TSTP Solution File: SEU350+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU350+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 : n021.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 15:30:18 EDT 2024
% Result : Theorem 0.22s 0.44s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 361
% Syntax : Number of formulae : 1210 ( 155 unt; 0 def)
% Number of atoms : 4402 ( 239 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 5607 (2415 ~;2577 |; 259 &)
% ( 290 <=>; 64 =>; 0 <=; 2 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 319 ( 317 usr; 284 prp; 0-3 aty)
% Number of functors : 30 ( 30 usr; 14 con; 0-2 aty)
% Number of variables : 1013 ( 961 !; 52 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2056,plain,
$false,
inference(avatar_sat_refutation,[],[f293,f298,f303,f308,f313,f318,f323,f328,f333,f338,f343,f348,f353,f358,f363,f368,f373,f378,f383,f388,f393,f398,f407,f411,f415,f419,f423,f427,f431,f435,f439,f443,f447,f451,f455,f459,f463,f467,f471,f477,f487,f494,f498,f502,f506,f510,f514,f518,f522,f527,f531,f535,f539,f543,f547,f551,f555,f559,f563,f574,f578,f582,f586,f591,f595,f599,f603,f607,f611,f619,f623,f627,f631,f635,f639,f643,f647,f651,f655,f671,f678,f682,f686,f690,f708,f712,f716,f720,f737,f741,f745,f749,f753,f757,f767,f771,f775,f779,f786,f790,f797,f801,f807,f811,f823,f827,f831,f835,f840,f850,f854,f861,f866,f871,f876,f881,f886,f891,f896,f901,f906,f911,f922,f930,f940,f947,f953,f962,f980,f984,f990,f994,f1001,f1005,f1006,f1007,f1010,f1029,f1033,f1037,f1041,f1045,f1060,f1064,f1072,f1076,f1080,f1087,f1091,f1095,f1099,f1104,f1113,f1118,f1139,f1143,f1153,f1157,f1161,f1170,f1177,f1181,f1186,f1190,f1194,f1205,f1210,f1220,f1224,f1228,f1242,f1249,f1253,f1257,f1273,f1282,f1286,f1290,f1301,f1305,f1314,f1319,f1324,f1331,f1336,f1347,f1356,f1364,f1368,f1386,f1396,f1402,f1409,f1416,f1424,f1428,f1432,f1436,f1440,f1444,f1453,f1457,f1461,f1465,f1469,f1473,f1491,f1495,f1499,f1503,f1507,f1511,f1539,f1543,f1551,f1556,f1560,f1565,f1569,f1573,f1577,f1581,f1585,f1613,f1617,f1627,f1636,f1646,f1650,f1654,f1658,f1668,f1674,f1680,f1684,f1692,f1696,f1700,f1704,f1729,f1743,f1748,f1752,f1756,f1761,f1775,f1789,f1800,f1814,f1828,f1836,f1850,f1854,f1873,f1877,f1889,f1894,f1916,f1921,f1927,f1935,f1940,f1945,f1950,f1956,f1960,f1965,f1975,f1977,f1979,f1993,f1994,f1995,f1997,f2007,f2010,f2012,f2017,f2027,f2029,f2034,f2038,f2044,f2051,f2055]) ).
fof(f2055,plain,
( ~ spl23_156
| spl23_23
| ~ spl23_272 ),
inference(avatar_split_clause,[],[f1998,f1963,f400,f1115]) ).
fof(f1115,plain,
( spl23_156
<=> latt_element_smaller(sK5,sK6,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_156])]) ).
fof(f400,plain,
( spl23_23
<=> relstr_set_smaller(poset_of_lattice(sK5),sK4,sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_23])]) ).
fof(f1963,plain,
( spl23_272
<=> ! [X0] :
( relstr_set_smaller(poset_of_lattice(sK5),X0,sK6)
| ~ latt_element_smaller(sK5,sK6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_272])]) ).
fof(f1998,plain,
( ~ latt_element_smaller(sK5,sK6,sK4)
| spl23_23
| ~ spl23_272 ),
inference(resolution,[],[f401,f1964]) ).
fof(f1964,plain,
( ! [X0] :
( relstr_set_smaller(poset_of_lattice(sK5),X0,sK6)
| ~ latt_element_smaller(sK5,sK6,X0) )
| ~ spl23_272 ),
inference(avatar_component_clause,[],[f1963]) ).
fof(f401,plain,
( ~ relstr_set_smaller(poset_of_lattice(sK5),sK4,sK6)
| spl23_23 ),
inference(avatar_component_clause,[],[f400]) ).
fof(f2051,plain,
( spl23_280
| ~ spl23_264
| ~ spl23_279 ),
inference(avatar_split_clause,[],[f2046,f2014,f1918,f2024]) ).
fof(f2024,plain,
( spl23_280
<=> in(sK9(the_carrier(sK5)),the_carrier(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_280])]) ).
fof(f1918,plain,
( spl23_264
<=> the_carrier(poset_of_lattice(sK5)) = the_carrier(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_264])]) ).
fof(f2014,plain,
( spl23_279
<=> in(sK9(the_carrier(poset_of_lattice(sK5))),the_carrier(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_279])]) ).
fof(f2046,plain,
( in(sK9(the_carrier(sK5)),the_carrier(sK5))
| ~ spl23_264
| ~ spl23_279 ),
inference(forward_demodulation,[],[f2016,f1920]) ).
fof(f1920,plain,
( the_carrier(poset_of_lattice(sK5)) = the_carrier(sK5)
| ~ spl23_264 ),
inference(avatar_component_clause,[],[f1918]) ).
fof(f2016,plain,
( in(sK9(the_carrier(poset_of_lattice(sK5))),the_carrier(sK5))
| ~ spl23_279 ),
inference(avatar_component_clause,[],[f2014]) ).
fof(f2044,plain,
( spl23_283
| ~ spl23_137
| ~ spl23_233
| ~ spl23_282 ),
inference(avatar_split_clause,[],[f2040,f2036,f1643,f992,f2042]) ).
fof(f2042,plain,
( spl23_283
<=> ! [X0] :
( latt_element_smaller(sK5,sK9(sK19),X0)
| ~ relstr_set_smaller(poset_of_lattice(sK5),X0,sK9(sK19)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_283])]) ).
fof(f992,plain,
( spl23_137
<=> ! [X0] :
( sK19 = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_137])]) ).
fof(f1643,plain,
( spl23_233
<=> empty(the_carrier(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_233])]) ).
fof(f2036,plain,
( spl23_282
<=> ! [X0] :
( ~ relstr_set_smaller(poset_of_lattice(sK5),X0,sK9(the_carrier(sK5)))
| latt_element_smaller(sK5,sK9(the_carrier(sK5)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_282])]) ).
fof(f2040,plain,
( ! [X0] :
( latt_element_smaller(sK5,sK9(sK19),X0)
| ~ relstr_set_smaller(poset_of_lattice(sK5),X0,sK9(sK19)) )
| ~ spl23_137
| ~ spl23_233
| ~ spl23_282 ),
inference(forward_demodulation,[],[f2039,f2020]) ).
fof(f2020,plain,
( sK19 = the_carrier(sK5)
| ~ spl23_137
| ~ spl23_233 ),
inference(resolution,[],[f1645,f993]) ).
fof(f993,plain,
( ! [X0] :
( ~ empty(X0)
| sK19 = X0 )
| ~ spl23_137 ),
inference(avatar_component_clause,[],[f992]) ).
fof(f1645,plain,
( empty(the_carrier(sK5))
| ~ spl23_233 ),
inference(avatar_component_clause,[],[f1643]) ).
fof(f2039,plain,
( ! [X0] :
( ~ relstr_set_smaller(poset_of_lattice(sK5),X0,sK9(sK19))
| latt_element_smaller(sK5,sK9(the_carrier(sK5)),X0) )
| ~ spl23_137
| ~ spl23_233
| ~ spl23_282 ),
inference(forward_demodulation,[],[f2037,f2020]) ).
fof(f2037,plain,
( ! [X0] :
( ~ relstr_set_smaller(poset_of_lattice(sK5),X0,sK9(the_carrier(sK5)))
| latt_element_smaller(sK5,sK9(the_carrier(sK5)),X0) )
| ~ spl23_282 ),
inference(avatar_component_clause,[],[f2036]) ).
fof(f2038,plain,
( spl23_1
| ~ spl23_2
| ~ spl23_3
| ~ spl23_273
| spl23_282
| ~ spl23_112
| ~ spl23_189 ),
inference(avatar_split_clause,[],[f1358,f1353,f852,f2036,f1968,f300,f295,f290]) ).
fof(f290,plain,
( spl23_1
<=> empty_carrier(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_1])]) ).
fof(f295,plain,
( spl23_2
<=> lattice(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_2])]) ).
fof(f300,plain,
( spl23_3
<=> latt_str(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_3])]) ).
fof(f1968,plain,
( spl23_273
<=> element(sK9(the_carrier(sK5)),the_carrier(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_273])]) ).
fof(f852,plain,
( spl23_112
<=> ! [X2,X0,X1] :
( latt_element_smaller(X1,X2,X0)
| ~ relstr_set_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2))
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_112])]) ).
fof(f1353,plain,
( spl23_189
<=> sK9(the_carrier(sK5)) = cast_to_el_of_LattPOSet(sK5,sK9(the_carrier(sK5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_189])]) ).
fof(f1358,plain,
( ! [X0] :
( ~ relstr_set_smaller(poset_of_lattice(sK5),X0,sK9(the_carrier(sK5)))
| latt_element_smaller(sK5,sK9(the_carrier(sK5)),X0)
| ~ element(sK9(the_carrier(sK5)),the_carrier(sK5))
| ~ latt_str(sK5)
| ~ lattice(sK5)
| empty_carrier(sK5) )
| ~ spl23_112
| ~ spl23_189 ),
inference(superposition,[],[f853,f1355]) ).
fof(f1355,plain,
( sK9(the_carrier(sK5)) = cast_to_el_of_LattPOSet(sK5,sK9(the_carrier(sK5)))
| ~ spl23_189 ),
inference(avatar_component_clause,[],[f1353]) ).
fof(f853,plain,
( ! [X2,X0,X1] :
( ~ relstr_set_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2))
| latt_element_smaller(X1,X2,X0)
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1) )
| ~ spl23_112 ),
inference(avatar_component_clause,[],[f852]) ).
fof(f2034,plain,
( spl23_281
| ~ spl23_39
| ~ spl23_200 ),
inference(avatar_split_clause,[],[f1445,f1434,f465,f2032]) ).
fof(f2032,plain,
( spl23_281
<=> ! [X0] : one_sorted_str(rel_str_of(X0,sK12(X0,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_281])]) ).
fof(f465,plain,
( spl23_39
<=> ! [X0] :
( one_sorted_str(X0)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_39])]) ).
fof(f1434,plain,
( spl23_200
<=> ! [X0] : rel_str(rel_str_of(X0,sK12(X0,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_200])]) ).
fof(f1445,plain,
( ! [X0] : one_sorted_str(rel_str_of(X0,sK12(X0,X0)))
| ~ spl23_39
| ~ spl23_200 ),
inference(resolution,[],[f1435,f466]) ).
fof(f466,plain,
( ! [X0] :
( ~ rel_str(X0)
| one_sorted_str(X0) )
| ~ spl23_39 ),
inference(avatar_component_clause,[],[f465]) ).
fof(f1435,plain,
( ! [X0] : rel_str(rel_str_of(X0,sK12(X0,X0)))
| ~ spl23_200 ),
inference(avatar_component_clause,[],[f1434]) ).
fof(f2029,plain,
( ~ spl23_233
| ~ spl23_60
| ~ spl23_232 ),
inference(avatar_split_clause,[],[f1719,f1639,f561,f1643]) ).
fof(f561,plain,
( spl23_60
<=> ! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_60])]) ).
fof(f1639,plain,
( spl23_232
<=> in(sK6,the_carrier(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_232])]) ).
fof(f1719,plain,
( ~ empty(the_carrier(sK5))
| ~ spl23_60
| ~ spl23_232 ),
inference(resolution,[],[f1641,f562]) ).
fof(f562,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) )
| ~ spl23_60 ),
inference(avatar_component_clause,[],[f561]) ).
fof(f1641,plain,
( in(sK6,the_carrier(sK5))
| ~ spl23_232 ),
inference(avatar_component_clause,[],[f1639]) ).
fof(f2027,plain,
( ~ spl23_280
| ~ spl23_264
| spl23_279 ),
inference(avatar_split_clause,[],[f2018,f2014,f1918,f2024]) ).
fof(f2018,plain,
( ~ in(sK9(the_carrier(sK5)),the_carrier(sK5))
| ~ spl23_264
| spl23_279 ),
inference(forward_demodulation,[],[f2015,f1920]) ).
fof(f2015,plain,
( ~ in(sK9(the_carrier(poset_of_lattice(sK5))),the_carrier(sK5))
| spl23_279 ),
inference(avatar_component_clause,[],[f2014]) ).
fof(f2017,plain,
( ~ spl23_277
| spl23_233
| spl23_1
| ~ spl23_2
| ~ spl23_3
| spl23_279
| ~ spl23_171
| ~ spl23_193 ),
inference(avatar_split_clause,[],[f1397,f1393,f1222,f2014,f300,f295,f290,f1643,f2000]) ).
fof(f2000,plain,
( spl23_277
<=> element(sK9(the_carrier(poset_of_lattice(sK5))),the_carrier(poset_of_lattice(sK5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_277])]) ).
fof(f1222,plain,
( spl23_171
<=> ! [X0,X1] :
( ~ element(X0,the_carrier(poset_of_lattice(X1)))
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1)
| empty(the_carrier(X1))
| in(cast_to_el_of_lattice(X1,X0),the_carrier(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_171])]) ).
fof(f1393,plain,
( spl23_193
<=> sK9(the_carrier(poset_of_lattice(sK5))) = cast_to_el_of_lattice(sK5,sK9(the_carrier(poset_of_lattice(sK5)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_193])]) ).
fof(f1397,plain,
( in(sK9(the_carrier(poset_of_lattice(sK5))),the_carrier(sK5))
| ~ latt_str(sK5)
| ~ lattice(sK5)
| empty_carrier(sK5)
| empty(the_carrier(sK5))
| ~ element(sK9(the_carrier(poset_of_lattice(sK5))),the_carrier(poset_of_lattice(sK5)))
| ~ spl23_171
| ~ spl23_193 ),
inference(superposition,[],[f1223,f1395]) ).
fof(f1395,plain,
( sK9(the_carrier(poset_of_lattice(sK5))) = cast_to_el_of_lattice(sK5,sK9(the_carrier(poset_of_lattice(sK5))))
| ~ spl23_193 ),
inference(avatar_component_clause,[],[f1393]) ).
fof(f1223,plain,
( ! [X0,X1] :
( in(cast_to_el_of_lattice(X1,X0),the_carrier(X1))
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1)
| empty(the_carrier(X1))
| ~ element(X0,the_carrier(poset_of_lattice(X1))) )
| ~ spl23_171 ),
inference(avatar_component_clause,[],[f1222]) ).
fof(f2012,plain,
( ~ spl23_273
| ~ spl23_264
| spl23_277 ),
inference(avatar_split_clause,[],[f2009,f2000,f1918,f1968]) ).
fof(f2009,plain,
( ~ element(sK9(the_carrier(sK5)),the_carrier(sK5))
| ~ spl23_264
| spl23_277 ),
inference(forward_demodulation,[],[f2002,f1920]) ).
fof(f2002,plain,
( ~ element(sK9(the_carrier(poset_of_lattice(sK5))),the_carrier(poset_of_lattice(sK5)))
| spl23_277 ),
inference(avatar_component_clause,[],[f2000]) ).
fof(f2010,plain,
( ~ spl23_273
| ~ spl23_264
| spl23_278 ),
inference(avatar_split_clause,[],[f2008,f2004,f1918,f1968]) ).
fof(f2004,plain,
( spl23_278
<=> element(sK9(the_carrier(poset_of_lattice(sK5))),the_carrier(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_278])]) ).
fof(f2008,plain,
( ~ element(sK9(the_carrier(sK5)),the_carrier(sK5))
| ~ spl23_264
| spl23_278 ),
inference(forward_demodulation,[],[f2005,f1920]) ).
fof(f2005,plain,
( ~ element(sK9(the_carrier(poset_of_lattice(sK5))),the_carrier(sK5))
| spl23_278 ),
inference(avatar_component_clause,[],[f2004]) ).
fof(f2007,plain,
( spl23_1
| ~ spl23_2
| ~ spl23_3
| ~ spl23_277
| spl23_278
| ~ spl23_105
| ~ spl23_193 ),
inference(avatar_split_clause,[],[f1398,f1393,f809,f2004,f2000,f300,f295,f290]) ).
fof(f809,plain,
( spl23_105
<=> ! [X0,X1] :
( element(cast_to_el_of_lattice(X0,X1),the_carrier(X0))
| ~ element(X1,the_carrier(poset_of_lattice(X0)))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_105])]) ).
fof(f1398,plain,
( element(sK9(the_carrier(poset_of_lattice(sK5))),the_carrier(sK5))
| ~ element(sK9(the_carrier(poset_of_lattice(sK5))),the_carrier(poset_of_lattice(sK5)))
| ~ latt_str(sK5)
| ~ lattice(sK5)
| empty_carrier(sK5)
| ~ spl23_105
| ~ spl23_193 ),
inference(superposition,[],[f810,f1395]) ).
fof(f810,plain,
( ! [X0,X1] :
( element(cast_to_el_of_lattice(X0,X1),the_carrier(X0))
| ~ element(X1,the_carrier(poset_of_lattice(X0)))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) )
| ~ spl23_105 ),
inference(avatar_component_clause,[],[f809]) ).
fof(f1997,plain,
( ~ spl23_23
| ~ spl23_156
| ~ spl23_127 ),
inference(avatar_split_clause,[],[f1119,f937,f1115,f400]) ).
fof(f937,plain,
( spl23_127
<=> sK6 = cast_to_el_of_lattice(sK5,sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_127])]) ).
fof(f1119,plain,
( ~ latt_element_smaller(sK5,sK6,sK4)
| ~ relstr_set_smaller(poset_of_lattice(sK5),sK4,sK6)
| ~ spl23_127 ),
inference(forward_demodulation,[],[f188,f939]) ).
fof(f939,plain,
( sK6 = cast_to_el_of_lattice(sK5,sK6)
| ~ spl23_127 ),
inference(avatar_component_clause,[],[f937]) ).
fof(f188,plain,
( ~ latt_element_smaller(sK5,cast_to_el_of_lattice(sK5,sK6),sK4)
| ~ relstr_set_smaller(poset_of_lattice(sK5),sK4,sK6) ),
inference(cnf_transformation,[],[f144]) ).
fof(f144,plain,
( ( ~ latt_element_smaller(sK5,cast_to_el_of_lattice(sK5,sK6),sK4)
| ~ relstr_set_smaller(poset_of_lattice(sK5),sK4,sK6) )
& ( latt_element_smaller(sK5,cast_to_el_of_lattice(sK5,sK6),sK4)
| relstr_set_smaller(poset_of_lattice(sK5),sK4,sK6) )
& element(sK6,the_carrier(poset_of_lattice(sK5)))
& latt_str(sK5)
& lattice(sK5)
& ~ empty_carrier(sK5) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f141,f143,f142]) ).
fof(f142,plain,
( ? [X0,X1] :
( ? [X2] :
( ( ~ latt_element_smaller(X1,cast_to_el_of_lattice(X1,X2),X0)
| ~ relstr_set_smaller(poset_of_lattice(X1),X0,X2) )
& ( latt_element_smaller(X1,cast_to_el_of_lattice(X1,X2),X0)
| relstr_set_smaller(poset_of_lattice(X1),X0,X2) )
& element(X2,the_carrier(poset_of_lattice(X1))) )
& latt_str(X1)
& lattice(X1)
& ~ empty_carrier(X1) )
=> ( ? [X2] :
( ( ~ latt_element_smaller(sK5,cast_to_el_of_lattice(sK5,X2),sK4)
| ~ relstr_set_smaller(poset_of_lattice(sK5),sK4,X2) )
& ( latt_element_smaller(sK5,cast_to_el_of_lattice(sK5,X2),sK4)
| relstr_set_smaller(poset_of_lattice(sK5),sK4,X2) )
& element(X2,the_carrier(poset_of_lattice(sK5))) )
& latt_str(sK5)
& lattice(sK5)
& ~ empty_carrier(sK5) ) ),
introduced(choice_axiom,[]) ).
fof(f143,plain,
( ? [X2] :
( ( ~ latt_element_smaller(sK5,cast_to_el_of_lattice(sK5,X2),sK4)
| ~ relstr_set_smaller(poset_of_lattice(sK5),sK4,X2) )
& ( latt_element_smaller(sK5,cast_to_el_of_lattice(sK5,X2),sK4)
| relstr_set_smaller(poset_of_lattice(sK5),sK4,X2) )
& element(X2,the_carrier(poset_of_lattice(sK5))) )
=> ( ( ~ latt_element_smaller(sK5,cast_to_el_of_lattice(sK5,sK6),sK4)
| ~ relstr_set_smaller(poset_of_lattice(sK5),sK4,sK6) )
& ( latt_element_smaller(sK5,cast_to_el_of_lattice(sK5,sK6),sK4)
| relstr_set_smaller(poset_of_lattice(sK5),sK4,sK6) )
& element(sK6,the_carrier(poset_of_lattice(sK5))) ) ),
introduced(choice_axiom,[]) ).
fof(f141,plain,
? [X0,X1] :
( ? [X2] :
( ( ~ latt_element_smaller(X1,cast_to_el_of_lattice(X1,X2),X0)
| ~ relstr_set_smaller(poset_of_lattice(X1),X0,X2) )
& ( latt_element_smaller(X1,cast_to_el_of_lattice(X1,X2),X0)
| relstr_set_smaller(poset_of_lattice(X1),X0,X2) )
& element(X2,the_carrier(poset_of_lattice(X1))) )
& latt_str(X1)
& lattice(X1)
& ~ empty_carrier(X1) ),
inference(flattening,[],[f140]) ).
fof(f140,plain,
? [X0,X1] :
( ? [X2] :
( ( ~ latt_element_smaller(X1,cast_to_el_of_lattice(X1,X2),X0)
| ~ relstr_set_smaller(poset_of_lattice(X1),X0,X2) )
& ( latt_element_smaller(X1,cast_to_el_of_lattice(X1,X2),X0)
| relstr_set_smaller(poset_of_lattice(X1),X0,X2) )
& element(X2,the_carrier(poset_of_lattice(X1))) )
& latt_str(X1)
& lattice(X1)
& ~ empty_carrier(X1) ),
inference(nnf_transformation,[],[f73]) ).
fof(f73,plain,
? [X0,X1] :
( ? [X2] :
( ( relstr_set_smaller(poset_of_lattice(X1),X0,X2)
<~> latt_element_smaller(X1,cast_to_el_of_lattice(X1,X2),X0) )
& element(X2,the_carrier(poset_of_lattice(X1))) )
& latt_str(X1)
& lattice(X1)
& ~ empty_carrier(X1) ),
inference(flattening,[],[f72]) ).
fof(f72,plain,
? [X0,X1] :
( ? [X2] :
( ( relstr_set_smaller(poset_of_lattice(X1),X0,X2)
<~> latt_element_smaller(X1,cast_to_el_of_lattice(X1,X2),X0) )
& element(X2,the_carrier(poset_of_lattice(X1))) )
& latt_str(X1)
& lattice(X1)
& ~ empty_carrier(X1) ),
inference(ennf_transformation,[],[f60]) ).
fof(f60,negated_conjecture,
~ ! [X0,X1] :
( ( latt_str(X1)
& lattice(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,the_carrier(poset_of_lattice(X1)))
=> ( relstr_set_smaller(poset_of_lattice(X1),X0,X2)
<=> latt_element_smaller(X1,cast_to_el_of_lattice(X1,X2),X0) ) ) ),
inference(negated_conjecture,[],[f59]) ).
fof(f59,conjecture,
! [X0,X1] :
( ( latt_str(X1)
& lattice(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,the_carrier(poset_of_lattice(X1)))
=> ( relstr_set_smaller(poset_of_lattice(X1),X0,X2)
<=> latt_element_smaller(X1,cast_to_el_of_lattice(X1,X2),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_lattice3) ).
fof(f1995,plain,
( ~ spl23_156
| spl23_24
| ~ spl23_127 ),
inference(avatar_split_clause,[],[f1120,f937,f404,f1115]) ).
fof(f404,plain,
( spl23_24
<=> latt_element_smaller(sK5,cast_to_el_of_lattice(sK5,sK6),sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_24])]) ).
fof(f1120,plain,
( ~ latt_element_smaller(sK5,sK6,sK4)
| spl23_24
| ~ spl23_127 ),
inference(forward_demodulation,[],[f405,f939]) ).
fof(f405,plain,
( ~ latt_element_smaller(sK5,cast_to_el_of_lattice(sK5,sK6),sK4)
| spl23_24 ),
inference(avatar_component_clause,[],[f404]) ).
fof(f1994,plain,
( spl23_156
| ~ spl23_23
| ~ spl23_271 ),
inference(avatar_split_clause,[],[f1961,f1958,f400,f1115]) ).
fof(f1958,plain,
( spl23_271
<=> ! [X0] :
( ~ relstr_set_smaller(poset_of_lattice(sK5),X0,sK6)
| latt_element_smaller(sK5,sK6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_271])]) ).
fof(f1961,plain,
( latt_element_smaller(sK5,sK6,sK4)
| ~ spl23_23
| ~ spl23_271 ),
inference(resolution,[],[f1959,f402]) ).
fof(f402,plain,
( relstr_set_smaller(poset_of_lattice(sK5),sK4,sK6)
| ~ spl23_23 ),
inference(avatar_component_clause,[],[f400]) ).
fof(f1959,plain,
( ! [X0] :
( ~ relstr_set_smaller(poset_of_lattice(sK5),X0,sK6)
| latt_element_smaller(sK5,sK6,X0) )
| ~ spl23_271 ),
inference(avatar_component_clause,[],[f1958]) ).
fof(f1993,plain,
( spl23_275
| ~ spl23_276
| ~ spl23_87
| ~ spl23_155
| ~ spl23_230 ),
inference(avatar_split_clause,[],[f1859,f1630,f1110,f710,f1990,f1986]) ).
fof(f1986,plain,
( spl23_275
<=> empty(the_carrier(sK22)) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_275])]) ).
fof(f1990,plain,
( spl23_276
<=> empty_carrier(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_276])]) ).
fof(f710,plain,
( spl23_87
<=> ! [X0,X1] :
( ~ empty_carrier(rel_str_of(X0,X1))
| ~ relation_of2(X1,X0,X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_87])]) ).
fof(f1110,plain,
( spl23_155
<=> sK22 = rel_str_of(the_carrier(sK22),the_InternalRel(sK22)) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_155])]) ).
fof(f1630,plain,
( spl23_230
<=> relation_of2(the_InternalRel(sK22),the_carrier(sK22),the_carrier(sK22)) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_230])]) ).
fof(f1859,plain,
( ~ empty_carrier(sK22)
| empty(the_carrier(sK22))
| ~ spl23_87
| ~ spl23_155
| ~ spl23_230 ),
inference(forward_demodulation,[],[f1855,f1112]) ).
fof(f1112,plain,
( sK22 = rel_str_of(the_carrier(sK22),the_InternalRel(sK22))
| ~ spl23_155 ),
inference(avatar_component_clause,[],[f1110]) ).
fof(f1855,plain,
( ~ empty_carrier(rel_str_of(the_carrier(sK22),the_InternalRel(sK22)))
| empty(the_carrier(sK22))
| ~ spl23_87
| ~ spl23_230 ),
inference(resolution,[],[f1631,f711]) ).
fof(f711,plain,
( ! [X0,X1] :
( ~ relation_of2(X1,X0,X0)
| ~ empty_carrier(rel_str_of(X0,X1))
| empty(X0) )
| ~ spl23_87 ),
inference(avatar_component_clause,[],[f710]) ).
fof(f1631,plain,
( relation_of2(the_InternalRel(sK22),the_carrier(sK22),the_carrier(sK22))
| ~ spl23_230 ),
inference(avatar_component_clause,[],[f1630]) ).
fof(f1979,plain,
( ~ spl23_40
| spl23_273 ),
inference(avatar_contradiction_clause,[],[f1978]) ).
fof(f1978,plain,
( $false
| ~ spl23_40
| spl23_273 ),
inference(resolution,[],[f1970,f470]) ).
fof(f470,plain,
( ! [X0] : element(sK9(X0),X0)
| ~ spl23_40 ),
inference(avatar_component_clause,[],[f469]) ).
fof(f469,plain,
( spl23_40
<=> ! [X0] : element(sK9(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_40])]) ).
fof(f1970,plain,
( ~ element(sK9(the_carrier(sK5)),the_carrier(sK5))
| spl23_273 ),
inference(avatar_component_clause,[],[f1968]) ).
fof(f1977,plain,
( ~ spl23_273
| ~ spl23_264
| spl23_274 ),
inference(avatar_split_clause,[],[f1976,f1972,f1918,f1968]) ).
fof(f1972,plain,
( spl23_274
<=> element(sK9(the_carrier(sK5)),the_carrier(poset_of_lattice(sK5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_274])]) ).
fof(f1976,plain,
( ~ element(sK9(the_carrier(sK5)),the_carrier(sK5))
| ~ spl23_264
| spl23_274 ),
inference(forward_demodulation,[],[f1973,f1920]) ).
fof(f1973,plain,
( ~ element(sK9(the_carrier(sK5)),the_carrier(poset_of_lattice(sK5)))
| spl23_274 ),
inference(avatar_component_clause,[],[f1972]) ).
fof(f1975,plain,
( spl23_1
| ~ spl23_2
| ~ spl23_3
| ~ spl23_273
| spl23_274
| ~ spl23_104
| ~ spl23_189 ),
inference(avatar_split_clause,[],[f1360,f1353,f805,f1972,f1968,f300,f295,f290]) ).
fof(f805,plain,
( spl23_104
<=> ! [X0,X1] :
( element(cast_to_el_of_LattPOSet(X0,X1),the_carrier(poset_of_lattice(X0)))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_104])]) ).
fof(f1360,plain,
( element(sK9(the_carrier(sK5)),the_carrier(poset_of_lattice(sK5)))
| ~ element(sK9(the_carrier(sK5)),the_carrier(sK5))
| ~ latt_str(sK5)
| ~ lattice(sK5)
| empty_carrier(sK5)
| ~ spl23_104
| ~ spl23_189 ),
inference(superposition,[],[f806,f1355]) ).
fof(f806,plain,
( ! [X0,X1] :
( element(cast_to_el_of_LattPOSet(X0,X1),the_carrier(poset_of_lattice(X0)))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) )
| ~ spl23_104 ),
inference(avatar_component_clause,[],[f805]) ).
fof(f1965,plain,
( spl23_1
| ~ spl23_2
| ~ spl23_3
| ~ spl23_192
| spl23_272
| ~ spl23_111
| ~ spl23_188 ),
inference(avatar_split_clause,[],[f1350,f1344,f848,f1963,f1383,f300,f295,f290]) ).
fof(f1383,plain,
( spl23_192
<=> element(sK6,the_carrier(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_192])]) ).
fof(f848,plain,
( spl23_111
<=> ! [X2,X0,X1] :
( relstr_set_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2))
| ~ latt_element_smaller(X1,X2,X0)
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_111])]) ).
fof(f1344,plain,
( spl23_188
<=> sK6 = cast_to_el_of_LattPOSet(sK5,sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_188])]) ).
fof(f1350,plain,
( ! [X0] :
( relstr_set_smaller(poset_of_lattice(sK5),X0,sK6)
| ~ latt_element_smaller(sK5,sK6,X0)
| ~ element(sK6,the_carrier(sK5))
| ~ latt_str(sK5)
| ~ lattice(sK5)
| empty_carrier(sK5) )
| ~ spl23_111
| ~ spl23_188 ),
inference(superposition,[],[f849,f1346]) ).
fof(f1346,plain,
( sK6 = cast_to_el_of_LattPOSet(sK5,sK6)
| ~ spl23_188 ),
inference(avatar_component_clause,[],[f1344]) ).
fof(f849,plain,
( ! [X2,X0,X1] :
( relstr_set_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2))
| ~ latt_element_smaller(X1,X2,X0)
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1) )
| ~ spl23_111 ),
inference(avatar_component_clause,[],[f848]) ).
fof(f1960,plain,
( spl23_1
| ~ spl23_2
| ~ spl23_3
| ~ spl23_192
| spl23_271
| ~ spl23_112
| ~ spl23_188 ),
inference(avatar_split_clause,[],[f1349,f1344,f852,f1958,f1383,f300,f295,f290]) ).
fof(f1349,plain,
( ! [X0] :
( ~ relstr_set_smaller(poset_of_lattice(sK5),X0,sK6)
| latt_element_smaller(sK5,sK6,X0)
| ~ element(sK6,the_carrier(sK5))
| ~ latt_str(sK5)
| ~ lattice(sK5)
| empty_carrier(sK5) )
| ~ spl23_112
| ~ spl23_188 ),
inference(superposition,[],[f853,f1346]) ).
fof(f1956,plain,
( spl23_270
| ~ spl23_195
| ~ spl23_262 ),
inference(avatar_split_clause,[],[f1912,f1891,f1407,f1953]) ).
fof(f1953,plain,
( spl23_270
<=> relation_of_lattice(sK5) = the_InternalRel(poset_of_lattice(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_270])]) ).
fof(f1407,plain,
( spl23_195
<=> ! [X0,X1] :
( rel_str_of(X0,X1) != poset_of_lattice(sK5)
| relation_of_lattice(sK5) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_195])]) ).
fof(f1891,plain,
( spl23_262
<=> poset_of_lattice(sK5) = rel_str_of(the_carrier(poset_of_lattice(sK5)),the_InternalRel(poset_of_lattice(sK5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_262])]) ).
fof(f1912,plain,
( relation_of_lattice(sK5) = the_InternalRel(poset_of_lattice(sK5))
| ~ spl23_195
| ~ spl23_262 ),
inference(trivial_inequality_removal,[],[f1905]) ).
fof(f1905,plain,
( poset_of_lattice(sK5) != poset_of_lattice(sK5)
| relation_of_lattice(sK5) = the_InternalRel(poset_of_lattice(sK5))
| ~ spl23_195
| ~ spl23_262 ),
inference(superposition,[],[f1408,f1893]) ).
fof(f1893,plain,
( poset_of_lattice(sK5) = rel_str_of(the_carrier(poset_of_lattice(sK5)),the_InternalRel(poset_of_lattice(sK5)))
| ~ spl23_262 ),
inference(avatar_component_clause,[],[f1891]) ).
fof(f1408,plain,
( ! [X0,X1] :
( rel_str_of(X0,X1) != poset_of_lattice(sK5)
| relation_of_lattice(sK5) = X1 )
| ~ spl23_195 ),
inference(avatar_component_clause,[],[f1407]) ).
fof(f1950,plain,
( spl23_1
| ~ spl23_3
| spl23_269
| ~ spl23_2
| ~ spl23_193
| ~ spl23_239 ),
inference(avatar_split_clause,[],[f1686,f1678,f1393,f295,f1947,f300,f290]) ).
fof(f1947,plain,
( spl23_269
<=> sK9(the_carrier(poset_of_lattice(sK5))) = cast_to_el_of_LattPOSet(sK5,sK9(the_carrier(poset_of_lattice(sK5)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_269])]) ).
fof(f1678,plain,
( spl23_239
<=> ! [X0] :
( ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| cast_to_el_of_lattice(X0,sK9(the_carrier(poset_of_lattice(X0)))) = cast_to_el_of_LattPOSet(X0,cast_to_el_of_lattice(X0,sK9(the_carrier(poset_of_lattice(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_239])]) ).
fof(f1686,plain,
( sK9(the_carrier(poset_of_lattice(sK5))) = cast_to_el_of_LattPOSet(sK5,sK9(the_carrier(poset_of_lattice(sK5))))
| ~ latt_str(sK5)
| empty_carrier(sK5)
| ~ spl23_2
| ~ spl23_193
| ~ spl23_239 ),
inference(forward_demodulation,[],[f1685,f1395]) ).
fof(f1685,plain,
( ~ latt_str(sK5)
| empty_carrier(sK5)
| cast_to_el_of_lattice(sK5,sK9(the_carrier(poset_of_lattice(sK5)))) = cast_to_el_of_LattPOSet(sK5,cast_to_el_of_lattice(sK5,sK9(the_carrier(poset_of_lattice(sK5)))))
| ~ spl23_2
| ~ spl23_239 ),
inference(resolution,[],[f1679,f297]) ).
fof(f297,plain,
( lattice(sK5)
| ~ spl23_2 ),
inference(avatar_component_clause,[],[f295]) ).
fof(f1679,plain,
( ! [X0] :
( ~ lattice(X0)
| ~ latt_str(X0)
| empty_carrier(X0)
| cast_to_el_of_lattice(X0,sK9(the_carrier(poset_of_lattice(X0)))) = cast_to_el_of_LattPOSet(X0,cast_to_el_of_lattice(X0,sK9(the_carrier(poset_of_lattice(X0))))) )
| ~ spl23_239 ),
inference(avatar_component_clause,[],[f1678]) ).
fof(f1945,plain,
( ~ spl23_115
| ~ spl23_183
| ~ spl23_181
| ~ spl23_170
| spl23_268
| ~ spl23_126
| ~ spl23_129
| ~ spl23_236 ),
inference(avatar_split_clause,[],[f1664,f1656,f950,f927,f1942,f1217,f1298,f1311,f868]) ).
fof(f868,plain,
( spl23_115
<=> sP2(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_115])]) ).
fof(f1311,plain,
( spl23_183
<=> reflexive(relation_of_lattice(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_183])]) ).
fof(f1298,plain,
( spl23_181
<=> antisymmetric(relation_of_lattice(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_181])]) ).
fof(f1217,plain,
( spl23_170
<=> transitive(relation_of_lattice(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_170])]) ).
fof(f1942,plain,
( spl23_268
<=> antisymmetric_relstr(poset_of_lattice(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_268])]) ).
fof(f927,plain,
( spl23_126
<=> k2_lattice3(sK5) = relation_of_lattice(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_126])]) ).
fof(f950,plain,
( spl23_129
<=> poset_of_lattice(sK5) = rel_str_of(the_carrier(sK5),relation_of_lattice(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_129])]) ).
fof(f1656,plain,
( spl23_236
<=> ! [X0] :
( antisymmetric_relstr(rel_str_of(the_carrier(X0),k2_lattice3(X0)))
| ~ transitive(k2_lattice3(X0))
| ~ antisymmetric(k2_lattice3(X0))
| ~ reflexive(k2_lattice3(X0))
| ~ sP2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_236])]) ).
fof(f1664,plain,
( antisymmetric_relstr(poset_of_lattice(sK5))
| ~ transitive(relation_of_lattice(sK5))
| ~ antisymmetric(relation_of_lattice(sK5))
| ~ reflexive(relation_of_lattice(sK5))
| ~ sP2(sK5)
| ~ spl23_126
| ~ spl23_129
| ~ spl23_236 ),
inference(forward_demodulation,[],[f1663,f952]) ).
fof(f952,plain,
( poset_of_lattice(sK5) = rel_str_of(the_carrier(sK5),relation_of_lattice(sK5))
| ~ spl23_129 ),
inference(avatar_component_clause,[],[f950]) ).
fof(f1663,plain,
( antisymmetric_relstr(rel_str_of(the_carrier(sK5),relation_of_lattice(sK5)))
| ~ transitive(relation_of_lattice(sK5))
| ~ antisymmetric(relation_of_lattice(sK5))
| ~ reflexive(relation_of_lattice(sK5))
| ~ sP2(sK5)
| ~ spl23_126
| ~ spl23_236 ),
inference(superposition,[],[f1657,f929]) ).
fof(f929,plain,
( k2_lattice3(sK5) = relation_of_lattice(sK5)
| ~ spl23_126 ),
inference(avatar_component_clause,[],[f927]) ).
fof(f1657,plain,
( ! [X0] :
( antisymmetric_relstr(rel_str_of(the_carrier(X0),k2_lattice3(X0)))
| ~ transitive(k2_lattice3(X0))
| ~ antisymmetric(k2_lattice3(X0))
| ~ reflexive(k2_lattice3(X0))
| ~ sP2(X0) )
| ~ spl23_236 ),
inference(avatar_component_clause,[],[f1656]) ).
fof(f1940,plain,
( ~ spl23_115
| ~ spl23_183
| ~ spl23_181
| ~ spl23_170
| spl23_267
| ~ spl23_126
| ~ spl23_129
| ~ spl23_235 ),
inference(avatar_split_clause,[],[f1662,f1652,f950,f927,f1937,f1217,f1298,f1311,f868]) ).
fof(f1937,plain,
( spl23_267
<=> transitive_relstr(poset_of_lattice(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_267])]) ).
fof(f1652,plain,
( spl23_235
<=> ! [X0] :
( transitive_relstr(rel_str_of(the_carrier(X0),k2_lattice3(X0)))
| ~ transitive(k2_lattice3(X0))
| ~ antisymmetric(k2_lattice3(X0))
| ~ reflexive(k2_lattice3(X0))
| ~ sP2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_235])]) ).
fof(f1662,plain,
( transitive_relstr(poset_of_lattice(sK5))
| ~ transitive(relation_of_lattice(sK5))
| ~ antisymmetric(relation_of_lattice(sK5))
| ~ reflexive(relation_of_lattice(sK5))
| ~ sP2(sK5)
| ~ spl23_126
| ~ spl23_129
| ~ spl23_235 ),
inference(forward_demodulation,[],[f1661,f952]) ).
fof(f1661,plain,
( transitive_relstr(rel_str_of(the_carrier(sK5),relation_of_lattice(sK5)))
| ~ transitive(relation_of_lattice(sK5))
| ~ antisymmetric(relation_of_lattice(sK5))
| ~ reflexive(relation_of_lattice(sK5))
| ~ sP2(sK5)
| ~ spl23_126
| ~ spl23_235 ),
inference(superposition,[],[f1653,f929]) ).
fof(f1653,plain,
( ! [X0] :
( transitive_relstr(rel_str_of(the_carrier(X0),k2_lattice3(X0)))
| ~ transitive(k2_lattice3(X0))
| ~ antisymmetric(k2_lattice3(X0))
| ~ reflexive(k2_lattice3(X0))
| ~ sP2(X0) )
| ~ spl23_235 ),
inference(avatar_component_clause,[],[f1652]) ).
fof(f1935,plain,
( ~ spl23_115
| ~ spl23_183
| ~ spl23_181
| ~ spl23_170
| spl23_266
| ~ spl23_126
| ~ spl23_129
| ~ spl23_234 ),
inference(avatar_split_clause,[],[f1660,f1648,f950,f927,f1932,f1217,f1298,f1311,f868]) ).
fof(f1932,plain,
( spl23_266
<=> reflexive_relstr(poset_of_lattice(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_266])]) ).
fof(f1648,plain,
( spl23_234
<=> ! [X0] :
( reflexive_relstr(rel_str_of(the_carrier(X0),k2_lattice3(X0)))
| ~ transitive(k2_lattice3(X0))
| ~ antisymmetric(k2_lattice3(X0))
| ~ reflexive(k2_lattice3(X0))
| ~ sP2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_234])]) ).
fof(f1660,plain,
( reflexive_relstr(poset_of_lattice(sK5))
| ~ transitive(relation_of_lattice(sK5))
| ~ antisymmetric(relation_of_lattice(sK5))
| ~ reflexive(relation_of_lattice(sK5))
| ~ sP2(sK5)
| ~ spl23_126
| ~ spl23_129
| ~ spl23_234 ),
inference(forward_demodulation,[],[f1659,f952]) ).
fof(f1659,plain,
( reflexive_relstr(rel_str_of(the_carrier(sK5),relation_of_lattice(sK5)))
| ~ transitive(relation_of_lattice(sK5))
| ~ antisymmetric(relation_of_lattice(sK5))
| ~ reflexive(relation_of_lattice(sK5))
| ~ sP2(sK5)
| ~ spl23_126
| ~ spl23_234 ),
inference(superposition,[],[f1649,f929]) ).
fof(f1649,plain,
( ! [X0] :
( reflexive_relstr(rel_str_of(the_carrier(X0),k2_lattice3(X0)))
| ~ transitive(k2_lattice3(X0))
| ~ antisymmetric(k2_lattice3(X0))
| ~ reflexive(k2_lattice3(X0))
| ~ sP2(X0) )
| ~ spl23_234 ),
inference(avatar_component_clause,[],[f1648]) ).
fof(f1927,plain,
( spl23_1
| ~ spl23_3
| spl23_265
| ~ spl23_2
| ~ spl23_189
| ~ spl23_237 ),
inference(avatar_split_clause,[],[f1670,f1666,f1353,f295,f1924,f300,f290]) ).
fof(f1924,plain,
( spl23_265
<=> sK9(the_carrier(sK5)) = cast_to_el_of_lattice(sK5,sK9(the_carrier(sK5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_265])]) ).
fof(f1666,plain,
( spl23_237
<=> ! [X0] :
( ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| cast_to_el_of_LattPOSet(X0,sK9(the_carrier(X0))) = cast_to_el_of_lattice(X0,cast_to_el_of_LattPOSet(X0,sK9(the_carrier(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_237])]) ).
fof(f1670,plain,
( sK9(the_carrier(sK5)) = cast_to_el_of_lattice(sK5,sK9(the_carrier(sK5)))
| ~ latt_str(sK5)
| empty_carrier(sK5)
| ~ spl23_2
| ~ spl23_189
| ~ spl23_237 ),
inference(forward_demodulation,[],[f1669,f1355]) ).
fof(f1669,plain,
( ~ latt_str(sK5)
| empty_carrier(sK5)
| cast_to_el_of_LattPOSet(sK5,sK9(the_carrier(sK5))) = cast_to_el_of_lattice(sK5,cast_to_el_of_LattPOSet(sK5,sK9(the_carrier(sK5))))
| ~ spl23_2
| ~ spl23_237 ),
inference(resolution,[],[f1667,f297]) ).
fof(f1667,plain,
( ! [X0] :
( ~ lattice(X0)
| ~ latt_str(X0)
| empty_carrier(X0)
| cast_to_el_of_LattPOSet(X0,sK9(the_carrier(X0))) = cast_to_el_of_lattice(X0,cast_to_el_of_LattPOSet(X0,sK9(the_carrier(X0)))) )
| ~ spl23_237 ),
inference(avatar_component_clause,[],[f1666]) ).
fof(f1921,plain,
( spl23_264
| ~ spl23_196
| ~ spl23_262 ),
inference(avatar_split_clause,[],[f1911,f1891,f1414,f1918]) ).
fof(f1414,plain,
( spl23_196
<=> ! [X0,X1] :
( rel_str_of(X0,X1) != poset_of_lattice(sK5)
| the_carrier(sK5) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_196])]) ).
fof(f1911,plain,
( the_carrier(poset_of_lattice(sK5)) = the_carrier(sK5)
| ~ spl23_196
| ~ spl23_262 ),
inference(trivial_inequality_removal,[],[f1906]) ).
fof(f1906,plain,
( poset_of_lattice(sK5) != poset_of_lattice(sK5)
| the_carrier(poset_of_lattice(sK5)) = the_carrier(sK5)
| ~ spl23_196
| ~ spl23_262 ),
inference(superposition,[],[f1415,f1893]) ).
fof(f1415,plain,
( ! [X0,X1] :
( rel_str_of(X0,X1) != poset_of_lattice(sK5)
| the_carrier(sK5) = X0 )
| ~ spl23_196 ),
inference(avatar_component_clause,[],[f1414]) ).
fof(f1916,plain,
( spl23_263
| ~ spl23_160
| ~ spl23_185 ),
inference(avatar_split_clause,[],[f1325,f1321,f1155,f1914]) ).
fof(f1914,plain,
( spl23_263
<=> ! [X0] :
( ~ in(X0,relation_of_lattice(sK5))
| element(X0,cartesian_product2(the_carrier(sK5),the_carrier(sK5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_263])]) ).
fof(f1155,plain,
( spl23_160
<=> ! [X0,X3,X2,X1] :
( element(X0,cartesian_product2(X1,X2))
| ~ in(X0,X3)
| ~ relation_of2_as_subset(X3,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_160])]) ).
fof(f1321,plain,
( spl23_185
<=> relation_of2_as_subset(relation_of_lattice(sK5),the_carrier(sK5),the_carrier(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_185])]) ).
fof(f1325,plain,
( ! [X0] :
( ~ in(X0,relation_of_lattice(sK5))
| element(X0,cartesian_product2(the_carrier(sK5),the_carrier(sK5))) )
| ~ spl23_160
| ~ spl23_185 ),
inference(resolution,[],[f1323,f1156]) ).
fof(f1156,plain,
( ! [X2,X3,X0,X1] :
( ~ relation_of2_as_subset(X3,X1,X2)
| ~ in(X0,X3)
| element(X0,cartesian_product2(X1,X2)) )
| ~ spl23_160 ),
inference(avatar_component_clause,[],[f1155]) ).
fof(f1323,plain,
( relation_of2_as_subset(relation_of_lattice(sK5),the_carrier(sK5),the_carrier(sK5))
| ~ spl23_185 ),
inference(avatar_component_clause,[],[f1321]) ).
fof(f1894,plain,
( spl23_262
| ~ spl23_116
| ~ spl23_217 ),
inference(avatar_split_clause,[],[f1552,f1549,f873,f1891]) ).
fof(f873,plain,
( spl23_116
<=> sP3(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_116])]) ).
fof(f1549,plain,
( spl23_217
<=> ! [X0] :
( poset_of_lattice(X0) = rel_str_of(the_carrier(poset_of_lattice(X0)),the_InternalRel(poset_of_lattice(X0)))
| ~ sP3(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_217])]) ).
fof(f1552,plain,
( poset_of_lattice(sK5) = rel_str_of(the_carrier(poset_of_lattice(sK5)),the_InternalRel(poset_of_lattice(sK5)))
| ~ spl23_116
| ~ spl23_217 ),
inference(resolution,[],[f1550,f875]) ).
fof(f875,plain,
( sP3(sK5)
| ~ spl23_116 ),
inference(avatar_component_clause,[],[f873]) ).
fof(f1550,plain,
( ! [X0] :
( ~ sP3(X0)
| poset_of_lattice(X0) = rel_str_of(the_carrier(poset_of_lattice(X0)),the_InternalRel(poset_of_lattice(X0))) )
| ~ spl23_217 ),
inference(avatar_component_clause,[],[f1549]) ).
fof(f1889,plain,
( spl23_260
| ~ spl23_261
| ~ spl23_155
| ~ spl23_195 ),
inference(avatar_split_clause,[],[f1412,f1407,f1110,f1886,f1882]) ).
fof(f1882,plain,
( spl23_260
<=> the_InternalRel(sK22) = relation_of_lattice(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_260])]) ).
fof(f1886,plain,
( spl23_261
<=> poset_of_lattice(sK5) = sK22 ),
introduced(avatar_definition,[new_symbols(naming,[spl23_261])]) ).
fof(f1412,plain,
( poset_of_lattice(sK5) != sK22
| the_InternalRel(sK22) = relation_of_lattice(sK5)
| ~ spl23_155
| ~ spl23_195 ),
inference(superposition,[],[f1408,f1112]) ).
fof(f1877,plain,
( ~ spl23_230
| spl23_259
| ~ spl23_98
| ~ spl23_155 ),
inference(avatar_split_clause,[],[f1124,f1110,f773,f1875,f1630]) ).
fof(f1875,plain,
( spl23_259
<=> ! [X0,X1] :
( rel_str_of(X0,X1) != sK22
| the_carrier(sK22) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_259])]) ).
fof(f773,plain,
( spl23_98
<=> ! [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,[spl23_98])]) ).
fof(f1124,plain,
( ! [X0,X1] :
( rel_str_of(X0,X1) != sK22
| the_carrier(sK22) = X0
| ~ relation_of2(the_InternalRel(sK22),the_carrier(sK22),the_carrier(sK22)) )
| ~ spl23_98
| ~ spl23_155 ),
inference(superposition,[],[f774,f1112]) ).
fof(f774,plain,
( ! [X2,X3,X0,X1] :
( rel_str_of(X0,X1) != rel_str_of(X2,X3)
| X0 = X2
| ~ relation_of2(X1,X0,X0) )
| ~ spl23_98 ),
inference(avatar_component_clause,[],[f773]) ).
fof(f1873,plain,
( spl23_257
| ~ spl23_258
| ~ spl23_154
| ~ spl23_195 ),
inference(avatar_split_clause,[],[f1411,f1407,f1101,f1870,f1866]) ).
fof(f1866,plain,
( spl23_257
<=> the_InternalRel(sK21) = relation_of_lattice(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_257])]) ).
fof(f1870,plain,
( spl23_258
<=> poset_of_lattice(sK5) = sK21 ),
introduced(avatar_definition,[new_symbols(naming,[spl23_258])]) ).
fof(f1101,plain,
( spl23_154
<=> sK21 = rel_str_of(the_carrier(sK21),the_InternalRel(sK21)) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_154])]) ).
fof(f1411,plain,
( poset_of_lattice(sK5) != sK21
| the_InternalRel(sK21) = relation_of_lattice(sK5)
| ~ spl23_154
| ~ spl23_195 ),
inference(superposition,[],[f1408,f1103]) ).
fof(f1103,plain,
( sK21 = rel_str_of(the_carrier(sK21),the_InternalRel(sK21))
| ~ spl23_154 ),
inference(avatar_component_clause,[],[f1101]) ).
fof(f1854,plain,
( ~ spl23_21
| ~ spl23_150
| spl23_230 ),
inference(avatar_split_clause,[],[f1637,f1630,f1085,f390]) ).
fof(f390,plain,
( spl23_21
<=> rel_str(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_21])]) ).
fof(f1085,plain,
( spl23_150
<=> ! [X0] :
( ~ rel_str(X0)
| relation_of2(the_InternalRel(X0),the_carrier(X0),the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_150])]) ).
fof(f1637,plain,
( ~ rel_str(sK22)
| ~ spl23_150
| spl23_230 ),
inference(resolution,[],[f1632,f1086]) ).
fof(f1086,plain,
( ! [X0] :
( relation_of2(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0) )
| ~ spl23_150 ),
inference(avatar_component_clause,[],[f1085]) ).
fof(f1632,plain,
( ~ relation_of2(the_InternalRel(sK22),the_carrier(sK22),the_carrier(sK22))
| spl23_230 ),
inference(avatar_component_clause,[],[f1630]) ).
fof(f1850,plain,
( ~ spl23_228
| spl23_256
| ~ spl23_98
| ~ spl23_154 ),
inference(avatar_split_clause,[],[f1108,f1101,f773,f1848,f1621]) ).
fof(f1621,plain,
( spl23_228
<=> relation_of2(the_InternalRel(sK21),the_carrier(sK21),the_carrier(sK21)) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_228])]) ).
fof(f1848,plain,
( spl23_256
<=> ! [X0,X1] :
( rel_str_of(X0,X1) != sK21
| the_carrier(sK21) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_256])]) ).
fof(f1108,plain,
( ! [X0,X1] :
( rel_str_of(X0,X1) != sK21
| the_carrier(sK21) = X0
| ~ relation_of2(the_InternalRel(sK21),the_carrier(sK21),the_carrier(sK21)) )
| ~ spl23_98
| ~ spl23_154 ),
inference(superposition,[],[f774,f1103]) ).
fof(f1836,plain,
( ~ spl23_15
| ~ spl23_150
| spl23_228 ),
inference(avatar_split_clause,[],[f1628,f1621,f1085,f360]) ).
fof(f360,plain,
( spl23_15
<=> rel_str(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_15])]) ).
fof(f1628,plain,
( ~ rel_str(sK21)
| ~ spl23_150
| spl23_228 ),
inference(resolution,[],[f1623,f1086]) ).
fof(f1623,plain,
( ~ relation_of2(the_InternalRel(sK21),the_carrier(sK21),the_carrier(sK21))
| spl23_228 ),
inference(avatar_component_clause,[],[f1621]) ).
fof(f1828,plain,
( spl23_255
| ~ spl23_105
| ~ spl23_182 ),
inference(avatar_split_clause,[],[f1307,f1303,f809,f1826]) ).
fof(f1826,plain,
( spl23_255
<=> ! [X0,X1] :
( ~ latt_str(poset_of_lattice(X0))
| ~ lattice(poset_of_lattice(X0))
| empty_carrier(poset_of_lattice(X0))
| cast_to_el_of_lattice(poset_of_lattice(X0),cast_to_el_of_lattice(poset_of_lattice(poset_of_lattice(X0)),X1)) = cast_to_el_of_lattice(X0,cast_to_el_of_lattice(poset_of_lattice(X0),cast_to_el_of_lattice(poset_of_lattice(poset_of_lattice(X0)),X1)))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| ~ element(X1,the_carrier(poset_of_lattice(poset_of_lattice(poset_of_lattice(X0)))))
| ~ latt_str(poset_of_lattice(poset_of_lattice(X0)))
| ~ lattice(poset_of_lattice(poset_of_lattice(X0)))
| empty_carrier(poset_of_lattice(poset_of_lattice(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_255])]) ).
fof(f1303,plain,
( spl23_182
<=> ! [X0,X1] :
( ~ element(X0,the_carrier(poset_of_lattice(poset_of_lattice(X1))))
| ~ latt_str(poset_of_lattice(X1))
| ~ lattice(poset_of_lattice(X1))
| empty_carrier(poset_of_lattice(X1))
| cast_to_el_of_lattice(poset_of_lattice(X1),X0) = cast_to_el_of_lattice(X1,cast_to_el_of_lattice(poset_of_lattice(X1),X0))
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_182])]) ).
fof(f1307,plain,
( ! [X0,X1] :
( ~ latt_str(poset_of_lattice(X0))
| ~ lattice(poset_of_lattice(X0))
| empty_carrier(poset_of_lattice(X0))
| cast_to_el_of_lattice(poset_of_lattice(X0),cast_to_el_of_lattice(poset_of_lattice(poset_of_lattice(X0)),X1)) = cast_to_el_of_lattice(X0,cast_to_el_of_lattice(poset_of_lattice(X0),cast_to_el_of_lattice(poset_of_lattice(poset_of_lattice(X0)),X1)))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| ~ element(X1,the_carrier(poset_of_lattice(poset_of_lattice(poset_of_lattice(X0)))))
| ~ latt_str(poset_of_lattice(poset_of_lattice(X0)))
| ~ lattice(poset_of_lattice(poset_of_lattice(X0)))
| empty_carrier(poset_of_lattice(poset_of_lattice(X0))) )
| ~ spl23_105
| ~ spl23_182 ),
inference(resolution,[],[f1304,f810]) ).
fof(f1304,plain,
( ! [X0,X1] :
( ~ element(X0,the_carrier(poset_of_lattice(poset_of_lattice(X1))))
| ~ latt_str(poset_of_lattice(X1))
| ~ lattice(poset_of_lattice(X1))
| empty_carrier(poset_of_lattice(X1))
| cast_to_el_of_lattice(poset_of_lattice(X1),X0) = cast_to_el_of_lattice(X1,cast_to_el_of_lattice(poset_of_lattice(X1),X0))
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1) )
| ~ spl23_182 ),
inference(avatar_component_clause,[],[f1303]) ).
fof(f1814,plain,
( spl23_254
| ~ spl23_104
| ~ spl23_177 ),
inference(avatar_split_clause,[],[f1274,f1271,f805,f1812]) ).
fof(f1812,plain,
( spl23_254
<=> ! [X0,X1] :
( ~ latt_str(poset_of_lattice(X0))
| ~ lattice(poset_of_lattice(X0))
| empty_carrier(poset_of_lattice(X0))
| cast_to_el_of_LattPOSet(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1)) = cast_to_el_of_LattPOSet(poset_of_lattice(poset_of_lattice(X0)),cast_to_el_of_LattPOSet(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1)))
| ~ latt_str(poset_of_lattice(poset_of_lattice(X0)))
| ~ lattice(poset_of_lattice(poset_of_lattice(X0)))
| empty_carrier(poset_of_lattice(poset_of_lattice(X0)))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_254])]) ).
fof(f1271,plain,
( spl23_177
<=> ! [X0,X1] :
( ~ element(X0,the_carrier(X1))
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1)
| cast_to_el_of_LattPOSet(X1,X0) = cast_to_el_of_LattPOSet(poset_of_lattice(X1),cast_to_el_of_LattPOSet(X1,X0))
| ~ latt_str(poset_of_lattice(X1))
| ~ lattice(poset_of_lattice(X1))
| empty_carrier(poset_of_lattice(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_177])]) ).
fof(f1274,plain,
( ! [X0,X1] :
( ~ latt_str(poset_of_lattice(X0))
| ~ lattice(poset_of_lattice(X0))
| empty_carrier(poset_of_lattice(X0))
| cast_to_el_of_LattPOSet(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1)) = cast_to_el_of_LattPOSet(poset_of_lattice(poset_of_lattice(X0)),cast_to_el_of_LattPOSet(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1)))
| ~ latt_str(poset_of_lattice(poset_of_lattice(X0)))
| ~ lattice(poset_of_lattice(poset_of_lattice(X0)))
| empty_carrier(poset_of_lattice(poset_of_lattice(X0)))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) )
| ~ spl23_104
| ~ spl23_177 ),
inference(resolution,[],[f1272,f806]) ).
fof(f1272,plain,
( ! [X0,X1] :
( ~ element(X0,the_carrier(X1))
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1)
| cast_to_el_of_LattPOSet(X1,X0) = cast_to_el_of_LattPOSet(poset_of_lattice(X1),cast_to_el_of_LattPOSet(X1,X0))
| ~ latt_str(poset_of_lattice(X1))
| ~ lattice(poset_of_lattice(X1))
| empty_carrier(poset_of_lattice(X1)) )
| ~ spl23_177 ),
inference(avatar_component_clause,[],[f1271]) ).
fof(f1800,plain,
( spl23_253
| ~ spl23_104
| ~ spl23_182 ),
inference(avatar_split_clause,[],[f1309,f1303,f805,f1798]) ).
fof(f1798,plain,
( spl23_253
<=> ! [X0,X1] :
( ~ latt_str(poset_of_lattice(X0))
| ~ lattice(poset_of_lattice(X0))
| empty_carrier(poset_of_lattice(X0))
| cast_to_el_of_lattice(poset_of_lattice(X0),cast_to_el_of_LattPOSet(poset_of_lattice(X0),X1)) = cast_to_el_of_lattice(X0,cast_to_el_of_lattice(poset_of_lattice(X0),cast_to_el_of_LattPOSet(poset_of_lattice(X0),X1)))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| ~ element(X1,the_carrier(poset_of_lattice(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_253])]) ).
fof(f1309,plain,
( ! [X0,X1] :
( ~ latt_str(poset_of_lattice(X0))
| ~ lattice(poset_of_lattice(X0))
| empty_carrier(poset_of_lattice(X0))
| cast_to_el_of_lattice(poset_of_lattice(X0),cast_to_el_of_LattPOSet(poset_of_lattice(X0),X1)) = cast_to_el_of_lattice(X0,cast_to_el_of_lattice(poset_of_lattice(X0),cast_to_el_of_LattPOSet(poset_of_lattice(X0),X1)))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| ~ element(X1,the_carrier(poset_of_lattice(X0))) )
| ~ spl23_104
| ~ spl23_182 ),
inference(duplicate_literal_removal,[],[f1306]) ).
fof(f1306,plain,
( ! [X0,X1] :
( ~ latt_str(poset_of_lattice(X0))
| ~ lattice(poset_of_lattice(X0))
| empty_carrier(poset_of_lattice(X0))
| cast_to_el_of_lattice(poset_of_lattice(X0),cast_to_el_of_LattPOSet(poset_of_lattice(X0),X1)) = cast_to_el_of_lattice(X0,cast_to_el_of_lattice(poset_of_lattice(X0),cast_to_el_of_LattPOSet(poset_of_lattice(X0),X1)))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| ~ element(X1,the_carrier(poset_of_lattice(X0)))
| ~ latt_str(poset_of_lattice(X0))
| ~ lattice(poset_of_lattice(X0))
| empty_carrier(poset_of_lattice(X0)) )
| ~ spl23_104
| ~ spl23_182 ),
inference(resolution,[],[f1304,f806]) ).
fof(f1789,plain,
( spl23_252
| ~ spl23_105
| ~ spl23_172 ),
inference(avatar_split_clause,[],[f1234,f1226,f809,f1787]) ).
fof(f1787,plain,
( spl23_252
<=> ! [X0,X1] :
( ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| cast_to_el_of_lattice(X0,cast_to_el_of_lattice(poset_of_lattice(X0),X1)) = cast_to_el_of_LattPOSet(X0,cast_to_el_of_lattice(X0,cast_to_el_of_lattice(poset_of_lattice(X0),X1)))
| ~ element(X1,the_carrier(poset_of_lattice(poset_of_lattice(X0))))
| ~ latt_str(poset_of_lattice(X0))
| ~ lattice(poset_of_lattice(X0))
| empty_carrier(poset_of_lattice(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_252])]) ).
fof(f1226,plain,
( spl23_172
<=> ! [X0,X1] :
( ~ element(X0,the_carrier(poset_of_lattice(X1)))
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1)
| cast_to_el_of_lattice(X1,X0) = cast_to_el_of_LattPOSet(X1,cast_to_el_of_lattice(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_172])]) ).
fof(f1234,plain,
( ! [X0,X1] :
( ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| cast_to_el_of_lattice(X0,cast_to_el_of_lattice(poset_of_lattice(X0),X1)) = cast_to_el_of_LattPOSet(X0,cast_to_el_of_lattice(X0,cast_to_el_of_lattice(poset_of_lattice(X0),X1)))
| ~ element(X1,the_carrier(poset_of_lattice(poset_of_lattice(X0))))
| ~ latt_str(poset_of_lattice(X0))
| ~ lattice(poset_of_lattice(X0))
| empty_carrier(poset_of_lattice(X0)) )
| ~ spl23_105
| ~ spl23_172 ),
inference(resolution,[],[f1227,f810]) ).
fof(f1227,plain,
( ! [X0,X1] :
( ~ element(X0,the_carrier(poset_of_lattice(X1)))
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1)
| cast_to_el_of_lattice(X1,X0) = cast_to_el_of_LattPOSet(X1,cast_to_el_of_lattice(X1,X0)) )
| ~ spl23_172 ),
inference(avatar_component_clause,[],[f1226]) ).
fof(f1775,plain,
( spl23_251
| ~ spl23_104
| ~ spl23_169 ),
inference(avatar_split_clause,[],[f1211,f1208,f805,f1773]) ).
fof(f1773,plain,
( spl23_251
<=> ! [X0,X1] :
( ~ latt_str(poset_of_lattice(X0))
| ~ lattice(poset_of_lattice(X0))
| empty_carrier(poset_of_lattice(X0))
| cast_to_el_of_LattPOSet(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1)) = cast_to_el_of_lattice(poset_of_lattice(X0),cast_to_el_of_LattPOSet(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1)))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_251])]) ).
fof(f1208,plain,
( spl23_169
<=> ! [X0,X1] :
( ~ element(X0,the_carrier(X1))
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1)
| cast_to_el_of_LattPOSet(X1,X0) = cast_to_el_of_lattice(X1,cast_to_el_of_LattPOSet(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_169])]) ).
fof(f1211,plain,
( ! [X0,X1] :
( ~ latt_str(poset_of_lattice(X0))
| ~ lattice(poset_of_lattice(X0))
| empty_carrier(poset_of_lattice(X0))
| cast_to_el_of_LattPOSet(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1)) = cast_to_el_of_lattice(poset_of_lattice(X0),cast_to_el_of_LattPOSet(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1)))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) )
| ~ spl23_104
| ~ spl23_169 ),
inference(resolution,[],[f1209,f806]) ).
fof(f1209,plain,
( ! [X0,X1] :
( ~ element(X0,the_carrier(X1))
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1)
| cast_to_el_of_LattPOSet(X1,X0) = cast_to_el_of_lattice(X1,cast_to_el_of_LattPOSet(X1,X0)) )
| ~ spl23_169 ),
inference(avatar_component_clause,[],[f1208]) ).
fof(f1761,plain,
( ~ spl23_250
| ~ spl23_61
| ~ spl23_232 ),
inference(avatar_split_clause,[],[f1721,f1639,f572,f1758]) ).
fof(f1758,plain,
( spl23_250
<=> in(the_carrier(sK5),sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_250])]) ).
fof(f572,plain,
( spl23_61
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_61])]) ).
fof(f1721,plain,
( ~ in(the_carrier(sK5),sK6)
| ~ spl23_61
| ~ spl23_232 ),
inference(resolution,[],[f1641,f573]) ).
fof(f573,plain,
( ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) )
| ~ spl23_61 ),
inference(avatar_component_clause,[],[f572]) ).
fof(f1756,plain,
( spl23_249
| ~ spl23_40
| ~ spl23_182 ),
inference(avatar_split_clause,[],[f1308,f1303,f469,f1754]) ).
fof(f1754,plain,
( spl23_249
<=> ! [X0] :
( ~ latt_str(poset_of_lattice(X0))
| ~ lattice(poset_of_lattice(X0))
| empty_carrier(poset_of_lattice(X0))
| cast_to_el_of_lattice(poset_of_lattice(X0),sK9(the_carrier(poset_of_lattice(poset_of_lattice(X0))))) = cast_to_el_of_lattice(X0,cast_to_el_of_lattice(poset_of_lattice(X0),sK9(the_carrier(poset_of_lattice(poset_of_lattice(X0))))))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_249])]) ).
fof(f1308,plain,
( ! [X0] :
( ~ latt_str(poset_of_lattice(X0))
| ~ lattice(poset_of_lattice(X0))
| empty_carrier(poset_of_lattice(X0))
| cast_to_el_of_lattice(poset_of_lattice(X0),sK9(the_carrier(poset_of_lattice(poset_of_lattice(X0))))) = cast_to_el_of_lattice(X0,cast_to_el_of_lattice(poset_of_lattice(X0),sK9(the_carrier(poset_of_lattice(poset_of_lattice(X0))))))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) )
| ~ spl23_40
| ~ spl23_182 ),
inference(resolution,[],[f1304,f470]) ).
fof(f1752,plain,
( spl23_248
| ~ spl23_105
| ~ spl23_177 ),
inference(avatar_split_clause,[],[f1278,f1271,f809,f1750]) ).
fof(f1750,plain,
( spl23_248
<=> ! [X0,X1] :
( ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| cast_to_el_of_LattPOSet(X0,cast_to_el_of_lattice(X0,X1)) = cast_to_el_of_LattPOSet(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,cast_to_el_of_lattice(X0,X1)))
| ~ latt_str(poset_of_lattice(X0))
| ~ lattice(poset_of_lattice(X0))
| empty_carrier(poset_of_lattice(X0))
| ~ element(X1,the_carrier(poset_of_lattice(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_248])]) ).
fof(f1278,plain,
( ! [X0,X1] :
( ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| cast_to_el_of_LattPOSet(X0,cast_to_el_of_lattice(X0,X1)) = cast_to_el_of_LattPOSet(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,cast_to_el_of_lattice(X0,X1)))
| ~ latt_str(poset_of_lattice(X0))
| ~ lattice(poset_of_lattice(X0))
| empty_carrier(poset_of_lattice(X0))
| ~ element(X1,the_carrier(poset_of_lattice(X0))) )
| ~ spl23_105
| ~ spl23_177 ),
inference(duplicate_literal_removal,[],[f1275]) ).
fof(f1275,plain,
( ! [X0,X1] :
( ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| cast_to_el_of_LattPOSet(X0,cast_to_el_of_lattice(X0,X1)) = cast_to_el_of_LattPOSet(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,cast_to_el_of_lattice(X0,X1)))
| ~ latt_str(poset_of_lattice(X0))
| ~ lattice(poset_of_lattice(X0))
| empty_carrier(poset_of_lattice(X0))
| ~ element(X1,the_carrier(poset_of_lattice(X0)))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) )
| ~ spl23_105
| ~ spl23_177 ),
inference(resolution,[],[f1272,f810]) ).
fof(f1748,plain,
( spl23_247
| ~ spl23_40
| ~ spl23_177 ),
inference(avatar_split_clause,[],[f1277,f1271,f469,f1746]) ).
fof(f1746,plain,
( spl23_247
<=> ! [X0] :
( ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| cast_to_el_of_LattPOSet(X0,sK9(the_carrier(X0))) = cast_to_el_of_LattPOSet(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,sK9(the_carrier(X0))))
| ~ latt_str(poset_of_lattice(X0))
| ~ lattice(poset_of_lattice(X0))
| empty_carrier(poset_of_lattice(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_247])]) ).
fof(f1277,plain,
( ! [X0] :
( ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| cast_to_el_of_LattPOSet(X0,sK9(the_carrier(X0))) = cast_to_el_of_LattPOSet(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,sK9(the_carrier(X0))))
| ~ latt_str(poset_of_lattice(X0))
| ~ lattice(poset_of_lattice(X0))
| empty_carrier(poset_of_lattice(X0)) )
| ~ spl23_40
| ~ spl23_177 ),
inference(resolution,[],[f1272,f470]) ).
fof(f1743,plain,
( spl23_246
| ~ spl23_91
| ~ spl23_141 ),
inference(avatar_split_clause,[],[f1050,f1031,f739,f1741]) ).
fof(f1741,plain,
( spl23_246
<=> ! [X0] :
( rel_str_of(X0,sK11(X0,X0)) = rel_str_of(the_carrier(rel_str_of(X0,sK11(X0,X0))),the_InternalRel(rel_str_of(X0,sK11(X0,X0))))
| ~ rel_str(rel_str_of(X0,sK11(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_246])]) ).
fof(f739,plain,
( spl23_91
<=> ! [X0] :
( rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0
| ~ strict_rel_str(X0)
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_91])]) ).
fof(f1031,plain,
( spl23_141
<=> ! [X0] : strict_rel_str(rel_str_of(X0,sK11(X0,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_141])]) ).
fof(f1050,plain,
( ! [X0] :
( rel_str_of(X0,sK11(X0,X0)) = rel_str_of(the_carrier(rel_str_of(X0,sK11(X0,X0))),the_InternalRel(rel_str_of(X0,sK11(X0,X0))))
| ~ rel_str(rel_str_of(X0,sK11(X0,X0))) )
| ~ spl23_91
| ~ spl23_141 ),
inference(resolution,[],[f1032,f740]) ).
fof(f740,plain,
( ! [X0] :
( ~ strict_rel_str(X0)
| rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0
| ~ rel_str(X0) )
| ~ spl23_91 ),
inference(avatar_component_clause,[],[f739]) ).
fof(f1032,plain,
( ! [X0] : strict_rel_str(rel_str_of(X0,sK11(X0,X0)))
| ~ spl23_141 ),
inference(avatar_component_clause,[],[f1031]) ).
fof(f1729,plain,
( spl23_245
| ~ spl23_105
| ~ spl23_169 ),
inference(avatar_split_clause,[],[f1215,f1208,f809,f1727]) ).
fof(f1727,plain,
( spl23_245
<=> ! [X0,X1] :
( ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| cast_to_el_of_LattPOSet(X0,cast_to_el_of_lattice(X0,X1)) = cast_to_el_of_lattice(X0,cast_to_el_of_LattPOSet(X0,cast_to_el_of_lattice(X0,X1)))
| ~ element(X1,the_carrier(poset_of_lattice(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_245])]) ).
fof(f1215,plain,
( ! [X0,X1] :
( ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| cast_to_el_of_LattPOSet(X0,cast_to_el_of_lattice(X0,X1)) = cast_to_el_of_lattice(X0,cast_to_el_of_LattPOSet(X0,cast_to_el_of_lattice(X0,X1)))
| ~ element(X1,the_carrier(poset_of_lattice(X0))) )
| ~ spl23_105
| ~ spl23_169 ),
inference(duplicate_literal_removal,[],[f1212]) ).
fof(f1212,plain,
( ! [X0,X1] :
( ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| cast_to_el_of_LattPOSet(X0,cast_to_el_of_lattice(X0,X1)) = cast_to_el_of_lattice(X0,cast_to_el_of_LattPOSet(X0,cast_to_el_of_lattice(X0,X1)))
| ~ element(X1,the_carrier(poset_of_lattice(X0)))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) )
| ~ spl23_105
| ~ spl23_169 ),
inference(resolution,[],[f1209,f810]) ).
fof(f1704,plain,
( spl23_244
| ~ spl23_150
| ~ spl23_180 ),
inference(avatar_split_clause,[],[f1296,f1288,f1085,f1702]) ).
fof(f1702,plain,
( spl23_244
<=> ! [X0] :
( antisymmetric_relstr(rel_str_of(the_carrier(X0),the_InternalRel(X0)))
| ~ transitive(the_InternalRel(X0))
| ~ antisymmetric(the_InternalRel(X0))
| ~ reflexive(the_InternalRel(X0))
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_244])]) ).
fof(f1288,plain,
( spl23_180
<=> ! [X0] :
( ~ relation_of2(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| antisymmetric_relstr(rel_str_of(the_carrier(X0),the_InternalRel(X0)))
| ~ transitive(the_InternalRel(X0))
| ~ antisymmetric(the_InternalRel(X0))
| ~ reflexive(the_InternalRel(X0))
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_180])]) ).
fof(f1296,plain,
( ! [X0] :
( antisymmetric_relstr(rel_str_of(the_carrier(X0),the_InternalRel(X0)))
| ~ transitive(the_InternalRel(X0))
| ~ antisymmetric(the_InternalRel(X0))
| ~ reflexive(the_InternalRel(X0))
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0) )
| ~ spl23_150
| ~ spl23_180 ),
inference(duplicate_literal_removal,[],[f1295]) ).
fof(f1295,plain,
( ! [X0] :
( antisymmetric_relstr(rel_str_of(the_carrier(X0),the_InternalRel(X0)))
| ~ transitive(the_InternalRel(X0))
| ~ antisymmetric(the_InternalRel(X0))
| ~ reflexive(the_InternalRel(X0))
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| ~ rel_str(X0) )
| ~ spl23_150
| ~ spl23_180 ),
inference(resolution,[],[f1289,f1086]) ).
fof(f1289,plain,
( ! [X0] :
( ~ relation_of2(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| antisymmetric_relstr(rel_str_of(the_carrier(X0),the_InternalRel(X0)))
| ~ transitive(the_InternalRel(X0))
| ~ antisymmetric(the_InternalRel(X0))
| ~ reflexive(the_InternalRel(X0))
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0) )
| ~ spl23_180 ),
inference(avatar_component_clause,[],[f1288]) ).
fof(f1700,plain,
( spl23_243
| ~ spl23_150
| ~ spl23_179 ),
inference(avatar_split_clause,[],[f1294,f1284,f1085,f1698]) ).
fof(f1698,plain,
( spl23_243
<=> ! [X0] :
( transitive_relstr(rel_str_of(the_carrier(X0),the_InternalRel(X0)))
| ~ transitive(the_InternalRel(X0))
| ~ antisymmetric(the_InternalRel(X0))
| ~ reflexive(the_InternalRel(X0))
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_243])]) ).
fof(f1284,plain,
( spl23_179
<=> ! [X0] :
( ~ relation_of2(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| transitive_relstr(rel_str_of(the_carrier(X0),the_InternalRel(X0)))
| ~ transitive(the_InternalRel(X0))
| ~ antisymmetric(the_InternalRel(X0))
| ~ reflexive(the_InternalRel(X0))
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_179])]) ).
fof(f1294,plain,
( ! [X0] :
( transitive_relstr(rel_str_of(the_carrier(X0),the_InternalRel(X0)))
| ~ transitive(the_InternalRel(X0))
| ~ antisymmetric(the_InternalRel(X0))
| ~ reflexive(the_InternalRel(X0))
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0) )
| ~ spl23_150
| ~ spl23_179 ),
inference(duplicate_literal_removal,[],[f1293]) ).
fof(f1293,plain,
( ! [X0] :
( transitive_relstr(rel_str_of(the_carrier(X0),the_InternalRel(X0)))
| ~ transitive(the_InternalRel(X0))
| ~ antisymmetric(the_InternalRel(X0))
| ~ reflexive(the_InternalRel(X0))
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| ~ rel_str(X0) )
| ~ spl23_150
| ~ spl23_179 ),
inference(resolution,[],[f1285,f1086]) ).
fof(f1285,plain,
( ! [X0] :
( ~ relation_of2(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| transitive_relstr(rel_str_of(the_carrier(X0),the_InternalRel(X0)))
| ~ transitive(the_InternalRel(X0))
| ~ antisymmetric(the_InternalRel(X0))
| ~ reflexive(the_InternalRel(X0))
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0) )
| ~ spl23_179 ),
inference(avatar_component_clause,[],[f1284]) ).
fof(f1696,plain,
( spl23_242
| ~ spl23_150
| ~ spl23_178 ),
inference(avatar_split_clause,[],[f1292,f1280,f1085,f1694]) ).
fof(f1694,plain,
( spl23_242
<=> ! [X0] :
( reflexive_relstr(rel_str_of(the_carrier(X0),the_InternalRel(X0)))
| ~ transitive(the_InternalRel(X0))
| ~ antisymmetric(the_InternalRel(X0))
| ~ reflexive(the_InternalRel(X0))
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_242])]) ).
fof(f1280,plain,
( spl23_178
<=> ! [X0] :
( ~ relation_of2(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| reflexive_relstr(rel_str_of(the_carrier(X0),the_InternalRel(X0)))
| ~ transitive(the_InternalRel(X0))
| ~ antisymmetric(the_InternalRel(X0))
| ~ reflexive(the_InternalRel(X0))
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_178])]) ).
fof(f1292,plain,
( ! [X0] :
( reflexive_relstr(rel_str_of(the_carrier(X0),the_InternalRel(X0)))
| ~ transitive(the_InternalRel(X0))
| ~ antisymmetric(the_InternalRel(X0))
| ~ reflexive(the_InternalRel(X0))
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0) )
| ~ spl23_150
| ~ spl23_178 ),
inference(duplicate_literal_removal,[],[f1291]) ).
fof(f1291,plain,
( ! [X0] :
( reflexive_relstr(rel_str_of(the_carrier(X0),the_InternalRel(X0)))
| ~ transitive(the_InternalRel(X0))
| ~ antisymmetric(the_InternalRel(X0))
| ~ reflexive(the_InternalRel(X0))
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| ~ rel_str(X0) )
| ~ spl23_150
| ~ spl23_178 ),
inference(resolution,[],[f1281,f1086]) ).
fof(f1281,plain,
( ! [X0] :
( ~ relation_of2(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| reflexive_relstr(rel_str_of(the_carrier(X0),the_InternalRel(X0)))
| ~ transitive(the_InternalRel(X0))
| ~ antisymmetric(the_InternalRel(X0))
| ~ reflexive(the_InternalRel(X0))
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0) )
| ~ spl23_178 ),
inference(avatar_component_clause,[],[f1280]) ).
fof(f1692,plain,
( spl23_241
| ~ spl23_104
| ~ spl23_172 ),
inference(avatar_split_clause,[],[f1237,f1226,f805,f1690]) ).
fof(f1690,plain,
( spl23_241
<=> ! [X0,X1] :
( ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| cast_to_el_of_lattice(X0,cast_to_el_of_LattPOSet(X0,X1)) = cast_to_el_of_LattPOSet(X0,cast_to_el_of_lattice(X0,cast_to_el_of_LattPOSet(X0,X1)))
| ~ element(X1,the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_241])]) ).
fof(f1237,plain,
( ! [X0,X1] :
( ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| cast_to_el_of_lattice(X0,cast_to_el_of_LattPOSet(X0,X1)) = cast_to_el_of_LattPOSet(X0,cast_to_el_of_lattice(X0,cast_to_el_of_LattPOSet(X0,X1)))
| ~ element(X1,the_carrier(X0)) )
| ~ spl23_104
| ~ spl23_172 ),
inference(duplicate_literal_removal,[],[f1233]) ).
fof(f1233,plain,
( ! [X0,X1] :
( ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| cast_to_el_of_lattice(X0,cast_to_el_of_LattPOSet(X0,X1)) = cast_to_el_of_LattPOSet(X0,cast_to_el_of_lattice(X0,cast_to_el_of_LattPOSet(X0,X1)))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) )
| ~ spl23_104
| ~ spl23_172 ),
inference(resolution,[],[f1227,f806]) ).
fof(f1684,plain,
( spl23_240
| ~ spl23_61
| ~ spl23_173 ),
inference(avatar_split_clause,[],[f1245,f1240,f572,f1682]) ).
fof(f1682,plain,
( spl23_240
<=> ! [X0,X1] :
( ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| empty(the_carrier(poset_of_lattice(X0)))
| ~ element(X1,the_carrier(X0))
| ~ in(the_carrier(poset_of_lattice(X0)),cast_to_el_of_LattPOSet(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_240])]) ).
fof(f1240,plain,
( spl23_173
<=> ! [X0,X1] :
( ~ element(X0,the_carrier(X1))
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1)
| empty(the_carrier(poset_of_lattice(X1)))
| in(cast_to_el_of_LattPOSet(X1,X0),the_carrier(poset_of_lattice(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_173])]) ).
fof(f1245,plain,
( ! [X0,X1] :
( ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| empty(the_carrier(poset_of_lattice(X0)))
| ~ element(X1,the_carrier(X0))
| ~ in(the_carrier(poset_of_lattice(X0)),cast_to_el_of_LattPOSet(X0,X1)) )
| ~ spl23_61
| ~ spl23_173 ),
inference(resolution,[],[f1241,f573]) ).
fof(f1241,plain,
( ! [X0,X1] :
( in(cast_to_el_of_LattPOSet(X1,X0),the_carrier(poset_of_lattice(X1)))
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1)
| empty(the_carrier(poset_of_lattice(X1)))
| ~ element(X0,the_carrier(X1)) )
| ~ spl23_173 ),
inference(avatar_component_clause,[],[f1240]) ).
fof(f1680,plain,
( spl23_239
| ~ spl23_40
| ~ spl23_172 ),
inference(avatar_split_clause,[],[f1236,f1226,f469,f1678]) ).
fof(f1236,plain,
( ! [X0] :
( ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| cast_to_el_of_lattice(X0,sK9(the_carrier(poset_of_lattice(X0)))) = cast_to_el_of_LattPOSet(X0,cast_to_el_of_lattice(X0,sK9(the_carrier(poset_of_lattice(X0))))) )
| ~ spl23_40
| ~ spl23_172 ),
inference(resolution,[],[f1227,f470]) ).
fof(f1674,plain,
( spl23_238
| ~ spl23_61
| ~ spl23_171 ),
inference(avatar_split_clause,[],[f1231,f1222,f572,f1672]) ).
fof(f1672,plain,
( spl23_238
<=> ! [X0,X1] :
( ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| empty(the_carrier(X0))
| ~ element(X1,the_carrier(poset_of_lattice(X0)))
| ~ in(the_carrier(X0),cast_to_el_of_lattice(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_238])]) ).
fof(f1231,plain,
( ! [X0,X1] :
( ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| empty(the_carrier(X0))
| ~ element(X1,the_carrier(poset_of_lattice(X0)))
| ~ in(the_carrier(X0),cast_to_el_of_lattice(X0,X1)) )
| ~ spl23_61
| ~ spl23_171 ),
inference(resolution,[],[f1223,f573]) ).
fof(f1668,plain,
( spl23_237
| ~ spl23_40
| ~ spl23_169 ),
inference(avatar_split_clause,[],[f1214,f1208,f469,f1666]) ).
fof(f1214,plain,
( ! [X0] :
( ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| cast_to_el_of_LattPOSet(X0,sK9(the_carrier(X0))) = cast_to_el_of_lattice(X0,cast_to_el_of_LattPOSet(X0,sK9(the_carrier(X0)))) )
| ~ spl23_40
| ~ spl23_169 ),
inference(resolution,[],[f1209,f470]) ).
fof(f1658,plain,
( spl23_236
| ~ spl23_151
| ~ spl23_176 ),
inference(avatar_split_clause,[],[f1268,f1255,f1089,f1656]) ).
fof(f1089,plain,
( spl23_151
<=> ! [X0] :
( ~ sP2(X0)
| relation_of2(k2_lattice3(X0),the_carrier(X0),the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_151])]) ).
fof(f1255,plain,
( spl23_176
<=> ! [X0] :
( ~ relation_of2(k2_lattice3(X0),the_carrier(X0),the_carrier(X0))
| antisymmetric_relstr(rel_str_of(the_carrier(X0),k2_lattice3(X0)))
| ~ transitive(k2_lattice3(X0))
| ~ antisymmetric(k2_lattice3(X0))
| ~ reflexive(k2_lattice3(X0))
| ~ sP2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_176])]) ).
fof(f1268,plain,
( ! [X0] :
( antisymmetric_relstr(rel_str_of(the_carrier(X0),k2_lattice3(X0)))
| ~ transitive(k2_lattice3(X0))
| ~ antisymmetric(k2_lattice3(X0))
| ~ reflexive(k2_lattice3(X0))
| ~ sP2(X0) )
| ~ spl23_151
| ~ spl23_176 ),
inference(duplicate_literal_removal,[],[f1266]) ).
fof(f1266,plain,
( ! [X0] :
( antisymmetric_relstr(rel_str_of(the_carrier(X0),k2_lattice3(X0)))
| ~ transitive(k2_lattice3(X0))
| ~ antisymmetric(k2_lattice3(X0))
| ~ reflexive(k2_lattice3(X0))
| ~ sP2(X0)
| ~ sP2(X0) )
| ~ spl23_151
| ~ spl23_176 ),
inference(resolution,[],[f1256,f1090]) ).
fof(f1090,plain,
( ! [X0] :
( relation_of2(k2_lattice3(X0),the_carrier(X0),the_carrier(X0))
| ~ sP2(X0) )
| ~ spl23_151 ),
inference(avatar_component_clause,[],[f1089]) ).
fof(f1256,plain,
( ! [X0] :
( ~ relation_of2(k2_lattice3(X0),the_carrier(X0),the_carrier(X0))
| antisymmetric_relstr(rel_str_of(the_carrier(X0),k2_lattice3(X0)))
| ~ transitive(k2_lattice3(X0))
| ~ antisymmetric(k2_lattice3(X0))
| ~ reflexive(k2_lattice3(X0))
| ~ sP2(X0) )
| ~ spl23_176 ),
inference(avatar_component_clause,[],[f1255]) ).
fof(f1654,plain,
( spl23_235
| ~ spl23_151
| ~ spl23_175 ),
inference(avatar_split_clause,[],[f1264,f1251,f1089,f1652]) ).
fof(f1251,plain,
( spl23_175
<=> ! [X0] :
( ~ relation_of2(k2_lattice3(X0),the_carrier(X0),the_carrier(X0))
| transitive_relstr(rel_str_of(the_carrier(X0),k2_lattice3(X0)))
| ~ transitive(k2_lattice3(X0))
| ~ antisymmetric(k2_lattice3(X0))
| ~ reflexive(k2_lattice3(X0))
| ~ sP2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_175])]) ).
fof(f1264,plain,
( ! [X0] :
( transitive_relstr(rel_str_of(the_carrier(X0),k2_lattice3(X0)))
| ~ transitive(k2_lattice3(X0))
| ~ antisymmetric(k2_lattice3(X0))
| ~ reflexive(k2_lattice3(X0))
| ~ sP2(X0) )
| ~ spl23_151
| ~ spl23_175 ),
inference(duplicate_literal_removal,[],[f1262]) ).
fof(f1262,plain,
( ! [X0] :
( transitive_relstr(rel_str_of(the_carrier(X0),k2_lattice3(X0)))
| ~ transitive(k2_lattice3(X0))
| ~ antisymmetric(k2_lattice3(X0))
| ~ reflexive(k2_lattice3(X0))
| ~ sP2(X0)
| ~ sP2(X0) )
| ~ spl23_151
| ~ spl23_175 ),
inference(resolution,[],[f1252,f1090]) ).
fof(f1252,plain,
( ! [X0] :
( ~ relation_of2(k2_lattice3(X0),the_carrier(X0),the_carrier(X0))
| transitive_relstr(rel_str_of(the_carrier(X0),k2_lattice3(X0)))
| ~ transitive(k2_lattice3(X0))
| ~ antisymmetric(k2_lattice3(X0))
| ~ reflexive(k2_lattice3(X0))
| ~ sP2(X0) )
| ~ spl23_175 ),
inference(avatar_component_clause,[],[f1251]) ).
fof(f1650,plain,
( spl23_234
| ~ spl23_151
| ~ spl23_174 ),
inference(avatar_split_clause,[],[f1260,f1247,f1089,f1648]) ).
fof(f1247,plain,
( spl23_174
<=> ! [X0] :
( ~ relation_of2(k2_lattice3(X0),the_carrier(X0),the_carrier(X0))
| reflexive_relstr(rel_str_of(the_carrier(X0),k2_lattice3(X0)))
| ~ transitive(k2_lattice3(X0))
| ~ antisymmetric(k2_lattice3(X0))
| ~ reflexive(k2_lattice3(X0))
| ~ sP2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_174])]) ).
fof(f1260,plain,
( ! [X0] :
( reflexive_relstr(rel_str_of(the_carrier(X0),k2_lattice3(X0)))
| ~ transitive(k2_lattice3(X0))
| ~ antisymmetric(k2_lattice3(X0))
| ~ reflexive(k2_lattice3(X0))
| ~ sP2(X0) )
| ~ spl23_151
| ~ spl23_174 ),
inference(duplicate_literal_removal,[],[f1258]) ).
fof(f1258,plain,
( ! [X0] :
( reflexive_relstr(rel_str_of(the_carrier(X0),k2_lattice3(X0)))
| ~ transitive(k2_lattice3(X0))
| ~ antisymmetric(k2_lattice3(X0))
| ~ reflexive(k2_lattice3(X0))
| ~ sP2(X0)
| ~ sP2(X0) )
| ~ spl23_151
| ~ spl23_174 ),
inference(resolution,[],[f1248,f1090]) ).
fof(f1248,plain,
( ! [X0] :
( ~ relation_of2(k2_lattice3(X0),the_carrier(X0),the_carrier(X0))
| reflexive_relstr(rel_str_of(the_carrier(X0),k2_lattice3(X0)))
| ~ transitive(k2_lattice3(X0))
| ~ antisymmetric(k2_lattice3(X0))
| ~ reflexive(k2_lattice3(X0))
| ~ sP2(X0) )
| ~ spl23_174 ),
inference(avatar_component_clause,[],[f1247]) ).
fof(f1646,plain,
( spl23_232
| spl23_233
| ~ spl23_75
| ~ spl23_192 ),
inference(avatar_split_clause,[],[f1390,f1383,f633,f1643,f1639]) ).
fof(f633,plain,
( spl23_75
<=> ! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_75])]) ).
fof(f1390,plain,
( empty(the_carrier(sK5))
| in(sK6,the_carrier(sK5))
| ~ spl23_75
| ~ spl23_192 ),
inference(resolution,[],[f1385,f634]) ).
fof(f634,plain,
( ! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) )
| ~ spl23_75 ),
inference(avatar_component_clause,[],[f633]) ).
fof(f1385,plain,
( element(sK6,the_carrier(sK5))
| ~ spl23_192 ),
inference(avatar_component_clause,[],[f1383]) ).
fof(f1636,plain,
( ~ spl23_230
| spl23_231
| ~ spl23_99
| ~ spl23_155 ),
inference(avatar_split_clause,[],[f1122,f1110,f777,f1634,f1630]) ).
fof(f1634,plain,
( spl23_231
<=> ! [X0,X1] :
( rel_str_of(X0,X1) != sK22
| the_InternalRel(sK22) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_231])]) ).
fof(f777,plain,
( spl23_99
<=> ! [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,[spl23_99])]) ).
fof(f1122,plain,
( ! [X0,X1] :
( rel_str_of(X0,X1) != sK22
| the_InternalRel(sK22) = X1
| ~ relation_of2(the_InternalRel(sK22),the_carrier(sK22),the_carrier(sK22)) )
| ~ spl23_99
| ~ spl23_155 ),
inference(superposition,[],[f778,f1112]) ).
fof(f778,plain,
( ! [X2,X3,X0,X1] :
( rel_str_of(X0,X1) != rel_str_of(X2,X3)
| X1 = X3
| ~ relation_of2(X1,X0,X0) )
| ~ spl23_99 ),
inference(avatar_component_clause,[],[f777]) ).
fof(f1627,plain,
( ~ spl23_228
| spl23_229
| ~ spl23_99
| ~ spl23_154 ),
inference(avatar_split_clause,[],[f1106,f1101,f777,f1625,f1621]) ).
fof(f1625,plain,
( spl23_229
<=> ! [X0,X1] :
( rel_str_of(X0,X1) != sK21
| the_InternalRel(sK21) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_229])]) ).
fof(f1106,plain,
( ! [X0,X1] :
( rel_str_of(X0,X1) != sK21
| the_InternalRel(sK21) = X1
| ~ relation_of2(the_InternalRel(sK21),the_carrier(sK21),the_carrier(sK21)) )
| ~ spl23_99
| ~ spl23_154 ),
inference(superposition,[],[f778,f1103]) ).
fof(f1617,plain,
( spl23_227
| ~ spl23_61
| ~ spl23_163 ),
inference(avatar_split_clause,[],[f1197,f1175,f572,f1615]) ).
fof(f1615,plain,
( spl23_227
<=> ! [X2,X0,X1] :
( empty(powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1)
| ~ in(powerset(cartesian_product2(X0,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_227])]) ).
fof(f1175,plain,
( spl23_163
<=> ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| empty(powerset(cartesian_product2(X1,X2)))
| in(X0,powerset(cartesian_product2(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_163])]) ).
fof(f1197,plain,
( ! [X2,X0,X1] :
( empty(powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1)
| ~ in(powerset(cartesian_product2(X0,X1)),X2) )
| ~ spl23_61
| ~ spl23_163 ),
inference(resolution,[],[f1176,f573]) ).
fof(f1176,plain,
( ! [X2,X0,X1] :
( in(X0,powerset(cartesian_product2(X1,X2)))
| empty(powerset(cartesian_product2(X1,X2)))
| ~ relation_of2_as_subset(X0,X1,X2) )
| ~ spl23_163 ),
inference(avatar_component_clause,[],[f1175]) ).
fof(f1613,plain,
( spl23_226
| ~ spl23_61
| ~ spl23_162 ),
inference(avatar_split_clause,[],[f1173,f1168,f572,f1611]) ).
fof(f1611,plain,
( spl23_226
<=> ! [X0] :
( empty_carrier(X0)
| empty(powerset(the_carrier(X0)))
| ~ one_sorted_str(X0)
| ~ in(powerset(the_carrier(X0)),sK8(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_226])]) ).
fof(f1168,plain,
( spl23_162
<=> ! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| empty(powerset(the_carrier(X0)))
| in(sK8(X0),powerset(the_carrier(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_162])]) ).
fof(f1173,plain,
( ! [X0] :
( empty_carrier(X0)
| empty(powerset(the_carrier(X0)))
| ~ one_sorted_str(X0)
| ~ in(powerset(the_carrier(X0)),sK8(X0)) )
| ~ spl23_61
| ~ spl23_162 ),
inference(resolution,[],[f1169,f573]) ).
fof(f1169,plain,
( ! [X0] :
( in(sK8(X0),powerset(the_carrier(X0)))
| empty_carrier(X0)
| empty(powerset(the_carrier(X0)))
| ~ one_sorted_str(X0) )
| ~ spl23_162 ),
inference(avatar_component_clause,[],[f1168]) ).
fof(f1585,plain,
( spl23_225
| ~ spl23_140
| ~ spl23_161 ),
inference(avatar_split_clause,[],[f1166,f1159,f1027,f1583]) ).
fof(f1583,plain,
( spl23_225
<=> ! [X0] :
( element(sK9(sK8(X0)),the_carrier(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| empty(sK8(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_225])]) ).
fof(f1027,plain,
( spl23_140
<=> ! [X0] :
( empty(X0)
| in(sK9(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_140])]) ).
fof(f1159,plain,
( spl23_161
<=> ! [X0,X1] :
( element(X0,the_carrier(X1))
| ~ in(X0,sK8(X1))
| ~ one_sorted_str(X1)
| empty_carrier(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_161])]) ).
fof(f1166,plain,
( ! [X0] :
( element(sK9(sK8(X0)),the_carrier(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| empty(sK8(X0)) )
| ~ spl23_140
| ~ spl23_161 ),
inference(resolution,[],[f1160,f1028]) ).
fof(f1028,plain,
( ! [X0] :
( in(sK9(X0),X0)
| empty(X0) )
| ~ spl23_140 ),
inference(avatar_component_clause,[],[f1027]) ).
fof(f1160,plain,
( ! [X0,X1] :
( ~ in(X0,sK8(X1))
| element(X0,the_carrier(X1))
| ~ one_sorted_str(X1)
| empty_carrier(X1) )
| ~ spl23_161 ),
inference(avatar_component_clause,[],[f1159]) ).
fof(f1581,plain,
( spl23_224
| ~ spl23_84
| ~ spl23_160 ),
inference(avatar_split_clause,[],[f1163,f1155,f684,f1579]) ).
fof(f1579,plain,
( spl23_224
<=> ! [X0,X1] :
( ~ in(X0,k2_lattice3(X1))
| element(X0,cartesian_product2(the_carrier(X1),the_carrier(X1)))
| ~ sP2(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_224])]) ).
fof(f684,plain,
( spl23_84
<=> ! [X0] :
( relation_of2_as_subset(k2_lattice3(X0),the_carrier(X0),the_carrier(X0))
| ~ sP2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_84])]) ).
fof(f1163,plain,
( ! [X0,X1] :
( ~ in(X0,k2_lattice3(X1))
| element(X0,cartesian_product2(the_carrier(X1),the_carrier(X1)))
| ~ sP2(X1) )
| ~ spl23_84
| ~ spl23_160 ),
inference(resolution,[],[f1156,f685]) ).
fof(f685,plain,
( ! [X0] :
( relation_of2_as_subset(k2_lattice3(X0),the_carrier(X0),the_carrier(X0))
| ~ sP2(X0) )
| ~ spl23_84 ),
inference(avatar_component_clause,[],[f684]) ).
fof(f1577,plain,
( spl23_223
| ~ spl23_82
| ~ spl23_160 ),
inference(avatar_split_clause,[],[f1162,f1155,f676,f1575]) ).
fof(f1575,plain,
( spl23_223
<=> ! [X0,X1] :
( ~ in(X0,the_InternalRel(X1))
| element(X0,cartesian_product2(the_carrier(X1),the_carrier(X1)))
| ~ rel_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_223])]) ).
fof(f676,plain,
( spl23_82
<=> ! [X0] :
( relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_82])]) ).
fof(f1162,plain,
( ! [X0,X1] :
( ~ in(X0,the_InternalRel(X1))
| element(X0,cartesian_product2(the_carrier(X1),the_carrier(X1)))
| ~ rel_str(X1) )
| ~ spl23_82
| ~ spl23_160 ),
inference(resolution,[],[f1156,f677]) ).
fof(f677,plain,
( ! [X0] :
( relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0) )
| ~ spl23_82 ),
inference(avatar_component_clause,[],[f676]) ).
fof(f1573,plain,
( spl23_222
| ~ spl23_98
| ~ spl23_155 ),
inference(avatar_split_clause,[],[f1123,f1110,f773,f1571]) ).
fof(f1571,plain,
( spl23_222
<=> ! [X0,X1] :
( rel_str_of(X0,X1) != sK22
| the_carrier(sK22) = X0
| ~ relation_of2(X1,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_222])]) ).
fof(f1123,plain,
( ! [X0,X1] :
( rel_str_of(X0,X1) != sK22
| the_carrier(sK22) = X0
| ~ relation_of2(X1,X0,X0) )
| ~ spl23_98
| ~ spl23_155 ),
inference(superposition,[],[f774,f1112]) ).
fof(f1569,plain,
( spl23_221
| ~ spl23_99
| ~ spl23_155 ),
inference(avatar_split_clause,[],[f1121,f1110,f777,f1567]) ).
fof(f1567,plain,
( spl23_221
<=> ! [X0,X1] :
( rel_str_of(X0,X1) != sK22
| the_InternalRel(sK22) = X1
| ~ relation_of2(X1,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_221])]) ).
fof(f1121,plain,
( ! [X0,X1] :
( rel_str_of(X0,X1) != sK22
| the_InternalRel(sK22) = X1
| ~ relation_of2(X1,X0,X0) )
| ~ spl23_99
| ~ spl23_155 ),
inference(superposition,[],[f778,f1112]) ).
fof(f1565,plain,
( spl23_220
| ~ spl23_39
| ~ spl23_197 ),
inference(avatar_split_clause,[],[f1487,f1421,f465,f1562]) ).
fof(f1562,plain,
( spl23_220
<=> one_sorted_str(poset_of_lattice(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_220])]) ).
fof(f1421,plain,
( spl23_197
<=> rel_str(poset_of_lattice(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_197])]) ).
fof(f1487,plain,
( one_sorted_str(poset_of_lattice(sK5))
| ~ spl23_39
| ~ spl23_197 ),
inference(resolution,[],[f1423,f466]) ).
fof(f1423,plain,
( rel_str(poset_of_lattice(sK5))
| ~ spl23_197 ),
inference(avatar_component_clause,[],[f1421]) ).
fof(f1560,plain,
( spl23_219
| ~ spl23_98
| ~ spl23_154 ),
inference(avatar_split_clause,[],[f1107,f1101,f773,f1558]) ).
fof(f1558,plain,
( spl23_219
<=> ! [X0,X1] :
( rel_str_of(X0,X1) != sK21
| the_carrier(sK21) = X0
| ~ relation_of2(X1,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_219])]) ).
fof(f1107,plain,
( ! [X0,X1] :
( rel_str_of(X0,X1) != sK21
| the_carrier(sK21) = X0
| ~ relation_of2(X1,X0,X0) )
| ~ spl23_98
| ~ spl23_154 ),
inference(superposition,[],[f774,f1103]) ).
fof(f1556,plain,
( spl23_218
| ~ spl23_99
| ~ spl23_154 ),
inference(avatar_split_clause,[],[f1105,f1101,f777,f1554]) ).
fof(f1554,plain,
( spl23_218
<=> ! [X0,X1] :
( rel_str_of(X0,X1) != sK21
| the_InternalRel(sK21) = X1
| ~ relation_of2(X1,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_218])]) ).
fof(f1105,plain,
( ! [X0,X1] :
( rel_str_of(X0,X1) != sK21
| the_InternalRel(sK21) = X1
| ~ relation_of2(X1,X0,X0) )
| ~ spl23_99
| ~ spl23_154 ),
inference(superposition,[],[f778,f1103]) ).
fof(f1551,plain,
( spl23_217
| ~ spl23_58
| ~ spl23_164 ),
inference(avatar_split_clause,[],[f1199,f1179,f553,f1549]) ).
fof(f553,plain,
( spl23_58
<=> ! [X0] :
( rel_str(poset_of_lattice(X0))
| ~ sP3(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_58])]) ).
fof(f1179,plain,
( spl23_164
<=> ! [X0] :
( poset_of_lattice(X0) = rel_str_of(the_carrier(poset_of_lattice(X0)),the_InternalRel(poset_of_lattice(X0)))
| ~ rel_str(poset_of_lattice(X0))
| ~ sP3(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_164])]) ).
fof(f1199,plain,
( ! [X0] :
( poset_of_lattice(X0) = rel_str_of(the_carrier(poset_of_lattice(X0)),the_InternalRel(poset_of_lattice(X0)))
| ~ sP3(X0) )
| ~ spl23_58
| ~ spl23_164 ),
inference(duplicate_literal_removal,[],[f1198]) ).
fof(f1198,plain,
( ! [X0] :
( poset_of_lattice(X0) = rel_str_of(the_carrier(poset_of_lattice(X0)),the_InternalRel(poset_of_lattice(X0)))
| ~ sP3(X0)
| ~ sP3(X0) )
| ~ spl23_58
| ~ spl23_164 ),
inference(resolution,[],[f1180,f554]) ).
fof(f554,plain,
( ! [X0] :
( rel_str(poset_of_lattice(X0))
| ~ sP3(X0) )
| ~ spl23_58 ),
inference(avatar_component_clause,[],[f553]) ).
fof(f1180,plain,
( ! [X0] :
( ~ rel_str(poset_of_lattice(X0))
| poset_of_lattice(X0) = rel_str_of(the_carrier(poset_of_lattice(X0)),the_InternalRel(poset_of_lattice(X0)))
| ~ sP3(X0) )
| ~ spl23_164 ),
inference(avatar_component_clause,[],[f1179]) ).
fof(f1543,plain,
( spl23_216
| ~ spl23_87
| ~ spl23_151 ),
inference(avatar_split_clause,[],[f1129,f1089,f710,f1541]) ).
fof(f1541,plain,
( spl23_216
<=> ! [X0] :
( ~ sP2(X0)
| ~ empty_carrier(rel_str_of(the_carrier(X0),k2_lattice3(X0)))
| empty(the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_216])]) ).
fof(f1129,plain,
( ! [X0] :
( ~ sP2(X0)
| ~ empty_carrier(rel_str_of(the_carrier(X0),k2_lattice3(X0)))
| empty(the_carrier(X0)) )
| ~ spl23_87
| ~ spl23_151 ),
inference(resolution,[],[f1090,f711]) ).
fof(f1539,plain,
( spl23_215
| ~ spl23_87
| ~ spl23_150 ),
inference(avatar_split_clause,[],[f1125,f1085,f710,f1537]) ).
fof(f1537,plain,
( spl23_215
<=> ! [X0] :
( ~ rel_str(X0)
| ~ empty_carrier(rel_str_of(the_carrier(X0),the_InternalRel(X0)))
| empty(the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_215])]) ).
fof(f1125,plain,
( ! [X0] :
( ~ rel_str(X0)
| ~ empty_carrier(rel_str_of(the_carrier(X0),the_InternalRel(X0)))
| empty(the_carrier(X0)) )
| ~ spl23_87
| ~ spl23_150 ),
inference(resolution,[],[f1086,f711]) ).
fof(f1511,plain,
( spl23_214
| ~ spl23_64
| ~ spl23_160 ),
inference(avatar_split_clause,[],[f1165,f1155,f584,f1509]) ).
fof(f1509,plain,
( spl23_214
<=> ! [X2,X0,X1] :
( ~ in(X0,sK12(X1,X2))
| element(X0,cartesian_product2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_214])]) ).
fof(f584,plain,
( spl23_64
<=> ! [X0,X1] : relation_of2_as_subset(sK12(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_64])]) ).
fof(f1165,plain,
( ! [X2,X0,X1] :
( ~ in(X0,sK12(X1,X2))
| element(X0,cartesian_product2(X1,X2)) )
| ~ spl23_64
| ~ spl23_160 ),
inference(resolution,[],[f1156,f585]) ).
fof(f585,plain,
( ! [X0,X1] : relation_of2_as_subset(sK12(X0,X1),X0,X1)
| ~ spl23_64 ),
inference(avatar_component_clause,[],[f584]) ).
fof(f1507,plain,
( spl23_213
| ~ spl23_144
| ~ spl23_160 ),
inference(avatar_split_clause,[],[f1164,f1155,f1043,f1505]) ).
fof(f1505,plain,
( spl23_213
<=> ! [X2,X0,X1] :
( ~ in(X0,sK11(X1,X2))
| element(X0,cartesian_product2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_213])]) ).
fof(f1043,plain,
( spl23_144
<=> ! [X0,X1] : relation_of2_as_subset(sK11(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_144])]) ).
fof(f1164,plain,
( ! [X2,X0,X1] :
( ~ in(X0,sK11(X1,X2))
| element(X0,cartesian_product2(X1,X2)) )
| ~ spl23_144
| ~ spl23_160 ),
inference(resolution,[],[f1156,f1044]) ).
fof(f1044,plain,
( ! [X0,X1] : relation_of2_as_subset(sK11(X0,X1),X0,X1)
| ~ spl23_144 ),
inference(avatar_component_clause,[],[f1043]) ).
fof(f1503,plain,
( spl23_212
| ~ spl23_61
| ~ spl23_158 ),
inference(avatar_split_clause,[],[f1149,f1141,f572,f1501]) ).
fof(f1501,plain,
( spl23_212
<=> ! [X0] :
( empty(powerset(X0))
| empty(X0)
| ~ in(powerset(X0),sK7(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_212])]) ).
fof(f1141,plain,
( spl23_158
<=> ! [X0] :
( empty(powerset(X0))
| in(sK7(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_158])]) ).
fof(f1149,plain,
( ! [X0] :
( empty(powerset(X0))
| empty(X0)
| ~ in(powerset(X0),sK7(X0)) )
| ~ spl23_61
| ~ spl23_158 ),
inference(resolution,[],[f1142,f573]) ).
fof(f1142,plain,
( ! [X0] :
( in(sK7(X0),powerset(X0))
| empty(powerset(X0))
| empty(X0) )
| ~ spl23_158 ),
inference(avatar_component_clause,[],[f1141]) ).
fof(f1499,plain,
( spl23_211
| ~ spl23_61
| ~ spl23_157 ),
inference(avatar_split_clause,[],[f1146,f1137,f572,f1497]) ).
fof(f1497,plain,
( spl23_211
<=> ! [X0,X1] :
( empty(powerset(X0))
| ~ subset(X1,X0)
| ~ in(powerset(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_211])]) ).
fof(f1137,plain,
( spl23_157
<=> ! [X0,X1] :
( empty(powerset(X0))
| in(X1,powerset(X0))
| ~ subset(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_157])]) ).
fof(f1146,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| ~ subset(X1,X0)
| ~ in(powerset(X0),X1) )
| ~ spl23_61
| ~ spl23_157 ),
inference(resolution,[],[f1138,f573]) ).
fof(f1138,plain,
( ! [X0,X1] :
( in(X1,powerset(X0))
| empty(powerset(X0))
| ~ subset(X1,X0) )
| ~ spl23_157 ),
inference(avatar_component_clause,[],[f1137]) ).
fof(f1495,plain,
( spl23_210
| ~ spl23_140
| ~ spl23_153 ),
inference(avatar_split_clause,[],[f1135,f1097,f1027,f1493]) ).
fof(f1493,plain,
( spl23_210
<=> ! [X0] :
( element(sK9(sK7(X0)),X0)
| empty(X0)
| empty(sK7(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_210])]) ).
fof(f1097,plain,
( spl23_153
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK7(X1))
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_153])]) ).
fof(f1135,plain,
( ! [X0] :
( element(sK9(sK7(X0)),X0)
| empty(X0)
| empty(sK7(X0)) )
| ~ spl23_140
| ~ spl23_153 ),
inference(resolution,[],[f1098,f1028]) ).
fof(f1098,plain,
( ! [X0,X1] :
( ~ in(X0,sK7(X1))
| element(X0,X1)
| empty(X1) )
| ~ spl23_153 ),
inference(avatar_component_clause,[],[f1097]) ).
fof(f1491,plain,
( spl23_209
| ~ spl23_140
| ~ spl23_149 ),
inference(avatar_split_clause,[],[f1083,f1078,f1027,f1489]) ).
fof(f1489,plain,
( spl23_209
<=> ! [X0] :
( element(sK9(sK9(powerset(X0))),X0)
| empty(sK9(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_209])]) ).
fof(f1078,plain,
( spl23_149
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK9(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_149])]) ).
fof(f1083,plain,
( ! [X0] :
( element(sK9(sK9(powerset(X0))),X0)
| empty(sK9(powerset(X0))) )
| ~ spl23_140
| ~ spl23_149 ),
inference(resolution,[],[f1079,f1028]) ).
fof(f1079,plain,
( ! [X0,X1] :
( ~ in(X0,sK9(powerset(X1)))
| element(X0,X1) )
| ~ spl23_149 ),
inference(avatar_component_clause,[],[f1078]) ).
fof(f1473,plain,
( spl23_208
| ~ spl23_76
| ~ spl23_151 ),
inference(avatar_split_clause,[],[f1131,f1089,f637,f1471]) ).
fof(f1471,plain,
( spl23_208
<=> ! [X0] :
( ~ sP2(X0)
| strict_rel_str(rel_str_of(the_carrier(X0),k2_lattice3(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_208])]) ).
fof(f637,plain,
( spl23_76
<=> ! [X0,X1] :
( strict_rel_str(rel_str_of(X0,X1))
| ~ relation_of2(X1,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_76])]) ).
fof(f1131,plain,
( ! [X0] :
( ~ sP2(X0)
| strict_rel_str(rel_str_of(the_carrier(X0),k2_lattice3(X0))) )
| ~ spl23_76
| ~ spl23_151 ),
inference(resolution,[],[f1090,f638]) ).
fof(f638,plain,
( ! [X0,X1] :
( ~ relation_of2(X1,X0,X0)
| strict_rel_str(rel_str_of(X0,X1)) )
| ~ spl23_76 ),
inference(avatar_component_clause,[],[f637]) ).
fof(f1469,plain,
( spl23_207
| ~ spl23_77
| ~ spl23_151 ),
inference(avatar_split_clause,[],[f1130,f1089,f641,f1467]) ).
fof(f1467,plain,
( spl23_207
<=> ! [X0] :
( ~ sP2(X0)
| rel_str(rel_str_of(the_carrier(X0),k2_lattice3(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_207])]) ).
fof(f641,plain,
( spl23_77
<=> ! [X0,X1] :
( rel_str(rel_str_of(X0,X1))
| ~ relation_of2(X1,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_77])]) ).
fof(f1130,plain,
( ! [X0] :
( ~ sP2(X0)
| rel_str(rel_str_of(the_carrier(X0),k2_lattice3(X0))) )
| ~ spl23_77
| ~ spl23_151 ),
inference(resolution,[],[f1090,f642]) ).
fof(f642,plain,
( ! [X0,X1] :
( ~ relation_of2(X1,X0,X0)
| rel_str(rel_str_of(X0,X1)) )
| ~ spl23_77 ),
inference(avatar_component_clause,[],[f641]) ).
fof(f1465,plain,
( spl23_206
| ~ spl23_76
| ~ spl23_150 ),
inference(avatar_split_clause,[],[f1127,f1085,f637,f1463]) ).
fof(f1463,plain,
( spl23_206
<=> ! [X0] :
( ~ rel_str(X0)
| strict_rel_str(rel_str_of(the_carrier(X0),the_InternalRel(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_206])]) ).
fof(f1127,plain,
( ! [X0] :
( ~ rel_str(X0)
| strict_rel_str(rel_str_of(the_carrier(X0),the_InternalRel(X0))) )
| ~ spl23_76
| ~ spl23_150 ),
inference(resolution,[],[f1086,f638]) ).
fof(f1461,plain,
( spl23_205
| ~ spl23_77
| ~ spl23_150 ),
inference(avatar_split_clause,[],[f1126,f1085,f641,f1459]) ).
fof(f1459,plain,
( spl23_205
<=> ! [X0] :
( ~ rel_str(X0)
| rel_str(rel_str_of(the_carrier(X0),the_InternalRel(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_205])]) ).
fof(f1126,plain,
( ! [X0] :
( ~ rel_str(X0)
| rel_str(rel_str_of(the_carrier(X0),the_InternalRel(X0))) )
| ~ spl23_77
| ~ spl23_150 ),
inference(resolution,[],[f1086,f642]) ).
fof(f1457,plain,
( spl23_204
| ~ spl23_87
| ~ spl23_143 ),
inference(avatar_split_clause,[],[f1052,f1039,f710,f1455]) ).
fof(f1455,plain,
( spl23_204
<=> ! [X0] :
( ~ empty_carrier(rel_str_of(X0,sK12(X0,X0)))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_204])]) ).
fof(f1039,plain,
( spl23_143
<=> ! [X0,X1] : relation_of2(sK12(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_143])]) ).
fof(f1052,plain,
( ! [X0] :
( ~ empty_carrier(rel_str_of(X0,sK12(X0,X0)))
| empty(X0) )
| ~ spl23_87
| ~ spl23_143 ),
inference(resolution,[],[f1040,f711]) ).
fof(f1040,plain,
( ! [X0,X1] : relation_of2(sK12(X0,X1),X0,X1)
| ~ spl23_143 ),
inference(avatar_component_clause,[],[f1039]) ).
fof(f1453,plain,
( spl23_203
| ~ spl23_76
| ~ spl23_129
| ~ spl23_186 ),
inference(avatar_split_clause,[],[f1381,f1328,f950,f637,f1450]) ).
fof(f1450,plain,
( spl23_203
<=> strict_rel_str(poset_of_lattice(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_203])]) ).
fof(f1328,plain,
( spl23_186
<=> relation_of2(relation_of_lattice(sK5),the_carrier(sK5),the_carrier(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_186])]) ).
fof(f1381,plain,
( strict_rel_str(poset_of_lattice(sK5))
| ~ spl23_76
| ~ spl23_129
| ~ spl23_186 ),
inference(forward_demodulation,[],[f1377,f952]) ).
fof(f1377,plain,
( strict_rel_str(rel_str_of(the_carrier(sK5),relation_of_lattice(sK5)))
| ~ spl23_76
| ~ spl23_186 ),
inference(resolution,[],[f1330,f638]) ).
fof(f1330,plain,
( relation_of2(relation_of_lattice(sK5),the_carrier(sK5),the_carrier(sK5))
| ~ spl23_186 ),
inference(avatar_component_clause,[],[f1328]) ).
fof(f1444,plain,
( spl23_202
| ~ spl23_140
| ~ spl23_146 ),
inference(avatar_split_clause,[],[f1068,f1062,f1027,f1442]) ).
fof(f1442,plain,
( spl23_202
<=> ! [X0] :
( ~ empty(X0)
| empty(sK9(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_202])]) ).
fof(f1062,plain,
( spl23_146
<=> ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK9(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_146])]) ).
fof(f1068,plain,
( ! [X0] :
( ~ empty(X0)
| empty(sK9(powerset(X0))) )
| ~ spl23_140
| ~ spl23_146 ),
inference(resolution,[],[f1063,f1028]) ).
fof(f1063,plain,
( ! [X0,X1] :
( ~ in(X1,sK9(powerset(X0)))
| ~ empty(X0) )
| ~ spl23_146 ),
inference(avatar_component_clause,[],[f1062]) ).
fof(f1440,plain,
( spl23_201
| ~ spl23_76
| ~ spl23_143 ),
inference(avatar_split_clause,[],[f1054,f1039,f637,f1438]) ).
fof(f1438,plain,
( spl23_201
<=> ! [X0] : strict_rel_str(rel_str_of(X0,sK12(X0,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_201])]) ).
fof(f1054,plain,
( ! [X0] : strict_rel_str(rel_str_of(X0,sK12(X0,X0)))
| ~ spl23_76
| ~ spl23_143 ),
inference(resolution,[],[f1040,f638]) ).
fof(f1436,plain,
( spl23_200
| ~ spl23_77
| ~ spl23_143 ),
inference(avatar_split_clause,[],[f1053,f1039,f641,f1434]) ).
fof(f1053,plain,
( ! [X0] : rel_str(rel_str_of(X0,sK12(X0,X0)))
| ~ spl23_77
| ~ spl23_143 ),
inference(resolution,[],[f1040,f642]) ).
fof(f1432,plain,
( spl23_199
| ~ spl23_39
| ~ spl23_142 ),
inference(avatar_split_clause,[],[f1051,f1035,f465,f1430]) ).
fof(f1430,plain,
( spl23_199
<=> ! [X0] : one_sorted_str(rel_str_of(X0,sK11(X0,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_199])]) ).
fof(f1035,plain,
( spl23_142
<=> ! [X0] : rel_str(rel_str_of(X0,sK11(X0,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_142])]) ).
fof(f1051,plain,
( ! [X0] : one_sorted_str(rel_str_of(X0,sK11(X0,X0)))
| ~ spl23_39
| ~ spl23_142 ),
inference(resolution,[],[f1036,f466]) ).
fof(f1036,plain,
( ! [X0] : rel_str(rel_str_of(X0,sK11(X0,X0)))
| ~ spl23_142 ),
inference(avatar_component_clause,[],[f1035]) ).
fof(f1428,plain,
( spl23_198
| ~ spl23_61
| ~ spl23_140 ),
inference(avatar_split_clause,[],[f1048,f1027,f572,f1426]) ).
fof(f1426,plain,
( spl23_198
<=> ! [X0] :
( empty(X0)
| ~ in(X0,sK9(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_198])]) ).
fof(f1048,plain,
( ! [X0] :
( empty(X0)
| ~ in(X0,sK9(X0)) )
| ~ spl23_61
| ~ spl23_140 ),
inference(resolution,[],[f1028,f573]) ).
fof(f1424,plain,
( spl23_197
| ~ spl23_77
| ~ spl23_129
| ~ spl23_186 ),
inference(avatar_split_clause,[],[f1380,f1328,f950,f641,f1421]) ).
fof(f1380,plain,
( rel_str(poset_of_lattice(sK5))
| ~ spl23_77
| ~ spl23_129
| ~ spl23_186 ),
inference(forward_demodulation,[],[f1376,f952]) ).
fof(f1376,plain,
( rel_str(rel_str_of(the_carrier(sK5),relation_of_lattice(sK5)))
| ~ spl23_77
| ~ spl23_186 ),
inference(resolution,[],[f1330,f642]) ).
fof(f1416,plain,
( ~ spl23_186
| spl23_196
| ~ spl23_98
| ~ spl23_129 ),
inference(avatar_split_clause,[],[f957,f950,f773,f1414,f1328]) ).
fof(f957,plain,
( ! [X0,X1] :
( rel_str_of(X0,X1) != poset_of_lattice(sK5)
| the_carrier(sK5) = X0
| ~ relation_of2(relation_of_lattice(sK5),the_carrier(sK5),the_carrier(sK5)) )
| ~ spl23_98
| ~ spl23_129 ),
inference(superposition,[],[f774,f952]) ).
fof(f1409,plain,
( ~ spl23_186
| spl23_195
| ~ spl23_99
| ~ spl23_129 ),
inference(avatar_split_clause,[],[f955,f950,f777,f1407,f1328]) ).
fof(f955,plain,
( ! [X0,X1] :
( rel_str_of(X0,X1) != poset_of_lattice(sK5)
| relation_of_lattice(sK5) = X1
| ~ relation_of2(relation_of_lattice(sK5),the_carrier(sK5),the_carrier(sK5)) )
| ~ spl23_99
| ~ spl23_129 ),
inference(superposition,[],[f778,f952]) ).
fof(f1402,plain,
( spl23_194
| ~ spl23_59
| ~ spl23_135 ),
inference(avatar_split_clause,[],[f985,f982,f557,f1400]) ).
fof(f1400,plain,
( spl23_194
<=> ! [X0] : element(sK19,powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_194])]) ).
fof(f557,plain,
( spl23_59
<=> ! [X0] : element(sK10(X0),powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_59])]) ).
fof(f982,plain,
( spl23_135
<=> ! [X0] : sK10(X0) = sK19 ),
introduced(avatar_definition,[new_symbols(naming,[spl23_135])]) ).
fof(f985,plain,
( ! [X0] : element(sK19,powerset(X0))
| ~ spl23_59
| ~ spl23_135 ),
inference(superposition,[],[f558,f983]) ).
fof(f983,plain,
( ! [X0] : sK10(X0) = sK19
| ~ spl23_135 ),
inference(avatar_component_clause,[],[f982]) ).
fof(f558,plain,
( ! [X0] : element(sK10(X0),powerset(X0))
| ~ spl23_59 ),
inference(avatar_component_clause,[],[f557]) ).
fof(f1396,plain,
( spl23_1
| spl23_193
| ~ spl23_3
| ~ spl23_2
| ~ spl23_168 ),
inference(avatar_split_clause,[],[f1206,f1203,f295,f300,f1393,f290]) ).
fof(f1203,plain,
( spl23_168
<=> ! [X0] :
( sK9(the_carrier(poset_of_lattice(X0))) = cast_to_el_of_lattice(X0,sK9(the_carrier(poset_of_lattice(X0))))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_168])]) ).
fof(f1206,plain,
( ~ latt_str(sK5)
| sK9(the_carrier(poset_of_lattice(sK5))) = cast_to_el_of_lattice(sK5,sK9(the_carrier(poset_of_lattice(sK5))))
| empty_carrier(sK5)
| ~ spl23_2
| ~ spl23_168 ),
inference(resolution,[],[f1204,f297]) ).
fof(f1204,plain,
( ! [X0] :
( ~ lattice(X0)
| ~ latt_str(X0)
| sK9(the_carrier(poset_of_lattice(X0))) = cast_to_el_of_lattice(X0,sK9(the_carrier(poset_of_lattice(X0))))
| empty_carrier(X0) )
| ~ spl23_168 ),
inference(avatar_component_clause,[],[f1203]) ).
fof(f1386,plain,
( spl23_1
| ~ spl23_2
| ~ spl23_3
| ~ spl23_4
| spl23_192
| ~ spl23_105
| ~ spl23_127 ),
inference(avatar_split_clause,[],[f942,f937,f809,f1383,f305,f300,f295,f290]) ).
fof(f305,plain,
( spl23_4
<=> element(sK6,the_carrier(poset_of_lattice(sK5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_4])]) ).
fof(f942,plain,
( element(sK6,the_carrier(sK5))
| ~ element(sK6,the_carrier(poset_of_lattice(sK5)))
| ~ latt_str(sK5)
| ~ lattice(sK5)
| empty_carrier(sK5)
| ~ spl23_105
| ~ spl23_127 ),
inference(superposition,[],[f810,f939]) ).
fof(f1368,plain,
( spl23_191
| ~ spl23_98
| ~ spl23_129 ),
inference(avatar_split_clause,[],[f956,f950,f773,f1366]) ).
fof(f1366,plain,
( spl23_191
<=> ! [X0,X1] :
( rel_str_of(X0,X1) != poset_of_lattice(sK5)
| the_carrier(sK5) = X0
| ~ relation_of2(X1,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_191])]) ).
fof(f956,plain,
( ! [X0,X1] :
( rel_str_of(X0,X1) != poset_of_lattice(sK5)
| the_carrier(sK5) = X0
| ~ relation_of2(X1,X0,X0) )
| ~ spl23_98
| ~ spl23_129 ),
inference(superposition,[],[f774,f952]) ).
fof(f1364,plain,
( spl23_190
| ~ spl23_99
| ~ spl23_129 ),
inference(avatar_split_clause,[],[f954,f950,f777,f1362]) ).
fof(f1362,plain,
( spl23_190
<=> ! [X0,X1] :
( rel_str_of(X0,X1) != poset_of_lattice(sK5)
| relation_of_lattice(sK5) = X1
| ~ relation_of2(X1,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_190])]) ).
fof(f954,plain,
( ! [X0,X1] :
( rel_str_of(X0,X1) != poset_of_lattice(sK5)
| relation_of_lattice(sK5) = X1
| ~ relation_of2(X1,X0,X0) )
| ~ spl23_99
| ~ spl23_129 ),
inference(superposition,[],[f778,f952]) ).
fof(f1356,plain,
( spl23_1
| spl23_189
| ~ spl23_3
| ~ spl23_2
| ~ spl23_167 ),
inference(avatar_split_clause,[],[f1201,f1192,f295,f300,f1353,f290]) ).
fof(f1192,plain,
( spl23_167
<=> ! [X0] :
( sK9(the_carrier(X0)) = cast_to_el_of_LattPOSet(X0,sK9(the_carrier(X0)))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_167])]) ).
fof(f1201,plain,
( ~ latt_str(sK5)
| sK9(the_carrier(sK5)) = cast_to_el_of_LattPOSet(sK5,sK9(the_carrier(sK5)))
| empty_carrier(sK5)
| ~ spl23_2
| ~ spl23_167 ),
inference(resolution,[],[f1193,f297]) ).
fof(f1193,plain,
( ! [X0] :
( ~ lattice(X0)
| ~ latt_str(X0)
| sK9(the_carrier(X0)) = cast_to_el_of_LattPOSet(X0,sK9(the_carrier(X0)))
| empty_carrier(X0) )
| ~ spl23_167 ),
inference(avatar_component_clause,[],[f1192]) ).
fof(f1347,plain,
( spl23_1
| ~ spl23_2
| ~ spl23_3
| spl23_188
| ~ spl23_4
| ~ spl23_127
| ~ spl23_172 ),
inference(avatar_split_clause,[],[f1238,f1226,f937,f305,f1344,f300,f295,f290]) ).
fof(f1238,plain,
( sK6 = cast_to_el_of_LattPOSet(sK5,sK6)
| ~ latt_str(sK5)
| ~ lattice(sK5)
| empty_carrier(sK5)
| ~ spl23_4
| ~ spl23_127
| ~ spl23_172 ),
inference(forward_demodulation,[],[f1235,f939]) ).
fof(f1235,plain,
( ~ latt_str(sK5)
| ~ lattice(sK5)
| empty_carrier(sK5)
| cast_to_el_of_lattice(sK5,sK6) = cast_to_el_of_LattPOSet(sK5,cast_to_el_of_lattice(sK5,sK6))
| ~ spl23_4
| ~ spl23_172 ),
inference(resolution,[],[f1227,f307]) ).
fof(f307,plain,
( element(sK6,the_carrier(poset_of_lattice(sK5)))
| ~ spl23_4 ),
inference(avatar_component_clause,[],[f305]) ).
fof(f1336,plain,
( ~ spl23_115
| spl23_187
| ~ spl23_83
| ~ spl23_126 ),
inference(avatar_split_clause,[],[f932,f927,f680,f1333,f868]) ).
fof(f1333,plain,
( spl23_187
<=> v1_partfun1(relation_of_lattice(sK5),the_carrier(sK5),the_carrier(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_187])]) ).
fof(f680,plain,
( spl23_83
<=> ! [X0] :
( v1_partfun1(k2_lattice3(X0),the_carrier(X0),the_carrier(X0))
| ~ sP2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_83])]) ).
fof(f932,plain,
( v1_partfun1(relation_of_lattice(sK5),the_carrier(sK5),the_carrier(sK5))
| ~ sP2(sK5)
| ~ spl23_83
| ~ spl23_126 ),
inference(superposition,[],[f681,f929]) ).
fof(f681,plain,
( ! [X0] :
( v1_partfun1(k2_lattice3(X0),the_carrier(X0),the_carrier(X0))
| ~ sP2(X0) )
| ~ spl23_83 ),
inference(avatar_component_clause,[],[f680]) ).
fof(f1331,plain,
( spl23_186
| ~ spl23_79
| ~ spl23_185 ),
inference(avatar_split_clause,[],[f1326,f1321,f649,f1328]) ).
fof(f649,plain,
( spl23_79
<=> ! [X2,X0,X1] :
( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_79])]) ).
fof(f1326,plain,
( relation_of2(relation_of_lattice(sK5),the_carrier(sK5),the_carrier(sK5))
| ~ spl23_79
| ~ spl23_185 ),
inference(resolution,[],[f1323,f650]) ).
fof(f650,plain,
( ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| relation_of2(X2,X0,X1) )
| ~ spl23_79 ),
inference(avatar_component_clause,[],[f649]) ).
fof(f1324,plain,
( ~ spl23_115
| spl23_185
| ~ spl23_84
| ~ spl23_126 ),
inference(avatar_split_clause,[],[f931,f927,f684,f1321,f868]) ).
fof(f931,plain,
( relation_of2_as_subset(relation_of_lattice(sK5),the_carrier(sK5),the_carrier(sK5))
| ~ sP2(sK5)
| ~ spl23_84
| ~ spl23_126 ),
inference(superposition,[],[f685,f929]) ).
fof(f1319,plain,
( spl23_184
| ~ spl23_28
| ~ spl23_118 ),
inference(avatar_split_clause,[],[f912,f883,f421,f1316]) ).
fof(f1316,plain,
( spl23_184
<=> one_sorted_str(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_184])]) ).
fof(f421,plain,
( spl23_28
<=> ! [X0] :
( one_sorted_str(X0)
| ~ meet_semilatt_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_28])]) ).
fof(f883,plain,
( spl23_118
<=> meet_semilatt_str(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_118])]) ).
fof(f912,plain,
( one_sorted_str(sK16)
| ~ spl23_28
| ~ spl23_118 ),
inference(resolution,[],[f885,f422]) ).
fof(f422,plain,
( ! [X0] :
( ~ meet_semilatt_str(X0)
| one_sorted_str(X0) )
| ~ spl23_28 ),
inference(avatar_component_clause,[],[f421]) ).
fof(f885,plain,
( meet_semilatt_str(sK16)
| ~ spl23_118 ),
inference(avatar_component_clause,[],[f883]) ).
fof(f1314,plain,
( ~ spl23_115
| spl23_183
| ~ spl23_50
| ~ spl23_126 ),
inference(avatar_split_clause,[],[f935,f927,f520,f1311,f868]) ).
fof(f520,plain,
( spl23_50
<=> ! [X0] :
( reflexive(k2_lattice3(X0))
| ~ sP2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_50])]) ).
fof(f935,plain,
( reflexive(relation_of_lattice(sK5))
| ~ sP2(sK5)
| ~ spl23_50
| ~ spl23_126 ),
inference(superposition,[],[f521,f929]) ).
fof(f521,plain,
( ! [X0] :
( reflexive(k2_lattice3(X0))
| ~ sP2(X0) )
| ~ spl23_50 ),
inference(avatar_component_clause,[],[f520]) ).
fof(f1305,plain,
( spl23_182
| ~ spl23_103
| ~ spl23_105 ),
inference(avatar_split_clause,[],[f817,f809,f799,f1303]) ).
fof(f799,plain,
( spl23_103
<=> ! [X0,X1] :
( cast_to_el_of_lattice(X0,X1) = X1
| ~ element(X1,the_carrier(poset_of_lattice(X0)))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_103])]) ).
fof(f817,plain,
( ! [X0,X1] :
( ~ element(X0,the_carrier(poset_of_lattice(poset_of_lattice(X1))))
| ~ latt_str(poset_of_lattice(X1))
| ~ lattice(poset_of_lattice(X1))
| empty_carrier(poset_of_lattice(X1))
| cast_to_el_of_lattice(poset_of_lattice(X1),X0) = cast_to_el_of_lattice(X1,cast_to_el_of_lattice(poset_of_lattice(X1),X0))
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1) )
| ~ spl23_103
| ~ spl23_105 ),
inference(resolution,[],[f810,f800]) ).
fof(f800,plain,
( ! [X0,X1] :
( ~ element(X1,the_carrier(poset_of_lattice(X0)))
| cast_to_el_of_lattice(X0,X1) = X1
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) )
| ~ spl23_103 ),
inference(avatar_component_clause,[],[f799]) ).
fof(f1301,plain,
( ~ spl23_115
| spl23_181
| ~ spl23_52
| ~ spl23_126 ),
inference(avatar_split_clause,[],[f934,f927,f529,f1298,f868]) ).
fof(f529,plain,
( spl23_52
<=> ! [X0] :
( antisymmetric(k2_lattice3(X0))
| ~ sP2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_52])]) ).
fof(f934,plain,
( antisymmetric(relation_of_lattice(sK5))
| ~ sP2(sK5)
| ~ spl23_52
| ~ spl23_126 ),
inference(superposition,[],[f530,f929]) ).
fof(f530,plain,
( ! [X0] :
( antisymmetric(k2_lattice3(X0))
| ~ sP2(X0) )
| ~ spl23_52 ),
inference(avatar_component_clause,[],[f529]) ).
fof(f1290,plain,
( spl23_180
| ~ spl23_101
| ~ spl23_109 ),
inference(avatar_split_clause,[],[f846,f833,f788,f1288]) ).
fof(f788,plain,
( spl23_101
<=> ! [X0] :
( v1_partfun1(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_101])]) ).
fof(f833,plain,
( spl23_109
<=> ! [X0,X1] :
( antisymmetric_relstr(rel_str_of(X0,X1))
| ~ relation_of2(X1,X0,X0)
| ~ v1_partfun1(X1,X0,X0)
| ~ transitive(X1)
| ~ antisymmetric(X1)
| ~ reflexive(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_109])]) ).
fof(f846,plain,
( ! [X0] :
( ~ relation_of2(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| antisymmetric_relstr(rel_str_of(the_carrier(X0),the_InternalRel(X0)))
| ~ transitive(the_InternalRel(X0))
| ~ antisymmetric(the_InternalRel(X0))
| ~ reflexive(the_InternalRel(X0))
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0) )
| ~ spl23_101
| ~ spl23_109 ),
inference(resolution,[],[f834,f789]) ).
fof(f789,plain,
( ! [X0] :
( v1_partfun1(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0) )
| ~ spl23_101 ),
inference(avatar_component_clause,[],[f788]) ).
fof(f834,plain,
( ! [X0,X1] :
( ~ v1_partfun1(X1,X0,X0)
| ~ relation_of2(X1,X0,X0)
| antisymmetric_relstr(rel_str_of(X0,X1))
| ~ transitive(X1)
| ~ antisymmetric(X1)
| ~ reflexive(X1) )
| ~ spl23_109 ),
inference(avatar_component_clause,[],[f833]) ).
fof(f1286,plain,
( spl23_179
| ~ spl23_101
| ~ spl23_108 ),
inference(avatar_split_clause,[],[f844,f829,f788,f1284]) ).
fof(f829,plain,
( spl23_108
<=> ! [X0,X1] :
( transitive_relstr(rel_str_of(X0,X1))
| ~ relation_of2(X1,X0,X0)
| ~ v1_partfun1(X1,X0,X0)
| ~ transitive(X1)
| ~ antisymmetric(X1)
| ~ reflexive(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_108])]) ).
fof(f844,plain,
( ! [X0] :
( ~ relation_of2(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| transitive_relstr(rel_str_of(the_carrier(X0),the_InternalRel(X0)))
| ~ transitive(the_InternalRel(X0))
| ~ antisymmetric(the_InternalRel(X0))
| ~ reflexive(the_InternalRel(X0))
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0) )
| ~ spl23_101
| ~ spl23_108 ),
inference(resolution,[],[f830,f789]) ).
fof(f830,plain,
( ! [X0,X1] :
( ~ v1_partfun1(X1,X0,X0)
| ~ relation_of2(X1,X0,X0)
| transitive_relstr(rel_str_of(X0,X1))
| ~ transitive(X1)
| ~ antisymmetric(X1)
| ~ reflexive(X1) )
| ~ spl23_108 ),
inference(avatar_component_clause,[],[f829]) ).
fof(f1282,plain,
( spl23_178
| ~ spl23_101
| ~ spl23_107 ),
inference(avatar_split_clause,[],[f842,f825,f788,f1280]) ).
fof(f825,plain,
( spl23_107
<=> ! [X0,X1] :
( reflexive_relstr(rel_str_of(X0,X1))
| ~ relation_of2(X1,X0,X0)
| ~ v1_partfun1(X1,X0,X0)
| ~ transitive(X1)
| ~ antisymmetric(X1)
| ~ reflexive(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_107])]) ).
fof(f842,plain,
( ! [X0] :
( ~ relation_of2(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| reflexive_relstr(rel_str_of(the_carrier(X0),the_InternalRel(X0)))
| ~ transitive(the_InternalRel(X0))
| ~ antisymmetric(the_InternalRel(X0))
| ~ reflexive(the_InternalRel(X0))
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0) )
| ~ spl23_101
| ~ spl23_107 ),
inference(resolution,[],[f826,f789]) ).
fof(f826,plain,
( ! [X0,X1] :
( ~ v1_partfun1(X1,X0,X0)
| ~ relation_of2(X1,X0,X0)
| reflexive_relstr(rel_str_of(X0,X1))
| ~ transitive(X1)
| ~ antisymmetric(X1)
| ~ reflexive(X1) )
| ~ spl23_107 ),
inference(avatar_component_clause,[],[f825]) ).
fof(f1273,plain,
( spl23_177
| ~ spl23_100
| ~ spl23_104 ),
inference(avatar_split_clause,[],[f813,f805,f784,f1271]) ).
fof(f784,plain,
( spl23_100
<=> ! [X0,X1] :
( cast_to_el_of_LattPOSet(X0,X1) = X1
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_100])]) ).
fof(f813,plain,
( ! [X0,X1] :
( ~ element(X0,the_carrier(X1))
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1)
| cast_to_el_of_LattPOSet(X1,X0) = cast_to_el_of_LattPOSet(poset_of_lattice(X1),cast_to_el_of_LattPOSet(X1,X0))
| ~ latt_str(poset_of_lattice(X1))
| ~ lattice(poset_of_lattice(X1))
| empty_carrier(poset_of_lattice(X1)) )
| ~ spl23_100
| ~ spl23_104 ),
inference(resolution,[],[f806,f785]) ).
fof(f785,plain,
( ! [X0,X1] :
( ~ element(X1,the_carrier(X0))
| cast_to_el_of_LattPOSet(X0,X1) = X1
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) )
| ~ spl23_100 ),
inference(avatar_component_clause,[],[f784]) ).
fof(f1257,plain,
( spl23_176
| ~ spl23_83
| ~ spl23_109 ),
inference(avatar_split_clause,[],[f845,f833,f680,f1255]) ).
fof(f845,plain,
( ! [X0] :
( ~ relation_of2(k2_lattice3(X0),the_carrier(X0),the_carrier(X0))
| antisymmetric_relstr(rel_str_of(the_carrier(X0),k2_lattice3(X0)))
| ~ transitive(k2_lattice3(X0))
| ~ antisymmetric(k2_lattice3(X0))
| ~ reflexive(k2_lattice3(X0))
| ~ sP2(X0) )
| ~ spl23_83
| ~ spl23_109 ),
inference(resolution,[],[f834,f681]) ).
fof(f1253,plain,
( spl23_175
| ~ spl23_83
| ~ spl23_108 ),
inference(avatar_split_clause,[],[f843,f829,f680,f1251]) ).
fof(f843,plain,
( ! [X0] :
( ~ relation_of2(k2_lattice3(X0),the_carrier(X0),the_carrier(X0))
| transitive_relstr(rel_str_of(the_carrier(X0),k2_lattice3(X0)))
| ~ transitive(k2_lattice3(X0))
| ~ antisymmetric(k2_lattice3(X0))
| ~ reflexive(k2_lattice3(X0))
| ~ sP2(X0) )
| ~ spl23_83
| ~ spl23_108 ),
inference(resolution,[],[f830,f681]) ).
fof(f1249,plain,
( spl23_174
| ~ spl23_83
| ~ spl23_107 ),
inference(avatar_split_clause,[],[f841,f825,f680,f1247]) ).
fof(f841,plain,
( ! [X0] :
( ~ relation_of2(k2_lattice3(X0),the_carrier(X0),the_carrier(X0))
| reflexive_relstr(rel_str_of(the_carrier(X0),k2_lattice3(X0)))
| ~ transitive(k2_lattice3(X0))
| ~ antisymmetric(k2_lattice3(X0))
| ~ reflexive(k2_lattice3(X0))
| ~ sP2(X0) )
| ~ spl23_83
| ~ spl23_107 ),
inference(resolution,[],[f826,f681]) ).
fof(f1242,plain,
( spl23_173
| ~ spl23_75
| ~ spl23_104 ),
inference(avatar_split_clause,[],[f814,f805,f633,f1240]) ).
fof(f814,plain,
( ! [X0,X1] :
( ~ element(X0,the_carrier(X1))
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1)
| empty(the_carrier(poset_of_lattice(X1)))
| in(cast_to_el_of_LattPOSet(X1,X0),the_carrier(poset_of_lattice(X1))) )
| ~ spl23_75
| ~ spl23_104 ),
inference(resolution,[],[f806,f634]) ).
fof(f1228,plain,
( spl23_172
| ~ spl23_100
| ~ spl23_105 ),
inference(avatar_split_clause,[],[f819,f809,f784,f1226]) ).
fof(f819,plain,
( ! [X0,X1] :
( ~ element(X0,the_carrier(poset_of_lattice(X1)))
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1)
| cast_to_el_of_lattice(X1,X0) = cast_to_el_of_LattPOSet(X1,cast_to_el_of_lattice(X1,X0)) )
| ~ spl23_100
| ~ spl23_105 ),
inference(duplicate_literal_removal,[],[f816]) ).
fof(f816,plain,
( ! [X0,X1] :
( ~ element(X0,the_carrier(poset_of_lattice(X1)))
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1)
| cast_to_el_of_lattice(X1,X0) = cast_to_el_of_LattPOSet(X1,cast_to_el_of_lattice(X1,X0))
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1) )
| ~ spl23_100
| ~ spl23_105 ),
inference(resolution,[],[f810,f785]) ).
fof(f1224,plain,
( spl23_171
| ~ spl23_75
| ~ spl23_105 ),
inference(avatar_split_clause,[],[f818,f809,f633,f1222]) ).
fof(f818,plain,
( ! [X0,X1] :
( ~ element(X0,the_carrier(poset_of_lattice(X1)))
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1)
| empty(the_carrier(X1))
| in(cast_to_el_of_lattice(X1,X0),the_carrier(X1)) )
| ~ spl23_75
| ~ spl23_105 ),
inference(resolution,[],[f810,f634]) ).
fof(f1220,plain,
( ~ spl23_115
| spl23_170
| ~ spl23_53
| ~ spl23_126 ),
inference(avatar_split_clause,[],[f933,f927,f533,f1217,f868]) ).
fof(f533,plain,
( spl23_53
<=> ! [X0] :
( transitive(k2_lattice3(X0))
| ~ sP2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_53])]) ).
fof(f933,plain,
( transitive(relation_of_lattice(sK5))
| ~ sP2(sK5)
| ~ spl23_53
| ~ spl23_126 ),
inference(superposition,[],[f534,f929]) ).
fof(f534,plain,
( ! [X0] :
( transitive(k2_lattice3(X0))
| ~ sP2(X0) )
| ~ spl23_53 ),
inference(avatar_component_clause,[],[f533]) ).
fof(f1210,plain,
( spl23_169
| ~ spl23_103
| ~ spl23_104 ),
inference(avatar_split_clause,[],[f815,f805,f799,f1208]) ).
fof(f815,plain,
( ! [X0,X1] :
( ~ element(X0,the_carrier(X1))
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1)
| cast_to_el_of_LattPOSet(X1,X0) = cast_to_el_of_lattice(X1,cast_to_el_of_LattPOSet(X1,X0)) )
| ~ spl23_103
| ~ spl23_104 ),
inference(duplicate_literal_removal,[],[f812]) ).
fof(f812,plain,
( ! [X0,X1] :
( ~ element(X0,the_carrier(X1))
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1)
| cast_to_el_of_LattPOSet(X1,X0) = cast_to_el_of_lattice(X1,cast_to_el_of_LattPOSet(X1,X0))
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1) )
| ~ spl23_103
| ~ spl23_104 ),
inference(resolution,[],[f806,f800]) ).
fof(f1205,plain,
( spl23_168
| ~ spl23_40
| ~ spl23_103 ),
inference(avatar_split_clause,[],[f803,f799,f469,f1203]) ).
fof(f803,plain,
( ! [X0] :
( sK9(the_carrier(poset_of_lattice(X0))) = cast_to_el_of_lattice(X0,sK9(the_carrier(poset_of_lattice(X0))))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) )
| ~ spl23_40
| ~ spl23_103 ),
inference(resolution,[],[f800,f470]) ).
fof(f1194,plain,
( spl23_167
| ~ spl23_40
| ~ spl23_100 ),
inference(avatar_split_clause,[],[f792,f784,f469,f1192]) ).
fof(f792,plain,
( ! [X0] :
( sK9(the_carrier(X0)) = cast_to_el_of_LattPOSet(X0,sK9(the_carrier(X0)))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) )
| ~ spl23_40
| ~ spl23_100 ),
inference(resolution,[],[f785,f470]) ).
fof(f1190,plain,
( spl23_166
| ~ spl23_46
| ~ spl23_91 ),
inference(avatar_split_clause,[],[f761,f739,f504,f1188]) ).
fof(f1188,plain,
( spl23_166
<=> ! [X0] :
( poset_of_lattice(X0) = rel_str_of(the_carrier(poset_of_lattice(X0)),the_InternalRel(poset_of_lattice(X0)))
| ~ rel_str(poset_of_lattice(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_166])]) ).
fof(f504,plain,
( spl23_46
<=> ! [X0] :
( strict_rel_str(poset_of_lattice(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_46])]) ).
fof(f761,plain,
( ! [X0] :
( poset_of_lattice(X0) = rel_str_of(the_carrier(poset_of_lattice(X0)),the_InternalRel(poset_of_lattice(X0)))
| ~ rel_str(poset_of_lattice(X0))
| ~ sP1(X0) )
| ~ spl23_46
| ~ spl23_91 ),
inference(resolution,[],[f740,f505]) ).
fof(f505,plain,
( ! [X0] :
( strict_rel_str(poset_of_lattice(X0))
| ~ sP1(X0) )
| ~ spl23_46 ),
inference(avatar_component_clause,[],[f504]) ).
fof(f1186,plain,
( ~ spl23_165
| ~ spl23_61
| ~ spl23_124 ),
inference(avatar_split_clause,[],[f924,f915,f572,f1183]) ).
fof(f1183,plain,
( spl23_165
<=> in(the_carrier(poset_of_lattice(sK5)),sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_165])]) ).
fof(f915,plain,
( spl23_124
<=> in(sK6,the_carrier(poset_of_lattice(sK5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_124])]) ).
fof(f924,plain,
( ~ in(the_carrier(poset_of_lattice(sK5)),sK6)
| ~ spl23_61
| ~ spl23_124 ),
inference(resolution,[],[f917,f573]) ).
fof(f917,plain,
( in(sK6,the_carrier(poset_of_lattice(sK5)))
| ~ spl23_124 ),
inference(avatar_component_clause,[],[f915]) ).
fof(f1181,plain,
( spl23_164
| ~ spl23_54
| ~ spl23_91 ),
inference(avatar_split_clause,[],[f760,f739,f537,f1179]) ).
fof(f537,plain,
( spl23_54
<=> ! [X0] :
( strict_rel_str(poset_of_lattice(X0))
| ~ sP3(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_54])]) ).
fof(f760,plain,
( ! [X0] :
( poset_of_lattice(X0) = rel_str_of(the_carrier(poset_of_lattice(X0)),the_InternalRel(poset_of_lattice(X0)))
| ~ rel_str(poset_of_lattice(X0))
| ~ sP3(X0) )
| ~ spl23_54
| ~ spl23_91 ),
inference(resolution,[],[f740,f538]) ).
fof(f538,plain,
( ! [X0] :
( strict_rel_str(poset_of_lattice(X0))
| ~ sP3(X0) )
| ~ spl23_54 ),
inference(avatar_component_clause,[],[f537]) ).
fof(f1177,plain,
( spl23_163
| ~ spl23_75
| ~ spl23_88 ),
inference(avatar_split_clause,[],[f725,f714,f633,f1175]) ).
fof(f714,plain,
( spl23_88
<=> ! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_88])]) ).
fof(f725,plain,
( ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| empty(powerset(cartesian_product2(X1,X2)))
| in(X0,powerset(cartesian_product2(X1,X2))) )
| ~ spl23_75
| ~ spl23_88 ),
inference(resolution,[],[f715,f634]) ).
fof(f715,plain,
( ! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) )
| ~ spl23_88 ),
inference(avatar_component_clause,[],[f714]) ).
fof(f1170,plain,
( spl23_162
| ~ spl23_75
| ~ spl23_86 ),
inference(avatar_split_clause,[],[f722,f706,f633,f1168]) ).
fof(f706,plain,
( spl23_86
<=> ! [X0] :
( element(sK8(X0),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_86])]) ).
fof(f722,plain,
( ! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| empty(powerset(the_carrier(X0)))
| in(sK8(X0),powerset(the_carrier(X0))) )
| ~ spl23_75
| ~ spl23_86 ),
inference(resolution,[],[f707,f634]) ).
fof(f707,plain,
( ! [X0] :
( element(sK8(X0),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0)
| empty_carrier(X0) )
| ~ spl23_86 ),
inference(avatar_component_clause,[],[f706]) ).
fof(f1161,plain,
( spl23_161
| ~ spl23_86
| ~ spl23_89 ),
inference(avatar_split_clause,[],[f729,f718,f706,f1159]) ).
fof(f718,plain,
( spl23_89
<=> ! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_89])]) ).
fof(f729,plain,
( ! [X0,X1] :
( element(X0,the_carrier(X1))
| ~ in(X0,sK8(X1))
| ~ one_sorted_str(X1)
| empty_carrier(X1) )
| ~ spl23_86
| ~ spl23_89 ),
inference(resolution,[],[f719,f707]) ).
fof(f719,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| element(X0,X2)
| ~ in(X0,X1) )
| ~ spl23_89 ),
inference(avatar_component_clause,[],[f718]) ).
fof(f1157,plain,
( spl23_160
| ~ spl23_88
| ~ spl23_89 ),
inference(avatar_split_clause,[],[f727,f718,f714,f1155]) ).
fof(f727,plain,
( ! [X2,X3,X0,X1] :
( element(X0,cartesian_product2(X1,X2))
| ~ in(X0,X3)
| ~ relation_of2_as_subset(X3,X1,X2) )
| ~ spl23_88
| ~ spl23_89 ),
inference(resolution,[],[f719,f715]) ).
fof(f1153,plain,
( spl23_159
| ~ spl23_85
| ~ spl23_88 ),
inference(avatar_split_clause,[],[f724,f714,f688,f1151]) ).
fof(f1151,plain,
( spl23_159
<=> ! [X2,X0,X1,X3] :
( ~ relation_of2_as_subset(X0,X1,X2)
| ~ empty(cartesian_product2(X1,X2))
| ~ in(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_159])]) ).
fof(f688,plain,
( spl23_85
<=> ! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_85])]) ).
fof(f724,plain,
( ! [X2,X3,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| ~ empty(cartesian_product2(X1,X2))
| ~ in(X3,X0) )
| ~ spl23_85
| ~ spl23_88 ),
inference(resolution,[],[f715,f689]) ).
fof(f689,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X0,X1) )
| ~ spl23_85 ),
inference(avatar_component_clause,[],[f688]) ).
fof(f1143,plain,
( spl23_158
| ~ spl23_66
| ~ spl23_75 ),
inference(avatar_split_clause,[],[f662,f633,f593,f1141]) ).
fof(f593,plain,
( spl23_66
<=> ! [X0] :
( element(sK7(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_66])]) ).
fof(f662,plain,
( ! [X0] :
( empty(powerset(X0))
| in(sK7(X0),powerset(X0))
| empty(X0) )
| ~ spl23_66
| ~ spl23_75 ),
inference(resolution,[],[f634,f594]) ).
fof(f594,plain,
( ! [X0] :
( element(sK7(X0),powerset(X0))
| empty(X0) )
| ~ spl23_66 ),
inference(avatar_component_clause,[],[f593]) ).
fof(f1139,plain,
( spl23_157
| ~ spl23_69
| ~ spl23_75 ),
inference(avatar_split_clause,[],[f660,f633,f605,f1137]) ).
fof(f605,plain,
( spl23_69
<=> ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_69])]) ).
fof(f660,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| in(X1,powerset(X0))
| ~ subset(X1,X0) )
| ~ spl23_69
| ~ spl23_75 ),
inference(resolution,[],[f634,f606]) ).
fof(f606,plain,
( ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) )
| ~ spl23_69 ),
inference(avatar_component_clause,[],[f605]) ).
fof(f1118,plain,
( spl23_156
| ~ spl23_24
| ~ spl23_127 ),
inference(avatar_split_clause,[],[f941,f937,f404,f1115]) ).
fof(f941,plain,
( latt_element_smaller(sK5,sK6,sK4)
| ~ spl23_24
| ~ spl23_127 ),
inference(superposition,[],[f406,f939]) ).
fof(f406,plain,
( latt_element_smaller(sK5,cast_to_el_of_lattice(sK5,sK6),sK4)
| ~ spl23_24 ),
inference(avatar_component_clause,[],[f404]) ).
fof(f1113,plain,
( ~ spl23_21
| spl23_155
| ~ spl23_22
| ~ spl23_91 ),
inference(avatar_split_clause,[],[f759,f739,f395,f1110,f390]) ).
fof(f395,plain,
( spl23_22
<=> strict_rel_str(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_22])]) ).
fof(f759,plain,
( sK22 = rel_str_of(the_carrier(sK22),the_InternalRel(sK22))
| ~ rel_str(sK22)
| ~ spl23_22
| ~ spl23_91 ),
inference(resolution,[],[f740,f397]) ).
fof(f397,plain,
( strict_rel_str(sK22)
| ~ spl23_22 ),
inference(avatar_component_clause,[],[f395]) ).
fof(f1104,plain,
( ~ spl23_15
| spl23_154
| ~ spl23_17
| ~ spl23_91 ),
inference(avatar_split_clause,[],[f758,f739,f370,f1101,f360]) ).
fof(f370,plain,
( spl23_17
<=> strict_rel_str(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_17])]) ).
fof(f758,plain,
( sK21 = rel_str_of(the_carrier(sK21),the_InternalRel(sK21))
| ~ rel_str(sK21)
| ~ spl23_17
| ~ spl23_91 ),
inference(resolution,[],[f740,f372]) ).
fof(f372,plain,
( strict_rel_str(sK21)
| ~ spl23_17 ),
inference(avatar_component_clause,[],[f370]) ).
fof(f1099,plain,
( spl23_153
| ~ spl23_66
| ~ spl23_89 ),
inference(avatar_split_clause,[],[f728,f718,f593,f1097]) ).
fof(f728,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK7(X1))
| empty(X1) )
| ~ spl23_66
| ~ spl23_89 ),
inference(resolution,[],[f719,f594]) ).
fof(f1095,plain,
( spl23_152
| ~ spl23_69
| ~ spl23_89 ),
inference(avatar_split_clause,[],[f726,f718,f605,f1093]) ).
fof(f1093,plain,
( spl23_152
<=> ! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_152])]) ).
fof(f726,plain,
( ! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,X1) )
| ~ spl23_69
| ~ spl23_89 ),
inference(resolution,[],[f719,f606]) ).
fof(f1091,plain,
( spl23_151
| ~ spl23_79
| ~ spl23_84 ),
inference(avatar_split_clause,[],[f699,f684,f649,f1089]) ).
fof(f699,plain,
( ! [X0] :
( ~ sP2(X0)
| relation_of2(k2_lattice3(X0),the_carrier(X0),the_carrier(X0)) )
| ~ spl23_79
| ~ spl23_84 ),
inference(resolution,[],[f685,f650]) ).
fof(f1087,plain,
( spl23_150
| ~ spl23_79
| ~ spl23_82 ),
inference(avatar_split_clause,[],[f691,f676,f649,f1085]) ).
fof(f691,plain,
( ! [X0] :
( ~ rel_str(X0)
| relation_of2(the_InternalRel(X0),the_carrier(X0),the_carrier(X0)) )
| ~ spl23_79
| ~ spl23_82 ),
inference(resolution,[],[f677,f650]) ).
fof(f1080,plain,
( spl23_149
| ~ spl23_40
| ~ spl23_89 ),
inference(avatar_split_clause,[],[f730,f718,f469,f1078]) ).
fof(f730,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK9(powerset(X1))) )
| ~ spl23_40
| ~ spl23_89 ),
inference(resolution,[],[f719,f470]) ).
fof(f1076,plain,
( spl23_148
| ~ spl23_63
| ~ spl23_87 ),
inference(avatar_split_clause,[],[f723,f710,f580,f1074]) ).
fof(f1074,plain,
( spl23_148
<=> ! [X0] :
( ~ empty_carrier(rel_str_of(X0,sK11(X0,X0)))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_148])]) ).
fof(f580,plain,
( spl23_63
<=> ! [X0,X1] : relation_of2(sK11(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_63])]) ).
fof(f723,plain,
( ! [X0] :
( ~ empty_carrier(rel_str_of(X0,sK11(X0,X0)))
| empty(X0) )
| ~ spl23_63
| ~ spl23_87 ),
inference(resolution,[],[f711,f581]) ).
fof(f581,plain,
( ! [X0,X1] : relation_of2(sK11(X0,X1),X0,X1)
| ~ spl23_63 ),
inference(avatar_component_clause,[],[f580]) ).
fof(f1072,plain,
( spl23_147
| ~ spl23_69
| ~ spl23_85 ),
inference(avatar_split_clause,[],[f700,f688,f605,f1070]) ).
fof(f1070,plain,
( spl23_147
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,X2)
| ~ subset(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_147])]) ).
fof(f700,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,X2)
| ~ subset(X2,X0) )
| ~ spl23_69
| ~ spl23_85 ),
inference(resolution,[],[f689,f606]) ).
fof(f1064,plain,
( spl23_146
| ~ spl23_40
| ~ spl23_85 ),
inference(avatar_split_clause,[],[f702,f688,f469,f1062]) ).
fof(f702,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK9(powerset(X0))) )
| ~ spl23_40
| ~ spl23_85 ),
inference(resolution,[],[f689,f470]) ).
fof(f1060,plain,
( spl23_145
| ~ spl23_12
| ~ spl23_26
| ~ spl23_44
| ~ spl23_59
| ~ spl23_75 ),
inference(avatar_split_clause,[],[f665,f633,f557,f496,f413,f345,f1058]) ).
fof(f1058,plain,
( spl23_145
<=> ! [X0] :
( in(sK19,powerset(X0))
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_145])]) ).
fof(f345,plain,
( spl23_12
<=> empty(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_12])]) ).
fof(f413,plain,
( spl23_26
<=> ! [X0] : empty(sK10(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_26])]) ).
fof(f496,plain,
( spl23_44
<=> ! [X0] :
( empty_set = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_44])]) ).
fof(f665,plain,
( ! [X0] :
( in(sK19,powerset(X0))
| empty(powerset(X0)) )
| ~ spl23_12
| ~ spl23_26
| ~ spl23_44
| ~ spl23_59
| ~ spl23_75 ),
inference(forward_demodulation,[],[f664,f568]) ).
fof(f568,plain,
( ! [X0] : sK10(X0) = sK19
| ~ spl23_12
| ~ spl23_26
| ~ spl23_44 ),
inference(forward_demodulation,[],[f567,f566]) ).
fof(f566,plain,
( empty_set = sK19
| ~ spl23_12
| ~ spl23_44 ),
inference(resolution,[],[f497,f347]) ).
fof(f347,plain,
( empty(sK19)
| ~ spl23_12 ),
inference(avatar_component_clause,[],[f345]) ).
fof(f497,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = X0 )
| ~ spl23_44 ),
inference(avatar_component_clause,[],[f496]) ).
fof(f567,plain,
( ! [X0] : empty_set = sK10(X0)
| ~ spl23_26
| ~ spl23_44 ),
inference(resolution,[],[f497,f414]) ).
fof(f414,plain,
( ! [X0] : empty(sK10(X0))
| ~ spl23_26 ),
inference(avatar_component_clause,[],[f413]) ).
fof(f664,plain,
( ! [X0] :
( empty(powerset(X0))
| in(sK10(X0),powerset(X0)) )
| ~ spl23_59
| ~ spl23_75 ),
inference(resolution,[],[f634,f558]) ).
fof(f1045,plain,
( spl23_144
| ~ spl23_63
| ~ spl23_80 ),
inference(avatar_split_clause,[],[f674,f653,f580,f1043]) ).
fof(f653,plain,
( spl23_80
<=> ! [X2,X0,X1] :
( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_80])]) ).
fof(f674,plain,
( ! [X0,X1] : relation_of2_as_subset(sK11(X0,X1),X0,X1)
| ~ spl23_63
| ~ spl23_80 ),
inference(resolution,[],[f654,f581]) ).
fof(f654,plain,
( ! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| relation_of2_as_subset(X2,X0,X1) )
| ~ spl23_80 ),
inference(avatar_component_clause,[],[f653]) ).
fof(f1041,plain,
( spl23_143
| ~ spl23_64
| ~ spl23_79 ),
inference(avatar_split_clause,[],[f673,f649,f584,f1039]) ).
fof(f673,plain,
( ! [X0,X1] : relation_of2(sK12(X0,X1),X0,X1)
| ~ spl23_64
| ~ spl23_79 ),
inference(resolution,[],[f650,f585]) ).
fof(f1037,plain,
( spl23_142
| ~ spl23_63
| ~ spl23_77 ),
inference(avatar_split_clause,[],[f672,f641,f580,f1035]) ).
fof(f672,plain,
( ! [X0] : rel_str(rel_str_of(X0,sK11(X0,X0)))
| ~ spl23_63
| ~ spl23_77 ),
inference(resolution,[],[f642,f581]) ).
fof(f1033,plain,
( spl23_141
| ~ spl23_63
| ~ spl23_76 ),
inference(avatar_split_clause,[],[f666,f637,f580,f1031]) ).
fof(f666,plain,
( ! [X0] : strict_rel_str(rel_str_of(X0,sK11(X0,X0)))
| ~ spl23_63
| ~ spl23_76 ),
inference(resolution,[],[f638,f581]) ).
fof(f1029,plain,
( spl23_140
| ~ spl23_40
| ~ spl23_75 ),
inference(avatar_split_clause,[],[f663,f633,f469,f1027]) ).
fof(f663,plain,
( ! [X0] :
( empty(X0)
| in(sK9(X0),X0) )
| ~ spl23_40
| ~ spl23_75 ),
inference(resolution,[],[f634,f470]) ).
fof(f1010,plain,
( spl23_137
| ~ spl23_44
| ~ spl23_130 ),
inference(avatar_split_clause,[],[f1008,f959,f496,f992]) ).
fof(f959,plain,
( spl23_130
<=> empty_set = sK19 ),
introduced(avatar_definition,[new_symbols(naming,[spl23_130])]) ).
fof(f1008,plain,
( ! [X0] :
( sK19 = X0
| ~ empty(X0) )
| ~ spl23_44
| ~ spl23_130 ),
inference(forward_demodulation,[],[f497,f961]) ).
fof(f961,plain,
( empty_set = sK19
| ~ spl23_130 ),
inference(avatar_component_clause,[],[f959]) ).
fof(f1007,plain,
( ~ spl23_5
| ~ spl23_138 ),
inference(avatar_contradiction_clause,[],[f1002]) ).
fof(f1002,plain,
( $false
| ~ spl23_5
| ~ spl23_138 ),
inference(resolution,[],[f997,f312]) ).
fof(f312,plain,
( empty(empty_set)
| ~ spl23_5 ),
inference(avatar_component_clause,[],[f310]) ).
fof(f310,plain,
( spl23_5
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_5])]) ).
fof(f997,plain,
( ! [X0] : ~ empty(X0)
| ~ spl23_138 ),
inference(avatar_component_clause,[],[f996]) ).
fof(f996,plain,
( spl23_138
<=> ! [X0] : ~ empty(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_138])]) ).
fof(f1006,plain,
( ~ spl23_12
| ~ spl23_138 ),
inference(avatar_contradiction_clause,[],[f1003]) ).
fof(f1003,plain,
( $false
| ~ spl23_12
| ~ spl23_138 ),
inference(resolution,[],[f997,f347]) ).
fof(f1005,plain,
( ~ spl23_26
| ~ spl23_138 ),
inference(avatar_contradiction_clause,[],[f1004]) ).
fof(f1004,plain,
( $false
| ~ spl23_26
| ~ spl23_138 ),
inference(resolution,[],[f997,f414]) ).
fof(f1001,plain,
( spl23_138
| spl23_139
| ~ spl23_12
| ~ spl23_26
| ~ spl23_44
| ~ spl23_59
| ~ spl23_85 ),
inference(avatar_split_clause,[],[f704,f688,f557,f496,f413,f345,f999,f996]) ).
fof(f999,plain,
( spl23_139
<=> ! [X1] : ~ in(X1,sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_139])]) ).
fof(f704,plain,
( ! [X0,X1] :
( ~ in(X1,sK19)
| ~ empty(X0) )
| ~ spl23_12
| ~ spl23_26
| ~ spl23_44
| ~ spl23_59
| ~ spl23_85 ),
inference(forward_demodulation,[],[f703,f568]) ).
fof(f703,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK10(X0)) )
| ~ spl23_59
| ~ spl23_85 ),
inference(resolution,[],[f689,f558]) ).
fof(f994,plain,
( spl23_137
| ~ spl23_12
| ~ spl23_70 ),
inference(avatar_split_clause,[],[f613,f609,f345,f992]) ).
fof(f609,plain,
( spl23_70
<=> ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_70])]) ).
fof(f613,plain,
( ! [X0] :
( sK19 = X0
| ~ empty(X0) )
| ~ spl23_12
| ~ spl23_70 ),
inference(resolution,[],[f610,f347]) ).
fof(f610,plain,
( ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) )
| ~ spl23_70 ),
inference(avatar_component_clause,[],[f609]) ).
fof(f990,plain,
( spl23_136
| ~ spl23_39
| ~ spl23_58 ),
inference(avatar_split_clause,[],[f570,f553,f465,f988]) ).
fof(f988,plain,
( spl23_136
<=> ! [X0] :
( ~ sP3(X0)
| one_sorted_str(poset_of_lattice(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_136])]) ).
fof(f570,plain,
( ! [X0] :
( ~ sP3(X0)
| one_sorted_str(poset_of_lattice(X0)) )
| ~ spl23_39
| ~ spl23_58 ),
inference(resolution,[],[f554,f466]) ).
fof(f984,plain,
( spl23_135
| ~ spl23_12
| ~ spl23_26
| ~ spl23_44 ),
inference(avatar_split_clause,[],[f568,f496,f413,f345,f982]) ).
fof(f980,plain,
( spl23_131
| ~ spl23_132
| ~ spl23_133
| spl23_134
| ~ spl23_4
| ~ spl23_100 ),
inference(avatar_split_clause,[],[f791,f784,f305,f977,f973,f969,f965]) ).
fof(f965,plain,
( spl23_131
<=> empty_carrier(poset_of_lattice(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_131])]) ).
fof(f969,plain,
( spl23_132
<=> lattice(poset_of_lattice(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_132])]) ).
fof(f973,plain,
( spl23_133
<=> latt_str(poset_of_lattice(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_133])]) ).
fof(f977,plain,
( spl23_134
<=> sK6 = cast_to_el_of_LattPOSet(poset_of_lattice(sK5),sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_134])]) ).
fof(f791,plain,
( sK6 = cast_to_el_of_LattPOSet(poset_of_lattice(sK5),sK6)
| ~ latt_str(poset_of_lattice(sK5))
| ~ lattice(poset_of_lattice(sK5))
| empty_carrier(poset_of_lattice(sK5))
| ~ spl23_4
| ~ spl23_100 ),
inference(resolution,[],[f785,f307]) ).
fof(f962,plain,
( spl23_130
| ~ spl23_12
| ~ spl23_44 ),
inference(avatar_split_clause,[],[f566,f496,f345,f959]) ).
fof(f953,plain,
( spl23_129
| ~ spl23_126
| ~ spl23_128 ),
inference(avatar_split_clause,[],[f948,f944,f927,f950]) ).
fof(f944,plain,
( spl23_128
<=> poset_of_lattice(sK5) = rel_str_of(the_carrier(sK5),k2_lattice3(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_128])]) ).
fof(f948,plain,
( poset_of_lattice(sK5) = rel_str_of(the_carrier(sK5),relation_of_lattice(sK5))
| ~ spl23_126
| ~ spl23_128 ),
inference(forward_demodulation,[],[f946,f929]) ).
fof(f946,plain,
( poset_of_lattice(sK5) = rel_str_of(the_carrier(sK5),k2_lattice3(sK5))
| ~ spl23_128 ),
inference(avatar_component_clause,[],[f944]) ).
fof(f947,plain,
( spl23_1
| spl23_128
| ~ spl23_3
| ~ spl23_2
| ~ spl23_97 ),
inference(avatar_split_clause,[],[f780,f769,f295,f300,f944,f290]) ).
fof(f769,plain,
( spl23_97
<=> ! [X0] :
( poset_of_lattice(X0) = rel_str_of(the_carrier(X0),k2_lattice3(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_97])]) ).
fof(f780,plain,
( ~ latt_str(sK5)
| poset_of_lattice(sK5) = rel_str_of(the_carrier(sK5),k2_lattice3(sK5))
| empty_carrier(sK5)
| ~ spl23_2
| ~ spl23_97 ),
inference(resolution,[],[f770,f297]) ).
fof(f770,plain,
( ! [X0] :
( ~ lattice(X0)
| ~ latt_str(X0)
| poset_of_lattice(X0) = rel_str_of(the_carrier(X0),k2_lattice3(X0))
| empty_carrier(X0) )
| ~ spl23_97 ),
inference(avatar_component_clause,[],[f769]) ).
fof(f940,plain,
( spl23_1
| ~ spl23_2
| ~ spl23_3
| spl23_127
| ~ spl23_4
| ~ spl23_103 ),
inference(avatar_split_clause,[],[f802,f799,f305,f937,f300,f295,f290]) ).
fof(f802,plain,
( sK6 = cast_to_el_of_lattice(sK5,sK6)
| ~ latt_str(sK5)
| ~ lattice(sK5)
| empty_carrier(sK5)
| ~ spl23_4
| ~ spl23_103 ),
inference(resolution,[],[f800,f307]) ).
fof(f930,plain,
( spl23_1
| spl23_126
| ~ spl23_3
| ~ spl23_2
| ~ spl23_92 ),
inference(avatar_split_clause,[],[f762,f743,f295,f300,f927,f290]) ).
fof(f743,plain,
( spl23_92
<=> ! [X0] :
( k2_lattice3(X0) = relation_of_lattice(X0)
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_92])]) ).
fof(f762,plain,
( ~ latt_str(sK5)
| k2_lattice3(sK5) = relation_of_lattice(sK5)
| empty_carrier(sK5)
| ~ spl23_2
| ~ spl23_92 ),
inference(resolution,[],[f744,f297]) ).
fof(f744,plain,
( ! [X0] :
( ~ lattice(X0)
| ~ latt_str(X0)
| k2_lattice3(X0) = relation_of_lattice(X0)
| empty_carrier(X0) )
| ~ spl23_92 ),
inference(avatar_component_clause,[],[f743]) ).
fof(f922,plain,
( spl23_124
| spl23_125
| ~ spl23_4
| ~ spl23_75 ),
inference(avatar_split_clause,[],[f661,f633,f305,f919,f915]) ).
fof(f919,plain,
( spl23_125
<=> empty(the_carrier(poset_of_lattice(sK5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_125])]) ).
fof(f661,plain,
( empty(the_carrier(poset_of_lattice(sK5)))
| in(sK6,the_carrier(poset_of_lattice(sK5)))
| ~ spl23_4
| ~ spl23_75 ),
inference(resolution,[],[f634,f307]) ).
fof(f911,plain,
( spl23_123
| ~ spl23_38
| ~ spl23_81 ),
inference(avatar_split_clause,[],[f698,f668,f461,f908]) ).
fof(f908,plain,
( spl23_123
<=> join_absorbing(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_123])]) ).
fof(f461,plain,
( spl23_38
<=> ! [X0] :
( join_absorbing(X0)
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_38])]) ).
fof(f668,plain,
( spl23_81
<=> sP0(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_81])]) ).
fof(f698,plain,
( join_absorbing(sK5)
| ~ spl23_38
| ~ spl23_81 ),
inference(resolution,[],[f670,f462]) ).
fof(f462,plain,
( ! [X0] :
( ~ sP0(X0)
| join_absorbing(X0) )
| ~ spl23_38 ),
inference(avatar_component_clause,[],[f461]) ).
fof(f670,plain,
( sP0(sK5)
| ~ spl23_81 ),
inference(avatar_component_clause,[],[f668]) ).
fof(f906,plain,
( spl23_122
| ~ spl23_21
| ~ spl23_39 ),
inference(avatar_split_clause,[],[f490,f465,f390,f903]) ).
fof(f903,plain,
( spl23_122
<=> one_sorted_str(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_122])]) ).
fof(f490,plain,
( one_sorted_str(sK22)
| ~ spl23_21
| ~ spl23_39 ),
inference(resolution,[],[f466,f392]) ).
fof(f392,plain,
( rel_str(sK22)
| ~ spl23_21 ),
inference(avatar_component_clause,[],[f390]) ).
fof(f901,plain,
( spl23_121
| ~ spl23_15
| ~ spl23_39 ),
inference(avatar_split_clause,[],[f489,f465,f360,f898]) ).
fof(f898,plain,
( spl23_121
<=> one_sorted_str(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_121])]) ).
fof(f489,plain,
( one_sorted_str(sK21)
| ~ spl23_15
| ~ spl23_39 ),
inference(resolution,[],[f466,f362]) ).
fof(f362,plain,
( rel_str(sK21)
| ~ spl23_15 ),
inference(avatar_component_clause,[],[f360]) ).
fof(f896,plain,
( spl23_120
| ~ spl23_11
| ~ spl23_39 ),
inference(avatar_split_clause,[],[f488,f465,f340,f893]) ).
fof(f893,plain,
( spl23_120
<=> one_sorted_str(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_120])]) ).
fof(f340,plain,
( spl23_11
<=> rel_str(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_11])]) ).
fof(f488,plain,
( one_sorted_str(sK18)
| ~ spl23_11
| ~ spl23_39 ),
inference(resolution,[],[f466,f342]) ).
fof(f342,plain,
( rel_str(sK18)
| ~ spl23_11 ),
inference(avatar_component_clause,[],[f340]) ).
fof(f891,plain,
( spl23_119
| ~ spl23_9
| ~ spl23_31 ),
inference(avatar_split_clause,[],[f482,f433,f330,f888]) ).
fof(f888,plain,
( spl23_119
<=> join_semilatt_str(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_119])]) ).
fof(f330,plain,
( spl23_9
<=> latt_str(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_9])]) ).
fof(f433,plain,
( spl23_31
<=> ! [X0] :
( join_semilatt_str(X0)
| ~ latt_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_31])]) ).
fof(f482,plain,
( join_semilatt_str(sK16)
| ~ spl23_9
| ~ spl23_31 ),
inference(resolution,[],[f434,f332]) ).
fof(f332,plain,
( latt_str(sK16)
| ~ spl23_9 ),
inference(avatar_component_clause,[],[f330]) ).
fof(f434,plain,
( ! [X0] :
( ~ latt_str(X0)
| join_semilatt_str(X0) )
| ~ spl23_31 ),
inference(avatar_component_clause,[],[f433]) ).
fof(f886,plain,
( spl23_118
| ~ spl23_9
| ~ spl23_30 ),
inference(avatar_split_clause,[],[f480,f429,f330,f883]) ).
fof(f429,plain,
( spl23_30
<=> ! [X0] :
( meet_semilatt_str(X0)
| ~ latt_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_30])]) ).
fof(f480,plain,
( meet_semilatt_str(sK16)
| ~ spl23_9
| ~ spl23_30 ),
inference(resolution,[],[f430,f332]) ).
fof(f430,plain,
( ! [X0] :
( ~ latt_str(X0)
| meet_semilatt_str(X0) )
| ~ spl23_30 ),
inference(avatar_component_clause,[],[f429]) ).
fof(f881,plain,
( spl23_117
| ~ spl23_7
| ~ spl23_29 ),
inference(avatar_split_clause,[],[f478,f425,f320,f878]) ).
fof(f878,plain,
( spl23_117
<=> one_sorted_str(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_117])]) ).
fof(f320,plain,
( spl23_7
<=> join_semilatt_str(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_7])]) ).
fof(f425,plain,
( spl23_29
<=> ! [X0] :
( one_sorted_str(X0)
| ~ join_semilatt_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_29])]) ).
fof(f478,plain,
( one_sorted_str(sK14)
| ~ spl23_7
| ~ spl23_29 ),
inference(resolution,[],[f426,f322]) ).
fof(f322,plain,
( join_semilatt_str(sK14)
| ~ spl23_7 ),
inference(avatar_component_clause,[],[f320]) ).
fof(f426,plain,
( ! [X0] :
( ~ join_semilatt_str(X0)
| one_sorted_str(X0) )
| ~ spl23_29 ),
inference(avatar_component_clause,[],[f425]) ).
fof(f876,plain,
( spl23_1
| spl23_116
| ~ spl23_3
| ~ spl23_2
| ~ spl23_74 ),
inference(avatar_split_clause,[],[f659,f629,f295,f300,f873,f290]) ).
fof(f629,plain,
( spl23_74
<=> ! [X0] :
( sP3(X0)
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_74])]) ).
fof(f659,plain,
( ~ latt_str(sK5)
| sP3(sK5)
| empty_carrier(sK5)
| ~ spl23_2
| ~ spl23_74 ),
inference(resolution,[],[f630,f297]) ).
fof(f630,plain,
( ! [X0] :
( ~ lattice(X0)
| ~ latt_str(X0)
| sP3(X0)
| empty_carrier(X0) )
| ~ spl23_74 ),
inference(avatar_component_clause,[],[f629]) ).
fof(f871,plain,
( spl23_1
| spl23_115
| ~ spl23_3
| ~ spl23_2
| ~ spl23_73 ),
inference(avatar_split_clause,[],[f658,f625,f295,f300,f868,f290]) ).
fof(f625,plain,
( spl23_73
<=> ! [X0] :
( sP2(X0)
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_73])]) ).
fof(f658,plain,
( ~ latt_str(sK5)
| sP2(sK5)
| empty_carrier(sK5)
| ~ spl23_2
| ~ spl23_73 ),
inference(resolution,[],[f626,f297]) ).
fof(f626,plain,
( ! [X0] :
( ~ lattice(X0)
| ~ latt_str(X0)
| sP2(X0)
| empty_carrier(X0) )
| ~ spl23_73 ),
inference(avatar_component_clause,[],[f625]) ).
fof(f866,plain,
( spl23_114
| ~ spl23_37
| ~ spl23_81 ),
inference(avatar_split_clause,[],[f697,f668,f457,f863]) ).
fof(f863,plain,
( spl23_114
<=> meet_absorbing(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_114])]) ).
fof(f457,plain,
( spl23_37
<=> ! [X0] :
( meet_absorbing(X0)
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_37])]) ).
fof(f697,plain,
( meet_absorbing(sK5)
| ~ spl23_37
| ~ spl23_81 ),
inference(resolution,[],[f670,f458]) ).
fof(f458,plain,
( ! [X0] :
( ~ sP0(X0)
| meet_absorbing(X0) )
| ~ spl23_37 ),
inference(avatar_component_clause,[],[f457]) ).
fof(f861,plain,
( spl23_1
| spl23_113
| ~ spl23_3
| ~ spl23_2
| ~ spl23_72 ),
inference(avatar_split_clause,[],[f657,f621,f295,f300,f858,f290]) ).
fof(f858,plain,
( spl23_113
<=> sP1(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_113])]) ).
fof(f621,plain,
( spl23_72
<=> ! [X0] :
( sP1(X0)
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_72])]) ).
fof(f657,plain,
( ~ latt_str(sK5)
| sP1(sK5)
| empty_carrier(sK5)
| ~ spl23_2
| ~ spl23_72 ),
inference(resolution,[],[f622,f297]) ).
fof(f622,plain,
( ! [X0] :
( ~ lattice(X0)
| ~ latt_str(X0)
| sP1(X0)
| empty_carrier(X0) )
| ~ spl23_72 ),
inference(avatar_component_clause,[],[f621]) ).
fof(f854,plain,
spl23_112,
inference(avatar_split_clause,[],[f257,f852]) ).
fof(f257,plain,
! [X2,X0,X1] :
( latt_element_smaller(X1,X2,X0)
| ~ relstr_set_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2))
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1) ),
inference(cnf_transformation,[],[f157]) ).
fof(f157,plain,
! [X0,X1] :
( ! [X2] :
( ( ( latt_element_smaller(X1,X2,X0)
| ~ relstr_set_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2)) )
& ( relstr_set_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2))
| ~ latt_element_smaller(X1,X2,X0) ) )
| ~ element(X2,the_carrier(X1)) )
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1) ),
inference(nnf_transformation,[],[f122]) ).
fof(f122,plain,
! [X0,X1] :
( ! [X2] :
( ( latt_element_smaller(X1,X2,X0)
<=> relstr_set_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2)) )
| ~ element(X2,the_carrier(X1)) )
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1) ),
inference(flattening,[],[f121]) ).
fof(f121,plain,
! [X0,X1] :
( ! [X2] :
( ( latt_element_smaller(X1,X2,X0)
<=> relstr_set_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2)) )
| ~ element(X2,the_carrier(X1)) )
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1) ),
inference(ennf_transformation,[],[f58]) ).
fof(f58,axiom,
! [X0,X1] :
( ( latt_str(X1)
& lattice(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ( latt_element_smaller(X1,X2,X0)
<=> relstr_set_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_lattice3) ).
fof(f850,plain,
spl23_111,
inference(avatar_split_clause,[],[f256,f848]) ).
fof(f256,plain,
! [X2,X0,X1] :
( relstr_set_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2))
| ~ latt_element_smaller(X1,X2,X0)
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1) ),
inference(cnf_transformation,[],[f157]) ).
fof(f840,plain,
( spl23_110
| ~ spl23_36
| ~ spl23_81 ),
inference(avatar_split_clause,[],[f696,f668,f453,f837]) ).
fof(f837,plain,
( spl23_110
<=> meet_associative(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_110])]) ).
fof(f453,plain,
( spl23_36
<=> ! [X0] :
( meet_associative(X0)
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_36])]) ).
fof(f696,plain,
( meet_associative(sK5)
| ~ spl23_36
| ~ spl23_81 ),
inference(resolution,[],[f670,f454]) ).
fof(f454,plain,
( ! [X0] :
( ~ sP0(X0)
| meet_associative(X0) )
| ~ spl23_36 ),
inference(avatar_component_clause,[],[f453]) ).
fof(f835,plain,
spl23_109,
inference(avatar_split_clause,[],[f261,f833]) ).
fof(f261,plain,
! [X0,X1] :
( antisymmetric_relstr(rel_str_of(X0,X1))
| ~ relation_of2(X1,X0,X0)
| ~ v1_partfun1(X1,X0,X0)
| ~ transitive(X1)
| ~ antisymmetric(X1)
| ~ reflexive(X1) ),
inference(cnf_transformation,[],[f124]) ).
fof(f124,plain,
! [X0,X1] :
( ( antisymmetric_relstr(rel_str_of(X0,X1))
& transitive_relstr(rel_str_of(X0,X1))
& reflexive_relstr(rel_str_of(X0,X1))
& strict_rel_str(rel_str_of(X0,X1)) )
| ~ relation_of2(X1,X0,X0)
| ~ v1_partfun1(X1,X0,X0)
| ~ transitive(X1)
| ~ antisymmetric(X1)
| ~ reflexive(X1) ),
inference(flattening,[],[f123]) ).
fof(f123,plain,
! [X0,X1] :
( ( antisymmetric_relstr(rel_str_of(X0,X1))
& transitive_relstr(rel_str_of(X0,X1))
& reflexive_relstr(rel_str_of(X0,X1))
& strict_rel_str(rel_str_of(X0,X1)) )
| ~ relation_of2(X1,X0,X0)
| ~ v1_partfun1(X1,X0,X0)
| ~ transitive(X1)
| ~ antisymmetric(X1)
| ~ reflexive(X1) ),
inference(ennf_transformation,[],[f41]) ).
fof(f41,axiom,
! [X0,X1] :
( ( relation_of2(X1,X0,X0)
& v1_partfun1(X1,X0,X0)
& transitive(X1)
& antisymmetric(X1)
& reflexive(X1) )
=> ( antisymmetric_relstr(rel_str_of(X0,X1))
& transitive_relstr(rel_str_of(X0,X1))
& reflexive_relstr(rel_str_of(X0,X1))
& strict_rel_str(rel_str_of(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_orders_2) ).
fof(f831,plain,
spl23_108,
inference(avatar_split_clause,[],[f260,f829]) ).
fof(f260,plain,
! [X0,X1] :
( transitive_relstr(rel_str_of(X0,X1))
| ~ relation_of2(X1,X0,X0)
| ~ v1_partfun1(X1,X0,X0)
| ~ transitive(X1)
| ~ antisymmetric(X1)
| ~ reflexive(X1) ),
inference(cnf_transformation,[],[f124]) ).
fof(f827,plain,
spl23_107,
inference(avatar_split_clause,[],[f259,f825]) ).
fof(f259,plain,
! [X0,X1] :
( reflexive_relstr(rel_str_of(X0,X1))
| ~ relation_of2(X1,X0,X0)
| ~ v1_partfun1(X1,X0,X0)
| ~ transitive(X1)
| ~ antisymmetric(X1)
| ~ reflexive(X1) ),
inference(cnf_transformation,[],[f124]) ).
fof(f823,plain,
spl23_106,
inference(avatar_split_clause,[],[f198,f821]) ).
fof(f821,plain,
( spl23_106
<=> ! [X0] :
( lattice(X0)
| ~ join_absorbing(X0)
| ~ meet_absorbing(X0)
| ~ meet_associative(X0)
| ~ meet_commutative(X0)
| ~ join_associative(X0)
| ~ join_commutative(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_106])]) ).
fof(f198,plain,
! [X0] :
( lattice(X0)
| ~ join_absorbing(X0)
| ~ meet_absorbing(X0)
| ~ meet_associative(X0)
| ~ meet_commutative(X0)
| ~ join_associative(X0)
| ~ join_commutative(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0] :
( ( lattice(X0)
& ~ empty_carrier(X0) )
| ~ join_absorbing(X0)
| ~ meet_absorbing(X0)
| ~ meet_associative(X0)
| ~ meet_commutative(X0)
| ~ join_associative(X0)
| ~ join_commutative(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(flattening,[],[f78]) ).
fof(f78,plain,
! [X0] :
( ( lattice(X0)
& ~ empty_carrier(X0) )
| ~ join_absorbing(X0)
| ~ meet_absorbing(X0)
| ~ meet_associative(X0)
| ~ meet_commutative(X0)
| ~ join_associative(X0)
| ~ join_commutative(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( latt_str(X0)
=> ( ( join_absorbing(X0)
& meet_absorbing(X0)
& meet_associative(X0)
& meet_commutative(X0)
& join_associative(X0)
& join_commutative(X0)
& ~ empty_carrier(X0) )
=> ( lattice(X0)
& ~ empty_carrier(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_lattices) ).
fof(f811,plain,
spl23_105,
inference(avatar_split_clause,[],[f255,f809]) ).
fof(f255,plain,
! [X0,X1] :
( element(cast_to_el_of_lattice(X0,X1),the_carrier(X0))
| ~ element(X1,the_carrier(poset_of_lattice(X0)))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f120,plain,
! [X0,X1] :
( element(cast_to_el_of_lattice(X0,X1),the_carrier(X0))
| ~ element(X1,the_carrier(poset_of_lattice(X0)))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f119]) ).
fof(f119,plain,
! [X0,X1] :
( element(cast_to_el_of_lattice(X0,X1),the_carrier(X0))
| ~ element(X1,the_carrier(poset_of_lattice(X0)))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0,X1] :
( ( element(X1,the_carrier(poset_of_lattice(X0)))
& latt_str(X0)
& lattice(X0)
& ~ empty_carrier(X0) )
=> element(cast_to_el_of_lattice(X0,X1),the_carrier(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_lattice3) ).
fof(f807,plain,
spl23_104,
inference(avatar_split_clause,[],[f254,f805]) ).
fof(f254,plain,
! [X0,X1] :
( element(cast_to_el_of_LattPOSet(X0,X1),the_carrier(poset_of_lattice(X0)))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f118]) ).
fof(f118,plain,
! [X0,X1] :
( element(cast_to_el_of_LattPOSet(X0,X1),the_carrier(poset_of_lattice(X0)))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f117]) ).
fof(f117,plain,
! [X0,X1] :
( element(cast_to_el_of_LattPOSet(X0,X1),the_carrier(poset_of_lattice(X0)))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0,X1] :
( ( element(X1,the_carrier(X0))
& latt_str(X0)
& lattice(X0)
& ~ empty_carrier(X0) )
=> element(cast_to_el_of_LattPOSet(X0,X1),the_carrier(poset_of_lattice(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_lattice3) ).
fof(f801,plain,
spl23_103,
inference(avatar_split_clause,[],[f232,f799]) ).
fof(f232,plain,
! [X0,X1] :
( cast_to_el_of_lattice(X0,X1) = X1
| ~ element(X1,the_carrier(poset_of_lattice(X0)))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f100,plain,
! [X0] :
( ! [X1] :
( cast_to_el_of_lattice(X0,X1) = X1
| ~ element(X1,the_carrier(poset_of_lattice(X0))) )
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f99]) ).
fof(f99,plain,
! [X0] :
( ! [X1] :
( cast_to_el_of_lattice(X0,X1) = X1
| ~ element(X1,the_carrier(poset_of_lattice(X0))) )
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( ( latt_str(X0)
& lattice(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,the_carrier(poset_of_lattice(X0)))
=> cast_to_el_of_lattice(X0,X1) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_lattice3) ).
fof(f797,plain,
( spl23_102
| ~ spl23_35
| ~ spl23_81 ),
inference(avatar_split_clause,[],[f695,f668,f449,f794]) ).
fof(f794,plain,
( spl23_102
<=> meet_commutative(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_102])]) ).
fof(f449,plain,
( spl23_35
<=> ! [X0] :
( meet_commutative(X0)
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_35])]) ).
fof(f695,plain,
( meet_commutative(sK5)
| ~ spl23_35
| ~ spl23_81 ),
inference(resolution,[],[f670,f450]) ).
fof(f450,plain,
( ! [X0] :
( ~ sP0(X0)
| meet_commutative(X0) )
| ~ spl23_35 ),
inference(avatar_component_clause,[],[f449]) ).
fof(f790,plain,
spl23_101,
inference(avatar_split_clause,[],[f239,f788]) ).
fof(f239,plain,
! [X0] :
( v1_partfun1(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f106,plain,
! [X0] :
( ( v1_partfun1(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
& transitive(the_InternalRel(X0))
& antisymmetric(the_InternalRel(X0))
& reflexive(the_InternalRel(X0)) )
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0) ),
inference(flattening,[],[f105]) ).
fof(f105,plain,
! [X0] :
( ( v1_partfun1(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
& transitive(the_InternalRel(X0))
& antisymmetric(the_InternalRel(X0))
& reflexive(the_InternalRel(X0)) )
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0) ),
inference(ennf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0] :
( ( rel_str(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0) )
=> ( v1_partfun1(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
& transitive(the_InternalRel(X0))
& antisymmetric(the_InternalRel(X0))
& reflexive(the_InternalRel(X0)) ) ),
inference(pure_predicate_removal,[],[f40]) ).
fof(f40,axiom,
! [X0] :
( ( rel_str(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0) )
=> ( v1_partfun1(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
& transitive(the_InternalRel(X0))
& antisymmetric(the_InternalRel(X0))
& reflexive(the_InternalRel(X0))
& relation(the_InternalRel(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_orders_2) ).
fof(f786,plain,
spl23_100,
inference(avatar_split_clause,[],[f231,f784]) ).
fof(f231,plain,
! [X0,X1] :
( cast_to_el_of_LattPOSet(X0,X1) = X1
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f98]) ).
fof(f98,plain,
! [X0] :
( ! [X1] :
( cast_to_el_of_LattPOSet(X0,X1) = X1
| ~ element(X1,the_carrier(X0)) )
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f97]) ).
fof(f97,plain,
! [X0] :
( ! [X1] :
( cast_to_el_of_LattPOSet(X0,X1) = X1
| ~ element(X1,the_carrier(X0)) )
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] :
( ( latt_str(X0)
& lattice(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> cast_to_el_of_LattPOSet(X0,X1) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_lattice3) ).
fof(f779,plain,
spl23_99,
inference(avatar_split_clause,[],[f250,f777]) ).
fof(f250,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,[],[f112]) ).
fof(f112,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,[],[f44]) ).
fof(f44,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/sandbox/benchmark/theBenchmark.p',free_g1_orders_2) ).
fof(f775,plain,
spl23_98,
inference(avatar_split_clause,[],[f249,f773]) ).
fof(f249,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,[],[f112]) ).
fof(f771,plain,
spl23_97,
inference(avatar_split_clause,[],[f212,f769]) ).
fof(f212,plain,
! [X0] :
( poset_of_lattice(X0) = rel_str_of(the_carrier(X0),k2_lattice3(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0] :
( poset_of_lattice(X0) = rel_str_of(the_carrier(X0),k2_lattice3(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f89]) ).
fof(f89,plain,
! [X0] :
( poset_of_lattice(X0) = rel_str_of(the_carrier(X0),k2_lattice3(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( ( latt_str(X0)
& lattice(X0)
& ~ empty_carrier(X0) )
=> poset_of_lattice(X0) = rel_str_of(the_carrier(X0),k2_lattice3(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_lattice3) ).
fof(f767,plain,
( spl23_96
| ~ spl23_34
| ~ spl23_81 ),
inference(avatar_split_clause,[],[f694,f668,f445,f764]) ).
fof(f764,plain,
( spl23_96
<=> join_associative(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_96])]) ).
fof(f445,plain,
( spl23_34
<=> ! [X0] :
( join_associative(X0)
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_34])]) ).
fof(f694,plain,
( join_associative(sK5)
| ~ spl23_34
| ~ spl23_81 ),
inference(resolution,[],[f670,f446]) ).
fof(f446,plain,
( ! [X0] :
( ~ sP0(X0)
| join_associative(X0) )
| ~ spl23_34 ),
inference(avatar_component_clause,[],[f445]) ).
fof(f757,plain,
spl23_95,
inference(avatar_split_clause,[],[f238,f755]) ).
fof(f755,plain,
( spl23_95
<=> ! [X0] :
( transitive(the_InternalRel(X0))
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_95])]) ).
fof(f238,plain,
! [X0] :
( transitive(the_InternalRel(X0))
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f753,plain,
spl23_94,
inference(avatar_split_clause,[],[f237,f751]) ).
fof(f751,plain,
( spl23_94
<=> ! [X0] :
( antisymmetric(the_InternalRel(X0))
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_94])]) ).
fof(f237,plain,
! [X0] :
( antisymmetric(the_InternalRel(X0))
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f749,plain,
spl23_93,
inference(avatar_split_clause,[],[f236,f747]) ).
fof(f747,plain,
( spl23_93
<=> ! [X0] :
( reflexive(the_InternalRel(X0))
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_93])]) ).
fof(f236,plain,
! [X0] :
( reflexive(the_InternalRel(X0))
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f745,plain,
spl23_92,
inference(avatar_split_clause,[],[f211,f743]) ).
fof(f211,plain,
! [X0] :
( k2_lattice3(X0) = relation_of_lattice(X0)
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0] :
( k2_lattice3(X0) = relation_of_lattice(X0)
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f87]) ).
fof(f87,plain,
! [X0] :
( k2_lattice3(X0) = relation_of_lattice(X0)
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f53]) ).
fof(f53,axiom,
! [X0] :
( ( latt_str(X0)
& lattice(X0)
& ~ empty_carrier(X0) )
=> k2_lattice3(X0) = relation_of_lattice(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_lattice3) ).
fof(f741,plain,
spl23_91,
inference(avatar_split_clause,[],[f209,f739]) ).
fof(f209,plain,
! [X0] :
( rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0
| ~ strict_rel_str(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
! [X0] :
( rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0
| ~ strict_rel_str(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f84]) ).
fof(f84,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/sandbox/benchmark/theBenchmark.p',abstractness_v1_orders_2) ).
fof(f737,plain,
( spl23_90
| ~ spl23_33
| ~ spl23_81 ),
inference(avatar_split_clause,[],[f693,f668,f441,f734]) ).
fof(f734,plain,
( spl23_90
<=> join_commutative(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_90])]) ).
fof(f441,plain,
( spl23_33
<=> ! [X0] :
( join_commutative(X0)
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_33])]) ).
fof(f693,plain,
( join_commutative(sK5)
| ~ spl23_33
| ~ spl23_81 ),
inference(resolution,[],[f670,f442]) ).
fof(f442,plain,
( ! [X0] :
( ~ sP0(X0)
| join_commutative(X0) )
| ~ spl23_33 ),
inference(avatar_component_clause,[],[f441]) ).
fof(f720,plain,
spl23_89,
inference(avatar_split_clause,[],[f268,f718]) ).
fof(f268,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f130]) ).
fof(f130,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f129]) ).
fof(f129,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f62]) ).
fof(f62,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f716,plain,
spl23_88,
inference(avatar_split_clause,[],[f267,f714]) ).
fof(f267,plain,
! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f128]) ).
fof(f128,plain,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> element(X2,powerset(cartesian_product2(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(f712,plain,
spl23_87,
inference(avatar_split_clause,[],[f252,f710]) ).
fof(f252,plain,
! [X0,X1] :
( ~ empty_carrier(rel_str_of(X0,X1))
| ~ relation_of2(X1,X0,X0)
| empty(X0) ),
inference(cnf_transformation,[],[f116]) ).
fof(f116,plain,
! [X0,X1] :
( ( strict_rel_str(rel_str_of(X0,X1))
& ~ empty_carrier(rel_str_of(X0,X1)) )
| ~ relation_of2(X1,X0,X0)
| empty(X0) ),
inference(flattening,[],[f115]) ).
fof(f115,plain,
! [X0,X1] :
( ( strict_rel_str(rel_str_of(X0,X1))
& ~ empty_carrier(rel_str_of(X0,X1)) )
| ~ relation_of2(X1,X0,X0)
| empty(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0,X1] :
( ( relation_of2(X1,X0,X0)
& ~ empty(X0) )
=> ( strict_rel_str(rel_str_of(X0,X1))
& ~ empty_carrier(rel_str_of(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_orders_2) ).
fof(f708,plain,
spl23_86,
inference(avatar_split_clause,[],[f234,f706]) ).
fof(f234,plain,
! [X0] :
( element(sK8(X0),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f152]) ).
fof(f152,plain,
! [X0] :
( ( ~ empty(sK8(X0))
& element(sK8(X0),powerset(the_carrier(X0))) )
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f104,f151]) ).
fof(f151,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
=> ( ~ empty(sK8(X0))
& element(sK8(X0),powerset(the_carrier(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f104,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f103]) ).
fof(f103,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f52]) ).
fof(f52,axiom,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_struct_0) ).
fof(f690,plain,
spl23_85,
inference(avatar_split_clause,[],[f271,f688]) ).
fof(f271,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f131]) ).
fof(f131,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f63]) ).
fof(f63,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f686,plain,
spl23_84,
inference(avatar_split_clause,[],[f223,f684]) ).
fof(f223,plain,
! [X0] :
( relation_of2_as_subset(k2_lattice3(X0),the_carrier(X0),the_carrier(X0))
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f149]) ).
fof(f149,plain,
! [X0] :
( ( relation_of2_as_subset(k2_lattice3(X0),the_carrier(X0),the_carrier(X0))
& v1_partfun1(k2_lattice3(X0),the_carrier(X0),the_carrier(X0))
& transitive(k2_lattice3(X0))
& antisymmetric(k2_lattice3(X0))
& reflexive(k2_lattice3(X0)) )
| ~ sP2(X0) ),
inference(nnf_transformation,[],[f136]) ).
fof(f136,plain,
! [X0] :
( ( relation_of2_as_subset(k2_lattice3(X0),the_carrier(X0),the_carrier(X0))
& v1_partfun1(k2_lattice3(X0),the_carrier(X0),the_carrier(X0))
& transitive(k2_lattice3(X0))
& antisymmetric(k2_lattice3(X0))
& reflexive(k2_lattice3(X0)) )
| ~ sP2(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f682,plain,
spl23_83,
inference(avatar_split_clause,[],[f222,f680]) ).
fof(f222,plain,
! [X0] :
( v1_partfun1(k2_lattice3(X0),the_carrier(X0),the_carrier(X0))
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f149]) ).
fof(f678,plain,
spl23_82,
inference(avatar_split_clause,[],[f208,f676]) ).
fof(f208,plain,
! [X0] :
( relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
! [X0] :
( relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0] :
( rel_str(X0)
=> relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_orders_2) ).
fof(f671,plain,
( ~ spl23_3
| spl23_1
| spl23_81
| ~ spl23_2
| ~ spl23_71 ),
inference(avatar_split_clause,[],[f656,f617,f295,f668,f290,f300]) ).
fof(f617,plain,
( spl23_71
<=> ! [X0] :
( sP0(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_71])]) ).
fof(f656,plain,
( sP0(sK5)
| empty_carrier(sK5)
| ~ latt_str(sK5)
| ~ spl23_2
| ~ spl23_71 ),
inference(resolution,[],[f618,f297]) ).
fof(f618,plain,
( ! [X0] :
( ~ lattice(X0)
| sP0(X0)
| empty_carrier(X0)
| ~ latt_str(X0) )
| ~ spl23_71 ),
inference(avatar_component_clause,[],[f617]) ).
fof(f655,plain,
spl23_80,
inference(avatar_split_clause,[],[f270,f653]) ).
fof(f270,plain,
! [X2,X0,X1] :
( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f162]) ).
fof(f162,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,[],[f54]) ).
fof(f54,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
<=> relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f651,plain,
spl23_79,
inference(avatar_split_clause,[],[f269,f649]) ).
fof(f269,plain,
! [X2,X0,X1] :
( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f162]) ).
fof(f647,plain,
spl23_78,
inference(avatar_split_clause,[],[f251,f645]) ).
fof(f645,plain,
( spl23_78
<=> ! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_78])]) ).
fof(f251,plain,
! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ),
inference(cnf_transformation,[],[f114]) ).
fof(f114,plain,
! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ),
inference(flattening,[],[f113]) ).
fof(f113,plain,
! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ),
inference(ennf_transformation,[],[f43]) ).
fof(f43,axiom,
! [X0,X1] :
( ( ~ empty(X1)
& ~ empty(X0) )
=> ~ empty(cartesian_product2(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_subset_1) ).
fof(f643,plain,
spl23_77,
inference(avatar_split_clause,[],[f248,f641]) ).
fof(f248,plain,
! [X0,X1] :
( rel_str(rel_str_of(X0,X1))
| ~ relation_of2(X1,X0,X0) ),
inference(cnf_transformation,[],[f111]) ).
fof(f111,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,[],[f9]) ).
fof(f9,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/sandbox/benchmark/theBenchmark.p',dt_g1_orders_2) ).
fof(f639,plain,
spl23_76,
inference(avatar_split_clause,[],[f247,f637]) ).
fof(f247,plain,
! [X0,X1] :
( strict_rel_str(rel_str_of(X0,X1))
| ~ relation_of2(X1,X0,X0) ),
inference(cnf_transformation,[],[f111]) ).
fof(f635,plain,
spl23_75,
inference(avatar_split_clause,[],[f246,f633]) ).
fof(f246,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f110]) ).
fof(f110,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f109]) ).
fof(f109,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f57]) ).
fof(f57,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f631,plain,
spl23_74,
inference(avatar_split_clause,[],[f230,f629]) ).
fof(f230,plain,
! [X0] :
( sP3(X0)
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f139]) ).
fof(f139,plain,
! [X0] :
( sP3(X0)
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(definition_folding,[],[f96,f138]) ).
fof(f138,plain,
! [X0] :
( ( rel_str(poset_of_lattice(X0))
& antisymmetric_relstr(poset_of_lattice(X0))
& transitive_relstr(poset_of_lattice(X0))
& reflexive_relstr(poset_of_lattice(X0))
& strict_rel_str(poset_of_lattice(X0)) )
| ~ sP3(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f96,plain,
! [X0] :
( ( rel_str(poset_of_lattice(X0))
& antisymmetric_relstr(poset_of_lattice(X0))
& transitive_relstr(poset_of_lattice(X0))
& reflexive_relstr(poset_of_lattice(X0))
& strict_rel_str(poset_of_lattice(X0)) )
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f95]) ).
fof(f95,plain,
! [X0] :
( ( rel_str(poset_of_lattice(X0))
& antisymmetric_relstr(poset_of_lattice(X0))
& transitive_relstr(poset_of_lattice(X0))
& reflexive_relstr(poset_of_lattice(X0))
& strict_rel_str(poset_of_lattice(X0)) )
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0] :
( ( latt_str(X0)
& lattice(X0)
& ~ empty_carrier(X0) )
=> ( rel_str(poset_of_lattice(X0))
& antisymmetric_relstr(poset_of_lattice(X0))
& transitive_relstr(poset_of_lattice(X0))
& reflexive_relstr(poset_of_lattice(X0))
& strict_rel_str(poset_of_lattice(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_lattice3) ).
fof(f627,plain,
spl23_73,
inference(avatar_split_clause,[],[f224,f625]) ).
fof(f224,plain,
! [X0] :
( sP2(X0)
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f137]) ).
fof(f137,plain,
! [X0] :
( sP2(X0)
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(definition_folding,[],[f94,f136]) ).
fof(f94,plain,
! [X0] :
( ( relation_of2_as_subset(k2_lattice3(X0),the_carrier(X0),the_carrier(X0))
& v1_partfun1(k2_lattice3(X0),the_carrier(X0),the_carrier(X0))
& transitive(k2_lattice3(X0))
& antisymmetric(k2_lattice3(X0))
& reflexive(k2_lattice3(X0)) )
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f93]) ).
fof(f93,plain,
! [X0] :
( ( relation_of2_as_subset(k2_lattice3(X0),the_carrier(X0),the_carrier(X0))
& v1_partfun1(k2_lattice3(X0),the_carrier(X0),the_carrier(X0))
& transitive(k2_lattice3(X0))
& antisymmetric(k2_lattice3(X0))
& reflexive(k2_lattice3(X0)) )
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0] :
( ( latt_str(X0)
& lattice(X0)
& ~ empty_carrier(X0) )
=> ( relation_of2_as_subset(k2_lattice3(X0),the_carrier(X0),the_carrier(X0))
& v1_partfun1(k2_lattice3(X0),the_carrier(X0),the_carrier(X0))
& transitive(k2_lattice3(X0))
& antisymmetric(k2_lattice3(X0))
& reflexive(k2_lattice3(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_lattice3) ).
fof(f623,plain,
spl23_72,
inference(avatar_split_clause,[],[f218,f621]) ).
fof(f218,plain,
! [X0] :
( sP1(X0)
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f135]) ).
fof(f135,plain,
! [X0] :
( sP1(X0)
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(definition_folding,[],[f92,f134]) ).
fof(f134,plain,
! [X0] :
( ( antisymmetric_relstr(poset_of_lattice(X0))
& transitive_relstr(poset_of_lattice(X0))
& reflexive_relstr(poset_of_lattice(X0))
& strict_rel_str(poset_of_lattice(X0))
& ~ empty_carrier(poset_of_lattice(X0)) )
| ~ sP1(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f92,plain,
! [X0] :
( ( antisymmetric_relstr(poset_of_lattice(X0))
& transitive_relstr(poset_of_lattice(X0))
& reflexive_relstr(poset_of_lattice(X0))
& strict_rel_str(poset_of_lattice(X0))
& ~ empty_carrier(poset_of_lattice(X0)) )
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f91]) ).
fof(f91,plain,
! [X0] :
( ( antisymmetric_relstr(poset_of_lattice(X0))
& transitive_relstr(poset_of_lattice(X0))
& reflexive_relstr(poset_of_lattice(X0))
& strict_rel_str(poset_of_lattice(X0))
& ~ empty_carrier(poset_of_lattice(X0)) )
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0] :
( ( latt_str(X0)
& lattice(X0)
& ~ empty_carrier(X0) )
=> ( antisymmetric_relstr(poset_of_lattice(X0))
& transitive_relstr(poset_of_lattice(X0))
& reflexive_relstr(poset_of_lattice(X0))
& strict_rel_str(poset_of_lattice(X0))
& ~ empty_carrier(poset_of_lattice(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_lattice3) ).
fof(f619,plain,
spl23_71,
inference(avatar_split_clause,[],[f206,f617]) ).
fof(f206,plain,
! [X0] :
( sP0(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f133]) ).
fof(f133,plain,
! [X0] :
( sP0(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(definition_folding,[],[f81,f132]) ).
fof(f132,plain,
! [X0] :
( ( join_absorbing(X0)
& meet_absorbing(X0)
& meet_associative(X0)
& meet_commutative(X0)
& join_associative(X0)
& join_commutative(X0)
& ~ empty_carrier(X0) )
| ~ sP0(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f81,plain,
! [X0] :
( ( join_absorbing(X0)
& meet_absorbing(X0)
& meet_associative(X0)
& meet_commutative(X0)
& join_associative(X0)
& join_commutative(X0)
& ~ empty_carrier(X0) )
| ~ lattice(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(flattening,[],[f80]) ).
fof(f80,plain,
! [X0] :
( ( join_absorbing(X0)
& meet_absorbing(X0)
& meet_associative(X0)
& meet_commutative(X0)
& join_associative(X0)
& join_commutative(X0)
& ~ empty_carrier(X0) )
| ~ lattice(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( latt_str(X0)
=> ( ( lattice(X0)
& ~ empty_carrier(X0) )
=> ( join_absorbing(X0)
& meet_absorbing(X0)
& meet_associative(X0)
& meet_commutative(X0)
& join_associative(X0)
& join_commutative(X0)
& ~ empty_carrier(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_lattices) ).
fof(f611,plain,
spl23_70,
inference(avatar_split_clause,[],[f263,f609]) ).
fof(f263,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f126]) ).
fof(f126,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f66]) ).
fof(f66,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(f607,plain,
spl23_69,
inference(avatar_split_clause,[],[f262,f605]) ).
fof(f262,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f125]) ).
fof(f125,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0,X1] :
( subset(X0,X1)
=> element(X0,powerset(X1)) ),
inference(unused_predicate_definition_removal,[],[f61]) ).
fof(f61,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f603,plain,
spl23_68,
inference(avatar_split_clause,[],[f235,f601]) ).
fof(f601,plain,
( spl23_68
<=> ! [X0] :
( ~ empty(sK8(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_68])]) ).
fof(f235,plain,
! [X0] :
( ~ empty(sK8(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f152]) ).
fof(f599,plain,
spl23_67,
inference(avatar_split_clause,[],[f233,f597]) ).
fof(f597,plain,
( spl23_67
<=> ! [X0] :
( ~ empty(the_carrier(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_67])]) ).
fof(f233,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f102,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f101]) ).
fof(f101,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ~ empty(the_carrier(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(f595,plain,
spl23_66,
inference(avatar_split_clause,[],[f191,f593]) ).
fof(f191,plain,
! [X0] :
( element(sK7(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f146]) ).
fof(f146,plain,
! [X0] :
( ( ~ empty(sK7(X0))
& element(sK7(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f74,f145]) ).
fof(f145,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( ~ empty(sK7(X0))
& element(sK7(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f74,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f46]) ).
fof(f46,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f591,plain,
( spl23_65
| ~ spl23_28
| ~ spl23_42 ),
inference(avatar_split_clause,[],[f564,f484,f421,f588]) ).
fof(f588,plain,
( spl23_65
<=> one_sorted_str(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_65])]) ).
fof(f484,plain,
( spl23_42
<=> meet_semilatt_str(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_42])]) ).
fof(f564,plain,
( one_sorted_str(sK5)
| ~ spl23_28
| ~ spl23_42 ),
inference(resolution,[],[f486,f422]) ).
fof(f486,plain,
( meet_semilatt_str(sK5)
| ~ spl23_42 ),
inference(avatar_component_clause,[],[f484]) ).
fof(f586,plain,
spl23_64,
inference(avatar_split_clause,[],[f266,f584]) ).
fof(f266,plain,
! [X0,X1] : relation_of2_as_subset(sK12(X0,X1),X0,X1),
inference(cnf_transformation,[],[f161]) ).
fof(f161,plain,
! [X0,X1] : relation_of2_as_subset(sK12(X0,X1),X0,X1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f35,f160]) ).
fof(f160,plain,
! [X0,X1] :
( ? [X2] : relation_of2_as_subset(X2,X0,X1)
=> relation_of2_as_subset(sK12(X0,X1),X0,X1) ),
introduced(choice_axiom,[]) ).
fof(f35,axiom,
! [X0,X1] :
? [X2] : relation_of2_as_subset(X2,X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_relset_1) ).
fof(f582,plain,
spl23_63,
inference(avatar_split_clause,[],[f265,f580]) ).
fof(f265,plain,
! [X0,X1] : relation_of2(sK11(X0,X1),X0,X1),
inference(cnf_transformation,[],[f159]) ).
fof(f159,plain,
! [X0,X1] : relation_of2(sK11(X0,X1),X0,X1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f33,f158]) ).
fof(f158,plain,
! [X0,X1] :
( ? [X2] : relation_of2(X2,X0,X1)
=> relation_of2(sK11(X0,X1),X0,X1) ),
introduced(choice_axiom,[]) ).
fof(f33,axiom,
! [X0,X1] :
? [X2] : relation_of2(X2,X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_relset_1) ).
fof(f578,plain,
spl23_62,
inference(avatar_split_clause,[],[f245,f576]) ).
fof(f576,plain,
( spl23_62
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_62])]) ).
fof(f245,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f108]) ).
fof(f108,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f56]) ).
fof(f56,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(f574,plain,
spl23_61,
inference(avatar_split_clause,[],[f244,f572]) ).
fof(f244,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f107]) ).
fof(f107,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/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f563,plain,
spl23_60,
inference(avatar_split_clause,[],[f264,f561]) ).
fof(f264,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f127]) ).
fof(f127,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f65]) ).
fof(f65,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f559,plain,
spl23_59,
inference(avatar_split_clause,[],[f241,f557]) ).
fof(f241,plain,
! [X0] : element(sK10(X0),powerset(X0)),
inference(cnf_transformation,[],[f156]) ).
fof(f156,plain,
! [X0] :
( empty(sK10(X0))
& element(sK10(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f49,f155]) ).
fof(f155,plain,
! [X0] :
( ? [X1] :
( empty(X1)
& element(X1,powerset(X0)) )
=> ( empty(sK10(X0))
& element(sK10(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f49,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f555,plain,
spl23_58,
inference(avatar_split_clause,[],[f229,f553]) ).
fof(f229,plain,
! [X0] :
( rel_str(poset_of_lattice(X0))
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f150]) ).
fof(f150,plain,
! [X0] :
( ( rel_str(poset_of_lattice(X0))
& antisymmetric_relstr(poset_of_lattice(X0))
& transitive_relstr(poset_of_lattice(X0))
& reflexive_relstr(poset_of_lattice(X0))
& strict_rel_str(poset_of_lattice(X0)) )
| ~ sP3(X0) ),
inference(nnf_transformation,[],[f138]) ).
fof(f551,plain,
spl23_57,
inference(avatar_split_clause,[],[f228,f549]) ).
fof(f549,plain,
( spl23_57
<=> ! [X0] :
( antisymmetric_relstr(poset_of_lattice(X0))
| ~ sP3(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_57])]) ).
fof(f228,plain,
! [X0] :
( antisymmetric_relstr(poset_of_lattice(X0))
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f150]) ).
fof(f547,plain,
spl23_56,
inference(avatar_split_clause,[],[f227,f545]) ).
fof(f545,plain,
( spl23_56
<=> ! [X0] :
( transitive_relstr(poset_of_lattice(X0))
| ~ sP3(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_56])]) ).
fof(f227,plain,
! [X0] :
( transitive_relstr(poset_of_lattice(X0))
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f150]) ).
fof(f543,plain,
spl23_55,
inference(avatar_split_clause,[],[f226,f541]) ).
fof(f541,plain,
( spl23_55
<=> ! [X0] :
( reflexive_relstr(poset_of_lattice(X0))
| ~ sP3(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_55])]) ).
fof(f226,plain,
! [X0] :
( reflexive_relstr(poset_of_lattice(X0))
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f150]) ).
fof(f539,plain,
spl23_54,
inference(avatar_split_clause,[],[f225,f537]) ).
fof(f225,plain,
! [X0] :
( strict_rel_str(poset_of_lattice(X0))
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f150]) ).
fof(f535,plain,
spl23_53,
inference(avatar_split_clause,[],[f221,f533]) ).
fof(f221,plain,
! [X0] :
( transitive(k2_lattice3(X0))
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f149]) ).
fof(f531,plain,
spl23_52,
inference(avatar_split_clause,[],[f220,f529]) ).
fof(f220,plain,
! [X0] :
( antisymmetric(k2_lattice3(X0))
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f149]) ).
fof(f527,plain,
( spl23_51
| ~ spl23_3
| ~ spl23_31 ),
inference(avatar_split_clause,[],[f481,f433,f300,f524]) ).
fof(f524,plain,
( spl23_51
<=> join_semilatt_str(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_51])]) ).
fof(f481,plain,
( join_semilatt_str(sK5)
| ~ spl23_3
| ~ spl23_31 ),
inference(resolution,[],[f434,f302]) ).
fof(f302,plain,
( latt_str(sK5)
| ~ spl23_3 ),
inference(avatar_component_clause,[],[f300]) ).
fof(f522,plain,
spl23_50,
inference(avatar_split_clause,[],[f219,f520]) ).
fof(f219,plain,
! [X0] :
( reflexive(k2_lattice3(X0))
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f149]) ).
fof(f518,plain,
spl23_49,
inference(avatar_split_clause,[],[f217,f516]) ).
fof(f516,plain,
( spl23_49
<=> ! [X0] :
( antisymmetric_relstr(poset_of_lattice(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_49])]) ).
fof(f217,plain,
! [X0] :
( antisymmetric_relstr(poset_of_lattice(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f148,plain,
! [X0] :
( ( antisymmetric_relstr(poset_of_lattice(X0))
& transitive_relstr(poset_of_lattice(X0))
& reflexive_relstr(poset_of_lattice(X0))
& strict_rel_str(poset_of_lattice(X0))
& ~ empty_carrier(poset_of_lattice(X0)) )
| ~ sP1(X0) ),
inference(nnf_transformation,[],[f134]) ).
fof(f514,plain,
spl23_48,
inference(avatar_split_clause,[],[f216,f512]) ).
fof(f512,plain,
( spl23_48
<=> ! [X0] :
( transitive_relstr(poset_of_lattice(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_48])]) ).
fof(f216,plain,
! [X0] :
( transitive_relstr(poset_of_lattice(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f510,plain,
spl23_47,
inference(avatar_split_clause,[],[f215,f508]) ).
fof(f508,plain,
( spl23_47
<=> ! [X0] :
( reflexive_relstr(poset_of_lattice(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_47])]) ).
fof(f215,plain,
! [X0] :
( reflexive_relstr(poset_of_lattice(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f506,plain,
spl23_46,
inference(avatar_split_clause,[],[f214,f504]) ).
fof(f214,plain,
! [X0] :
( strict_rel_str(poset_of_lattice(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f502,plain,
spl23_45,
inference(avatar_split_clause,[],[f213,f500]) ).
fof(f500,plain,
( spl23_45
<=> ! [X0] :
( ~ empty_carrier(poset_of_lattice(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_45])]) ).
fof(f213,plain,
! [X0] :
( ~ empty_carrier(poset_of_lattice(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f498,plain,
spl23_44,
inference(avatar_split_clause,[],[f210,f496]) ).
fof(f210,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f64]) ).
fof(f64,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f494,plain,
spl23_43,
inference(avatar_split_clause,[],[f192,f492]) ).
fof(f492,plain,
( spl23_43
<=> ! [X0] :
( ~ empty(sK7(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_43])]) ).
fof(f192,plain,
! [X0] :
( ~ empty(sK7(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f146]) ).
fof(f487,plain,
( spl23_42
| ~ spl23_3
| ~ spl23_30 ),
inference(avatar_split_clause,[],[f479,f429,f300,f484]) ).
fof(f479,plain,
( meet_semilatt_str(sK5)
| ~ spl23_3
| ~ spl23_30 ),
inference(resolution,[],[f430,f302]) ).
fof(f477,plain,
( spl23_41
| ~ spl23_8
| ~ spl23_28 ),
inference(avatar_split_clause,[],[f472,f421,f325,f474]) ).
fof(f474,plain,
( spl23_41
<=> one_sorted_str(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_41])]) ).
fof(f325,plain,
( spl23_8
<=> meet_semilatt_str(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_8])]) ).
fof(f472,plain,
( one_sorted_str(sK15)
| ~ spl23_8
| ~ spl23_28 ),
inference(resolution,[],[f422,f327]) ).
fof(f327,plain,
( meet_semilatt_str(sK15)
| ~ spl23_8 ),
inference(avatar_component_clause,[],[f325]) ).
fof(f471,plain,
spl23_40,
inference(avatar_split_clause,[],[f240,f469]) ).
fof(f240,plain,
! [X0] : element(sK9(X0),X0),
inference(cnf_transformation,[],[f154]) ).
fof(f154,plain,
! [X0] : element(sK9(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f34,f153]) ).
fof(f153,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK9(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f34,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f467,plain,
spl23_39,
inference(avatar_split_clause,[],[f207,f465]) ).
fof(f207,plain,
! [X0] :
( one_sorted_str(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0] :
( one_sorted_str(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0] :
( rel_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_orders_2) ).
fof(f463,plain,
spl23_38,
inference(avatar_split_clause,[],[f205,f461]) ).
fof(f205,plain,
! [X0] :
( join_absorbing(X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f147]) ).
fof(f147,plain,
! [X0] :
( ( join_absorbing(X0)
& meet_absorbing(X0)
& meet_associative(X0)
& meet_commutative(X0)
& join_associative(X0)
& join_commutative(X0)
& ~ empty_carrier(X0) )
| ~ sP0(X0) ),
inference(nnf_transformation,[],[f132]) ).
fof(f459,plain,
spl23_37,
inference(avatar_split_clause,[],[f204,f457]) ).
fof(f204,plain,
! [X0] :
( meet_absorbing(X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f147]) ).
fof(f455,plain,
spl23_36,
inference(avatar_split_clause,[],[f203,f453]) ).
fof(f203,plain,
! [X0] :
( meet_associative(X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f147]) ).
fof(f451,plain,
spl23_35,
inference(avatar_split_clause,[],[f202,f449]) ).
fof(f202,plain,
! [X0] :
( meet_commutative(X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f147]) ).
fof(f447,plain,
spl23_34,
inference(avatar_split_clause,[],[f201,f445]) ).
fof(f201,plain,
! [X0] :
( join_associative(X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f147]) ).
fof(f443,plain,
spl23_33,
inference(avatar_split_clause,[],[f200,f441]) ).
fof(f200,plain,
! [X0] :
( join_commutative(X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f147]) ).
fof(f439,plain,
spl23_32,
inference(avatar_split_clause,[],[f199,f437]) ).
fof(f437,plain,
( spl23_32
<=> ! [X0] :
( ~ empty_carrier(X0)
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_32])]) ).
fof(f199,plain,
! [X0] :
( ~ empty_carrier(X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f147]) ).
fof(f435,plain,
spl23_31,
inference(avatar_split_clause,[],[f196,f433]) ).
fof(f196,plain,
! [X0] :
( join_semilatt_str(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0] :
( ( join_semilatt_str(X0)
& meet_semilatt_str(X0) )
| ~ latt_str(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0] :
( latt_str(X0)
=> ( join_semilatt_str(X0)
& meet_semilatt_str(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l3_lattices) ).
fof(f431,plain,
spl23_30,
inference(avatar_split_clause,[],[f195,f429]) ).
fof(f195,plain,
! [X0] :
( meet_semilatt_str(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f427,plain,
spl23_29,
inference(avatar_split_clause,[],[f194,f425]) ).
fof(f194,plain,
! [X0] :
( one_sorted_str(X0)
| ~ join_semilatt_str(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0] :
( one_sorted_str(X0)
| ~ join_semilatt_str(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0] :
( join_semilatt_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l2_lattices) ).
fof(f423,plain,
spl23_28,
inference(avatar_split_clause,[],[f193,f421]) ).
fof(f193,plain,
! [X0] :
( one_sorted_str(X0)
| ~ meet_semilatt_str(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0] :
( one_sorted_str(X0)
| ~ meet_semilatt_str(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0] :
( meet_semilatt_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_lattices) ).
fof(f419,plain,
spl23_27,
inference(avatar_split_clause,[],[f243,f417]) ).
fof(f417,plain,
( spl23_27
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_27])]) ).
fof(f243,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f55]) ).
fof(f55,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f415,plain,
spl23_26,
inference(avatar_split_clause,[],[f242,f413]) ).
fof(f242,plain,
! [X0] : empty(sK10(X0)),
inference(cnf_transformation,[],[f156]) ).
fof(f411,plain,
spl23_25,
inference(avatar_split_clause,[],[f190,f409]) ).
fof(f409,plain,
( spl23_25
<=> ! [X0] : ~ empty(powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_25])]) ).
fof(f190,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f407,plain,
( spl23_23
| spl23_24 ),
inference(avatar_split_clause,[],[f187,f404,f400]) ).
fof(f187,plain,
( latt_element_smaller(sK5,cast_to_el_of_lattice(sK5,sK6),sK4)
| relstr_set_smaller(poset_of_lattice(sK5),sK4,sK6) ),
inference(cnf_transformation,[],[f144]) ).
fof(f398,plain,
spl23_22,
inference(avatar_split_clause,[],[f288,f395]) ).
fof(f288,plain,
strict_rel_str(sK22),
inference(cnf_transformation,[],[f182]) ).
fof(f182,plain,
( strict_rel_str(sK22)
& rel_str(sK22) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22])],[f45,f181]) ).
fof(f181,plain,
( ? [X0] :
( strict_rel_str(X0)
& rel_str(X0) )
=> ( strict_rel_str(sK22)
& rel_str(sK22) ) ),
introduced(choice_axiom,[]) ).
fof(f45,axiom,
? [X0] :
( strict_rel_str(X0)
& rel_str(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_orders_2) ).
fof(f393,plain,
spl23_21,
inference(avatar_split_clause,[],[f287,f390]) ).
fof(f287,plain,
rel_str(sK22),
inference(cnf_transformation,[],[f182]) ).
fof(f388,plain,
spl23_20,
inference(avatar_split_clause,[],[f286,f385]) ).
fof(f385,plain,
( spl23_20
<=> antisymmetric_relstr(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_20])]) ).
fof(f286,plain,
antisymmetric_relstr(sK21),
inference(cnf_transformation,[],[f180]) ).
fof(f180,plain,
( antisymmetric_relstr(sK21)
& transitive_relstr(sK21)
& reflexive_relstr(sK21)
& strict_rel_str(sK21)
& ~ empty_carrier(sK21)
& rel_str(sK21) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f48,f179]) ).
fof(f179,plain,
( ? [X0] :
( antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& strict_rel_str(X0)
& ~ empty_carrier(X0)
& rel_str(X0) )
=> ( antisymmetric_relstr(sK21)
& transitive_relstr(sK21)
& reflexive_relstr(sK21)
& strict_rel_str(sK21)
& ~ empty_carrier(sK21)
& rel_str(sK21) ) ),
introduced(choice_axiom,[]) ).
fof(f48,axiom,
? [X0] :
( antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& strict_rel_str(X0)
& ~ empty_carrier(X0)
& rel_str(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_orders_2) ).
fof(f383,plain,
spl23_19,
inference(avatar_split_clause,[],[f285,f380]) ).
fof(f380,plain,
( spl23_19
<=> transitive_relstr(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_19])]) ).
fof(f285,plain,
transitive_relstr(sK21),
inference(cnf_transformation,[],[f180]) ).
fof(f378,plain,
spl23_18,
inference(avatar_split_clause,[],[f284,f375]) ).
fof(f375,plain,
( spl23_18
<=> reflexive_relstr(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_18])]) ).
fof(f284,plain,
reflexive_relstr(sK21),
inference(cnf_transformation,[],[f180]) ).
fof(f373,plain,
spl23_17,
inference(avatar_split_clause,[],[f283,f370]) ).
fof(f283,plain,
strict_rel_str(sK21),
inference(cnf_transformation,[],[f180]) ).
fof(f368,plain,
~ spl23_16,
inference(avatar_split_clause,[],[f282,f365]) ).
fof(f365,plain,
( spl23_16
<=> empty_carrier(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_16])]) ).
fof(f282,plain,
~ empty_carrier(sK21),
inference(cnf_transformation,[],[f180]) ).
fof(f363,plain,
spl23_15,
inference(avatar_split_clause,[],[f281,f360]) ).
fof(f281,plain,
rel_str(sK21),
inference(cnf_transformation,[],[f180]) ).
fof(f358,plain,
~ spl23_14,
inference(avatar_split_clause,[],[f280,f355]) ).
fof(f355,plain,
( spl23_14
<=> empty_carrier(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_14])]) ).
fof(f280,plain,
~ empty_carrier(sK20),
inference(cnf_transformation,[],[f178]) ).
fof(f178,plain,
( ~ empty_carrier(sK20)
& one_sorted_str(sK20) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f51,f177]) ).
fof(f177,plain,
( ? [X0] :
( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ( ~ empty_carrier(sK20)
& one_sorted_str(sK20) ) ),
introduced(choice_axiom,[]) ).
fof(f51,axiom,
? [X0] :
( ~ empty_carrier(X0)
& one_sorted_str(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_struct_0) ).
fof(f353,plain,
spl23_13,
inference(avatar_split_clause,[],[f279,f350]) ).
fof(f350,plain,
( spl23_13
<=> one_sorted_str(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_13])]) ).
fof(f279,plain,
one_sorted_str(sK20),
inference(cnf_transformation,[],[f178]) ).
fof(f348,plain,
spl23_12,
inference(avatar_split_clause,[],[f278,f345]) ).
fof(f278,plain,
empty(sK19),
inference(cnf_transformation,[],[f176]) ).
fof(f176,plain,
empty(sK19),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f47,f175]) ).
fof(f175,plain,
( ? [X0] : empty(X0)
=> empty(sK19) ),
introduced(choice_axiom,[]) ).
fof(f47,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f343,plain,
spl23_11,
inference(avatar_split_clause,[],[f277,f340]) ).
fof(f277,plain,
rel_str(sK18),
inference(cnf_transformation,[],[f174]) ).
fof(f174,plain,
rel_str(sK18),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f29,f173]) ).
fof(f173,plain,
( ? [X0] : rel_str(X0)
=> rel_str(sK18) ),
introduced(choice_axiom,[]) ).
fof(f29,axiom,
? [X0] : rel_str(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_orders_2) ).
fof(f338,plain,
spl23_10,
inference(avatar_split_clause,[],[f276,f335]) ).
fof(f335,plain,
( spl23_10
<=> one_sorted_str(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_10])]) ).
fof(f276,plain,
one_sorted_str(sK17),
inference(cnf_transformation,[],[f172]) ).
fof(f172,plain,
one_sorted_str(sK17),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f30,f171]) ).
fof(f171,plain,
( ? [X0] : one_sorted_str(X0)
=> one_sorted_str(sK17) ),
introduced(choice_axiom,[]) ).
fof(f30,axiom,
? [X0] : one_sorted_str(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_struct_0) ).
fof(f333,plain,
spl23_9,
inference(avatar_split_clause,[],[f275,f330]) ).
fof(f275,plain,
latt_str(sK16),
inference(cnf_transformation,[],[f170]) ).
fof(f170,plain,
latt_str(sK16),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f32,f169]) ).
fof(f169,plain,
( ? [X0] : latt_str(X0)
=> latt_str(sK16) ),
introduced(choice_axiom,[]) ).
fof(f32,axiom,
? [X0] : latt_str(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l3_lattices) ).
fof(f328,plain,
spl23_8,
inference(avatar_split_clause,[],[f274,f325]) ).
fof(f274,plain,
meet_semilatt_str(sK15),
inference(cnf_transformation,[],[f168]) ).
fof(f168,plain,
meet_semilatt_str(sK15),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f28,f167]) ).
fof(f167,plain,
( ? [X0] : meet_semilatt_str(X0)
=> meet_semilatt_str(sK15) ),
introduced(choice_axiom,[]) ).
fof(f28,axiom,
? [X0] : meet_semilatt_str(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_lattices) ).
fof(f323,plain,
spl23_7,
inference(avatar_split_clause,[],[f273,f320]) ).
fof(f273,plain,
join_semilatt_str(sK14),
inference(cnf_transformation,[],[f166]) ).
fof(f166,plain,
join_semilatt_str(sK14),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f31,f165]) ).
fof(f165,plain,
( ? [X0] : join_semilatt_str(X0)
=> join_semilatt_str(sK14) ),
introduced(choice_axiom,[]) ).
fof(f31,axiom,
? [X0] : join_semilatt_str(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l2_lattices) ).
fof(f318,plain,
~ spl23_6,
inference(avatar_split_clause,[],[f272,f315]) ).
fof(f315,plain,
( spl23_6
<=> empty(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_6])]) ).
fof(f272,plain,
~ empty(sK13),
inference(cnf_transformation,[],[f164]) ).
fof(f164,plain,
~ empty(sK13),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f50,f163]) ).
fof(f163,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK13) ),
introduced(choice_axiom,[]) ).
fof(f50,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f313,plain,
spl23_5,
inference(avatar_split_clause,[],[f189,f310]) ).
fof(f189,plain,
empty(empty_set),
inference(cnf_transformation,[],[f39]) ).
fof(f39,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f308,plain,
spl23_4,
inference(avatar_split_clause,[],[f186,f305]) ).
fof(f186,plain,
element(sK6,the_carrier(poset_of_lattice(sK5))),
inference(cnf_transformation,[],[f144]) ).
fof(f303,plain,
spl23_3,
inference(avatar_split_clause,[],[f185,f300]) ).
fof(f185,plain,
latt_str(sK5),
inference(cnf_transformation,[],[f144]) ).
fof(f298,plain,
spl23_2,
inference(avatar_split_clause,[],[f184,f295]) ).
fof(f184,plain,
lattice(sK5),
inference(cnf_transformation,[],[f144]) ).
fof(f293,plain,
~ spl23_1,
inference(avatar_split_clause,[],[f183,f290]) ).
fof(f183,plain,
~ empty_carrier(sK5),
inference(cnf_transformation,[],[f144]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU350+1 : TPTP v8.1.2. Released v3.3.0.
% 0.13/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n021.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon Apr 29 20:36:40 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.37 % (28044)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (28047)WARNING: value z3 for option sas not known
% 0.15/0.38 % (28048)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (28046)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38 % (28045)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (28049)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)
% 0.15/0.39 % (28047)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)
% 0.15/0.39 % (28051)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)
% 0.15/0.39 % (28050)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)
% 0.15/0.39 TRYING [1]
% 0.15/0.39 TRYING [2]
% 0.15/0.39 TRYING [3]
% 0.15/0.40 TRYING [1]
% 0.15/0.40 TRYING [4]
% 0.15/0.40 TRYING [1]
% 0.15/0.41 TRYING [2]
% 0.15/0.41 TRYING [2]
% 0.15/0.41 TRYING [3]
% 0.15/0.42 TRYING [4]
% 0.15/0.43 % (28049)First to succeed.
% 0.15/0.43 TRYING [3]
% 0.22/0.44 TRYING [5]
% 0.22/0.44 % (28047)Also succeeded, but the first one will report.
% 0.22/0.44 % (28049)Refutation found. Thanks to Tanya!
% 0.22/0.44 % SZS status Theorem for theBenchmark
% 0.22/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.46 % (28049)------------------------------
% 0.22/0.46 % (28049)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.46 % (28049)Termination reason: Refutation
% 0.22/0.46
% 0.22/0.46 % (28049)Memory used [KB]: 1729
% 0.22/0.46 % (28049)Time elapsed: 0.059 s
% 0.22/0.46 % (28049)Instructions burned: 89 (million)
% 0.22/0.46 % (28049)------------------------------
% 0.22/0.46 % (28049)------------------------------
% 0.22/0.46 % (28044)Success in time 0.085 s
%------------------------------------------------------------------------------