TSTP Solution File: SEU323-10 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU323-10 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 09:33:41 EDT 2024
% Result : Unsatisfiable 0.21s 0.44s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 210
% Syntax : Number of formulae : 726 ( 51 unt; 0 def)
% Number of atoms : 1994 ( 539 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 2353 (1085 ~;1083 |; 0 &)
% ( 185 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 187 ( 185 usr; 186 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 5 con; 0-4 aty)
% Number of variables : 207 ( 207 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1971,plain,
$false,
inference(avatar_sat_refutation,[],[f30,f35,f40,f45,f50,f55,f59,f63,f67,f71,f75,f82,f87,f91,f101,f107,f113,f117,f139,f143,f163,f167,f187,f192,f212,f224,f228,f267,f272,f277,f285,f296,f303,f308,f315,f322,f327,f332,f343,f348,f355,f359,f365,f369,f378,f385,f390,f396,f400,f410,f417,f422,f434,f438,f444,f448,f453,f458,f480,f485,f489,f495,f514,f518,f526,f531,f535,f546,f556,f561,f577,f581,f588,f621,f637,f648,f653,f746,f751,f756,f883,f936,f967,f972,f977,f987,f992,f1001,f1009,f1014,f1019,f1025,f1059,f1065,f1075,f1143,f1177,f1182,f1190,f1194,f1209,f1214,f1220,f1241,f1246,f1253,f1257,f1262,f1273,f1291,f1300,f1305,f1310,f1315,f1320,f1325,f1330,f1335,f1340,f1345,f1354,f1465,f1470,f1475,f1485,f1490,f1495,f1510,f1520,f1525,f1530,f1535,f1540,f1545,f1550,f1555,f1564,f1581,f1586,f1591,f1596,f1601,f1606,f1611,f1628,f1633,f1638,f1643,f1648,f1653,f1658,f1663,f1668,f1673,f1680,f1695,f1702,f1707,f1712,f1717,f1724,f1729,f1734,f1739,f1744,f1811,f1816,f1821,f1826,f1857,f1862,f1867,f1872,f1877,f1897,f1904,f1910,f1915,f1929,f1936,f1941,f1949,f1956,f1962,f1969,f1970]) ).
fof(f1970,plain,
( spl0_4
| ~ spl0_10
| ~ spl0_182 ),
inference(avatar_split_clause,[],[f1950,f1946,f69,f42]) ).
fof(f42,plain,
( spl0_4
<=> true = open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f69,plain,
( spl0_10
<=> ! [X2,X0,X1] : ifeq(X0,X0,X1,X2) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f1946,plain,
( spl0_182
<=> true = ifeq(true,true,open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f1950,plain,
( true = open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A)
| ~ spl0_10
| ~ spl0_182 ),
inference(superposition,[],[f1948,f70]) ).
fof(f70,plain,
( ! [X2,X0,X1] : ifeq(X0,X0,X1,X2) = X1
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f69]) ).
fof(f1948,plain,
( true = ifeq(true,true,open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A),true)
| ~ spl0_182 ),
inference(avatar_component_clause,[],[f1946]) ).
fof(f1969,plain,
( spl0_185
| ~ spl0_9
| ~ spl0_50
| ~ spl0_62
| ~ spl0_95 ),
inference(avatar_split_clause,[],[f1108,f1073,f493,f408,f65,f1966]) ).
fof(f1966,plain,
( spl0_185
<=> interior(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A))))) = ifeq2(true,true,subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A))))),interior(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f65,plain,
( spl0_9
<=> ! [X2,X0,X1] : ifeq2(X0,X0,X1,X2) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f408,plain,
( spl0_50
<=> ! [X0] : interior(sK2_t51_tops_1_A,X0) = ifeq2(element(X0,powerset(the_carrier(sK2_t51_tops_1_A))),true,subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),X0))),interior(sK2_t51_tops_1_A,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f493,plain,
( spl0_62
<=> ! [X0] : sK4_existence_m1_subset_1_B(powerset(X0)) = ifeq2(true,true,subset_complement(X0,subset_complement(X0,sK4_existence_m1_subset_1_B(powerset(X0)))),sK4_existence_m1_subset_1_B(powerset(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f1073,plain,
( spl0_95
<=> ! [X0] : true = element(subset_complement(X0,sK4_existence_m1_subset_1_B(powerset(X0))),powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f1108,plain,
( interior(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A))))) = ifeq2(true,true,subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A))))),interior(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A))))))
| ~ spl0_9
| ~ spl0_50
| ~ spl0_62
| ~ spl0_95 ),
inference(forward_demodulation,[],[f1088,f519]) ).
fof(f519,plain,
( ! [X0] : sK4_existence_m1_subset_1_B(powerset(X0)) = subset_complement(X0,subset_complement(X0,sK4_existence_m1_subset_1_B(powerset(X0))))
| ~ spl0_9
| ~ spl0_62 ),
inference(superposition,[],[f494,f66]) ).
fof(f66,plain,
( ! [X2,X0,X1] : ifeq2(X0,X0,X1,X2) = X1
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f65]) ).
fof(f494,plain,
( ! [X0] : sK4_existence_m1_subset_1_B(powerset(X0)) = ifeq2(true,true,subset_complement(X0,subset_complement(X0,sK4_existence_m1_subset_1_B(powerset(X0)))),sK4_existence_m1_subset_1_B(powerset(X0)))
| ~ spl0_62 ),
inference(avatar_component_clause,[],[f493]) ).
fof(f1088,plain,
( interior(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A))))) = ifeq2(true,true,subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),subset_complement(the_carrier(sK2_t51_tops_1_A),sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A))))))),interior(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A))))))
| ~ spl0_50
| ~ spl0_95 ),
inference(superposition,[],[f409,f1074]) ).
fof(f1074,plain,
( ! [X0] : true = element(subset_complement(X0,sK4_existence_m1_subset_1_B(powerset(X0))),powerset(X0))
| ~ spl0_95 ),
inference(avatar_component_clause,[],[f1073]) ).
fof(f409,plain,
( ! [X0] : interior(sK2_t51_tops_1_A,X0) = ifeq2(element(X0,powerset(the_carrier(sK2_t51_tops_1_A))),true,subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),X0))),interior(sK2_t51_tops_1_A,X0))
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f408]) ).
fof(f1962,plain,
( spl0_184
| ~ spl0_10
| ~ spl0_152
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f1957,f1953,f1660,f69,f1959]) ).
fof(f1959,plain,
( spl0_184
<=> topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)) = ifeq2(true,true,subset_complement(the_carrier(sK2_t51_tops_1_A),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f1660,plain,
( spl0_152
<=> true = ifeq(true,true,element(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f1953,plain,
( spl0_183
<=> topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)) = ifeq2(element(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),true,subset_complement(the_carrier(sK2_t51_tops_1_A),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f1957,plain,
( topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)) = ifeq2(true,true,subset_complement(the_carrier(sK2_t51_tops_1_A),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)))
| ~ spl0_10
| ~ spl0_152
| ~ spl0_183 ),
inference(forward_demodulation,[],[f1955,f1689]) ).
fof(f1689,plain,
( true = element(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A)))
| ~ spl0_10
| ~ spl0_152 ),
inference(superposition,[],[f1662,f70]) ).
fof(f1662,plain,
( true = ifeq(true,true,element(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),true)
| ~ spl0_152 ),
inference(avatar_component_clause,[],[f1660]) ).
fof(f1955,plain,
( topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)) = ifeq2(element(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),true,subset_complement(the_carrier(sK2_t51_tops_1_A),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)))
| ~ spl0_183 ),
inference(avatar_component_clause,[],[f1953]) ).
fof(f1956,plain,
( spl0_183
| ~ spl0_15
| ~ spl0_82 ),
inference(avatar_split_clause,[],[f947,f933,f99,f1953]) ).
fof(f99,plain,
( spl0_15
<=> ! [X0,X1] : ifeq2(element(X1,powerset(X0)),true,subset_complement(X0,subset_complement(X0,X1)),X1) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f933,plain,
( spl0_82
<=> interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B) = subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f947,plain,
( topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)) = ifeq2(element(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),true,subset_complement(the_carrier(sK2_t51_tops_1_A),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)))
| ~ spl0_15
| ~ spl0_82 ),
inference(superposition,[],[f100,f935]) ).
fof(f935,plain,
( interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B) = subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)))
| ~ spl0_82 ),
inference(avatar_component_clause,[],[f933]) ).
fof(f100,plain,
( ! [X0,X1] : ifeq2(element(X1,powerset(X0)),true,subset_complement(X0,subset_complement(X0,X1)),X1) = X1
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f1949,plain,
( spl0_182
| ~ spl0_10
| ~ spl0_134
| ~ spl0_152
| ~ spl0_181 ),
inference(avatar_split_clause,[],[f1944,f1938,f1660,f1542,f69,f1946]) ).
fof(f1542,plain,
( spl0_134
<=> true = ifeq(true,true,closed_subset(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),sK2_t51_tops_1_A),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f1938,plain,
( spl0_181
<=> true = ifeq(element(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),true,ifeq(closed_subset(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),sK2_t51_tops_1_A),true,open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A),true),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f1944,plain,
( true = ifeq(true,true,open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A),true)
| ~ spl0_10
| ~ spl0_134
| ~ spl0_152
| ~ spl0_181 ),
inference(forward_demodulation,[],[f1943,f1689]) ).
fof(f1943,plain,
( true = ifeq(element(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),true,open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A),true)
| ~ spl0_10
| ~ spl0_134
| ~ spl0_181 ),
inference(forward_demodulation,[],[f1942,f70]) ).
fof(f1942,plain,
( true = ifeq(element(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),true,ifeq(true,true,open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A),true),true)
| ~ spl0_10
| ~ spl0_134
| ~ spl0_181 ),
inference(forward_demodulation,[],[f1940,f1571]) ).
fof(f1571,plain,
( true = closed_subset(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),sK2_t51_tops_1_A)
| ~ spl0_10
| ~ spl0_134 ),
inference(superposition,[],[f1544,f70]) ).
fof(f1544,plain,
( true = ifeq(true,true,closed_subset(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),sK2_t51_tops_1_A),true)
| ~ spl0_134 ),
inference(avatar_component_clause,[],[f1542]) ).
fof(f1940,plain,
( true = ifeq(element(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),true,ifeq(closed_subset(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),sK2_t51_tops_1_A),true,open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A),true),true)
| ~ spl0_181 ),
inference(avatar_component_clause,[],[f1938]) ).
fof(f1941,plain,
( spl0_181
| ~ spl0_48
| ~ spl0_82 ),
inference(avatar_split_clause,[],[f941,f933,f394,f1938]) ).
fof(f394,plain,
( spl0_48
<=> ! [X0] : true = ifeq(element(X0,powerset(the_carrier(sK2_t51_tops_1_A))),true,ifeq(closed_subset(X0,sK2_t51_tops_1_A),true,open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),X0),sK2_t51_tops_1_A),true),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f941,plain,
( true = ifeq(element(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),true,ifeq(closed_subset(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),sK2_t51_tops_1_A),true,open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A),true),true)
| ~ spl0_48
| ~ spl0_82 ),
inference(superposition,[],[f395,f935]) ).
fof(f395,plain,
( ! [X0] : true = ifeq(element(X0,powerset(the_carrier(sK2_t51_tops_1_A))),true,ifeq(closed_subset(X0,sK2_t51_tops_1_A),true,open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),X0),sK2_t51_tops_1_A),true),true)
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f394]) ).
fof(f1936,plain,
( spl0_180
| ~ spl0_10
| ~ spl0_152
| ~ spl0_179 ),
inference(avatar_split_clause,[],[f1931,f1926,f1660,f69,f1933]) ).
fof(f1933,plain,
( spl0_180
<=> true = ifeq(open_subset(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),sK2_t51_tops_1_A),true,closed_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f1926,plain,
( spl0_179
<=> true = ifeq(open_subset(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),sK2_t51_tops_1_A),true,ifeq(element(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),true,closed_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A),true),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f1931,plain,
( true = ifeq(open_subset(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),sK2_t51_tops_1_A),true,closed_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A),true)
| ~ spl0_10
| ~ spl0_152
| ~ spl0_179 ),
inference(forward_demodulation,[],[f1930,f70]) ).
fof(f1930,plain,
( true = ifeq(open_subset(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),sK2_t51_tops_1_A),true,ifeq(true,true,closed_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A),true),true)
| ~ spl0_10
| ~ spl0_152
| ~ spl0_179 ),
inference(forward_demodulation,[],[f1928,f1689]) ).
fof(f1928,plain,
( true = ifeq(open_subset(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),sK2_t51_tops_1_A),true,ifeq(element(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),true,closed_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A),true),true)
| ~ spl0_179 ),
inference(avatar_component_clause,[],[f1926]) ).
fof(f1929,plain,
( spl0_179
| ~ spl0_49
| ~ spl0_82 ),
inference(avatar_split_clause,[],[f940,f933,f398,f1926]) ).
fof(f398,plain,
( spl0_49
<=> ! [X0] : true = ifeq(open_subset(X0,sK2_t51_tops_1_A),true,ifeq(element(X0,powerset(the_carrier(sK2_t51_tops_1_A))),true,closed_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),X0),sK2_t51_tops_1_A),true),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f940,plain,
( true = ifeq(open_subset(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),sK2_t51_tops_1_A),true,ifeq(element(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),true,closed_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A),true),true)
| ~ spl0_49
| ~ spl0_82 ),
inference(superposition,[],[f399,f935]) ).
fof(f399,plain,
( ! [X0] : true = ifeq(open_subset(X0,sK2_t51_tops_1_A),true,ifeq(element(X0,powerset(the_carrier(sK2_t51_tops_1_A))),true,closed_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),X0),sK2_t51_tops_1_A),true),true)
| ~ spl0_49 ),
inference(avatar_component_clause,[],[f398]) ).
fof(f1915,plain,
( spl0_178
| ~ spl0_9
| ~ spl0_172
| ~ spl0_176 ),
inference(avatar_split_clause,[],[f1905,f1901,f1864,f65,f1912]) ).
fof(f1912,plain,
( spl0_178
<=> interior(sK2_t51_tops_1_A,topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B)) = ifeq2(true,true,subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,interior(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)))),interior(sK2_t51_tops_1_A,topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f1864,plain,
( spl0_172
<=> interior(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)) = ifeq2(true,true,subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),interior(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f1901,plain,
( spl0_176
<=> interior(sK2_t51_tops_1_A,topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B)) = ifeq2(true,true,subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B)))),interior(sK2_t51_tops_1_A,topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f1905,plain,
( interior(sK2_t51_tops_1_A,topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B)) = ifeq2(true,true,subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,interior(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)))),interior(sK2_t51_tops_1_A,topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B)))
| ~ spl0_9
| ~ spl0_172
| ~ spl0_176 ),
inference(forward_demodulation,[],[f1903,f1887]) ).
fof(f1887,plain,
( subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B)) = interior(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))
| ~ spl0_9
| ~ spl0_172 ),
inference(superposition,[],[f1866,f66]) ).
fof(f1866,plain,
( interior(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)) = ifeq2(true,true,subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),interior(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)))
| ~ spl0_172 ),
inference(avatar_component_clause,[],[f1864]) ).
fof(f1903,plain,
( interior(sK2_t51_tops_1_A,topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B)) = ifeq2(true,true,subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B)))),interior(sK2_t51_tops_1_A,topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B)))
| ~ spl0_176 ),
inference(avatar_component_clause,[],[f1901]) ).
fof(f1910,plain,
( spl0_177
| ~ spl0_50
| ~ spl0_80 ),
inference(avatar_split_clause,[],[f839,f753,f408,f1907]) ).
fof(f1907,plain,
( spl0_177
<=> interior(sK2_t51_tops_1_A,interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)) = ifeq2(true,true,subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)))),interior(sK2_t51_tops_1_A,interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f753,plain,
( spl0_80
<=> true = element(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f839,plain,
( interior(sK2_t51_tops_1_A,interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)) = ifeq2(true,true,subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)))),interior(sK2_t51_tops_1_A,interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)))
| ~ spl0_50
| ~ spl0_80 ),
inference(superposition,[],[f409,f755]) ).
fof(f755,plain,
( true = element(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A)))
| ~ spl0_80 ),
inference(avatar_component_clause,[],[f753]) ).
fof(f1904,plain,
( spl0_176
| ~ spl0_50
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f792,f748,f408,f1901]) ).
fof(f748,plain,
( spl0_79
<=> true = element(topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f792,plain,
( interior(sK2_t51_tops_1_A,topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B)) = ifeq2(true,true,subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B)))),interior(sK2_t51_tops_1_A,topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B)))
| ~ spl0_50
| ~ spl0_79 ),
inference(superposition,[],[f409,f750]) ).
fof(f750,plain,
( true = element(topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A)))
| ~ spl0_79 ),
inference(avatar_component_clause,[],[f748]) ).
fof(f1897,plain,
( spl0_175
| ~ spl0_9
| ~ spl0_48
| ~ spl0_62
| ~ spl0_95 ),
inference(avatar_split_clause,[],[f1111,f1073,f493,f394,f65,f1894]) ).
fof(f1894,plain,
( spl0_175
<=> true = ifeq(true,true,ifeq(closed_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A)))),sK2_t51_tops_1_A),true,open_subset(sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A))),sK2_t51_tops_1_A),true),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f1111,plain,
( true = ifeq(true,true,ifeq(closed_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A)))),sK2_t51_tops_1_A),true,open_subset(sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A))),sK2_t51_tops_1_A),true),true)
| ~ spl0_9
| ~ spl0_48
| ~ spl0_62
| ~ spl0_95 ),
inference(forward_demodulation,[],[f1090,f519]) ).
fof(f1090,plain,
( true = ifeq(true,true,ifeq(closed_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A)))),sK2_t51_tops_1_A),true,open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),subset_complement(the_carrier(sK2_t51_tops_1_A),sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A))))),sK2_t51_tops_1_A),true),true)
| ~ spl0_48
| ~ spl0_95 ),
inference(superposition,[],[f395,f1074]) ).
fof(f1877,plain,
( spl0_174
| ~ spl0_50
| ~ spl0_92 ),
inference(avatar_split_clause,[],[f1036,f1023,f408,f1874]) ).
fof(f1874,plain,
( spl0_174
<=> interior(sK2_t51_tops_1_A,the_carrier(sK2_t51_tops_1_A)) = ifeq2(true,true,subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),the_carrier(sK2_t51_tops_1_A)))),interior(sK2_t51_tops_1_A,the_carrier(sK2_t51_tops_1_A))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f1023,plain,
( spl0_92
<=> ! [X0] : true = element(X0,powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f1036,plain,
( interior(sK2_t51_tops_1_A,the_carrier(sK2_t51_tops_1_A)) = ifeq2(true,true,subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),the_carrier(sK2_t51_tops_1_A)))),interior(sK2_t51_tops_1_A,the_carrier(sK2_t51_tops_1_A)))
| ~ spl0_50
| ~ spl0_92 ),
inference(superposition,[],[f409,f1024]) ).
fof(f1024,plain,
( ! [X0] : true = element(X0,powerset(X0))
| ~ spl0_92 ),
inference(avatar_component_clause,[],[f1023]) ).
fof(f1872,plain,
( spl0_173
| ~ spl0_48
| ~ spl0_80 ),
inference(avatar_split_clause,[],[f841,f753,f394,f1869]) ).
fof(f1869,plain,
( spl0_173
<=> true = ifeq(true,true,ifeq(closed_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A),true,open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),sK2_t51_tops_1_A),true),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f841,plain,
( true = ifeq(true,true,ifeq(closed_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A),true,open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),sK2_t51_tops_1_A),true),true)
| ~ spl0_48
| ~ spl0_80 ),
inference(superposition,[],[f395,f755]) ).
fof(f1867,plain,
( spl0_172
| ~ spl0_10
| ~ spl0_39
| ~ spl0_50
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f767,f743,f408,f340,f69,f1864]) ).
fof(f340,plain,
( spl0_39
<=> true = ifeq(true,true,element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f743,plain,
( spl0_78
<=> sK1_t51_tops_1_B = subset_complement(the_carrier(sK2_t51_tops_1_A),subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f767,plain,
( interior(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)) = ifeq2(true,true,subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),interior(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)))
| ~ spl0_10
| ~ spl0_39
| ~ spl0_50
| ~ spl0_78 ),
inference(forward_demodulation,[],[f758,f349]) ).
fof(f349,plain,
( true = element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A)))
| ~ spl0_10
| ~ spl0_39 ),
inference(superposition,[],[f342,f70]) ).
fof(f342,plain,
( true = ifeq(true,true,element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),true)
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f340]) ).
fof(f758,plain,
( interior(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)) = ifeq2(element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),true,subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),interior(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)))
| ~ spl0_50
| ~ spl0_78 ),
inference(superposition,[],[f409,f745]) ).
fof(f745,plain,
( sK1_t51_tops_1_B = subset_complement(the_carrier(sK2_t51_tops_1_A),subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))
| ~ spl0_78 ),
inference(avatar_component_clause,[],[f743]) ).
fof(f1862,plain,
( spl0_171
| ~ spl0_50
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f701,f650,f408,f1859]) ).
fof(f1859,plain,
( spl0_171
<=> interior(sK2_t51_tops_1_A,sK3_rc1_tops_1_B(sK2_t51_tops_1_A)) = ifeq2(true,true,subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK3_rc1_tops_1_B(sK2_t51_tops_1_A)))),interior(sK2_t51_tops_1_A,sK3_rc1_tops_1_B(sK2_t51_tops_1_A))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f650,plain,
( spl0_77
<=> true = element(sK3_rc1_tops_1_B(sK2_t51_tops_1_A),powerset(the_carrier(sK2_t51_tops_1_A))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f701,plain,
( interior(sK2_t51_tops_1_A,sK3_rc1_tops_1_B(sK2_t51_tops_1_A)) = ifeq2(true,true,subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK3_rc1_tops_1_B(sK2_t51_tops_1_A)))),interior(sK2_t51_tops_1_A,sK3_rc1_tops_1_B(sK2_t51_tops_1_A)))
| ~ spl0_50
| ~ spl0_77 ),
inference(superposition,[],[f409,f652]) ).
fof(f652,plain,
( true = element(sK3_rc1_tops_1_B(sK2_t51_tops_1_A),powerset(the_carrier(sK2_t51_tops_1_A)))
| ~ spl0_77 ),
inference(avatar_component_clause,[],[f650]) ).
fof(f1857,plain,
( spl0_170
| ~ spl0_50
| ~ spl0_76 ),
inference(avatar_split_clause,[],[f656,f645,f408,f1854]) ).
fof(f1854,plain,
( spl0_170
<=> interior(sK2_t51_tops_1_A,sK7_rc6_pre_topc_B(sK2_t51_tops_1_A)) = ifeq2(true,true,subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK7_rc6_pre_topc_B(sK2_t51_tops_1_A)))),interior(sK2_t51_tops_1_A,sK7_rc6_pre_topc_B(sK2_t51_tops_1_A))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f645,plain,
( spl0_76
<=> true = element(sK7_rc6_pre_topc_B(sK2_t51_tops_1_A),powerset(the_carrier(sK2_t51_tops_1_A))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f656,plain,
( interior(sK2_t51_tops_1_A,sK7_rc6_pre_topc_B(sK2_t51_tops_1_A)) = ifeq2(true,true,subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK7_rc6_pre_topc_B(sK2_t51_tops_1_A)))),interior(sK2_t51_tops_1_A,sK7_rc6_pre_topc_B(sK2_t51_tops_1_A)))
| ~ spl0_50
| ~ spl0_76 ),
inference(superposition,[],[f409,f647]) ).
fof(f647,plain,
( true = element(sK7_rc6_pre_topc_B(sK2_t51_tops_1_A),powerset(the_carrier(sK2_t51_tops_1_A)))
| ~ spl0_76 ),
inference(avatar_component_clause,[],[f645]) ).
fof(f1826,plain,
( spl0_169
| ~ spl0_9
| ~ spl0_10
| ~ spl0_49
| ~ spl0_62
| ~ spl0_95 ),
inference(avatar_split_clause,[],[f1110,f1073,f493,f398,f69,f65,f1823]) ).
fof(f1823,plain,
( spl0_169
<=> true = ifeq(open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A)))),sK2_t51_tops_1_A),true,closed_subset(sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A))),sK2_t51_tops_1_A),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f1110,plain,
( true = ifeq(open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A)))),sK2_t51_tops_1_A),true,closed_subset(sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A))),sK2_t51_tops_1_A),true)
| ~ spl0_9
| ~ spl0_10
| ~ spl0_49
| ~ spl0_62
| ~ spl0_95 ),
inference(forward_demodulation,[],[f1109,f519]) ).
fof(f1109,plain,
( true = ifeq(open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A)))),sK2_t51_tops_1_A),true,closed_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),subset_complement(the_carrier(sK2_t51_tops_1_A),sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A))))),sK2_t51_tops_1_A),true)
| ~ spl0_10
| ~ spl0_49
| ~ spl0_95 ),
inference(forward_demodulation,[],[f1089,f70]) ).
fof(f1089,plain,
( true = ifeq(open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A)))),sK2_t51_tops_1_A),true,ifeq(true,true,closed_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),subset_complement(the_carrier(sK2_t51_tops_1_A),sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A))))),sK2_t51_tops_1_A),true),true)
| ~ spl0_49
| ~ spl0_95 ),
inference(superposition,[],[f399,f1074]) ).
fof(f1821,plain,
( spl0_168
| ~ spl0_48
| ~ spl0_92 ),
inference(avatar_split_clause,[],[f1038,f1023,f394,f1818]) ).
fof(f1818,plain,
( spl0_168
<=> true = ifeq(true,true,ifeq(closed_subset(the_carrier(sK2_t51_tops_1_A),sK2_t51_tops_1_A),true,open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),the_carrier(sK2_t51_tops_1_A)),sK2_t51_tops_1_A),true),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f1038,plain,
( true = ifeq(true,true,ifeq(closed_subset(the_carrier(sK2_t51_tops_1_A),sK2_t51_tops_1_A),true,open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),the_carrier(sK2_t51_tops_1_A)),sK2_t51_tops_1_A),true),true)
| ~ spl0_48
| ~ spl0_92 ),
inference(superposition,[],[f395,f1024]) ).
fof(f1816,plain,
( spl0_167
| ~ spl0_10
| ~ spl0_91 ),
inference(avatar_split_clause,[],[f1020,f1016,f69,f1813]) ).
fof(f1813,plain,
( spl0_167
<=> true = ifeq(closed_subset(sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A))),sK2_t51_tops_1_A),true,open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A)))),sK2_t51_tops_1_A),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f1016,plain,
( spl0_91
<=> true = ifeq(true,true,ifeq(closed_subset(sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A))),sK2_t51_tops_1_A),true,open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A)))),sK2_t51_tops_1_A),true),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f1020,plain,
( true = ifeq(closed_subset(sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A))),sK2_t51_tops_1_A),true,open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A)))),sK2_t51_tops_1_A),true)
| ~ spl0_10
| ~ spl0_91 ),
inference(superposition,[],[f1018,f70]) ).
fof(f1018,plain,
( true = ifeq(true,true,ifeq(closed_subset(sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A))),sK2_t51_tops_1_A),true,open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A)))),sK2_t51_tops_1_A),true),true)
| ~ spl0_91 ),
inference(avatar_component_clause,[],[f1016]) ).
fof(f1811,plain,
( spl0_166
| ~ spl0_48
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f703,f650,f394,f1808]) ).
fof(f1808,plain,
( spl0_166
<=> true = ifeq(true,true,ifeq(closed_subset(sK3_rc1_tops_1_B(sK2_t51_tops_1_A),sK2_t51_tops_1_A),true,open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK3_rc1_tops_1_B(sK2_t51_tops_1_A)),sK2_t51_tops_1_A),true),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f703,plain,
( true = ifeq(true,true,ifeq(closed_subset(sK3_rc1_tops_1_B(sK2_t51_tops_1_A),sK2_t51_tops_1_A),true,open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK3_rc1_tops_1_B(sK2_t51_tops_1_A)),sK2_t51_tops_1_A),true),true)
| ~ spl0_48
| ~ spl0_77 ),
inference(superposition,[],[f395,f652]) ).
fof(f1744,plain,
( spl0_165
| ~ spl0_43
| ~ spl0_95 ),
inference(avatar_split_clause,[],[f1092,f1073,f363,f1741]) ).
fof(f1741,plain,
( spl0_165
<=> true = ifeq(true,true,element(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A))))),powerset(the_carrier(sK2_t51_tops_1_A))),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f363,plain,
( spl0_43
<=> ! [X0] : true = ifeq(element(X0,powerset(the_carrier(sK2_t51_tops_1_A))),true,element(topstr_closure(sK2_t51_tops_1_A,X0),powerset(the_carrier(sK2_t51_tops_1_A))),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f1092,plain,
( true = ifeq(true,true,element(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A))))),powerset(the_carrier(sK2_t51_tops_1_A))),true)
| ~ spl0_43
| ~ spl0_95 ),
inference(superposition,[],[f364,f1074]) ).
fof(f364,plain,
( ! [X0] : true = ifeq(element(X0,powerset(the_carrier(sK2_t51_tops_1_A))),true,element(topstr_closure(sK2_t51_tops_1_A,X0),powerset(the_carrier(sK2_t51_tops_1_A))),true)
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f363]) ).
fof(f1739,plain,
( spl0_164
| ~ spl0_44
| ~ spl0_95 ),
inference(avatar_split_clause,[],[f1091,f1073,f367,f1736]) ).
fof(f1736,plain,
( spl0_164
<=> true = ifeq(true,true,element(interior(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A))))),powerset(the_carrier(sK2_t51_tops_1_A))),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f367,plain,
( spl0_44
<=> ! [X0] : true = ifeq(element(X0,powerset(the_carrier(sK2_t51_tops_1_A))),true,element(interior(sK2_t51_tops_1_A,X0),powerset(the_carrier(sK2_t51_tops_1_A))),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f1091,plain,
( true = ifeq(true,true,element(interior(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A))))),powerset(the_carrier(sK2_t51_tops_1_A))),true)
| ~ spl0_44
| ~ spl0_95 ),
inference(superposition,[],[f368,f1074]) ).
fof(f368,plain,
( ! [X0] : true = ifeq(element(X0,powerset(the_carrier(sK2_t51_tops_1_A))),true,element(interior(sK2_t51_tops_1_A,X0),powerset(the_carrier(sK2_t51_tops_1_A))),true)
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f367]) ).
fof(f1734,plain,
( spl0_163
| ~ spl0_9
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f1060,f1056,f65,f1731]) ).
fof(f1731,plain,
( spl0_163
<=> interior(sK2_t51_tops_1_A,sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A)))) = subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f1056,plain,
( spl0_93
<=> interior(sK2_t51_tops_1_A,sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A)))) = ifeq2(true,true,subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A)))))),interior(sK2_t51_tops_1_A,sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f1060,plain,
( interior(sK2_t51_tops_1_A,sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A)))) = subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A))))))
| ~ spl0_9
| ~ spl0_93 ),
inference(superposition,[],[f1058,f66]) ).
fof(f1058,plain,
( interior(sK2_t51_tops_1_A,sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A)))) = ifeq2(true,true,subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A)))))),interior(sK2_t51_tops_1_A,sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A)))))
| ~ spl0_93 ),
inference(avatar_component_clause,[],[f1056]) ).
fof(f1729,plain,
( spl0_162
| ~ spl0_15
| ~ spl0_80 ),
inference(avatar_split_clause,[],[f852,f753,f99,f1726]) ).
fof(f1726,plain,
( spl0_162
<=> interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B) = ifeq2(true,true,subset_complement(the_carrier(sK2_t51_tops_1_A),subset_complement(the_carrier(sK2_t51_tops_1_A),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B))),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f852,plain,
( interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B) = ifeq2(true,true,subset_complement(the_carrier(sK2_t51_tops_1_A),subset_complement(the_carrier(sK2_t51_tops_1_A),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B))),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B))
| ~ spl0_15
| ~ spl0_80 ),
inference(superposition,[],[f100,f755]) ).
fof(f1724,plain,
( spl0_161
| ~ spl0_15
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f805,f748,f99,f1721]) ).
fof(f1721,plain,
( spl0_161
<=> topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B) = ifeq2(true,true,subset_complement(the_carrier(sK2_t51_tops_1_A),subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B))),topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f805,plain,
( topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B) = ifeq2(true,true,subset_complement(the_carrier(sK2_t51_tops_1_A),subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B))),topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B))
| ~ spl0_15
| ~ spl0_79 ),
inference(superposition,[],[f100,f750]) ).
fof(f1717,plain,
( spl0_160
| ~ spl0_10
| ~ spl0_49
| ~ spl0_80 ),
inference(avatar_split_clause,[],[f859,f753,f398,f69,f1714]) ).
fof(f1714,plain,
( spl0_160
<=> true = ifeq(open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A),true,closed_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),sK2_t51_tops_1_A),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f859,plain,
( true = ifeq(open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A),true,closed_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),sK2_t51_tops_1_A),true)
| ~ spl0_10
| ~ spl0_49
| ~ spl0_80 ),
inference(forward_demodulation,[],[f840,f70]) ).
fof(f840,plain,
( true = ifeq(open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A),true,ifeq(true,true,closed_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),sK2_t51_tops_1_A),true),true)
| ~ spl0_49
| ~ spl0_80 ),
inference(superposition,[],[f399,f755]) ).
fof(f1712,plain,
( spl0_159
| ~ spl0_10
| ~ spl0_49
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f812,f748,f398,f69,f1709]) ).
fof(f1709,plain,
( spl0_159
<=> true = ifeq(open_subset(topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A),true,closed_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),sK2_t51_tops_1_A),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f812,plain,
( true = ifeq(open_subset(topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A),true,closed_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),sK2_t51_tops_1_A),true)
| ~ spl0_10
| ~ spl0_49
| ~ spl0_79 ),
inference(forward_demodulation,[],[f793,f70]) ).
fof(f793,plain,
( true = ifeq(open_subset(topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A),true,ifeq(true,true,closed_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),sK2_t51_tops_1_A),true),true)
| ~ spl0_49
| ~ spl0_79 ),
inference(superposition,[],[f399,f750]) ).
fof(f1707,plain,
( spl0_158
| ~ spl0_10
| ~ spl0_120 ),
inference(avatar_split_clause,[],[f1459,f1342,f69,f1704]) ).
fof(f1704,plain,
( spl0_158
<=> true = closed_subset(topstr_closure(sK2_t51_tops_1_A,the_carrier(sK2_t51_tops_1_A)),sK2_t51_tops_1_A) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f1342,plain,
( spl0_120
<=> true = ifeq(true,true,closed_subset(topstr_closure(sK2_t51_tops_1_A,the_carrier(sK2_t51_tops_1_A)),sK2_t51_tops_1_A),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f1459,plain,
( true = closed_subset(topstr_closure(sK2_t51_tops_1_A,the_carrier(sK2_t51_tops_1_A)),sK2_t51_tops_1_A)
| ~ spl0_10
| ~ spl0_120 ),
inference(superposition,[],[f1344,f70]) ).
fof(f1344,plain,
( true = ifeq(true,true,closed_subset(topstr_closure(sK2_t51_tops_1_A,the_carrier(sK2_t51_tops_1_A)),sK2_t51_tops_1_A),true)
| ~ spl0_120 ),
inference(avatar_component_clause,[],[f1342]) ).
fof(f1702,plain,
( spl0_157
| ~ spl0_10
| ~ spl0_39
| ~ spl0_48
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f770,f743,f394,f340,f69,f1699]) ).
fof(f1699,plain,
( spl0_157
<=> true = ifeq(true,true,ifeq(closed_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),sK2_t51_tops_1_A),true,open_subset(sK1_t51_tops_1_B,sK2_t51_tops_1_A),true),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f770,plain,
( true = ifeq(true,true,ifeq(closed_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),sK2_t51_tops_1_A),true,open_subset(sK1_t51_tops_1_B,sK2_t51_tops_1_A),true),true)
| ~ spl0_10
| ~ spl0_39
| ~ spl0_48
| ~ spl0_78 ),
inference(forward_demodulation,[],[f760,f349]) ).
fof(f760,plain,
( true = ifeq(element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),true,ifeq(closed_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),sK2_t51_tops_1_A),true,open_subset(sK1_t51_tops_1_B,sK2_t51_tops_1_A),true),true)
| ~ spl0_48
| ~ spl0_78 ),
inference(superposition,[],[f395,f745]) ).
fof(f1695,plain,
( spl0_156
| ~ spl0_42
| ~ spl0_95 ),
inference(avatar_split_clause,[],[f1093,f1073,f357,f1692]) ).
fof(f1692,plain,
( spl0_156
<=> true = ifeq(true,true,closed_subset(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A))))),sK2_t51_tops_1_A),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f357,plain,
( spl0_42
<=> ! [X0] : true = ifeq(element(X0,powerset(the_carrier(sK2_t51_tops_1_A))),true,closed_subset(topstr_closure(sK2_t51_tops_1_A,X0),sK2_t51_tops_1_A),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f1093,plain,
( true = ifeq(true,true,closed_subset(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A))))),sK2_t51_tops_1_A),true)
| ~ spl0_42
| ~ spl0_95 ),
inference(superposition,[],[f358,f1074]) ).
fof(f358,plain,
( ! [X0] : true = ifeq(element(X0,powerset(the_carrier(sK2_t51_tops_1_A))),true,closed_subset(topstr_closure(sK2_t51_tops_1_A,X0),sK2_t51_tops_1_A),true)
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f357]) ).
fof(f1680,plain,
( spl0_155
| ~ spl0_10
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f1357,f1322,f69,f1677]) ).
fof(f1677,plain,
( spl0_155
<=> true = subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),the_carrier(sK2_t51_tops_1_A)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f1322,plain,
( spl0_116
<=> true = ifeq(true,true,subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),the_carrier(sK2_t51_tops_1_A)),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f1357,plain,
( true = subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),the_carrier(sK2_t51_tops_1_A))
| ~ spl0_10
| ~ spl0_116 ),
inference(superposition,[],[f1324,f70]) ).
fof(f1324,plain,
( true = ifeq(true,true,subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),the_carrier(sK2_t51_tops_1_A)),true)
| ~ spl0_116 ),
inference(avatar_component_clause,[],[f1322]) ).
fof(f1673,plain,
( spl0_154
| ~ spl0_10
| ~ spl0_49
| ~ spl0_92 ),
inference(avatar_split_clause,[],[f1053,f1023,f398,f69,f1670]) ).
fof(f1670,plain,
( spl0_154
<=> true = ifeq(open_subset(the_carrier(sK2_t51_tops_1_A),sK2_t51_tops_1_A),true,closed_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),the_carrier(sK2_t51_tops_1_A)),sK2_t51_tops_1_A),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f1053,plain,
( true = ifeq(open_subset(the_carrier(sK2_t51_tops_1_A),sK2_t51_tops_1_A),true,closed_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),the_carrier(sK2_t51_tops_1_A)),sK2_t51_tops_1_A),true)
| ~ spl0_10
| ~ spl0_49
| ~ spl0_92 ),
inference(forward_demodulation,[],[f1037,f70]) ).
fof(f1037,plain,
( true = ifeq(open_subset(the_carrier(sK2_t51_tops_1_A),sK2_t51_tops_1_A),true,ifeq(true,true,closed_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),the_carrier(sK2_t51_tops_1_A)),sK2_t51_tops_1_A),true),true)
| ~ spl0_49
| ~ spl0_92 ),
inference(superposition,[],[f399,f1024]) ).
fof(f1668,plain,
( spl0_153
| ~ spl0_16
| ~ spl0_80
| ~ spl0_82 ),
inference(avatar_split_clause,[],[f962,f933,f753,f105,f1665]) ).
fof(f1665,plain,
( spl0_153
<=> true = ifeq(element(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),true,true,true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f105,plain,
( spl0_16
<=> ! [X0,X1] : true = ifeq(element(X1,powerset(X0)),true,element(subset_complement(X0,X1),powerset(X0)),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f962,plain,
( true = ifeq(element(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),true,true,true)
| ~ spl0_16
| ~ spl0_80
| ~ spl0_82 ),
inference(forward_demodulation,[],[f946,f755]) ).
fof(f946,plain,
( true = ifeq(element(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),true,element(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),true)
| ~ spl0_16
| ~ spl0_82 ),
inference(superposition,[],[f106,f935]) ).
fof(f106,plain,
( ! [X0,X1] : true = ifeq(element(X1,powerset(X0)),true,element(subset_complement(X0,X1),powerset(X0)),true)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f1663,plain,
( spl0_152
| ~ spl0_43
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f890,f880,f363,f1660]) ).
fof(f880,plain,
( spl0_81
<=> true = element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f890,plain,
( true = ifeq(true,true,element(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),true)
| ~ spl0_43
| ~ spl0_81 ),
inference(superposition,[],[f364,f882]) ).
fof(f882,plain,
( true = element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A)))
| ~ spl0_81 ),
inference(avatar_component_clause,[],[f880]) ).
fof(f1658,plain,
( spl0_151
| ~ spl0_44
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f889,f880,f367,f1655]) ).
fof(f1655,plain,
( spl0_151
<=> true = ifeq(true,true,element(interior(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f889,plain,
( true = ifeq(true,true,element(interior(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),true)
| ~ spl0_44
| ~ spl0_81 ),
inference(superposition,[],[f368,f882]) ).
fof(f1653,plain,
( spl0_150
| ~ spl0_16
| ~ spl0_80 ),
inference(avatar_split_clause,[],[f851,f753,f105,f1650]) ).
fof(f1650,plain,
( spl0_150
<=> true = ifeq(true,true,element(subset_complement(the_carrier(sK2_t51_tops_1_A),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f851,plain,
( true = ifeq(true,true,element(subset_complement(the_carrier(sK2_t51_tops_1_A),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),true)
| ~ spl0_16
| ~ spl0_80 ),
inference(superposition,[],[f106,f755]) ).
fof(f1648,plain,
( spl0_149
| ~ spl0_16
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f804,f748,f105,f1645]) ).
fof(f1645,plain,
( spl0_149
<=> true = ifeq(true,true,element(subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f804,plain,
( true = ifeq(true,true,element(subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),true)
| ~ spl0_16
| ~ spl0_79 ),
inference(superposition,[],[f106,f750]) ).
fof(f1643,plain,
( spl0_148
| ~ spl0_15
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f714,f650,f99,f1640]) ).
fof(f1640,plain,
( spl0_148
<=> sK3_rc1_tops_1_B(sK2_t51_tops_1_A) = ifeq2(true,true,subset_complement(the_carrier(sK2_t51_tops_1_A),subset_complement(the_carrier(sK2_t51_tops_1_A),sK3_rc1_tops_1_B(sK2_t51_tops_1_A))),sK3_rc1_tops_1_B(sK2_t51_tops_1_A)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f714,plain,
( sK3_rc1_tops_1_B(sK2_t51_tops_1_A) = ifeq2(true,true,subset_complement(the_carrier(sK2_t51_tops_1_A),subset_complement(the_carrier(sK2_t51_tops_1_A),sK3_rc1_tops_1_B(sK2_t51_tops_1_A))),sK3_rc1_tops_1_B(sK2_t51_tops_1_A))
| ~ spl0_15
| ~ spl0_77 ),
inference(superposition,[],[f100,f652]) ).
fof(f1638,plain,
( spl0_147
| ~ spl0_10
| ~ spl0_49
| ~ spl0_76 ),
inference(avatar_split_clause,[],[f675,f645,f398,f69,f1635]) ).
fof(f1635,plain,
( spl0_147
<=> true = ifeq(open_subset(sK7_rc6_pre_topc_B(sK2_t51_tops_1_A),sK2_t51_tops_1_A),true,closed_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK7_rc6_pre_topc_B(sK2_t51_tops_1_A)),sK2_t51_tops_1_A),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f675,plain,
( true = ifeq(open_subset(sK7_rc6_pre_topc_B(sK2_t51_tops_1_A),sK2_t51_tops_1_A),true,closed_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK7_rc6_pre_topc_B(sK2_t51_tops_1_A)),sK2_t51_tops_1_A),true)
| ~ spl0_10
| ~ spl0_49
| ~ spl0_76 ),
inference(forward_demodulation,[],[f657,f70]) ).
fof(f657,plain,
( true = ifeq(open_subset(sK7_rc6_pre_topc_B(sK2_t51_tops_1_A),sK2_t51_tops_1_A),true,ifeq(true,true,closed_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK7_rc6_pre_topc_B(sK2_t51_tops_1_A)),sK2_t51_tops_1_A),true),true)
| ~ spl0_49
| ~ spl0_76 ),
inference(superposition,[],[f399,f647]) ).
fof(f1633,plain,
( spl0_146
| ~ spl0_10
| ~ spl0_114 ),
inference(avatar_split_clause,[],[f1355,f1312,f69,f1630]) ).
fof(f1630,plain,
( spl0_146
<=> true = subset(topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B),the_carrier(sK2_t51_tops_1_A)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f1312,plain,
( spl0_114
<=> true = ifeq(true,true,subset(topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B),the_carrier(sK2_t51_tops_1_A)),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f1355,plain,
( true = subset(topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B),the_carrier(sK2_t51_tops_1_A))
| ~ spl0_10
| ~ spl0_114 ),
inference(superposition,[],[f1314,f70]) ).
fof(f1314,plain,
( true = ifeq(true,true,subset(topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B),the_carrier(sK2_t51_tops_1_A)),true)
| ~ spl0_114 ),
inference(avatar_component_clause,[],[f1312]) ).
fof(f1628,plain,
( spl0_145
| ~ spl0_15
| ~ spl0_76 ),
inference(avatar_split_clause,[],[f669,f645,f99,f1625]) ).
fof(f1625,plain,
( spl0_145
<=> sK7_rc6_pre_topc_B(sK2_t51_tops_1_A) = ifeq2(true,true,subset_complement(the_carrier(sK2_t51_tops_1_A),subset_complement(the_carrier(sK2_t51_tops_1_A),sK7_rc6_pre_topc_B(sK2_t51_tops_1_A))),sK7_rc6_pre_topc_B(sK2_t51_tops_1_A)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f669,plain,
( sK7_rc6_pre_topc_B(sK2_t51_tops_1_A) = ifeq2(true,true,subset_complement(the_carrier(sK2_t51_tops_1_A),subset_complement(the_carrier(sK2_t51_tops_1_A),sK7_rc6_pre_topc_B(sK2_t51_tops_1_A))),sK7_rc6_pre_topc_B(sK2_t51_tops_1_A))
| ~ spl0_15
| ~ spl0_76 ),
inference(superposition,[],[f100,f647]) ).
fof(f1611,plain,
( spl0_144
| ~ spl0_43
| ~ spl0_80 ),
inference(avatar_split_clause,[],[f843,f753,f363,f1608]) ).
fof(f1608,plain,
( spl0_144
<=> true = ifeq(true,true,element(topstr_closure(sK2_t51_tops_1_A,interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f843,plain,
( true = ifeq(true,true,element(topstr_closure(sK2_t51_tops_1_A,interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),true)
| ~ spl0_43
| ~ spl0_80 ),
inference(superposition,[],[f364,f755]) ).
fof(f1606,plain,
( spl0_143
| ~ spl0_44
| ~ spl0_80 ),
inference(avatar_split_clause,[],[f842,f753,f367,f1603]) ).
fof(f1603,plain,
( spl0_143
<=> true = ifeq(true,true,element(interior(sK2_t51_tops_1_A,interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f842,plain,
( true = ifeq(true,true,element(interior(sK2_t51_tops_1_A,interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),true)
| ~ spl0_44
| ~ spl0_80 ),
inference(superposition,[],[f368,f755]) ).
fof(f1601,plain,
( spl0_142
| ~ spl0_43
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f796,f748,f363,f1598]) ).
fof(f1598,plain,
( spl0_142
<=> true = ifeq(true,true,element(topstr_closure(sK2_t51_tops_1_A,topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f796,plain,
( true = ifeq(true,true,element(topstr_closure(sK2_t51_tops_1_A,topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),true)
| ~ spl0_43
| ~ spl0_79 ),
inference(superposition,[],[f364,f750]) ).
fof(f1596,plain,
( spl0_141
| ~ spl0_10
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1348,f1307,f69,f1593]) ).
fof(f1593,plain,
( spl0_141
<=> true = closed_subset(topstr_closure(sK2_t51_tops_1_A,sK3_rc1_tops_1_B(sK2_t51_tops_1_A)),sK2_t51_tops_1_A) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f1307,plain,
( spl0_113
<=> true = ifeq(true,true,closed_subset(topstr_closure(sK2_t51_tops_1_A,sK3_rc1_tops_1_B(sK2_t51_tops_1_A)),sK2_t51_tops_1_A),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f1348,plain,
( true = closed_subset(topstr_closure(sK2_t51_tops_1_A,sK3_rc1_tops_1_B(sK2_t51_tops_1_A)),sK2_t51_tops_1_A)
| ~ spl0_10
| ~ spl0_113 ),
inference(superposition,[],[f1309,f70]) ).
fof(f1309,plain,
( true = ifeq(true,true,closed_subset(topstr_closure(sK2_t51_tops_1_A,sK3_rc1_tops_1_B(sK2_t51_tops_1_A)),sK2_t51_tops_1_A),true)
| ~ spl0_113 ),
inference(avatar_component_clause,[],[f1307]) ).
fof(f1591,plain,
( spl0_140
| ~ spl0_44
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f795,f748,f367,f1588]) ).
fof(f1588,plain,
( spl0_140
<=> true = ifeq(true,true,element(interior(sK2_t51_tops_1_A,topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f795,plain,
( true = ifeq(true,true,element(interior(sK2_t51_tops_1_A,topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),powerset(the_carrier(sK2_t51_tops_1_A))),true)
| ~ spl0_44
| ~ spl0_79 ),
inference(superposition,[],[f368,f750]) ).
fof(f1586,plain,
( spl0_139
| ~ spl0_16
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f713,f650,f105,f1583]) ).
fof(f1583,plain,
( spl0_139
<=> true = ifeq(true,true,element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK3_rc1_tops_1_B(sK2_t51_tops_1_A)),powerset(the_carrier(sK2_t51_tops_1_A))),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f713,plain,
( true = ifeq(true,true,element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK3_rc1_tops_1_B(sK2_t51_tops_1_A)),powerset(the_carrier(sK2_t51_tops_1_A))),true)
| ~ spl0_16
| ~ spl0_77 ),
inference(superposition,[],[f106,f652]) ).
fof(f1581,plain,
( spl0_138
| ~ spl0_16
| ~ spl0_76 ),
inference(avatar_split_clause,[],[f668,f645,f105,f1578]) ).
fof(f1578,plain,
( spl0_138
<=> true = ifeq(true,true,element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK7_rc6_pre_topc_B(sK2_t51_tops_1_A)),powerset(the_carrier(sK2_t51_tops_1_A))),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f668,plain,
( true = ifeq(true,true,element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK7_rc6_pre_topc_B(sK2_t51_tops_1_A)),powerset(the_carrier(sK2_t51_tops_1_A))),true)
| ~ spl0_16
| ~ spl0_76 ),
inference(superposition,[],[f106,f647]) ).
fof(f1564,plain,
( spl0_137
| ~ spl0_10
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f1346,f1297,f69,f1561]) ).
fof(f1561,plain,
( spl0_137
<=> true = closed_subset(topstr_closure(sK2_t51_tops_1_A,sK7_rc6_pre_topc_B(sK2_t51_tops_1_A)),sK2_t51_tops_1_A) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f1297,plain,
( spl0_111
<=> true = ifeq(true,true,closed_subset(topstr_closure(sK2_t51_tops_1_A,sK7_rc6_pre_topc_B(sK2_t51_tops_1_A)),sK2_t51_tops_1_A),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f1346,plain,
( true = closed_subset(topstr_closure(sK2_t51_tops_1_A,sK7_rc6_pre_topc_B(sK2_t51_tops_1_A)),sK2_t51_tops_1_A)
| ~ spl0_10
| ~ spl0_111 ),
inference(superposition,[],[f1299,f70]) ).
fof(f1299,plain,
( true = ifeq(true,true,closed_subset(topstr_closure(sK2_t51_tops_1_A,sK7_rc6_pre_topc_B(sK2_t51_tops_1_A)),sK2_t51_tops_1_A),true)
| ~ spl0_111 ),
inference(avatar_component_clause,[],[f1297]) ).
fof(f1555,plain,
( spl0_136
| ~ spl0_43
| ~ spl0_92 ),
inference(avatar_split_clause,[],[f1040,f1023,f363,f1552]) ).
fof(f1552,plain,
( spl0_136
<=> true = ifeq(true,true,element(topstr_closure(sK2_t51_tops_1_A,the_carrier(sK2_t51_tops_1_A)),powerset(the_carrier(sK2_t51_tops_1_A))),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f1040,plain,
( true = ifeq(true,true,element(topstr_closure(sK2_t51_tops_1_A,the_carrier(sK2_t51_tops_1_A)),powerset(the_carrier(sK2_t51_tops_1_A))),true)
| ~ spl0_43
| ~ spl0_92 ),
inference(superposition,[],[f364,f1024]) ).
fof(f1550,plain,
( spl0_135
| ~ spl0_44
| ~ spl0_92 ),
inference(avatar_split_clause,[],[f1039,f1023,f367,f1547]) ).
fof(f1547,plain,
( spl0_135
<=> true = ifeq(true,true,element(interior(sK2_t51_tops_1_A,the_carrier(sK2_t51_tops_1_A)),powerset(the_carrier(sK2_t51_tops_1_A))),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f1039,plain,
( true = ifeq(true,true,element(interior(sK2_t51_tops_1_A,the_carrier(sK2_t51_tops_1_A)),powerset(the_carrier(sK2_t51_tops_1_A))),true)
| ~ spl0_44
| ~ spl0_92 ),
inference(superposition,[],[f368,f1024]) ).
fof(f1545,plain,
( spl0_134
| ~ spl0_42
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f891,f880,f357,f1542]) ).
fof(f891,plain,
( true = ifeq(true,true,closed_subset(topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),sK2_t51_tops_1_A),true)
| ~ spl0_42
| ~ spl0_81 ),
inference(superposition,[],[f358,f882]) ).
fof(f1540,plain,
( spl0_133
| ~ spl0_10
| ~ spl0_39
| ~ spl0_49
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f769,f743,f398,f340,f69,f1537]) ).
fof(f1537,plain,
( spl0_133
<=> true = ifeq(open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),sK2_t51_tops_1_A),true,closed_subset(sK1_t51_tops_1_B,sK2_t51_tops_1_A),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f769,plain,
( true = ifeq(open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),sK2_t51_tops_1_A),true,closed_subset(sK1_t51_tops_1_B,sK2_t51_tops_1_A),true)
| ~ spl0_10
| ~ spl0_39
| ~ spl0_49
| ~ spl0_78 ),
inference(forward_demodulation,[],[f768,f70]) ).
fof(f768,plain,
( true = ifeq(open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),sK2_t51_tops_1_A),true,ifeq(true,true,closed_subset(sK1_t51_tops_1_B,sK2_t51_tops_1_A),true),true)
| ~ spl0_10
| ~ spl0_39
| ~ spl0_49
| ~ spl0_78 ),
inference(forward_demodulation,[],[f759,f349]) ).
fof(f759,plain,
( true = ifeq(open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),sK2_t51_tops_1_A),true,ifeq(element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),true,closed_subset(sK1_t51_tops_1_B,sK2_t51_tops_1_A),true),true)
| ~ spl0_49
| ~ spl0_78 ),
inference(superposition,[],[f399,f745]) ).
fof(f1535,plain,
( spl0_132
| ~ spl0_43
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f705,f650,f363,f1532]) ).
fof(f1532,plain,
( spl0_132
<=> true = ifeq(true,true,element(topstr_closure(sK2_t51_tops_1_A,sK3_rc1_tops_1_B(sK2_t51_tops_1_A)),powerset(the_carrier(sK2_t51_tops_1_A))),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f705,plain,
( true = ifeq(true,true,element(topstr_closure(sK2_t51_tops_1_A,sK3_rc1_tops_1_B(sK2_t51_tops_1_A)),powerset(the_carrier(sK2_t51_tops_1_A))),true)
| ~ spl0_43
| ~ spl0_77 ),
inference(superposition,[],[f364,f652]) ).
fof(f1530,plain,
( spl0_131
| ~ spl0_44
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f704,f650,f367,f1527]) ).
fof(f1527,plain,
( spl0_131
<=> true = ifeq(true,true,element(interior(sK2_t51_tops_1_A,sK3_rc1_tops_1_B(sK2_t51_tops_1_A)),powerset(the_carrier(sK2_t51_tops_1_A))),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f704,plain,
( true = ifeq(true,true,element(interior(sK2_t51_tops_1_A,sK3_rc1_tops_1_B(sK2_t51_tops_1_A)),powerset(the_carrier(sK2_t51_tops_1_A))),true)
| ~ spl0_44
| ~ spl0_77 ),
inference(superposition,[],[f368,f652]) ).
fof(f1525,plain,
( spl0_130
| ~ spl0_43
| ~ spl0_76 ),
inference(avatar_split_clause,[],[f660,f645,f363,f1522]) ).
fof(f1522,plain,
( spl0_130
<=> true = ifeq(true,true,element(topstr_closure(sK2_t51_tops_1_A,sK7_rc6_pre_topc_B(sK2_t51_tops_1_A)),powerset(the_carrier(sK2_t51_tops_1_A))),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f660,plain,
( true = ifeq(true,true,element(topstr_closure(sK2_t51_tops_1_A,sK7_rc6_pre_topc_B(sK2_t51_tops_1_A)),powerset(the_carrier(sK2_t51_tops_1_A))),true)
| ~ spl0_43
| ~ spl0_76 ),
inference(superposition,[],[f364,f647]) ).
fof(f1520,plain,
( spl0_129
| ~ spl0_44
| ~ spl0_76 ),
inference(avatar_split_clause,[],[f659,f645,f367,f1517]) ).
fof(f1517,plain,
( spl0_129
<=> true = ifeq(true,true,element(interior(sK2_t51_tops_1_A,sK7_rc6_pre_topc_B(sK2_t51_tops_1_A)),powerset(the_carrier(sK2_t51_tops_1_A))),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f659,plain,
( true = ifeq(true,true,element(interior(sK2_t51_tops_1_A,sK7_rc6_pre_topc_B(sK2_t51_tops_1_A)),powerset(the_carrier(sK2_t51_tops_1_A))),true)
| ~ spl0_44
| ~ spl0_76 ),
inference(superposition,[],[f368,f647]) ).
fof(f1510,plain,
( spl0_128
| ~ spl0_10
| ~ spl0_37
| ~ spl0_48
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f596,f543,f394,f324,f69,f1507]) ).
fof(f1507,plain,
( spl0_128
<=> true = ifeq(true,true,open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),sK2_t51_tops_1_A),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f324,plain,
( spl0_37
<=> true = ifeq(true,true,element(topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f543,plain,
( spl0_68
<=> true = closed_subset(topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f596,plain,
( true = ifeq(true,true,open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),sK2_t51_tops_1_A),true)
| ~ spl0_10
| ~ spl0_37
| ~ spl0_48
| ~ spl0_68 ),
inference(forward_demodulation,[],[f595,f335]) ).
fof(f335,plain,
( true = element(topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A)))
| ~ spl0_10
| ~ spl0_37 ),
inference(superposition,[],[f326,f70]) ).
fof(f326,plain,
( true = ifeq(true,true,element(topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),true)
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f324]) ).
fof(f595,plain,
( true = ifeq(element(topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),true,open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),sK2_t51_tops_1_A),true)
| ~ spl0_10
| ~ spl0_48
| ~ spl0_68 ),
inference(forward_demodulation,[],[f591,f70]) ).
fof(f591,plain,
( true = ifeq(element(topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),true,ifeq(true,true,open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),sK2_t51_tops_1_A),true),true)
| ~ spl0_48
| ~ spl0_68 ),
inference(superposition,[],[f395,f545]) ).
fof(f545,plain,
( true = closed_subset(topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A)
| ~ spl0_68 ),
inference(avatar_component_clause,[],[f543]) ).
fof(f1495,plain,
( spl0_127
| ~ spl0_12
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f901,f880,f80,f1492]) ).
fof(f1492,plain,
( spl0_127
<=> true = ifeq(subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),the_carrier(sK2_t51_tops_1_A)),true,true,true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f80,plain,
( spl0_12
<=> ! [X0,X1] : true = ifeq(subset(X0,X1),true,element(X0,powerset(X1)),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f901,plain,
( true = ifeq(subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),the_carrier(sK2_t51_tops_1_A)),true,true,true)
| ~ spl0_12
| ~ spl0_81 ),
inference(superposition,[],[f81,f882]) ).
fof(f81,plain,
( ! [X0,X1] : true = ifeq(subset(X0,X1),true,element(X0,powerset(X1)),true)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f1490,plain,
( spl0_126
| ~ spl0_14
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f900,f880,f89,f1487]) ).
fof(f1487,plain,
( spl0_126
<=> true = ifeq(true,true,subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),the_carrier(sK2_t51_tops_1_A)),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f89,plain,
( spl0_14
<=> ! [X0,X1] : true = ifeq(element(X0,powerset(X1)),true,subset(X0,X1),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f900,plain,
( true = ifeq(true,true,subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),the_carrier(sK2_t51_tops_1_A)),true)
| ~ spl0_14
| ~ spl0_81 ),
inference(superposition,[],[f90,f882]) ).
fof(f90,plain,
( ! [X0,X1] : true = ifeq(element(X0,powerset(X1)),true,subset(X0,X1),true)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f1485,plain,
( spl0_125
| ~ spl0_42
| ~ spl0_80 ),
inference(avatar_split_clause,[],[f844,f753,f357,f1482]) ).
fof(f1482,plain,
( spl0_125
<=> true = ifeq(true,true,closed_subset(topstr_closure(sK2_t51_tops_1_A,interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),sK2_t51_tops_1_A),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f844,plain,
( true = ifeq(true,true,closed_subset(topstr_closure(sK2_t51_tops_1_A,interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),sK2_t51_tops_1_A),true)
| ~ spl0_42
| ~ spl0_80 ),
inference(superposition,[],[f358,f755]) ).
fof(f1475,plain,
( spl0_124
| ~ spl0_42
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f797,f748,f357,f1472]) ).
fof(f1472,plain,
( spl0_124
<=> true = ifeq(true,true,closed_subset(topstr_closure(sK2_t51_tops_1_A,topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),sK2_t51_tops_1_A),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f797,plain,
( true = ifeq(true,true,closed_subset(topstr_closure(sK2_t51_tops_1_A,topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),sK2_t51_tops_1_A),true)
| ~ spl0_42
| ~ spl0_79 ),
inference(superposition,[],[f358,f750]) ).
fof(f1470,plain,
( spl0_123
| ~ spl0_10
| ~ spl0_34
| ~ spl0_47
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f504,f398,f387,f305,f69,f1467]) ).
fof(f1467,plain,
( spl0_123
<=> true = ifeq(true,true,closed_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK3_rc1_tops_1_B(sK2_t51_tops_1_A)),sK2_t51_tops_1_A),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f305,plain,
( spl0_34
<=> true = ifeq(true,true,element(sK3_rc1_tops_1_B(sK2_t51_tops_1_A),powerset(the_carrier(sK2_t51_tops_1_A))),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f387,plain,
( spl0_47
<=> true = open_subset(sK3_rc1_tops_1_B(sK2_t51_tops_1_A),sK2_t51_tops_1_A) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f504,plain,
( true = ifeq(true,true,closed_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK3_rc1_tops_1_B(sK2_t51_tops_1_A)),sK2_t51_tops_1_A),true)
| ~ spl0_10
| ~ spl0_34
| ~ spl0_47
| ~ spl0_49 ),
inference(forward_demodulation,[],[f503,f70]) ).
fof(f503,plain,
( true = ifeq(true,true,ifeq(true,true,closed_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK3_rc1_tops_1_B(sK2_t51_tops_1_A)),sK2_t51_tops_1_A),true),true)
| ~ spl0_10
| ~ spl0_34
| ~ spl0_47
| ~ spl0_49 ),
inference(forward_demodulation,[],[f498,f316]) ).
fof(f316,plain,
( true = element(sK3_rc1_tops_1_B(sK2_t51_tops_1_A),powerset(the_carrier(sK2_t51_tops_1_A)))
| ~ spl0_10
| ~ spl0_34 ),
inference(superposition,[],[f307,f70]) ).
fof(f307,plain,
( true = ifeq(true,true,element(sK3_rc1_tops_1_B(sK2_t51_tops_1_A),powerset(the_carrier(sK2_t51_tops_1_A))),true)
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f305]) ).
fof(f498,plain,
( true = ifeq(true,true,ifeq(element(sK3_rc1_tops_1_B(sK2_t51_tops_1_A),powerset(the_carrier(sK2_t51_tops_1_A))),true,closed_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK3_rc1_tops_1_B(sK2_t51_tops_1_A)),sK2_t51_tops_1_A),true),true)
| ~ spl0_47
| ~ spl0_49 ),
inference(superposition,[],[f399,f389]) ).
fof(f389,plain,
( true = open_subset(sK3_rc1_tops_1_B(sK2_t51_tops_1_A),sK2_t51_tops_1_A)
| ~ spl0_47 ),
inference(avatar_component_clause,[],[f387]) ).
fof(f1465,plain,
( spl0_122
| ~ spl0_10
| ~ spl0_33
| ~ spl0_41
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f464,f394,f352,f300,f69,f1462]) ).
fof(f1462,plain,
( spl0_122
<=> true = ifeq(true,true,open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK7_rc6_pre_topc_B(sK2_t51_tops_1_A)),sK2_t51_tops_1_A),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f300,plain,
( spl0_33
<=> true = ifeq(true,true,element(sK7_rc6_pre_topc_B(sK2_t51_tops_1_A),powerset(the_carrier(sK2_t51_tops_1_A))),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f352,plain,
( spl0_41
<=> true = closed_subset(sK7_rc6_pre_topc_B(sK2_t51_tops_1_A),sK2_t51_tops_1_A) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f464,plain,
( true = ifeq(true,true,open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK7_rc6_pre_topc_B(sK2_t51_tops_1_A)),sK2_t51_tops_1_A),true)
| ~ spl0_10
| ~ spl0_33
| ~ spl0_41
| ~ spl0_48 ),
inference(forward_demodulation,[],[f463,f309]) ).
fof(f309,plain,
( true = element(sK7_rc6_pre_topc_B(sK2_t51_tops_1_A),powerset(the_carrier(sK2_t51_tops_1_A)))
| ~ spl0_10
| ~ spl0_33 ),
inference(superposition,[],[f302,f70]) ).
fof(f302,plain,
( true = ifeq(true,true,element(sK7_rc6_pre_topc_B(sK2_t51_tops_1_A),powerset(the_carrier(sK2_t51_tops_1_A))),true)
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f300]) ).
fof(f463,plain,
( true = ifeq(element(sK7_rc6_pre_topc_B(sK2_t51_tops_1_A),powerset(the_carrier(sK2_t51_tops_1_A))),true,open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK7_rc6_pre_topc_B(sK2_t51_tops_1_A)),sK2_t51_tops_1_A),true)
| ~ spl0_10
| ~ spl0_41
| ~ spl0_48 ),
inference(forward_demodulation,[],[f460,f70]) ).
fof(f460,plain,
( true = ifeq(element(sK7_rc6_pre_topc_B(sK2_t51_tops_1_A),powerset(the_carrier(sK2_t51_tops_1_A))),true,ifeq(true,true,open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK7_rc6_pre_topc_B(sK2_t51_tops_1_A)),sK2_t51_tops_1_A),true),true)
| ~ spl0_41
| ~ spl0_48 ),
inference(superposition,[],[f395,f354]) ).
fof(f354,plain,
( true = closed_subset(sK7_rc6_pre_topc_B(sK2_t51_tops_1_A),sK2_t51_tops_1_A)
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f352]) ).
fof(f1354,plain,
( spl0_121
| ~ spl0_10
| ~ spl0_108 ),
inference(avatar_split_clause,[],[f1294,f1259,f69,f1351]) ).
fof(f1351,plain,
( spl0_121
<=> true = subset(sK3_rc1_tops_1_B(sK2_t51_tops_1_A),the_carrier(sK2_t51_tops_1_A)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f1259,plain,
( spl0_108
<=> true = ifeq(true,true,subset(sK3_rc1_tops_1_B(sK2_t51_tops_1_A),the_carrier(sK2_t51_tops_1_A)),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f1294,plain,
( true = subset(sK3_rc1_tops_1_B(sK2_t51_tops_1_A),the_carrier(sK2_t51_tops_1_A))
| ~ spl0_10
| ~ spl0_108 ),
inference(superposition,[],[f1261,f70]) ).
fof(f1261,plain,
( true = ifeq(true,true,subset(sK3_rc1_tops_1_B(sK2_t51_tops_1_A),the_carrier(sK2_t51_tops_1_A)),true)
| ~ spl0_108 ),
inference(avatar_component_clause,[],[f1259]) ).
fof(f1345,plain,
( spl0_120
| ~ spl0_42
| ~ spl0_92 ),
inference(avatar_split_clause,[],[f1041,f1023,f357,f1342]) ).
fof(f1041,plain,
( true = ifeq(true,true,closed_subset(topstr_closure(sK2_t51_tops_1_A,the_carrier(sK2_t51_tops_1_A)),sK2_t51_tops_1_A),true)
| ~ spl0_42
| ~ spl0_92 ),
inference(superposition,[],[f358,f1024]) ).
fof(f1340,plain,
( spl0_119
| ~ spl0_10
| ~ spl0_87 ),
inference(avatar_split_clause,[],[f995,f989,f69,f1337]) ).
fof(f1337,plain,
( spl0_119
<=> true = element(interior(sK2_t51_tops_1_A,sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A)))),powerset(the_carrier(sK2_t51_tops_1_A))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f989,plain,
( spl0_87
<=> true = ifeq(true,true,element(interior(sK2_t51_tops_1_A,sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A)))),powerset(the_carrier(sK2_t51_tops_1_A))),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f995,plain,
( true = element(interior(sK2_t51_tops_1_A,sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A)))),powerset(the_carrier(sK2_t51_tops_1_A)))
| ~ spl0_10
| ~ spl0_87 ),
inference(superposition,[],[f991,f70]) ).
fof(f991,plain,
( true = ifeq(true,true,element(interior(sK2_t51_tops_1_A,sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A)))),powerset(the_carrier(sK2_t51_tops_1_A))),true)
| ~ spl0_87 ),
inference(avatar_component_clause,[],[f989]) ).
fof(f1335,plain,
( spl0_118
| ~ spl0_10
| ~ spl0_86 ),
inference(avatar_split_clause,[],[f993,f984,f69,f1332]) ).
fof(f1332,plain,
( spl0_118
<=> true = element(topstr_closure(sK2_t51_tops_1_A,sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A)))),powerset(the_carrier(sK2_t51_tops_1_A))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f984,plain,
( spl0_86
<=> true = ifeq(true,true,element(topstr_closure(sK2_t51_tops_1_A,sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A)))),powerset(the_carrier(sK2_t51_tops_1_A))),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f993,plain,
( true = element(topstr_closure(sK2_t51_tops_1_A,sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A)))),powerset(the_carrier(sK2_t51_tops_1_A)))
| ~ spl0_10
| ~ spl0_86 ),
inference(superposition,[],[f986,f70]) ).
fof(f986,plain,
( true = ifeq(true,true,element(topstr_closure(sK2_t51_tops_1_A,sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A)))),powerset(the_carrier(sK2_t51_tops_1_A))),true)
| ~ spl0_86 ),
inference(avatar_component_clause,[],[f984]) ).
fof(f1330,plain,
( spl0_117
| ~ spl0_12
| ~ spl0_80 ),
inference(avatar_split_clause,[],[f854,f753,f80,f1327]) ).
fof(f1327,plain,
( spl0_117
<=> true = ifeq(subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),the_carrier(sK2_t51_tops_1_A)),true,true,true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f854,plain,
( true = ifeq(subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),the_carrier(sK2_t51_tops_1_A)),true,true,true)
| ~ spl0_12
| ~ spl0_80 ),
inference(superposition,[],[f81,f755]) ).
fof(f1325,plain,
( spl0_116
| ~ spl0_14
| ~ spl0_80 ),
inference(avatar_split_clause,[],[f853,f753,f89,f1322]) ).
fof(f853,plain,
( true = ifeq(true,true,subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),the_carrier(sK2_t51_tops_1_A)),true)
| ~ spl0_14
| ~ spl0_80 ),
inference(superposition,[],[f90,f755]) ).
fof(f1320,plain,
( spl0_115
| ~ spl0_12
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f807,f748,f80,f1317]) ).
fof(f1317,plain,
( spl0_115
<=> true = ifeq(subset(topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B),the_carrier(sK2_t51_tops_1_A)),true,true,true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f807,plain,
( true = ifeq(subset(topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B),the_carrier(sK2_t51_tops_1_A)),true,true,true)
| ~ spl0_12
| ~ spl0_79 ),
inference(superposition,[],[f81,f750]) ).
fof(f1315,plain,
( spl0_114
| ~ spl0_14
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f806,f748,f89,f1312]) ).
fof(f806,plain,
( true = ifeq(true,true,subset(topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B),the_carrier(sK2_t51_tops_1_A)),true)
| ~ spl0_14
| ~ spl0_79 ),
inference(superposition,[],[f90,f750]) ).
fof(f1310,plain,
( spl0_113
| ~ spl0_42
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f706,f650,f357,f1307]) ).
fof(f706,plain,
( true = ifeq(true,true,closed_subset(topstr_closure(sK2_t51_tops_1_A,sK3_rc1_tops_1_B(sK2_t51_tops_1_A)),sK2_t51_tops_1_A),true)
| ~ spl0_42
| ~ spl0_77 ),
inference(superposition,[],[f358,f652]) ).
fof(f1305,plain,
( spl0_112
| ~ spl0_10
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f1292,f974,f69,f1302]) ).
fof(f1302,plain,
( spl0_112
<=> true = subset(sK7_rc6_pre_topc_B(sK2_t51_tops_1_A),the_carrier(sK2_t51_tops_1_A)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f974,plain,
( spl0_85
<=> true = ifeq(true,true,subset(sK7_rc6_pre_topc_B(sK2_t51_tops_1_A),the_carrier(sK2_t51_tops_1_A)),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f1292,plain,
( true = subset(sK7_rc6_pre_topc_B(sK2_t51_tops_1_A),the_carrier(sK2_t51_tops_1_A))
| ~ spl0_10
| ~ spl0_85 ),
inference(superposition,[],[f976,f70]) ).
fof(f976,plain,
( true = ifeq(true,true,subset(sK7_rc6_pre_topc_B(sK2_t51_tops_1_A),the_carrier(sK2_t51_tops_1_A)),true)
| ~ spl0_85 ),
inference(avatar_component_clause,[],[f974]) ).
fof(f1300,plain,
( spl0_111
| ~ spl0_42
| ~ spl0_76 ),
inference(avatar_split_clause,[],[f661,f645,f357,f1297]) ).
fof(f661,plain,
( true = ifeq(true,true,closed_subset(topstr_closure(sK2_t51_tops_1_A,sK7_rc6_pre_topc_B(sK2_t51_tops_1_A)),sK2_t51_tops_1_A),true)
| ~ spl0_42
| ~ spl0_76 ),
inference(superposition,[],[f358,f647]) ).
fof(f1291,plain,
( spl0_110
| ~ spl0_12
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f716,f650,f80,f1288]) ).
fof(f1288,plain,
( spl0_110
<=> true = ifeq(subset(sK3_rc1_tops_1_B(sK2_t51_tops_1_A),the_carrier(sK2_t51_tops_1_A)),true,true,true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f716,plain,
( true = ifeq(subset(sK3_rc1_tops_1_B(sK2_t51_tops_1_A),the_carrier(sK2_t51_tops_1_A)),true,true,true)
| ~ spl0_12
| ~ spl0_77 ),
inference(superposition,[],[f81,f652]) ).
fof(f1273,plain,
( spl0_109
| ~ spl0_10
| ~ spl0_74 ),
inference(avatar_split_clause,[],[f625,f619,f69,f1271]) ).
fof(f1271,plain,
( spl0_109
<=> ! [X0] : true = ifeq(closed_subset(sK4_existence_m1_subset_1_B(powerset(the_carrier(X0))),X0),true,ifeq(topological_space(X0),true,ifeq(top_str(X0),true,open_subset(subset_complement(the_carrier(X0),sK4_existence_m1_subset_1_B(powerset(the_carrier(X0)))),X0),true),true),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f619,plain,
( spl0_74
<=> ! [X0] : true = ifeq(true,true,ifeq(closed_subset(sK4_existence_m1_subset_1_B(powerset(the_carrier(X0))),X0),true,ifeq(topological_space(X0),true,ifeq(top_str(X0),true,open_subset(subset_complement(the_carrier(X0),sK4_existence_m1_subset_1_B(powerset(the_carrier(X0)))),X0),true),true),true),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f625,plain,
( ! [X0] : true = ifeq(closed_subset(sK4_existence_m1_subset_1_B(powerset(the_carrier(X0))),X0),true,ifeq(topological_space(X0),true,ifeq(top_str(X0),true,open_subset(subset_complement(the_carrier(X0),sK4_existence_m1_subset_1_B(powerset(the_carrier(X0)))),X0),true),true),true)
| ~ spl0_10
| ~ spl0_74 ),
inference(superposition,[],[f620,f70]) ).
fof(f620,plain,
( ! [X0] : true = ifeq(true,true,ifeq(closed_subset(sK4_existence_m1_subset_1_B(powerset(the_carrier(X0))),X0),true,ifeq(topological_space(X0),true,ifeq(top_str(X0),true,open_subset(subset_complement(the_carrier(X0),sK4_existence_m1_subset_1_B(powerset(the_carrier(X0)))),X0),true),true),true),true)
| ~ spl0_74 ),
inference(avatar_component_clause,[],[f619]) ).
fof(f1262,plain,
( spl0_108
| ~ spl0_14
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f715,f650,f89,f1259]) ).
fof(f715,plain,
( true = ifeq(true,true,subset(sK3_rc1_tops_1_B(sK2_t51_tops_1_A),the_carrier(sK2_t51_tops_1_A)),true)
| ~ spl0_14
| ~ spl0_77 ),
inference(superposition,[],[f90,f652]) ).
fof(f1257,plain,
( spl0_107
| ~ spl0_9
| ~ spl0_75 ),
inference(avatar_split_clause,[],[f640,f635,f65,f1255]) ).
fof(f1255,plain,
( spl0_107
<=> ! [X0] : interior(X0,sK4_existence_m1_subset_1_B(powerset(the_carrier(X0)))) = ifeq2(top_str(X0),true,subset_complement(the_carrier(X0),topstr_closure(X0,subset_complement(the_carrier(X0),sK4_existence_m1_subset_1_B(powerset(the_carrier(X0)))))),interior(X0,sK4_existence_m1_subset_1_B(powerset(the_carrier(X0))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f635,plain,
( spl0_75
<=> ! [X0] : interior(X0,sK4_existence_m1_subset_1_B(powerset(the_carrier(X0)))) = ifeq2(true,true,ifeq2(top_str(X0),true,subset_complement(the_carrier(X0),topstr_closure(X0,subset_complement(the_carrier(X0),sK4_existence_m1_subset_1_B(powerset(the_carrier(X0)))))),interior(X0,sK4_existence_m1_subset_1_B(powerset(the_carrier(X0))))),interior(X0,sK4_existence_m1_subset_1_B(powerset(the_carrier(X0))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f640,plain,
( ! [X0] : interior(X0,sK4_existence_m1_subset_1_B(powerset(the_carrier(X0)))) = ifeq2(top_str(X0),true,subset_complement(the_carrier(X0),topstr_closure(X0,subset_complement(the_carrier(X0),sK4_existence_m1_subset_1_B(powerset(the_carrier(X0)))))),interior(X0,sK4_existence_m1_subset_1_B(powerset(the_carrier(X0)))))
| ~ spl0_9
| ~ spl0_75 ),
inference(superposition,[],[f636,f66]) ).
fof(f636,plain,
( ! [X0] : interior(X0,sK4_existence_m1_subset_1_B(powerset(the_carrier(X0)))) = ifeq2(true,true,ifeq2(top_str(X0),true,subset_complement(the_carrier(X0),topstr_closure(X0,subset_complement(the_carrier(X0),sK4_existence_m1_subset_1_B(powerset(the_carrier(X0)))))),interior(X0,sK4_existence_m1_subset_1_B(powerset(the_carrier(X0))))),interior(X0,sK4_existence_m1_subset_1_B(powerset(the_carrier(X0)))))
| ~ spl0_75 ),
inference(avatar_component_clause,[],[f635]) ).
fof(f1253,plain,
( spl0_106
| ~ spl0_8
| ~ spl0_71 ),
inference(avatar_split_clause,[],[f582,f575,f61,f1250]) ).
fof(f1250,plain,
( spl0_106
<=> true = ifeq(true,true,ifeq(closed_subset(sK4_existence_m1_subset_1_B(powerset(the_carrier(sK5_existence_l1_pre_topc_A))),sK5_existence_l1_pre_topc_A),true,ifeq(topological_space(sK5_existence_l1_pre_topc_A),true,open_subset(subset_complement(the_carrier(sK5_existence_l1_pre_topc_A),sK4_existence_m1_subset_1_B(powerset(the_carrier(sK5_existence_l1_pre_topc_A)))),sK5_existence_l1_pre_topc_A),true),true),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f61,plain,
( spl0_8
<=> ! [X0] : true = element(sK4_existence_m1_subset_1_B(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f575,plain,
( spl0_71
<=> ! [X0] : true = ifeq(element(X0,powerset(the_carrier(sK5_existence_l1_pre_topc_A))),true,ifeq(closed_subset(X0,sK5_existence_l1_pre_topc_A),true,ifeq(topological_space(sK5_existence_l1_pre_topc_A),true,open_subset(subset_complement(the_carrier(sK5_existence_l1_pre_topc_A),X0),sK5_existence_l1_pre_topc_A),true),true),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f582,plain,
( true = ifeq(true,true,ifeq(closed_subset(sK4_existence_m1_subset_1_B(powerset(the_carrier(sK5_existence_l1_pre_topc_A))),sK5_existence_l1_pre_topc_A),true,ifeq(topological_space(sK5_existence_l1_pre_topc_A),true,open_subset(subset_complement(the_carrier(sK5_existence_l1_pre_topc_A),sK4_existence_m1_subset_1_B(powerset(the_carrier(sK5_existence_l1_pre_topc_A)))),sK5_existence_l1_pre_topc_A),true),true),true)
| ~ spl0_8
| ~ spl0_71 ),
inference(superposition,[],[f576,f62]) ).
fof(f62,plain,
( ! [X0] : true = element(sK4_existence_m1_subset_1_B(X0),X0)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f576,plain,
( ! [X0] : true = ifeq(element(X0,powerset(the_carrier(sK5_existence_l1_pre_topc_A))),true,ifeq(closed_subset(X0,sK5_existence_l1_pre_topc_A),true,ifeq(topological_space(sK5_existence_l1_pre_topc_A),true,open_subset(subset_complement(the_carrier(sK5_existence_l1_pre_topc_A),X0),sK5_existence_l1_pre_topc_A),true),true),true)
| ~ spl0_71 ),
inference(avatar_component_clause,[],[f575]) ).
fof(f1246,plain,
( spl0_105
| ~ spl0_8
| ~ spl0_69 ),
inference(avatar_split_clause,[],[f557,f554,f61,f1243]) ).
fof(f1243,plain,
( spl0_105
<=> interior(sK5_existence_l1_pre_topc_A,sK4_existence_m1_subset_1_B(powerset(the_carrier(sK5_existence_l1_pre_topc_A)))) = ifeq2(true,true,subset_complement(the_carrier(sK5_existence_l1_pre_topc_A),topstr_closure(sK5_existence_l1_pre_topc_A,subset_complement(the_carrier(sK5_existence_l1_pre_topc_A),sK4_existence_m1_subset_1_B(powerset(the_carrier(sK5_existence_l1_pre_topc_A)))))),interior(sK5_existence_l1_pre_topc_A,sK4_existence_m1_subset_1_B(powerset(the_carrier(sK5_existence_l1_pre_topc_A))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f554,plain,
( spl0_69
<=> ! [X0] : interior(sK5_existence_l1_pre_topc_A,X0) = ifeq2(element(X0,powerset(the_carrier(sK5_existence_l1_pre_topc_A))),true,subset_complement(the_carrier(sK5_existence_l1_pre_topc_A),topstr_closure(sK5_existence_l1_pre_topc_A,subset_complement(the_carrier(sK5_existence_l1_pre_topc_A),X0))),interior(sK5_existence_l1_pre_topc_A,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f557,plain,
( interior(sK5_existence_l1_pre_topc_A,sK4_existence_m1_subset_1_B(powerset(the_carrier(sK5_existence_l1_pre_topc_A)))) = ifeq2(true,true,subset_complement(the_carrier(sK5_existence_l1_pre_topc_A),topstr_closure(sK5_existence_l1_pre_topc_A,subset_complement(the_carrier(sK5_existence_l1_pre_topc_A),sK4_existence_m1_subset_1_B(powerset(the_carrier(sK5_existence_l1_pre_topc_A)))))),interior(sK5_existence_l1_pre_topc_A,sK4_existence_m1_subset_1_B(powerset(the_carrier(sK5_existence_l1_pre_topc_A)))))
| ~ spl0_8
| ~ spl0_69 ),
inference(superposition,[],[f555,f62]) ).
fof(f555,plain,
( ! [X0] : interior(sK5_existence_l1_pre_topc_A,X0) = ifeq2(element(X0,powerset(the_carrier(sK5_existence_l1_pre_topc_A))),true,subset_complement(the_carrier(sK5_existence_l1_pre_topc_A),topstr_closure(sK5_existence_l1_pre_topc_A,subset_complement(the_carrier(sK5_existence_l1_pre_topc_A),X0))),interior(sK5_existence_l1_pre_topc_A,X0))
| ~ spl0_69 ),
inference(avatar_component_clause,[],[f554]) ).
fof(f1241,plain,
( spl0_104
| ~ spl0_8
| ~ spl0_10
| ~ spl0_72 ),
inference(avatar_split_clause,[],[f584,f579,f69,f61,f1238]) ).
fof(f1238,plain,
( spl0_104
<=> true = ifeq(open_subset(sK4_existence_m1_subset_1_B(powerset(the_carrier(sK5_existence_l1_pre_topc_A))),sK5_existence_l1_pre_topc_A),true,ifeq(topological_space(sK5_existence_l1_pre_topc_A),true,closed_subset(subset_complement(the_carrier(sK5_existence_l1_pre_topc_A),sK4_existence_m1_subset_1_B(powerset(the_carrier(sK5_existence_l1_pre_topc_A)))),sK5_existence_l1_pre_topc_A),true),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f579,plain,
( spl0_72
<=> ! [X0] : true = ifeq(open_subset(X0,sK5_existence_l1_pre_topc_A),true,ifeq(element(X0,powerset(the_carrier(sK5_existence_l1_pre_topc_A))),true,ifeq(topological_space(sK5_existence_l1_pre_topc_A),true,closed_subset(subset_complement(the_carrier(sK5_existence_l1_pre_topc_A),X0),sK5_existence_l1_pre_topc_A),true),true),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f584,plain,
( true = ifeq(open_subset(sK4_existence_m1_subset_1_B(powerset(the_carrier(sK5_existence_l1_pre_topc_A))),sK5_existence_l1_pre_topc_A),true,ifeq(topological_space(sK5_existence_l1_pre_topc_A),true,closed_subset(subset_complement(the_carrier(sK5_existence_l1_pre_topc_A),sK4_existence_m1_subset_1_B(powerset(the_carrier(sK5_existence_l1_pre_topc_A)))),sK5_existence_l1_pre_topc_A),true),true)
| ~ spl0_8
| ~ spl0_10
| ~ spl0_72 ),
inference(forward_demodulation,[],[f583,f70]) ).
fof(f583,plain,
( true = ifeq(open_subset(sK4_existence_m1_subset_1_B(powerset(the_carrier(sK5_existence_l1_pre_topc_A))),sK5_existence_l1_pre_topc_A),true,ifeq(true,true,ifeq(topological_space(sK5_existence_l1_pre_topc_A),true,closed_subset(subset_complement(the_carrier(sK5_existence_l1_pre_topc_A),sK4_existence_m1_subset_1_B(powerset(the_carrier(sK5_existence_l1_pre_topc_A)))),sK5_existence_l1_pre_topc_A),true),true),true)
| ~ spl0_8
| ~ spl0_72 ),
inference(superposition,[],[f580,f62]) ).
fof(f580,plain,
( ! [X0] : true = ifeq(open_subset(X0,sK5_existence_l1_pre_topc_A),true,ifeq(element(X0,powerset(the_carrier(sK5_existence_l1_pre_topc_A))),true,ifeq(topological_space(sK5_existence_l1_pre_topc_A),true,closed_subset(subset_complement(the_carrier(sK5_existence_l1_pre_topc_A),X0),sK5_existence_l1_pre_topc_A),true),true),true)
| ~ spl0_72 ),
inference(avatar_component_clause,[],[f579]) ).
fof(f1220,plain,
( spl0_103
| ~ spl0_10
| ~ spl0_70 ),
inference(avatar_split_clause,[],[f565,f559,f69,f1218]) ).
fof(f1218,plain,
( spl0_103
<=> ! [X0] : true = ifeq(topological_space(X0),true,ifeq(top_str(X0),true,closed_subset(topstr_closure(X0,sK4_existence_m1_subset_1_B(powerset(the_carrier(X0)))),X0),true),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f559,plain,
( spl0_70
<=> ! [X0] : true = ifeq(true,true,ifeq(topological_space(X0),true,ifeq(top_str(X0),true,closed_subset(topstr_closure(X0,sK4_existence_m1_subset_1_B(powerset(the_carrier(X0)))),X0),true),true),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f565,plain,
( ! [X0] : true = ifeq(topological_space(X0),true,ifeq(top_str(X0),true,closed_subset(topstr_closure(X0,sK4_existence_m1_subset_1_B(powerset(the_carrier(X0)))),X0),true),true)
| ~ spl0_10
| ~ spl0_70 ),
inference(superposition,[],[f560,f70]) ).
fof(f560,plain,
( ! [X0] : true = ifeq(true,true,ifeq(topological_space(X0),true,ifeq(top_str(X0),true,closed_subset(topstr_closure(X0,sK4_existence_m1_subset_1_B(powerset(the_carrier(X0)))),X0),true),true),true)
| ~ spl0_70 ),
inference(avatar_component_clause,[],[f559]) ).
fof(f1214,plain,
( spl0_102
| ~ spl0_8
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f527,f524,f61,f1211]) ).
fof(f1211,plain,
( spl0_102
<=> true = ifeq(true,true,ifeq(topological_space(sK5_existence_l1_pre_topc_A),true,closed_subset(topstr_closure(sK5_existence_l1_pre_topc_A,sK4_existence_m1_subset_1_B(powerset(the_carrier(sK5_existence_l1_pre_topc_A)))),sK5_existence_l1_pre_topc_A),true),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f524,plain,
( spl0_65
<=> ! [X0] : true = ifeq(element(X0,powerset(the_carrier(sK5_existence_l1_pre_topc_A))),true,ifeq(topological_space(sK5_existence_l1_pre_topc_A),true,closed_subset(topstr_closure(sK5_existence_l1_pre_topc_A,X0),sK5_existence_l1_pre_topc_A),true),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f527,plain,
( true = ifeq(true,true,ifeq(topological_space(sK5_existence_l1_pre_topc_A),true,closed_subset(topstr_closure(sK5_existence_l1_pre_topc_A,sK4_existence_m1_subset_1_B(powerset(the_carrier(sK5_existence_l1_pre_topc_A)))),sK5_existence_l1_pre_topc_A),true),true)
| ~ spl0_8
| ~ spl0_65 ),
inference(superposition,[],[f525,f62]) ).
fof(f525,plain,
( ! [X0] : true = ifeq(element(X0,powerset(the_carrier(sK5_existence_l1_pre_topc_A))),true,ifeq(topological_space(sK5_existence_l1_pre_topc_A),true,closed_subset(topstr_closure(sK5_existence_l1_pre_topc_A,X0),sK5_existence_l1_pre_topc_A),true),true)
| ~ spl0_65 ),
inference(avatar_component_clause,[],[f524]) ).
fof(f1209,plain,
( spl0_101
| ~ spl0_12
| ~ spl0_76 ),
inference(avatar_split_clause,[],[f671,f645,f80,f1206]) ).
fof(f1206,plain,
( spl0_101
<=> true = ifeq(subset(sK7_rc6_pre_topc_B(sK2_t51_tops_1_A),the_carrier(sK2_t51_tops_1_A)),true,true,true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f671,plain,
( true = ifeq(subset(sK7_rc6_pre_topc_B(sK2_t51_tops_1_A),the_carrier(sK2_t51_tops_1_A)),true,true,true)
| ~ spl0_12
| ~ spl0_76 ),
inference(superposition,[],[f81,f647]) ).
fof(f1194,plain,
( spl0_100
| ~ spl0_10
| ~ spl0_67 ),
inference(avatar_split_clause,[],[f549,f533,f69,f1192]) ).
fof(f1192,plain,
( spl0_100
<=> ! [X0] : true = ifeq(top_str(X0),true,element(interior(X0,sK4_existence_m1_subset_1_B(powerset(the_carrier(X0)))),powerset(the_carrier(X0))),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f533,plain,
( spl0_67
<=> ! [X0] : true = ifeq(true,true,ifeq(top_str(X0),true,element(interior(X0,sK4_existence_m1_subset_1_B(powerset(the_carrier(X0)))),powerset(the_carrier(X0))),true),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f549,plain,
( ! [X0] : true = ifeq(top_str(X0),true,element(interior(X0,sK4_existence_m1_subset_1_B(powerset(the_carrier(X0)))),powerset(the_carrier(X0))),true)
| ~ spl0_10
| ~ spl0_67 ),
inference(superposition,[],[f534,f70]) ).
fof(f534,plain,
( ! [X0] : true = ifeq(true,true,ifeq(top_str(X0),true,element(interior(X0,sK4_existence_m1_subset_1_B(powerset(the_carrier(X0)))),powerset(the_carrier(X0))),true),true)
| ~ spl0_67 ),
inference(avatar_component_clause,[],[f533]) ).
fof(f1190,plain,
( spl0_99
| ~ spl0_10
| ~ spl0_66 ),
inference(avatar_split_clause,[],[f538,f529,f69,f1188]) ).
fof(f1188,plain,
( spl0_99
<=> ! [X0] : true = ifeq(top_str(X0),true,element(topstr_closure(X0,sK4_existence_m1_subset_1_B(powerset(the_carrier(X0)))),powerset(the_carrier(X0))),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f529,plain,
( spl0_66
<=> ! [X0] : true = ifeq(true,true,ifeq(top_str(X0),true,element(topstr_closure(X0,sK4_existence_m1_subset_1_B(powerset(the_carrier(X0)))),powerset(the_carrier(X0))),true),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f538,plain,
( ! [X0] : true = ifeq(top_str(X0),true,element(topstr_closure(X0,sK4_existence_m1_subset_1_B(powerset(the_carrier(X0)))),powerset(the_carrier(X0))),true)
| ~ spl0_10
| ~ spl0_66 ),
inference(superposition,[],[f530,f70]) ).
fof(f530,plain,
( ! [X0] : true = ifeq(true,true,ifeq(top_str(X0),true,element(topstr_closure(X0,sK4_existence_m1_subset_1_B(powerset(the_carrier(X0)))),powerset(the_carrier(X0))),true),true)
| ~ spl0_66 ),
inference(avatar_component_clause,[],[f529]) ).
fof(f1182,plain,
( spl0_98
| ~ spl0_8
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f522,f516,f61,f1179]) ).
fof(f1179,plain,
( spl0_98
<=> true = ifeq(true,true,element(interior(sK5_existence_l1_pre_topc_A,sK4_existence_m1_subset_1_B(powerset(the_carrier(sK5_existence_l1_pre_topc_A)))),powerset(the_carrier(sK5_existence_l1_pre_topc_A))),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f516,plain,
( spl0_64
<=> ! [X0] : true = ifeq(element(X0,powerset(the_carrier(sK5_existence_l1_pre_topc_A))),true,element(interior(sK5_existence_l1_pre_topc_A,X0),powerset(the_carrier(sK5_existence_l1_pre_topc_A))),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f522,plain,
( true = ifeq(true,true,element(interior(sK5_existence_l1_pre_topc_A,sK4_existence_m1_subset_1_B(powerset(the_carrier(sK5_existence_l1_pre_topc_A)))),powerset(the_carrier(sK5_existence_l1_pre_topc_A))),true)
| ~ spl0_8
| ~ spl0_64 ),
inference(superposition,[],[f517,f62]) ).
fof(f517,plain,
( ! [X0] : true = ifeq(element(X0,powerset(the_carrier(sK5_existence_l1_pre_topc_A))),true,element(interior(sK5_existence_l1_pre_topc_A,X0),powerset(the_carrier(sK5_existence_l1_pre_topc_A))),true)
| ~ spl0_64 ),
inference(avatar_component_clause,[],[f516]) ).
fof(f1177,plain,
( spl0_97
| ~ spl0_8
| ~ spl0_63 ),
inference(avatar_split_clause,[],[f521,f512,f61,f1174]) ).
fof(f1174,plain,
( spl0_97
<=> true = ifeq(true,true,element(topstr_closure(sK5_existence_l1_pre_topc_A,sK4_existence_m1_subset_1_B(powerset(the_carrier(sK5_existence_l1_pre_topc_A)))),powerset(the_carrier(sK5_existence_l1_pre_topc_A))),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f512,plain,
( spl0_63
<=> ! [X0] : true = ifeq(element(X0,powerset(the_carrier(sK5_existence_l1_pre_topc_A))),true,element(topstr_closure(sK5_existence_l1_pre_topc_A,X0),powerset(the_carrier(sK5_existence_l1_pre_topc_A))),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f521,plain,
( true = ifeq(true,true,element(topstr_closure(sK5_existence_l1_pre_topc_A,sK4_existence_m1_subset_1_B(powerset(the_carrier(sK5_existence_l1_pre_topc_A)))),powerset(the_carrier(sK5_existence_l1_pre_topc_A))),true)
| ~ spl0_8
| ~ spl0_63 ),
inference(superposition,[],[f513,f62]) ).
fof(f513,plain,
( ! [X0] : true = ifeq(element(X0,powerset(the_carrier(sK5_existence_l1_pre_topc_A))),true,element(topstr_closure(sK5_existence_l1_pre_topc_A,X0),powerset(the_carrier(sK5_existence_l1_pre_topc_A))),true)
| ~ spl0_63 ),
inference(avatar_component_clause,[],[f512]) ).
fof(f1143,plain,
( spl0_96
| ~ spl0_9
| ~ spl0_62 ),
inference(avatar_split_clause,[],[f519,f493,f65,f1141]) ).
fof(f1141,plain,
( spl0_96
<=> ! [X0] : sK4_existence_m1_subset_1_B(powerset(X0)) = subset_complement(X0,subset_complement(X0,sK4_existence_m1_subset_1_B(powerset(X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f1075,plain,
( spl0_95
| ~ spl0_10
| ~ spl0_61 ),
inference(avatar_split_clause,[],[f490,f487,f69,f1073]) ).
fof(f487,plain,
( spl0_61
<=> ! [X0] : true = ifeq(true,true,element(subset_complement(X0,sK4_existence_m1_subset_1_B(powerset(X0))),powerset(X0)),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f490,plain,
( ! [X0] : true = element(subset_complement(X0,sK4_existence_m1_subset_1_B(powerset(X0))),powerset(X0))
| ~ spl0_10
| ~ spl0_61 ),
inference(superposition,[],[f488,f70]) ).
fof(f488,plain,
( ! [X0] : true = ifeq(true,true,element(subset_complement(X0,sK4_existence_m1_subset_1_B(powerset(X0))),powerset(X0)),true)
| ~ spl0_61 ),
inference(avatar_component_clause,[],[f487]) ).
fof(f1065,plain,
( spl0_94
| ~ spl0_10
| ~ spl0_56 ),
inference(avatar_split_clause,[],[f474,f446,f69,f1063]) ).
fof(f1063,plain,
( spl0_94
<=> ! [X0] : true = subset(sK4_existence_m1_subset_1_B(powerset(X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f446,plain,
( spl0_56
<=> ! [X0] : true = ifeq(true,true,subset(sK4_existence_m1_subset_1_B(powerset(X0)),X0),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f474,plain,
( ! [X0] : true = subset(sK4_existence_m1_subset_1_B(powerset(X0)),X0)
| ~ spl0_10
| ~ spl0_56 ),
inference(superposition,[],[f447,f70]) ).
fof(f447,plain,
( ! [X0] : true = ifeq(true,true,subset(sK4_existence_m1_subset_1_B(powerset(X0)),X0),true)
| ~ spl0_56 ),
inference(avatar_component_clause,[],[f446]) ).
fof(f1059,plain,
( spl0_93
| ~ spl0_8
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f412,f408,f61,f1056]) ).
fof(f412,plain,
( interior(sK2_t51_tops_1_A,sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A)))) = ifeq2(true,true,subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A)))))),interior(sK2_t51_tops_1_A,sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A)))))
| ~ spl0_8
| ~ spl0_50 ),
inference(superposition,[],[f409,f62]) ).
fof(f1025,plain,
( spl0_92
| ~ spl0_10
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f439,f432,f69,f1023]) ).
fof(f432,plain,
( spl0_53
<=> ! [X0] : true = ifeq(true,true,element(X0,powerset(X0)),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f439,plain,
( ! [X0] : true = element(X0,powerset(X0))
| ~ spl0_10
| ~ spl0_53 ),
inference(superposition,[],[f433,f70]) ).
fof(f433,plain,
( ! [X0] : true = ifeq(true,true,element(X0,powerset(X0)),true)
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f432]) ).
fof(f1019,plain,
( spl0_91
| ~ spl0_8
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f402,f394,f61,f1016]) ).
fof(f402,plain,
( true = ifeq(true,true,ifeq(closed_subset(sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A))),sK2_t51_tops_1_A),true,open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A)))),sK2_t51_tops_1_A),true),true)
| ~ spl0_8
| ~ spl0_48 ),
inference(superposition,[],[f395,f62]) ).
fof(f1014,plain,
( spl0_90
| ~ spl0_10
| ~ spl0_83 ),
inference(avatar_split_clause,[],[f978,f964,f69,f1011]) ).
fof(f1011,plain,
( spl0_90
<=> true = closed_subset(topstr_closure(sK2_t51_tops_1_A,sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A)))),sK2_t51_tops_1_A) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f964,plain,
( spl0_83
<=> true = ifeq(true,true,closed_subset(topstr_closure(sK2_t51_tops_1_A,sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A)))),sK2_t51_tops_1_A),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f978,plain,
( true = closed_subset(topstr_closure(sK2_t51_tops_1_A,sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A)))),sK2_t51_tops_1_A)
| ~ spl0_10
| ~ spl0_83 ),
inference(superposition,[],[f966,f70]) ).
fof(f966,plain,
( true = ifeq(true,true,closed_subset(topstr_closure(sK2_t51_tops_1_A,sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A)))),sK2_t51_tops_1_A),true)
| ~ spl0_83 ),
inference(avatar_component_clause,[],[f964]) ).
fof(f1009,plain,
( spl0_89
| ~ spl0_8
| ~ spl0_10
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f406,f398,f69,f61,f1006]) ).
fof(f1006,plain,
( spl0_89
<=> true = ifeq(open_subset(sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A))),sK2_t51_tops_1_A),true,closed_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A)))),sK2_t51_tops_1_A),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f406,plain,
( true = ifeq(open_subset(sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A))),sK2_t51_tops_1_A),true,closed_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A)))),sK2_t51_tops_1_A),true)
| ~ spl0_8
| ~ spl0_10
| ~ spl0_49 ),
inference(forward_demodulation,[],[f404,f70]) ).
fof(f404,plain,
( true = ifeq(open_subset(sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A))),sK2_t51_tops_1_A),true,ifeq(true,true,closed_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A)))),sK2_t51_tops_1_A),true),true)
| ~ spl0_8
| ~ spl0_49 ),
inference(superposition,[],[f399,f62]) ).
fof(f1001,plain,
( spl0_88
| ~ spl0_10
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f423,f414,f69,f998]) ).
fof(f998,plain,
( spl0_88
<=> true = one_sorted_str(sK5_existence_l1_pre_topc_A) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f414,plain,
( spl0_51
<=> true = ifeq(true,true,one_sorted_str(sK5_existence_l1_pre_topc_A),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f423,plain,
( true = one_sorted_str(sK5_existence_l1_pre_topc_A)
| ~ spl0_10
| ~ spl0_51 ),
inference(superposition,[],[f416,f70]) ).
fof(f416,plain,
( true = ifeq(true,true,one_sorted_str(sK5_existence_l1_pre_topc_A),true)
| ~ spl0_51 ),
inference(avatar_component_clause,[],[f414]) ).
fof(f992,plain,
( spl0_87
| ~ spl0_8
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f373,f367,f61,f989]) ).
fof(f373,plain,
( true = ifeq(true,true,element(interior(sK2_t51_tops_1_A,sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A)))),powerset(the_carrier(sK2_t51_tops_1_A))),true)
| ~ spl0_8
| ~ spl0_44 ),
inference(superposition,[],[f368,f62]) ).
fof(f987,plain,
( spl0_86
| ~ spl0_8
| ~ spl0_43 ),
inference(avatar_split_clause,[],[f371,f363,f61,f984]) ).
fof(f371,plain,
( true = ifeq(true,true,element(topstr_closure(sK2_t51_tops_1_A,sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A)))),powerset(the_carrier(sK2_t51_tops_1_A))),true)
| ~ spl0_8
| ~ spl0_43 ),
inference(superposition,[],[f364,f62]) ).
fof(f977,plain,
( spl0_85
| ~ spl0_14
| ~ spl0_76 ),
inference(avatar_split_clause,[],[f670,f645,f89,f974]) ).
fof(f670,plain,
( true = ifeq(true,true,subset(sK7_rc6_pre_topc_B(sK2_t51_tops_1_A),the_carrier(sK2_t51_tops_1_A)),true)
| ~ spl0_14
| ~ spl0_76 ),
inference(superposition,[],[f90,f647]) ).
fof(f972,plain,
( spl0_84
| ~ spl0_10
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f379,f375,f69,f969]) ).
fof(f969,plain,
( spl0_84
<=> true = ifeq(closed_subset(sK1_t51_tops_1_B,sK2_t51_tops_1_A),true,open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),sK2_t51_tops_1_A),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f375,plain,
( spl0_45
<=> true = ifeq(true,true,ifeq(closed_subset(sK1_t51_tops_1_B,sK2_t51_tops_1_A),true,open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),sK2_t51_tops_1_A),true),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f379,plain,
( true = ifeq(closed_subset(sK1_t51_tops_1_B,sK2_t51_tops_1_A),true,open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),sK2_t51_tops_1_A),true)
| ~ spl0_10
| ~ spl0_45 ),
inference(superposition,[],[f377,f70]) ).
fof(f377,plain,
( true = ifeq(true,true,ifeq(closed_subset(sK1_t51_tops_1_B,sK2_t51_tops_1_A),true,open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),sK2_t51_tops_1_A),true),true)
| ~ spl0_45 ),
inference(avatar_component_clause,[],[f375]) ).
fof(f967,plain,
( spl0_83
| ~ spl0_8
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f361,f357,f61,f964]) ).
fof(f361,plain,
( true = ifeq(true,true,closed_subset(topstr_closure(sK2_t51_tops_1_A,sK4_existence_m1_subset_1_B(powerset(the_carrier(sK2_t51_tops_1_A)))),sK2_t51_tops_1_A),true)
| ~ spl0_8
| ~ spl0_42 ),
inference(superposition,[],[f358,f62]) ).
fof(f936,plain,
( spl0_82
| ~ spl0_9
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f391,f382,f65,f933]) ).
fof(f382,plain,
( spl0_46
<=> interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B) = ifeq2(true,true,subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f391,plain,
( interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B) = subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)))
| ~ spl0_9
| ~ spl0_46 ),
inference(superposition,[],[f384,f66]) ).
fof(f384,plain,
( interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B) = ifeq2(true,true,subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B))
| ~ spl0_46 ),
inference(avatar_component_clause,[],[f382]) ).
fof(f883,plain,
( spl0_81
| ~ spl0_10
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f349,f340,f69,f880]) ).
fof(f756,plain,
( spl0_80
| ~ spl0_10
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f337,f329,f69,f753]) ).
fof(f329,plain,
( spl0_38
<=> true = ifeq(true,true,element(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f337,plain,
( true = element(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A)))
| ~ spl0_10
| ~ spl0_38 ),
inference(superposition,[],[f331,f70]) ).
fof(f331,plain,
( true = ifeq(true,true,element(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),true)
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f329]) ).
fof(f751,plain,
( spl0_79
| ~ spl0_10
| ~ spl0_37 ),
inference(avatar_split_clause,[],[f335,f324,f69,f748]) ).
fof(f746,plain,
( spl0_78
| ~ spl0_9
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f333,f319,f65,f743]) ).
fof(f319,plain,
( spl0_36
<=> sK1_t51_tops_1_B = ifeq2(true,true,subset_complement(the_carrier(sK2_t51_tops_1_A),subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),sK1_t51_tops_1_B) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f333,plain,
( sK1_t51_tops_1_B = subset_complement(the_carrier(sK2_t51_tops_1_A),subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))
| ~ spl0_9
| ~ spl0_36 ),
inference(superposition,[],[f321,f66]) ).
fof(f321,plain,
( sK1_t51_tops_1_B = ifeq2(true,true,subset_complement(the_carrier(sK2_t51_tops_1_A),subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),sK1_t51_tops_1_B)
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f319]) ).
fof(f653,plain,
( spl0_77
| ~ spl0_10
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f316,f305,f69,f650]) ).
fof(f648,plain,
( spl0_76
| ~ spl0_10
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f309,f300,f69,f645]) ).
fof(f637,plain,
( spl0_75
| ~ spl0_8
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f214,f210,f61,f635]) ).
fof(f210,plain,
( spl0_25
<=> ! [X0,X1] : interior(X0,X1) = ifeq2(element(X1,powerset(the_carrier(X0))),true,ifeq2(top_str(X0),true,subset_complement(the_carrier(X0),topstr_closure(X0,subset_complement(the_carrier(X0),X1))),interior(X0,X1)),interior(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f214,plain,
( ! [X0] : interior(X0,sK4_existence_m1_subset_1_B(powerset(the_carrier(X0)))) = ifeq2(true,true,ifeq2(top_str(X0),true,subset_complement(the_carrier(X0),topstr_closure(X0,subset_complement(the_carrier(X0),sK4_existence_m1_subset_1_B(powerset(the_carrier(X0)))))),interior(X0,sK4_existence_m1_subset_1_B(powerset(the_carrier(X0))))),interior(X0,sK4_existence_m1_subset_1_B(powerset(the_carrier(X0)))))
| ~ spl0_8
| ~ spl0_25 ),
inference(superposition,[],[f211,f62]) ).
fof(f211,plain,
( ! [X0,X1] : interior(X0,X1) = ifeq2(element(X1,powerset(the_carrier(X0))),true,ifeq2(top_str(X0),true,subset_complement(the_carrier(X0),topstr_closure(X0,subset_complement(the_carrier(X0),X1))),interior(X0,X1)),interior(X0,X1))
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f210]) ).
fof(f621,plain,
( spl0_74
| ~ spl0_8
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f230,f222,f61,f619]) ).
fof(f222,plain,
( spl0_26
<=> ! [X0,X1] : true = ifeq(element(X1,powerset(the_carrier(X0))),true,ifeq(closed_subset(X1,X0),true,ifeq(topological_space(X0),true,ifeq(top_str(X0),true,open_subset(subset_complement(the_carrier(X0),X1),X0),true),true),true),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f230,plain,
( ! [X0] : true = ifeq(true,true,ifeq(closed_subset(sK4_existence_m1_subset_1_B(powerset(the_carrier(X0))),X0),true,ifeq(topological_space(X0),true,ifeq(top_str(X0),true,open_subset(subset_complement(the_carrier(X0),sK4_existence_m1_subset_1_B(powerset(the_carrier(X0)))),X0),true),true),true),true)
| ~ spl0_8
| ~ spl0_26 ),
inference(superposition,[],[f223,f62]) ).
fof(f223,plain,
( ! [X0,X1] : true = ifeq(element(X1,powerset(the_carrier(X0))),true,ifeq(closed_subset(X1,X0),true,ifeq(topological_space(X0),true,ifeq(top_str(X0),true,open_subset(subset_complement(the_carrier(X0),X1),X0),true),true),true),true)
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f222]) ).
fof(f588,plain,
( spl0_73
| ~ spl0_8
| ~ spl0_10
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f255,f226,f69,f61,f586]) ).
fof(f586,plain,
( spl0_73
<=> ! [X0] : true = ifeq(open_subset(sK4_existence_m1_subset_1_B(powerset(the_carrier(X0))),X0),true,ifeq(topological_space(X0),true,ifeq(top_str(X0),true,closed_subset(subset_complement(the_carrier(X0),sK4_existence_m1_subset_1_B(powerset(the_carrier(X0)))),X0),true),true),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f226,plain,
( spl0_27
<=> ! [X0,X1] : true = ifeq(open_subset(X1,X0),true,ifeq(element(X1,powerset(the_carrier(X0))),true,ifeq(topological_space(X0),true,ifeq(top_str(X0),true,closed_subset(subset_complement(the_carrier(X0),X1),X0),true),true),true),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f255,plain,
( ! [X0] : true = ifeq(open_subset(sK4_existence_m1_subset_1_B(powerset(the_carrier(X0))),X0),true,ifeq(topological_space(X0),true,ifeq(top_str(X0),true,closed_subset(subset_complement(the_carrier(X0),sK4_existence_m1_subset_1_B(powerset(the_carrier(X0)))),X0),true),true),true)
| ~ spl0_8
| ~ spl0_10
| ~ spl0_27 ),
inference(forward_demodulation,[],[f246,f70]) ).
fof(f246,plain,
( ! [X0] : true = ifeq(open_subset(sK4_existence_m1_subset_1_B(powerset(the_carrier(X0))),X0),true,ifeq(true,true,ifeq(topological_space(X0),true,ifeq(top_str(X0),true,closed_subset(subset_complement(the_carrier(X0),sK4_existence_m1_subset_1_B(powerset(the_carrier(X0)))),X0),true),true),true),true)
| ~ spl0_8
| ~ spl0_27 ),
inference(superposition,[],[f227,f62]) ).
fof(f227,plain,
( ! [X0,X1] : true = ifeq(open_subset(X1,X0),true,ifeq(element(X1,powerset(the_carrier(X0))),true,ifeq(topological_space(X0),true,ifeq(top_str(X0),true,closed_subset(subset_complement(the_carrier(X0),X1),X0),true),true),true),true)
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f226]) ).
fof(f581,plain,
( spl0_72
| ~ spl0_6
| ~ spl0_10
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f262,f226,f69,f52,f579]) ).
fof(f52,plain,
( spl0_6
<=> true = top_str(sK5_existence_l1_pre_topc_A) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f262,plain,
( ! [X0] : true = ifeq(open_subset(X0,sK5_existence_l1_pre_topc_A),true,ifeq(element(X0,powerset(the_carrier(sK5_existence_l1_pre_topc_A))),true,ifeq(topological_space(sK5_existence_l1_pre_topc_A),true,closed_subset(subset_complement(the_carrier(sK5_existence_l1_pre_topc_A),X0),sK5_existence_l1_pre_topc_A),true),true),true)
| ~ spl0_6
| ~ spl0_10
| ~ spl0_27 ),
inference(forward_demodulation,[],[f249,f70]) ).
fof(f249,plain,
( ! [X0] : true = ifeq(open_subset(X0,sK5_existence_l1_pre_topc_A),true,ifeq(element(X0,powerset(the_carrier(sK5_existence_l1_pre_topc_A))),true,ifeq(topological_space(sK5_existence_l1_pre_topc_A),true,ifeq(true,true,closed_subset(subset_complement(the_carrier(sK5_existence_l1_pre_topc_A),X0),sK5_existence_l1_pre_topc_A),true),true),true),true)
| ~ spl0_6
| ~ spl0_27 ),
inference(superposition,[],[f227,f54]) ).
fof(f54,plain,
( true = top_str(sK5_existence_l1_pre_topc_A)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f52]) ).
fof(f577,plain,
( spl0_71
| ~ spl0_6
| ~ spl0_10
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f244,f222,f69,f52,f575]) ).
fof(f244,plain,
( ! [X0] : true = ifeq(element(X0,powerset(the_carrier(sK5_existence_l1_pre_topc_A))),true,ifeq(closed_subset(X0,sK5_existence_l1_pre_topc_A),true,ifeq(topological_space(sK5_existence_l1_pre_topc_A),true,open_subset(subset_complement(the_carrier(sK5_existence_l1_pre_topc_A),X0),sK5_existence_l1_pre_topc_A),true),true),true)
| ~ spl0_6
| ~ spl0_10
| ~ spl0_26 ),
inference(forward_demodulation,[],[f233,f70]) ).
fof(f233,plain,
( ! [X0] : true = ifeq(element(X0,powerset(the_carrier(sK5_existence_l1_pre_topc_A))),true,ifeq(closed_subset(X0,sK5_existence_l1_pre_topc_A),true,ifeq(topological_space(sK5_existence_l1_pre_topc_A),true,ifeq(true,true,open_subset(subset_complement(the_carrier(sK5_existence_l1_pre_topc_A),X0),sK5_existence_l1_pre_topc_A),true),true),true),true)
| ~ spl0_6
| ~ spl0_26 ),
inference(superposition,[],[f223,f54]) ).
fof(f561,plain,
( spl0_70
| ~ spl0_8
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f194,f185,f61,f559]) ).
fof(f185,plain,
( spl0_23
<=> ! [X0,X1] : true = ifeq(element(X1,powerset(the_carrier(X0))),true,ifeq(topological_space(X0),true,ifeq(top_str(X0),true,closed_subset(topstr_closure(X0,X1),X0),true),true),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f194,plain,
( ! [X0] : true = ifeq(true,true,ifeq(topological_space(X0),true,ifeq(top_str(X0),true,closed_subset(topstr_closure(X0,sK4_existence_m1_subset_1_B(powerset(the_carrier(X0)))),X0),true),true),true)
| ~ spl0_8
| ~ spl0_23 ),
inference(superposition,[],[f186,f62]) ).
fof(f186,plain,
( ! [X0,X1] : true = ifeq(element(X1,powerset(the_carrier(X0))),true,ifeq(topological_space(X0),true,ifeq(top_str(X0),true,closed_subset(topstr_closure(X0,X1),X0),true),true),true)
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f185]) ).
fof(f556,plain,
( spl0_69
| ~ spl0_6
| ~ spl0_9
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f220,f210,f65,f52,f554]) ).
fof(f220,plain,
( ! [X0] : interior(sK5_existence_l1_pre_topc_A,X0) = ifeq2(element(X0,powerset(the_carrier(sK5_existence_l1_pre_topc_A))),true,subset_complement(the_carrier(sK5_existence_l1_pre_topc_A),topstr_closure(sK5_existence_l1_pre_topc_A,subset_complement(the_carrier(sK5_existence_l1_pre_topc_A),X0))),interior(sK5_existence_l1_pre_topc_A,X0))
| ~ spl0_6
| ~ spl0_9
| ~ spl0_25 ),
inference(forward_demodulation,[],[f216,f66]) ).
fof(f216,plain,
( ! [X0] : interior(sK5_existence_l1_pre_topc_A,X0) = ifeq2(element(X0,powerset(the_carrier(sK5_existence_l1_pre_topc_A))),true,ifeq2(true,true,subset_complement(the_carrier(sK5_existence_l1_pre_topc_A),topstr_closure(sK5_existence_l1_pre_topc_A,subset_complement(the_carrier(sK5_existence_l1_pre_topc_A),X0))),interior(sK5_existence_l1_pre_topc_A,X0)),interior(sK5_existence_l1_pre_topc_A,X0))
| ~ spl0_6
| ~ spl0_25 ),
inference(superposition,[],[f211,f54]) ).
fof(f546,plain,
( spl0_68
| ~ spl0_10
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f297,f293,f69,f543]) ).
fof(f293,plain,
( spl0_32
<=> true = ifeq(true,true,closed_subset(topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f297,plain,
( true = closed_subset(topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A)
| ~ spl0_10
| ~ spl0_32 ),
inference(superposition,[],[f295,f70]) ).
fof(f295,plain,
( true = ifeq(true,true,closed_subset(topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A),true)
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f293]) ).
fof(f535,plain,
( spl0_67
| ~ spl0_8
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f177,f165,f61,f533]) ).
fof(f165,plain,
( spl0_22
<=> ! [X0,X1] : true = ifeq(element(X1,powerset(the_carrier(X0))),true,ifeq(top_str(X0),true,element(interior(X0,X1),powerset(the_carrier(X0))),true),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f177,plain,
( ! [X0] : true = ifeq(true,true,ifeq(top_str(X0),true,element(interior(X0,sK4_existence_m1_subset_1_B(powerset(the_carrier(X0)))),powerset(the_carrier(X0))),true),true)
| ~ spl0_8
| ~ spl0_22 ),
inference(superposition,[],[f166,f62]) ).
fof(f166,plain,
( ! [X0,X1] : true = ifeq(element(X1,powerset(the_carrier(X0))),true,ifeq(top_str(X0),true,element(interior(X0,X1),powerset(the_carrier(X0))),true),true)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f165]) ).
fof(f531,plain,
( spl0_66
| ~ spl0_8
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f169,f161,f61,f529]) ).
fof(f161,plain,
( spl0_21
<=> ! [X0,X1] : true = ifeq(element(X1,powerset(the_carrier(X0))),true,ifeq(top_str(X0),true,element(topstr_closure(X0,X1),powerset(the_carrier(X0))),true),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f169,plain,
( ! [X0] : true = ifeq(true,true,ifeq(top_str(X0),true,element(topstr_closure(X0,sK4_existence_m1_subset_1_B(powerset(the_carrier(X0)))),powerset(the_carrier(X0))),true),true)
| ~ spl0_8
| ~ spl0_21 ),
inference(superposition,[],[f162,f62]) ).
fof(f162,plain,
( ! [X0,X1] : true = ifeq(element(X1,powerset(the_carrier(X0))),true,ifeq(top_str(X0),true,element(topstr_closure(X0,X1),powerset(the_carrier(X0))),true),true)
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f526,plain,
( spl0_65
| ~ spl0_6
| ~ spl0_10
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f208,f185,f69,f52,f524]) ).
fof(f208,plain,
( ! [X0] : true = ifeq(element(X0,powerset(the_carrier(sK5_existence_l1_pre_topc_A))),true,ifeq(topological_space(sK5_existence_l1_pre_topc_A),true,closed_subset(topstr_closure(sK5_existence_l1_pre_topc_A,X0),sK5_existence_l1_pre_topc_A),true),true)
| ~ spl0_6
| ~ spl0_10
| ~ spl0_23 ),
inference(forward_demodulation,[],[f197,f70]) ).
fof(f197,plain,
( ! [X0] : true = ifeq(element(X0,powerset(the_carrier(sK5_existence_l1_pre_topc_A))),true,ifeq(topological_space(sK5_existence_l1_pre_topc_A),true,ifeq(true,true,closed_subset(topstr_closure(sK5_existence_l1_pre_topc_A,X0),sK5_existence_l1_pre_topc_A),true),true),true)
| ~ spl0_6
| ~ spl0_23 ),
inference(superposition,[],[f186,f54]) ).
fof(f518,plain,
( spl0_64
| ~ spl0_6
| ~ spl0_10
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f183,f165,f69,f52,f516]) ).
fof(f183,plain,
( ! [X0] : true = ifeq(element(X0,powerset(the_carrier(sK5_existence_l1_pre_topc_A))),true,element(interior(sK5_existence_l1_pre_topc_A,X0),powerset(the_carrier(sK5_existence_l1_pre_topc_A))),true)
| ~ spl0_6
| ~ spl0_10
| ~ spl0_22 ),
inference(forward_demodulation,[],[f179,f70]) ).
fof(f179,plain,
( ! [X0] : true = ifeq(element(X0,powerset(the_carrier(sK5_existence_l1_pre_topc_A))),true,ifeq(true,true,element(interior(sK5_existence_l1_pre_topc_A,X0),powerset(the_carrier(sK5_existence_l1_pre_topc_A))),true),true)
| ~ spl0_6
| ~ spl0_22 ),
inference(superposition,[],[f166,f54]) ).
fof(f514,plain,
( spl0_63
| ~ spl0_6
| ~ spl0_10
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f175,f161,f69,f52,f512]) ).
fof(f175,plain,
( ! [X0] : true = ifeq(element(X0,powerset(the_carrier(sK5_existence_l1_pre_topc_A))),true,element(topstr_closure(sK5_existence_l1_pre_topc_A,X0),powerset(the_carrier(sK5_existence_l1_pre_topc_A))),true)
| ~ spl0_6
| ~ spl0_10
| ~ spl0_21 ),
inference(forward_demodulation,[],[f171,f70]) ).
fof(f171,plain,
( ! [X0] : true = ifeq(element(X0,powerset(the_carrier(sK5_existence_l1_pre_topc_A))),true,ifeq(true,true,element(topstr_closure(sK5_existence_l1_pre_topc_A,X0),powerset(the_carrier(sK5_existence_l1_pre_topc_A))),true),true)
| ~ spl0_6
| ~ spl0_21 ),
inference(superposition,[],[f162,f54]) ).
fof(f495,plain,
( spl0_62
| ~ spl0_8
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f103,f99,f61,f493]) ).
fof(f103,plain,
( ! [X0] : sK4_existence_m1_subset_1_B(powerset(X0)) = ifeq2(true,true,subset_complement(X0,subset_complement(X0,sK4_existence_m1_subset_1_B(powerset(X0)))),sK4_existence_m1_subset_1_B(powerset(X0)))
| ~ spl0_8
| ~ spl0_15 ),
inference(superposition,[],[f100,f62]) ).
fof(f489,plain,
( spl0_61
| ~ spl0_8
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f109,f105,f61,f487]) ).
fof(f109,plain,
( ! [X0] : true = ifeq(true,true,element(subset_complement(X0,sK4_existence_m1_subset_1_B(powerset(X0))),powerset(X0)),true)
| ~ spl0_8
| ~ spl0_16 ),
inference(superposition,[],[f106,f62]) ).
fof(f485,plain,
( spl0_60
| ~ spl0_6
| ~ spl0_10
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f159,f141,f69,f52,f482]) ).
fof(f482,plain,
( spl0_60
<=> true = ifeq(topological_space(sK5_existence_l1_pre_topc_A),true,element(sK3_rc1_tops_1_B(sK5_existence_l1_pre_topc_A),powerset(the_carrier(sK5_existence_l1_pre_topc_A))),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f141,plain,
( spl0_20
<=> ! [X0] : true = ifeq(topological_space(X0),true,ifeq(top_str(X0),true,element(sK3_rc1_tops_1_B(X0),powerset(the_carrier(X0))),true),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f159,plain,
( true = ifeq(topological_space(sK5_existence_l1_pre_topc_A),true,element(sK3_rc1_tops_1_B(sK5_existence_l1_pre_topc_A),powerset(the_carrier(sK5_existence_l1_pre_topc_A))),true)
| ~ spl0_6
| ~ spl0_10
| ~ spl0_20 ),
inference(forward_demodulation,[],[f154,f70]) ).
fof(f154,plain,
( true = ifeq(topological_space(sK5_existence_l1_pre_topc_A),true,ifeq(true,true,element(sK3_rc1_tops_1_B(sK5_existence_l1_pre_topc_A),powerset(the_carrier(sK5_existence_l1_pre_topc_A))),true),true)
| ~ spl0_6
| ~ spl0_20 ),
inference(superposition,[],[f142,f54]) ).
fof(f142,plain,
( ! [X0] : true = ifeq(topological_space(X0),true,ifeq(top_str(X0),true,element(sK3_rc1_tops_1_B(X0),powerset(the_carrier(X0))),true),true)
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f141]) ).
fof(f480,plain,
( spl0_59
| ~ spl0_6
| ~ spl0_10
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f151,f137,f69,f52,f477]) ).
fof(f477,plain,
( spl0_59
<=> true = ifeq(topological_space(sK5_existence_l1_pre_topc_A),true,element(sK7_rc6_pre_topc_B(sK5_existence_l1_pre_topc_A),powerset(the_carrier(sK5_existence_l1_pre_topc_A))),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f137,plain,
( spl0_19
<=> ! [X0] : true = ifeq(topological_space(X0),true,ifeq(top_str(X0),true,element(sK7_rc6_pre_topc_B(X0),powerset(the_carrier(X0))),true),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f151,plain,
( true = ifeq(topological_space(sK5_existence_l1_pre_topc_A),true,element(sK7_rc6_pre_topc_B(sK5_existence_l1_pre_topc_A),powerset(the_carrier(sK5_existence_l1_pre_topc_A))),true)
| ~ spl0_6
| ~ spl0_10
| ~ spl0_19 ),
inference(forward_demodulation,[],[f146,f70]) ).
fof(f146,plain,
( true = ifeq(topological_space(sK5_existence_l1_pre_topc_A),true,ifeq(true,true,element(sK7_rc6_pre_topc_B(sK5_existence_l1_pre_topc_A),powerset(the_carrier(sK5_existence_l1_pre_topc_A))),true),true)
| ~ spl0_6
| ~ spl0_19 ),
inference(superposition,[],[f138,f54]) ).
fof(f138,plain,
( ! [X0] : true = ifeq(topological_space(X0),true,ifeq(top_str(X0),true,element(sK7_rc6_pre_topc_B(X0),powerset(the_carrier(X0))),true),true)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f458,plain,
( spl0_58
| ~ spl0_6
| ~ spl0_10
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f135,f115,f69,f52,f455]) ).
fof(f455,plain,
( spl0_58
<=> true = ifeq(topological_space(sK5_existence_l1_pre_topc_A),true,open_subset(sK3_rc1_tops_1_B(sK5_existence_l1_pre_topc_A),sK5_existence_l1_pre_topc_A),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f115,plain,
( spl0_18
<=> ! [X0] : true = ifeq(topological_space(X0),true,ifeq(top_str(X0),true,open_subset(sK3_rc1_tops_1_B(X0),X0),true),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f135,plain,
( true = ifeq(topological_space(sK5_existence_l1_pre_topc_A),true,open_subset(sK3_rc1_tops_1_B(sK5_existence_l1_pre_topc_A),sK5_existence_l1_pre_topc_A),true)
| ~ spl0_6
| ~ spl0_10
| ~ spl0_18 ),
inference(forward_demodulation,[],[f130,f70]) ).
fof(f130,plain,
( true = ifeq(topological_space(sK5_existence_l1_pre_topc_A),true,ifeq(true,true,open_subset(sK3_rc1_tops_1_B(sK5_existence_l1_pre_topc_A),sK5_existence_l1_pre_topc_A),true),true)
| ~ spl0_6
| ~ spl0_18 ),
inference(superposition,[],[f116,f54]) ).
fof(f116,plain,
( ! [X0] : true = ifeq(topological_space(X0),true,ifeq(top_str(X0),true,open_subset(sK3_rc1_tops_1_B(X0),X0),true),true)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f453,plain,
( spl0_57
| ~ spl0_6
| ~ spl0_10
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f125,f111,f69,f52,f450]) ).
fof(f450,plain,
( spl0_57
<=> true = ifeq(topological_space(sK5_existence_l1_pre_topc_A),true,closed_subset(sK7_rc6_pre_topc_B(sK5_existence_l1_pre_topc_A),sK5_existence_l1_pre_topc_A),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f111,plain,
( spl0_17
<=> ! [X0] : true = ifeq(topological_space(X0),true,ifeq(top_str(X0),true,closed_subset(sK7_rc6_pre_topc_B(X0),X0),true),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f125,plain,
( true = ifeq(topological_space(sK5_existence_l1_pre_topc_A),true,closed_subset(sK7_rc6_pre_topc_B(sK5_existence_l1_pre_topc_A),sK5_existence_l1_pre_topc_A),true)
| ~ spl0_6
| ~ spl0_10
| ~ spl0_17 ),
inference(forward_demodulation,[],[f120,f70]) ).
fof(f120,plain,
( true = ifeq(topological_space(sK5_existence_l1_pre_topc_A),true,ifeq(true,true,closed_subset(sK7_rc6_pre_topc_B(sK5_existence_l1_pre_topc_A),sK5_existence_l1_pre_topc_A),true),true)
| ~ spl0_6
| ~ spl0_17 ),
inference(superposition,[],[f112,f54]) ).
fof(f112,plain,
( ! [X0] : true = ifeq(topological_space(X0),true,ifeq(top_str(X0),true,closed_subset(sK7_rc6_pre_topc_B(X0),X0),true),true)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f448,plain,
( spl0_56
| ~ spl0_8
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f96,f89,f61,f446]) ).
fof(f96,plain,
( ! [X0] : true = ifeq(true,true,subset(sK4_existence_m1_subset_1_B(powerset(X0)),X0),true)
| ~ spl0_8
| ~ spl0_14 ),
inference(superposition,[],[f90,f62]) ).
fof(f444,plain,
( spl0_55
| ~ spl0_8
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f94,f80,f61,f442]) ).
fof(f442,plain,
( spl0_55
<=> ! [X0] : true = ifeq(subset(sK4_existence_m1_subset_1_B(powerset(X0)),X0),true,true,true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f94,plain,
( ! [X0] : true = ifeq(subset(sK4_existence_m1_subset_1_B(powerset(X0)),X0),true,true,true)
| ~ spl0_8
| ~ spl0_12 ),
inference(superposition,[],[f81,f62]) ).
fof(f438,plain,
( spl0_54
| ~ spl0_7
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f97,f89,f57,f436]) ).
fof(f436,plain,
( spl0_54
<=> ! [X0] : true = ifeq(element(X0,powerset(X0)),true,true,true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f57,plain,
( spl0_7
<=> ! [X0] : true = subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f97,plain,
( ! [X0] : true = ifeq(element(X0,powerset(X0)),true,true,true)
| ~ spl0_7
| ~ spl0_14 ),
inference(superposition,[],[f90,f58]) ).
fof(f58,plain,
( ! [X0] : true = subset(X0,X0)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f434,plain,
( spl0_53
| ~ spl0_7
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f92,f80,f57,f432]) ).
fof(f92,plain,
( ! [X0] : true = ifeq(true,true,element(X0,powerset(X0)),true)
| ~ spl0_7
| ~ spl0_12 ),
inference(superposition,[],[f81,f58]) ).
fof(f422,plain,
( spl0_52
| ~ spl0_5
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f78,f73,f47,f419]) ).
fof(f419,plain,
( spl0_52
<=> true = ifeq(top_str(sK6_existence_l1_struct_0_A),true,true,true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f47,plain,
( spl0_5
<=> true = one_sorted_str(sK6_existence_l1_struct_0_A) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f73,plain,
( spl0_11
<=> ! [X0] : true = ifeq(top_str(X0),true,one_sorted_str(X0),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f78,plain,
( true = ifeq(top_str(sK6_existence_l1_struct_0_A),true,true,true)
| ~ spl0_5
| ~ spl0_11 ),
inference(superposition,[],[f74,f49]) ).
fof(f49,plain,
( true = one_sorted_str(sK6_existence_l1_struct_0_A)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f74,plain,
( ! [X0] : true = ifeq(top_str(X0),true,one_sorted_str(X0),true)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f417,plain,
( spl0_51
| ~ spl0_6
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f77,f73,f52,f414]) ).
fof(f77,plain,
( true = ifeq(true,true,one_sorted_str(sK5_existence_l1_pre_topc_A),true)
| ~ spl0_6
| ~ spl0_11 ),
inference(superposition,[],[f74,f54]) ).
fof(f410,plain,
( spl0_50
| ~ spl0_1
| ~ spl0_9
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f219,f210,f65,f27,f408]) ).
fof(f27,plain,
( spl0_1
<=> true = top_str(sK2_t51_tops_1_A) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f219,plain,
( ! [X0] : interior(sK2_t51_tops_1_A,X0) = ifeq2(element(X0,powerset(the_carrier(sK2_t51_tops_1_A))),true,subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),X0))),interior(sK2_t51_tops_1_A,X0))
| ~ spl0_1
| ~ spl0_9
| ~ spl0_25 ),
inference(forward_demodulation,[],[f215,f66]) ).
fof(f215,plain,
( ! [X0] : interior(sK2_t51_tops_1_A,X0) = ifeq2(element(X0,powerset(the_carrier(sK2_t51_tops_1_A))),true,ifeq2(true,true,subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),X0))),interior(sK2_t51_tops_1_A,X0)),interior(sK2_t51_tops_1_A,X0))
| ~ spl0_1
| ~ spl0_25 ),
inference(superposition,[],[f211,f29]) ).
fof(f29,plain,
( true = top_str(sK2_t51_tops_1_A)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f27]) ).
fof(f400,plain,
( spl0_49
| ~ spl0_1
| ~ spl0_2
| ~ spl0_10
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f258,f226,f69,f32,f27,f398]) ).
fof(f32,plain,
( spl0_2
<=> true = topological_space(sK2_t51_tops_1_A) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f258,plain,
( ! [X0] : true = ifeq(open_subset(X0,sK2_t51_tops_1_A),true,ifeq(element(X0,powerset(the_carrier(sK2_t51_tops_1_A))),true,closed_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),X0),sK2_t51_tops_1_A),true),true)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_10
| ~ spl0_27 ),
inference(forward_demodulation,[],[f257,f70]) ).
fof(f257,plain,
( ! [X0] : true = ifeq(open_subset(X0,sK2_t51_tops_1_A),true,ifeq(element(X0,powerset(the_carrier(sK2_t51_tops_1_A))),true,ifeq(true,true,closed_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),X0),sK2_t51_tops_1_A),true),true),true)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_10
| ~ spl0_27 ),
inference(forward_demodulation,[],[f256,f29]) ).
fof(f256,plain,
( ! [X0] : true = ifeq(open_subset(X0,sK2_t51_tops_1_A),true,ifeq(element(X0,powerset(the_carrier(sK2_t51_tops_1_A))),true,ifeq(top_str(sK2_t51_tops_1_A),true,closed_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),X0),sK2_t51_tops_1_A),true),true),true)
| ~ spl0_2
| ~ spl0_10
| ~ spl0_27 ),
inference(forward_demodulation,[],[f247,f70]) ).
fof(f247,plain,
( ! [X0] : true = ifeq(open_subset(X0,sK2_t51_tops_1_A),true,ifeq(element(X0,powerset(the_carrier(sK2_t51_tops_1_A))),true,ifeq(true,true,ifeq(top_str(sK2_t51_tops_1_A),true,closed_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),X0),sK2_t51_tops_1_A),true),true),true),true)
| ~ spl0_2
| ~ spl0_27 ),
inference(superposition,[],[f227,f34]) ).
fof(f34,plain,
( true = topological_space(sK2_t51_tops_1_A)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f32]) ).
fof(f396,plain,
( spl0_48
| ~ spl0_1
| ~ spl0_2
| ~ spl0_10
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f240,f222,f69,f32,f27,f394]) ).
fof(f240,plain,
( ! [X0] : true = ifeq(element(X0,powerset(the_carrier(sK2_t51_tops_1_A))),true,ifeq(closed_subset(X0,sK2_t51_tops_1_A),true,open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),X0),sK2_t51_tops_1_A),true),true)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_10
| ~ spl0_26 ),
inference(forward_demodulation,[],[f239,f70]) ).
fof(f239,plain,
( ! [X0] : true = ifeq(element(X0,powerset(the_carrier(sK2_t51_tops_1_A))),true,ifeq(closed_subset(X0,sK2_t51_tops_1_A),true,ifeq(true,true,open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),X0),sK2_t51_tops_1_A),true),true),true)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_10
| ~ spl0_26 ),
inference(forward_demodulation,[],[f238,f29]) ).
fof(f238,plain,
( ! [X0] : true = ifeq(element(X0,powerset(the_carrier(sK2_t51_tops_1_A))),true,ifeq(closed_subset(X0,sK2_t51_tops_1_A),true,ifeq(top_str(sK2_t51_tops_1_A),true,open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),X0),sK2_t51_tops_1_A),true),true),true)
| ~ spl0_2
| ~ spl0_10
| ~ spl0_26 ),
inference(forward_demodulation,[],[f231,f70]) ).
fof(f231,plain,
( ! [X0] : true = ifeq(element(X0,powerset(the_carrier(sK2_t51_tops_1_A))),true,ifeq(closed_subset(X0,sK2_t51_tops_1_A),true,ifeq(true,true,ifeq(top_str(sK2_t51_tops_1_A),true,open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),X0),sK2_t51_tops_1_A),true),true),true),true)
| ~ spl0_2
| ~ spl0_26 ),
inference(superposition,[],[f223,f34]) ).
fof(f390,plain,
( spl0_47
| ~ spl0_10
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f290,f282,f69,f387]) ).
fof(f282,plain,
( spl0_31
<=> true = ifeq(true,true,open_subset(sK3_rc1_tops_1_B(sK2_t51_tops_1_A),sK2_t51_tops_1_A),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f290,plain,
( true = open_subset(sK3_rc1_tops_1_B(sK2_t51_tops_1_A),sK2_t51_tops_1_A)
| ~ spl0_10
| ~ spl0_31 ),
inference(superposition,[],[f284,f70]) ).
fof(f284,plain,
( true = ifeq(true,true,open_subset(sK3_rc1_tops_1_B(sK2_t51_tops_1_A),sK2_t51_tops_1_A),true)
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f282]) ).
fof(f385,plain,
( spl0_46
| ~ spl0_1
| ~ spl0_3
| ~ spl0_9
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f218,f210,f65,f37,f27,f382]) ).
fof(f37,plain,
( spl0_3
<=> true = element(sK1_t51_tops_1_B,powerset(the_carrier(sK2_t51_tops_1_A))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f218,plain,
( interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B) = ifeq2(true,true,subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B))
| ~ spl0_1
| ~ spl0_3
| ~ spl0_9
| ~ spl0_25 ),
inference(forward_demodulation,[],[f217,f66]) ).
fof(f217,plain,
( interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B) = ifeq2(true,true,ifeq2(true,true,subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B))
| ~ spl0_1
| ~ spl0_3
| ~ spl0_25 ),
inference(forward_demodulation,[],[f213,f29]) ).
fof(f213,plain,
( interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B) = ifeq2(true,true,ifeq2(top_str(sK2_t51_tops_1_A),true,subset_complement(the_carrier(sK2_t51_tops_1_A),topstr_closure(sK2_t51_tops_1_A,subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B))),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B)),interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B))
| ~ spl0_3
| ~ spl0_25 ),
inference(superposition,[],[f211,f39]) ).
fof(f39,plain,
( true = element(sK1_t51_tops_1_B,powerset(the_carrier(sK2_t51_tops_1_A)))
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f37]) ).
fof(f378,plain,
( spl0_45
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_10
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f237,f222,f69,f37,f32,f27,f375]) ).
fof(f237,plain,
( true = ifeq(true,true,ifeq(closed_subset(sK1_t51_tops_1_B,sK2_t51_tops_1_A),true,open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),sK2_t51_tops_1_A),true),true)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_10
| ~ spl0_26 ),
inference(forward_demodulation,[],[f236,f70]) ).
fof(f236,plain,
( true = ifeq(true,true,ifeq(closed_subset(sK1_t51_tops_1_B,sK2_t51_tops_1_A),true,ifeq(true,true,open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),sK2_t51_tops_1_A),true),true),true)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_10
| ~ spl0_26 ),
inference(forward_demodulation,[],[f235,f34]) ).
fof(f235,plain,
( true = ifeq(true,true,ifeq(closed_subset(sK1_t51_tops_1_B,sK2_t51_tops_1_A),true,ifeq(topological_space(sK2_t51_tops_1_A),true,open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),sK2_t51_tops_1_A),true),true),true)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_26 ),
inference(forward_demodulation,[],[f234,f70]) ).
fof(f234,plain,
( true = ifeq(true,true,ifeq(closed_subset(sK1_t51_tops_1_B,sK2_t51_tops_1_A),true,ifeq(topological_space(sK2_t51_tops_1_A),true,ifeq(true,true,open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),sK2_t51_tops_1_A),true),true),true),true)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_26 ),
inference(forward_demodulation,[],[f229,f29]) ).
fof(f229,plain,
( true = ifeq(true,true,ifeq(closed_subset(sK1_t51_tops_1_B,sK2_t51_tops_1_A),true,ifeq(topological_space(sK2_t51_tops_1_A),true,ifeq(top_str(sK2_t51_tops_1_A),true,open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),sK2_t51_tops_1_A),true),true),true),true)
| ~ spl0_3
| ~ spl0_26 ),
inference(superposition,[],[f223,f39]) ).
fof(f369,plain,
( spl0_44
| ~ spl0_1
| ~ spl0_10
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f182,f165,f69,f27,f367]) ).
fof(f182,plain,
( ! [X0] : true = ifeq(element(X0,powerset(the_carrier(sK2_t51_tops_1_A))),true,element(interior(sK2_t51_tops_1_A,X0),powerset(the_carrier(sK2_t51_tops_1_A))),true)
| ~ spl0_1
| ~ spl0_10
| ~ spl0_22 ),
inference(forward_demodulation,[],[f178,f70]) ).
fof(f178,plain,
( ! [X0] : true = ifeq(element(X0,powerset(the_carrier(sK2_t51_tops_1_A))),true,ifeq(true,true,element(interior(sK2_t51_tops_1_A,X0),powerset(the_carrier(sK2_t51_tops_1_A))),true),true)
| ~ spl0_1
| ~ spl0_22 ),
inference(superposition,[],[f166,f29]) ).
fof(f365,plain,
( spl0_43
| ~ spl0_1
| ~ spl0_10
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f174,f161,f69,f27,f363]) ).
fof(f174,plain,
( ! [X0] : true = ifeq(element(X0,powerset(the_carrier(sK2_t51_tops_1_A))),true,element(topstr_closure(sK2_t51_tops_1_A,X0),powerset(the_carrier(sK2_t51_tops_1_A))),true)
| ~ spl0_1
| ~ spl0_10
| ~ spl0_21 ),
inference(forward_demodulation,[],[f170,f70]) ).
fof(f170,plain,
( ! [X0] : true = ifeq(element(X0,powerset(the_carrier(sK2_t51_tops_1_A))),true,ifeq(true,true,element(topstr_closure(sK2_t51_tops_1_A,X0),powerset(the_carrier(sK2_t51_tops_1_A))),true),true)
| ~ spl0_1
| ~ spl0_21 ),
inference(superposition,[],[f162,f29]) ).
fof(f359,plain,
( spl0_42
| ~ spl0_1
| ~ spl0_2
| ~ spl0_10
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f204,f185,f69,f32,f27,f357]) ).
fof(f204,plain,
( ! [X0] : true = ifeq(element(X0,powerset(the_carrier(sK2_t51_tops_1_A))),true,closed_subset(topstr_closure(sK2_t51_tops_1_A,X0),sK2_t51_tops_1_A),true)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_10
| ~ spl0_23 ),
inference(forward_demodulation,[],[f203,f70]) ).
fof(f203,plain,
( ! [X0] : true = ifeq(element(X0,powerset(the_carrier(sK2_t51_tops_1_A))),true,ifeq(true,true,closed_subset(topstr_closure(sK2_t51_tops_1_A,X0),sK2_t51_tops_1_A),true),true)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_10
| ~ spl0_23 ),
inference(forward_demodulation,[],[f202,f29]) ).
fof(f202,plain,
( ! [X0] : true = ifeq(element(X0,powerset(the_carrier(sK2_t51_tops_1_A))),true,ifeq(top_str(sK2_t51_tops_1_A),true,closed_subset(topstr_closure(sK2_t51_tops_1_A,X0),sK2_t51_tops_1_A),true),true)
| ~ spl0_2
| ~ spl0_10
| ~ spl0_23 ),
inference(forward_demodulation,[],[f195,f70]) ).
fof(f195,plain,
( ! [X0] : true = ifeq(element(X0,powerset(the_carrier(sK2_t51_tops_1_A))),true,ifeq(true,true,ifeq(top_str(sK2_t51_tops_1_A),true,closed_subset(topstr_closure(sK2_t51_tops_1_A,X0),sK2_t51_tops_1_A),true),true),true)
| ~ spl0_2
| ~ spl0_23 ),
inference(superposition,[],[f186,f34]) ).
fof(f355,plain,
( spl0_41
| ~ spl0_10
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f288,f274,f69,f352]) ).
fof(f274,plain,
( spl0_30
<=> true = ifeq(true,true,closed_subset(sK7_rc6_pre_topc_B(sK2_t51_tops_1_A),sK2_t51_tops_1_A),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f288,plain,
( true = closed_subset(sK7_rc6_pre_topc_B(sK2_t51_tops_1_A),sK2_t51_tops_1_A)
| ~ spl0_10
| ~ spl0_30 ),
inference(superposition,[],[f276,f70]) ).
fof(f276,plain,
( true = ifeq(true,true,closed_subset(sK7_rc6_pre_topc_B(sK2_t51_tops_1_A),sK2_t51_tops_1_A),true)
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f274]) ).
fof(f348,plain,
( spl0_40
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_10
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f254,f226,f69,f37,f32,f27,f345]) ).
fof(f345,plain,
( spl0_40
<=> true = ifeq(open_subset(sK1_t51_tops_1_B,sK2_t51_tops_1_A),true,closed_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),sK2_t51_tops_1_A),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f254,plain,
( true = ifeq(open_subset(sK1_t51_tops_1_B,sK2_t51_tops_1_A),true,closed_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),sK2_t51_tops_1_A),true)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_10
| ~ spl0_27 ),
inference(forward_demodulation,[],[f253,f70]) ).
fof(f253,plain,
( true = ifeq(open_subset(sK1_t51_tops_1_B,sK2_t51_tops_1_A),true,ifeq(true,true,closed_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),sK2_t51_tops_1_A),true),true)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_10
| ~ spl0_27 ),
inference(forward_demodulation,[],[f252,f34]) ).
fof(f252,plain,
( true = ifeq(open_subset(sK1_t51_tops_1_B,sK2_t51_tops_1_A),true,ifeq(topological_space(sK2_t51_tops_1_A),true,closed_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),sK2_t51_tops_1_A),true),true)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_27 ),
inference(forward_demodulation,[],[f251,f70]) ).
fof(f251,plain,
( true = ifeq(open_subset(sK1_t51_tops_1_B,sK2_t51_tops_1_A),true,ifeq(topological_space(sK2_t51_tops_1_A),true,ifeq(true,true,closed_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),sK2_t51_tops_1_A),true),true),true)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_27 ),
inference(forward_demodulation,[],[f250,f29]) ).
fof(f250,plain,
( true = ifeq(open_subset(sK1_t51_tops_1_B,sK2_t51_tops_1_A),true,ifeq(topological_space(sK2_t51_tops_1_A),true,ifeq(top_str(sK2_t51_tops_1_A),true,closed_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),sK2_t51_tops_1_A),true),true),true)
| ~ spl0_3
| ~ spl0_10
| ~ spl0_27 ),
inference(forward_demodulation,[],[f245,f70]) ).
fof(f245,plain,
( true = ifeq(open_subset(sK1_t51_tops_1_B,sK2_t51_tops_1_A),true,ifeq(true,true,ifeq(topological_space(sK2_t51_tops_1_A),true,ifeq(top_str(sK2_t51_tops_1_A),true,closed_subset(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),sK2_t51_tops_1_A),true),true),true),true)
| ~ spl0_3
| ~ spl0_27 ),
inference(superposition,[],[f227,f39]) ).
fof(f343,plain,
( spl0_39
| ~ spl0_3
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f108,f105,f37,f340]) ).
fof(f108,plain,
( true = ifeq(true,true,element(subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),true)
| ~ spl0_3
| ~ spl0_16 ),
inference(superposition,[],[f106,f39]) ).
fof(f332,plain,
( spl0_38
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f181,f165,f69,f37,f27,f329]) ).
fof(f181,plain,
( true = ifeq(true,true,element(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),true)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_22 ),
inference(forward_demodulation,[],[f180,f70]) ).
fof(f180,plain,
( true = ifeq(true,true,ifeq(true,true,element(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),true),true)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_22 ),
inference(forward_demodulation,[],[f176,f29]) ).
fof(f176,plain,
( true = ifeq(true,true,ifeq(top_str(sK2_t51_tops_1_A),true,element(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),true),true)
| ~ spl0_3
| ~ spl0_22 ),
inference(superposition,[],[f166,f39]) ).
fof(f327,plain,
( spl0_37
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f173,f161,f69,f37,f27,f324]) ).
fof(f173,plain,
( true = ifeq(true,true,element(topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),true)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_21 ),
inference(forward_demodulation,[],[f172,f70]) ).
fof(f172,plain,
( true = ifeq(true,true,ifeq(true,true,element(topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),true),true)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_21 ),
inference(forward_demodulation,[],[f168,f29]) ).
fof(f168,plain,
( true = ifeq(true,true,ifeq(top_str(sK2_t51_tops_1_A),true,element(topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B),powerset(the_carrier(sK2_t51_tops_1_A))),true),true)
| ~ spl0_3
| ~ spl0_21 ),
inference(superposition,[],[f162,f39]) ).
fof(f322,plain,
( spl0_36
| ~ spl0_3
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f102,f99,f37,f319]) ).
fof(f102,plain,
( sK1_t51_tops_1_B = ifeq2(true,true,subset_complement(the_carrier(sK2_t51_tops_1_A),subset_complement(the_carrier(sK2_t51_tops_1_A),sK1_t51_tops_1_B)),sK1_t51_tops_1_B)
| ~ spl0_3
| ~ spl0_15 ),
inference(superposition,[],[f100,f39]) ).
fof(f315,plain,
( spl0_35
| ~ spl0_10
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f286,f269,f69,f312]) ).
fof(f312,plain,
( spl0_35
<=> true = subset(sK1_t51_tops_1_B,the_carrier(sK2_t51_tops_1_A)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f269,plain,
( spl0_29
<=> true = ifeq(true,true,subset(sK1_t51_tops_1_B,the_carrier(sK2_t51_tops_1_A)),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f286,plain,
( true = subset(sK1_t51_tops_1_B,the_carrier(sK2_t51_tops_1_A))
| ~ spl0_10
| ~ spl0_29 ),
inference(superposition,[],[f271,f70]) ).
fof(f271,plain,
( true = ifeq(true,true,subset(sK1_t51_tops_1_B,the_carrier(sK2_t51_tops_1_A)),true)
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f269]) ).
fof(f308,plain,
( spl0_34
| ~ spl0_1
| ~ spl0_2
| ~ spl0_10
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f156,f141,f69,f32,f27,f305]) ).
fof(f156,plain,
( true = ifeq(true,true,element(sK3_rc1_tops_1_B(sK2_t51_tops_1_A),powerset(the_carrier(sK2_t51_tops_1_A))),true)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_10
| ~ spl0_20 ),
inference(forward_demodulation,[],[f155,f70]) ).
fof(f155,plain,
( true = ifeq(true,true,ifeq(true,true,element(sK3_rc1_tops_1_B(sK2_t51_tops_1_A),powerset(the_carrier(sK2_t51_tops_1_A))),true),true)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_20 ),
inference(forward_demodulation,[],[f152,f29]) ).
fof(f152,plain,
( true = ifeq(true,true,ifeq(top_str(sK2_t51_tops_1_A),true,element(sK3_rc1_tops_1_B(sK2_t51_tops_1_A),powerset(the_carrier(sK2_t51_tops_1_A))),true),true)
| ~ spl0_2
| ~ spl0_20 ),
inference(superposition,[],[f142,f34]) ).
fof(f303,plain,
( spl0_33
| ~ spl0_1
| ~ spl0_2
| ~ spl0_10
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f148,f137,f69,f32,f27,f300]) ).
fof(f148,plain,
( true = ifeq(true,true,element(sK7_rc6_pre_topc_B(sK2_t51_tops_1_A),powerset(the_carrier(sK2_t51_tops_1_A))),true)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_10
| ~ spl0_19 ),
inference(forward_demodulation,[],[f147,f70]) ).
fof(f147,plain,
( true = ifeq(true,true,ifeq(true,true,element(sK7_rc6_pre_topc_B(sK2_t51_tops_1_A),powerset(the_carrier(sK2_t51_tops_1_A))),true),true)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_19 ),
inference(forward_demodulation,[],[f144,f29]) ).
fof(f144,plain,
( true = ifeq(true,true,ifeq(top_str(sK2_t51_tops_1_A),true,element(sK7_rc6_pre_topc_B(sK2_t51_tops_1_A),powerset(the_carrier(sK2_t51_tops_1_A))),true),true)
| ~ spl0_2
| ~ spl0_19 ),
inference(superposition,[],[f138,f34]) ).
fof(f296,plain,
( spl0_32
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_10
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f201,f185,f69,f37,f32,f27,f293]) ).
fof(f201,plain,
( true = ifeq(true,true,closed_subset(topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A),true)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_10
| ~ spl0_23 ),
inference(forward_demodulation,[],[f200,f70]) ).
fof(f200,plain,
( true = ifeq(true,true,ifeq(true,true,closed_subset(topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A),true),true)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_10
| ~ spl0_23 ),
inference(forward_demodulation,[],[f199,f34]) ).
fof(f199,plain,
( true = ifeq(true,true,ifeq(topological_space(sK2_t51_tops_1_A),true,closed_subset(topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A),true),true)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_23 ),
inference(forward_demodulation,[],[f198,f70]) ).
fof(f198,plain,
( true = ifeq(true,true,ifeq(topological_space(sK2_t51_tops_1_A),true,ifeq(true,true,closed_subset(topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A),true),true),true)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_23 ),
inference(forward_demodulation,[],[f193,f29]) ).
fof(f193,plain,
( true = ifeq(true,true,ifeq(topological_space(sK2_t51_tops_1_A),true,ifeq(top_str(sK2_t51_tops_1_A),true,closed_subset(topstr_closure(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A),true),true),true)
| ~ spl0_3
| ~ spl0_23 ),
inference(superposition,[],[f186,f39]) ).
fof(f285,plain,
( spl0_31
| ~ spl0_1
| ~ spl0_2
| ~ spl0_10
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f132,f115,f69,f32,f27,f282]) ).
fof(f132,plain,
( true = ifeq(true,true,open_subset(sK3_rc1_tops_1_B(sK2_t51_tops_1_A),sK2_t51_tops_1_A),true)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_10
| ~ spl0_18 ),
inference(forward_demodulation,[],[f131,f70]) ).
fof(f131,plain,
( true = ifeq(true,true,ifeq(true,true,open_subset(sK3_rc1_tops_1_B(sK2_t51_tops_1_A),sK2_t51_tops_1_A),true),true)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_18 ),
inference(forward_demodulation,[],[f128,f29]) ).
fof(f128,plain,
( true = ifeq(true,true,ifeq(top_str(sK2_t51_tops_1_A),true,open_subset(sK3_rc1_tops_1_B(sK2_t51_tops_1_A),sK2_t51_tops_1_A),true),true)
| ~ spl0_2
| ~ spl0_18 ),
inference(superposition,[],[f116,f34]) ).
fof(f277,plain,
( spl0_30
| ~ spl0_1
| ~ spl0_2
| ~ spl0_10
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f122,f111,f69,f32,f27,f274]) ).
fof(f122,plain,
( true = ifeq(true,true,closed_subset(sK7_rc6_pre_topc_B(sK2_t51_tops_1_A),sK2_t51_tops_1_A),true)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_10
| ~ spl0_17 ),
inference(forward_demodulation,[],[f121,f70]) ).
fof(f121,plain,
( true = ifeq(true,true,ifeq(true,true,closed_subset(sK7_rc6_pre_topc_B(sK2_t51_tops_1_A),sK2_t51_tops_1_A),true),true)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_17 ),
inference(forward_demodulation,[],[f118,f29]) ).
fof(f118,plain,
( true = ifeq(true,true,ifeq(top_str(sK2_t51_tops_1_A),true,closed_subset(sK7_rc6_pre_topc_B(sK2_t51_tops_1_A),sK2_t51_tops_1_A),true),true)
| ~ spl0_2
| ~ spl0_17 ),
inference(superposition,[],[f112,f34]) ).
fof(f272,plain,
( spl0_29
| ~ spl0_3
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f95,f89,f37,f269]) ).
fof(f95,plain,
( true = ifeq(true,true,subset(sK1_t51_tops_1_B,the_carrier(sK2_t51_tops_1_A)),true)
| ~ spl0_3
| ~ spl0_14 ),
inference(superposition,[],[f90,f39]) ).
fof(f267,plain,
( spl0_28
| ~ spl0_3
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f93,f80,f37,f264]) ).
fof(f264,plain,
( spl0_28
<=> true = ifeq(subset(sK1_t51_tops_1_B,the_carrier(sK2_t51_tops_1_A)),true,true,true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f93,plain,
( true = ifeq(subset(sK1_t51_tops_1_B,the_carrier(sK2_t51_tops_1_A)),true,true,true)
| ~ spl0_3
| ~ spl0_12 ),
inference(superposition,[],[f81,f39]) ).
fof(f228,plain,
spl0_27,
inference(avatar_split_clause,[],[f12,f226]) ).
fof(f12,axiom,
! [X0,X1] : true = ifeq(open_subset(X1,X0),true,ifeq(element(X1,powerset(the_carrier(X0))),true,ifeq(topological_space(X0),true,ifeq(top_str(X0),true,closed_subset(subset_complement(the_carrier(X0),X1),X0),true),true),true),true),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_tops_1) ).
fof(f224,plain,
spl0_26,
inference(avatar_split_clause,[],[f3,f222]) ).
fof(f3,axiom,
! [X0,X1] : true = ifeq(element(X1,powerset(the_carrier(X0))),true,ifeq(closed_subset(X1,X0),true,ifeq(topological_space(X0),true,ifeq(top_str(X0),true,open_subset(subset_complement(the_carrier(X0),X1),X0),true),true),true),true),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_tops_1) ).
fof(f212,plain,
spl0_25,
inference(avatar_split_clause,[],[f21,f210]) ).
fof(f21,axiom,
! [X0,X1] : interior(X0,X1) = ifeq2(element(X1,powerset(the_carrier(X0))),true,ifeq2(top_str(X0),true,subset_complement(the_carrier(X0),topstr_closure(X0,subset_complement(the_carrier(X0),X1))),interior(X0,X1)),interior(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tops_1) ).
fof(f192,plain,
( spl0_24
| ~ spl0_10
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f126,f84,f69,f189]) ).
fof(f189,plain,
( spl0_24
<=> true = one_sorted_str(sK2_t51_tops_1_A) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f84,plain,
( spl0_13
<=> true = ifeq(true,true,one_sorted_str(sK2_t51_tops_1_A),true) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f126,plain,
( true = one_sorted_str(sK2_t51_tops_1_A)
| ~ spl0_10
| ~ spl0_13 ),
inference(superposition,[],[f86,f70]) ).
fof(f86,plain,
( true = ifeq(true,true,one_sorted_str(sK2_t51_tops_1_A),true)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f187,plain,
spl0_23,
inference(avatar_split_clause,[],[f11,f185]) ).
fof(f11,axiom,
! [X0,X1] : true = ifeq(element(X1,powerset(the_carrier(X0))),true,ifeq(topological_space(X0),true,ifeq(top_str(X0),true,closed_subset(topstr_closure(X0,X1),X0),true),true),true),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_tops_1) ).
fof(f167,plain,
spl0_22,
inference(avatar_split_clause,[],[f15,f165]) ).
fof(f15,axiom,
! [X0,X1] : true = ifeq(element(X1,powerset(the_carrier(X0))),true,ifeq(top_str(X0),true,element(interior(X0,X1),powerset(the_carrier(X0))),true),true),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_tops_1) ).
fof(f163,plain,
spl0_21,
inference(avatar_split_clause,[],[f10,f161]) ).
fof(f10,axiom,
! [X0,X1] : true = ifeq(element(X1,powerset(the_carrier(X0))),true,ifeq(top_str(X0),true,element(topstr_closure(X0,X1),powerset(the_carrier(X0))),true),true),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_pre_topc) ).
fof(f143,plain,
spl0_20,
inference(avatar_split_clause,[],[f18,f141]) ).
fof(f18,axiom,
! [X0] : true = ifeq(topological_space(X0),true,ifeq(top_str(X0),true,element(sK3_rc1_tops_1_B(X0),powerset(the_carrier(X0))),true),true),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_tops_1) ).
fof(f139,plain,
spl0_19,
inference(avatar_split_clause,[],[f4,f137]) ).
fof(f4,axiom,
! [X0] : true = ifeq(topological_space(X0),true,ifeq(top_str(X0),true,element(sK7_rc6_pre_topc_B(X0),powerset(the_carrier(X0))),true),true),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc6_pre_topc_1) ).
fof(f117,plain,
spl0_18,
inference(avatar_split_clause,[],[f17,f115]) ).
fof(f17,axiom,
! [X0] : true = ifeq(topological_space(X0),true,ifeq(top_str(X0),true,open_subset(sK3_rc1_tops_1_B(X0),X0),true),true),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_tops_1_1) ).
fof(f113,plain,
spl0_17,
inference(avatar_split_clause,[],[f5,f111]) ).
fof(f5,axiom,
! [X0] : true = ifeq(topological_space(X0),true,ifeq(top_str(X0),true,closed_subset(sK7_rc6_pre_topc_B(X0),X0),true),true),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc6_pre_topc) ).
fof(f107,plain,
spl0_16,
inference(avatar_split_clause,[],[f9,f105]) ).
fof(f9,axiom,
! [X0,X1] : true = ifeq(element(X1,powerset(X0)),true,element(subset_complement(X0,X1),powerset(X0)),true),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_subset_1) ).
fof(f101,plain,
spl0_15,
inference(avatar_split_clause,[],[f6,f99]) ).
fof(f6,axiom,
! [X0,X1] : ifeq2(element(X1,powerset(X0)),true,subset_complement(X0,subset_complement(X0,X1)),X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
fof(f91,plain,
spl0_14,
inference(avatar_split_clause,[],[f20,f89]) ).
fof(f20,axiom,
! [X0,X1] : true = ifeq(element(X0,powerset(X1)),true,subset(X0,X1),true),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f87,plain,
( spl0_13
| ~ spl0_1
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f76,f73,f27,f84]) ).
fof(f76,plain,
( true = ifeq(true,true,one_sorted_str(sK2_t51_tops_1_A),true)
| ~ spl0_1
| ~ spl0_11 ),
inference(superposition,[],[f74,f29]) ).
fof(f82,plain,
spl0_12,
inference(avatar_split_clause,[],[f19,f80]) ).
fof(f19,axiom,
! [X0,X1] : true = ifeq(subset(X0,X1),true,element(X0,powerset(X1)),true),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset_1) ).
fof(f75,plain,
spl0_11,
inference(avatar_split_clause,[],[f16,f73]) ).
fof(f16,axiom,
! [X0] : true = ifeq(top_str(X0),true,one_sorted_str(X0),true),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
fof(f71,plain,
spl0_10,
inference(avatar_split_clause,[],[f2,f69]) ).
fof(f2,axiom,
! [X2,X0,X1] : ifeq(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_001) ).
fof(f67,plain,
spl0_9,
inference(avatar_split_clause,[],[f1,f65]) ).
fof(f1,axiom,
! [X2,X0,X1] : ifeq2(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
fof(f63,plain,
spl0_8,
inference(avatar_split_clause,[],[f14,f61]) ).
fof(f14,axiom,
! [X0] : true = element(sK4_existence_m1_subset_1_B(X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f59,plain,
spl0_7,
inference(avatar_split_clause,[],[f7,f57]) ).
fof(f7,axiom,
! [X0] : true = subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f55,plain,
spl0_6,
inference(avatar_split_clause,[],[f13,f52]) ).
fof(f13,axiom,
true = top_str(sK5_existence_l1_pre_topc_A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_pre_topc) ).
fof(f50,plain,
spl0_5,
inference(avatar_split_clause,[],[f8,f47]) ).
fof(f8,axiom,
true = one_sorted_str(sK6_existence_l1_struct_0_A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
fof(f45,plain,
~ spl0_4,
inference(avatar_split_clause,[],[f25,f42]) ).
fof(f25,axiom,
true != open_subset(interior(sK2_t51_tops_1_A,sK1_t51_tops_1_B),sK2_t51_tops_1_A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_tops_1_3) ).
fof(f40,plain,
spl0_3,
inference(avatar_split_clause,[],[f24,f37]) ).
fof(f24,axiom,
true = element(sK1_t51_tops_1_B,powerset(the_carrier(sK2_t51_tops_1_A))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_tops_1_2) ).
fof(f35,plain,
spl0_2,
inference(avatar_split_clause,[],[f23,f32]) ).
fof(f23,axiom,
true = topological_space(sK2_t51_tops_1_A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_tops_1_1) ).
fof(f30,plain,
spl0_1,
inference(avatar_split_clause,[],[f22,f27]) ).
fof(f22,axiom,
true = top_str(sK2_t51_tops_1_A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_tops_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU323-10 : TPTP v8.1.2. Released v7.3.0.
% 0.14/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n005.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri May 3 11:22:26 EDT 2024
% 0.21/0.36 % CPUTime :
% 0.21/0.36 % (26187)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.38 % (26195)WARNING: value z3 for option sas not known
% 0.21/0.38 % (26193)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.38 % (26197)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)
% 0.21/0.38 % (26199)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)
% 0.21/0.38 % (26194)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.38 % (26195)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)
% 0.21/0.38 % (26196)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.38 % (26198)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)
% 0.21/0.39 TRYING [1]
% 0.21/0.39 TRYING [2]
% 0.21/0.40 TRYING [3]
% 0.21/0.41 TRYING [1]
% 0.21/0.41 TRYING [2]
% 0.21/0.43 % (26197)First to succeed.
% 0.21/0.44 % (26197)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-26187"
% 0.21/0.44 % (26197)Refutation found. Thanks to Tanya!
% 0.21/0.44 % SZS status Unsatisfiable for theBenchmark
% 0.21/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.45 % (26197)------------------------------
% 0.21/0.45 % (26197)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.45 % (26197)Termination reason: Refutation
% 0.21/0.45
% 0.21/0.45 % (26197)Memory used [KB]: 1719
% 0.21/0.45 % (26197)Time elapsed: 0.066 s
% 0.21/0.45 % (26197)Instructions burned: 110 (million)
% 0.21/0.45 % (26187)Success in time 0.088 s
%------------------------------------------------------------------------------