f1186]) ).
fof(f1186,plain,
( spl34_139
<=> ! [X0] :
( finite(sK9(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_139])]) ).
fof(f336,plain,
! [X0] :
( finite(sK9(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f206]) ).
fof(f1184,plain,
spl34_138,
inference(avatar_split_clause,[],[f335,f1182]) ).
fof(f335,plain,
! [X0] :
( ~ empty(sK9(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f206]) ).
fof(f1180,plain,
spl34_137,
inference(avatar_split_clause,[],[f333,f1178]) ).
fof(f333,plain,
! [X0] :
( ~ empty(sK8(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f204]) ).
fof(f1176,plain,
spl34_136,
inference(avatar_split_clause,[],[f318,f1174]) ).
fof(f1174,plain,
( spl34_136
<=> ! [X0] :
( ~ trivial_carrier(boole_POSet(X0))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_136])]) ).
fof(f318,plain,
! [X0] :
( ~ trivial_carrier(boole_POSet(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f202]) ).
fof(f202,plain,
! [X0] :
( ( complete_relstr(boole_POSet(X0))
& with_infima_relstr(boole_POSet(X0))
& with_suprema_relstr(boole_POSet(X0))
& join_complete_relstr(boole_POSet(X0))
& up_complete_relstr(boole_POSet(X0))
& bounded_relstr(boole_POSet(X0))
& upper_bounded_relstr(boole_POSet(X0))
& lower_bounded_relstr(boole_POSet(X0))
& antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ trivial_carrier(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) )
| ~ sP0(X0) ),
inference(nnf_transformation,[],[f188]) ).
fof(f188,plain,
! [X0] :
( ( complete_relstr(boole_POSet(X0))
& with_infima_relstr(boole_POSet(X0))
& with_suprema_relstr(boole_POSet(X0))
& join_complete_relstr(boole_POSet(X0))
& up_complete_relstr(boole_POSet(X0))
& bounded_relstr(boole_POSet(X0))
& upper_bounded_relstr(boole_POSet(X0))
& lower_bounded_relstr(boole_POSet(X0))
& antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ trivial_carrier(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) )
| ~ sP0(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f1172,plain,
spl34_135,
inference(avatar_split_clause,[],[f272,f1170]) ).
fof(f272,plain,
! [X0] : empty_set = bottom_of_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f75]) ).
fof(f75,axiom,
! [X0] : empty_set = bottom_of_relstr(boole_POSet(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_yellow_1) ).
fof(f1163,plain,
( spl34_134
| spl34_2
| ~ spl34_109 ),
inference(avatar_split_clause,[],[f1140,f1043,f527,f1160]) ).
fof(f1160,plain,
( spl34_134
<=> sP0(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_134])]) ).
fof(f1140,plain,
( sP0(sK6)
| spl34_2
| ~ spl34_109 ),
inference(resolution,[],[f1044,f529]) ).
fof(f529,plain,
( ~ empty(sK6)
| spl34_2 ),
inference(avatar_component_clause,[],[f527]) ).
fof(f1158,plain,
( spl34_133
| spl34_1
| ~ spl34_109 ),
inference(avatar_split_clause,[],[f1139,f1043,f522,f1155]) ).
fof(f1155,plain,
( spl34_133
<=> sP0(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_133])]) ).
fof(f522,plain,
( spl34_1
<=> empty(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_1])]) ).
fof(f1139,plain,
( sP0(sK5)
| spl34_1
| ~ spl34_109 ),
inference(resolution,[],[f1044,f524]) ).
fof(f524,plain,
( ~ empty(sK5)
| spl34_1 ),
inference(avatar_component_clause,[],[f522]) ).
fof(f1137,plain,
spl34_132,
inference(avatar_split_clause,[],[f415,f1135]) ).
fof(f415,plain,
! [X0] : element(sK15(X0),X0),
inference(cnf_transformation,[],[f223]) ).
fof(f223,plain,
! [X0] : element(sK15(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f37,f222]) ).
fof(f222,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK15(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f37,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f1133,plain,
spl34_131,
inference(avatar_split_clause,[],[f398,f1131]) ).
fof(f398,plain,
! [X0] :
( finite(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f159]) ).
fof(f159,plain,
! [X0] :
( finite(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( empty(X0)
=> finite(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
fof(f1129,plain,
spl34_130,
inference(avatar_split_clause,[],[f391,f1127]) ).
fof(f1127,plain,
( spl34_130
<=> ! [X0] :
( upper_bounded_relstr(X0)
| ~ sP3(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_130])]) ).
fof(f391,plain,
! [X0] :
( upper_bounded_relstr(X0)
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f213]) ).
fof(f213,plain,
! [X0] :
( ( upper_bounded_relstr(X0)
& with_suprema_relstr(X0)
& antisymmetric_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ sP3(X0) ),
inference(nnf_transformation,[],[f194]) ).
fof(f1125,plain,
spl34_129,
inference(avatar_split_clause,[],[f390,f1123]) ).
fof(f1123,plain,
( spl34_129
<=> ! [X0] :
( with_suprema_relstr(X0)
| ~ sP3(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_129])]) ).
fof(f390,plain,
! [X0] :
( with_suprema_relstr(X0)
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f213]) ).
fof(f1121,plain,
spl34_128,
inference(avatar_split_clause,[],[f389,f1119]) ).
fof(f1119,plain,
( spl34_128
<=> ! [X0] :
( antisymmetric_relstr(X0)
| ~ sP3(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_128])]) ).
fof(f389,plain,
! [X0] :
( antisymmetric_relstr(X0)
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f213]) ).
fof(f1117,plain,
spl34_127,
inference(avatar_split_clause,[],[f388,f1115]) ).
fof(f1115,plain,
( spl34_127
<=> ! [X0] :
( reflexive_relstr(X0)
| ~ sP3(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_127])]) ).
fof(f388,plain,
! [X0] :
( reflexive_relstr(X0)
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f213]) ).
fof(f1113,plain,
spl34_126,
inference(avatar_split_clause,[],[f387,f1111]) ).
fof(f1111,plain,
( spl34_126
<=> ! [X0] :
( ~ empty_carrier(X0)
| ~ sP3(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_126])]) ).
fof(f387,plain,
! [X0] :
( ~ empty_carrier(X0)
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f213]) ).
fof(f1109,plain,
spl34_125,
inference(avatar_split_clause,[],[f381,f1107]) ).
fof(f1107,plain,
( spl34_125
<=> ! [X0] :
( bounded_relstr(X0)
| ~ sP2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_125])]) ).
fof(f381,plain,
! [X0] :
( bounded_relstr(X0)
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f212]) ).
fof(f212,plain,
! [X0] :
( ( bounded_relstr(X0)
& upper_bounded_relstr(X0)
& lower_bounded_relstr(X0)
& complete_relstr(X0)
& with_infima_relstr(X0)
& with_suprema_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ sP2(X0) ),
inference(nnf_transformation,[],[f192]) ).
fof(f1105,plain,
spl34_124,
inference(avatar_split_clause,[],[f380,f1103]) ).
fof(f1103,plain,
( spl34_124
<=> ! [X0] :
( upper_bounded_relstr(X0)
| ~ sP2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_124])]) ).
fof(f380,plain,
! [X0] :
( upper_bounded_relstr(X0)
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f212]) ).
fof(f1101,plain,
spl34_123,
inference(avatar_split_clause,[],[f379,f1099]) ).
fof(f1099,plain,
( spl34_123
<=> ! [X0] :
( lower_bounded_relstr(X0)
| ~ sP2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_123])]) ).
fof(f379,plain,
! [X0] :
( lower_bounded_relstr(X0)
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f212]) ).
fof(f1097,plain,
spl34_122,
inference(avatar_split_clause,[],[f378,f1095]) ).
fof(f1095,plain,
( spl34_122
<=> ! [X0] :
( complete_relstr(X0)
| ~ sP2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_122])]) ).
fof(f378,plain,
! [X0] :
( complete_relstr(X0)
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f212]) ).
fof(f1093,plain,
spl34_121,
inference(avatar_split_clause,[],[f377,f1091]) ).
fof(f1091,plain,
( spl34_121
<=> ! [X0] :
( with_infima_relstr(X0)
| ~ sP2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_121])]) ).
fof(f377,plain,
! [X0] :
( with_infima_relstr(X0)
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f212]) ).
fof(f1089,plain,
spl34_120,
inference(avatar_split_clause,[],[f376,f1087]) ).
fof(f1087,plain,
( spl34_120
<=> ! [X0] :
( with_suprema_relstr(X0)
| ~ sP2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_120])]) ).
fof(f376,plain,
! [X0] :
( with_suprema_relstr(X0)
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f212]) ).
fof(f1085,plain,
spl34_119,
inference(avatar_split_clause,[],[f375,f1083]) ).
fof(f1083,plain,
( spl34_119
<=> ! [X0] :
( antisymmetric_relstr(X0)
| ~ sP2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_119])]) ).
fof(f375,plain,
! [X0] :
( antisymmetric_relstr(X0)
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f212]) ).
fof(f1081,plain,
spl34_118,
inference(avatar_split_clause,[],[f374,f1079]) ).
fof(f1079,plain,
( spl34_118
<=> ! [X0] :
( transitive_relstr(X0)
| ~ sP2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_118])]) ).
fof(f374,plain,
! [X0] :
( transitive_relstr(X0)
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f212]) ).
fof(f1077,plain,
spl34_117,
inference(avatar_split_clause,[],[f373,f1075]) ).
fof(f1075,plain,
( spl34_117
<=> ! [X0] :
( reflexive_relstr(X0)
| ~ sP2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_117])]) ).
fof(f373,plain,
! [X0] :
( reflexive_relstr(X0)
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f212]) ).
fof(f1073,plain,
spl34_116,
inference(avatar_split_clause,[],[f372,f1071]) ).
fof(f1071,plain,
( spl34_116
<=> ! [X0] :
( ~ empty_carrier(X0)
| ~ sP2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_116])]) ).
fof(f372,plain,
! [X0] :
( ~ empty_carrier(X0)
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f212]) ).
fof(f1069,plain,
spl34_115,
inference(avatar_split_clause,[],[f363,f1067]) ).
fof(f1067,plain,
( spl34_115
<=> ! [X0] :
( complete_relstr(X0)
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_115])]) ).
fof(f363,plain,
! [X0] :
( complete_relstr(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f211]) ).
fof(f211,plain,
! [X0] :
( ( complete_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ sP1(X0) ),
inference(nnf_transformation,[],[f190]) ).
fof(f1065,plain,
spl34_114,
inference(avatar_split_clause,[],[f362,f1063]) ).
fof(f1063,plain,
( spl34_114
<=> ! [X0] :
( antisymmetric_relstr(X0)
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_114])]) ).
fof(f362,plain,
! [X0] :
( antisymmetric_relstr(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f211]) ).
fof(f1061,plain,
spl34_113,
inference(avatar_split_clause,[],[f361,f1059]) ).
fof(f1059,plain,
( spl34_113
<=> ! [X0] :
( transitive_relstr(X0)
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_113])]) ).
fof(f361,plain,
! [X0] :
( transitive_relstr(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f211]) ).
fof(f1057,plain,
spl34_112,
inference(avatar_split_clause,[],[f360,f1055]) ).
fof(f1055,plain,
( spl34_112
<=> ! [X0] :
( reflexive_relstr(X0)
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_112])]) ).
fof(f360,plain,
! [X0] :
( reflexive_relstr(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f211]) ).
fof(f1053,plain,
spl34_111,
inference(avatar_split_clause,[],[f359,f1051]) ).
fof(f1051,plain,
( spl34_111
<=> ! [X0] :
( ~ empty_carrier(X0)
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_111])]) ).
fof(f359,plain,
! [X0] :
( ~ empty_carrier(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f211]) ).
fof(f1049,plain,
spl34_110,
inference(avatar_split_clause,[],[f344,f1047]) ).
fof(f344,plain,
! [X0] :
( one_sorted_str(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f126]) ).
fof(f126,plain,
! [X0] :
( one_sorted_str(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,axiom,
! [X0] :
( rel_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_orders_2) ).
fof(f1045,plain,
spl34_109,
inference(avatar_split_clause,[],[f331,f1043]) ).
fof(f331,plain,
! [X0] :
( sP0(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f189]) ).
fof(f189,plain,
! [X0] :
( sP0(X0)
| empty(X0) ),
inference(definition_folding,[],[f120,f188]) ).
fof(f120,plain,
! [X0] :
( ( complete_relstr(boole_POSet(X0))
& with_infima_relstr(boole_POSet(X0))
& with_suprema_relstr(boole_POSet(X0))
& join_complete_relstr(boole_POSet(X0))
& up_complete_relstr(boole_POSet(X0))
& bounded_relstr(boole_POSet(X0))
& upper_bounded_relstr(boole_POSet(X0))
& lower_bounded_relstr(boole_POSet(X0))
& antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ trivial_carrier(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f103]) ).
fof(f103,plain,
! [X0] :
( ~ empty(X0)
=> ( complete_relstr(boole_POSet(X0))
& with_infima_relstr(boole_POSet(X0))
& with_suprema_relstr(boole_POSet(X0))
& join_complete_relstr(boole_POSet(X0))
& up_complete_relstr(boole_POSet(X0))
& bounded_relstr(boole_POSet(X0))
& upper_bounded_relstr(boole_POSet(X0))
& lower_bounded_relstr(boole_POSet(X0))
& antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ trivial_carrier(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) ) ),
inference(pure_predicate_removal,[],[f101]) ).
fof(f101,plain,
! [X0] :
( ~ empty(X0)
=> ( complete_relstr(boole_POSet(X0))
& with_infima_relstr(boole_POSet(X0))
& with_suprema_relstr(boole_POSet(X0))
& ~ v1_yellow_3(boole_POSet(X0))
& join_complete_relstr(boole_POSet(X0))
& up_complete_relstr(boole_POSet(X0))
& bounded_relstr(boole_POSet(X0))
& upper_bounded_relstr(boole_POSet(X0))
& lower_bounded_relstr(boole_POSet(X0))
& antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ trivial_carrier(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) ) ),
inference(pure_predicate_removal,[],[f99]) ).
fof(f99,plain,
! [X0] :
( ~ empty(X0)
=> ( complete_relstr(boole_POSet(X0))
& with_infima_relstr(boole_POSet(X0))
& with_suprema_relstr(boole_POSet(X0))
& distributive_relstr(boole_POSet(X0))
& ~ v1_yellow_3(boole_POSet(X0))
& join_complete_relstr(boole_POSet(X0))
& up_complete_relstr(boole_POSet(X0))
& bounded_relstr(boole_POSet(X0))
& upper_bounded_relstr(boole_POSet(X0))
& lower_bounded_relstr(boole_POSet(X0))
& antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ trivial_carrier(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) ) ),
inference(pure_predicate_removal,[],[f95]) ).
fof(f95,plain,
! [X0] :
( ~ empty(X0)
=> ( complete_relstr(boole_POSet(X0))
& with_infima_relstr(boole_POSet(X0))
& with_suprema_relstr(boole_POSet(X0))
& heyting_relstr(boole_POSet(X0))
& distributive_relstr(boole_POSet(X0))
& ~ v1_yellow_3(boole_POSet(X0))
& join_complete_relstr(boole_POSet(X0))
& up_complete_relstr(boole_POSet(X0))
& bounded_relstr(boole_POSet(X0))
& upper_bounded_relstr(boole_POSet(X0))
& lower_bounded_relstr(boole_POSet(X0))
& antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ trivial_carrier(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) ) ),
inference(pure_predicate_removal,[],[f92]) ).
fof(f92,plain,
! [X0] :
( ~ empty(X0)
=> ( complete_relstr(boole_POSet(X0))
& with_infima_relstr(boole_POSet(X0))
& with_suprema_relstr(boole_POSet(X0))
& complemented_relstr(boole_POSet(X0))
& heyting_relstr(boole_POSet(X0))
& distributive_relstr(boole_POSet(X0))
& ~ v1_yellow_3(boole_POSet(X0))
& join_complete_relstr(boole_POSet(X0))
& up_complete_relstr(boole_POSet(X0))
& bounded_relstr(boole_POSet(X0))
& upper_bounded_relstr(boole_POSet(X0))
& lower_bounded_relstr(boole_POSet(X0))
& antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ trivial_carrier(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) ) ),
inference(pure_predicate_removal,[],[f44]) ).
fof(f44,axiom,
! [X0] :
( ~ empty(X0)
=> ( complete_relstr(boole_POSet(X0))
& with_infima_relstr(boole_POSet(X0))
& with_suprema_relstr(boole_POSet(X0))
& boolean_relstr(boole_POSet(X0))
& complemented_relstr(boole_POSet(X0))
& heyting_relstr(boole_POSet(X0))
& distributive_relstr(boole_POSet(X0))
& ~ v1_yellow_3(boole_POSet(X0))
& join_complete_relstr(boole_POSet(X0))
& up_complete_relstr(boole_POSet(X0))
& bounded_relstr(boole_POSet(X0))
& upper_bounded_relstr(boole_POSet(X0))
& lower_bounded_relstr(boole_POSet(X0))
& antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ trivial_carrier(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_waybel_7) ).
fof(f1041,plain,
spl34_108,
inference(avatar_split_clause,[],[f421,f1039]) ).
fof(f1039,plain,
( spl34_108
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_108])]) ).
fof(f421,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f87]) ).
fof(f87,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f74]) ).
fof(f74,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f1037,plain,
spl34_107,
inference(avatar_split_clause,[],[f420,f1035]) ).
fof(f1035,plain,
( spl34_107
<=> ! [X0] : finite(sK17(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_107])]) ).
fof(f420,plain,
! [X0] : finite(sK17(X0)),
inference(cnf_transformation,[],[f227]) ).
fof(f1033,plain,
spl34_106,
inference(avatar_split_clause,[],[f419,f1031]) ).
fof(f419,plain,
! [X0] : ~ empty(sK17(X0)),
inference(cnf_transformation,[],[f227]) ).
fof(f1029,plain,
spl34_105,
inference(avatar_split_clause,[],[f417,f1027]) ).
fof(f417,plain,
! [X0] : empty(sK16(X0)),
inference(cnf_transformation,[],[f225]) ).
fof(f1025,plain,
spl34_104,
inference(avatar_split_clause,[],[f316,f1023]) ).
fof(f316,plain,
! [X0] : rel_str(boole_POSet(X0)),
inference(cnf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0] :
( rel_str(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_yellow_1) ).
fof(f1021,plain,
spl34_103,
inference(avatar_split_clause,[],[f290,f1019]) ).
fof(f1019,plain,
( spl34_103
<=> ! [X0] : complete_relstr(boole_POSet(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_103])]) ).
fof(f290,plain,
! [X0] : complete_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f104]) ).
fof(f104,plain,
! [X0] :
( complete_relstr(boole_POSet(X0))
& with_infima_relstr(boole_POSet(X0))
& with_suprema_relstr(boole_POSet(X0))
& join_complete_relstr(boole_POSet(X0))
& up_complete_relstr(boole_POSet(X0))
& bounded_relstr(boole_POSet(X0))
& upper_bounded_relstr(boole_POSet(X0))
& lower_bounded_relstr(boole_POSet(X0))
& antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) ),
inference(pure_predicate_removal,[],[f89]) ).
fof(f89,plain,
! [X0] :
( complete_relstr(boole_POSet(X0))
& with_infima_relstr(boole_POSet(X0))
& with_suprema_relstr(boole_POSet(X0))
& ~ v1_yellow_3(boole_POSet(X0))
& join_complete_relstr(boole_POSet(X0))
& up_complete_relstr(boole_POSet(X0))
& bounded_relstr(boole_POSet(X0))
& upper_bounded_relstr(boole_POSet(X0))
& lower_bounded_relstr(boole_POSet(X0))
& antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) ),
inference(pure_predicate_removal,[],[f49]) ).
fof(f49,axiom,
! [X0] :
( complete_relstr(boole_POSet(X0))
& with_infima_relstr(boole_POSet(X0))
& with_suprema_relstr(boole_POSet(X0))
& ~ v1_yellow_3(boole_POSet(X0))
& join_complete_relstr(boole_POSet(X0))
& up_complete_relstr(boole_POSet(X0))
& directed_relstr(boole_POSet(X0))
& bounded_relstr(boole_POSet(X0))
& upper_bounded_relstr(boole_POSet(X0))
& lower_bounded_relstr(boole_POSet(X0))
& antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_yellow_6) ).
fof(f1017,plain,
spl34_102,
inference(avatar_split_clause,[],[f289,f1015]) ).
fof(f1015,plain,
( spl34_102
<=> ! [X0] : with_infima_relstr(boole_POSet(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_102])]) ).
fof(f289,plain,
! [X0] : with_infima_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f104]) ).
fof(f1013,plain,
spl34_101,
inference(avatar_split_clause,[],[f288,f1011]) ).
fof(f1011,plain,
( spl34_101
<=> ! [X0] : with_suprema_relstr(boole_POSet(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_101])]) ).
fof(f288,plain,
! [X0] : with_suprema_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f104]) ).
fof(f1009,plain,
spl34_100,
inference(avatar_split_clause,[],[f287,f1007]) ).
fof(f1007,plain,
( spl34_100
<=> ! [X0] : join_complete_relstr(boole_POSet(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_100])]) ).
fof(f287,plain,
! [X0] : join_complete_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f104]) ).
fof(f1005,plain,
spl34_99,
inference(avatar_split_clause,[],[f286,f1003]) ).
fof(f1003,plain,
( spl34_99
<=> ! [X0] : up_complete_relstr(boole_POSet(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_99])]) ).
fof(f286,plain,
! [X0] : up_complete_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f104]) ).
fof(f1001,plain,
spl34_98,
inference(avatar_split_clause,[],[f285,f999]) ).
fof(f999,plain,
( spl34_98
<=> ! [X0] : bounded_relstr(boole_POSet(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_98])]) ).
fof(f285,plain,
! [X0] : bounded_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f104]) ).
fof(f997,plain,
spl34_97,
inference(avatar_split_clause,[],[f284,f995]) ).
fof(f995,plain,
( spl34_97
<=> ! [X0] : upper_bounded_relstr(boole_POSet(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_97])]) ).
fof(f284,plain,
! [X0] : upper_bounded_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f104]) ).
fof(f993,plain,
spl34_96,
inference(avatar_split_clause,[],[f283,f991]) ).
fof(f283,plain,
! [X0] : lower_bounded_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f104]) ).
fof(f989,plain,
spl34_95,
inference(avatar_split_clause,[],[f277,f987]) ).
fof(f277,plain,
! [X0] : antisymmetric_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f47]) ).
fof(f47,axiom,
! [X0] :
( antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_yellow_1) ).
fof(f985,plain,
spl34_94,
inference(avatar_split_clause,[],[f276,f983]) ).
fof(f276,plain,
! [X0] : transitive_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f47]) ).
fof(f981,plain,
spl34_93,
inference(avatar_split_clause,[],[f275,f979]) ).
fof(f275,plain,
! [X0] : reflexive_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f47]) ).
fof(f977,plain,
spl34_92,
inference(avatar_split_clause,[],[f274,f975]) ).
fof(f975,plain,
( spl34_92
<=> ! [X0] : strict_rel_str(boole_POSet(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_92])]) ).
fof(f274,plain,
! [X0] : strict_rel_str(boole_POSet(X0)),
inference(cnf_transformation,[],[f47]) ).
fof(f973,plain,
spl34_91,
inference(avatar_split_clause,[],[f273,f971]) ).
fof(f273,plain,
! [X0] : ~ empty_carrier(boole_POSet(X0)),
inference(cnf_transformation,[],[f47]) ).
fof(f969,plain,
spl34_90,
inference(avatar_split_clause,[],[f271,f967]) ).
fof(f271,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f965,plain,
spl34_89,
inference(avatar_split_clause,[],[f520,f962]) ).
fof(f520,plain,
empty(sK33),
inference(cnf_transformation,[],[f260]) ).
fof(f260,plain,
empty(sK33),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK33])],[f114,f259]) ).
fof(f259,plain,
( ? [X0] : empty(X0)
=> empty(sK33) ),
introduced(choice_axiom,[]) ).
fof(f114,plain,
? [X0] : empty(X0),
inference(pure_predicate_removal,[],[f56]) ).
fof(f56,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f960,plain,
spl34_88,
inference(avatar_split_clause,[],[f519,f957]) ).
fof(f957,plain,
( spl34_88
<=> bounded_relstr(sK32) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_88])]) ).
fof(f519,plain,
bounded_relstr(sK32),
inference(cnf_transformation,[],[f258]) ).
fof(f258,plain,
( bounded_relstr(sK32)
& upper_bounded_relstr(sK32)
& lower_bounded_relstr(sK32)
& complete_relstr(sK32)
& with_infima_relstr(sK32)
& with_suprema_relstr(sK32)
& antisymmetric_relstr(sK32)
& transitive_relstr(sK32)
& reflexive_relstr(sK32)
& ~ empty_carrier(sK32)
& rel_str(sK32) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK32])],[f64,f257]) ).
fof(f257,plain,
( ? [X0] :
( bounded_relstr(X0)
& upper_bounded_relstr(X0)
& lower_bounded_relstr(X0)
& complete_relstr(X0)
& with_infima_relstr(X0)
& with_suprema_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0)
& rel_str(X0) )
=> ( bounded_relstr(sK32)
& upper_bounded_relstr(sK32)
& lower_bounded_relstr(sK32)
& complete_relstr(sK32)
& with_infima_relstr(sK32)
& with_suprema_relstr(sK32)
& antisymmetric_relstr(sK32)
& transitive_relstr(sK32)
& reflexive_relstr(sK32)
& ~ empty_carrier(sK32)
& rel_str(sK32) ) ),
introduced(choice_axiom,[]) ).
fof(f64,axiom,
? [X0] :
( bounded_relstr(X0)
& upper_bounded_relstr(X0)
& lower_bounded_relstr(X0)
& complete_relstr(X0)
& with_infima_relstr(X0)
& with_suprema_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0)
& rel_str(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_yellow_0) ).
fof(f955,plain,
spl34_87,
inference(avatar_split_clause,[],[f518,f952]) ).
fof(f952,plain,
( spl34_87
<=> upper_bounded_relstr(sK32) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_87])]) ).
fof(f518,plain,
upper_bounded_relstr(sK32),
inference(cnf_transformation,[],[f258]) ).
fof(f950,plain,
spl34_86,
inference(avatar_split_clause,[],[f517,f947]) ).
fof(f947,plain,
( spl34_86
<=> lower_bounded_relstr(sK32) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_86])]) ).
fof(f517,plain,
lower_bounded_relstr(sK32),
inference(cnf_transformation,[],[f258]) ).
fof(f945,plain,
spl34_85,
inference(avatar_split_clause,[],[f516,f942]) ).
fof(f516,plain,
complete_relstr(sK32),
inference(cnf_transformation,[],[f258]) ).
fof(f940,plain,
spl34_84,
inference(avatar_split_clause,[],[f515,f937]) ).
fof(f937,plain,
( spl34_84
<=> with_infima_relstr(sK32) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_84])]) ).
fof(f515,plain,
with_infima_relstr(sK32),
inference(cnf_transformation,[],[f258]) ).
fof(f935,plain,
spl34_83,
inference(avatar_split_clause,[],[f514,f932]) ).
fof(f932,plain,
( spl34_83
<=> with_suprema_relstr(sK32) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_83])]) ).
fof(f514,plain,
with_suprema_relstr(sK32),
inference(cnf_transformation,[],[f258]) ).
fof(f930,plain,
spl34_82,
inference(avatar_split_clause,[],[f513,f927]) ).
fof(f927,plain,
( spl34_82
<=> antisymmetric_relstr(sK32) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_82])]) ).
fof(f513,plain,
antisymmetric_relstr(sK32),
inference(cnf_transformation,[],[f258]) ).
fof(f925,plain,
spl34_81,
inference(avatar_split_clause,[],[f512,f922]) ).
fof(f922,plain,
( spl34_81
<=> transitive_relstr(sK32) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_81])]) ).
fof(f512,plain,
transitive_relstr(sK32),
inference(cnf_transformation,[],[f258]) ).
fof(f920,plain,
spl34_80,
inference(avatar_split_clause,[],[f511,f917]) ).
fof(f511,plain,
reflexive_relstr(sK32),
inference(cnf_transformation,[],[f258]) ).
fof(f915,plain,
~ spl34_79,
inference(avatar_split_clause,[],[f510,f912]) ).
fof(f510,plain,
~ empty_carrier(sK32),
inference(cnf_transformation,[],[f258]) ).
fof(f910,plain,
spl34_78,
inference(avatar_split_clause,[],[f509,f907]) ).
fof(f509,plain,
rel_str(sK32),
inference(cnf_transformation,[],[f258]) ).
fof(f905,plain,
spl34_77,
inference(avatar_split_clause,[],[f508,f902]) ).
fof(f902,plain,
( spl34_77
<=> antisymmetric_relstr(sK31) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_77])]) ).
fof(f508,plain,
antisymmetric_relstr(sK31),
inference(cnf_transformation,[],[f256]) ).
fof(f256,plain,
( antisymmetric_relstr(sK31)
& transitive_relstr(sK31)
& reflexive_relstr(sK31)
& ~ empty_carrier(sK31)
& rel_str(sK31) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK31])],[f110,f255]) ).
fof(f255,plain,
( ? [X0] :
( antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0)
& rel_str(X0) )
=> ( antisymmetric_relstr(sK31)
& transitive_relstr(sK31)
& reflexive_relstr(sK31)
& ~ empty_carrier(sK31)
& rel_str(sK31) ) ),
introduced(choice_axiom,[]) ).
fof(f110,plain,
? [X0] :
( antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0)
& rel_str(X0) ),
inference(pure_predicate_removal,[],[f52]) ).
fof(f52,axiom,
? [X0] :
( connected_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0)
& rel_str(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc12_waybel_0) ).
fof(f900,plain,
spl34_76,
inference(avatar_split_clause,[],[f507,f897]) ).
fof(f897,plain,
( spl34_76
<=> transitive_relstr(sK31) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_76])]) ).
fof(f507,plain,
transitive_relstr(sK31),
inference(cnf_transformation,[],[f256]) ).
fof(f895,plain,
spl34_75,
inference(avatar_split_clause,[],[f506,f892]) ).
fof(f892,plain,
( spl34_75
<=> reflexive_relstr(sK31) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_75])]) ).
fof(f506,plain,
reflexive_relstr(sK31),
inference(cnf_transformation,[],[f256]) ).
fof(f890,plain,
~ spl34_74,
inference(avatar_split_clause,[],[f505,f887]) ).
fof(f887,plain,
( spl34_74
<=> empty_carrier(sK31) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_74])]) ).
fof(f505,plain,
~ empty_carrier(sK31),
inference(cnf_transformation,[],[f256]) ).
fof(f885,plain,
spl34_73,
inference(avatar_split_clause,[],[f504,f882]) ).
fof(f504,plain,
rel_str(sK31),
inference(cnf_transformation,[],[f256]) ).
fof(f880,plain,
spl34_72,
inference(avatar_split_clause,[],[f503,f877]) ).
fof(f877,plain,
( spl34_72
<=> join_complete_relstr(sK30) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_72])]) ).
fof(f503,plain,
join_complete_relstr(sK30),
inference(cnf_transformation,[],[f254]) ).
fof(f254,plain,
( join_complete_relstr(sK30)
& up_complete_relstr(sK30)
& bounded_relstr(sK30)
& upper_bounded_relstr(sK30)
& lower_bounded_relstr(sK30)
& complete_relstr(sK30)
& with_infima_relstr(sK30)
& with_suprema_relstr(sK30)
& antisymmetric_relstr(sK30)
& transitive_relstr(sK30)
& reflexive_relstr(sK30)
& strict_rel_str(sK30)
& ~ empty_carrier(sK30)
& rel_str(sK30) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK30])],[f53,f253]) ).
fof(f253,plain,
( ? [X0] :
( join_complete_relstr(X0)
& up_complete_relstr(X0)
& bounded_relstr(X0)
& upper_bounded_relstr(X0)
& lower_bounded_relstr(X0)
& complete_relstr(X0)
& with_infima_relstr(X0)
& with_suprema_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& strict_rel_str(X0)
& ~ empty_carrier(X0)
& rel_str(X0) )
=> ( join_complete_relstr(sK30)
& up_complete_relstr(sK30)
& bounded_relstr(sK30)
& upper_bounded_relstr(sK30)
& lower_bounded_relstr(sK30)
& complete_relstr(sK30)
& with_infima_relstr(sK30)
& with_suprema_relstr(sK30)
& antisymmetric_relstr(sK30)
& transitive_relstr(sK30)
& reflexive_relstr(sK30)
& strict_rel_str(sK30)
& ~ empty_carrier(sK30)
& rel_str(sK30) ) ),
introduced(choice_axiom,[]) ).
fof(f53,axiom,
? [X0] :
( join_complete_relstr(X0)
& up_complete_relstr(X0)
& bounded_relstr(X0)
& upper_bounded_relstr(X0)
& lower_bounded_relstr(X0)
& complete_relstr(X0)
& with_infima_relstr(X0)
& with_suprema_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& strict_rel_str(X0)
& ~ empty_carrier(X0)
& rel_str(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc13_waybel_0) ).
fof(f875,plain,
spl34_71,
inference(avatar_split_clause,[],[f502,f872]) ).
fof(f872,plain,
( spl34_71
<=> up_complete_relstr(sK30) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_71])]) ).
fof(f502,plain,
up_complete_relstr(sK30),
inference(cnf_transformation,[],[f254]) ).
fof(f870,plain,
spl34_70,
inference(avatar_split_clause,[],[f501,f867]) ).
fof(f867,plain,
( spl34_70
<=> bounded_relstr(sK30) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_70])]) ).
fof(f501,plain,
bounded_relstr(sK30),
inference(cnf_transformation,[],[f254]) ).
fof(f865,plain,
spl34_69,
inference(avatar_split_clause,[],[f500,f862]) ).
fof(f862,plain,
( spl34_69
<=> upper_bounded_relstr(sK30) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_69])]) ).
fof(f500,plain,
upper_bounded_relstr(sK30),
inference(cnf_transformation,[],[f254]) ).
fof(f860,plain,
spl34_68,
inference(avatar_split_clause,[],[f499,f857]) ).
fof(f857,plain,
( spl34_68
<=> lower_bounded_relstr(sK30) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_68])]) ).
fof(f499,plain,
lower_bounded_relstr(sK30),
inference(cnf_transformation,[],[f254]) ).
fof(f855,plain,
spl34_67,
inference(avatar_split_clause,[],[f498,f852]) ).
fof(f852,plain,
( spl34_67
<=> complete_relstr(sK30) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_67])]) ).
fof(f498,plain,
complete_relstr(sK30),
inference(cnf_transformation,[],[f254]) ).
fof(f850,plain,
spl34_66,
inference(avatar_split_clause,[],[f497,f847]) ).
fof(f847,plain,
( spl34_66
<=> with_infima_relstr(sK30) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_66])]) ).
fof(f497,plain,
with_infima_relstr(sK30),
inference(cnf_transformation,[],[f254]) ).
fof(f845,plain,
spl34_65,
inference(avatar_split_clause,[],[f496,f842]) ).
fof(f842,plain,
( spl34_65
<=> with_suprema_relstr(sK30) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_65])]) ).
fof(f496,plain,
with_suprema_relstr(sK30),
inference(cnf_transformation,[],[f254]) ).
fof(f840,plain,
spl34_64,
inference(avatar_split_clause,[],[f495,f837]) ).
fof(f837,plain,
( spl34_64
<=> antisymmetric_relstr(sK30) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_64])]) ).
fof(f495,plain,
antisymmetric_relstr(sK30),
inference(cnf_transformation,[],[f254]) ).
fof(f835,plain,
spl34_63,
inference(avatar_split_clause,[],[f494,f832]) ).
fof(f832,plain,
( spl34_63
<=> transitive_relstr(sK30) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_63])]) ).
fof(f494,plain,
transitive_relstr(sK30),
inference(cnf_transformation,[],[f254]) ).
fof(f830,plain,
spl34_62,
inference(avatar_split_clause,[],[f493,f827]) ).
fof(f827,plain,
( spl34_62
<=> reflexive_relstr(sK30) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_62])]) ).
fof(f493,plain,
reflexive_relstr(sK30),
inference(cnf_transformation,[],[f254]) ).
fof(f825,plain,
spl34_61,
inference(avatar_split_clause,[],[f492,f822]) ).
fof(f492,plain,
strict_rel_str(sK30),
inference(cnf_transformation,[],[f254]) ).
fof(f820,plain,
~ spl34_60,
inference(avatar_split_clause,[],[f491,f817]) ).
fof(f817,plain,
( spl34_60
<=> empty_carrier(sK30) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_60])]) ).
fof(f491,plain,
~ empty_carrier(sK30),
inference(cnf_transformation,[],[f254]) ).
fof(f815,plain,
spl34_59,
inference(avatar_split_clause,[],[f490,f812]) ).
fof(f490,plain,
rel_str(sK30),
inference(cnf_transformation,[],[f254]) ).
fof(f810,plain,
spl34_58,
inference(avatar_split_clause,[],[f489,f807]) ).
fof(f489,plain,
trivial_carrier(sK29),
inference(cnf_transformation,[],[f252]) ).
fof(f252,plain,
( trivial_carrier(sK29)
& complete_relstr(sK29)
& with_infima_relstr(sK29)
& with_suprema_relstr(sK29)
& antisymmetric_relstr(sK29)
& transitive_relstr(sK29)
& reflexive_relstr(sK29)
& strict_rel_str(sK29)
& ~ empty_carrier(sK29)
& rel_str(sK29) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK29])],[f59,f251]) ).
fof(f251,plain,
( ? [X0] :
( trivial_carrier(X0)
& complete_relstr(X0)
& with_infima_relstr(X0)
& with_suprema_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& strict_rel_str(X0)
& ~ empty_carrier(X0)
& rel_str(X0) )
=> ( trivial_carrier(sK29)
& complete_relstr(sK29)
& with_infima_relstr(sK29)
& with_suprema_relstr(sK29)
& antisymmetric_relstr(sK29)
& transitive_relstr(sK29)
& reflexive_relstr(sK29)
& strict_rel_str(sK29)
& ~ empty_carrier(sK29)
& rel_str(sK29) ) ),
introduced(choice_axiom,[]) ).
fof(f59,axiom,
? [X0] :
( trivial_carrier(X0)
& complete_relstr(X0)
& with_infima_relstr(X0)
& with_suprema_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& strict_rel_str(X0)
& ~ empty_carrier(X0)
& rel_str(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_yellow_0) ).
fof(f805,plain,
spl34_57,
inference(avatar_split_clause,[],[f488,f802]) ).
fof(f488,plain,
complete_relstr(sK29),
inference(cnf_transformation,[],[f252]) ).
fof(f800,plain,
spl34_56,
inference(avatar_split_clause,[],[f487,f797]) ).
fof(f797,plain,
( spl34_56
<=> with_infima_relstr(sK29) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_56])]) ).
fof(f487,plain,
with_infima_relstr(sK29),
inference(cnf_transformation,[],[f252]) ).
fof(f795,plain,
spl34_55,
inference(avatar_split_clause,[],[f486,f792]) ).
fof(f792,plain,
( spl34_55
<=> with_suprema_relstr(sK29) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_55])]) ).
fof(f486,plain,
with_suprema_relstr(sK29),
inference(cnf_transformation,[],[f252]) ).
fof(f790,plain,
spl34_54,
inference(avatar_split_clause,[],[f485,f787]) ).
fof(f787,plain,
( spl34_54
<=> antisymmetric_relstr(sK29) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_54])]) ).
fof(f485,plain,
antisymmetric_relstr(sK29),
inference(cnf_transformation,[],[f252]) ).
fof(f785,plain,
spl34_53,
inference(avatar_split_clause,[],[f484,f782]) ).
fof(f782,plain,
( spl34_53
<=> transitive_relstr(sK29) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_53])]) ).
fof(f484,plain,
transitive_relstr(sK29),
inference(cnf_transformation,[],[f252]) ).
fof(f780,plain,
spl34_52,
inference(avatar_split_clause,[],[f483,f777]) ).
fof(f483,plain,
reflexive_relstr(sK29),
inference(cnf_transformation,[],[f252]) ).
fof(f775,plain,
spl34_51,
inference(avatar_split_clause,[],[f482,f772]) ).
fof(f482,plain,
strict_rel_str(sK29),
inference(cnf_transformation,[],[f252]) ).
fof(f770,plain,
~ spl34_50,
inference(avatar_split_clause,[],[f481,f767]) ).
fof(f481,plain,
~ empty_carrier(sK29),
inference(cnf_transformation,[],[f252]) ).
fof(f765,plain,
spl34_49,
inference(avatar_split_clause,[],[f480,f762]) ).
fof(f480,plain,
rel_str(sK29),
inference(cnf_transformation,[],[f252]) ).
fof(f760,plain,
spl34_48,
inference(avatar_split_clause,[],[f479,f757]) ).
fof(f479,plain,
complete_relstr(sK28),
inference(cnf_transformation,[],[f250]) ).
fof(f250,plain,
( complete_relstr(sK28)
& with_infima_relstr(sK28)
& with_suprema_relstr(sK28)
& antisymmetric_relstr(sK28)
& transitive_relstr(sK28)
& reflexive_relstr(sK28)
& strict_rel_str(sK28)
& ~ empty_carrier(sK28)
& rel_str(sK28) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28])],[f60,f249]) ).
fof(f249,plain,
( ? [X0] :
( complete_relstr(X0)
& with_infima_relstr(X0)
& with_suprema_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& strict_rel_str(X0)
& ~ empty_carrier(X0)
& rel_str(X0) )
=> ( complete_relstr(sK28)
& with_infima_relstr(sK28)
& with_suprema_relstr(sK28)
& antisymmetric_relstr(sK28)
& transitive_relstr(sK28)
& reflexive_relstr(sK28)
& strict_rel_str(sK28)
& ~ empty_carrier(sK28)
& rel_str(sK28) ) ),
introduced(choice_axiom,[]) ).
fof(f60,axiom,
? [X0] :
( complete_relstr(X0)
& with_infima_relstr(X0)
& with_suprema_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& strict_rel_str(X0)
& ~ empty_carrier(X0)
& rel_str(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_lattice3) ).
fof(f755,plain,
spl34_47,
inference(avatar_split_clause,[],[f478,f752]) ).
fof(f752,plain,
( spl34_47
<=> with_infima_relstr(sK28) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_47])]) ).
fof(f478,plain,
with_infima_relstr(sK28),
inference(cnf_transformation,[],[f250]) ).
fof(f750,plain,
spl34_46,
inference(avatar_split_clause,[],[f477,f747]) ).
fof(f747,plain,
( spl34_46
<=> with_suprema_relstr(sK28) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_46])]) ).
fof(f477,plain,
with_suprema_relstr(sK28),
inference(cnf_transformation,[],[f250]) ).
fof(f745,plain,
spl34_45,
inference(avatar_split_clause,[],[f476,f742]) ).
fof(f742,plain,
( spl34_45
<=> antisymmetric_relstr(sK28) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_45])]) ).
fof(f476,plain,
antisymmetric_relstr(sK28),
inference(cnf_transformation,[],[f250]) ).
fof(f740,plain,
spl34_44,
inference(avatar_split_clause,[],[f475,f737]) ).
fof(f737,plain,
( spl34_44
<=> transitive_relstr(sK28) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_44])]) ).
fof(f475,plain,
transitive_relstr(sK28),
inference(cnf_transformation,[],[f250]) ).
fof(f735,plain,
spl34_43,
inference(avatar_split_clause,[],[f474,f732]) ).
fof(f474,plain,
reflexive_relstr(sK28),
inference(cnf_transformation,[],[f250]) ).
fof(f730,plain,
spl34_42,
inference(avatar_split_clause,[],[f473,f727]) ).
fof(f473,plain,
strict_rel_str(sK28),
inference(cnf_transformation,[],[f250]) ).
fof(f725,plain,
~ spl34_41,
inference(avatar_split_clause,[],[f472,f722]) ).
fof(f472,plain,
~ empty_carrier(sK28),
inference(cnf_transformation,[],[f250]) ).
fof(f720,plain,
spl34_40,
inference(avatar_split_clause,[],[f471,f717]) ).
fof(f471,plain,
rel_str(sK28),
inference(cnf_transformation,[],[f250]) ).
fof(f715,plain,
spl34_39,
inference(avatar_split_clause,[],[f470,f712]) ).
fof(f470,plain,
complete_relstr(sK27),
inference(cnf_transformation,[],[f248]) ).
fof(f248,plain,
( complete_relstr(sK27)
& antisymmetric_relstr(sK27)
& transitive_relstr(sK27)
& reflexive_relstr(sK27)
& strict_rel_str(sK27)
& ~ empty_carrier(sK27)
& rel_str(sK27) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27])],[f55,f247]) ).
fof(f247,plain,
( ? [X0] :
( complete_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& strict_rel_str(X0)
& ~ empty_carrier(X0)
& rel_str(X0) )
=> ( complete_relstr(sK27)
& antisymmetric_relstr(sK27)
& transitive_relstr(sK27)
& reflexive_relstr(sK27)
& strict_rel_str(sK27)
& ~ empty_carrier(sK27)
& rel_str(sK27) ) ),
introduced(choice_axiom,[]) ).
fof(f55,axiom,
? [X0] :
( complete_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& strict_rel_str(X0)
& ~ empty_carrier(X0)
& rel_str(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_lattice3) ).
fof(f710,plain,
spl34_38,
inference(avatar_split_clause,[],[f469,f707]) ).
fof(f707,plain,
( spl34_38
<=> antisymmetric_relstr(sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_38])]) ).
fof(f469,plain,
antisymmetric_relstr(sK27),
inference(cnf_transformation,[],[f248]) ).
fof(f705,plain,
spl34_37,
inference(avatar_split_clause,[],[f468,f702]) ).
fof(f702,plain,
( spl34_37
<=> transitive_relstr(sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_37])]) ).
fof(f468,plain,
transitive_relstr(sK27),
inference(cnf_transformation,[],[f248]) ).
fof(f700,plain,
spl34_36,
inference(avatar_split_clause,[],[f467,f697]) ).
fof(f467,plain,
reflexive_relstr(sK27),
inference(cnf_transformation,[],[f248]) ).
fof(f695,plain,
spl34_35,
inference(avatar_split_clause,[],[f466,f692]) ).
fof(f466,plain,
strict_rel_str(sK27),
inference(cnf_transformation,[],[f248]) ).
fof(f690,plain,
~ spl34_34,
inference(avatar_split_clause,[],[f465,f687]) ).
fof(f465,plain,
~ empty_carrier(sK27),
inference(cnf_transformation,[],[f248]) ).
fof(f685,plain,
spl34_33,
inference(avatar_split_clause,[],[f464,f682]) ).
fof(f464,plain,
rel_str(sK27),
inference(cnf_transformation,[],[f248]) ).
fof(f680,plain,
spl34_32,
inference(avatar_split_clause,[],[f463,f677]) ).
fof(f677,plain,
( spl34_32
<=> transitive_relstr(sK26) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_32])]) ).
fof(f463,plain,
transitive_relstr(sK26),
inference(cnf_transformation,[],[f246]) ).
fof(f246,plain,
( transitive_relstr(sK26)
& strict_rel_str(sK26)
& ~ empty_carrier(sK26)
& rel_str(sK26) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f90,f245]) ).
fof(f245,plain,
( ? [X0] :
( transitive_relstr(X0)
& strict_rel_str(X0)
& ~ empty_carrier(X0)
& rel_str(X0) )
=> ( transitive_relstr(sK26)
& strict_rel_str(sK26)
& ~ empty_carrier(sK26)
& rel_str(sK26) ) ),
introduced(choice_axiom,[]) ).
fof(f90,plain,
? [X0] :
( transitive_relstr(X0)
& strict_rel_str(X0)
& ~ empty_carrier(X0)
& rel_str(X0) ),
inference(pure_predicate_removal,[],[f71]) ).
fof(f71,axiom,
? [X0] :
( directed_relstr(X0)
& transitive_relstr(X0)
& strict_rel_str(X0)
& ~ empty_carrier(X0)
& rel_str(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_yellow_6) ).
fof(f675,plain,
spl34_31,
inference(avatar_split_clause,[],[f462,f672]) ).
fof(f462,plain,
strict_rel_str(sK26),
inference(cnf_transformation,[],[f246]) ).
fof(f670,plain,
~ spl34_30,
inference(avatar_split_clause,[],[f461,f667]) ).
fof(f667,plain,
( spl34_30
<=> empty_carrier(sK26) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_30])]) ).
fof(f461,plain,
~ empty_carrier(sK26),
inference(cnf_transformation,[],[f246]) ).
fof(f665,plain,
spl34_29,
inference(avatar_split_clause,[],[f460,f662]) ).
fof(f460,plain,
rel_str(sK26),
inference(cnf_transformation,[],[f246]) ).
fof(f660,plain,
spl34_28,
inference(avatar_split_clause,[],[f459,f657]) ).
fof(f657,plain,
( spl34_28
<=> with_infima_relstr(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_28])]) ).
fof(f459,plain,
with_infima_relstr(sK25),
inference(cnf_transformation,[],[f244]) ).
fof(f244,plain,
( with_infima_relstr(sK25)
& with_suprema_relstr(sK25)
& bounded_relstr(sK25)
& upper_bounded_relstr(sK25)
& lower_bounded_relstr(sK25)
& antisymmetric_relstr(sK25)
& transitive_relstr(sK25)
& reflexive_relstr(sK25)
& strict_rel_str(sK25)
& ~ trivial_carrier(sK25)
& ~ empty_carrier(sK25)
& rel_str(sK25) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f106,f243]) ).
fof(f243,plain,
( ? [X0] :
( with_infima_relstr(X0)
& with_suprema_relstr(X0)
& bounded_relstr(X0)
& upper_bounded_relstr(X0)
& lower_bounded_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& strict_rel_str(X0)
& ~ trivial_carrier(X0)
& ~ empty_carrier(X0)
& rel_str(X0) )
=> ( with_infima_relstr(sK25)
& with_suprema_relstr(sK25)
& bounded_relstr(sK25)
& upper_bounded_relstr(sK25)
& lower_bounded_relstr(sK25)
& antisymmetric_relstr(sK25)
& transitive_relstr(sK25)
& reflexive_relstr(sK25)
& strict_rel_str(sK25)
& ~ trivial_carrier(sK25)
& ~ empty_carrier(sK25)
& rel_str(sK25) ) ),
introduced(choice_axiom,[]) ).
fof(f106,plain,
? [X0] :
( with_infima_relstr(X0)
& with_suprema_relstr(X0)
& bounded_relstr(X0)
& upper_bounded_relstr(X0)
& lower_bounded_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& strict_rel_str(X0)
& ~ trivial_carrier(X0)
& ~ empty_carrier(X0)
& rel_str(X0) ),
inference(pure_predicate_removal,[],[f100]) ).
fof(f100,plain,
? [X0] :
( with_infima_relstr(X0)
& with_suprema_relstr(X0)
& ~ v1_yellow_3(X0)
& bounded_relstr(X0)
& upper_bounded_relstr(X0)
& lower_bounded_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& strict_rel_str(X0)
& ~ trivial_carrier(X0)
& ~ empty_carrier(X0)
& rel_str(X0) ),
inference(pure_predicate_removal,[],[f98]) ).
fof(f98,plain,
? [X0] :
( with_infima_relstr(X0)
& with_suprema_relstr(X0)
& distributive_relstr(X0)
& ~ v1_yellow_3(X0)
& bounded_relstr(X0)
& upper_bounded_relstr(X0)
& lower_bounded_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& strict_rel_str(X0)
& ~ trivial_carrier(X0)
& ~ empty_carrier(X0)
& rel_str(X0) ),
inference(pure_predicate_removal,[],[f94]) ).
fof(f94,plain,
? [X0] :
( with_infima_relstr(X0)
& with_suprema_relstr(X0)
& heyting_relstr(X0)
& distributive_relstr(X0)
& ~ v1_yellow_3(X0)
& bounded_relstr(X0)
& upper_bounded_relstr(X0)
& lower_bounded_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& strict_rel_str(X0)
& ~ trivial_carrier(X0)
& ~ empty_carrier(X0)
& rel_str(X0) ),
inference(pure_predicate_removal,[],[f91]) ).
fof(f91,plain,
? [X0] :
( with_infima_relstr(X0)
& with_suprema_relstr(X0)
& complemented_relstr(X0)
& heyting_relstr(X0)
& distributive_relstr(X0)
& ~ v1_yellow_3(X0)
& bounded_relstr(X0)
& upper_bounded_relstr(X0)
& lower_bounded_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& strict_rel_str(X0)
& ~ trivial_carrier(X0)
& ~ empty_carrier(X0)
& rel_str(X0) ),
inference(pure_predicate_removal,[],[f58]) ).
fof(f58,axiom,
? [X0] :
( with_infima_relstr(X0)
& with_suprema_relstr(X0)
& boolean_relstr(X0)
& complemented_relstr(X0)
& heyting_relstr(X0)
& distributive_relstr(X0)
& ~ v1_yellow_3(X0)
& bounded_relstr(X0)
& upper_bounded_relstr(X0)
& lower_bounded_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& strict_rel_str(X0)
& ~ trivial_carrier(X0)
& ~ empty_carrier(X0)
& rel_str(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_waybel_7) ).
fof(f655,plain,
spl34_27,
inference(avatar_split_clause,[],[f458,f652]) ).
fof(f652,plain,
( spl34_27
<=> with_suprema_relstr(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_27])]) ).
fof(f458,plain,
with_suprema_relstr(sK25),
inference(cnf_transformation,[],[f244]) ).
fof(f650,plain,
spl34_26,
inference(avatar_split_clause,[],[f457,f647]) ).
fof(f647,plain,
( spl34_26
<=> bounded_relstr(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_26])]) ).
fof(f457,plain,
bounded_relstr(sK25),
inference(cnf_transformation,[],[f244]) ).
fof(f645,plain,
spl34_25,
inference(avatar_split_clause,[],[f456,f642]) ).
fof(f642,plain,
( spl34_25
<=> upper_bounded_relstr(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_25])]) ).
fof(f456,plain,
upper_bounded_relstr(sK25),
inference(cnf_transformation,[],[f244]) ).
fof(f640,plain,
spl34_24,
inference(avatar_split_clause,[],[f455,f637]) ).
fof(f637,plain,
( spl34_24
<=> lower_bounded_relstr(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_24])]) ).
fof(f455,plain,
lower_bounded_relstr(sK25),
inference(cnf_transformation,[],[f244]) ).
fof(f635,plain,
spl34_23,
inference(avatar_split_clause,[],[f454,f632]) ).
fof(f632,plain,
( spl34_23
<=> antisymmetric_relstr(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_23])]) ).
fof(f454,plain,
antisymmetric_relstr(sK25),
inference(cnf_transformation,[],[f244]) ).
fof(f630,plain,
spl34_22,
inference(avatar_split_clause,[],[f453,f627]) ).
fof(f627,plain,
( spl34_22
<=> transitive_relstr(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_22])]) ).
fof(f453,plain,
transitive_relstr(sK25),
inference(cnf_transformation,[],[f244]) ).
fof(f625,plain,
spl34_21,
inference(avatar_split_clause,[],[f452,f622]) ).
fof(f622,plain,
( spl34_21
<=> reflexive_relstr(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_21])]) ).
fof(f452,plain,
reflexive_relstr(sK25),
inference(cnf_transformation,[],[f244]) ).
fof(f620,plain,
spl34_20,
inference(avatar_split_clause,[],[f451,f617]) ).
fof(f451,plain,
strict_rel_str(sK25),
inference(cnf_transformation,[],[f244]) ).
fof(f615,plain,
~ spl34_19,
inference(avatar_split_clause,[],[f450,f612]) ).
fof(f612,plain,
( spl34_19
<=> trivial_carrier(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_19])]) ).
fof(f450,plain,
~ trivial_carrier(sK25),
inference(cnf_transformation,[],[f244]) ).
fof(f610,plain,
~ spl34_18,
inference(avatar_split_clause,[],[f449,f607]) ).
fof(f607,plain,
( spl34_18
<=> empty_carrier(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_18])]) ).
fof(f449,plain,
~ empty_carrier(sK25),
inference(cnf_transformation,[],[f244]) ).
fof(f605,plain,
spl34_17,
inference(avatar_split_clause,[],[f448,f602]) ).
fof(f448,plain,
rel_str(sK25),
inference(cnf_transformation,[],[f244]) ).
fof(f600,plain,
~ spl34_16,
inference(avatar_split_clause,[],[f447,f597]) ).
fof(f597,plain,
( spl34_16
<=> empty_carrier(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_16])]) ).
fof(f447,plain,
~ empty_carrier(sK24),
inference(cnf_transformation,[],[f242]) ).
fof(f242,plain,
( ~ empty_carrier(sK24)
& one_sorted_str(sK24) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f67,f241]) ).
fof(f241,plain,
( ? [X0] :
( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ( ~ empty_carrier(sK24)
& one_sorted_str(sK24) ) ),
introduced(choice_axiom,[]) ).
fof(f67,axiom,
? [X0] :
( ~ empty_carrier(X0)
& one_sorted_str(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
fof(f595,plain,
spl34_15,
inference(avatar_split_clause,[],[f446,f592]) ).
fof(f592,plain,
( spl34_15
<=> one_sorted_str(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_15])]) ).
fof(f446,plain,
one_sorted_str(sK24),
inference(cnf_transformation,[],[f242]) ).
fof(f590,plain,
spl34_14,
inference(avatar_split_clause,[],[f445,f587]) ).
fof(f587,plain,
( spl34_14
<=> finite(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_14])]) ).
fof(f445,plain,
finite(sK23),
inference(cnf_transformation,[],[f240]) ).
fof(f240,plain,
( finite(sK23)
& ~ empty(sK23) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f54,f239]) ).
fof(f239,plain,
( ? [X0] :
( finite(X0)
& ~ empty(X0) )
=> ( finite(sK23)
& ~ empty(sK23) ) ),
introduced(choice_axiom,[]) ).
fof(f54,axiom,
? [X0] :
( finite(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
fof(f585,plain,
~ spl34_13,
inference(avatar_split_clause,[],[f444,f582]) ).
fof(f444,plain,
~ empty(sK23),
inference(cnf_transformation,[],[f240]) ).
fof(f580,plain,
~ spl34_12,
inference(avatar_split_clause,[],[f443,f577]) ).
fof(f443,plain,
~ empty(sK22),
inference(cnf_transformation,[],[f238]) ).
fof(f238,plain,
~ empty(sK22),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22])],[f117,f237]) ).
fof(f237,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK22) ),
introduced(choice_axiom,[]) ).
fof(f117,plain,
? [X0] : ~ empty(X0),
inference(pure_predicate_removal,[],[f61]) ).
fof(f61,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f575,plain,
spl34_11,
inference(avatar_split_clause,[],[f442,f572]) ).
fof(f442,plain,
rel_str(sK21),
inference(cnf_transformation,[],[f236]) ).
fof(f236,plain,
rel_str(sK21),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f34,f235]) ).
fof(f235,plain,
( ? [X0] : rel_str(X0)
=> rel_str(sK21) ),
introduced(choice_axiom,[]) ).
fof(f34,axiom,
? [X0] : rel_str(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_orders_2) ).
fof(f570,plain,
spl34_10,
inference(avatar_split_clause,[],[f441,f567]) ).
fof(f567,plain,
( spl34_10
<=> one_sorted_str(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_10])]) ).
fof(f441,plain,
one_sorted_str(sK20),
inference(cnf_transformation,[],[f234]) ).
fof(f234,plain,
one_sorted_str(sK20),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f35,f233]) ).
fof(f233,plain,
( ? [X0] : one_sorted_str(X0)
=> one_sorted_str(sK20) ),
introduced(choice_axiom,[]) ).
fof(f35,axiom,
? [X0] : one_sorted_str(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
fof(f565,plain,
spl34_9,
inference(avatar_split_clause,[],[f269,f562]) ).
fof(f269,plain,
empty(empty_set),
inference(cnf_transformation,[],[f115]) ).
fof(f115,plain,
empty(empty_set),
inference(pure_predicate_removal,[],[f45]) ).
fof(f45,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f560,plain,
spl34_8,
inference(avatar_split_clause,[],[f266,f557]) ).
fof(f266,plain,
element(sK6,powerset(the_carrier(boole_POSet(sK5)))),
inference(cnf_transformation,[],[f201]) ).
fof(f201,plain,
( empty(sK7)
& in(sK7,sK6)
& element(sK6,powerset(the_carrier(boole_POSet(sK5))))
& proper_element(sK6,powerset(the_carrier(boole_POSet(sK5))))
& upper_relstr_subset(sK6,boole_POSet(sK5))
& filtered_subset(sK6,boole_POSet(sK5))
& ~ empty(sK6)
& ~ empty(sK5) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f119,f200,f199,f198]) ).
fof(f198,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( empty(X2)
& in(X2,X1) )
& element(X1,powerset(the_carrier(boole_POSet(X0))))
& proper_element(X1,powerset(the_carrier(boole_POSet(X0))))
& upper_relstr_subset(X1,boole_POSet(X0))
& filtered_subset(X1,boole_POSet(X0))
& ~ empty(X1) )
& ~ empty(X0) )
=> ( ? [X1] :
( ? [X2] :
( empty(X2)
& in(X2,X1) )
& element(X1,powerset(the_carrier(boole_POSet(sK5))))
& proper_element(X1,powerset(the_carrier(boole_POSet(sK5))))
& upper_relstr_subset(X1,boole_POSet(sK5))
& filtered_subset(X1,boole_POSet(sK5))
& ~ empty(X1) )
& ~ empty(sK5) ) ),
introduced(choice_axiom,[]) ).
fof(f199,plain,
( ? [X1] :
( ? [X2] :
( empty(X2)
& in(X2,X1) )
& element(X1,powerset(the_carrier(boole_POSet(sK5))))
& proper_element(X1,powerset(the_carrier(boole_POSet(sK5))))
& upper_relstr_subset(X1,boole_POSet(sK5))
& filtered_subset(X1,boole_POSet(sK5))
& ~ empty(X1) )
=> ( ? [X2] :
( empty(X2)
& in(X2,sK6) )
& element(sK6,powerset(the_carrier(boole_POSet(sK5))))
& proper_element(sK6,powerset(the_carrier(boole_POSet(sK5))))
& upper_relstr_subset(sK6,boole_POSet(sK5))
& filtered_subset(sK6,boole_POSet(sK5))
& ~ empty(sK6) ) ),
introduced(choice_axiom,[]) ).
fof(f200,plain,
( ? [X2] :
( empty(X2)
& in(X2,sK6) )
=> ( empty(sK7)
& in(sK7,sK6) ) ),
introduced(choice_axiom,[]) ).
fof(f119,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( empty(X2)
& in(X2,X1) )
& element(X1,powerset(the_carrier(boole_POSet(X0))))
& proper_element(X1,powerset(the_carrier(boole_POSet(X0))))
& upper_relstr_subset(X1,boole_POSet(X0))
& filtered_subset(X1,boole_POSet(X0))
& ~ empty(X1) )
& ~ empty(X0) ),
inference(flattening,[],[f118]) ).
fof(f118,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( empty(X2)
& in(X2,X1) )
& element(X1,powerset(the_carrier(boole_POSet(X0))))
& proper_element(X1,powerset(the_carrier(boole_POSet(X0))))
& upper_relstr_subset(X1,boole_POSet(X0))
& filtered_subset(X1,boole_POSet(X0))
& ~ empty(X1) )
& ~ empty(X0) ),
inference(ennf_transformation,[],[f79]) ).
fof(f79,negated_conjecture,
~ ! [X0] :
( ~ empty(X0)
=> ! [X1] :
( ( element(X1,powerset(the_carrier(boole_POSet(X0))))
& proper_element(X1,powerset(the_carrier(boole_POSet(X0))))
& upper_relstr_subset(X1,boole_POSet(X0))
& filtered_subset(X1,boole_POSet(X0))
& ~ empty(X1) )
=> ! [X2] :
~ ( empty(X2)
& in(X2,X1) ) ) ),
inference(negated_conjecture,[],[f78]) ).
fof(f78,conjecture,
! [X0] :
( ~ empty(X0)
=> ! [X1] :
( ( element(X1,powerset(the_carrier(boole_POSet(X0))))
& proper_element(X1,powerset(the_carrier(boole_POSet(X0))))
& upper_relstr_subset(X1,boole_POSet(X0))
& filtered_subset(X1,boole_POSet(X0))
& ~ empty(X1) )
=> ! [X2] :
~ ( empty(X2)
& in(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_yellow19) ).
fof(f555,plain,
spl34_7,
inference(avatar_split_clause,[],[f265,f552]) ).
fof(f265,plain,
proper_element(sK6,powerset(the_carrier(boole_POSet(sK5)))),
inference(cnf_transformation,[],[f201]) ).
fof(f550,plain,
spl34_6,
inference(avatar_split_clause,[],[f264,f547]) ).
fof(f264,plain,
upper_relstr_subset(sK6,boole_POSet(sK5)),
inference(cnf_transformation,[],[f201]) ).
fof(f545,plain,
spl34_5,
inference(avatar_split_clause,[],[f263,f542]) ).
fof(f263,plain,
filtered_subset(sK6,boole_POSet(sK5)),
inference(cnf_transformation,[],[f201]) ).
fof(f540,plain,
spl34_4,
inference(avatar_split_clause,[],[f267,f537]) ).
fof(f267,plain,
in(sK7,sK6),
inference(cnf_transformation,[],[f201]) ).
fof(f535,plain,
spl34_3,
inference(avatar_split_clause,[],[f268,f532]) ).
fof(f268,plain,
empty(sK7),
inference(cnf_transformation,[],[f201]) ).
fof(f530,plain,
~ spl34_2,
inference(avatar_split_clause,[],[f262,f527]) ).
fof(f262,plain,
~ empty(sK6),
inference(cnf_transformation,[],[f201]) ).
fof(f525,plain,
~ spl34_1,
inference(avatar_split_clause,[],[f261,f522]) ).
fof(f261,plain,
~ empty(sK5),
inference(cnf_transformation,[],[f201]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SEU387+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.09 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.08/0.28 % Computer : n024.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 300
% 0.08/0.28 % DateTime : Mon Apr 29 20:29:06 EDT 2024
% 0.08/0.28 % CPUTime :
% 0.12/0.28 % (2822)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.29 % (2827)WARNING: value z3 for option sas not known
% 0.12/0.29 % (2828)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.12/0.29 % (2825)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.12/0.29 % (2829)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.12/0.29 % (2827)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.12/0.29 % (2830)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.12/0.29 % (2831)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.12/0.29 TRYING [1]
% 0.12/0.30 TRYING [2]
% 0.12/0.30 TRYING [3]
% 0.12/0.30 % (2826)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.12/0.30 TRYING [1]
% 0.12/0.30 TRYING [4]
% 0.12/0.30 TRYING [2]
% 0.12/0.31 % (2829)First to succeed.
% 0.12/0.31 TRYING [3]
% 0.12/0.31 TRYING [5]
% 0.12/0.31 % (2827)Also succeeded, but the first one will report.
% 0.12/0.31 % (2829)Refutation found. Thanks to Tanya!
% 0.12/0.31 % SZS status Theorem for theBenchmark
% 0.12/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.32 % (2829)------------------------------
% 0.12/0.32 % (2829)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.12/0.32 % (2829)Termination reason: Refutation
% 0.12/0.32
% 0.12/0.32 % (2829)Memory used [KB]: 1676
% 0.12/0.32 % (2829)Time elapsed: 0.024 s
% 0.12/0.32 % (2829)Instructions burned: 66 (million)
% 0.12/0.32 % (2829)------------------------------
% 0.12/0.32 % (2829)------------------------------
% 0.12/0.32 % (2822)Success in time 0.038 s
%------------------------------------------------------------------------------