TSTP Solution File: SET860-2 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET860-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n008.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 09:19:32 EDT 2024
% Result : Unsatisfiable 0.17s 0.45s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 169
% Syntax : Number of formulae : 515 ( 30 unt; 0 def)
% Number of atoms : 1708 ( 47 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 2073 ( 880 ~;1048 |; 0 &)
% ( 145 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 149 ( 147 usr; 146 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 1140 (1140 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1967,plain,
$false,
inference(avatar_sat_refutation,[],[f29,f34,f38,f42,f46,f50,f54,f58,f62,f66,f70,f74,f79,f83,f98,f102,f106,f110,f114,f118,f131,f135,f139,f158,f162,f166,f173,f184,f190,f196,f202,f215,f221,f225,f229,f233,f237,f241,f245,f312,f321,f325,f329,f333,f392,f396,f405,f409,f413,f417,f467,f494,f500,f527,f531,f602,f606,f626,f663,f674,f678,f684,f690,f694,f698,f702,f706,f710,f714,f718,f722,f726,f730,f734,f738,f764,f785,f789,f797,f803,f807,f817,f822,f827,f832,f837,f852,f857,f862,f868,f872,f876,f880,f891,f899,f903,f947,f953,f957,f1024,f1030,f1036,f1041,f1046,f1061,f1105,f1109,f1113,f1125,f1129,f1133,f1137,f1141,f1145,f1158,f1162,f1166,f1170,f1315,f1439,f1443,f1535,f1571,f1577,f1581,f1585,f1589,f1595,f1601,f1605,f1609,f1677,f1828,f1832,f1836,f1840,f1844,f1871,f1875,f1879,f1883,f1887,f1891,f1895,f1899,f1966]) ).
fof(f1966,plain,
( spl0_2
| ~ spl0_13
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1864,f1675,f77,f31]) ).
fof(f31,plain,
( spl0_2
<=> c_lessequals(v_B,c_Union(v_C,t_a),tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f77,plain,
( spl0_13
<=> ! [X4,X2,X3] :
( c_lessequals(X2,X4,tc_set(X3))
| c_in(c_Main_OsubsetI__1(X2,X4,X3),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f1675,plain,
( spl0_132
<=> ! [X0] :
( ~ c_in(c_Main_OsubsetI__1(X0,c_Union(v_C,t_a),t_a),v_B,t_a)
| c_lessequals(X0,c_Union(v_C,t_a),tc_set(t_a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f1864,plain,
( c_lessequals(v_B,c_Union(v_C,t_a),tc_set(t_a))
| ~ spl0_13
| ~ spl0_132 ),
inference(duplicate_literal_removal,[],[f1848]) ).
fof(f1848,plain,
( c_lessequals(v_B,c_Union(v_C,t_a),tc_set(t_a))
| c_lessequals(v_B,c_Union(v_C,t_a),tc_set(t_a))
| ~ spl0_13
| ~ spl0_132 ),
inference(resolution,[],[f1676,f78]) ).
fof(f78,plain,
( ! [X2,X3,X4] :
( c_in(c_Main_OsubsetI__1(X2,X4,X3),X2,X3)
| c_lessequals(X2,X4,tc_set(X3)) )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f1676,plain,
( ! [X0] :
( ~ c_in(c_Main_OsubsetI__1(X0,c_Union(v_C,t_a),t_a),v_B,t_a)
| c_lessequals(X0,c_Union(v_C,t_a),tc_set(t_a)) )
| ~ spl0_132 ),
inference(avatar_component_clause,[],[f1675]) ).
fof(f1899,plain,
( spl0_145
| ~ spl0_38
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f522,f498,f239,f1897]) ).
fof(f1897,plain,
( spl0_145
<=> ! [X0,X3,X2,X1] :
( c_Main_OsubsetI__1(c_insert(X0,X1,X2),c_union(X3,X1,X2),X2) = X0
| c_lessequals(c_insert(X0,X1,X2),c_union(X3,X1,X2),tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f239,plain,
( spl0_38
<=> ! [X0,X3,X2,X1] :
( c_lessequals(X0,c_union(X1,X2,X3),tc_set(X3))
| ~ c_in(c_Main_OsubsetI__1(X0,c_union(X1,X2,X3),X3),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f498,plain,
( spl0_53
<=> ! [X0,X3,X2,X1] :
( c_in(c_Main_OsubsetI__1(c_insert(X0,X1,X2),X3,X2),X1,X2)
| c_Main_OsubsetI__1(c_insert(X0,X1,X2),X3,X2) = X0
| c_lessequals(c_insert(X0,X1,X2),X3,tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f522,plain,
( ! [X2,X3,X0,X1] :
( c_Main_OsubsetI__1(c_insert(X0,X1,X2),c_union(X3,X1,X2),X2) = X0
| c_lessequals(c_insert(X0,X1,X2),c_union(X3,X1,X2),tc_set(X2)) )
| ~ spl0_38
| ~ spl0_53 ),
inference(duplicate_literal_removal,[],[f502]) ).
fof(f502,plain,
( ! [X2,X3,X0,X1] :
( c_Main_OsubsetI__1(c_insert(X0,X1,X2),c_union(X3,X1,X2),X2) = X0
| c_lessequals(c_insert(X0,X1,X2),c_union(X3,X1,X2),tc_set(X2))
| c_lessequals(c_insert(X0,X1,X2),c_union(X3,X1,X2),tc_set(X2)) )
| ~ spl0_38
| ~ spl0_53 ),
inference(resolution,[],[f499,f240]) ).
fof(f240,plain,
( ! [X2,X3,X0,X1] :
( ~ c_in(c_Main_OsubsetI__1(X0,c_union(X1,X2,X3),X3),X2,X3)
| c_lessequals(X0,c_union(X1,X2,X3),tc_set(X3)) )
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f239]) ).
fof(f499,plain,
( ! [X2,X3,X0,X1] :
( c_in(c_Main_OsubsetI__1(c_insert(X0,X1,X2),X3,X2),X1,X2)
| c_Main_OsubsetI__1(c_insert(X0,X1,X2),X3,X2) = X0
| c_lessequals(c_insert(X0,X1,X2),X3,tc_set(X2)) )
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f498]) ).
fof(f1895,plain,
( spl0_144
| ~ spl0_39
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f521,f498,f243,f1893]) ).
fof(f1893,plain,
( spl0_144
<=> ! [X0,X3,X2,X1] :
( c_Main_OsubsetI__1(c_insert(X0,X1,X2),c_insert(X3,X1,X2),X2) = X0
| c_lessequals(c_insert(X0,X1,X2),c_insert(X3,X1,X2),tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f243,plain,
( spl0_39
<=> ! [X0,X3,X2,X1] :
( c_lessequals(X0,c_insert(X1,X2,X3),tc_set(X3))
| ~ c_in(c_Main_OsubsetI__1(X0,c_insert(X1,X2,X3),X3),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f521,plain,
( ! [X2,X3,X0,X1] :
( c_Main_OsubsetI__1(c_insert(X0,X1,X2),c_insert(X3,X1,X2),X2) = X0
| c_lessequals(c_insert(X0,X1,X2),c_insert(X3,X1,X2),tc_set(X2)) )
| ~ spl0_39
| ~ spl0_53 ),
inference(duplicate_literal_removal,[],[f503]) ).
fof(f503,plain,
( ! [X2,X3,X0,X1] :
( c_Main_OsubsetI__1(c_insert(X0,X1,X2),c_insert(X3,X1,X2),X2) = X0
| c_lessequals(c_insert(X0,X1,X2),c_insert(X3,X1,X2),tc_set(X2))
| c_lessequals(c_insert(X0,X1,X2),c_insert(X3,X1,X2),tc_set(X2)) )
| ~ spl0_39
| ~ spl0_53 ),
inference(resolution,[],[f499,f244]) ).
fof(f244,plain,
( ! [X2,X3,X0,X1] :
( ~ c_in(c_Main_OsubsetI__1(X0,c_insert(X1,X2,X3),X3),X2,X3)
| c_lessequals(X0,c_insert(X1,X2,X3),tc_set(X3)) )
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f243]) ).
fof(f1891,plain,
( spl0_143
| ~ spl0_6
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f482,f465,f48,f1889]) ).
fof(f1889,plain,
( spl0_143
<=> ! [X4,X0,X3,X2,X1] :
( c_in(X0,c_Union(c_inter(X1,c_insert(X2,X3,tc_set(X4)),tc_set(X4)),X4),X4)
| ~ c_in(X2,X1,tc_set(X4))
| ~ c_in(X0,X2,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f48,plain,
( spl0_6
<=> ! [X4,X5,X3] : c_in(X5,c_insert(X5,X4,X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f465,plain,
( spl0_51
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_in(X0,X1,X2)
| c_in(X0,c_Union(c_inter(X3,X4,tc_set(X2)),X2),X2)
| ~ c_in(X1,X3,tc_set(X2))
| ~ c_in(X1,X4,tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f482,plain,
( ! [X2,X3,X0,X1,X4] :
( c_in(X0,c_Union(c_inter(X1,c_insert(X2,X3,tc_set(X4)),tc_set(X4)),X4),X4)
| ~ c_in(X2,X1,tc_set(X4))
| ~ c_in(X0,X2,X4) )
| ~ spl0_6
| ~ spl0_51 ),
inference(resolution,[],[f466,f49]) ).
fof(f49,plain,
( ! [X3,X4,X5] : c_in(X5,c_insert(X5,X4,X3),X3)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f466,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_in(X1,X4,tc_set(X2))
| c_in(X0,c_Union(c_inter(X3,X4,tc_set(X2)),X2),X2)
| ~ c_in(X1,X3,tc_set(X2))
| ~ c_in(X0,X1,X2) )
| ~ spl0_51 ),
inference(avatar_component_clause,[],[f465]) ).
fof(f1887,plain,
( spl0_142
| ~ spl0_19
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f375,f323,f112,f1885]) ).
fof(f1885,plain,
( spl0_142
<=> ! [X4,X0,X3,X2,X1] :
( c_in(X0,c_Union(c_insert(X1,X2,tc_set(X3)),X3),X3)
| ~ c_in(X0,c_Main_OUnionE__1(X4,X2,X3),X3)
| ~ c_in(X4,c_Union(X2,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f112,plain,
( spl0_19
<=> ! [X6,X2,X3] :
( ~ c_in(X2,c_Union(X6,X3),X3)
| c_in(c_Main_OUnionE__1(X2,X6,X3),X6,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f323,plain,
( spl0_42
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_in(X0,X1,X2)
| c_in(X0,c_Union(c_insert(X3,X4,tc_set(X2)),X2),X2)
| ~ c_in(X1,X4,tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f375,plain,
( ! [X2,X3,X0,X1,X4] :
( c_in(X0,c_Union(c_insert(X1,X2,tc_set(X3)),X3),X3)
| ~ c_in(X0,c_Main_OUnionE__1(X4,X2,X3),X3)
| ~ c_in(X4,c_Union(X2,X3),X3) )
| ~ spl0_19
| ~ spl0_42 ),
inference(resolution,[],[f324,f113]) ).
fof(f113,plain,
( ! [X2,X3,X6] :
( c_in(c_Main_OUnionE__1(X2,X6,X3),X6,tc_set(X3))
| ~ c_in(X2,c_Union(X6,X3),X3) )
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f324,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_in(X1,X4,tc_set(X2))
| c_in(X0,c_Union(c_insert(X3,X4,tc_set(X2)),X2),X2)
| ~ c_in(X0,X1,X2) )
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f323]) ).
fof(f1883,plain,
( spl0_141
| ~ spl0_12
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f370,f323,f72,f1881]) ).
fof(f1881,plain,
( spl0_141
<=> ! [X5,X4,X0,X3,X2,X1] :
( c_in(X0,c_Union(c_insert(X1,c_insert(X2,X3,tc_set(X4)),tc_set(X4)),X4),X4)
| ~ c_in(X0,X5,X4)
| ~ c_in(X5,X3,tc_set(X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f72,plain,
( spl0_12
<=> ! [X3,X4,X9,X8] :
( ~ c_in(X8,X4,X3)
| c_in(X8,c_insert(X9,X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f370,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( c_in(X0,c_Union(c_insert(X1,c_insert(X2,X3,tc_set(X4)),tc_set(X4)),X4),X4)
| ~ c_in(X0,X5,X4)
| ~ c_in(X5,X3,tc_set(X4)) )
| ~ spl0_12
| ~ spl0_42 ),
inference(resolution,[],[f324,f73]) ).
fof(f73,plain,
( ! [X3,X8,X9,X4] :
( c_in(X8,c_insert(X9,X4,X3),X3)
| ~ c_in(X8,X4,X3) )
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f1879,plain,
( spl0_140
| ~ spl0_11
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f367,f323,f68,f1877]) ).
fof(f1877,plain,
( spl0_140
<=> ! [X5,X4,X0,X3,X2,X1] :
( c_in(X0,c_Union(c_insert(X1,c_union(X2,X3,tc_set(X4)),tc_set(X4)),X4),X4)
| ~ c_in(X0,X5,X4)
| ~ c_in(X5,X3,tc_set(X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f68,plain,
( spl0_11
<=> ! [X4,X3,X2,X1] :
( ~ c_in(X1,X4,X3)
| c_in(X1,c_union(X2,X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f367,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( c_in(X0,c_Union(c_insert(X1,c_union(X2,X3,tc_set(X4)),tc_set(X4)),X4),X4)
| ~ c_in(X0,X5,X4)
| ~ c_in(X5,X3,tc_set(X4)) )
| ~ spl0_11
| ~ spl0_42 ),
inference(resolution,[],[f324,f69]) ).
fof(f69,plain,
( ! [X2,X3,X1,X4] :
( c_in(X1,c_union(X2,X4,X3),X3)
| ~ c_in(X1,X4,X3) )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f1875,plain,
( spl0_139
| ~ spl0_8
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f364,f323,f56,f1873]) ).
fof(f1873,plain,
( spl0_139
<=> ! [X4,X0,X3,X2,X1] :
( c_in(X0,c_Union(c_insert(X1,c_uminus(X2,tc_set(tc_set(X3))),tc_set(X3)),X3),X3)
| ~ c_in(X0,X4,X3)
| c_in(X4,X2,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f56,plain,
( spl0_8
<=> ! [X2,X1,X3] :
( c_in(X1,X2,X3)
| c_in(X1,c_uminus(X2,tc_set(X3)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f364,plain,
( ! [X2,X3,X0,X1,X4] :
( c_in(X0,c_Union(c_insert(X1,c_uminus(X2,tc_set(tc_set(X3))),tc_set(X3)),X3),X3)
| ~ c_in(X0,X4,X3)
| c_in(X4,X2,tc_set(X3)) )
| ~ spl0_8
| ~ spl0_42 ),
inference(resolution,[],[f324,f57]) ).
fof(f57,plain,
( ! [X2,X3,X1] :
( c_in(X1,c_uminus(X2,tc_set(X3)),X3)
| c_in(X1,X2,X3) )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f1871,plain,
( spl0_138
| ~ spl0_19
| ~ spl0_41 ),
inference(avatar_split_clause,[],[f361,f319,f112,f1869]) ).
fof(f1869,plain,
( spl0_138
<=> ! [X4,X0,X3,X2,X1] :
( c_in(X0,c_Union(c_union(X1,X2,tc_set(X3)),X3),X3)
| ~ c_in(X0,c_Main_OUnionE__1(X4,X2,X3),X3)
| ~ c_in(X4,c_Union(X2,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f319,plain,
( spl0_41
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_in(X0,X1,X2)
| c_in(X0,c_Union(c_union(X3,X4,tc_set(X2)),X2),X2)
| ~ c_in(X1,X4,tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f361,plain,
( ! [X2,X3,X0,X1,X4] :
( c_in(X0,c_Union(c_union(X1,X2,tc_set(X3)),X3),X3)
| ~ c_in(X0,c_Main_OUnionE__1(X4,X2,X3),X3)
| ~ c_in(X4,c_Union(X2,X3),X3) )
| ~ spl0_19
| ~ spl0_41 ),
inference(resolution,[],[f320,f113]) ).
fof(f320,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_in(X1,X4,tc_set(X2))
| c_in(X0,c_Union(c_union(X3,X4,tc_set(X2)),X2),X2)
| ~ c_in(X0,X1,X2) )
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f319]) ).
fof(f1844,plain,
( spl0_137
| ~ spl0_12
| ~ spl0_41 ),
inference(avatar_split_clause,[],[f356,f319,f72,f1842]) ).
fof(f1842,plain,
( spl0_137
<=> ! [X5,X4,X0,X3,X2,X1] :
( c_in(X0,c_Union(c_union(X1,c_insert(X2,X3,tc_set(X4)),tc_set(X4)),X4),X4)
| ~ c_in(X0,X5,X4)
| ~ c_in(X5,X3,tc_set(X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f356,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( c_in(X0,c_Union(c_union(X1,c_insert(X2,X3,tc_set(X4)),tc_set(X4)),X4),X4)
| ~ c_in(X0,X5,X4)
| ~ c_in(X5,X3,tc_set(X4)) )
| ~ spl0_12
| ~ spl0_41 ),
inference(resolution,[],[f320,f73]) ).
fof(f1840,plain,
( spl0_136
| ~ spl0_11
| ~ spl0_41 ),
inference(avatar_split_clause,[],[f353,f319,f68,f1838]) ).
fof(f1838,plain,
( spl0_136
<=> ! [X5,X4,X0,X3,X2,X1] :
( c_in(X0,c_Union(c_union(X1,c_union(X2,X3,tc_set(X4)),tc_set(X4)),X4),X4)
| ~ c_in(X0,X5,X4)
| ~ c_in(X5,X3,tc_set(X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f353,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( c_in(X0,c_Union(c_union(X1,c_union(X2,X3,tc_set(X4)),tc_set(X4)),X4),X4)
| ~ c_in(X0,X5,X4)
| ~ c_in(X5,X3,tc_set(X4)) )
| ~ spl0_11
| ~ spl0_41 ),
inference(resolution,[],[f320,f69]) ).
fof(f1836,plain,
( spl0_135
| ~ spl0_8
| ~ spl0_41 ),
inference(avatar_split_clause,[],[f350,f319,f56,f1834]) ).
fof(f1834,plain,
( spl0_135
<=> ! [X4,X0,X3,X2,X1] :
( c_in(X0,c_Union(c_union(X1,c_uminus(X2,tc_set(tc_set(X3))),tc_set(X3)),X3),X3)
| ~ c_in(X0,X4,X3)
| c_in(X4,X2,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f350,plain,
( ! [X2,X3,X0,X1,X4] :
( c_in(X0,c_Union(c_union(X1,c_uminus(X2,tc_set(tc_set(X3))),tc_set(X3)),X3),X3)
| ~ c_in(X0,X4,X3)
| c_in(X4,X2,tc_set(X3)) )
| ~ spl0_8
| ~ spl0_41 ),
inference(resolution,[],[f320,f57]) ).
fof(f1832,plain,
( spl0_134
| ~ spl0_13
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f343,f310,f77,f1830]) ).
fof(f1830,plain,
( spl0_134
<=> ! [X0,X3,X2,X1] :
( c_in(c_Main_OsubsetI__1(X0,X1,X2),c_Union(c_uminus(X3,tc_set(tc_set(X2))),X2),X2)
| c_in(X0,X3,tc_set(X2))
| c_lessequals(X0,X1,tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f310,plain,
( spl0_40
<=> ! [X0,X3,X2,X1] :
( ~ c_in(X0,X1,X2)
| c_in(X0,c_Union(c_uminus(X3,tc_set(tc_set(X2))),X2),X2)
| c_in(X1,X3,tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f343,plain,
( ! [X2,X3,X0,X1] :
( c_in(c_Main_OsubsetI__1(X0,X1,X2),c_Union(c_uminus(X3,tc_set(tc_set(X2))),X2),X2)
| c_in(X0,X3,tc_set(X2))
| c_lessequals(X0,X1,tc_set(X2)) )
| ~ spl0_13
| ~ spl0_40 ),
inference(resolution,[],[f311,f78]) ).
fof(f311,plain,
( ! [X2,X3,X0,X1] :
( ~ c_in(X0,X1,X2)
| c_in(X0,c_Union(c_uminus(X3,tc_set(tc_set(X2))),X2),X2)
| c_in(X1,X3,tc_set(X2)) )
| ~ spl0_40 ),
inference(avatar_component_clause,[],[f310]) ).
fof(f1828,plain,
( spl0_133
| ~ spl0_23
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f216,f213,f137,f1826]) ).
fof(f1826,plain,
( spl0_133
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_in(X0,X1,tc_set(X2))
| ~ c_in(X3,X0,X2)
| c_in(X3,c_Union(c_Union(c_insert(X1,X4,tc_set(tc_set(X2))),tc_set(X2)),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f137,plain,
( spl0_23
<=> ! [X3,X7,X6,X2] :
( ~ c_in(X2,X7,X3)
| ~ c_in(X7,X6,tc_set(X3))
| c_in(X2,c_Union(X6,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f213,plain,
( spl0_32
<=> ! [X0,X3,X2,X1] :
( ~ c_in(X0,X1,X2)
| c_in(X0,c_Union(c_insert(X1,X3,tc_set(X2)),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f216,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_in(X0,X1,tc_set(X2))
| ~ c_in(X3,X0,X2)
| c_in(X3,c_Union(c_Union(c_insert(X1,X4,tc_set(tc_set(X2))),tc_set(X2)),X2),X2) )
| ~ spl0_23
| ~ spl0_32 ),
inference(resolution,[],[f214,f138]) ).
fof(f138,plain,
( ! [X2,X3,X6,X7] :
( ~ c_in(X7,X6,tc_set(X3))
| ~ c_in(X2,X7,X3)
| c_in(X2,c_Union(X6,X3),X3) )
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f214,plain,
( ! [X2,X3,X0,X1] :
( c_in(X0,c_Union(c_insert(X1,X3,tc_set(X2)),X2),X2)
| ~ c_in(X0,X1,X2) )
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f213]) ).
fof(f1677,plain,
( spl0_132
| ~ spl0_14
| ~ spl0_94 ),
inference(avatar_split_clause,[],[f1561,f886,f81,f1675]) ).
fof(f81,plain,
( spl0_14
<=> ! [X4,X2,X3] :
( c_lessequals(X2,X4,tc_set(X3))
| ~ c_in(c_Main_OsubsetI__1(X2,X4,X3),X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f886,plain,
( spl0_94
<=> ! [X1] :
( ~ c_in(X1,v_B,t_a)
| c_in(X1,c_Union(v_C,t_a),t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f1561,plain,
( ! [X0] :
( ~ c_in(c_Main_OsubsetI__1(X0,c_Union(v_C,t_a),t_a),v_B,t_a)
| c_lessequals(X0,c_Union(v_C,t_a),tc_set(t_a)) )
| ~ spl0_14
| ~ spl0_94 ),
inference(resolution,[],[f887,f82]) ).
fof(f82,plain,
( ! [X2,X3,X4] :
( ~ c_in(c_Main_OsubsetI__1(X2,X4,X3),X4,X3)
| c_lessequals(X2,X4,tc_set(X3)) )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f887,plain,
( ! [X1] :
( c_in(X1,c_Union(v_C,t_a),t_a)
| ~ c_in(X1,v_B,t_a) )
| ~ spl0_94 ),
inference(avatar_component_clause,[],[f886]) ).
fof(f1609,plain,
( spl0_131
| ~ spl0_58 ),
inference(avatar_split_clause,[],[f659,f624,f1607]) ).
fof(f1607,plain,
( spl0_131
<=> ! [X2,X0,X1] :
( c_in(c_Main_OUnionE__1(X0,c_union(X1,X1,tc_set(X2)),X2),X1,tc_set(X2))
| ~ c_in(X0,c_Union(c_union(X1,X1,tc_set(X2)),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f624,plain,
( spl0_58
<=> ! [X0,X3,X2,X1] :
( c_in(c_Main_OUnionE__1(X0,c_union(X1,X2,tc_set(X3)),X3),X2,tc_set(X3))
| c_in(c_Main_OUnionE__1(X0,c_union(X1,X2,tc_set(X3)),X3),X1,tc_set(X3))
| ~ c_in(X0,c_Union(c_union(X1,X2,tc_set(X3)),X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f659,plain,
( ! [X2,X0,X1] :
( c_in(c_Main_OUnionE__1(X0,c_union(X1,X1,tc_set(X2)),X2),X1,tc_set(X2))
| ~ c_in(X0,c_Union(c_union(X1,X1,tc_set(X2)),X2),X2) )
| ~ spl0_58 ),
inference(factoring,[],[f625]) ).
fof(f625,plain,
( ! [X2,X3,X0,X1] :
( c_in(c_Main_OUnionE__1(X0,c_union(X1,X2,tc_set(X3)),X3),X2,tc_set(X3))
| c_in(c_Main_OUnionE__1(X0,c_union(X1,X2,tc_set(X3)),X3),X1,tc_set(X3))
| ~ c_in(X0,c_Union(c_union(X1,X2,tc_set(X3)),X3),X3) )
| ~ spl0_58 ),
inference(avatar_component_clause,[],[f624]) ).
fof(f1605,plain,
( spl0_130
| ~ spl0_5
| ~ spl0_58 ),
inference(avatar_split_clause,[],[f656,f624,f44,f1603]) ).
fof(f1603,plain,
( spl0_130
<=> ! [X2,X0,X1] :
( c_in(c_Main_OUnionE__1(X0,c_union(c_emptyset,X1,tc_set(X2)),X2),X1,tc_set(X2))
| ~ c_in(X0,c_Union(c_union(c_emptyset,X1,tc_set(X2)),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f44,plain,
( spl0_5
<=> ! [X8,X3] : ~ c_in(X8,c_emptyset,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f656,plain,
( ! [X2,X0,X1] :
( c_in(c_Main_OUnionE__1(X0,c_union(c_emptyset,X1,tc_set(X2)),X2),X1,tc_set(X2))
| ~ c_in(X0,c_Union(c_union(c_emptyset,X1,tc_set(X2)),X2),X2) )
| ~ spl0_5
| ~ spl0_58 ),
inference(resolution,[],[f625,f45]) ).
fof(f45,plain,
( ! [X3,X8] : ~ c_in(X8,c_emptyset,X3)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f1601,plain,
( spl0_129
| ~ spl0_5
| ~ spl0_58 ),
inference(avatar_split_clause,[],[f640,f624,f44,f1599]) ).
fof(f1599,plain,
( spl0_129
<=> ! [X2,X0,X1] :
( c_in(c_Main_OUnionE__1(X0,c_union(X1,c_emptyset,tc_set(X2)),X2),X1,tc_set(X2))
| ~ c_in(X0,c_Union(c_union(X1,c_emptyset,tc_set(X2)),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f640,plain,
( ! [X2,X0,X1] :
( c_in(c_Main_OUnionE__1(X0,c_union(X1,c_emptyset,tc_set(X2)),X2),X1,tc_set(X2))
| ~ c_in(X0,c_Union(c_union(X1,c_emptyset,tc_set(X2)),X2),X2) )
| ~ spl0_5
| ~ spl0_58 ),
inference(resolution,[],[f625,f45]) ).
fof(f1595,plain,
( spl0_128
| ~ spl0_30
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f579,f529,f194,f1593]) ).
fof(f1593,plain,
( spl0_128
<=> ! [X2,X0,X1] :
( c_in(c_Main_OsubsetI__1(c_union(c_Union(c_emptyset,X0),X1,X0),X2,X0),X1,X0)
| c_lessequals(c_union(c_Union(c_emptyset,X0),X1,X0),X2,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f194,plain,
( spl0_30
<=> ! [X0,X1] : ~ c_in(X0,c_Union(c_emptyset,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f529,plain,
( spl0_55
<=> ! [X0,X3,X2,X1] :
( c_in(c_Main_OsubsetI__1(c_union(X0,X1,X2),X3,X2),X1,X2)
| c_in(c_Main_OsubsetI__1(c_union(X0,X1,X2),X3,X2),X0,X2)
| c_lessequals(c_union(X0,X1,X2),X3,tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f579,plain,
( ! [X2,X0,X1] :
( c_in(c_Main_OsubsetI__1(c_union(c_Union(c_emptyset,X0),X1,X0),X2,X0),X1,X0)
| c_lessequals(c_union(c_Union(c_emptyset,X0),X1,X0),X2,tc_set(X0)) )
| ~ spl0_30
| ~ spl0_55 ),
inference(resolution,[],[f530,f195]) ).
fof(f195,plain,
( ! [X0,X1] : ~ c_in(X0,c_Union(c_emptyset,X1),X1)
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f194]) ).
fof(f530,plain,
( ! [X2,X3,X0,X1] :
( c_in(c_Main_OsubsetI__1(c_union(X0,X1,X2),X3,X2),X1,X2)
| c_in(c_Main_OsubsetI__1(c_union(X0,X1,X2),X3,X2),X0,X2)
| c_lessequals(c_union(X0,X1,X2),X3,tc_set(X2)) )
| ~ spl0_55 ),
inference(avatar_component_clause,[],[f529]) ).
fof(f1589,plain,
( spl0_127
| ~ spl0_30
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f558,f529,f194,f1587]) ).
fof(f1587,plain,
( spl0_127
<=> ! [X2,X0,X1] :
( c_in(c_Main_OsubsetI__1(c_union(X0,c_Union(c_emptyset,X1),X1),X2,X1),X0,X1)
| c_lessequals(c_union(X0,c_Union(c_emptyset,X1),X1),X2,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f558,plain,
( ! [X2,X0,X1] :
( c_in(c_Main_OsubsetI__1(c_union(X0,c_Union(c_emptyset,X1),X1),X2,X1),X0,X1)
| c_lessequals(c_union(X0,c_Union(c_emptyset,X1),X1),X2,tc_set(X1)) )
| ~ spl0_30
| ~ spl0_55 ),
inference(resolution,[],[f530,f195]) ).
fof(f1585,plain,
( spl0_126
| ~ spl0_12
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f342,f310,f72,f1583]) ).
fof(f1583,plain,
( spl0_126
<=> ! [X4,X0,X3,X2,X1] :
( c_in(X0,c_Union(c_uminus(X1,tc_set(tc_set(X2))),X2),X2)
| c_in(c_insert(X3,X4,X2),X1,tc_set(X2))
| ~ c_in(X0,X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f342,plain,
( ! [X2,X3,X0,X1,X4] :
( c_in(X0,c_Union(c_uminus(X1,tc_set(tc_set(X2))),X2),X2)
| c_in(c_insert(X3,X4,X2),X1,tc_set(X2))
| ~ c_in(X0,X4,X2) )
| ~ spl0_12
| ~ spl0_40 ),
inference(resolution,[],[f311,f73]) ).
fof(f1581,plain,
( spl0_125
| ~ spl0_11
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f339,f310,f68,f1579]) ).
fof(f1579,plain,
( spl0_125
<=> ! [X4,X0,X3,X2,X1] :
( c_in(X0,c_Union(c_uminus(X1,tc_set(tc_set(X2))),X2),X2)
| c_in(c_union(X3,X4,X2),X1,tc_set(X2))
| ~ c_in(X0,X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f339,plain,
( ! [X2,X3,X0,X1,X4] :
( c_in(X0,c_Union(c_uminus(X1,tc_set(tc_set(X2))),X2),X2)
| c_in(c_union(X3,X4,X2),X1,tc_set(X2))
| ~ c_in(X0,X4,X2) )
| ~ spl0_11
| ~ spl0_40 ),
inference(resolution,[],[f311,f69]) ).
fof(f1577,plain,
( spl0_124
| ~ spl0_8
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f336,f310,f56,f1575]) ).
fof(f1575,plain,
( spl0_124
<=> ! [X0,X3,X2,X1] :
( c_in(X0,c_Union(c_uminus(X1,tc_set(tc_set(X2))),X2),X2)
| c_in(c_uminus(X3,tc_set(X2)),X1,tc_set(X2))
| c_in(X0,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f336,plain,
( ! [X2,X3,X0,X1] :
( c_in(X0,c_Union(c_uminus(X1,tc_set(tc_set(X2))),X2),X2)
| c_in(c_uminus(X3,tc_set(X2)),X1,tc_set(X2))
| c_in(X0,X3,X2) )
| ~ spl0_8
| ~ spl0_40 ),
inference(resolution,[],[f311,f57]) ).
fof(f1571,plain,
( spl0_123
| ~ spl0_30
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f510,f498,f194,f1569]) ).
fof(f1569,plain,
( spl0_123
<=> ! [X2,X0,X1] :
( c_Main_OsubsetI__1(c_insert(X0,c_Union(c_emptyset,X1),X1),X2,X1) = X0
| c_lessequals(c_insert(X0,c_Union(c_emptyset,X1),X1),X2,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f510,plain,
( ! [X2,X0,X1] :
( c_Main_OsubsetI__1(c_insert(X0,c_Union(c_emptyset,X1),X1),X2,X1) = X0
| c_lessequals(c_insert(X0,c_Union(c_emptyset,X1),X1),X2,tc_set(X1)) )
| ~ spl0_30
| ~ spl0_53 ),
inference(resolution,[],[f499,f195]) ).
fof(f1535,plain,
( spl0_122
| ~ spl0_5
| ~ spl0_56 ),
inference(avatar_split_clause,[],[f620,f600,f44,f1533]) ).
fof(f1533,plain,
( spl0_122
<=> ! [X2,X0,X1] :
( c_Main_OUnionE__1(X0,c_insert(X1,c_emptyset,tc_set(X2)),X2) = X1
| ~ c_in(X0,c_Union(c_insert(X1,c_emptyset,tc_set(X2)),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f600,plain,
( spl0_56
<=> ! [X0,X3,X2,X1] :
( c_in(c_Main_OUnionE__1(X0,c_insert(X1,X2,tc_set(X3)),X3),X2,tc_set(X3))
| c_Main_OUnionE__1(X0,c_insert(X1,X2,tc_set(X3)),X3) = X1
| ~ c_in(X0,c_Union(c_insert(X1,X2,tc_set(X3)),X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f620,plain,
( ! [X2,X0,X1] :
( c_Main_OUnionE__1(X0,c_insert(X1,c_emptyset,tc_set(X2)),X2) = X1
| ~ c_in(X0,c_Union(c_insert(X1,c_emptyset,tc_set(X2)),X2),X2) )
| ~ spl0_5
| ~ spl0_56 ),
inference(resolution,[],[f601,f45]) ).
fof(f601,plain,
( ! [X2,X3,X0,X1] :
( c_in(c_Main_OUnionE__1(X0,c_insert(X1,X2,tc_set(X3)),X3),X2,tc_set(X3))
| c_Main_OUnionE__1(X0,c_insert(X1,X2,tc_set(X3)),X3) = X1
| ~ c_in(X0,c_Union(c_insert(X1,X2,tc_set(X3)),X3),X3) )
| ~ spl0_56 ),
inference(avatar_component_clause,[],[f600]) ).
fof(f1443,plain,
( spl0_121
| ~ spl0_26
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f495,f492,f164,f1441]) ).
fof(f1441,plain,
( spl0_121
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_set(X2))
| c_uminus(X1,tc_set(X2)) = c_uminus(X0,tc_set(X2))
| ~ c_lessequals(X1,X0,tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f164,plain,
( spl0_26
<=> ! [X2,X4,X3] :
( ~ c_lessequals(X4,X2,tc_set(X3))
| c_lessequals(c_uminus(X2,tc_set(X3)),c_uminus(X4,tc_set(X3)),tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f492,plain,
( spl0_52
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_set(X2))
| ~ c_lessequals(c_uminus(X0,tc_set(X2)),c_uminus(X1,tc_set(X2)),tc_set(X2))
| c_uminus(X1,tc_set(X2)) = c_uminus(X0,tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f495,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_set(X2))
| c_uminus(X1,tc_set(X2)) = c_uminus(X0,tc_set(X2))
| ~ c_lessequals(X1,X0,tc_set(X2)) )
| ~ spl0_26
| ~ spl0_52 ),
inference(resolution,[],[f493,f165]) ).
fof(f165,plain,
( ! [X2,X3,X4] :
( c_lessequals(c_uminus(X2,tc_set(X3)),c_uminus(X4,tc_set(X3)),tc_set(X3))
| ~ c_lessequals(X4,X2,tc_set(X3)) )
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f493,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_uminus(X0,tc_set(X2)),c_uminus(X1,tc_set(X2)),tc_set(X2))
| ~ c_lessequals(X0,X1,tc_set(X2))
| c_uminus(X1,tc_set(X2)) = c_uminus(X0,tc_set(X2)) )
| ~ spl0_52 ),
inference(avatar_component_clause,[],[f492]) ).
fof(f1439,plain,
( spl0_120
| ~ spl0_4
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f479,f465,f40,f1437]) ).
fof(f1437,plain,
( spl0_120
<=> ! [X0,X3,X2,X1] :
( c_in(X0,c_Union(c_inter(X1,c_UNIV,tc_set(X2)),X2),X2)
| ~ c_in(X3,X1,tc_set(X2))
| ~ c_in(X0,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f40,plain,
( spl0_4
<=> ! [X5,X3] : c_in(X5,c_UNIV,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f479,plain,
( ! [X2,X3,X0,X1] :
( c_in(X0,c_Union(c_inter(X1,c_UNIV,tc_set(X2)),X2),X2)
| ~ c_in(X3,X1,tc_set(X2))
| ~ c_in(X0,X3,X2) )
| ~ spl0_4
| ~ spl0_51 ),
inference(resolution,[],[f466,f41]) ).
fof(f41,plain,
( ! [X3,X5] : c_in(X5,c_UNIV,X3)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f40]) ).
fof(f1315,plain,
( spl0_1
| ~ spl0_14
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1154,f1103,f81,f26]) ).
fof(f26,plain,
( spl0_1
<=> c_lessequals(c_Union(v_C,t_a),v_A,tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f1103,plain,
( spl0_107
<=> ! [X0] :
( c_in(c_Main_OsubsetI__1(c_Union(v_C,t_a),X0,t_a),v_A,t_a)
| c_lessequals(c_Union(v_C,t_a),X0,tc_set(t_a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f1154,plain,
( c_lessequals(c_Union(v_C,t_a),v_A,tc_set(t_a))
| ~ spl0_14
| ~ spl0_107 ),
inference(duplicate_literal_removal,[],[f1146]) ).
fof(f1146,plain,
( c_lessequals(c_Union(v_C,t_a),v_A,tc_set(t_a))
| c_lessequals(c_Union(v_C,t_a),v_A,tc_set(t_a))
| ~ spl0_14
| ~ spl0_107 ),
inference(resolution,[],[f1104,f82]) ).
fof(f1104,plain,
( ! [X0] :
( c_in(c_Main_OsubsetI__1(c_Union(v_C,t_a),X0,t_a),v_A,t_a)
| c_lessequals(c_Union(v_C,t_a),X0,tc_set(t_a)) )
| ~ spl0_107 ),
inference(avatar_component_clause,[],[f1103]) ).
fof(f1170,plain,
( spl0_119
| ~ spl0_14
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f598,f529,f81,f1168]) ).
fof(f1168,plain,
( spl0_119
<=> ! [X2,X0,X1] :
( c_in(c_Main_OsubsetI__1(c_union(X0,X1,X2),X1,X2),X0,X2)
| c_lessequals(c_union(X0,X1,X2),X1,tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f598,plain,
( ! [X2,X0,X1] :
( c_in(c_Main_OsubsetI__1(c_union(X0,X1,X2),X1,X2),X0,X2)
| c_lessequals(c_union(X0,X1,X2),X1,tc_set(X2)) )
| ~ spl0_14
| ~ spl0_55 ),
inference(duplicate_literal_removal,[],[f548]) ).
fof(f548,plain,
( ! [X2,X0,X1] :
( c_in(c_Main_OsubsetI__1(c_union(X0,X1,X2),X1,X2),X0,X2)
| c_lessequals(c_union(X0,X1,X2),X1,tc_set(X2))
| c_lessequals(c_union(X0,X1,X2),X1,tc_set(X2)) )
| ~ spl0_14
| ~ spl0_55 ),
inference(resolution,[],[f530,f82]) ).
fof(f1166,plain,
( spl0_118
| ~ spl0_14
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f594,f529,f81,f1164]) ).
fof(f1164,plain,
( spl0_118
<=> ! [X2,X0,X1] :
( c_in(c_Main_OsubsetI__1(c_union(X0,X1,X2),X0,X2),X1,X2)
| c_lessequals(c_union(X0,X1,X2),X0,tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f594,plain,
( ! [X2,X0,X1] :
( c_in(c_Main_OsubsetI__1(c_union(X0,X1,X2),X0,X2),X1,X2)
| c_lessequals(c_union(X0,X1,X2),X0,tc_set(X2)) )
| ~ spl0_14
| ~ spl0_55 ),
inference(duplicate_literal_removal,[],[f569]) ).
fof(f569,plain,
( ! [X2,X0,X1] :
( c_in(c_Main_OsubsetI__1(c_union(X0,X1,X2),X0,X2),X1,X2)
| c_lessequals(c_union(X0,X1,X2),X0,tc_set(X2))
| c_lessequals(c_union(X0,X1,X2),X0,tc_set(X2)) )
| ~ spl0_14
| ~ spl0_55 ),
inference(resolution,[],[f530,f82]) ).
fof(f1162,plain,
( spl0_117
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f590,f529,f1160]) ).
fof(f1160,plain,
( spl0_117
<=> ! [X2,X0,X1] :
( c_in(c_Main_OsubsetI__1(c_union(X0,X0,X1),X2,X1),X0,X1)
| c_lessequals(c_union(X0,X0,X1),X2,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f590,plain,
( ! [X2,X0,X1] :
( c_in(c_Main_OsubsetI__1(c_union(X0,X0,X1),X2,X1),X0,X1)
| c_lessequals(c_union(X0,X0,X1),X2,tc_set(X1)) )
| ~ spl0_55 ),
inference(factoring,[],[f530]) ).
fof(f1158,plain,
( spl0_116
| ~ spl0_5
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f587,f529,f44,f1156]) ).
fof(f1156,plain,
( spl0_116
<=> ! [X2,X0,X1] :
( c_in(c_Main_OsubsetI__1(c_union(c_emptyset,X0,X1),X2,X1),X0,X1)
| c_lessequals(c_union(c_emptyset,X0,X1),X2,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f587,plain,
( ! [X2,X0,X1] :
( c_in(c_Main_OsubsetI__1(c_union(c_emptyset,X0,X1),X2,X1),X0,X1)
| c_lessequals(c_union(c_emptyset,X0,X1),X2,tc_set(X1)) )
| ~ spl0_5
| ~ spl0_55 ),
inference(resolution,[],[f530,f45]) ).
fof(f1145,plain,
( spl0_115
| ~ spl0_5
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f566,f529,f44,f1143]) ).
fof(f1143,plain,
( spl0_115
<=> ! [X2,X0,X1] :
( c_in(c_Main_OsubsetI__1(c_union(X0,c_emptyset,X1),X2,X1),X0,X1)
| c_lessequals(c_union(X0,c_emptyset,X1),X2,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f566,plain,
( ! [X2,X0,X1] :
( c_in(c_Main_OsubsetI__1(c_union(X0,c_emptyset,X1),X2,X1),X0,X1)
| c_lessequals(c_union(X0,c_emptyset,X1),X2,tc_set(X1)) )
| ~ spl0_5
| ~ spl0_55 ),
inference(resolution,[],[f530,f45]) ).
fof(f1141,plain,
( spl0_114
| ~ spl0_13
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f547,f525,f77,f1139]) ).
fof(f1139,plain,
( spl0_114
<=> ! [X2,X0,X1] :
( ~ c_in(c_Main_OsubsetI__1(X0,c_inter(X1,X0,X2),X2),X1,X2)
| c_lessequals(X0,c_inter(X1,X0,X2),tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f525,plain,
( spl0_54
<=> ! [X0,X3,X2,X1] :
( ~ c_in(c_Main_OsubsetI__1(X0,c_inter(X1,X2,X3),X3),X1,X3)
| ~ c_in(c_Main_OsubsetI__1(X0,c_inter(X1,X2,X3),X3),X2,X3)
| c_lessequals(X0,c_inter(X1,X2,X3),tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f547,plain,
( ! [X2,X0,X1] :
( ~ c_in(c_Main_OsubsetI__1(X0,c_inter(X1,X0,X2),X2),X1,X2)
| c_lessequals(X0,c_inter(X1,X0,X2),tc_set(X2)) )
| ~ spl0_13
| ~ spl0_54 ),
inference(duplicate_literal_removal,[],[f532]) ).
fof(f532,plain,
( ! [X2,X0,X1] :
( ~ c_in(c_Main_OsubsetI__1(X0,c_inter(X1,X0,X2),X2),X1,X2)
| c_lessequals(X0,c_inter(X1,X0,X2),tc_set(X2))
| c_lessequals(X0,c_inter(X1,X0,X2),tc_set(X2)) )
| ~ spl0_13
| ~ spl0_54 ),
inference(resolution,[],[f526,f78]) ).
fof(f526,plain,
( ! [X2,X3,X0,X1] :
( ~ c_in(c_Main_OsubsetI__1(X0,c_inter(X1,X2,X3),X3),X2,X3)
| ~ c_in(c_Main_OsubsetI__1(X0,c_inter(X1,X2,X3),X3),X1,X3)
| c_lessequals(X0,c_inter(X1,X2,X3),tc_set(X3)) )
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f525]) ).
fof(f1137,plain,
( spl0_113
| ~ spl0_4
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f541,f525,f40,f1135]) ).
fof(f1135,plain,
( spl0_113
<=> ! [X2,X0,X1] :
( ~ c_in(c_Main_OsubsetI__1(X0,c_inter(X1,c_UNIV,X2),X2),X1,X2)
| c_lessequals(X0,c_inter(X1,c_UNIV,X2),tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f541,plain,
( ! [X2,X0,X1] :
( ~ c_in(c_Main_OsubsetI__1(X0,c_inter(X1,c_UNIV,X2),X2),X1,X2)
| c_lessequals(X0,c_inter(X1,c_UNIV,X2),tc_set(X2)) )
| ~ spl0_4
| ~ spl0_54 ),
inference(resolution,[],[f526,f41]) ).
fof(f1133,plain,
( spl0_112
| ~ spl0_6
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f369,f323,f48,f1131]) ).
fof(f1131,plain,
( spl0_112
<=> ! [X4,X0,X3,X2,X1] :
( c_in(X0,c_Union(c_insert(X1,c_insert(X2,X3,tc_set(X4)),tc_set(X4)),X4),X4)
| ~ c_in(X0,X2,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f369,plain,
( ! [X2,X3,X0,X1,X4] :
( c_in(X0,c_Union(c_insert(X1,c_insert(X2,X3,tc_set(X4)),tc_set(X4)),X4),X4)
| ~ c_in(X0,X2,X4) )
| ~ spl0_6
| ~ spl0_42 ),
inference(resolution,[],[f324,f49]) ).
fof(f1129,plain,
( spl0_111
| ~ spl0_6
| ~ spl0_41 ),
inference(avatar_split_clause,[],[f355,f319,f48,f1127]) ).
fof(f1127,plain,
( spl0_111
<=> ! [X4,X0,X3,X2,X1] :
( c_in(X0,c_Union(c_union(X1,c_insert(X2,X3,tc_set(X4)),tc_set(X4)),X4),X4)
| ~ c_in(X0,X2,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f355,plain,
( ! [X2,X3,X0,X1,X4] :
( c_in(X0,c_Union(c_union(X1,c_insert(X2,X3,tc_set(X4)),tc_set(X4)),X4),X4)
| ~ c_in(X0,X2,X4) )
| ~ spl0_6
| ~ spl0_41 ),
inference(resolution,[],[f320,f49]) ).
fof(f1125,plain,
( spl0_110
| ~ spl0_6
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f341,f310,f48,f1123]) ).
fof(f1123,plain,
( spl0_110
<=> ! [X0,X3,X2,X1] :
( c_in(X0,c_Union(c_uminus(X1,tc_set(tc_set(X2))),X2),X2)
| c_in(c_insert(X0,X3,X2),X1,tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f341,plain,
( ! [X2,X3,X0,X1] :
( c_in(X0,c_Union(c_uminus(X1,tc_set(tc_set(X2))),X2),X2)
| c_in(c_insert(X0,X3,X2),X1,tc_set(X2)) )
| ~ spl0_6
| ~ spl0_40 ),
inference(resolution,[],[f311,f49]) ).
fof(f1113,plain,
( spl0_109
| ~ spl0_14
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f523,f498,f81,f1111]) ).
fof(f1111,plain,
( spl0_109
<=> ! [X2,X0,X1] :
( c_Main_OsubsetI__1(c_insert(X0,X1,X2),X1,X2) = X0
| c_lessequals(c_insert(X0,X1,X2),X1,tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f523,plain,
( ! [X2,X0,X1] :
( c_Main_OsubsetI__1(c_insert(X0,X1,X2),X1,X2) = X0
| c_lessequals(c_insert(X0,X1,X2),X1,tc_set(X2)) )
| ~ spl0_14
| ~ spl0_53 ),
inference(duplicate_literal_removal,[],[f501]) ).
fof(f501,plain,
( ! [X2,X0,X1] :
( c_Main_OsubsetI__1(c_insert(X0,X1,X2),X1,X2) = X0
| c_lessequals(c_insert(X0,X1,X2),X1,tc_set(X2))
| c_lessequals(c_insert(X0,X1,X2),X1,tc_set(X2)) )
| ~ spl0_14
| ~ spl0_53 ),
inference(resolution,[],[f499,f82]) ).
fof(f1109,plain,
( spl0_108
| ~ spl0_5
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f518,f498,f44,f1107]) ).
fof(f1107,plain,
( spl0_108
<=> ! [X2,X0,X1] :
( c_Main_OsubsetI__1(c_insert(X0,c_emptyset,X1),X2,X1) = X0
| c_lessequals(c_insert(X0,c_emptyset,X1),X2,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f518,plain,
( ! [X2,X0,X1] :
( c_Main_OsubsetI__1(c_insert(X0,c_emptyset,X1),X2,X1) = X0
| c_lessequals(c_insert(X0,c_emptyset,X1),X2,tc_set(X1)) )
| ~ spl0_5
| ~ spl0_53 ),
inference(resolution,[],[f499,f45]) ).
fof(f1105,plain,
( spl0_107
| ~ spl0_13
| ~ spl0_95 ),
inference(avatar_split_clause,[],[f958,f889,f77,f1103]) ).
fof(f889,plain,
( spl0_95
<=> ! [X0] :
( ~ c_in(X0,c_Union(v_C,t_a),t_a)
| c_in(X0,v_A,t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f958,plain,
( ! [X0] :
( c_in(c_Main_OsubsetI__1(c_Union(v_C,t_a),X0,t_a),v_A,t_a)
| c_lessequals(c_Union(v_C,t_a),X0,tc_set(t_a)) )
| ~ spl0_13
| ~ spl0_95 ),
inference(resolution,[],[f890,f78]) ).
fof(f890,plain,
( ! [X0] :
( ~ c_in(X0,c_Union(v_C,t_a),t_a)
| c_in(X0,v_A,t_a) )
| ~ spl0_95 ),
inference(avatar_component_clause,[],[f889]) ).
fof(f1061,plain,
( spl0_106
| ~ spl0_8
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f383,f331,f56,f1059]) ).
fof(f1059,plain,
( spl0_106
<=> ! [X0,X3,X2,X1] :
( c_in(X0,c_uminus(X1,tc_set(X2)),X2)
| ~ c_lessequals(X1,X3,tc_set(X2))
| c_in(X0,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f331,plain,
( spl0_44
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,X1,tc_set(X2))
| c_in(X3,c_uminus(X0,tc_set(X2)),X2)
| ~ c_in(X3,c_uminus(X1,tc_set(X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f383,plain,
( ! [X2,X3,X0,X1] :
( c_in(X0,c_uminus(X1,tc_set(X2)),X2)
| ~ c_lessequals(X1,X3,tc_set(X2))
| c_in(X0,X3,X2) )
| ~ spl0_8
| ~ spl0_44 ),
inference(resolution,[],[f332,f57]) ).
fof(f332,plain,
( ! [X2,X3,X0,X1] :
( ~ c_in(X3,c_uminus(X1,tc_set(X2)),X2)
| c_in(X3,c_uminus(X0,tc_set(X2)),X2)
| ~ c_lessequals(X0,X1,tc_set(X2)) )
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f331]) ).
fof(f1046,plain,
( spl0_105
| ~ spl0_4
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f338,f310,f40,f1044]) ).
fof(f1044,plain,
( spl0_105
<=> ! [X2,X0,X1] :
( c_in(X0,c_Union(c_uminus(X1,tc_set(tc_set(X2))),X2),X2)
| c_in(c_UNIV,X1,tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f338,plain,
( ! [X2,X0,X1] :
( c_in(X0,c_Union(c_uminus(X1,tc_set(tc_set(X2))),X2),X2)
| c_in(c_UNIV,X1,tc_set(X2)) )
| ~ spl0_4
| ~ spl0_40 ),
inference(resolution,[],[f311,f41]) ).
fof(f1041,plain,
( spl0_104
| ~ spl0_4
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f366,f323,f40,f1039]) ).
fof(f1039,plain,
( spl0_104
<=> ! [X0,X3,X2,X1] :
( c_in(X0,c_Union(c_insert(X1,c_UNIV,tc_set(X2)),X2),X2)
| ~ c_in(X0,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f366,plain,
( ! [X2,X3,X0,X1] :
( c_in(X0,c_Union(c_insert(X1,c_UNIV,tc_set(X2)),X2),X2)
| ~ c_in(X0,X3,X2) )
| ~ spl0_4
| ~ spl0_42 ),
inference(resolution,[],[f324,f41]) ).
fof(f1036,plain,
( spl0_103
| ~ spl0_4
| ~ spl0_41 ),
inference(avatar_split_clause,[],[f352,f319,f40,f1034]) ).
fof(f1034,plain,
( spl0_103
<=> ! [X0,X3,X2,X1] :
( c_in(X0,c_Union(c_union(X1,c_UNIV,tc_set(X2)),X2),X2)
| ~ c_in(X0,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f352,plain,
( ! [X2,X3,X0,X1] :
( c_in(X0,c_Union(c_union(X1,c_UNIV,tc_set(X2)),X2),X2)
| ~ c_in(X0,X3,X2) )
| ~ spl0_4
| ~ spl0_41 ),
inference(resolution,[],[f320,f41]) ).
fof(f1030,plain,
( spl0_102
| ~ spl0_30
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f445,f411,f194,f1028]) ).
fof(f1028,plain,
( spl0_102
<=> ! [X2,X0,X1] : ~ c_in(X0,c_Union(c_inter(X1,c_Union(c_emptyset,tc_set(X2)),tc_set(X2)),X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f411,plain,
( spl0_49
<=> ! [X0,X3,X2,X1] :
( ~ c_in(X0,c_Union(c_inter(X1,X2,tc_set(X3)),X3),X3)
| c_in(c_Main_OUnionE__1(X0,c_inter(X1,X2,tc_set(X3)),X3),X2,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f445,plain,
( ! [X2,X0,X1] : ~ c_in(X0,c_Union(c_inter(X1,c_Union(c_emptyset,tc_set(X2)),tc_set(X2)),X2),X2)
| ~ spl0_30
| ~ spl0_49 ),
inference(resolution,[],[f412,f195]) ).
fof(f412,plain,
( ! [X2,X3,X0,X1] :
( c_in(c_Main_OUnionE__1(X0,c_inter(X1,X2,tc_set(X3)),X3),X2,tc_set(X3))
| ~ c_in(X0,c_Union(c_inter(X1,X2,tc_set(X3)),X3),X3) )
| ~ spl0_49 ),
inference(avatar_component_clause,[],[f411]) ).
fof(f1024,plain,
( spl0_101
| ~ spl0_30
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f430,f407,f194,f1022]) ).
fof(f1022,plain,
( spl0_101
<=> ! [X2,X0,X1] : ~ c_in(X0,c_Union(c_inter(c_Union(c_emptyset,tc_set(X1)),X2,tc_set(X1)),X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f407,plain,
( spl0_48
<=> ! [X0,X3,X2,X1] :
( ~ c_in(X0,c_Union(c_inter(X1,X2,tc_set(X3)),X3),X3)
| c_in(c_Main_OUnionE__1(X0,c_inter(X1,X2,tc_set(X3)),X3),X1,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f430,plain,
( ! [X2,X0,X1] : ~ c_in(X0,c_Union(c_inter(c_Union(c_emptyset,tc_set(X1)),X2,tc_set(X1)),X1),X1)
| ~ spl0_30
| ~ spl0_48 ),
inference(resolution,[],[f408,f195]) ).
fof(f408,plain,
( ! [X2,X3,X0,X1] :
( c_in(c_Main_OUnionE__1(X0,c_inter(X1,X2,tc_set(X3)),X3),X1,tc_set(X3))
| ~ c_in(X0,c_Union(c_inter(X1,X2,tc_set(X3)),X3),X3) )
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f407]) ).
fof(f957,plain,
( spl0_100
| ~ spl0_3
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f578,f529,f36,f955]) ).
fof(f955,plain,
( spl0_100
<=> ! [X0,X1] :
( c_in(c_Main_OsubsetI__1(c_union(v_C,X0,tc_set(t_a)),X1,tc_set(t_a)),X0,tc_set(t_a))
| c_lessequals(c_union(v_C,X0,tc_set(t_a)),X1,tc_set(tc_set(t_a)))
| c_lessequals(c_Main_OsubsetI__1(c_union(v_C,X0,tc_set(t_a)),X1,tc_set(t_a)),v_A,tc_set(t_a))
| c_lessequals(v_B,c_Main_OsubsetI__1(c_union(v_C,X0,tc_set(t_a)),X1,tc_set(t_a)),tc_set(t_a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f36,plain,
( spl0_3
<=> ! [X0] :
( ~ c_in(X0,v_C,tc_set(t_a))
| c_lessequals(X0,v_A,tc_set(t_a))
| c_lessequals(v_B,X0,tc_set(t_a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f578,plain,
( ! [X0,X1] :
( c_in(c_Main_OsubsetI__1(c_union(v_C,X0,tc_set(t_a)),X1,tc_set(t_a)),X0,tc_set(t_a))
| c_lessequals(c_union(v_C,X0,tc_set(t_a)),X1,tc_set(tc_set(t_a)))
| c_lessequals(c_Main_OsubsetI__1(c_union(v_C,X0,tc_set(t_a)),X1,tc_set(t_a)),v_A,tc_set(t_a))
| c_lessequals(v_B,c_Main_OsubsetI__1(c_union(v_C,X0,tc_set(t_a)),X1,tc_set(t_a)),tc_set(t_a)) )
| ~ spl0_3
| ~ spl0_55 ),
inference(resolution,[],[f530,f37]) ).
fof(f37,plain,
( ! [X0] :
( ~ c_in(X0,v_C,tc_set(t_a))
| c_lessequals(X0,v_A,tc_set(t_a))
| c_lessequals(v_B,X0,tc_set(t_a)) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f36]) ).
fof(f953,plain,
( spl0_99
| ~ spl0_3
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f557,f529,f36,f951]) ).
fof(f951,plain,
( spl0_99
<=> ! [X0,X1] :
( c_in(c_Main_OsubsetI__1(c_union(X0,v_C,tc_set(t_a)),X1,tc_set(t_a)),X0,tc_set(t_a))
| c_lessequals(c_union(X0,v_C,tc_set(t_a)),X1,tc_set(tc_set(t_a)))
| c_lessequals(c_Main_OsubsetI__1(c_union(X0,v_C,tc_set(t_a)),X1,tc_set(t_a)),v_A,tc_set(t_a))
| c_lessequals(v_B,c_Main_OsubsetI__1(c_union(X0,v_C,tc_set(t_a)),X1,tc_set(t_a)),tc_set(t_a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f557,plain,
( ! [X0,X1] :
( c_in(c_Main_OsubsetI__1(c_union(X0,v_C,tc_set(t_a)),X1,tc_set(t_a)),X0,tc_set(t_a))
| c_lessequals(c_union(X0,v_C,tc_set(t_a)),X1,tc_set(tc_set(t_a)))
| c_lessequals(c_Main_OsubsetI__1(c_union(X0,v_C,tc_set(t_a)),X1,tc_set(t_a)),v_A,tc_set(t_a))
| c_lessequals(v_B,c_Main_OsubsetI__1(c_union(X0,v_C,tc_set(t_a)),X1,tc_set(t_a)),tc_set(t_a)) )
| ~ spl0_3
| ~ spl0_55 ),
inference(resolution,[],[f530,f37]) ).
fof(f947,plain,
( spl0_98
| ~ spl0_3
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f509,f498,f36,f945]) ).
fof(f945,plain,
( spl0_98
<=> ! [X0,X1] :
( c_Main_OsubsetI__1(c_insert(X0,v_C,tc_set(t_a)),X1,tc_set(t_a)) = X0
| c_lessequals(c_insert(X0,v_C,tc_set(t_a)),X1,tc_set(tc_set(t_a)))
| c_lessequals(c_Main_OsubsetI__1(c_insert(X0,v_C,tc_set(t_a)),X1,tc_set(t_a)),v_A,tc_set(t_a))
| c_lessequals(v_B,c_Main_OsubsetI__1(c_insert(X0,v_C,tc_set(t_a)),X1,tc_set(t_a)),tc_set(t_a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f509,plain,
( ! [X0,X1] :
( c_Main_OsubsetI__1(c_insert(X0,v_C,tc_set(t_a)),X1,tc_set(t_a)) = X0
| c_lessequals(c_insert(X0,v_C,tc_set(t_a)),X1,tc_set(tc_set(t_a)))
| c_lessequals(c_Main_OsubsetI__1(c_insert(X0,v_C,tc_set(t_a)),X1,tc_set(t_a)),v_A,tc_set(t_a))
| c_lessequals(v_B,c_Main_OsubsetI__1(c_insert(X0,v_C,tc_set(t_a)),X1,tc_set(t_a)),tc_set(t_a)) )
| ~ spl0_3
| ~ spl0_53 ),
inference(resolution,[],[f499,f37]) ).
fof(f903,plain,
( spl0_97
| ~ spl0_3
| ~ spl0_58 ),
inference(avatar_split_clause,[],[f648,f624,f36,f901]) ).
fof(f901,plain,
( spl0_97
<=> ! [X0,X1] :
( c_in(c_Main_OUnionE__1(X0,c_union(v_C,X1,tc_set(t_a)),t_a),X1,tc_set(t_a))
| ~ c_in(X0,c_Union(c_union(v_C,X1,tc_set(t_a)),t_a),t_a)
| c_lessequals(c_Main_OUnionE__1(X0,c_union(v_C,X1,tc_set(t_a)),t_a),v_A,tc_set(t_a))
| c_lessequals(v_B,c_Main_OUnionE__1(X0,c_union(v_C,X1,tc_set(t_a)),t_a),tc_set(t_a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f648,plain,
( ! [X0,X1] :
( c_in(c_Main_OUnionE__1(X0,c_union(v_C,X1,tc_set(t_a)),t_a),X1,tc_set(t_a))
| ~ c_in(X0,c_Union(c_union(v_C,X1,tc_set(t_a)),t_a),t_a)
| c_lessequals(c_Main_OUnionE__1(X0,c_union(v_C,X1,tc_set(t_a)),t_a),v_A,tc_set(t_a))
| c_lessequals(v_B,c_Main_OUnionE__1(X0,c_union(v_C,X1,tc_set(t_a)),t_a),tc_set(t_a)) )
| ~ spl0_3
| ~ spl0_58 ),
inference(resolution,[],[f625,f37]) ).
fof(f899,plain,
( spl0_96
| ~ spl0_3
| ~ spl0_58 ),
inference(avatar_split_clause,[],[f632,f624,f36,f897]) ).
fof(f897,plain,
( spl0_96
<=> ! [X0,X1] :
( c_in(c_Main_OUnionE__1(X0,c_union(X1,v_C,tc_set(t_a)),t_a),X1,tc_set(t_a))
| ~ c_in(X0,c_Union(c_union(X1,v_C,tc_set(t_a)),t_a),t_a)
| c_lessequals(c_Main_OUnionE__1(X0,c_union(X1,v_C,tc_set(t_a)),t_a),v_A,tc_set(t_a))
| c_lessequals(v_B,c_Main_OUnionE__1(X0,c_union(X1,v_C,tc_set(t_a)),t_a),tc_set(t_a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f632,plain,
( ! [X0,X1] :
( c_in(c_Main_OUnionE__1(X0,c_union(X1,v_C,tc_set(t_a)),t_a),X1,tc_set(t_a))
| ~ c_in(X0,c_Union(c_union(X1,v_C,tc_set(t_a)),t_a),t_a)
| c_lessequals(c_Main_OUnionE__1(X0,c_union(X1,v_C,tc_set(t_a)),t_a),v_A,tc_set(t_a))
| c_lessequals(v_B,c_Main_OUnionE__1(X0,c_union(X1,v_C,tc_set(t_a)),t_a),tc_set(t_a)) )
| ~ spl0_3
| ~ spl0_58 ),
inference(resolution,[],[f625,f37]) ).
fof(f891,plain,
( spl0_94
| spl0_95
| ~ spl0_43
| ~ spl0_72 ),
inference(avatar_split_clause,[],[f847,f724,f327,f889,f886]) ).
fof(f327,plain,
( spl0_43
<=> ! [X0,X3,X2,X1] :
( ~ c_in(X0,c_Main_OUnionE__1(X1,X2,X3),X3)
| c_in(X0,c_Union(X2,X3),X3)
| ~ c_in(X1,c_Union(X2,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f724,plain,
( spl0_72
<=> ! [X0,X1] :
( c_in(X0,v_A,t_a)
| ~ c_in(X0,c_Union(v_C,t_a),t_a)
| c_in(X1,c_Main_OUnionE__1(X0,v_C,t_a),t_a)
| ~ c_in(X1,v_B,t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f847,plain,
( ! [X0,X1] :
( ~ c_in(X0,c_Union(v_C,t_a),t_a)
| c_in(X0,v_A,t_a)
| ~ c_in(X1,v_B,t_a)
| c_in(X1,c_Union(v_C,t_a),t_a) )
| ~ spl0_43
| ~ spl0_72 ),
inference(duplicate_literal_removal,[],[f840]) ).
fof(f840,plain,
( ! [X0,X1] :
( ~ c_in(X0,c_Union(v_C,t_a),t_a)
| c_in(X0,v_A,t_a)
| ~ c_in(X1,v_B,t_a)
| c_in(X1,c_Union(v_C,t_a),t_a)
| ~ c_in(X0,c_Union(v_C,t_a),t_a) )
| ~ spl0_43
| ~ spl0_72 ),
inference(resolution,[],[f725,f328]) ).
fof(f328,plain,
( ! [X2,X3,X0,X1] :
( ~ c_in(X0,c_Main_OUnionE__1(X1,X2,X3),X3)
| c_in(X0,c_Union(X2,X3),X3)
| ~ c_in(X1,c_Union(X2,X3),X3) )
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f327]) ).
fof(f725,plain,
( ! [X0,X1] :
( c_in(X1,c_Main_OUnionE__1(X0,v_C,t_a),t_a)
| ~ c_in(X0,c_Union(v_C,t_a),t_a)
| c_in(X0,v_A,t_a)
| ~ c_in(X1,v_B,t_a) )
| ~ spl0_72 ),
inference(avatar_component_clause,[],[f724]) ).
fof(f880,plain,
( spl0_93
| ~ spl0_34
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f307,f243,f223,f878]) ).
fof(f878,plain,
( spl0_93
<=> ! [X0,X3,X2,X1] : c_lessequals(c_inter(X0,X1,X2),c_insert(X3,X0,X2),tc_set(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f223,plain,
( spl0_34
<=> ! [X0,X3,X2,X1] :
( c_lessequals(c_inter(X0,X1,X2),X3,tc_set(X2))
| c_in(c_Main_OsubsetI__1(c_inter(X0,X1,X2),X3,X2),X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f307,plain,
( ! [X2,X3,X0,X1] : c_lessequals(c_inter(X0,X1,X2),c_insert(X3,X0,X2),tc_set(X2))
| ~ spl0_34
| ~ spl0_39 ),
inference(duplicate_literal_removal,[],[f298]) ).
fof(f298,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_inter(X0,X1,X2),c_insert(X3,X0,X2),tc_set(X2))
| c_lessequals(c_inter(X0,X1,X2),c_insert(X3,X0,X2),tc_set(X2)) )
| ~ spl0_34
| ~ spl0_39 ),
inference(resolution,[],[f244,f224]) ).
fof(f224,plain,
( ! [X2,X3,X0,X1] :
( c_in(c_Main_OsubsetI__1(c_inter(X0,X1,X2),X3,X2),X0,X2)
| c_lessequals(c_inter(X0,X1,X2),X3,tc_set(X2)) )
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f223]) ).
fof(f876,plain,
( spl0_92
| ~ spl0_35
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f306,f243,f227,f874]) ).
fof(f874,plain,
( spl0_92
<=> ! [X2,X0,X1,X3] : c_lessequals(c_inter(X0,X1,X2),c_insert(X3,X1,X2),tc_set(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f227,plain,
( spl0_35
<=> ! [X0,X3,X2,X1] :
( c_lessequals(c_inter(X0,X1,X2),X3,tc_set(X2))
| c_in(c_Main_OsubsetI__1(c_inter(X0,X1,X2),X3,X2),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f306,plain,
( ! [X2,X3,X0,X1] : c_lessequals(c_inter(X0,X1,X2),c_insert(X3,X1,X2),tc_set(X2))
| ~ spl0_35
| ~ spl0_39 ),
inference(duplicate_literal_removal,[],[f299]) ).
fof(f299,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_inter(X0,X1,X2),c_insert(X3,X1,X2),tc_set(X2))
| c_lessequals(c_inter(X0,X1,X2),c_insert(X3,X1,X2),tc_set(X2)) )
| ~ spl0_35
| ~ spl0_39 ),
inference(resolution,[],[f244,f228]) ).
fof(f228,plain,
( ! [X2,X3,X0,X1] :
( c_in(c_Main_OsubsetI__1(c_inter(X0,X1,X2),X3,X2),X1,X2)
| c_lessequals(c_inter(X0,X1,X2),X3,tc_set(X2)) )
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f227]) ).
fof(f872,plain,
( spl0_91
| ~ spl0_34
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f295,f239,f223,f870]) ).
fof(f870,plain,
( spl0_91
<=> ! [X0,X3,X2,X1] : c_lessequals(c_inter(X0,X1,X2),c_union(X3,X0,X2),tc_set(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f295,plain,
( ! [X2,X3,X0,X1] : c_lessequals(c_inter(X0,X1,X2),c_union(X3,X0,X2),tc_set(X2))
| ~ spl0_34
| ~ spl0_38 ),
inference(duplicate_literal_removal,[],[f286]) ).
fof(f286,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_inter(X0,X1,X2),c_union(X3,X0,X2),tc_set(X2))
| c_lessequals(c_inter(X0,X1,X2),c_union(X3,X0,X2),tc_set(X2)) )
| ~ spl0_34
| ~ spl0_38 ),
inference(resolution,[],[f240,f224]) ).
fof(f868,plain,
( spl0_90
| ~ spl0_35
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f294,f239,f227,f866]) ).
fof(f866,plain,
( spl0_90
<=> ! [X2,X0,X1,X3] : c_lessequals(c_inter(X0,X1,X2),c_union(X3,X1,X2),tc_set(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f294,plain,
( ! [X2,X3,X0,X1] : c_lessequals(c_inter(X0,X1,X2),c_union(X3,X1,X2),tc_set(X2))
| ~ spl0_35
| ~ spl0_38 ),
inference(duplicate_literal_removal,[],[f287]) ).
fof(f287,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_inter(X0,X1,X2),c_union(X3,X1,X2),tc_set(X2))
| c_lessequals(c_inter(X0,X1,X2),c_union(X3,X1,X2),tc_set(X2)) )
| ~ spl0_35
| ~ spl0_38 ),
inference(resolution,[],[f240,f228]) ).
fof(f862,plain,
( spl0_89
| ~ spl0_3
| ~ spl0_56 ),
inference(avatar_split_clause,[],[f612,f600,f36,f860]) ).
fof(f860,plain,
( spl0_89
<=> ! [X0,X1] :
( c_Main_OUnionE__1(X0,c_insert(X1,v_C,tc_set(t_a)),t_a) = X1
| ~ c_in(X0,c_Union(c_insert(X1,v_C,tc_set(t_a)),t_a),t_a)
| c_lessequals(c_Main_OUnionE__1(X0,c_insert(X1,v_C,tc_set(t_a)),t_a),v_A,tc_set(t_a))
| c_lessequals(v_B,c_Main_OUnionE__1(X0,c_insert(X1,v_C,tc_set(t_a)),t_a),tc_set(t_a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f612,plain,
( ! [X0,X1] :
( c_Main_OUnionE__1(X0,c_insert(X1,v_C,tc_set(t_a)),t_a) = X1
| ~ c_in(X0,c_Union(c_insert(X1,v_C,tc_set(t_a)),t_a),t_a)
| c_lessequals(c_Main_OUnionE__1(X0,c_insert(X1,v_C,tc_set(t_a)),t_a),v_A,tc_set(t_a))
| c_lessequals(v_B,c_Main_OUnionE__1(X0,c_insert(X1,v_C,tc_set(t_a)),t_a),tc_set(t_a)) )
| ~ spl0_3
| ~ spl0_56 ),
inference(resolution,[],[f601,f37]) ).
fof(f857,plain,
( spl0_88
| ~ spl0_5
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f452,f411,f44,f855]) ).
fof(f855,plain,
( spl0_88
<=> ! [X2,X0,X1] : ~ c_in(X0,c_Union(c_inter(X1,c_emptyset,tc_set(X2)),X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f452,plain,
( ! [X2,X0,X1] : ~ c_in(X0,c_Union(c_inter(X1,c_emptyset,tc_set(X2)),X2),X2)
| ~ spl0_5
| ~ spl0_49 ),
inference(resolution,[],[f412,f45]) ).
fof(f852,plain,
( spl0_87
| ~ spl0_5
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f437,f407,f44,f850]) ).
fof(f850,plain,
( spl0_87
<=> ! [X2,X0,X1] : ~ c_in(X0,c_Union(c_inter(c_emptyset,X1,tc_set(X2)),X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f437,plain,
( ! [X2,X0,X1] : ~ c_in(X0,c_Union(c_inter(c_emptyset,X1,tc_set(X2)),X2),X2)
| ~ spl0_5
| ~ spl0_48 ),
inference(resolution,[],[f408,f45]) ).
fof(f837,plain,
( spl0_86
| ~ spl0_4
| ~ spl0_47 ),
inference(avatar_split_clause,[],[f422,f403,f40,f835]) ).
fof(f835,plain,
( spl0_86
<=> ! [X0,X1] : ~ c_in(X0,c_Union(c_uminus(c_UNIV,tc_set(tc_set(X1))),X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f403,plain,
( spl0_47
<=> ! [X2,X0,X1] :
( ~ c_in(X0,c_Union(c_uminus(X1,tc_set(tc_set(X2))),X2),X2)
| ~ c_in(c_Main_OUnionE__1(X0,c_uminus(X1,tc_set(tc_set(X2))),X2),X1,tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f422,plain,
( ! [X0,X1] : ~ c_in(X0,c_Union(c_uminus(c_UNIV,tc_set(tc_set(X1))),X1),X1)
| ~ spl0_4
| ~ spl0_47 ),
inference(resolution,[],[f404,f41]) ).
fof(f404,plain,
( ! [X2,X0,X1] :
( ~ c_in(c_Main_OUnionE__1(X0,c_uminus(X1,tc_set(tc_set(X2))),X2),X1,tc_set(X2))
| ~ c_in(X0,c_Union(c_uminus(X1,tc_set(tc_set(X2))),X2),X2) )
| ~ spl0_47 ),
inference(avatar_component_clause,[],[f403]) ).
fof(f832,plain,
( spl0_85
| ~ spl0_30
| ~ spl0_37 ),
inference(avatar_split_clause,[],[f277,f235,f194,f830]) ).
fof(f830,plain,
( spl0_85
<=> ! [X0,X1] : c_lessequals(X0,c_uminus(c_Union(c_emptyset,X1),tc_set(X1)),tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f235,plain,
( spl0_37
<=> ! [X2,X0,X1] :
( c_lessequals(X0,c_uminus(X1,tc_set(X2)),tc_set(X2))
| c_in(c_Main_OsubsetI__1(X0,c_uminus(X1,tc_set(X2)),X2),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f277,plain,
( ! [X0,X1] : c_lessequals(X0,c_uminus(c_Union(c_emptyset,X1),tc_set(X1)),tc_set(X1))
| ~ spl0_30
| ~ spl0_37 ),
inference(resolution,[],[f236,f195]) ).
fof(f236,plain,
( ! [X2,X0,X1] :
( c_in(c_Main_OsubsetI__1(X0,c_uminus(X1,tc_set(X2)),X2),X1,X2)
| c_lessequals(X0,c_uminus(X1,tc_set(X2)),tc_set(X2)) )
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f235]) ).
fof(f827,plain,
( spl0_84
| ~ spl0_30
| ~ spl0_35 ),
inference(avatar_split_clause,[],[f266,f227,f194,f825]) ).
fof(f825,plain,
( spl0_84
<=> ! [X2,X0,X1] : c_lessequals(c_inter(X0,c_Union(c_emptyset,X1),X1),X2,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f266,plain,
( ! [X2,X0,X1] : c_lessequals(c_inter(X0,c_Union(c_emptyset,X1),X1),X2,tc_set(X1))
| ~ spl0_30
| ~ spl0_35 ),
inference(resolution,[],[f228,f195]) ).
fof(f822,plain,
( spl0_83
| ~ spl0_30
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f255,f223,f194,f820]) ).
fof(f820,plain,
( spl0_83
<=> ! [X2,X0,X1] : c_lessequals(c_inter(c_Union(c_emptyset,X0),X1,X0),X2,tc_set(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f255,plain,
( ! [X2,X0,X1] : c_lessequals(c_inter(c_Union(c_emptyset,X0),X1,X0),X2,tc_set(X0))
| ~ spl0_30
| ~ spl0_34 ),
inference(resolution,[],[f224,f195]) ).
fof(f817,plain,
( spl0_82
| ~ spl0_19
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f198,f194,f112,f815]) ).
fof(f815,plain,
( spl0_82
<=> ! [X0,X1] : ~ c_in(X0,c_Union(c_Union(c_emptyset,tc_set(X1)),X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f198,plain,
( ! [X0,X1] : ~ c_in(X0,c_Union(c_Union(c_emptyset,tc_set(X1)),X1),X1)
| ~ spl0_19
| ~ spl0_30 ),
inference(resolution,[],[f195,f113]) ).
fof(f807,plain,
( spl0_81
| ~ spl0_3
| ~ spl0_37 ),
inference(avatar_split_clause,[],[f276,f235,f36,f805]) ).
fof(f805,plain,
( spl0_81
<=> ! [X0] :
( c_lessequals(X0,c_uminus(v_C,tc_set(tc_set(t_a))),tc_set(tc_set(t_a)))
| c_lessequals(c_Main_OsubsetI__1(X0,c_uminus(v_C,tc_set(tc_set(t_a))),tc_set(t_a)),v_A,tc_set(t_a))
| c_lessequals(v_B,c_Main_OsubsetI__1(X0,c_uminus(v_C,tc_set(tc_set(t_a))),tc_set(t_a)),tc_set(t_a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f276,plain,
( ! [X0] :
( c_lessequals(X0,c_uminus(v_C,tc_set(tc_set(t_a))),tc_set(tc_set(t_a)))
| c_lessequals(c_Main_OsubsetI__1(X0,c_uminus(v_C,tc_set(tc_set(t_a))),tc_set(t_a)),v_A,tc_set(t_a))
| c_lessequals(v_B,c_Main_OsubsetI__1(X0,c_uminus(v_C,tc_set(tc_set(t_a))),tc_set(t_a)),tc_set(t_a)) )
| ~ spl0_3
| ~ spl0_37 ),
inference(resolution,[],[f236,f37]) ).
fof(f803,plain,
( spl0_80
| ~ spl0_3
| ~ spl0_35 ),
inference(avatar_split_clause,[],[f265,f227,f36,f801]) ).
fof(f801,plain,
( spl0_80
<=> ! [X0,X1] :
( c_lessequals(c_inter(X0,v_C,tc_set(t_a)),X1,tc_set(tc_set(t_a)))
| c_lessequals(c_Main_OsubsetI__1(c_inter(X0,v_C,tc_set(t_a)),X1,tc_set(t_a)),v_A,tc_set(t_a))
| c_lessequals(v_B,c_Main_OsubsetI__1(c_inter(X0,v_C,tc_set(t_a)),X1,tc_set(t_a)),tc_set(t_a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f265,plain,
( ! [X0,X1] :
( c_lessequals(c_inter(X0,v_C,tc_set(t_a)),X1,tc_set(tc_set(t_a)))
| c_lessequals(c_Main_OsubsetI__1(c_inter(X0,v_C,tc_set(t_a)),X1,tc_set(t_a)),v_A,tc_set(t_a))
| c_lessequals(v_B,c_Main_OsubsetI__1(c_inter(X0,v_C,tc_set(t_a)),X1,tc_set(t_a)),tc_set(t_a)) )
| ~ spl0_3
| ~ spl0_35 ),
inference(resolution,[],[f228,f37]) ).
fof(f797,plain,
( spl0_79
| ~ spl0_3
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f254,f223,f36,f795]) ).
fof(f795,plain,
( spl0_79
<=> ! [X0,X1] :
( c_lessequals(c_inter(v_C,X0,tc_set(t_a)),X1,tc_set(tc_set(t_a)))
| c_lessequals(c_Main_OsubsetI__1(c_inter(v_C,X0,tc_set(t_a)),X1,tc_set(t_a)),v_A,tc_set(t_a))
| c_lessequals(v_B,c_Main_OsubsetI__1(c_inter(v_C,X0,tc_set(t_a)),X1,tc_set(t_a)),tc_set(t_a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f254,plain,
( ! [X0,X1] :
( c_lessequals(c_inter(v_C,X0,tc_set(t_a)),X1,tc_set(tc_set(t_a)))
| c_lessequals(c_Main_OsubsetI__1(c_inter(v_C,X0,tc_set(t_a)),X1,tc_set(t_a)),v_A,tc_set(t_a))
| c_lessequals(v_B,c_Main_OsubsetI__1(c_inter(v_C,X0,tc_set(t_a)),X1,tc_set(t_a)),tc_set(t_a)) )
| ~ spl0_3
| ~ spl0_34 ),
inference(resolution,[],[f224,f37]) ).
fof(f789,plain,
( spl0_78
| ~ spl0_3
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f444,f411,f36,f787]) ).
fof(f787,plain,
( spl0_78
<=> ! [X0,X1] :
( ~ c_in(X0,c_Union(c_inter(X1,v_C,tc_set(t_a)),t_a),t_a)
| c_lessequals(c_Main_OUnionE__1(X0,c_inter(X1,v_C,tc_set(t_a)),t_a),v_A,tc_set(t_a))
| c_lessequals(v_B,c_Main_OUnionE__1(X0,c_inter(X1,v_C,tc_set(t_a)),t_a),tc_set(t_a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f444,plain,
( ! [X0,X1] :
( ~ c_in(X0,c_Union(c_inter(X1,v_C,tc_set(t_a)),t_a),t_a)
| c_lessequals(c_Main_OUnionE__1(X0,c_inter(X1,v_C,tc_set(t_a)),t_a),v_A,tc_set(t_a))
| c_lessequals(v_B,c_Main_OUnionE__1(X0,c_inter(X1,v_C,tc_set(t_a)),t_a),tc_set(t_a)) )
| ~ spl0_3
| ~ spl0_49 ),
inference(resolution,[],[f412,f37]) ).
fof(f785,plain,
( spl0_77
| ~ spl0_3
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f429,f407,f36,f783]) ).
fof(f783,plain,
( spl0_77
<=> ! [X0,X1] :
( ~ c_in(X0,c_Union(c_inter(v_C,X1,tc_set(t_a)),t_a),t_a)
| c_lessequals(c_Main_OUnionE__1(X0,c_inter(v_C,X1,tc_set(t_a)),t_a),v_A,tc_set(t_a))
| c_lessequals(v_B,c_Main_OUnionE__1(X0,c_inter(v_C,X1,tc_set(t_a)),t_a),tc_set(t_a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f429,plain,
( ! [X0,X1] :
( ~ c_in(X0,c_Union(c_inter(v_C,X1,tc_set(t_a)),t_a),t_a)
| c_lessequals(c_Main_OUnionE__1(X0,c_inter(v_C,X1,tc_set(t_a)),t_a),v_A,tc_set(t_a))
| c_lessequals(v_B,c_Main_OUnionE__1(X0,c_inter(v_C,X1,tc_set(t_a)),t_a),tc_set(t_a)) )
| ~ spl0_3
| ~ spl0_48 ),
inference(resolution,[],[f408,f37]) ).
fof(f764,plain,
( spl0_76
| ~ spl0_61
| ~ spl0_63 ),
inference(avatar_split_clause,[],[f741,f688,f676,f762]) ).
fof(f762,plain,
( spl0_76
<=> ! [X0] : c_emptyset = c_Union(c_emptyset,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f676,plain,
( spl0_61
<=> ! [X0,X1] : c_lessequals(c_Union(c_emptyset,X0),X1,tc_set(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f688,plain,
( spl0_63
<=> ! [X0,X1] :
( ~ c_lessequals(X0,c_emptyset,tc_set(X1))
| c_emptyset = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f741,plain,
( ! [X0] : c_emptyset = c_Union(c_emptyset,X0)
| ~ spl0_61
| ~ spl0_63 ),
inference(resolution,[],[f689,f677]) ).
fof(f677,plain,
( ! [X0,X1] : c_lessequals(c_Union(c_emptyset,X0),X1,tc_set(X0))
| ~ spl0_61 ),
inference(avatar_component_clause,[],[f676]) ).
fof(f689,plain,
( ! [X0,X1] :
( ~ c_lessequals(X0,c_emptyset,tc_set(X1))
| c_emptyset = X0 )
| ~ spl0_63 ),
inference(avatar_component_clause,[],[f688]) ).
fof(f738,plain,
( spl0_75
| ~ spl0_13
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f308,f243,f77,f736]) ).
fof(f736,plain,
( spl0_75
<=> ! [X2,X0,X1] : c_lessequals(X0,c_insert(X1,X0,X2),tc_set(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f308,plain,
( ! [X2,X0,X1] : c_lessequals(X0,c_insert(X1,X0,X2),tc_set(X2))
| ~ spl0_13
| ~ spl0_39 ),
inference(duplicate_literal_removal,[],[f297]) ).
fof(f297,plain,
( ! [X2,X0,X1] :
( c_lessequals(X0,c_insert(X1,X0,X2),tc_set(X2))
| c_lessequals(X0,c_insert(X1,X0,X2),tc_set(X2)) )
| ~ spl0_13
| ~ spl0_39 ),
inference(resolution,[],[f244,f78]) ).
fof(f734,plain,
( spl0_74
| ~ spl0_4
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f303,f243,f40,f732]) ).
fof(f732,plain,
( spl0_74
<=> ! [X2,X0,X1] : c_lessequals(X0,c_insert(X1,c_UNIV,X2),tc_set(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f303,plain,
( ! [X2,X0,X1] : c_lessequals(X0,c_insert(X1,c_UNIV,X2),tc_set(X2))
| ~ spl0_4
| ~ spl0_39 ),
inference(resolution,[],[f244,f41]) ).
fof(f730,plain,
( spl0_73
| ~ spl0_13
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f296,f239,f77,f728]) ).
fof(f728,plain,
( spl0_73
<=> ! [X2,X0,X1] : c_lessequals(X0,c_union(X1,X0,X2),tc_set(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f296,plain,
( ! [X2,X0,X1] : c_lessequals(X0,c_union(X1,X0,X2),tc_set(X2))
| ~ spl0_13
| ~ spl0_38 ),
inference(duplicate_literal_removal,[],[f285]) ).
fof(f285,plain,
( ! [X2,X0,X1] :
( c_lessequals(X0,c_union(X1,X0,X2),tc_set(X2))
| c_lessequals(X0,c_union(X1,X0,X2),tc_set(X2)) )
| ~ spl0_13
| ~ spl0_38 ),
inference(resolution,[],[f240,f78]) ).
fof(f726,plain,
( spl0_72
| ~ spl0_16
| ~ spl0_57 ),
inference(avatar_split_clause,[],[f686,f604,f100,f724]) ).
fof(f100,plain,
( spl0_16
<=> ! [X4,X3,X2,X1] :
( ~ c_in(X1,X2,X3)
| c_in(X1,X4,X3)
| ~ c_lessequals(X2,X4,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f604,plain,
( spl0_57
<=> ! [X0] :
( c_lessequals(v_B,c_Main_OUnionE__1(X0,v_C,t_a),tc_set(t_a))
| c_in(X0,v_A,t_a)
| ~ c_in(X0,c_Union(v_C,t_a),t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f686,plain,
( ! [X0,X1] :
( c_in(X0,v_A,t_a)
| ~ c_in(X0,c_Union(v_C,t_a),t_a)
| c_in(X1,c_Main_OUnionE__1(X0,v_C,t_a),t_a)
| ~ c_in(X1,v_B,t_a) )
| ~ spl0_16
| ~ spl0_57 ),
inference(resolution,[],[f605,f101]) ).
fof(f101,plain,
( ! [X2,X3,X1,X4] :
( ~ c_lessequals(X2,X4,tc_set(X3))
| c_in(X1,X4,X3)
| ~ c_in(X1,X2,X3) )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f100]) ).
fof(f605,plain,
( ! [X0] :
( c_lessequals(v_B,c_Main_OUnionE__1(X0,v_C,t_a),tc_set(t_a))
| c_in(X0,v_A,t_a)
| ~ c_in(X0,c_Union(v_C,t_a),t_a) )
| ~ spl0_57 ),
inference(avatar_component_clause,[],[f604]) ).
fof(f722,plain,
( spl0_71
| ~ spl0_4
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f291,f239,f40,f720]) ).
fof(f720,plain,
( spl0_71
<=> ! [X2,X0,X1] : c_lessequals(X0,c_union(X1,c_UNIV,X2),tc_set(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f291,plain,
( ! [X2,X0,X1] : c_lessequals(X0,c_union(X1,c_UNIV,X2),tc_set(X2))
| ~ spl0_4
| ~ spl0_38 ),
inference(resolution,[],[f240,f41]) ).
fof(f718,plain,
( spl0_70
| ~ spl0_5
| ~ spl0_37 ),
inference(avatar_split_clause,[],[f282,f235,f44,f716]) ).
fof(f716,plain,
( spl0_70
<=> ! [X0,X1] : c_lessequals(X0,c_uminus(c_emptyset,tc_set(X1)),tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f282,plain,
( ! [X0,X1] : c_lessequals(X0,c_uminus(c_emptyset,tc_set(X1)),tc_set(X1))
| ~ spl0_5
| ~ spl0_37 ),
inference(resolution,[],[f236,f45]) ).
fof(f714,plain,
( spl0_69
| ~ spl0_14
| ~ spl0_35 ),
inference(avatar_split_clause,[],[f273,f227,f81,f712]) ).
fof(f712,plain,
( spl0_69
<=> ! [X2,X0,X1] : c_lessequals(c_inter(X0,X1,X2),X1,tc_set(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f273,plain,
( ! [X2,X0,X1] : c_lessequals(c_inter(X0,X1,X2),X1,tc_set(X2))
| ~ spl0_14
| ~ spl0_35 ),
inference(duplicate_literal_removal,[],[f263]) ).
fof(f263,plain,
( ! [X2,X0,X1] :
( c_lessequals(c_inter(X0,X1,X2),X1,tc_set(X2))
| c_lessequals(c_inter(X0,X1,X2),X1,tc_set(X2)) )
| ~ spl0_14
| ~ spl0_35 ),
inference(resolution,[],[f228,f82]) ).
fof(f710,plain,
( spl0_68
| ~ spl0_5
| ~ spl0_35 ),
inference(avatar_split_clause,[],[f271,f227,f44,f708]) ).
fof(f708,plain,
( spl0_68
<=> ! [X2,X0,X1] : c_lessequals(c_inter(X0,c_emptyset,X1),X2,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f271,plain,
( ! [X2,X0,X1] : c_lessequals(c_inter(X0,c_emptyset,X1),X2,tc_set(X1))
| ~ spl0_5
| ~ spl0_35 ),
inference(resolution,[],[f228,f45]) ).
fof(f706,plain,
( spl0_67
| ~ spl0_14
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f262,f223,f81,f704]) ).
fof(f704,plain,
( spl0_67
<=> ! [X2,X0,X1] : c_lessequals(c_inter(X0,X1,X2),X0,tc_set(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f262,plain,
( ! [X2,X0,X1] : c_lessequals(c_inter(X0,X1,X2),X0,tc_set(X2))
| ~ spl0_14
| ~ spl0_34 ),
inference(duplicate_literal_removal,[],[f252]) ).
fof(f252,plain,
( ! [X2,X0,X1] :
( c_lessequals(c_inter(X0,X1,X2),X0,tc_set(X2))
| c_lessequals(c_inter(X0,X1,X2),X0,tc_set(X2)) )
| ~ spl0_14
| ~ spl0_34 ),
inference(resolution,[],[f224,f82]) ).
fof(f702,plain,
( spl0_66
| ~ spl0_5
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f260,f223,f44,f700]) ).
fof(f700,plain,
( spl0_66
<=> ! [X2,X0,X1] : c_lessequals(c_inter(c_emptyset,X0,X1),X2,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f260,plain,
( ! [X2,X0,X1] : c_lessequals(c_inter(c_emptyset,X0,X1),X2,tc_set(X1))
| ~ spl0_5
| ~ spl0_34 ),
inference(resolution,[],[f224,f45]) ).
fof(f698,plain,
( spl0_65
| ~ spl0_4
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f249,f219,f40,f696]) ).
fof(f696,plain,
( spl0_65
<=> ! [X0,X1] : c_lessequals(c_uminus(c_UNIV,tc_set(X0)),X1,tc_set(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f219,plain,
( spl0_33
<=> ! [X2,X0,X1] :
( c_lessequals(c_uminus(X0,tc_set(X1)),X2,tc_set(X1))
| ~ c_in(c_Main_OsubsetI__1(c_uminus(X0,tc_set(X1)),X2,X1),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f249,plain,
( ! [X0,X1] : c_lessequals(c_uminus(c_UNIV,tc_set(X0)),X1,tc_set(X0))
| ~ spl0_4
| ~ spl0_33 ),
inference(resolution,[],[f220,f41]) ).
fof(f220,plain,
( ! [X2,X0,X1] :
( ~ c_in(c_Main_OsubsetI__1(c_uminus(X0,tc_set(X1)),X2,X1),X0,X1)
| c_lessequals(c_uminus(X0,tc_set(X1)),X2,tc_set(X1)) )
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f219]) ).
fof(f694,plain,
( spl0_64
| ~ spl0_17
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f176,f156,f104,f692]) ).
fof(f692,plain,
( spl0_64
<=> ! [X0,X1] :
( ~ c_lessequals(c_UNIV,X0,tc_set(X1))
| c_UNIV = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f104,plain,
( spl0_17
<=> ! [X4,X2,X3] :
( X2 = X4
| ~ c_lessequals(X2,X4,tc_set(X3))
| ~ c_lessequals(X4,X2,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f156,plain,
( spl0_24
<=> ! [X0,X1] : c_lessequals(X0,c_UNIV,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f176,plain,
( ! [X0,X1] :
( ~ c_lessequals(c_UNIV,X0,tc_set(X1))
| c_UNIV = X0 )
| ~ spl0_17
| ~ spl0_24 ),
inference(resolution,[],[f157,f105]) ).
fof(f105,plain,
( ! [X2,X3,X4] :
( ~ c_lessequals(X4,X2,tc_set(X3))
| ~ c_lessequals(X2,X4,tc_set(X3))
| X2 = X4 )
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f157,plain,
( ! [X0,X1] : c_lessequals(X0,c_UNIV,tc_set(X1))
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f156]) ).
fof(f690,plain,
( spl0_63
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f174,f108,f104,f688]) ).
fof(f108,plain,
( spl0_18
<=> ! [X0,X1] : c_lessequals(c_emptyset,X0,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f174,plain,
( ! [X0,X1] :
( ~ c_lessequals(X0,c_emptyset,tc_set(X1))
| c_emptyset = X0 )
| ~ spl0_17
| ~ spl0_18 ),
inference(resolution,[],[f109,f105]) ).
fof(f109,plain,
( ! [X0,X1] : c_lessequals(c_emptyset,X0,tc_set(X1))
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f684,plain,
( spl0_62
| ~ spl0_17
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f191,f188,f104,f682]) ).
fof(f682,plain,
( spl0_62
<=> ! [X0] :
( c_lessequals(v_C,X0,tc_set(tc_set(t_a)))
| c_lessequals(v_B,c_Main_OsubsetI__1(v_C,X0,tc_set(t_a)),tc_set(t_a))
| ~ c_lessequals(v_A,c_Main_OsubsetI__1(v_C,X0,tc_set(t_a)),tc_set(t_a))
| v_A = c_Main_OsubsetI__1(v_C,X0,tc_set(t_a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f188,plain,
( spl0_29
<=> ! [X0] :
( c_lessequals(v_C,X0,tc_set(tc_set(t_a)))
| c_lessequals(c_Main_OsubsetI__1(v_C,X0,tc_set(t_a)),v_A,tc_set(t_a))
| c_lessequals(v_B,c_Main_OsubsetI__1(v_C,X0,tc_set(t_a)),tc_set(t_a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f191,plain,
( ! [X0] :
( c_lessequals(v_C,X0,tc_set(tc_set(t_a)))
| c_lessequals(v_B,c_Main_OsubsetI__1(v_C,X0,tc_set(t_a)),tc_set(t_a))
| ~ c_lessequals(v_A,c_Main_OsubsetI__1(v_C,X0,tc_set(t_a)),tc_set(t_a))
| v_A = c_Main_OsubsetI__1(v_C,X0,tc_set(t_a)) )
| ~ spl0_17
| ~ spl0_29 ),
inference(resolution,[],[f189,f105]) ).
fof(f189,plain,
( ! [X0] :
( c_lessequals(c_Main_OsubsetI__1(v_C,X0,tc_set(t_a)),v_A,tc_set(t_a))
| c_lessequals(v_C,X0,tc_set(tc_set(t_a)))
| c_lessequals(v_B,c_Main_OsubsetI__1(v_C,X0,tc_set(t_a)),tc_set(t_a)) )
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f188]) ).
fof(f678,plain,
( spl0_61
| ~ spl0_13
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f197,f194,f77,f676]) ).
fof(f197,plain,
( ! [X0,X1] : c_lessequals(c_Union(c_emptyset,X0),X1,tc_set(X0))
| ~ spl0_13
| ~ spl0_30 ),
inference(resolution,[],[f195,f78]) ).
fof(f674,plain,
( spl0_60
| ~ spl0_17
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f185,f182,f104,f672]) ).
fof(f672,plain,
( spl0_60
<=> ! [X0] :
( ~ c_in(X0,c_Union(v_C,t_a),t_a)
| c_lessequals(v_B,c_Main_OUnionE__1(X0,v_C,t_a),tc_set(t_a))
| ~ c_lessequals(v_A,c_Main_OUnionE__1(X0,v_C,t_a),tc_set(t_a))
| v_A = c_Main_OUnionE__1(X0,v_C,t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f182,plain,
( spl0_28
<=> ! [X0] :
( ~ c_in(X0,c_Union(v_C,t_a),t_a)
| c_lessequals(c_Main_OUnionE__1(X0,v_C,t_a),v_A,tc_set(t_a))
| c_lessequals(v_B,c_Main_OUnionE__1(X0,v_C,t_a),tc_set(t_a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f185,plain,
( ! [X0] :
( ~ c_in(X0,c_Union(v_C,t_a),t_a)
| c_lessequals(v_B,c_Main_OUnionE__1(X0,v_C,t_a),tc_set(t_a))
| ~ c_lessequals(v_A,c_Main_OUnionE__1(X0,v_C,t_a),tc_set(t_a))
| v_A = c_Main_OUnionE__1(X0,v_C,t_a) )
| ~ spl0_17
| ~ spl0_28 ),
inference(resolution,[],[f183,f105]) ).
fof(f183,plain,
( ! [X0] :
( c_lessequals(c_Main_OUnionE__1(X0,v_C,t_a),v_A,tc_set(t_a))
| ~ c_in(X0,c_Union(v_C,t_a),t_a)
| c_lessequals(v_B,c_Main_OUnionE__1(X0,v_C,t_a),tc_set(t_a)) )
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f182]) ).
fof(f663,plain,
( spl0_59
| ~ spl0_16
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f192,f188,f100,f661]) ).
fof(f661,plain,
( spl0_59
<=> ! [X0,X1] :
( c_lessequals(v_C,X0,tc_set(tc_set(t_a)))
| c_lessequals(v_B,c_Main_OsubsetI__1(v_C,X0,tc_set(t_a)),tc_set(t_a))
| c_in(X1,v_A,t_a)
| ~ c_in(X1,c_Main_OsubsetI__1(v_C,X0,tc_set(t_a)),t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f192,plain,
( ! [X0,X1] :
( c_lessequals(v_C,X0,tc_set(tc_set(t_a)))
| c_lessequals(v_B,c_Main_OsubsetI__1(v_C,X0,tc_set(t_a)),tc_set(t_a))
| c_in(X1,v_A,t_a)
| ~ c_in(X1,c_Main_OsubsetI__1(v_C,X0,tc_set(t_a)),t_a) )
| ~ spl0_16
| ~ spl0_29 ),
inference(resolution,[],[f189,f101]) ).
fof(f626,plain,
( spl0_58
| ~ spl0_19
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f145,f133,f112,f624]) ).
fof(f133,plain,
( spl0_22
<=> ! [X4,X3,X2,X1] :
( c_in(X1,X2,X3)
| c_in(X1,X4,X3)
| ~ c_in(X1,c_union(X2,X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f145,plain,
( ! [X2,X3,X0,X1] :
( c_in(c_Main_OUnionE__1(X0,c_union(X1,X2,tc_set(X3)),X3),X2,tc_set(X3))
| c_in(c_Main_OUnionE__1(X0,c_union(X1,X2,tc_set(X3)),X3),X1,tc_set(X3))
| ~ c_in(X0,c_Union(c_union(X1,X2,tc_set(X3)),X3),X3) )
| ~ spl0_19
| ~ spl0_22 ),
inference(resolution,[],[f134,f113]) ).
fof(f134,plain,
( ! [X2,X3,X1,X4] :
( ~ c_in(X1,c_union(X2,X4,X3),X3)
| c_in(X1,X4,X3)
| c_in(X1,X2,X3) )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f606,plain,
( spl0_57
| ~ spl0_15
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f473,f394,f96,f604]) ).
fof(f96,plain,
( spl0_15
<=> ! [X6,X2,X3] :
( ~ c_in(X2,c_Union(X6,X3),X3)
| c_in(X2,c_Main_OUnionE__1(X2,X6,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f394,plain,
( spl0_46
<=> ! [X0,X1] :
( ~ c_in(X0,c_Union(v_C,t_a),t_a)
| c_lessequals(v_B,c_Main_OUnionE__1(X0,v_C,t_a),tc_set(t_a))
| c_in(X1,v_A,t_a)
| ~ c_in(X1,c_Main_OUnionE__1(X0,v_C,t_a),t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f473,plain,
( ! [X0] :
( c_lessequals(v_B,c_Main_OUnionE__1(X0,v_C,t_a),tc_set(t_a))
| c_in(X0,v_A,t_a)
| ~ c_in(X0,c_Union(v_C,t_a),t_a) )
| ~ spl0_15
| ~ spl0_46 ),
inference(duplicate_literal_removal,[],[f468]) ).
fof(f468,plain,
( ! [X0] :
( c_lessequals(v_B,c_Main_OUnionE__1(X0,v_C,t_a),tc_set(t_a))
| c_in(X0,v_A,t_a)
| ~ c_in(X0,c_Union(v_C,t_a),t_a)
| ~ c_in(X0,c_Union(v_C,t_a),t_a) )
| ~ spl0_15
| ~ spl0_46 ),
inference(resolution,[],[f395,f97]) ).
fof(f97,plain,
( ! [X2,X3,X6] :
( c_in(X2,c_Main_OUnionE__1(X2,X6,X3),X3)
| ~ c_in(X2,c_Union(X6,X3),X3) )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f395,plain,
( ! [X0,X1] :
( ~ c_in(X1,c_Main_OUnionE__1(X0,v_C,t_a),t_a)
| c_lessequals(v_B,c_Main_OUnionE__1(X0,v_C,t_a),tc_set(t_a))
| c_in(X1,v_A,t_a)
| ~ c_in(X0,c_Union(v_C,t_a),t_a) )
| ~ spl0_46 ),
inference(avatar_component_clause,[],[f394]) ).
fof(f602,plain,
( spl0_56
| ~ spl0_19
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f127,f116,f112,f600]) ).
fof(f116,plain,
( spl0_20
<=> ! [X3,X8,X9,X2] :
( X8 = X9
| c_in(X8,X2,X3)
| ~ c_in(X8,c_insert(X9,X2,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f127,plain,
( ! [X2,X3,X0,X1] :
( c_in(c_Main_OUnionE__1(X0,c_insert(X1,X2,tc_set(X3)),X3),X2,tc_set(X3))
| c_Main_OUnionE__1(X0,c_insert(X1,X2,tc_set(X3)),X3) = X1
| ~ c_in(X0,c_Union(c_insert(X1,X2,tc_set(X3)),X3),X3) )
| ~ spl0_19
| ~ spl0_20 ),
inference(resolution,[],[f117,f113]) ).
fof(f117,plain,
( ! [X2,X3,X8,X9] :
( ~ c_in(X8,c_insert(X9,X2,X3),X3)
| c_in(X8,X2,X3)
| X8 = X9 )
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f531,plain,
( spl0_55
| ~ spl0_13
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f144,f133,f77,f529]) ).
fof(f144,plain,
( ! [X2,X3,X0,X1] :
( c_in(c_Main_OsubsetI__1(c_union(X0,X1,X2),X3,X2),X1,X2)
| c_in(c_Main_OsubsetI__1(c_union(X0,X1,X2),X3,X2),X0,X2)
| c_lessequals(c_union(X0,X1,X2),X3,tc_set(X2)) )
| ~ spl0_13
| ~ spl0_22 ),
inference(resolution,[],[f134,f78]) ).
fof(f527,plain,
( spl0_54
| ~ spl0_14
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f142,f129,f81,f525]) ).
fof(f129,plain,
( spl0_21
<=> ! [X4,X3,X2,X1] :
( ~ c_in(X1,X4,X3)
| ~ c_in(X1,X2,X3)
| c_in(X1,c_inter(X2,X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f142,plain,
( ! [X2,X3,X0,X1] :
( ~ c_in(c_Main_OsubsetI__1(X0,c_inter(X1,X2,X3),X3),X1,X3)
| ~ c_in(c_Main_OsubsetI__1(X0,c_inter(X1,X2,X3),X3),X2,X3)
| c_lessequals(X0,c_inter(X1,X2,X3),tc_set(X3)) )
| ~ spl0_14
| ~ spl0_21 ),
inference(resolution,[],[f130,f82]) ).
fof(f130,plain,
( ! [X2,X3,X1,X4] :
( c_in(X1,c_inter(X2,X4,X3),X3)
| ~ c_in(X1,X2,X3)
| ~ c_in(X1,X4,X3) )
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f500,plain,
( spl0_53
| ~ spl0_13
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f126,f116,f77,f498]) ).
fof(f126,plain,
( ! [X2,X3,X0,X1] :
( c_in(c_Main_OsubsetI__1(c_insert(X0,X1,X2),X3,X2),X1,X2)
| c_Main_OsubsetI__1(c_insert(X0,X1,X2),X3,X2) = X0
| c_lessequals(c_insert(X0,X1,X2),X3,tc_set(X2)) )
| ~ spl0_13
| ~ spl0_20 ),
inference(resolution,[],[f117,f78]) ).
fof(f494,plain,
( spl0_52
| ~ spl0_17
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f167,f164,f104,f492]) ).
fof(f167,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_set(X2))
| ~ c_lessequals(c_uminus(X0,tc_set(X2)),c_uminus(X1,tc_set(X2)),tc_set(X2))
| c_uminus(X1,tc_set(X2)) = c_uminus(X0,tc_set(X2)) )
| ~ spl0_17
| ~ spl0_26 ),
inference(resolution,[],[f165,f105]) ).
fof(f467,plain,
( spl0_51
| ~ spl0_21
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f147,f137,f129,f465]) ).
fof(f147,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_in(X0,X1,X2)
| c_in(X0,c_Union(c_inter(X3,X4,tc_set(X2)),X2),X2)
| ~ c_in(X1,X3,tc_set(X2))
| ~ c_in(X1,X4,tc_set(X2)) )
| ~ spl0_21
| ~ spl0_23 ),
inference(resolution,[],[f138,f130]) ).
fof(f417,plain,
( spl0_50
| ~ spl0_15
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f150,f137,f96,f415]) ).
fof(f415,plain,
( spl0_50
<=> ! [X0,X3,X2,X1] :
( ~ c_in(X0,X1,X2)
| c_in(X0,c_Union(c_Main_OUnionE__1(X1,X3,tc_set(X2)),X2),X2)
| ~ c_in(X1,c_Union(X3,tc_set(X2)),tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f150,plain,
( ! [X2,X3,X0,X1] :
( ~ c_in(X0,X1,X2)
| c_in(X0,c_Union(c_Main_OUnionE__1(X1,X3,tc_set(X2)),X2),X2)
| ~ c_in(X1,c_Union(X3,tc_set(X2)),tc_set(X2)) )
| ~ spl0_15
| ~ spl0_23 ),
inference(resolution,[],[f138,f97]) ).
fof(f413,plain,
( spl0_49
| ~ spl0_9
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f122,f112,f60,f411]) ).
fof(f60,plain,
( spl0_9
<=> ! [X4,X3,X2,X1] :
( c_in(X1,X4,X3)
| ~ c_in(X1,c_inter(X2,X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f122,plain,
( ! [X2,X3,X0,X1] :
( ~ c_in(X0,c_Union(c_inter(X1,X2,tc_set(X3)),X3),X3)
| c_in(c_Main_OUnionE__1(X0,c_inter(X1,X2,tc_set(X3)),X3),X2,tc_set(X3)) )
| ~ spl0_9
| ~ spl0_19 ),
inference(resolution,[],[f113,f61]) ).
fof(f61,plain,
( ! [X2,X3,X1,X4] :
( ~ c_in(X1,c_inter(X2,X4,X3),X3)
| c_in(X1,X4,X3) )
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f409,plain,
( spl0_48
| ~ spl0_10
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f121,f112,f64,f407]) ).
fof(f64,plain,
( spl0_10
<=> ! [X4,X3,X2,X1] :
( c_in(X1,X2,X3)
| ~ c_in(X1,c_inter(X2,X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f121,plain,
( ! [X2,X3,X0,X1] :
( ~ c_in(X0,c_Union(c_inter(X1,X2,tc_set(X3)),X3),X3)
| c_in(c_Main_OUnionE__1(X0,c_inter(X1,X2,tc_set(X3)),X3),X1,tc_set(X3)) )
| ~ spl0_10
| ~ spl0_19 ),
inference(resolution,[],[f113,f65]) ).
fof(f65,plain,
( ! [X2,X3,X1,X4] :
( ~ c_in(X1,c_inter(X2,X4,X3),X3)
| c_in(X1,X2,X3) )
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f405,plain,
( spl0_47
| ~ spl0_7
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f120,f112,f52,f403]) ).
fof(f52,plain,
( spl0_7
<=> ! [X2,X1,X3] :
( ~ c_in(X1,X2,X3)
| ~ c_in(X1,c_uminus(X2,tc_set(X3)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f120,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,c_Union(c_uminus(X1,tc_set(tc_set(X2))),X2),X2)
| ~ c_in(c_Main_OUnionE__1(X0,c_uminus(X1,tc_set(tc_set(X2))),X2),X1,tc_set(X2)) )
| ~ spl0_7
| ~ spl0_19 ),
inference(resolution,[],[f113,f53]) ).
fof(f53,plain,
( ! [X2,X3,X1] :
( ~ c_in(X1,c_uminus(X2,tc_set(X3)),X3)
| ~ c_in(X1,X2,X3) )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f52]) ).
fof(f396,plain,
( spl0_46
| ~ spl0_16
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f186,f182,f100,f394]) ).
fof(f186,plain,
( ! [X0,X1] :
( ~ c_in(X0,c_Union(v_C,t_a),t_a)
| c_lessequals(v_B,c_Main_OUnionE__1(X0,v_C,t_a),tc_set(t_a))
| c_in(X1,v_A,t_a)
| ~ c_in(X1,c_Main_OUnionE__1(X0,v_C,t_a),t_a) )
| ~ spl0_16
| ~ spl0_28 ),
inference(resolution,[],[f183,f101]) ).
fof(f392,plain,
( spl0_45
| ~ spl0_13
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f153,f137,f77,f390]) ).
fof(f390,plain,
( spl0_45
<=> ! [X0,X3,X2,X1] :
( ~ c_in(X0,c_Main_OsubsetI__1(X1,X2,tc_set(X3)),X3)
| c_in(X0,c_Union(X1,X3),X3)
| c_lessequals(X1,X2,tc_set(tc_set(X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f153,plain,
( ! [X2,X3,X0,X1] :
( ~ c_in(X0,c_Main_OsubsetI__1(X1,X2,tc_set(X3)),X3)
| c_in(X0,c_Union(X1,X3),X3)
| c_lessequals(X1,X2,tc_set(tc_set(X3))) )
| ~ spl0_13
| ~ spl0_23 ),
inference(resolution,[],[f138,f78]) ).
fof(f333,plain,
( spl0_44
| ~ spl0_16
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f168,f164,f100,f331]) ).
fof(f168,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,tc_set(X2))
| c_in(X3,c_uminus(X0,tc_set(X2)),X2)
| ~ c_in(X3,c_uminus(X1,tc_set(X2)),X2) )
| ~ spl0_16
| ~ spl0_26 ),
inference(resolution,[],[f165,f101]) ).
fof(f329,plain,
( spl0_43
| ~ spl0_19
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f154,f137,f112,f327]) ).
fof(f154,plain,
( ! [X2,X3,X0,X1] :
( ~ c_in(X0,c_Main_OUnionE__1(X1,X2,X3),X3)
| c_in(X0,c_Union(X2,X3),X3)
| ~ c_in(X1,c_Union(X2,X3),X3) )
| ~ spl0_19
| ~ spl0_23 ),
inference(resolution,[],[f138,f113]) ).
fof(f325,plain,
( spl0_42
| ~ spl0_12
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f152,f137,f72,f323]) ).
fof(f152,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_in(X0,X1,X2)
| c_in(X0,c_Union(c_insert(X3,X4,tc_set(X2)),X2),X2)
| ~ c_in(X1,X4,tc_set(X2)) )
| ~ spl0_12
| ~ spl0_23 ),
inference(resolution,[],[f138,f73]) ).
fof(f321,plain,
( spl0_41
| ~ spl0_11
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f149,f137,f68,f319]) ).
fof(f149,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_in(X0,X1,X2)
| c_in(X0,c_Union(c_union(X3,X4,tc_set(X2)),X2),X2)
| ~ c_in(X1,X4,tc_set(X2)) )
| ~ spl0_11
| ~ spl0_23 ),
inference(resolution,[],[f138,f69]) ).
fof(f312,plain,
( spl0_40
| ~ spl0_8
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f146,f137,f56,f310]) ).
fof(f146,plain,
( ! [X2,X3,X0,X1] :
( ~ c_in(X0,X1,X2)
| c_in(X0,c_Union(c_uminus(X3,tc_set(tc_set(X2))),X2),X2)
| c_in(X1,X3,tc_set(X2)) )
| ~ spl0_8
| ~ spl0_23 ),
inference(resolution,[],[f138,f57]) ).
fof(f245,plain,
( spl0_39
| ~ spl0_12
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f93,f81,f72,f243]) ).
fof(f93,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X0,c_insert(X1,X2,X3),tc_set(X3))
| ~ c_in(c_Main_OsubsetI__1(X0,c_insert(X1,X2,X3),X3),X2,X3) )
| ~ spl0_12
| ~ spl0_14 ),
inference(resolution,[],[f82,f73]) ).
fof(f241,plain,
( spl0_38
| ~ spl0_11
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f92,f81,f68,f239]) ).
fof(f92,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X0,c_union(X1,X2,X3),tc_set(X3))
| ~ c_in(c_Main_OsubsetI__1(X0,c_union(X1,X2,X3),X3),X2,X3) )
| ~ spl0_11
| ~ spl0_14 ),
inference(resolution,[],[f82,f69]) ).
fof(f237,plain,
( spl0_37
| ~ spl0_8
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f90,f81,f56,f235]) ).
fof(f90,plain,
( ! [X2,X0,X1] :
( c_lessequals(X0,c_uminus(X1,tc_set(X2)),tc_set(X2))
| c_in(c_Main_OsubsetI__1(X0,c_uminus(X1,tc_set(X2)),X2),X1,X2) )
| ~ spl0_8
| ~ spl0_14 ),
inference(resolution,[],[f82,f57]) ).
fof(f233,plain,
( spl0_36
| ~ spl0_4
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f205,f200,f40,f231]) ).
fof(f231,plain,
( spl0_36
<=> ! [X0,X1] : c_in(X0,c_Union(c_UNIV,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f200,plain,
( spl0_31
<=> ! [X2,X0,X1] :
( ~ c_in(X0,X1,X2)
| c_in(X0,c_Union(c_UNIV,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f205,plain,
( ! [X0,X1] : c_in(X0,c_Union(c_UNIV,X1),X1)
| ~ spl0_4
| ~ spl0_31 ),
inference(resolution,[],[f201,f41]) ).
fof(f201,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,X1,X2)
| c_in(X0,c_Union(c_UNIV,X2),X2) )
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f200]) ).
fof(f229,plain,
( spl0_35
| ~ spl0_9
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f87,f77,f60,f227]) ).
fof(f87,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_inter(X0,X1,X2),X3,tc_set(X2))
| c_in(c_Main_OsubsetI__1(c_inter(X0,X1,X2),X3,X2),X1,X2) )
| ~ spl0_9
| ~ spl0_13 ),
inference(resolution,[],[f78,f61]) ).
fof(f225,plain,
( spl0_34
| ~ spl0_10
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f86,f77,f64,f223]) ).
fof(f86,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_inter(X0,X1,X2),X3,tc_set(X2))
| c_in(c_Main_OsubsetI__1(c_inter(X0,X1,X2),X3,X2),X0,X2) )
| ~ spl0_10
| ~ spl0_13 ),
inference(resolution,[],[f78,f65]) ).
fof(f221,plain,
( spl0_33
| ~ spl0_7
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f85,f77,f52,f219]) ).
fof(f85,plain,
( ! [X2,X0,X1] :
( c_lessequals(c_uminus(X0,tc_set(X1)),X2,tc_set(X1))
| ~ c_in(c_Main_OsubsetI__1(c_uminus(X0,tc_set(X1)),X2,X1),X0,X1) )
| ~ spl0_7
| ~ spl0_13 ),
inference(resolution,[],[f78,f53]) ).
fof(f215,plain,
( spl0_32
| ~ spl0_6
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f151,f137,f48,f213]) ).
fof(f151,plain,
( ! [X2,X3,X0,X1] :
( ~ c_in(X0,X1,X2)
| c_in(X0,c_Union(c_insert(X1,X3,tc_set(X2)),X2),X2) )
| ~ spl0_6
| ~ spl0_23 ),
inference(resolution,[],[f138,f49]) ).
fof(f202,plain,
( spl0_31
| ~ spl0_4
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f148,f137,f40,f200]) ).
fof(f148,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,X1,X2)
| c_in(X0,c_Union(c_UNIV,X2),X2) )
| ~ spl0_4
| ~ spl0_23 ),
inference(resolution,[],[f138,f41]) ).
fof(f196,plain,
( spl0_30
| ~ spl0_5
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f123,f112,f44,f194]) ).
fof(f123,plain,
( ! [X0,X1] : ~ c_in(X0,c_Union(c_emptyset,X1),X1)
| ~ spl0_5
| ~ spl0_19 ),
inference(resolution,[],[f113,f45]) ).
fof(f190,plain,
( spl0_29
| ~ spl0_3
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f84,f77,f36,f188]) ).
fof(f84,plain,
( ! [X0] :
( c_lessequals(v_C,X0,tc_set(tc_set(t_a)))
| c_lessequals(c_Main_OsubsetI__1(v_C,X0,tc_set(t_a)),v_A,tc_set(t_a))
| c_lessequals(v_B,c_Main_OsubsetI__1(v_C,X0,tc_set(t_a)),tc_set(t_a)) )
| ~ spl0_3
| ~ spl0_13 ),
inference(resolution,[],[f78,f37]) ).
fof(f184,plain,
( spl0_28
| ~ spl0_3
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f119,f112,f36,f182]) ).
fof(f119,plain,
( ! [X0] :
( ~ c_in(X0,c_Union(v_C,t_a),t_a)
| c_lessequals(c_Main_OUnionE__1(X0,v_C,t_a),v_A,tc_set(t_a))
| c_lessequals(v_B,c_Main_OUnionE__1(X0,v_C,t_a),tc_set(t_a)) )
| ~ spl0_3
| ~ spl0_19 ),
inference(resolution,[],[f113,f37]) ).
fof(f173,plain,
( spl0_27
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f94,f81,f77,f171]) ).
fof(f171,plain,
( spl0_27
<=> ! [X0,X1] : c_lessequals(X0,X0,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f94,plain,
( ! [X0,X1] : c_lessequals(X0,X0,tc_set(X1))
| ~ spl0_13
| ~ spl0_14 ),
inference(duplicate_literal_removal,[],[f89]) ).
fof(f89,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,tc_set(X1))
| c_lessequals(X0,X0,tc_set(X1)) )
| ~ spl0_13
| ~ spl0_14 ),
inference(resolution,[],[f82,f78]) ).
fof(f166,plain,
spl0_26,
inference(avatar_split_clause,[],[f7,f164]) ).
fof(f7,axiom,
! [X2,X3,X4] :
( ~ c_lessequals(X4,X2,tc_set(X3))
| c_lessequals(c_uminus(X2,tc_set(X3)),c_uminus(X4,tc_set(X3)),tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff__iff2_0) ).
fof(f162,plain,
spl0_25,
inference(avatar_split_clause,[],[f6,f160]) ).
fof(f160,plain,
( spl0_25
<=> ! [X2,X4,X3] :
( c_lessequals(X4,X2,tc_set(X3))
| ~ c_lessequals(c_uminus(X2,tc_set(X3)),c_uminus(X4,tc_set(X3)),tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f6,axiom,
! [X2,X3,X4] :
( c_lessequals(X4,X2,tc_set(X3))
| ~ c_lessequals(c_uminus(X2,tc_set(X3)),c_uminus(X4,tc_set(X3)),tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff__iff1_0) ).
fof(f158,plain,
( spl0_24
| ~ spl0_4
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f91,f81,f40,f156]) ).
fof(f91,plain,
( ! [X0,X1] : c_lessequals(X0,c_UNIV,tc_set(X1))
| ~ spl0_4
| ~ spl0_14 ),
inference(resolution,[],[f82,f41]) ).
fof(f139,plain,
spl0_23,
inference(avatar_split_clause,[],[f16,f137]) ).
fof(f16,axiom,
! [X2,X3,X6,X7] :
( ~ c_in(X2,X7,X3)
| ~ c_in(X7,X6,tc_set(X3))
| c_in(X2,c_Union(X6,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnionI_0) ).
fof(f135,plain,
spl0_22,
inference(avatar_split_clause,[],[f13,f133]) ).
fof(f13,axiom,
! [X2,X3,X1,X4] :
( c_in(X1,X2,X3)
| c_in(X1,X4,X3)
| ~ c_in(X1,c_union(X2,X4,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnE_0) ).
fof(f131,plain,
spl0_21,
inference(avatar_split_clause,[],[f10,f129]) ).
fof(f10,axiom,
! [X2,X3,X1,X4] :
( ~ c_in(X1,X4,X3)
| ~ c_in(X1,X2,X3)
| c_in(X1,c_inter(X2,X4,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OIntI_0) ).
fof(f118,plain,
spl0_20,
inference(avatar_split_clause,[],[f20,f116]) ).
fof(f20,axiom,
! [X2,X3,X8,X9] :
( X8 = X9
| c_in(X8,X2,X3)
| ~ c_in(X8,c_insert(X9,X2,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertE_0) ).
fof(f114,plain,
spl0_19,
inference(avatar_split_clause,[],[f14,f112]) ).
fof(f14,axiom,
! [X2,X3,X6] :
( ~ c_in(X2,c_Union(X6,X3),X3)
| c_in(c_Main_OUnionE__1(X2,X6,X3),X6,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnionE_0) ).
fof(f110,plain,
( spl0_18
| ~ spl0_5
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f88,f77,f44,f108]) ).
fof(f88,plain,
( ! [X0,X1] : c_lessequals(c_emptyset,X0,tc_set(X1))
| ~ spl0_5
| ~ spl0_13 ),
inference(resolution,[],[f78,f45]) ).
fof(f106,plain,
spl0_17,
inference(avatar_split_clause,[],[f24,f104]) ).
fof(f24,axiom,
! [X2,X3,X4] :
( X2 = X4
| ~ c_lessequals(X2,X4,tc_set(X3))
| ~ c_lessequals(X4,X2,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
fof(f102,plain,
spl0_16,
inference(avatar_split_clause,[],[f21,f100]) ).
fof(f21,axiom,
! [X2,X3,X1,X4] :
( ~ c_in(X1,X2,X3)
| c_in(X1,X4,X3)
| ~ c_lessequals(X2,X4,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
fof(f98,plain,
spl0_15,
inference(avatar_split_clause,[],[f15,f96]) ).
fof(f15,axiom,
! [X2,X3,X6] :
( ~ c_in(X2,c_Union(X6,X3),X3)
| c_in(X2,c_Main_OUnionE__1(X2,X6,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnionE_1) ).
fof(f83,plain,
spl0_14,
inference(avatar_split_clause,[],[f23,f81]) ).
fof(f23,axiom,
! [X2,X3,X4] :
( c_lessequals(X2,X4,tc_set(X3))
| ~ c_in(c_Main_OsubsetI__1(X2,X4,X3),X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
fof(f79,plain,
spl0_13,
inference(avatar_split_clause,[],[f22,f77]) ).
fof(f22,axiom,
! [X2,X3,X4] :
( c_lessequals(X2,X4,tc_set(X3))
| c_in(c_Main_OsubsetI__1(X2,X4,X3),X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
fof(f74,plain,
spl0_12,
inference(avatar_split_clause,[],[f18,f72]) ).
fof(f18,axiom,
! [X3,X8,X9,X4] :
( ~ c_in(X8,X4,X3)
| c_in(X8,c_insert(X9,X4,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertCI_0) ).
fof(f70,plain,
spl0_11,
inference(avatar_split_clause,[],[f12,f68]) ).
fof(f12,axiom,
! [X2,X3,X1,X4] :
( ~ c_in(X1,X4,X3)
| c_in(X1,c_union(X2,X4,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnCI_0) ).
fof(f66,plain,
spl0_10,
inference(avatar_split_clause,[],[f9,f64]) ).
fof(f9,axiom,
! [X2,X3,X1,X4] :
( c_in(X1,X2,X3)
| ~ c_in(X1,c_inter(X2,X4,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OIntE_1) ).
fof(f62,plain,
spl0_9,
inference(avatar_split_clause,[],[f8,f60]) ).
fof(f8,axiom,
! [X2,X3,X1,X4] :
( c_in(X1,X4,X3)
| ~ c_in(X1,c_inter(X2,X4,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OIntE_0) ).
fof(f58,plain,
spl0_8,
inference(avatar_split_clause,[],[f5,f56]) ).
fof(f5,axiom,
! [X2,X3,X1] :
( c_in(X1,X2,X3)
| c_in(X1,c_uminus(X2,tc_set(X3)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OComplI_0) ).
fof(f54,plain,
spl0_7,
inference(avatar_split_clause,[],[f4,f52]) ).
fof(f4,axiom,
! [X2,X3,X1] :
( ~ c_in(X1,X2,X3)
| ~ c_in(X1,c_uminus(X2,tc_set(X3)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OComplD__dest_0) ).
fof(f50,plain,
spl0_6,
inference(avatar_split_clause,[],[f19,f48]) ).
fof(f19,axiom,
! [X3,X4,X5] : c_in(X5,c_insert(X5,X4,X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).
fof(f46,plain,
spl0_5,
inference(avatar_split_clause,[],[f17,f44]) ).
fof(f17,axiom,
! [X3,X8] : ~ c_in(X8,c_emptyset,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OemptyE_0) ).
fof(f42,plain,
spl0_4,
inference(avatar_split_clause,[],[f11,f40]) ).
fof(f11,axiom,
! [X3,X5] : c_in(X5,c_UNIV,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).
fof(f38,plain,
spl0_3,
inference(avatar_split_clause,[],[f3,f36]) ).
fof(f3,axiom,
! [X0] :
( ~ c_in(X0,v_C,tc_set(t_a))
| c_lessequals(X0,v_A,tc_set(t_a))
| c_lessequals(v_B,X0,tc_set(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f34,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f2,f31]) ).
fof(f2,axiom,
~ c_lessequals(v_B,c_Union(v_C,t_a),tc_set(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f29,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f1,f26]) ).
fof(f1,axiom,
~ c_lessequals(c_Union(v_C,t_a),v_A,tc_set(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SET860-2 : TPTP v8.1.2. Released v3.2.0.
% 0.10/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.33 % Computer : n008.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri May 3 16:18:38 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.11/0.33 % (2176)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.35 % (2179)WARNING: value z3 for option sas not known
% 0.11/0.35 % (2180)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.11/0.35 % (2182)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)
% 0.11/0.35 % (2177)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.11/0.35 % (2178)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.11/0.35 % (2179)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)
% 0.11/0.35 % (2181)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)
% 0.11/0.35 % (2183)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)
% 0.11/0.35 TRYING [1]
% 0.11/0.35 TRYING [2]
% 0.11/0.35 TRYING [3]
% 0.11/0.36 TRYING [1]
% 0.11/0.36 TRYING [2]
% 0.11/0.36 TRYING [4]
% 0.11/0.38 TRYING [3]
% 0.11/0.39 TRYING [5]
% 0.17/0.44 % (2181)First to succeed.
% 0.17/0.45 % (2181)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2176"
% 0.17/0.45 % (2181)Refutation found. Thanks to Tanya!
% 0.17/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.45 % (2181)------------------------------
% 0.17/0.45 % (2181)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.17/0.45 % (2181)Termination reason: Refutation
% 0.17/0.45
% 0.17/0.45 % (2181)Memory used [KB]: 2161
% 0.17/0.45 % (2181)Time elapsed: 0.100 s
% 0.17/0.45 % (2181)Instructions burned: 188 (million)
% 0.17/0.45 % (2176)Success in time 0.113 s
%------------------------------------------------------------------------------