TSTP Solution File: SEU341+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU341+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 15:29:20 EDT 2024
% Result : Theorem 0.19s 0.39s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 178
% Syntax : Number of formulae : 553 ( 102 unt; 0 def)
% Number of atoms : 1708 ( 25 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 1997 ( 842 ~; 808 |; 157 &)
% ( 138 <=>; 52 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 152 ( 150 usr; 135 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 524 ( 494 !; 30 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1073,plain,
$false,
inference(avatar_sat_refutation,[],[f198,f203,f208,f213,f218,f223,f228,f233,f238,f243,f248,f253,f258,f263,f268,f273,f278,f283,f288,f293,f298,f302,f306,f310,f314,f318,f322,f326,f330,f334,f338,f342,f346,f350,f354,f358,f362,f366,f370,f374,f387,f393,f397,f401,f405,f413,f417,f421,f427,f431,f435,f442,f446,f450,f454,f458,f462,f466,f470,f474,f478,f483,f487,f491,f544,f573,f583,f593,f611,f615,f621,f625,f632,f648,f663,f672,f677,f682,f687,f695,f700,f702,f709,f720,f724,f727,f728,f780,f788,f799,f804,f812,f815,f816,f834,f845,f848,f849,f871,f875,f879,f883,f884,f926,f931,f936,f940,f945,f953,f957,f961,f965,f969,f973,f977,f981,f995,f1004,f1008,f1012,f1016,f1020,f1024,f1028,f1035,f1039,f1043,f1047,f1051,f1055,f1059,f1063,f1067,f1071,f1072]) ).
fof(f1072,plain,
( ~ spl11_5
| spl11_7
| ~ spl11_117 ),
inference(avatar_split_clause,[],[f1029,f993,f225,f215]) ).
fof(f215,plain,
( spl11_5
<=> in(sK4,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_5])]) ).
fof(f225,plain,
( spl11_7
<=> point_neighbourhood(sK3,sK2,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_7])]) ).
fof(f993,plain,
( spl11_117
<=> ! [X0] :
( ~ in(X0,sK3)
| point_neighbourhood(sK3,sK2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_117])]) ).
fof(f1029,plain,
( ~ in(sK4,sK3)
| spl11_7
| ~ spl11_117 ),
inference(resolution,[],[f994,f227]) ).
fof(f227,plain,
( ~ point_neighbourhood(sK3,sK2,sK4)
| spl11_7 ),
inference(avatar_component_clause,[],[f225]) ).
fof(f994,plain,
( ! [X0] :
( point_neighbourhood(sK3,sK2,X0)
| ~ in(X0,sK3) )
| ~ spl11_117 ),
inference(avatar_component_clause,[],[f993]) ).
fof(f1071,plain,
( spl11_134
| ~ spl11_50
| ~ spl11_60 ),
inference(avatar_split_clause,[],[f545,f472,f429,f1069]) ).
fof(f1069,plain,
( spl11_134
<=> ! [X0,X1] :
( v1_membered(X0)
| ~ v2_membered(X1)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_134])]) ).
fof(f429,plain,
( spl11_50
<=> ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_50])]) ).
fof(f472,plain,
( spl11_60
<=> ! [X0,X1] :
( v1_membered(X1)
| ~ element(X1,powerset(X0))
| ~ v2_membered(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_60])]) ).
fof(f545,plain,
( ! [X0,X1] :
( v1_membered(X0)
| ~ v2_membered(X1)
| ~ subset(X0,X1) )
| ~ spl11_50
| ~ spl11_60 ),
inference(resolution,[],[f473,f430]) ).
fof(f430,plain,
( ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) )
| ~ spl11_50 ),
inference(avatar_component_clause,[],[f429]) ).
fof(f473,plain,
( ! [X0,X1] :
( ~ element(X1,powerset(X0))
| v1_membered(X1)
| ~ v2_membered(X0) )
| ~ spl11_60 ),
inference(avatar_component_clause,[],[f472]) ).
fof(f1067,plain,
( spl11_133
| ~ spl11_49
| ~ spl11_59 ),
inference(avatar_split_clause,[],[f536,f468,f425,f1065]) ).
fof(f1065,plain,
( spl11_133
<=> ! [X0] :
( v3_membered(sK5(X0))
| ~ v3_membered(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_133])]) ).
fof(f425,plain,
( spl11_49
<=> ! [X0] :
( element(sK5(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_49])]) ).
fof(f468,plain,
( spl11_59
<=> ! [X0,X1] :
( v3_membered(X1)
| ~ element(X1,powerset(X0))
| ~ v3_membered(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_59])]) ).
fof(f536,plain,
( ! [X0] :
( v3_membered(sK5(X0))
| ~ v3_membered(X0)
| empty(X0) )
| ~ spl11_49
| ~ spl11_59 ),
inference(resolution,[],[f469,f426]) ).
fof(f426,plain,
( ! [X0] :
( element(sK5(X0),powerset(X0))
| empty(X0) )
| ~ spl11_49 ),
inference(avatar_component_clause,[],[f425]) ).
fof(f469,plain,
( ! [X0,X1] :
( ~ element(X1,powerset(X0))
| v3_membered(X1)
| ~ v3_membered(X0) )
| ~ spl11_59 ),
inference(avatar_component_clause,[],[f468]) ).
fof(f1063,plain,
( spl11_132
| ~ spl11_50
| ~ spl11_59 ),
inference(avatar_split_clause,[],[f534,f468,f429,f1061]) ).
fof(f1061,plain,
( spl11_132
<=> ! [X0,X1] :
( v3_membered(X0)
| ~ v3_membered(X1)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_132])]) ).
fof(f534,plain,
( ! [X0,X1] :
( v3_membered(X0)
| ~ v3_membered(X1)
| ~ subset(X0,X1) )
| ~ spl11_50
| ~ spl11_59 ),
inference(resolution,[],[f469,f430]) ).
fof(f1059,plain,
( spl11_131
| ~ spl11_49
| ~ spl11_58 ),
inference(avatar_split_clause,[],[f530,f464,f425,f1057]) ).
fof(f1057,plain,
( spl11_131
<=> ! [X0] :
( v2_membered(sK5(X0))
| ~ v3_membered(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_131])]) ).
fof(f464,plain,
( spl11_58
<=> ! [X0,X1] :
( v2_membered(X1)
| ~ element(X1,powerset(X0))
| ~ v3_membered(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_58])]) ).
fof(f530,plain,
( ! [X0] :
( v2_membered(sK5(X0))
| ~ v3_membered(X0)
| empty(X0) )
| ~ spl11_49
| ~ spl11_58 ),
inference(resolution,[],[f465,f426]) ).
fof(f465,plain,
( ! [X0,X1] :
( ~ element(X1,powerset(X0))
| v2_membered(X1)
| ~ v3_membered(X0) )
| ~ spl11_58 ),
inference(avatar_component_clause,[],[f464]) ).
fof(f1055,plain,
( spl11_130
| ~ spl11_50
| ~ spl11_58 ),
inference(avatar_split_clause,[],[f528,f464,f429,f1053]) ).
fof(f1053,plain,
( spl11_130
<=> ! [X0,X1] :
( v2_membered(X0)
| ~ v3_membered(X1)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_130])]) ).
fof(f528,plain,
( ! [X0,X1] :
( v2_membered(X0)
| ~ v3_membered(X1)
| ~ subset(X0,X1) )
| ~ spl11_50
| ~ spl11_58 ),
inference(resolution,[],[f465,f430]) ).
fof(f1051,plain,
( spl11_129
| ~ spl11_49
| ~ spl11_57 ),
inference(avatar_split_clause,[],[f524,f460,f425,f1049]) ).
fof(f1049,plain,
( spl11_129
<=> ! [X0] :
( v1_membered(sK5(X0))
| ~ v3_membered(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_129])]) ).
fof(f460,plain,
( spl11_57
<=> ! [X0,X1] :
( v1_membered(X1)
| ~ element(X1,powerset(X0))
| ~ v3_membered(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_57])]) ).
fof(f524,plain,
( ! [X0] :
( v1_membered(sK5(X0))
| ~ v3_membered(X0)
| empty(X0) )
| ~ spl11_49
| ~ spl11_57 ),
inference(resolution,[],[f461,f426]) ).
fof(f461,plain,
( ! [X0,X1] :
( ~ element(X1,powerset(X0))
| v1_membered(X1)
| ~ v3_membered(X0) )
| ~ spl11_57 ),
inference(avatar_component_clause,[],[f460]) ).
fof(f1047,plain,
( spl11_128
| ~ spl11_50
| ~ spl11_57 ),
inference(avatar_split_clause,[],[f522,f460,f429,f1045]) ).
fof(f1045,plain,
( spl11_128
<=> ! [X0,X1] :
( v1_membered(X0)
| ~ v3_membered(X1)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_128])]) ).
fof(f522,plain,
( ! [X0,X1] :
( v1_membered(X0)
| ~ v3_membered(X1)
| ~ subset(X0,X1) )
| ~ spl11_50
| ~ spl11_57 ),
inference(resolution,[],[f461,f430]) ).
fof(f1043,plain,
( spl11_127
| ~ spl11_49
| ~ spl11_56 ),
inference(avatar_split_clause,[],[f518,f456,f425,f1041]) ).
fof(f1041,plain,
( spl11_127
<=> ! [X0] :
( v4_membered(sK5(X0))
| ~ v4_membered(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_127])]) ).
fof(f456,plain,
( spl11_56
<=> ! [X0,X1] :
( v4_membered(X1)
| ~ element(X1,powerset(X0))
| ~ v4_membered(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_56])]) ).
fof(f518,plain,
( ! [X0] :
( v4_membered(sK5(X0))
| ~ v4_membered(X0)
| empty(X0) )
| ~ spl11_49
| ~ spl11_56 ),
inference(resolution,[],[f457,f426]) ).
fof(f457,plain,
( ! [X0,X1] :
( ~ element(X1,powerset(X0))
| v4_membered(X1)
| ~ v4_membered(X0) )
| ~ spl11_56 ),
inference(avatar_component_clause,[],[f456]) ).
fof(f1039,plain,
( spl11_126
| ~ spl11_50
| ~ spl11_56 ),
inference(avatar_split_clause,[],[f516,f456,f429,f1037]) ).
fof(f1037,plain,
( spl11_126
<=> ! [X0,X1] :
( v4_membered(X0)
| ~ v4_membered(X1)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_126])]) ).
fof(f516,plain,
( ! [X0,X1] :
( v4_membered(X0)
| ~ v4_membered(X1)
| ~ subset(X0,X1) )
| ~ spl11_50
| ~ spl11_56 ),
inference(resolution,[],[f457,f430]) ).
fof(f1035,plain,
( spl11_125
| ~ spl11_49
| ~ spl11_55 ),
inference(avatar_split_clause,[],[f512,f452,f425,f1033]) ).
fof(f1033,plain,
( spl11_125
<=> ! [X0] :
( v3_membered(sK5(X0))
| ~ v4_membered(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_125])]) ).
fof(f452,plain,
( spl11_55
<=> ! [X0,X1] :
( v3_membered(X1)
| ~ element(X1,powerset(X0))
| ~ v4_membered(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_55])]) ).
fof(f512,plain,
( ! [X0] :
( v3_membered(sK5(X0))
| ~ v4_membered(X0)
| empty(X0) )
| ~ spl11_49
| ~ spl11_55 ),
inference(resolution,[],[f453,f426]) ).
fof(f453,plain,
( ! [X0,X1] :
( ~ element(X1,powerset(X0))
| v3_membered(X1)
| ~ v4_membered(X0) )
| ~ spl11_55 ),
inference(avatar_component_clause,[],[f452]) ).
fof(f1028,plain,
( spl11_124
| ~ spl11_50
| ~ spl11_55 ),
inference(avatar_split_clause,[],[f510,f452,f429,f1026]) ).
fof(f1026,plain,
( spl11_124
<=> ! [X0,X1] :
( v3_membered(X0)
| ~ v4_membered(X1)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_124])]) ).
fof(f510,plain,
( ! [X0,X1] :
( v3_membered(X0)
| ~ v4_membered(X1)
| ~ subset(X0,X1) )
| ~ spl11_50
| ~ spl11_55 ),
inference(resolution,[],[f453,f430]) ).
fof(f1024,plain,
( spl11_123
| ~ spl11_49
| ~ spl11_54 ),
inference(avatar_split_clause,[],[f506,f448,f425,f1022]) ).
fof(f1022,plain,
( spl11_123
<=> ! [X0] :
( v2_membered(sK5(X0))
| ~ v4_membered(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_123])]) ).
fof(f448,plain,
( spl11_54
<=> ! [X0,X1] :
( v2_membered(X1)
| ~ element(X1,powerset(X0))
| ~ v4_membered(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_54])]) ).
fof(f506,plain,
( ! [X0] :
( v2_membered(sK5(X0))
| ~ v4_membered(X0)
| empty(X0) )
| ~ spl11_49
| ~ spl11_54 ),
inference(resolution,[],[f449,f426]) ).
fof(f449,plain,
( ! [X0,X1] :
( ~ element(X1,powerset(X0))
| v2_membered(X1)
| ~ v4_membered(X0) )
| ~ spl11_54 ),
inference(avatar_component_clause,[],[f448]) ).
fof(f1020,plain,
( spl11_122
| ~ spl11_50
| ~ spl11_54 ),
inference(avatar_split_clause,[],[f504,f448,f429,f1018]) ).
fof(f1018,plain,
( spl11_122
<=> ! [X0,X1] :
( v2_membered(X0)
| ~ v4_membered(X1)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_122])]) ).
fof(f504,plain,
( ! [X0,X1] :
( v2_membered(X0)
| ~ v4_membered(X1)
| ~ subset(X0,X1) )
| ~ spl11_50
| ~ spl11_54 ),
inference(resolution,[],[f449,f430]) ).
fof(f1016,plain,
( spl11_121
| ~ spl11_49
| ~ spl11_53 ),
inference(avatar_split_clause,[],[f500,f444,f425,f1014]) ).
fof(f1014,plain,
( spl11_121
<=> ! [X0] :
( v1_membered(sK5(X0))
| ~ v4_membered(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_121])]) ).
fof(f444,plain,
( spl11_53
<=> ! [X0,X1] :
( v1_membered(X1)
| ~ element(X1,powerset(X0))
| ~ v4_membered(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_53])]) ).
fof(f500,plain,
( ! [X0] :
( v1_membered(sK5(X0))
| ~ v4_membered(X0)
| empty(X0) )
| ~ spl11_49
| ~ spl11_53 ),
inference(resolution,[],[f445,f426]) ).
fof(f445,plain,
( ! [X0,X1] :
( ~ element(X1,powerset(X0))
| v1_membered(X1)
| ~ v4_membered(X0) )
| ~ spl11_53 ),
inference(avatar_component_clause,[],[f444]) ).
fof(f1012,plain,
( spl11_120
| ~ spl11_50
| ~ spl11_53 ),
inference(avatar_split_clause,[],[f498,f444,f429,f1010]) ).
fof(f1010,plain,
( spl11_120
<=> ! [X0,X1] :
( v1_membered(X0)
| ~ v4_membered(X1)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_120])]) ).
fof(f498,plain,
( ! [X0,X1] :
( v1_membered(X0)
| ~ v4_membered(X1)
| ~ subset(X0,X1) )
| ~ spl11_50
| ~ spl11_53 ),
inference(resolution,[],[f445,f430]) ).
fof(f1008,plain,
( spl11_119
| ~ spl11_49
| ~ spl11_52 ),
inference(avatar_split_clause,[],[f494,f440,f425,f1006]) ).
fof(f1006,plain,
( spl11_119
<=> ! [X0] :
( sP0(sK5(X0))
| ~ v5_membered(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_119])]) ).
fof(f440,plain,
( spl11_52
<=> ! [X0,X1] :
( sP0(X1)
| ~ element(X1,powerset(X0))
| ~ v5_membered(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_52])]) ).
fof(f494,plain,
( ! [X0] :
( sP0(sK5(X0))
| ~ v5_membered(X0)
| empty(X0) )
| ~ spl11_49
| ~ spl11_52 ),
inference(resolution,[],[f441,f426]) ).
fof(f441,plain,
( ! [X0,X1] :
( ~ element(X1,powerset(X0))
| sP0(X1)
| ~ v5_membered(X0) )
| ~ spl11_52 ),
inference(avatar_component_clause,[],[f440]) ).
fof(f1004,plain,
( spl11_118
| ~ spl11_50
| ~ spl11_52 ),
inference(avatar_split_clause,[],[f492,f440,f429,f1002]) ).
fof(f1002,plain,
( spl11_118
<=> ! [X0,X1] :
( sP0(X0)
| ~ v5_membered(X1)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_118])]) ).
fof(f492,plain,
( ! [X0,X1] :
( sP0(X0)
| ~ v5_membered(X1)
| ~ subset(X0,X1) )
| ~ spl11_50
| ~ spl11_52 ),
inference(resolution,[],[f441,f430]) ).
fof(f995,plain,
( spl11_117
| ~ spl11_87
| ~ spl11_108 ),
inference(avatar_split_clause,[],[f949,f943,f707,f993]) ).
fof(f707,plain,
( spl11_87
<=> ! [X0] :
( element(X0,the_carrier(sK2))
| ~ in(X0,sK3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_87])]) ).
fof(f943,plain,
( spl11_108
<=> ! [X0] :
( ~ in(X0,sK3)
| ~ element(X0,the_carrier(sK2))
| point_neighbourhood(sK3,sK2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_108])]) ).
fof(f949,plain,
( ! [X0] :
( ~ in(X0,sK3)
| point_neighbourhood(sK3,sK2,X0) )
| ~ spl11_87
| ~ spl11_108 ),
inference(duplicate_literal_removal,[],[f946]) ).
fof(f946,plain,
( ! [X0] :
( ~ in(X0,sK3)
| point_neighbourhood(sK3,sK2,X0)
| ~ in(X0,sK3) )
| ~ spl11_87
| ~ spl11_108 ),
inference(resolution,[],[f944,f708]) ).
fof(f708,plain,
( ! [X0] :
( element(X0,the_carrier(sK2))
| ~ in(X0,sK3) )
| ~ spl11_87 ),
inference(avatar_component_clause,[],[f707]) ).
fof(f944,plain,
( ! [X0] :
( ~ element(X0,the_carrier(sK2))
| ~ in(X0,sK3)
| point_neighbourhood(sK3,sK2,X0) )
| ~ spl11_108 ),
inference(avatar_component_clause,[],[f943]) ).
fof(f981,plain,
( spl11_116
| ~ spl11_40
| ~ spl11_64 ),
inference(avatar_split_clause,[],[f567,f489,f372,f979]) ).
fof(f979,plain,
( spl11_116
<=> ! [X0] :
( empty(X0)
| in(sK6(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_116])]) ).
fof(f372,plain,
( spl11_40
<=> ! [X0] : element(sK6(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_40])]) ).
fof(f489,plain,
( spl11_64
<=> ! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_64])]) ).
fof(f567,plain,
( ! [X0] :
( empty(X0)
| in(sK6(X0),X0) )
| ~ spl11_40
| ~ spl11_64 ),
inference(resolution,[],[f490,f373]) ).
fof(f373,plain,
( ! [X0] : element(sK6(X0),X0)
| ~ spl11_40 ),
inference(avatar_component_clause,[],[f372]) ).
fof(f490,plain,
( ! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) )
| ~ spl11_64 ),
inference(avatar_component_clause,[],[f489]) ).
fof(f977,plain,
( spl11_115
| ~ spl11_40
| ~ spl11_63 ),
inference(avatar_split_clause,[],[f560,f485,f372,f975]) ).
fof(f975,plain,
( spl11_115
<=> ! [X0] :
( v1_membered(sK6(powerset(X0)))
| ~ v1_membered(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_115])]) ).
fof(f485,plain,
( spl11_63
<=> ! [X0,X1] :
( v1_membered(X1)
| ~ element(X1,powerset(X0))
| ~ v1_membered(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_63])]) ).
fof(f560,plain,
( ! [X0] :
( v1_membered(sK6(powerset(X0)))
| ~ v1_membered(X0) )
| ~ spl11_40
| ~ spl11_63 ),
inference(resolution,[],[f486,f373]) ).
fof(f486,plain,
( ! [X0,X1] :
( ~ element(X1,powerset(X0))
| v1_membered(X1)
| ~ v1_membered(X0) )
| ~ spl11_63 ),
inference(avatar_component_clause,[],[f485]) ).
fof(f973,plain,
( spl11_114
| ~ spl11_40
| ~ spl11_61 ),
inference(avatar_split_clause,[],[f554,f476,f372,f971]) ).
fof(f971,plain,
( spl11_114
<=> ! [X0] :
( v2_membered(sK6(powerset(X0)))
| ~ v2_membered(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_114])]) ).
fof(f476,plain,
( spl11_61
<=> ! [X0,X1] :
( v2_membered(X1)
| ~ element(X1,powerset(X0))
| ~ v2_membered(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_61])]) ).
fof(f554,plain,
( ! [X0] :
( v2_membered(sK6(powerset(X0)))
| ~ v2_membered(X0) )
| ~ spl11_40
| ~ spl11_61 ),
inference(resolution,[],[f477,f373]) ).
fof(f477,plain,
( ! [X0,X1] :
( ~ element(X1,powerset(X0))
| v2_membered(X1)
| ~ v2_membered(X0) )
| ~ spl11_61 ),
inference(avatar_component_clause,[],[f476]) ).
fof(f969,plain,
( spl11_113
| ~ spl11_40
| ~ spl11_60 ),
inference(avatar_split_clause,[],[f548,f472,f372,f967]) ).
fof(f967,plain,
( spl11_113
<=> ! [X0] :
( v1_membered(sK6(powerset(X0)))
| ~ v2_membered(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_113])]) ).
fof(f548,plain,
( ! [X0] :
( v1_membered(sK6(powerset(X0)))
| ~ v2_membered(X0) )
| ~ spl11_40
| ~ spl11_60 ),
inference(resolution,[],[f473,f373]) ).
fof(f965,plain,
( spl11_112
| ~ spl11_40
| ~ spl11_59 ),
inference(avatar_split_clause,[],[f537,f468,f372,f963]) ).
fof(f963,plain,
( spl11_112
<=> ! [X0] :
( v3_membered(sK6(powerset(X0)))
| ~ v3_membered(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_112])]) ).
fof(f537,plain,
( ! [X0] :
( v3_membered(sK6(powerset(X0)))
| ~ v3_membered(X0) )
| ~ spl11_40
| ~ spl11_59 ),
inference(resolution,[],[f469,f373]) ).
fof(f961,plain,
( spl11_111
| ~ spl11_40
| ~ spl11_58 ),
inference(avatar_split_clause,[],[f531,f464,f372,f959]) ).
fof(f959,plain,
( spl11_111
<=> ! [X0] :
( v2_membered(sK6(powerset(X0)))
| ~ v3_membered(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_111])]) ).
fof(f531,plain,
( ! [X0] :
( v2_membered(sK6(powerset(X0)))
| ~ v3_membered(X0) )
| ~ spl11_40
| ~ spl11_58 ),
inference(resolution,[],[f465,f373]) ).
fof(f957,plain,
( spl11_110
| ~ spl11_40
| ~ spl11_57 ),
inference(avatar_split_clause,[],[f525,f460,f372,f955]) ).
fof(f955,plain,
( spl11_110
<=> ! [X0] :
( v1_membered(sK6(powerset(X0)))
| ~ v3_membered(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_110])]) ).
fof(f525,plain,
( ! [X0] :
( v1_membered(sK6(powerset(X0)))
| ~ v3_membered(X0) )
| ~ spl11_40
| ~ spl11_57 ),
inference(resolution,[],[f461,f373]) ).
fof(f953,plain,
( spl11_109
| ~ spl11_40
| ~ spl11_56 ),
inference(avatar_split_clause,[],[f519,f456,f372,f951]) ).
fof(f951,plain,
( spl11_109
<=> ! [X0] :
( v4_membered(sK6(powerset(X0)))
| ~ v4_membered(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_109])]) ).
fof(f519,plain,
( ! [X0] :
( v4_membered(sK6(powerset(X0)))
| ~ v4_membered(X0) )
| ~ spl11_40
| ~ spl11_56 ),
inference(resolution,[],[f457,f373]) ).
fof(f945,plain,
( spl11_108
| ~ spl11_92
| ~ spl11_107 ),
inference(avatar_split_clause,[],[f941,f938,f785,f943]) ).
fof(f785,plain,
( spl11_92
<=> sK3 = interior(sK2,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_92])]) ).
fof(f938,plain,
( spl11_107
<=> ! [X0] :
( ~ in(X0,interior(sK2,sK3))
| ~ element(X0,the_carrier(sK2))
| point_neighbourhood(sK3,sK2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_107])]) ).
fof(f941,plain,
( ! [X0] :
( ~ in(X0,sK3)
| ~ element(X0,the_carrier(sK2))
| point_neighbourhood(sK3,sK2,X0) )
| ~ spl11_92
| ~ spl11_107 ),
inference(forward_demodulation,[],[f939,f787]) ).
fof(f787,plain,
( sK3 = interior(sK2,sK3)
| ~ spl11_92 ),
inference(avatar_component_clause,[],[f785]) ).
fof(f939,plain,
( ! [X0] :
( ~ in(X0,interior(sK2,sK3))
| ~ element(X0,the_carrier(sK2))
| point_neighbourhood(sK3,sK2,X0) )
| ~ spl11_107 ),
inference(avatar_component_clause,[],[f938]) ).
fof(f940,plain,
( spl11_1
| ~ spl11_2
| ~ spl11_3
| spl11_107
| ~ spl11_8
| ~ spl11_72 ),
inference(avatar_split_clause,[],[f765,f623,f230,f938,f205,f200,f195]) ).
fof(f195,plain,
( spl11_1
<=> empty_carrier(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_1])]) ).
fof(f200,plain,
( spl11_2
<=> topological_space(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_2])]) ).
fof(f205,plain,
( spl11_3
<=> top_str(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_3])]) ).
fof(f230,plain,
( spl11_8
<=> element(sK3,powerset(the_carrier(sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_8])]) ).
fof(f623,plain,
( spl11_72
<=> ! [X2,X0,X1] :
( point_neighbourhood(X2,X0,X1)
| ~ in(X1,interior(X0,X2))
| ~ element(X2,powerset(the_carrier(X0)))
| ~ element(X1,the_carrier(X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_72])]) ).
fof(f765,plain,
( ! [X0] :
( ~ in(X0,interior(sK2,sK3))
| point_neighbourhood(sK3,sK2,X0)
| ~ element(X0,the_carrier(sK2))
| ~ top_str(sK2)
| ~ topological_space(sK2)
| empty_carrier(sK2) )
| ~ spl11_8
| ~ spl11_72 ),
inference(resolution,[],[f624,f232]) ).
fof(f232,plain,
( element(sK3,powerset(the_carrier(sK2)))
| ~ spl11_8 ),
inference(avatar_component_clause,[],[f230]) ).
fof(f624,plain,
( ! [X2,X0,X1] :
( ~ element(X2,powerset(the_carrier(X0)))
| ~ in(X1,interior(X0,X2))
| point_neighbourhood(X2,X0,X1)
| ~ element(X1,the_carrier(X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) )
| ~ spl11_72 ),
inference(avatar_component_clause,[],[f623]) ).
fof(f936,plain,
( ~ spl11_106
| ~ spl11_47
| ~ spl11_90 ),
inference(avatar_split_clause,[],[f782,f773,f415,f933]) ).
fof(f933,plain,
( spl11_106
<=> in(powerset(the_carrier(sK2)),sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_106])]) ).
fof(f415,plain,
( spl11_47
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_47])]) ).
fof(f773,plain,
( spl11_90
<=> in(sK3,powerset(the_carrier(sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_90])]) ).
fof(f782,plain,
( ~ in(powerset(the_carrier(sK2)),sK3)
| ~ spl11_47
| ~ spl11_90 ),
inference(resolution,[],[f775,f416]) ).
fof(f416,plain,
( ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) )
| ~ spl11_47 ),
inference(avatar_component_clause,[],[f415]) ).
fof(f775,plain,
( in(sK3,powerset(the_carrier(sK2)))
| ~ spl11_90 ),
inference(avatar_component_clause,[],[f773]) ).
fof(f931,plain,
( spl11_105
| ~ spl11_92
| ~ spl11_104 ),
inference(avatar_split_clause,[],[f927,f924,f785,f929]) ).
fof(f929,plain,
( spl11_105
<=> ! [X0] :
( in(X0,sK3)
| ~ point_neighbourhood(sK3,sK2,X0)
| ~ element(X0,the_carrier(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_105])]) ).
fof(f924,plain,
( spl11_104
<=> ! [X0] :
( ~ point_neighbourhood(sK3,sK2,X0)
| ~ element(X0,the_carrier(sK2))
| in(X0,interior(sK2,sK3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_104])]) ).
fof(f927,plain,
( ! [X0] :
( in(X0,sK3)
| ~ point_neighbourhood(sK3,sK2,X0)
| ~ element(X0,the_carrier(sK2)) )
| ~ spl11_92
| ~ spl11_104 ),
inference(forward_demodulation,[],[f925,f787]) ).
fof(f925,plain,
( ! [X0] :
( ~ point_neighbourhood(sK3,sK2,X0)
| ~ element(X0,the_carrier(sK2))
| in(X0,interior(sK2,sK3)) )
| ~ spl11_104 ),
inference(avatar_component_clause,[],[f924]) ).
fof(f926,plain,
( spl11_1
| ~ spl11_2
| ~ spl11_3
| spl11_104
| ~ spl11_8
| ~ spl11_71 ),
inference(avatar_split_clause,[],[f756,f619,f230,f924,f205,f200,f195]) ).
fof(f619,plain,
( spl11_71
<=> ! [X2,X0,X1] :
( in(X1,interior(X0,X2))
| ~ point_neighbourhood(X2,X0,X1)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ element(X1,the_carrier(X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_71])]) ).
fof(f756,plain,
( ! [X0] :
( ~ point_neighbourhood(sK3,sK2,X0)
| in(X0,interior(sK2,sK3))
| ~ element(X0,the_carrier(sK2))
| ~ top_str(sK2)
| ~ topological_space(sK2)
| empty_carrier(sK2) )
| ~ spl11_8
| ~ spl11_71 ),
inference(resolution,[],[f620,f232]) ).
fof(f620,plain,
( ! [X2,X0,X1] :
( ~ element(X2,powerset(the_carrier(X0)))
| ~ point_neighbourhood(X2,X0,X1)
| in(X1,interior(X0,X2))
| ~ element(X1,the_carrier(X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) )
| ~ spl11_71 ),
inference(avatar_component_clause,[],[f619]) ).
fof(f884,plain,
( ~ spl11_2
| ~ spl11_3
| ~ spl11_97 ),
inference(avatar_split_clause,[],[f837,f832,f205,f200]) ).
fof(f832,plain,
( spl11_97
<=> ! [X0] :
( ~ topological_space(X0)
| ~ top_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_97])]) ).
fof(f837,plain,
( ~ topological_space(sK2)
| ~ spl11_3
| ~ spl11_97 ),
inference(resolution,[],[f833,f207]) ).
fof(f207,plain,
( top_str(sK2)
| ~ spl11_3 ),
inference(avatar_component_clause,[],[f205]) ).
fof(f833,plain,
( ! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0) )
| ~ spl11_97 ),
inference(avatar_component_clause,[],[f832]) ).
fof(f883,plain,
( spl11_103
| ~ spl11_40
| ~ spl11_55 ),
inference(avatar_split_clause,[],[f513,f452,f372,f881]) ).
fof(f881,plain,
( spl11_103
<=> ! [X0] :
( v3_membered(sK6(powerset(X0)))
| ~ v4_membered(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_103])]) ).
fof(f513,plain,
( ! [X0] :
( v3_membered(sK6(powerset(X0)))
| ~ v4_membered(X0) )
| ~ spl11_40
| ~ spl11_55 ),
inference(resolution,[],[f453,f373]) ).
fof(f879,plain,
( spl11_102
| ~ spl11_40
| ~ spl11_54 ),
inference(avatar_split_clause,[],[f507,f448,f372,f877]) ).
fof(f877,plain,
( spl11_102
<=> ! [X0] :
( v2_membered(sK6(powerset(X0)))
| ~ v4_membered(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_102])]) ).
fof(f507,plain,
( ! [X0] :
( v2_membered(sK6(powerset(X0)))
| ~ v4_membered(X0) )
| ~ spl11_40
| ~ spl11_54 ),
inference(resolution,[],[f449,f373]) ).
fof(f875,plain,
( spl11_101
| ~ spl11_40
| ~ spl11_53 ),
inference(avatar_split_clause,[],[f501,f444,f372,f873]) ).
fof(f873,plain,
( spl11_101
<=> ! [X0] :
( v1_membered(sK6(powerset(X0)))
| ~ v4_membered(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_101])]) ).
fof(f501,plain,
( ! [X0] :
( v1_membered(sK6(powerset(X0)))
| ~ v4_membered(X0) )
| ~ spl11_40
| ~ spl11_53 ),
inference(resolution,[],[f445,f373]) ).
fof(f871,plain,
( spl11_100
| ~ spl11_40
| ~ spl11_52 ),
inference(avatar_split_clause,[],[f495,f440,f372,f869]) ).
fof(f869,plain,
( spl11_100
<=> ! [X0] :
( sP0(sK6(powerset(X0)))
| ~ v5_membered(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_100])]) ).
fof(f495,plain,
( ! [X0] :
( sP0(sK6(powerset(X0)))
| ~ v5_membered(X0) )
| ~ spl11_40
| ~ spl11_52 ),
inference(resolution,[],[f441,f373]) ).
fof(f849,plain,
( ~ spl11_9
| ~ spl11_98 ),
inference(avatar_contradiction_clause,[],[f846]) ).
fof(f846,plain,
( $false
| ~ spl11_9
| ~ spl11_98 ),
inference(resolution,[],[f841,f237]) ).
fof(f237,plain,
( empty(empty_set)
| ~ spl11_9 ),
inference(avatar_component_clause,[],[f235]) ).
fof(f235,plain,
( spl11_9
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_9])]) ).
fof(f841,plain,
( ! [X0] : ~ empty(X0)
| ~ spl11_98 ),
inference(avatar_component_clause,[],[f840]) ).
fof(f840,plain,
( spl11_98
<=> ! [X0] : ~ empty(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_98])]) ).
fof(f848,plain,
( ~ spl11_23
| ~ spl11_98 ),
inference(avatar_contradiction_clause,[],[f847]) ).
fof(f847,plain,
( $false
| ~ spl11_23
| ~ spl11_98 ),
inference(resolution,[],[f841,f305]) ).
fof(f305,plain,
( ! [X0] : empty(sK7(X0))
| ~ spl11_23 ),
inference(avatar_component_clause,[],[f304]) ).
fof(f304,plain,
( spl11_23
<=> ! [X0] : empty(sK7(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_23])]) ).
fof(f845,plain,
( spl11_98
| spl11_99
| ~ spl11_23
| ~ spl11_43
| ~ spl11_44
| ~ spl11_66 ),
inference(avatar_split_clause,[],[f579,f571,f399,f395,f304,f843,f840]) ).
fof(f843,plain,
( spl11_99
<=> ! [X1] : ~ in(X1,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_99])]) ).
fof(f395,plain,
( spl11_43
<=> ! [X0] :
( empty_set = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_43])]) ).
fof(f399,plain,
( spl11_44
<=> ! [X0] : element(sK7(X0),powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_44])]) ).
fof(f571,plain,
( spl11_66
<=> ! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_66])]) ).
fof(f579,plain,
( ! [X0,X1] :
( ~ in(X1,empty_set)
| ~ empty(X0) )
| ~ spl11_23
| ~ spl11_43
| ~ spl11_44
| ~ spl11_66 ),
inference(forward_demodulation,[],[f578,f407]) ).
fof(f407,plain,
( ! [X0] : empty_set = sK7(X0)
| ~ spl11_23
| ~ spl11_43 ),
inference(resolution,[],[f396,f305]) ).
fof(f396,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = X0 )
| ~ spl11_43 ),
inference(avatar_component_clause,[],[f395]) ).
fof(f578,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK7(X0)) )
| ~ spl11_44
| ~ spl11_66 ),
inference(resolution,[],[f572,f400]) ).
fof(f400,plain,
( ! [X0] : element(sK7(X0),powerset(X0))
| ~ spl11_44 ),
inference(avatar_component_clause,[],[f399]) ).
fof(f572,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X0,X1) )
| ~ spl11_66 ),
inference(avatar_component_clause,[],[f571]) ).
fof(f834,plain,
( spl11_97
| ~ spl11_40
| ~ spl11_73 ),
inference(avatar_split_clause,[],[f793,f627,f372,f832]) ).
fof(f627,plain,
( spl11_73
<=> ! [X2,X0] :
( ~ element(X2,powerset(the_carrier(X0)))
| ~ topological_space(X0)
| ~ top_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_73])]) ).
fof(f793,plain,
( ! [X0] :
( ~ topological_space(X0)
| ~ top_str(X0) )
| ~ spl11_40
| ~ spl11_73 ),
inference(resolution,[],[f628,f373]) ).
fof(f628,plain,
( ! [X2,X0] :
( ~ element(X2,powerset(the_carrier(X0)))
| ~ topological_space(X0)
| ~ top_str(X0) )
| ~ spl11_73 ),
inference(avatar_component_clause,[],[f627]) ).
fof(f816,plain,
( ~ spl11_14
| ~ spl11_95 ),
inference(avatar_contradiction_clause,[],[f813]) ).
fof(f813,plain,
( $false
| ~ spl11_14
| ~ spl11_95 ),
inference(resolution,[],[f807,f262]) ).
fof(f262,plain,
( v5_membered(empty_set)
| ~ spl11_14 ),
inference(avatar_component_clause,[],[f260]) ).
fof(f260,plain,
( spl11_14
<=> v5_membered(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_14])]) ).
fof(f807,plain,
( ! [X0] : ~ v5_membered(X0)
| ~ spl11_95 ),
inference(avatar_component_clause,[],[f806]) ).
fof(f806,plain,
( spl11_95
<=> ! [X0] : ~ v5_membered(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_95])]) ).
fof(f815,plain,
( ~ spl11_21
| ~ spl11_95 ),
inference(avatar_contradiction_clause,[],[f814]) ).
fof(f814,plain,
( $false
| ~ spl11_21
| ~ spl11_95 ),
inference(resolution,[],[f807,f297]) ).
fof(f297,plain,
( v5_membered(sK10)
| ~ spl11_21 ),
inference(avatar_component_clause,[],[f295]) ).
fof(f295,plain,
( spl11_21
<=> v5_membered(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_21])]) ).
fof(f812,plain,
( spl11_95
| spl11_96
| ~ spl11_23
| ~ spl11_43
| ~ spl11_44
| ~ spl11_52 ),
inference(avatar_split_clause,[],[f497,f440,f399,f395,f304,f809,f806]) ).
fof(f809,plain,
( spl11_96
<=> sP0(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_96])]) ).
fof(f497,plain,
( ! [X0] :
( sP0(empty_set)
| ~ v5_membered(X0) )
| ~ spl11_23
| ~ spl11_43
| ~ spl11_44
| ~ spl11_52 ),
inference(forward_demodulation,[],[f496,f407]) ).
fof(f496,plain,
( ! [X0] :
( sP0(sK7(X0))
| ~ v5_membered(X0) )
| ~ spl11_44
| ~ spl11_52 ),
inference(resolution,[],[f441,f400]) ).
fof(f804,plain,
( spl11_94
| ~ spl11_23
| ~ spl11_43 ),
inference(avatar_split_clause,[],[f407,f395,f304,f802]) ).
fof(f802,plain,
( spl11_94
<=> ! [X0] : empty_set = sK7(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_94])]) ).
fof(f799,plain,
( spl11_93
| ~ spl11_23
| ~ spl11_36 ),
inference(avatar_split_clause,[],[f378,f356,f304,f797]) ).
fof(f797,plain,
( spl11_93
<=> ! [X0] : sP1(sK7(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_93])]) ).
fof(f356,plain,
( spl11_36
<=> ! [X0] :
( sP1(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_36])]) ).
fof(f378,plain,
( ! [X0] : sP1(sK7(X0))
| ~ spl11_23
| ~ spl11_36 ),
inference(resolution,[],[f357,f305]) ).
fof(f357,plain,
( ! [X0] :
( ~ empty(X0)
| sP1(X0) )
| ~ spl11_36 ),
inference(avatar_component_clause,[],[f356]) ).
fof(f788,plain,
( ~ spl11_4
| spl11_92
| ~ spl11_3
| ~ spl11_8
| ~ spl11_74 ),
inference(avatar_split_clause,[],[f635,f630,f230,f205,f785,f210]) ).
fof(f210,plain,
( spl11_4
<=> open_subset(sK3,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_4])]) ).
fof(f630,plain,
( spl11_74
<=> ! [X1,X3] :
( interior(X1,X3) = X3
| ~ top_str(X1)
| ~ element(X3,powerset(the_carrier(X1)))
| ~ open_subset(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_74])]) ).
fof(f635,plain,
( ~ top_str(sK2)
| sK3 = interior(sK2,sK3)
| ~ open_subset(sK3,sK2)
| ~ spl11_8
| ~ spl11_74 ),
inference(resolution,[],[f631,f232]) ).
fof(f631,plain,
( ! [X3,X1] :
( ~ element(X3,powerset(the_carrier(X1)))
| ~ top_str(X1)
| interior(X1,X3) = X3
| ~ open_subset(X3,X1) )
| ~ spl11_74 ),
inference(avatar_component_clause,[],[f630]) ).
fof(f780,plain,
( spl11_90
| spl11_91
| ~ spl11_8
| ~ spl11_64 ),
inference(avatar_split_clause,[],[f564,f489,f230,f777,f773]) ).
fof(f777,plain,
( spl11_91
<=> empty(powerset(the_carrier(sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_91])]) ).
fof(f564,plain,
( empty(powerset(the_carrier(sK2)))
| in(sK3,powerset(the_carrier(sK2)))
| ~ spl11_8
| ~ spl11_64 ),
inference(resolution,[],[f490,f232]) ).
fof(f728,plain,
( ~ spl11_3
| ~ spl11_89 ),
inference(avatar_contradiction_clause,[],[f725]) ).
fof(f725,plain,
( $false
| ~ spl11_3
| ~ spl11_89 ),
inference(resolution,[],[f723,f207]) ).
fof(f723,plain,
( ! [X0] : ~ top_str(X0)
| ~ spl11_89 ),
inference(avatar_component_clause,[],[f722]) ).
fof(f722,plain,
( spl11_89
<=> ! [X0] : ~ top_str(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_89])]) ).
fof(f727,plain,
( ~ spl11_15
| ~ spl11_89 ),
inference(avatar_contradiction_clause,[],[f726]) ).
fof(f726,plain,
( $false
| ~ spl11_15
| ~ spl11_89 ),
inference(resolution,[],[f723,f267]) ).
fof(f267,plain,
( top_str(sK9)
| ~ spl11_15 ),
inference(avatar_component_clause,[],[f265]) ).
fof(f265,plain,
( spl11_15
<=> top_str(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_15])]) ).
fof(f724,plain,
( spl11_89
| ~ spl11_40
| ~ spl11_75 ),
inference(avatar_split_clause,[],[f652,f643,f372,f722]) ).
fof(f643,plain,
( spl11_75
<=> ! [X1,X3] :
( ~ element(X3,powerset(the_carrier(X1)))
| ~ top_str(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_75])]) ).
fof(f652,plain,
( ! [X0] : ~ top_str(X0)
| ~ spl11_40
| ~ spl11_75 ),
inference(resolution,[],[f644,f373]) ).
fof(f644,plain,
( ! [X3,X1] :
( ~ element(X3,powerset(the_carrier(X1)))
| ~ top_str(X1) )
| ~ spl11_75 ),
inference(avatar_component_clause,[],[f643]) ).
fof(f720,plain,
( ~ spl11_88
| ~ spl11_47
| ~ spl11_86 ),
inference(avatar_split_clause,[],[f704,f697,f415,f717]) ).
fof(f717,plain,
( spl11_88
<=> in(the_carrier(sK2),sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_88])]) ).
fof(f697,plain,
( spl11_86
<=> in(sK4,the_carrier(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_86])]) ).
fof(f704,plain,
( ~ in(the_carrier(sK2),sK4)
| ~ spl11_47
| ~ spl11_86 ),
inference(resolution,[],[f699,f416]) ).
fof(f699,plain,
( in(sK4,the_carrier(sK2))
| ~ spl11_86 ),
inference(avatar_component_clause,[],[f697]) ).
fof(f709,plain,
( spl11_87
| ~ spl11_8
| ~ spl11_67 ),
inference(avatar_split_clause,[],[f585,f581,f230,f707]) ).
fof(f581,plain,
( spl11_67
<=> ! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_67])]) ).
fof(f585,plain,
( ! [X0] :
( element(X0,the_carrier(sK2))
| ~ in(X0,sK3) )
| ~ spl11_8
| ~ spl11_67 ),
inference(resolution,[],[f582,f232]) ).
fof(f582,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| element(X0,X2)
| ~ in(X0,X1) )
| ~ spl11_67 ),
inference(avatar_component_clause,[],[f581]) ).
fof(f702,plain,
( ~ spl11_5
| ~ spl11_84 ),
inference(avatar_contradiction_clause,[],[f701]) ).
fof(f701,plain,
( $false
| ~ spl11_5
| ~ spl11_84 ),
inference(resolution,[],[f690,f217]) ).
fof(f217,plain,
( in(sK4,sK3)
| ~ spl11_5 ),
inference(avatar_component_clause,[],[f215]) ).
fof(f690,plain,
( ! [X0] : ~ in(X0,sK3)
| ~ spl11_84 ),
inference(avatar_component_clause,[],[f689]) ).
fof(f689,plain,
( spl11_84
<=> ! [X0] : ~ in(X0,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_84])]) ).
fof(f700,plain,
( spl11_86
| spl11_85
| ~ spl11_6
| ~ spl11_64 ),
inference(avatar_split_clause,[],[f565,f489,f220,f692,f697]) ).
fof(f692,plain,
( spl11_85
<=> empty(the_carrier(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_85])]) ).
fof(f220,plain,
( spl11_6
<=> element(sK4,the_carrier(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_6])]) ).
fof(f565,plain,
( empty(the_carrier(sK2))
| in(sK4,the_carrier(sK2))
| ~ spl11_6
| ~ spl11_64 ),
inference(resolution,[],[f490,f222]) ).
fof(f222,plain,
( element(sK4,the_carrier(sK2))
| ~ spl11_6 ),
inference(avatar_component_clause,[],[f220]) ).
fof(f695,plain,
( spl11_84
| ~ spl11_85
| ~ spl11_8
| ~ spl11_66 ),
inference(avatar_split_clause,[],[f575,f571,f230,f692,f689]) ).
fof(f575,plain,
( ! [X0] :
( ~ empty(the_carrier(sK2))
| ~ in(X0,sK3) )
| ~ spl11_8
| ~ spl11_66 ),
inference(resolution,[],[f572,f232]) ).
fof(f687,plain,
( ~ spl11_83
| spl11_80
| ~ spl11_8
| ~ spl11_63 ),
inference(avatar_split_clause,[],[f558,f485,f230,f669,f684]) ).
fof(f684,plain,
( spl11_83
<=> v1_membered(the_carrier(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_83])]) ).
fof(f669,plain,
( spl11_80
<=> v1_membered(sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_80])]) ).
fof(f558,plain,
( v1_membered(sK3)
| ~ v1_membered(the_carrier(sK2))
| ~ spl11_8
| ~ spl11_63 ),
inference(resolution,[],[f486,f232]) ).
fof(f682,plain,
( ~ spl11_82
| spl11_80
| ~ spl11_8
| ~ spl11_60 ),
inference(avatar_split_clause,[],[f546,f472,f230,f669,f679]) ).
fof(f679,plain,
( spl11_82
<=> v2_membered(the_carrier(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_82])]) ).
fof(f546,plain,
( v1_membered(sK3)
| ~ v2_membered(the_carrier(sK2))
| ~ spl11_8
| ~ spl11_60 ),
inference(resolution,[],[f473,f232]) ).
fof(f677,plain,
( ~ spl11_81
| spl11_80
| ~ spl11_8
| ~ spl11_57 ),
inference(avatar_split_clause,[],[f523,f460,f230,f669,f674]) ).
fof(f674,plain,
( spl11_81
<=> v3_membered(the_carrier(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_81])]) ).
fof(f523,plain,
( v1_membered(sK3)
| ~ v3_membered(the_carrier(sK2))
| ~ spl11_8
| ~ spl11_57 ),
inference(resolution,[],[f461,f232]) ).
fof(f672,plain,
( ~ spl11_79
| spl11_80
| ~ spl11_8
| ~ spl11_53 ),
inference(avatar_split_clause,[],[f499,f444,f230,f669,f665]) ).
fof(f665,plain,
( spl11_79
<=> v4_membered(the_carrier(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_79])]) ).
fof(f499,plain,
( v1_membered(sK3)
| ~ v4_membered(the_carrier(sK2))
| ~ spl11_8
| ~ spl11_53 ),
inference(resolution,[],[f445,f232]) ).
fof(f663,plain,
( ~ spl11_77
| spl11_78
| ~ spl11_8
| ~ spl11_52 ),
inference(avatar_split_clause,[],[f493,f440,f230,f660,f656]) ).
fof(f656,plain,
( spl11_77
<=> v5_membered(the_carrier(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_77])]) ).
fof(f660,plain,
( spl11_78
<=> sP0(sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_78])]) ).
fof(f493,plain,
( sP0(sK3)
| ~ v5_membered(the_carrier(sK2))
| ~ spl11_8
| ~ spl11_52 ),
inference(resolution,[],[f441,f232]) ).
fof(f648,plain,
( spl11_75
| spl11_76 ),
inference(avatar_split_clause,[],[f171,f646,f643]) ).
fof(f646,plain,
( spl11_76
<=> ! [X2,X0] :
( open_subset(X2,X0)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X2,powerset(the_carrier(X0)))
| interior(X0,X2) != X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_76])]) ).
fof(f171,plain,
! [X2,X3,X0,X1] :
( open_subset(X2,X0)
| interior(X0,X2) != X2
| ~ element(X3,powerset(the_carrier(X1)))
| ~ element(X2,powerset(the_carrier(X0)))
| ~ top_str(X1)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( open_subset(X2,X0)
| interior(X0,X2) != X2 )
& ( interior(X1,X3) = X3
| ~ open_subset(X3,X1) ) )
| ~ element(X3,powerset(the_carrier(X1))) )
| ~ element(X2,powerset(the_carrier(X0))) )
| ~ top_str(X1) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(flattening,[],[f82]) ).
fof(f82,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( open_subset(X2,X0)
| interior(X0,X2) != X2 )
& ( interior(X1,X3) = X3
| ~ open_subset(X3,X1) ) )
| ~ element(X3,powerset(the_carrier(X1))) )
| ~ element(X2,powerset(the_carrier(X0))) )
| ~ top_str(X1) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X0)))
=> ! [X3] :
( element(X3,powerset(the_carrier(X1)))
=> ( ( interior(X0,X2) = X2
=> open_subset(X2,X0) )
& ( open_subset(X3,X1)
=> interior(X1,X3) = X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_tops_1) ).
fof(f632,plain,
( spl11_73
| spl11_74 ),
inference(avatar_split_clause,[],[f170,f630,f627]) ).
fof(f170,plain,
! [X2,X3,X0,X1] :
( interior(X1,X3) = X3
| ~ open_subset(X3,X1)
| ~ element(X3,powerset(the_carrier(X1)))
| ~ element(X2,powerset(the_carrier(X0)))
| ~ top_str(X1)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f625,plain,
spl11_72,
inference(avatar_split_clause,[],[f169,f623]) ).
fof(f169,plain,
! [X2,X0,X1] :
( point_neighbourhood(X2,X0,X1)
| ~ in(X1,interior(X0,X2))
| ~ element(X2,powerset(the_carrier(X0)))
| ~ element(X1,the_carrier(X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f113]) ).
fof(f113,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( point_neighbourhood(X2,X0,X1)
| ~ in(X1,interior(X0,X2)) )
& ( in(X1,interior(X0,X2))
| ~ point_neighbourhood(X2,X0,X1) ) )
| ~ element(X2,powerset(the_carrier(X0))) )
| ~ element(X1,the_carrier(X0)) )
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(nnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( point_neighbourhood(X2,X0,X1)
<=> in(X1,interior(X0,X2)) )
| ~ element(X2,powerset(the_carrier(X0))) )
| ~ element(X1,the_carrier(X0)) )
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f80]) ).
fof(f80,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( point_neighbourhood(X2,X0,X1)
<=> in(X1,interior(X0,X2)) )
| ~ element(X2,powerset(the_carrier(X0))) )
| ~ element(X1,the_carrier(X0)) )
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,powerset(the_carrier(X0)))
=> ( point_neighbourhood(X2,X0,X1)
<=> in(X1,interior(X0,X2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_connsp_2) ).
fof(f621,plain,
spl11_71,
inference(avatar_split_clause,[],[f168,f619]) ).
fof(f168,plain,
! [X2,X0,X1] :
( in(X1,interior(X0,X2))
| ~ point_neighbourhood(X2,X0,X1)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ element(X1,the_carrier(X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f113]) ).
fof(f615,plain,
spl11_70,
inference(avatar_split_clause,[],[f179,f613]) ).
fof(f613,plain,
( spl11_70
<=> ! [X2,X0,X1] :
( element(X2,powerset(the_carrier(X0)))
| ~ point_neighbourhood(X2,X0,X1)
| ~ element(X1,the_carrier(X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_70])]) ).
fof(f179,plain,
! [X2,X0,X1] :
( element(X2,powerset(the_carrier(X0)))
| ~ point_neighbourhood(X2,X0,X1)
| ~ element(X1,the_carrier(X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
! [X0,X1] :
( ! [X2] :
( element(X2,powerset(the_carrier(X0)))
| ~ point_neighbourhood(X2,X0,X1) )
| ~ element(X1,the_carrier(X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f88]) ).
fof(f88,plain,
! [X0,X1] :
( ! [X2] :
( element(X2,powerset(the_carrier(X0)))
| ~ point_neighbourhood(X2,X0,X1) )
| ~ element(X1,the_carrier(X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0,X1] :
( ( element(X1,the_carrier(X0))
& top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ! [X2] :
( point_neighbourhood(X2,X0,X1)
=> element(X2,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_connsp_2) ).
fof(f611,plain,
spl11_69,
inference(avatar_split_clause,[],[f180,f609]) ).
fof(f609,plain,
( spl11_69
<=> ! [X0,X1] :
( point_neighbourhood(sK8(X0,X1),X0,X1)
| ~ element(X1,the_carrier(X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_69])]) ).
fof(f180,plain,
! [X0,X1] :
( point_neighbourhood(sK8(X0,X1),X0,X1)
| ~ element(X1,the_carrier(X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f119,plain,
! [X0,X1] :
( point_neighbourhood(sK8(X0,X1),X0,X1)
| ~ element(X1,the_carrier(X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f91,f118]) ).
fof(f118,plain,
! [X0,X1] :
( ? [X2] : point_neighbourhood(X2,X0,X1)
=> point_neighbourhood(sK8(X0,X1),X0,X1) ),
introduced(choice_axiom,[]) ).
fof(f91,plain,
! [X0,X1] :
( ? [X2] : point_neighbourhood(X2,X0,X1)
| ~ element(X1,the_carrier(X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f90]) ).
fof(f90,plain,
! [X0,X1] :
( ? [X2] : point_neighbourhood(X2,X0,X1)
| ~ element(X1,the_carrier(X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0,X1] :
( ( element(X1,the_carrier(X0))
& top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ? [X2] : point_neighbourhood(X2,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_connsp_2) ).
fof(f593,plain,
spl11_68,
inference(avatar_split_clause,[],[f181,f591]) ).
fof(f591,plain,
( spl11_68
<=> ! [X0,X1] :
( element(interior(X0,X1),powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_68])]) ).
fof(f181,plain,
! [X0,X1] :
( element(interior(X0,X1),powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f93,plain,
! [X0,X1] :
( element(interior(X0,X1),powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(flattening,[],[f92]) ).
fof(f92,plain,
! [X0,X1] :
( element(interior(X0,X1),powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0,X1] :
( ( element(X1,powerset(the_carrier(X0)))
& top_str(X0) )
=> element(interior(X0,X1),powerset(the_carrier(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_tops_1) ).
fof(f583,plain,
spl11_67,
inference(avatar_split_clause,[],[f185,f581]) ).
fof(f185,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f98]) ).
fof(f98,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f97]) ).
fof(f97,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f39,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f573,plain,
spl11_66,
inference(avatar_split_clause,[],[f186,f571]) ).
fof(f186,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f99]) ).
fof(f99,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f43]) ).
fof(f43,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f544,plain,
( spl11_65
| ~ spl11_5
| ~ spl11_48 ),
inference(avatar_split_clause,[],[f423,f419,f215,f541]) ).
fof(f541,plain,
( spl11_65
<=> element(sK4,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_65])]) ).
fof(f419,plain,
( spl11_48
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_48])]) ).
fof(f423,plain,
( element(sK4,sK3)
| ~ spl11_5
| ~ spl11_48 ),
inference(resolution,[],[f420,f217]) ).
fof(f420,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) )
| ~ spl11_48 ),
inference(avatar_component_clause,[],[f419]) ).
fof(f491,plain,
spl11_64,
inference(avatar_split_clause,[],[f178,f489]) ).
fof(f178,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f87]) ).
fof(f87,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f86]) ).
fof(f86,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f487,plain,
spl11_63,
inference(avatar_split_clause,[],[f167,f485]) ).
fof(f167,plain,
! [X0,X1] :
( v1_membered(X1)
| ~ element(X1,powerset(X0))
| ~ v1_membered(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0] :
( ! [X1] :
( v1_membered(X1)
| ~ element(X1,powerset(X0)) )
| ~ v1_membered(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( v1_membered(X0)
=> ! [X1] :
( element(X1,powerset(X0))
=> v1_membered(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc16_membered) ).
fof(f483,plain,
( ~ spl11_62
| ~ spl11_5
| ~ spl11_47 ),
inference(avatar_split_clause,[],[f422,f415,f215,f480]) ).
fof(f480,plain,
( spl11_62
<=> in(sK3,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_62])]) ).
fof(f422,plain,
( ~ in(sK3,sK4)
| ~ spl11_5
| ~ spl11_47 ),
inference(resolution,[],[f416,f217]) ).
fof(f478,plain,
spl11_61,
inference(avatar_split_clause,[],[f166,f476]) ).
fof(f166,plain,
! [X0,X1] :
( v2_membered(X1)
| ~ element(X1,powerset(X0))
| ~ v2_membered(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
! [X0] :
( ! [X1] :
( ( v2_membered(X1)
& v1_membered(X1) )
| ~ element(X1,powerset(X0)) )
| ~ v2_membered(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0] :
( v2_membered(X0)
=> ! [X1] :
( element(X1,powerset(X0))
=> ( v2_membered(X1)
& v1_membered(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc17_membered) ).
fof(f474,plain,
spl11_60,
inference(avatar_split_clause,[],[f165,f472]) ).
fof(f165,plain,
! [X0,X1] :
( v1_membered(X1)
| ~ element(X1,powerset(X0))
| ~ v2_membered(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f470,plain,
spl11_59,
inference(avatar_split_clause,[],[f163,f468]) ).
fof(f163,plain,
! [X0,X1] :
( v3_membered(X1)
| ~ element(X1,powerset(X0))
| ~ v3_membered(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0] :
( ! [X1] :
( ( v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1) )
| ~ element(X1,powerset(X0)) )
| ~ v3_membered(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] :
( v3_membered(X0)
=> ! [X1] :
( element(X1,powerset(X0))
=> ( v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc18_membered) ).
fof(f466,plain,
spl11_58,
inference(avatar_split_clause,[],[f162,f464]) ).
fof(f162,plain,
! [X0,X1] :
( v2_membered(X1)
| ~ element(X1,powerset(X0))
| ~ v3_membered(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f462,plain,
spl11_57,
inference(avatar_split_clause,[],[f161,f460]) ).
fof(f161,plain,
! [X0,X1] :
( v1_membered(X1)
| ~ element(X1,powerset(X0))
| ~ v3_membered(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f458,plain,
spl11_56,
inference(avatar_split_clause,[],[f159,f456]) ).
fof(f159,plain,
! [X0,X1] :
( v4_membered(X1)
| ~ element(X1,powerset(X0))
| ~ v4_membered(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
! [X0] :
( ! [X1] :
( ( v4_membered(X1)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1) )
| ~ element(X1,powerset(X0)) )
| ~ v4_membered(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] :
( v4_membered(X0)
=> ! [X1] :
( element(X1,powerset(X0))
=> ( v4_membered(X1)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc19_membered) ).
fof(f454,plain,
spl11_55,
inference(avatar_split_clause,[],[f158,f452]) ).
fof(f158,plain,
! [X0,X1] :
( v3_membered(X1)
| ~ element(X1,powerset(X0))
| ~ v4_membered(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f450,plain,
spl11_54,
inference(avatar_split_clause,[],[f157,f448]) ).
fof(f157,plain,
! [X0,X1] :
( v2_membered(X1)
| ~ element(X1,powerset(X0))
| ~ v4_membered(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f446,plain,
spl11_53,
inference(avatar_split_clause,[],[f156,f444]) ).
fof(f156,plain,
! [X0,X1] :
( v1_membered(X1)
| ~ element(X1,powerset(X0))
| ~ v4_membered(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f442,plain,
spl11_52,
inference(avatar_split_clause,[],[f147,f440]) ).
fof(f147,plain,
! [X0,X1] :
( sP0(X1)
| ~ element(X1,powerset(X0))
| ~ v5_membered(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f101,plain,
! [X0] :
( ! [X1] :
( sP0(X1)
| ~ element(X1,powerset(X0)) )
| ~ v5_membered(X0) ),
inference(definition_folding,[],[f70,f100]) ).
fof(f100,plain,
! [X1] :
( ( v5_membered(X1)
& v4_membered(X1)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1) )
| ~ sP0(X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f70,plain,
! [X0] :
( ! [X1] :
( ( v5_membered(X1)
& v4_membered(X1)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1) )
| ~ element(X1,powerset(X0)) )
| ~ v5_membered(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0] :
( v5_membered(X0)
=> ! [X1] :
( element(X1,powerset(X0))
=> ( v5_membered(X1)
& v4_membered(X1)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc20_membered) ).
fof(f435,plain,
spl11_51,
inference(avatar_split_clause,[],[f183,f433]) ).
fof(f433,plain,
( spl11_51
<=> ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_51])]) ).
fof(f183,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f95,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f46]) ).
fof(f46,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(f431,plain,
spl11_50,
inference(avatar_split_clause,[],[f182,f429]) ).
fof(f182,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f94]) ).
fof(f94,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0,X1] :
( subset(X0,X1)
=> element(X0,powerset(X1)) ),
inference(unused_predicate_definition_removal,[],[f38]) ).
fof(f38,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f427,plain,
spl11_49,
inference(avatar_split_clause,[],[f139,f425]) ).
fof(f139,plain,
! [X0] :
( element(sK5(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f109,plain,
! [X0] :
( ( ~ empty(sK5(X0))
& element(sK5(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f68,f108]) ).
fof(f108,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( ~ empty(sK5(X0))
& element(sK5(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f68,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f421,plain,
spl11_48,
inference(avatar_split_clause,[],[f177,f419]) ).
fof(f177,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(f417,plain,
spl11_47,
inference(avatar_split_clause,[],[f176,f415]) ).
fof(f176,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f84,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f413,plain,
( ~ spl11_46
| ~ spl11_5
| ~ spl11_45 ),
inference(avatar_split_clause,[],[f408,f403,f215,f410]) ).
fof(f410,plain,
( spl11_46
<=> empty(sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_46])]) ).
fof(f403,plain,
( spl11_45
<=> ! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_45])]) ).
fof(f408,plain,
( ~ empty(sK3)
| ~ spl11_5
| ~ spl11_45 ),
inference(resolution,[],[f404,f217]) ).
fof(f404,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) )
| ~ spl11_45 ),
inference(avatar_component_clause,[],[f403]) ).
fof(f405,plain,
spl11_45,
inference(avatar_split_clause,[],[f184,f403]) ).
fof(f184,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f96]) ).
fof(f96,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f401,plain,
spl11_44,
inference(avatar_split_clause,[],[f173,f399]) ).
fof(f173,plain,
! [X0] : element(sK7(X0),powerset(X0)),
inference(cnf_transformation,[],[f117]) ).
fof(f117,plain,
! [X0] :
( empty(sK7(X0))
& element(sK7(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f34,f116]) ).
fof(f116,plain,
! [X0] :
( ? [X1] :
( empty(X1)
& element(X1,powerset(X0)) )
=> ( empty(sK7(X0))
& element(sK7(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f34,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f397,plain,
spl11_43,
inference(avatar_split_clause,[],[f148,f395]) ).
fof(f148,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f44]) ).
fof(f44,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f393,plain,
spl11_42,
inference(avatar_split_clause,[],[f140,f391]) ).
fof(f391,plain,
( spl11_42
<=> ! [X0] :
( ~ empty(sK5(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_42])]) ).
fof(f140,plain,
! [X0] :
( ~ empty(sK5(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f387,plain,
( spl11_41
| ~ spl11_9
| ~ spl11_36 ),
inference(avatar_split_clause,[],[f377,f356,f235,f384]) ).
fof(f384,plain,
( spl11_41
<=> sP1(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_41])]) ).
fof(f377,plain,
( sP1(empty_set)
| ~ spl11_9
| ~ spl11_36 ),
inference(resolution,[],[f357,f237]) ).
fof(f374,plain,
spl11_40,
inference(avatar_split_clause,[],[f172,f372]) ).
fof(f172,plain,
! [X0] : element(sK6(X0),X0),
inference(cnf_transformation,[],[f115]) ).
fof(f115,plain,
! [X0] : element(sK6(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f29,f114]) ).
fof(f114,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK6(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f29,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f370,plain,
spl11_39,
inference(avatar_split_clause,[],[f164,f368]) ).
fof(f368,plain,
( spl11_39
<=> ! [X0] :
( v1_membered(X0)
| ~ v2_membered(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_39])]) ).
fof(f164,plain,
! [X0] :
( v1_membered(X0)
| ~ v2_membered(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0] :
( v1_membered(X0)
| ~ v2_membered(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0] :
( v2_membered(X0)
=> v1_membered(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_membered) ).
fof(f366,plain,
spl11_38,
inference(avatar_split_clause,[],[f160,f364]) ).
fof(f364,plain,
( spl11_38
<=> ! [X0] :
( v2_membered(X0)
| ~ v3_membered(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_38])]) ).
fof(f160,plain,
! [X0] :
( v2_membered(X0)
| ~ v3_membered(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0] :
( v2_membered(X0)
| ~ v3_membered(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] :
( v3_membered(X0)
=> v2_membered(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_membered) ).
fof(f362,plain,
spl11_37,
inference(avatar_split_clause,[],[f155,f360]) ).
fof(f360,plain,
( spl11_37
<=> ! [X0] :
( v3_membered(X0)
| ~ v4_membered(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_37])]) ).
fof(f155,plain,
! [X0] :
( v3_membered(X0)
| ~ v4_membered(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f73,plain,
! [X0] :
( v3_membered(X0)
| ~ v4_membered(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0] :
( v4_membered(X0)
=> v3_membered(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_membered) ).
fof(f358,plain,
spl11_36,
inference(avatar_split_clause,[],[f154,f356]) ).
fof(f154,plain,
! [X0] :
( sP1(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f103,plain,
! [X0] :
( sP1(X0)
| ~ empty(X0) ),
inference(definition_folding,[],[f72,f102]) ).
fof(f102,plain,
! [X0] :
( ( v5_membered(X0)
& v4_membered(X0)
& v3_membered(X0)
& v2_membered(X0)
& v1_membered(X0) )
| ~ sP1(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f72,plain,
! [X0] :
( ( v5_membered(X0)
& v4_membered(X0)
& v3_membered(X0)
& v2_membered(X0)
& v1_membered(X0) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] :
( empty(X0)
=> ( v5_membered(X0)
& v4_membered(X0)
& v3_membered(X0)
& v2_membered(X0)
& v1_membered(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc15_membered) ).
fof(f354,plain,
spl11_35,
inference(avatar_split_clause,[],[f153,f352]) ).
fof(f352,plain,
( spl11_35
<=> ! [X0] :
( v5_membered(X0)
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_35])]) ).
fof(f153,plain,
! [X0] :
( v5_membered(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f112]) ).
fof(f112,plain,
! [X0] :
( ( v5_membered(X0)
& v4_membered(X0)
& v3_membered(X0)
& v2_membered(X0)
& v1_membered(X0) )
| ~ sP1(X0) ),
inference(nnf_transformation,[],[f102]) ).
fof(f350,plain,
spl11_34,
inference(avatar_split_clause,[],[f152,f348]) ).
fof(f348,plain,
( spl11_34
<=> ! [X0] :
( v4_membered(X0)
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_34])]) ).
fof(f152,plain,
! [X0] :
( v4_membered(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f112]) ).
fof(f346,plain,
spl11_33,
inference(avatar_split_clause,[],[f151,f344]) ).
fof(f344,plain,
( spl11_33
<=> ! [X0] :
( v3_membered(X0)
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_33])]) ).
fof(f151,plain,
! [X0] :
( v3_membered(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f112]) ).
fof(f342,plain,
spl11_32,
inference(avatar_split_clause,[],[f150,f340]) ).
fof(f340,plain,
( spl11_32
<=> ! [X0] :
( v2_membered(X0)
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_32])]) ).
fof(f150,plain,
! [X0] :
( v2_membered(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f112]) ).
fof(f338,plain,
spl11_31,
inference(avatar_split_clause,[],[f149,f336]) ).
fof(f336,plain,
( spl11_31
<=> ! [X0] :
( v1_membered(X0)
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_31])]) ).
fof(f149,plain,
! [X0] :
( v1_membered(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f112]) ).
fof(f334,plain,
spl11_30,
inference(avatar_split_clause,[],[f146,f332]) ).
fof(f332,plain,
( spl11_30
<=> ! [X0] :
( v5_membered(X0)
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_30])]) ).
fof(f146,plain,
! [X0] :
( v5_membered(X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f111]) ).
fof(f111,plain,
! [X0] :
( ( v5_membered(X0)
& v4_membered(X0)
& v3_membered(X0)
& v2_membered(X0)
& v1_membered(X0) )
| ~ sP0(X0) ),
inference(rectify,[],[f110]) ).
fof(f110,plain,
! [X1] :
( ( v5_membered(X1)
& v4_membered(X1)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1) )
| ~ sP0(X1) ),
inference(nnf_transformation,[],[f100]) ).
fof(f330,plain,
spl11_29,
inference(avatar_split_clause,[],[f145,f328]) ).
fof(f328,plain,
( spl11_29
<=> ! [X0] :
( v4_membered(X0)
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_29])]) ).
fof(f145,plain,
! [X0] :
( v4_membered(X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f111]) ).
fof(f326,plain,
spl11_28,
inference(avatar_split_clause,[],[f144,f324]) ).
fof(f324,plain,
( spl11_28
<=> ! [X0] :
( v3_membered(X0)
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_28])]) ).
fof(f144,plain,
! [X0] :
( v3_membered(X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f111]) ).
fof(f322,plain,
spl11_27,
inference(avatar_split_clause,[],[f143,f320]) ).
fof(f320,plain,
( spl11_27
<=> ! [X0] :
( v2_membered(X0)
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_27])]) ).
fof(f143,plain,
! [X0] :
( v2_membered(X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f111]) ).
fof(f318,plain,
spl11_26,
inference(avatar_split_clause,[],[f142,f316]) ).
fof(f316,plain,
( spl11_26
<=> ! [X0] :
( v1_membered(X0)
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_26])]) ).
fof(f142,plain,
! [X0] :
( v1_membered(X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f111]) ).
fof(f314,plain,
spl11_25,
inference(avatar_split_clause,[],[f141,f312]) ).
fof(f312,plain,
( spl11_25
<=> ! [X0] :
( v4_membered(X0)
| ~ v5_membered(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_25])]) ).
fof(f141,plain,
! [X0] :
( v4_membered(X0)
| ~ v5_membered(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0] :
( v4_membered(X0)
| ~ v5_membered(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0] :
( v5_membered(X0)
=> v4_membered(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_membered) ).
fof(f310,plain,
spl11_24,
inference(avatar_split_clause,[],[f175,f308]) ).
fof(f308,plain,
( spl11_24
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_24])]) ).
fof(f175,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f35]) ).
fof(f35,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f306,plain,
spl11_23,
inference(avatar_split_clause,[],[f174,f304]) ).
fof(f174,plain,
! [X0] : empty(sK7(X0)),
inference(cnf_transformation,[],[f117]) ).
fof(f302,plain,
spl11_22,
inference(avatar_split_clause,[],[f138,f300]) ).
fof(f300,plain,
( spl11_22
<=> ! [X0] : ~ empty(powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_22])]) ).
fof(f138,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f298,plain,
spl11_21,
inference(avatar_split_clause,[],[f193,f295]) ).
fof(f193,plain,
v5_membered(sK10),
inference(cnf_transformation,[],[f123]) ).
fof(f123,plain,
( v5_membered(sK10)
& v4_membered(sK10)
& v3_membered(sK10)
& v2_membered(sK10)
& v1_membered(sK10)
& ~ empty(sK10) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f32,f122]) ).
fof(f122,plain,
( ? [X0] :
( v5_membered(X0)
& v4_membered(X0)
& v3_membered(X0)
& v2_membered(X0)
& v1_membered(X0)
& ~ empty(X0) )
=> ( v5_membered(sK10)
& v4_membered(sK10)
& v3_membered(sK10)
& v2_membered(sK10)
& v1_membered(sK10)
& ~ empty(sK10) ) ),
introduced(choice_axiom,[]) ).
fof(f32,axiom,
? [X0] :
( v5_membered(X0)
& v4_membered(X0)
& v3_membered(X0)
& v2_membered(X0)
& v1_membered(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_membered) ).
fof(f293,plain,
spl11_20,
inference(avatar_split_clause,[],[f192,f290]) ).
fof(f290,plain,
( spl11_20
<=> v4_membered(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_20])]) ).
fof(f192,plain,
v4_membered(sK10),
inference(cnf_transformation,[],[f123]) ).
fof(f288,plain,
spl11_19,
inference(avatar_split_clause,[],[f191,f285]) ).
fof(f285,plain,
( spl11_19
<=> v3_membered(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_19])]) ).
fof(f191,plain,
v3_membered(sK10),
inference(cnf_transformation,[],[f123]) ).
fof(f283,plain,
spl11_18,
inference(avatar_split_clause,[],[f190,f280]) ).
fof(f280,plain,
( spl11_18
<=> v2_membered(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_18])]) ).
fof(f190,plain,
v2_membered(sK10),
inference(cnf_transformation,[],[f123]) ).
fof(f278,plain,
spl11_17,
inference(avatar_split_clause,[],[f189,f275]) ).
fof(f275,plain,
( spl11_17
<=> v1_membered(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_17])]) ).
fof(f189,plain,
v1_membered(sK10),
inference(cnf_transformation,[],[f123]) ).
fof(f273,plain,
~ spl11_16,
inference(avatar_split_clause,[],[f188,f270]) ).
fof(f270,plain,
( spl11_16
<=> empty(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_16])]) ).
fof(f188,plain,
~ empty(sK10),
inference(cnf_transformation,[],[f123]) ).
fof(f268,plain,
spl11_15,
inference(avatar_split_clause,[],[f187,f265]) ).
fof(f187,plain,
top_str(sK9),
inference(cnf_transformation,[],[f121]) ).
fof(f121,plain,
top_str(sK9),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f26,f120]) ).
fof(f120,plain,
( ? [X0] : top_str(X0)
=> top_str(sK9) ),
introduced(choice_axiom,[]) ).
fof(f26,axiom,
? [X0] : top_str(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_pre_topc) ).
fof(f263,plain,
spl11_14,
inference(avatar_split_clause,[],[f137,f260]) ).
fof(f137,plain,
v5_membered(empty_set),
inference(cnf_transformation,[],[f31]) ).
fof(f31,axiom,
( v5_membered(empty_set)
& v4_membered(empty_set)
& v3_membered(empty_set)
& v2_membered(empty_set)
& v1_membered(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_membered) ).
fof(f258,plain,
spl11_13,
inference(avatar_split_clause,[],[f136,f255]) ).
fof(f255,plain,
( spl11_13
<=> v4_membered(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_13])]) ).
fof(f136,plain,
v4_membered(empty_set),
inference(cnf_transformation,[],[f31]) ).
fof(f253,plain,
spl11_12,
inference(avatar_split_clause,[],[f135,f250]) ).
fof(f250,plain,
( spl11_12
<=> v3_membered(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_12])]) ).
fof(f135,plain,
v3_membered(empty_set),
inference(cnf_transformation,[],[f31]) ).
fof(f248,plain,
spl11_11,
inference(avatar_split_clause,[],[f134,f245]) ).
fof(f245,plain,
( spl11_11
<=> v2_membered(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_11])]) ).
fof(f134,plain,
v2_membered(empty_set),
inference(cnf_transformation,[],[f31]) ).
fof(f243,plain,
spl11_10,
inference(avatar_split_clause,[],[f133,f240]) ).
fof(f240,plain,
( spl11_10
<=> v1_membered(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_10])]) ).
fof(f133,plain,
v1_membered(empty_set),
inference(cnf_transformation,[],[f31]) ).
fof(f238,plain,
spl11_9,
inference(avatar_split_clause,[],[f132,f235]) ).
fof(f132,plain,
empty(empty_set),
inference(cnf_transformation,[],[f31]) ).
fof(f233,plain,
spl11_8,
inference(avatar_split_clause,[],[f127,f230]) ).
fof(f127,plain,
element(sK3,powerset(the_carrier(sK2))),
inference(cnf_transformation,[],[f107]) ).
fof(f107,plain,
( ~ point_neighbourhood(sK3,sK2,sK4)
& in(sK4,sK3)
& open_subset(sK3,sK2)
& element(sK4,the_carrier(sK2))
& element(sK3,powerset(the_carrier(sK2)))
& top_str(sK2)
& topological_space(sK2)
& ~ empty_carrier(sK2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f67,f106,f105,f104]) ).
fof(f104,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ~ point_neighbourhood(X1,X0,X2)
& in(X2,X1)
& open_subset(X1,X0)
& element(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(X0))) )
& top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ( ? [X1] :
( ? [X2] :
( ~ point_neighbourhood(X1,sK2,X2)
& in(X2,X1)
& open_subset(X1,sK2)
& element(X2,the_carrier(sK2)) )
& element(X1,powerset(the_carrier(sK2))) )
& top_str(sK2)
& topological_space(sK2)
& ~ empty_carrier(sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f105,plain,
( ? [X1] :
( ? [X2] :
( ~ point_neighbourhood(X1,sK2,X2)
& in(X2,X1)
& open_subset(X1,sK2)
& element(X2,the_carrier(sK2)) )
& element(X1,powerset(the_carrier(sK2))) )
=> ( ? [X2] :
( ~ point_neighbourhood(sK3,sK2,X2)
& in(X2,sK3)
& open_subset(sK3,sK2)
& element(X2,the_carrier(sK2)) )
& element(sK3,powerset(the_carrier(sK2))) ) ),
introduced(choice_axiom,[]) ).
fof(f106,plain,
( ? [X2] :
( ~ point_neighbourhood(sK3,sK2,X2)
& in(X2,sK3)
& open_subset(sK3,sK2)
& element(X2,the_carrier(sK2)) )
=> ( ~ point_neighbourhood(sK3,sK2,sK4)
& in(sK4,sK3)
& open_subset(sK3,sK2)
& element(sK4,the_carrier(sK2)) ) ),
introduced(choice_axiom,[]) ).
fof(f67,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ point_neighbourhood(X1,X0,X2)
& in(X2,X1)
& open_subset(X1,X0)
& element(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(X0))) )
& top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) ),
inference(flattening,[],[f66]) ).
fof(f66,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ point_neighbourhood(X1,X0,X2)
& in(X2,X1)
& open_subset(X1,X0)
& element(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(X0))) )
& top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,negated_conjecture,
~ ! [X0] :
( ( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( ( in(X2,X1)
& open_subset(X1,X0) )
=> point_neighbourhood(X1,X0,X2) ) ) ) ),
inference(negated_conjecture,[],[f41]) ).
fof(f41,conjecture,
! [X0] :
( ( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( ( in(X2,X1)
& open_subset(X1,X0) )
=> point_neighbourhood(X1,X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_connsp_2) ).
fof(f228,plain,
~ spl11_7,
inference(avatar_split_clause,[],[f131,f225]) ).
fof(f131,plain,
~ point_neighbourhood(sK3,sK2,sK4),
inference(cnf_transformation,[],[f107]) ).
fof(f223,plain,
spl11_6,
inference(avatar_split_clause,[],[f128,f220]) ).
fof(f128,plain,
element(sK4,the_carrier(sK2)),
inference(cnf_transformation,[],[f107]) ).
fof(f218,plain,
spl11_5,
inference(avatar_split_clause,[],[f130,f215]) ).
fof(f130,plain,
in(sK4,sK3),
inference(cnf_transformation,[],[f107]) ).
fof(f213,plain,
spl11_4,
inference(avatar_split_clause,[],[f129,f210]) ).
fof(f129,plain,
open_subset(sK3,sK2),
inference(cnf_transformation,[],[f107]) ).
fof(f208,plain,
spl11_3,
inference(avatar_split_clause,[],[f126,f205]) ).
fof(f126,plain,
top_str(sK2),
inference(cnf_transformation,[],[f107]) ).
fof(f203,plain,
spl11_2,
inference(avatar_split_clause,[],[f125,f200]) ).
fof(f125,plain,
topological_space(sK2),
inference(cnf_transformation,[],[f107]) ).
fof(f198,plain,
~ spl11_1,
inference(avatar_split_clause,[],[f124,f195]) ).
fof(f124,plain,
~ empty_carrier(sK2),
inference(cnf_transformation,[],[f107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU341+1 : TPTP v8.1.2. Released v3.3.0.
% 0.06/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35 % Computer : n010.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Apr 29 20:18:05 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % (419)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.37 % (422)WARNING: value z3 for option sas not known
% 0.13/0.37 % (421)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.37 % (423)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.37 % (426)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)
% 0.13/0.37 % (424)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)
% 0.13/0.37 % (425)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)
% 0.13/0.37 % (422)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)
% 0.13/0.37 % (420)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.37 TRYING [1]
% 0.13/0.37 TRYING [2]
% 0.13/0.37 TRYING [3]
% 0.13/0.38 TRYING [4]
% 0.13/0.38 TRYING [1]
% 0.13/0.38 TRYING [1]
% 0.13/0.38 TRYING [2]
% 0.13/0.38 TRYING [2]
% 0.13/0.38 TRYING [5]
% 0.13/0.38 TRYING [3]
% 0.19/0.38 % (424)First to succeed.
% 0.19/0.39 TRYING [4]
% 0.19/0.39 % (422)Also succeeded, but the first one will report.
% 0.19/0.39 TRYING [5]
% 0.19/0.39 % (424)Refutation found. Thanks to Tanya!
% 0.19/0.39 % SZS status Theorem for theBenchmark
% 0.19/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.40 % (424)------------------------------
% 0.19/0.40 % (424)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.19/0.40 % (424)Termination reason: Refutation
% 0.19/0.40
% 0.19/0.40 % (424)Memory used [KB]: 1206
% 0.19/0.40 % (424)Time elapsed: 0.022 s
% 0.19/0.40 % (424)Instructions burned: 38 (million)
% 0.19/0.40 % (424)------------------------------
% 0.19/0.40 % (424)------------------------------
% 0.19/0.40 % (419)Success in time 0.038 s
%------------------------------------------------------------------------------