TSTP Solution File: SEU311+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU311+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 : n012.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 15:28:15 EDT 2024
% Result : Theorem 0.16s 0.38s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 93
% Syntax : Number of formulae : 656 ( 61 unt; 0 def)
% Number of atoms : 2024 ( 29 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 2417 (1049 ~;1083 |; 182 &)
% ( 54 <=>; 47 =>; 0 <=; 2 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 62 ( 60 usr; 46 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 6 con; 0-2 aty)
% Number of variables : 745 ( 700 !; 45 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1487,plain,
$false,
inference(avatar_sat_refutation,[],[f302,f316,f331,f434,f443,f444,f445,f446,f603,f611,f638,f655,f675,f682,f690,f725,f776,f786,f792,f838,f850,f860,f899,f918,f1109,f1133,f1170,f1184,f1317,f1337,f1366,f1395,f1431,f1460,f1466,f1475,f1486]) ).
fof(f1486,plain,
~ spl15_43,
inference(avatar_contradiction_clause,[],[f1485]) ).
fof(f1485,plain,
( $false
| ~ spl15_43 ),
inference(subsumption_resolution,[],[f1484,f1030]) ).
fof(f1030,plain,
element(sK10(sK3,sK4),powerset(powerset(the_carrier(sK3)))),
inference(duplicate_literal_removal,[],[f1028]) ).
fof(f1028,plain,
( element(sK10(sK3,sK4),powerset(powerset(the_carrier(sK3))))
| element(sK10(sK3,sK4),powerset(powerset(the_carrier(sK3)))) ),
inference(resolution,[],[f710,f199]) ).
fof(f199,plain,
! [X0,X1] :
( in(sK11(X0,X1),X0)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f125]) ).
fof(f125,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ( ~ in(sK11(X0,X1),X1)
& in(sK11(X0,X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f92,f124]) ).
fof(f124,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK11(X0,X1),X1)
& in(sK11(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f92,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
=> in(X2,X1) )
=> element(X0,powerset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l71_subset_1) ).
fof(f710,plain,
! [X0] :
( ~ in(sK11(X0,powerset(the_carrier(sK3))),sK10(sK3,sK4))
| element(X0,powerset(powerset(the_carrier(sK3)))) ),
inference(resolution,[],[f700,f200]) ).
fof(f200,plain,
! [X0,X1] :
( ~ in(sK11(X0,X1),X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f125]) ).
fof(f700,plain,
! [X0] :
( in(X0,powerset(the_carrier(sK3)))
| ~ in(X0,sK10(sK3,sK4)) ),
inference(subsumption_resolution,[],[f699,f132]) ).
fof(f132,plain,
topological_space(sK3),
inference(cnf_transformation,[],[f105]) ).
fof(f105,plain,
( ! [X2] :
( ( ( ~ in(set_difference(cast_as_carrier_subset(sK3),sK5(X2)),sK4)
| ~ in(sK5(X2),X2) )
& ( in(set_difference(cast_as_carrier_subset(sK3),sK5(X2)),sK4)
| in(sK5(X2),X2) )
& element(sK5(X2),powerset(the_carrier(sK3))) )
| ~ element(X2,powerset(powerset(the_carrier(sK3)))) )
& element(sK4,powerset(powerset(the_carrier(sK3))))
& top_str(sK3)
& topological_space(sK3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f102,f104,f103]) ).
fof(f103,plain,
( ? [X0,X1] :
( ! [X2] :
( ? [X3] :
( ( ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| ~ in(X3,X2) )
& ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| in(X3,X2) )
& element(X3,powerset(the_carrier(X0))) )
| ~ element(X2,powerset(powerset(the_carrier(X0)))) )
& element(X1,powerset(powerset(the_carrier(X0))))
& top_str(X0)
& topological_space(X0) )
=> ( ! [X2] :
( ? [X3] :
( ( ~ in(set_difference(cast_as_carrier_subset(sK3),X3),sK4)
| ~ in(X3,X2) )
& ( in(set_difference(cast_as_carrier_subset(sK3),X3),sK4)
| in(X3,X2) )
& element(X3,powerset(the_carrier(sK3))) )
| ~ element(X2,powerset(powerset(the_carrier(sK3)))) )
& element(sK4,powerset(powerset(the_carrier(sK3))))
& top_str(sK3)
& topological_space(sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f104,plain,
! [X2] :
( ? [X3] :
( ( ~ in(set_difference(cast_as_carrier_subset(sK3),X3),sK4)
| ~ in(X3,X2) )
& ( in(set_difference(cast_as_carrier_subset(sK3),X3),sK4)
| in(X3,X2) )
& element(X3,powerset(the_carrier(sK3))) )
=> ( ( ~ in(set_difference(cast_as_carrier_subset(sK3),sK5(X2)),sK4)
| ~ in(sK5(X2),X2) )
& ( in(set_difference(cast_as_carrier_subset(sK3),sK5(X2)),sK4)
| in(sK5(X2),X2) )
& element(sK5(X2),powerset(the_carrier(sK3))) ) ),
introduced(choice_axiom,[]) ).
fof(f102,plain,
? [X0,X1] :
( ! [X2] :
( ? [X3] :
( ( ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| ~ in(X3,X2) )
& ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| in(X3,X2) )
& element(X3,powerset(the_carrier(X0))) )
| ~ element(X2,powerset(powerset(the_carrier(X0)))) )
& element(X1,powerset(powerset(the_carrier(X0))))
& top_str(X0)
& topological_space(X0) ),
inference(flattening,[],[f101]) ).
fof(f101,plain,
? [X0,X1] :
( ! [X2] :
( ? [X3] :
( ( ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| ~ in(X3,X2) )
& ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| in(X3,X2) )
& element(X3,powerset(the_carrier(X0))) )
| ~ element(X2,powerset(powerset(the_carrier(X0)))) )
& element(X1,powerset(powerset(the_carrier(X0))))
& top_str(X0)
& topological_space(X0) ),
inference(nnf_transformation,[],[f66]) ).
fof(f66,plain,
? [X0,X1] :
( ! [X2] :
( ? [X3] :
( ( in(X3,X2)
<~> in(set_difference(cast_as_carrier_subset(X0),X3),X1) )
& element(X3,powerset(the_carrier(X0))) )
| ~ element(X2,powerset(powerset(the_carrier(X0)))) )
& element(X1,powerset(powerset(the_carrier(X0))))
& top_str(X0)
& topological_space(X0) ),
inference(flattening,[],[f65]) ).
fof(f65,plain,
? [X0,X1] :
( ! [X2] :
( ? [X3] :
( ( in(X3,X2)
<~> in(set_difference(cast_as_carrier_subset(X0),X3),X1) )
& element(X3,powerset(the_carrier(X0))) )
| ~ element(X2,powerset(powerset(the_carrier(X0)))) )
& element(X1,powerset(powerset(the_carrier(X0))))
& top_str(X0)
& topological_space(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,negated_conjecture,
~ ! [X0,X1] :
( ( element(X1,powerset(powerset(the_carrier(X0))))
& top_str(X0)
& topological_space(X0) )
=> ? [X2] :
( ! [X3] :
( element(X3,powerset(the_carrier(X0)))
=> ( in(X3,X2)
<=> in(set_difference(cast_as_carrier_subset(X0),X3),X1) ) )
& element(X2,powerset(powerset(the_carrier(X0)))) ) ),
inference(negated_conjecture,[],[f1]) ).
fof(f1,conjecture,
! [X0,X1] :
( ( element(X1,powerset(powerset(the_carrier(X0))))
& top_str(X0)
& topological_space(X0) )
=> ? [X2] :
( ! [X3] :
( element(X3,powerset(the_carrier(X0)))
=> ( in(X3,X2)
<=> in(set_difference(cast_as_carrier_subset(X0),X3),X1) ) )
& element(X2,powerset(powerset(the_carrier(X0)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_subset_1__e2_37_1_1__pre_topc) ).
fof(f699,plain,
! [X0] :
( ~ in(X0,sK10(sK3,sK4))
| in(X0,powerset(the_carrier(sK3)))
| ~ topological_space(sK3) ),
inference(subsumption_resolution,[],[f695,f133]) ).
fof(f133,plain,
top_str(sK3),
inference(cnf_transformation,[],[f105]) ).
fof(f695,plain,
! [X0] :
( ~ in(X0,sK10(sK3,sK4))
| in(X0,powerset(the_carrier(sK3)))
| ~ top_str(sK3)
| ~ topological_space(sK3) ),
inference(resolution,[],[f196,f134]) ).
fof(f134,plain,
element(sK4,powerset(powerset(the_carrier(sK3)))),
inference(cnf_transformation,[],[f105]) ).
fof(f196,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ in(X3,sK10(X0,X1))
| in(X3,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f123]) ).
fof(f123,plain,
! [X0,X1] :
( ! [X3] :
( ( in(X3,sK10(X0,X1))
| ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| ~ in(X3,powerset(the_carrier(X0))) )
& ( ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& in(X3,powerset(the_carrier(X0))) )
| ~ in(X3,sK10(X0,X1)) ) )
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f121,f122]) ).
fof(f122,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( in(X3,X2)
| ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| ~ in(X3,powerset(the_carrier(X0))) )
& ( ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& in(X3,powerset(the_carrier(X0))) )
| ~ in(X3,X2) ) )
=> ! [X3] :
( ( in(X3,sK10(X0,X1))
| ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| ~ in(X3,powerset(the_carrier(X0))) )
& ( ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& in(X3,powerset(the_carrier(X0))) )
| ~ in(X3,sK10(X0,X1)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f121,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( in(X3,X2)
| ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| ~ in(X3,powerset(the_carrier(X0))) )
& ( ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& in(X3,powerset(the_carrier(X0))) )
| ~ in(X3,X2) ) )
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(flattening,[],[f120]) ).
fof(f120,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( in(X3,X2)
| ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| ~ in(X3,powerset(the_carrier(X0))) )
& ( ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& in(X3,powerset(the_carrier(X0))) )
| ~ in(X3,X2) ) )
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(nnf_transformation,[],[f91]) ).
fof(f91,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& in(X3,powerset(the_carrier(X0))) ) )
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(flattening,[],[f90]) ).
fof(f90,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& in(X3,powerset(the_carrier(X0))) ) )
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0,X1] :
( ( element(X1,powerset(powerset(the_carrier(X0))))
& top_str(X0)
& topological_space(X0) )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& in(X3,powerset(the_carrier(X0))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e2_37_1_1__pre_topc__1) ).
fof(f1484,plain,
( ~ element(sK10(sK3,sK4),powerset(powerset(the_carrier(sK3))))
| ~ spl15_43 ),
inference(subsumption_resolution,[],[f1476,f1430]) ).
fof(f1430,plain,
( in(sK5(sK10(sK3,sK4)),sK10(sK3,sK4))
| ~ spl15_43 ),
inference(avatar_component_clause,[],[f1428]) ).
fof(f1428,plain,
( spl15_43
<=> in(sK5(sK10(sK3,sK4)),sK10(sK3,sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_43])]) ).
fof(f1476,plain,
( ~ in(sK5(sK10(sK3,sK4)),sK10(sK3,sK4))
| ~ element(sK10(sK3,sK4),powerset(powerset(the_carrier(sK3))))
| ~ spl15_43 ),
inference(resolution,[],[f1430,f745]) ).
fof(f745,plain,
! [X0] :
( ~ in(sK5(X0),sK10(sK3,sK4))
| ~ in(sK5(X0),X0)
| ~ element(X0,powerset(powerset(the_carrier(sK3)))) ),
inference(subsumption_resolution,[],[f744,f132]) ).
fof(f744,plain,
! [X0] :
( ~ in(sK5(X0),sK10(sK3,sK4))
| ~ topological_space(sK3)
| ~ in(sK5(X0),X0)
| ~ element(X0,powerset(powerset(the_carrier(sK3)))) ),
inference(subsumption_resolution,[],[f743,f133]) ).
fof(f743,plain,
! [X0] :
( ~ in(sK5(X0),sK10(sK3,sK4))
| ~ top_str(sK3)
| ~ topological_space(sK3)
| ~ in(sK5(X0),X0)
| ~ element(X0,powerset(powerset(the_carrier(sK3)))) ),
inference(subsumption_resolution,[],[f738,f134]) ).
fof(f738,plain,
! [X0] :
( ~ in(sK5(X0),sK10(sK3,sK4))
| ~ element(sK4,powerset(powerset(the_carrier(sK3))))
| ~ top_str(sK3)
| ~ topological_space(sK3)
| ~ in(sK5(X0),X0)
| ~ element(X0,powerset(powerset(the_carrier(sK3)))) ),
inference(resolution,[],[f197,f137]) ).
fof(f137,plain,
! [X2] :
( ~ in(set_difference(cast_as_carrier_subset(sK3),sK5(X2)),sK4)
| ~ in(sK5(X2),X2)
| ~ element(X2,powerset(powerset(the_carrier(sK3)))) ),
inference(cnf_transformation,[],[f105]) ).
fof(f197,plain,
! [X3,X0,X1] :
( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| ~ in(X3,sK10(X0,X1))
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f123]) ).
fof(f1475,plain,
( ~ spl15_44
| spl15_45
| ~ spl15_31 ),
inference(avatar_split_clause,[],[f1119,f1102,f1472,f1468]) ).
fof(f1468,plain,
( spl15_44
<=> in(sK5(sK6(powerset(the_carrier(sK3)))),powerset(the_carrier(sK3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_44])]) ).
fof(f1472,plain,
( spl15_45
<=> in(sK5(sK6(powerset(the_carrier(sK3)))),sK10(sK3,sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_45])]) ).
fof(f1102,plain,
( spl15_31
<=> in(set_difference(cast_as_carrier_subset(sK3),sK5(sK6(powerset(the_carrier(sK3))))),sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_31])]) ).
fof(f1119,plain,
( in(sK5(sK6(powerset(the_carrier(sK3)))),sK10(sK3,sK4))
| ~ in(sK5(sK6(powerset(the_carrier(sK3)))),powerset(the_carrier(sK3)))
| ~ spl15_31 ),
inference(subsumption_resolution,[],[f1118,f132]) ).
fof(f1118,plain,
( in(sK5(sK6(powerset(the_carrier(sK3)))),sK10(sK3,sK4))
| ~ in(sK5(sK6(powerset(the_carrier(sK3)))),powerset(the_carrier(sK3)))
| ~ topological_space(sK3)
| ~ spl15_31 ),
inference(subsumption_resolution,[],[f1117,f133]) ).
fof(f1117,plain,
( in(sK5(sK6(powerset(the_carrier(sK3)))),sK10(sK3,sK4))
| ~ in(sK5(sK6(powerset(the_carrier(sK3)))),powerset(the_carrier(sK3)))
| ~ top_str(sK3)
| ~ topological_space(sK3)
| ~ spl15_31 ),
inference(subsumption_resolution,[],[f1115,f134]) ).
fof(f1115,plain,
( in(sK5(sK6(powerset(the_carrier(sK3)))),sK10(sK3,sK4))
| ~ in(sK5(sK6(powerset(the_carrier(sK3)))),powerset(the_carrier(sK3)))
| ~ element(sK4,powerset(powerset(the_carrier(sK3))))
| ~ top_str(sK3)
| ~ topological_space(sK3)
| ~ spl15_31 ),
inference(resolution,[],[f1104,f198]) ).
fof(f198,plain,
! [X3,X0,X1] :
( ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| in(X3,sK10(X0,X1))
| ~ in(X3,powerset(the_carrier(X0)))
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f123]) ).
fof(f1104,plain,
( in(set_difference(cast_as_carrier_subset(sK3),sK5(sK6(powerset(the_carrier(sK3))))),sK4)
| ~ spl15_31 ),
inference(avatar_component_clause,[],[f1102]) ).
fof(f1466,plain,
( ~ spl15_42
| ~ spl15_43 ),
inference(avatar_contradiction_clause,[],[f1465]) ).
fof(f1465,plain,
( $false
| ~ spl15_42
| ~ spl15_43 ),
inference(global_subsumption,[],[f173,f176,f132,f133,f138,f203,f204,f205,f206,f207,f208,f209,f210,f139,f174,f143,f144,f145,f146,f147,f148,f149,f152,f153,f154,f155,f156,f157,f158,f163,f167,f172,f211,f216,f217,f218,f212,f219,f220,f134,f221,f213,f222,f223,f224,f214,f225,f226,f227,f215,f228,f141,f229,f230,f151,f232,f233,f246,f184,f202,f185,f186,f187,f188,f189,f190,f191,f192,f193,f194,f195,f140,f177,f250,f178,f252,f253,f254,f255,f256,f251,f263,f264,f259,f265,f179,f180,f181,f182,f183,f201,f260,f142,f150,f291,f292,f159,f320,f294,f322,f337,f160,f347,f338,f339,f340,f341,f293,f321,f346,f348,f349,f350,f161,f358,f357,f351,f352,f162,f364,f363,f164,f370,f369,f165,f378,f377,f166,f384,f383,f168,f390,f389,f169,f398,f170,f404,f397,f403,f175,f409,f290,f318,f343,f354,f199,f418,f419,f360,f366,f374,f380,f386,f394,f200,f455,f456,f457,f458,f461,f470,f471,f472,f400,f407,f274,f135,f500,f501,f502,f504,f505,f507,f411,f412,f413,f414,f415,f488,f512,f519,f521,f280,f171,f416,f555,f417,f568,f490,f531,f498,f499,f136,f620,f621,f624,f627,f625,f629,f616,f617,f137,f503,f506,f508,f196,f691,f692,f698,f700,f707,f711,f708,f713,f715,f716,f706,f728,f197,f734,f739,f740,f741,f542,f543,f544,f545,f546,f547,f548,f549,f550,f551,f198,f757,f552,f454,f747,f748,f742,f920,f921,f749,f750,f751,f907,f570,f582,f761,f745,f971,f980,f981,f988,f991,f990,f993,f982,f513,f925,f931,f710,f1030,f1048,f1052,f1053,f1054,f517,f623,f712,f1069,f557,f558,f559,f694,f1081,f1082,f1083,f1084,f1086,f1087,f1089,f1092,f1093,f1099,f1097,f560,f561,f562,f563,f564,f565,f566,f567,f622,f923,f1136,f1137,f1138,f1139,f1140,f1141,f1142,f1143,f1144,f1145,f1147,f1148,f1150,f1152,f1159,f1153,f1161,f701,f1163,f1164,f1165,f1154,f1166,f1075,f1076,f1077,f1078,f1079,f1135,f619,f697,f1201,f1202,f1203,f999,f1008,f487,f735,f1245,f1247,f1256,f1250,f1252,f1253,f1255,f1258,f1263,f1261,f553,f1205,f1268,f1217,f1283,f614,f736,f1328,f1329,f1330,f756,f1419,f1420,f1032,f1426,f1439,f1440,f1441,f1463,f1464,f1430]) ).
fof(f1464,plain,
( ~ in(sK5(sK10(sK3,sK4)),sK10(sK3,sK4))
| ~ spl15_42 ),
inference(subsumption_resolution,[],[f1438,f1030]) ).
fof(f1438,plain,
( ~ in(sK5(sK10(sK3,sK4)),sK10(sK3,sK4))
| ~ element(sK10(sK3,sK4),powerset(powerset(the_carrier(sK3))))
| ~ spl15_42 ),
inference(resolution,[],[f1426,f137]) ).
fof(f1463,plain,
( in(sK5(sK10(sK3,sK4)),sK10(sK3,sK4))
| ~ in(sK5(sK10(sK3,sK4)),powerset(the_carrier(sK3)))
| ~ spl15_42 ),
inference(subsumption_resolution,[],[f1462,f132]) ).
fof(f1462,plain,
( in(sK5(sK10(sK3,sK4)),sK10(sK3,sK4))
| ~ in(sK5(sK10(sK3,sK4)),powerset(the_carrier(sK3)))
| ~ topological_space(sK3)
| ~ spl15_42 ),
inference(subsumption_resolution,[],[f1461,f133]) ).
fof(f1461,plain,
( in(sK5(sK10(sK3,sK4)),sK10(sK3,sK4))
| ~ in(sK5(sK10(sK3,sK4)),powerset(the_carrier(sK3)))
| ~ top_str(sK3)
| ~ topological_space(sK3)
| ~ spl15_42 ),
inference(subsumption_resolution,[],[f1443,f134]) ).
fof(f1443,plain,
( in(sK5(sK10(sK3,sK4)),sK10(sK3,sK4))
| ~ in(sK5(sK10(sK3,sK4)),powerset(the_carrier(sK3)))
| ~ element(sK4,powerset(powerset(the_carrier(sK3))))
| ~ top_str(sK3)
| ~ topological_space(sK3)
| ~ spl15_42 ),
inference(resolution,[],[f1426,f198]) ).
fof(f1441,plain,
( ~ in(sK4,set_difference(cast_as_carrier_subset(sK3),sK5(sK10(sK3,sK4))))
| ~ spl15_42 ),
inference(resolution,[],[f1426,f195]) ).
fof(f1440,plain,
( element(set_difference(cast_as_carrier_subset(sK3),sK5(sK10(sK3,sK4))),sK4)
| ~ spl15_42 ),
inference(resolution,[],[f1426,f409]) ).
fof(f1439,plain,
( empty(set_difference(cast_as_carrier_subset(sK3),sK5(sK10(sK3,sK4))))
| ~ element(sK4,set_difference(cast_as_carrier_subset(sK3),sK5(sK10(sK3,sK4))))
| ~ spl15_42 ),
inference(resolution,[],[f1426,f407]) ).
fof(f1426,plain,
( in(set_difference(cast_as_carrier_subset(sK3),sK5(sK10(sK3,sK4))),sK4)
| ~ spl15_42 ),
inference(avatar_component_clause,[],[f1424]) ).
fof(f1424,plain,
( spl15_42
<=> in(set_difference(cast_as_carrier_subset(sK3),sK5(sK10(sK3,sK4))),sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_42])]) ).
fof(f1032,plain,
( in(sK5(sK10(sK3,sK4)),sK10(sK3,sK4))
| in(set_difference(cast_as_carrier_subset(sK3),sK5(sK10(sK3,sK4))),sK4) ),
inference(resolution,[],[f1030,f136]) ).
fof(f1420,plain,
! [X0,X1] :
( ~ in(X0,powerset(the_carrier(X1)))
| ~ element(powerset(set_difference(cast_as_carrier_subset(X1),X0)),powerset(powerset(the_carrier(X1))))
| ~ top_str(X1)
| ~ topological_space(X1)
| in(X0,sK10(X1,powerset(set_difference(cast_as_carrier_subset(X1),X0)))) ),
inference(subsumption_resolution,[],[f1405,f139]) ).
fof(f1405,plain,
! [X0,X1] :
( ~ in(X0,powerset(the_carrier(X1)))
| ~ element(powerset(set_difference(cast_as_carrier_subset(X1),X0)),powerset(powerset(the_carrier(X1))))
| ~ top_str(X1)
| ~ topological_space(X1)
| in(X0,sK10(X1,powerset(set_difference(cast_as_carrier_subset(X1),X0))))
| empty(powerset(set_difference(cast_as_carrier_subset(X1),X0))) ),
inference(resolution,[],[f756,f455]) ).
fof(f1419,plain,
! [X2,X0,X1] :
( ~ in(X0,powerset(the_carrier(X1)))
| ~ element(powerset(X2),powerset(powerset(the_carrier(X1))))
| ~ top_str(X1)
| ~ topological_space(X1)
| in(X0,sK10(X1,powerset(X2)))
| ~ empty(set_difference(cast_as_carrier_subset(X1),X0)) ),
inference(subsumption_resolution,[],[f1404,f139]) ).
fof(f1404,plain,
! [X2,X0,X1] :
( ~ in(X0,powerset(the_carrier(X1)))
| ~ element(powerset(X2),powerset(powerset(the_carrier(X1))))
| ~ top_str(X1)
| ~ topological_space(X1)
| in(X0,sK10(X1,powerset(X2)))
| empty(powerset(X2))
| ~ empty(set_difference(cast_as_carrier_subset(X1),X0)) ),
inference(resolution,[],[f756,f418]) ).
fof(f756,plain,
! [X2,X0,X1] :
( ~ element(set_difference(cast_as_carrier_subset(X1),X0),X2)
| ~ in(X0,powerset(the_carrier(X1)))
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ top_str(X1)
| ~ topological_space(X1)
| in(X0,sK10(X1,X2))
| empty(X2) ),
inference(resolution,[],[f198,f175]) ).
fof(f1330,plain,
! [X2,X0,X1] :
( ~ element(sK11(set_difference(cast_as_carrier_subset(X0),X1),X2),powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ in(X1,sK10(X0,sK11(set_difference(cast_as_carrier_subset(X0),X1),X2)))
| element(set_difference(cast_as_carrier_subset(X0),X1),powerset(X2)) ),
inference(resolution,[],[f736,f199]) ).
fof(f1329,plain,
! [X2,X3,X0,X1] :
( ~ element(set_difference(cast_as_carrier_subset(X0),X1),powerset(powerset(the_carrier(X2))))
| ~ top_str(X2)
| ~ topological_space(X2)
| ~ in(X3,sK10(X2,set_difference(cast_as_carrier_subset(X0),X1)))
| ~ in(X1,sK10(X0,set_difference(cast_as_carrier_subset(X2),X3)))
| ~ element(set_difference(cast_as_carrier_subset(X2),X3),powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(resolution,[],[f736,f197]) ).
fof(f1328,plain,
! [X2,X0,X1] :
( ~ element(X0,powerset(powerset(the_carrier(X1))))
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ in(X2,sK10(X1,X0))
| ~ element(X0,set_difference(cast_as_carrier_subset(X1),X2))
| empty(set_difference(cast_as_carrier_subset(X1),X2)) ),
inference(resolution,[],[f736,f175]) ).
fof(f736,plain,
! [X2,X0,X1] :
( ~ in(X2,set_difference(cast_as_carrier_subset(X1),X0))
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ in(X0,sK10(X1,X2)) ),
inference(resolution,[],[f197,f195]) ).
fof(f614,plain,
( in(sK5(powerset(the_carrier(sK3))),powerset(the_carrier(sK3)))
| in(set_difference(cast_as_carrier_subset(sK3),sK5(powerset(the_carrier(sK3)))),sK4) ),
inference(resolution,[],[f136,f455]) ).
fof(f1283,plain,
! [X0] :
( empty_set = sK8(sK8(sK8(sK8(sK8(sK8(sK8(sK8(sK8(X0)))))))))
| ~ empty(X0) ),
inference(resolution,[],[f1217,f250]) ).
fof(f1217,plain,
! [X0] :
( ~ empty(X0)
| empty_set = sK8(sK8(sK8(sK8(sK8(sK8(sK8(sK8(X0)))))))) ),
inference(resolution,[],[f1008,f250]) ).
fof(f1268,plain,
! [X0,X1] :
( ~ empty(X0)
| sK8(sK8(sK8(X0))) = sK8(sK8(sK8(sK8(X1))))
| ~ empty(X1) ),
inference(resolution,[],[f1205,f250]) ).
fof(f1205,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ empty(X0)
| sK8(sK8(sK8(X0))) = sK8(sK8(sK8(X1))) ),
inference(resolution,[],[f999,f250]) ).
fof(f553,plain,
! [X0] :
( ~ element(powerset(the_carrier(X0)),sK7(X0))
| ~ topological_space(X0)
| ~ top_str(X0)
| empty(sK7(X0)) ),
inference(resolution,[],[f171,f488]) ).
fof(f1261,plain,
! [X0] :
( ~ element(sK4,set_difference(cast_as_carrier_subset(sK3),X0))
| ~ in(X0,sK10(sK3,sK4))
| empty(set_difference(cast_as_carrier_subset(sK3),X0)) ),
inference(resolution,[],[f1255,f488]) ).
fof(f1263,plain,
! [X0] :
( ~ in(X0,sK10(sK3,sK10(sK3,sK4)))
| ~ element(sK10(sK3,sK4),set_difference(cast_as_carrier_subset(sK3),X0))
| empty(set_difference(cast_as_carrier_subset(sK3),X0)) ),
inference(resolution,[],[f1258,f488]) ).
fof(f1258,plain,
! [X0] :
( element(set_difference(cast_as_carrier_subset(sK3),X0),sK10(sK3,sK4))
| ~ in(X0,sK10(sK3,sK10(sK3,sK4))) ),
inference(subsumption_resolution,[],[f1257,f132]) ).
fof(f1257,plain,
! [X0] :
( ~ in(X0,sK10(sK3,sK10(sK3,sK4)))
| ~ topological_space(sK3)
| element(set_difference(cast_as_carrier_subset(sK3),X0),sK10(sK3,sK4)) ),
inference(subsumption_resolution,[],[f1251,f133]) ).
fof(f1251,plain,
! [X0] :
( ~ in(X0,sK10(sK3,sK10(sK3,sK4)))
| ~ top_str(sK3)
| ~ topological_space(sK3)
| element(set_difference(cast_as_carrier_subset(sK3),X0),sK10(sK3,sK4)) ),
inference(resolution,[],[f735,f1030]) ).
fof(f1255,plain,
! [X0] :
( element(set_difference(cast_as_carrier_subset(sK3),X0),sK4)
| ~ in(X0,sK10(sK3,sK4)) ),
inference(subsumption_resolution,[],[f1254,f132]) ).
fof(f1254,plain,
! [X0] :
( ~ in(X0,sK10(sK3,sK4))
| ~ topological_space(sK3)
| element(set_difference(cast_as_carrier_subset(sK3),X0),sK4) ),
inference(subsumption_resolution,[],[f1248,f133]) ).
fof(f1248,plain,
! [X0] :
( ~ in(X0,sK10(sK3,sK4))
| ~ top_str(sK3)
| ~ topological_space(sK3)
| element(set_difference(cast_as_carrier_subset(sK3),X0),sK4) ),
inference(resolution,[],[f735,f134]) ).
fof(f1253,plain,
! [X2,X0,X1] :
( ~ in(X0,sK10(X1,sK11(powerset(powerset(the_carrier(X1))),X2)))
| ~ top_str(X1)
| ~ topological_space(X1)
| element(set_difference(cast_as_carrier_subset(X1),X0),sK11(powerset(powerset(the_carrier(X1))),X2))
| element(powerset(powerset(the_carrier(X1))),powerset(X2)) ),
inference(resolution,[],[f735,f416]) ).
fof(f1252,plain,
! [X2,X3,X0,X1] :
( ~ in(X0,sK10(X1,sK10(X2,X3)))
| ~ top_str(X1)
| ~ topological_space(X1)
| element(set_difference(cast_as_carrier_subset(X1),X0),sK10(X2,X3))
| ~ topological_space(X2)
| ~ empty(X3)
| ~ top_str(X2) ),
inference(resolution,[],[f735,f923]) ).
fof(f1250,plain,
! [X0,X1] :
( ~ in(X0,sK10(X1,sK8(powerset(powerset(the_carrier(X1))))))
| ~ top_str(X1)
| ~ topological_space(X1)
| element(set_difference(cast_as_carrier_subset(X1),X0),sK8(powerset(powerset(the_carrier(X1))))) ),
inference(resolution,[],[f735,f172]) ).
fof(f1256,plain,
! [X0,X1] :
( ~ in(X0,sK10(X1,sK6(powerset(the_carrier(X1)))))
| ~ top_str(X1)
| ~ topological_space(X1)
| element(set_difference(cast_as_carrier_subset(X1),X0),sK6(powerset(the_carrier(X1)))) ),
inference(subsumption_resolution,[],[f1249,f139]) ).
fof(f1249,plain,
! [X0,X1] :
( ~ in(X0,sK10(X1,sK6(powerset(the_carrier(X1)))))
| ~ top_str(X1)
| ~ topological_space(X1)
| element(set_difference(cast_as_carrier_subset(X1),X0),sK6(powerset(the_carrier(X1))))
| empty(powerset(the_carrier(X1))) ),
inference(resolution,[],[f735,f140]) ).
fof(f1247,plain,
! [X0,X1] :
( ~ in(X0,sK10(X1,empty_set))
| ~ top_str(X1)
| ~ topological_space(X1)
| element(set_difference(cast_as_carrier_subset(X1),X0),empty_set) ),
inference(resolution,[],[f735,f246]) ).
fof(f1245,plain,
! [X0,X1] :
( ~ in(X0,sK10(X1,powerset(the_carrier(X1))))
| ~ top_str(X1)
| ~ topological_space(X1)
| element(set_difference(cast_as_carrier_subset(X1),X0),powerset(the_carrier(X1))) ),
inference(resolution,[],[f735,f455]) ).
fof(f735,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ in(X0,sK10(X1,X2))
| ~ top_str(X1)
| ~ topological_space(X1)
| element(set_difference(cast_as_carrier_subset(X1),X0),X2) ),
inference(resolution,[],[f197,f409]) ).
fof(f487,plain,
! [X0,X1] :
( ~ element(X0,sK11(X0,X1))
| empty(sK11(X0,X1))
| element(X0,powerset(X1)) ),
inference(resolution,[],[f407,f199]) ).
fof(f1008,plain,
! [X0] :
( ~ empty(X0)
| empty_set = sK8(sK8(sK8(sK8(sK8(sK8(sK8(X0))))))) ),
inference(resolution,[],[f931,f250]) ).
fof(f999,plain,
! [X0,X1] :
( ~ empty(X1)
| sK8(sK8(sK8(X0))) = sK8(sK8(X1))
| ~ empty(X0) ),
inference(resolution,[],[f925,f250]) ).
fof(f1203,plain,
! [X0,X1] :
( in(sK11(sK10(X0,sK8(powerset(powerset(the_carrier(X0))))),X1),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| element(sK10(X0,sK8(powerset(powerset(the_carrier(X0))))),powerset(X1)) ),
inference(resolution,[],[f697,f199]) ).
fof(f1202,plain,
! [X2,X0,X1] :
( in(set_difference(cast_as_carrier_subset(X0),X1),powerset(the_carrier(X2)))
| ~ top_str(X2)
| ~ topological_space(X2)
| ~ in(X1,sK10(X0,sK10(X2,sK8(powerset(powerset(the_carrier(X2)))))))
| ~ element(sK10(X2,sK8(powerset(powerset(the_carrier(X2))))),powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(resolution,[],[f697,f197]) ).
fof(f1201,plain,
! [X0,X1] :
( in(X0,powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ element(X0,sK10(X1,sK8(powerset(powerset(the_carrier(X1))))))
| empty(sK10(X1,sK8(powerset(powerset(the_carrier(X1)))))) ),
inference(resolution,[],[f697,f175]) ).
fof(f697,plain,
! [X0,X1] :
( ~ in(X0,sK10(X1,sK8(powerset(powerset(the_carrier(X1))))))
| in(X0,powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ topological_space(X1) ),
inference(resolution,[],[f196,f172]) ).
fof(f619,plain,
( in(sK5(sK8(powerset(powerset(the_carrier(sK3))))),sK8(powerset(powerset(the_carrier(sK3)))))
| in(set_difference(cast_as_carrier_subset(sK3),sK5(sK8(powerset(powerset(the_carrier(sK3)))))),sK4) ),
inference(resolution,[],[f136,f172]) ).
fof(f1135,plain,
! [X2,X0,X1] :
( ~ topological_space(X0)
| ~ empty(X1)
| ~ top_str(X0)
| sP0(sK10(X0,X1))
| ~ v5_membered(X2) ),
inference(resolution,[],[f923,f150]) ).
fof(f1079,plain,
! [X0,X1] :
( v1_membered(sK11(powerset(X0),X1))
| ~ v5_membered(X0)
| element(powerset(X0),powerset(X1)) ),
inference(resolution,[],[f557,f145]) ).
fof(f1078,plain,
! [X0,X1] :
( v2_membered(sK11(powerset(X0),X1))
| ~ v5_membered(X0)
| element(powerset(X0),powerset(X1)) ),
inference(resolution,[],[f557,f146]) ).
fof(f1077,plain,
! [X0,X1] :
( v3_membered(sK11(powerset(X0),X1))
| ~ v5_membered(X0)
| element(powerset(X0),powerset(X1)) ),
inference(resolution,[],[f557,f147]) ).
fof(f1076,plain,
! [X0,X1] :
( v4_membered(sK11(powerset(X0),X1))
| ~ v5_membered(X0)
| element(powerset(X0),powerset(X1)) ),
inference(resolution,[],[f557,f148]) ).
fof(f1075,plain,
! [X0,X1] :
( v5_membered(sK11(powerset(X0),X1))
| ~ v5_membered(X0)
| element(powerset(X0),powerset(X1)) ),
inference(resolution,[],[f557,f149]) ).
fof(f1166,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ~ empty(X1)
| ~ element(sK4,set_difference(cast_as_carrier_subset(sK3),sK5(sK10(X0,X1))))
| empty(set_difference(cast_as_carrier_subset(sK3),sK5(sK10(X0,X1)))) ),
inference(resolution,[],[f1154,f175]) ).
fof(f1154,plain,
! [X0,X1] :
( ~ in(sK4,set_difference(cast_as_carrier_subset(sK3),sK5(sK10(X1,X0))))
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ empty(X0) ),
inference(resolution,[],[f1150,f195]) ).
fof(f1165,plain,
! [X0,X1] :
( in(sK11(sK10(X0,sK6(powerset(the_carrier(X0)))),X1),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| element(sK10(X0,sK6(powerset(the_carrier(X0)))),powerset(X1)) ),
inference(resolution,[],[f701,f199]) ).
fof(f1164,plain,
! [X2,X0,X1] :
( in(set_difference(cast_as_carrier_subset(X0),X1),powerset(the_carrier(X2)))
| ~ top_str(X2)
| ~ topological_space(X2)
| ~ in(X1,sK10(X0,sK10(X2,sK6(powerset(the_carrier(X2))))))
| ~ element(sK10(X2,sK6(powerset(the_carrier(X2)))),powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(resolution,[],[f701,f197]) ).
fof(f1163,plain,
! [X0,X1] :
( in(X0,powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ element(X0,sK10(X1,sK6(powerset(the_carrier(X1)))))
| empty(sK10(X1,sK6(powerset(the_carrier(X1))))) ),
inference(resolution,[],[f701,f175]) ).
fof(f701,plain,
! [X0,X1] :
( ~ in(X0,sK10(X1,sK6(powerset(the_carrier(X1)))))
| in(X0,powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ topological_space(X1) ),
inference(subsumption_resolution,[],[f696,f139]) ).
fof(f696,plain,
! [X0,X1] :
( ~ in(X0,sK10(X1,sK6(powerset(the_carrier(X1)))))
| in(X0,powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ topological_space(X1)
| empty(powerset(the_carrier(X1))) ),
inference(resolution,[],[f196,f140]) ).
fof(f1161,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ~ empty(X1)
| ~ element(sK4,set_difference(cast_as_carrier_subset(sK3),sK5(sK10(X0,X1))))
| empty(set_difference(cast_as_carrier_subset(sK3),sK5(sK10(X0,X1)))) ),
inference(resolution,[],[f1153,f488]) ).
fof(f1153,plain,
! [X0,X1] :
( element(set_difference(cast_as_carrier_subset(sK3),sK5(sK10(X1,X0))),sK4)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ empty(X0) ),
inference(resolution,[],[f1150,f409]) ).
fof(f1159,plain,
! [X0,X1] :
( ~ empty(X0)
| ~ top_str(X1)
| ~ topological_space(X1)
| in(sK5(sK10(X1,X0)),sK10(sK3,sK4))
| ~ in(sK5(sK10(X1,X0)),powerset(the_carrier(sK3))) ),
inference(subsumption_resolution,[],[f1158,f132]) ).
fof(f1158,plain,
! [X0,X1] :
( ~ empty(X0)
| ~ top_str(X1)
| ~ topological_space(X1)
| in(sK5(sK10(X1,X0)),sK10(sK3,sK4))
| ~ in(sK5(sK10(X1,X0)),powerset(the_carrier(sK3)))
| ~ topological_space(sK3) ),
inference(subsumption_resolution,[],[f1157,f133]) ).
fof(f1157,plain,
! [X0,X1] :
( ~ empty(X0)
| ~ top_str(X1)
| ~ topological_space(X1)
| in(sK5(sK10(X1,X0)),sK10(sK3,sK4))
| ~ in(sK5(sK10(X1,X0)),powerset(the_carrier(sK3)))
| ~ top_str(sK3)
| ~ topological_space(sK3) ),
inference(subsumption_resolution,[],[f1156,f134]) ).
fof(f1156,plain,
! [X0,X1] :
( ~ empty(X0)
| ~ top_str(X1)
| ~ topological_space(X1)
| in(sK5(sK10(X1,X0)),sK10(sK3,sK4))
| ~ in(sK5(sK10(X1,X0)),powerset(the_carrier(sK3)))
| ~ element(sK4,powerset(powerset(the_carrier(sK3))))
| ~ top_str(sK3)
| ~ topological_space(sK3) ),
inference(resolution,[],[f1150,f198]) ).
fof(f1152,plain,
! [X0,X1] :
( ~ empty(X0)
| ~ top_str(X1)
| ~ topological_space(X1)
| empty(set_difference(cast_as_carrier_subset(sK3),sK5(sK10(X1,X0))))
| ~ element(sK4,set_difference(cast_as_carrier_subset(sK3),sK5(sK10(X1,X0)))) ),
inference(resolution,[],[f1150,f407]) ).
fof(f1150,plain,
! [X0,X1] :
( in(set_difference(cast_as_carrier_subset(sK3),sK5(sK10(X0,X1))),sK4)
| ~ empty(X1)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(subsumption_resolution,[],[f1146,f742]) ).
fof(f1146,plain,
! [X0,X1] :
( ~ topological_space(X0)
| ~ empty(X1)
| ~ top_str(X0)
| in(sK5(sK10(X0,X1)),sK10(X0,X1))
| in(set_difference(cast_as_carrier_subset(sK3),sK5(sK10(X0,X1))),sK4) ),
inference(resolution,[],[f923,f136]) ).
fof(f1148,plain,
! [X2,X0,X1] :
( ~ topological_space(X0)
| ~ empty(X1)
| ~ top_str(X0)
| ~ element(powerset(X2),sK10(X0,X1))
| empty(sK10(X0,X1)) ),
inference(resolution,[],[f923,f488]) ).
fof(f1147,plain,
! [X2,X3,X0,X1] :
( ~ topological_space(X0)
| ~ empty(X1)
| ~ top_str(X0)
| ~ in(X2,sK10(X3,sK10(X0,X1)))
| in(X2,powerset(the_carrier(X3)))
| ~ top_str(X3)
| ~ topological_space(X3) ),
inference(resolution,[],[f923,f196]) ).
fof(f1145,plain,
! [X2,X0,X1] :
( ~ topological_space(X0)
| ~ empty(X1)
| ~ top_str(X0)
| v1_membered(sK10(X0,X1))
| ~ v1_membered(X2) ),
inference(resolution,[],[f923,f170]) ).
fof(f1144,plain,
! [X2,X0,X1] :
( ~ topological_space(X0)
| ~ empty(X1)
| ~ top_str(X0)
| v2_membered(sK10(X0,X1))
| ~ v2_membered(X2) ),
inference(resolution,[],[f923,f169]) ).
fof(f1143,plain,
! [X2,X0,X1] :
( ~ topological_space(X0)
| ~ empty(X1)
| ~ top_str(X0)
| v1_membered(sK10(X0,X1))
| ~ v2_membered(X2) ),
inference(resolution,[],[f923,f168]) ).
fof(f1142,plain,
! [X2,X0,X1] :
( ~ topological_space(X0)
| ~ empty(X1)
| ~ top_str(X0)
| v3_membered(sK10(X0,X1))
| ~ v3_membered(X2) ),
inference(resolution,[],[f923,f166]) ).
fof(f1141,plain,
! [X2,X0,X1] :
( ~ topological_space(X0)
| ~ empty(X1)
| ~ top_str(X0)
| v2_membered(sK10(X0,X1))
| ~ v3_membered(X2) ),
inference(resolution,[],[f923,f165]) ).
fof(f1140,plain,
! [X2,X0,X1] :
( ~ topological_space(X0)
| ~ empty(X1)
| ~ top_str(X0)
| v1_membered(sK10(X0,X1))
| ~ v3_membered(X2) ),
inference(resolution,[],[f923,f164]) ).
fof(f1139,plain,
! [X2,X0,X1] :
( ~ topological_space(X0)
| ~ empty(X1)
| ~ top_str(X0)
| v4_membered(sK10(X0,X1))
| ~ v4_membered(X2) ),
inference(resolution,[],[f923,f162]) ).
fof(f1138,plain,
! [X2,X0,X1] :
( ~ topological_space(X0)
| ~ empty(X1)
| ~ top_str(X0)
| v3_membered(sK10(X0,X1))
| ~ v4_membered(X2) ),
inference(resolution,[],[f923,f161]) ).
fof(f1137,plain,
! [X2,X0,X1] :
( ~ topological_space(X0)
| ~ empty(X1)
| ~ top_str(X0)
| v2_membered(sK10(X0,X1))
| ~ v4_membered(X2) ),
inference(resolution,[],[f923,f160]) ).
fof(f1136,plain,
! [X2,X0,X1] :
( ~ topological_space(X0)
| ~ empty(X1)
| ~ top_str(X0)
| v1_membered(sK10(X0,X1))
| ~ v4_membered(X2) ),
inference(resolution,[],[f923,f159]) ).
fof(f923,plain,
! [X2,X0,X1] :
( element(sK10(X0,X1),powerset(X2))
| ~ topological_space(X0)
| ~ empty(X1)
| ~ top_str(X0) ),
inference(resolution,[],[f742,f199]) ).
fof(f622,plain,
( in(sK5(sK6(powerset(the_carrier(sK3)))),sK6(powerset(the_carrier(sK3))))
| in(set_difference(cast_as_carrier_subset(sK3),sK5(sK6(powerset(the_carrier(sK3))))),sK4) ),
inference(subsumption_resolution,[],[f618,f139]) ).
fof(f618,plain,
( in(sK5(sK6(powerset(the_carrier(sK3)))),sK6(powerset(the_carrier(sK3))))
| in(set_difference(cast_as_carrier_subset(sK3),sK5(sK6(powerset(the_carrier(sK3))))),sK4)
| empty(powerset(the_carrier(sK3))) ),
inference(resolution,[],[f136,f140]) ).
fof(f567,plain,
! [X0,X1] :
( v1_membered(sK11(powerset(X0),X1))
| element(powerset(X0),powerset(X1))
| ~ v1_membered(X0) ),
inference(resolution,[],[f416,f170]) ).
fof(f566,plain,
! [X0,X1] :
( v2_membered(sK11(powerset(X0),X1))
| element(powerset(X0),powerset(X1))
| ~ v2_membered(X0) ),
inference(resolution,[],[f416,f169]) ).
fof(f565,plain,
! [X0,X1] :
( v1_membered(sK11(powerset(X0),X1))
| element(powerset(X0),powerset(X1))
| ~ v2_membered(X0) ),
inference(resolution,[],[f416,f168]) ).
fof(f564,plain,
! [X0,X1] :
( v3_membered(sK11(powerset(X0),X1))
| element(powerset(X0),powerset(X1))
| ~ v3_membered(X0) ),
inference(resolution,[],[f416,f166]) ).
fof(f563,plain,
! [X0,X1] :
( v2_membered(sK11(powerset(X0),X1))
| element(powerset(X0),powerset(X1))
| ~ v3_membered(X0) ),
inference(resolution,[],[f416,f165]) ).
fof(f562,plain,
! [X0,X1] :
( v1_membered(sK11(powerset(X0),X1))
| element(powerset(X0),powerset(X1))
| ~ v3_membered(X0) ),
inference(resolution,[],[f416,f164]) ).
fof(f561,plain,
! [X0,X1] :
( v4_membered(sK11(powerset(X0),X1))
| element(powerset(X0),powerset(X1))
| ~ v4_membered(X0) ),
inference(resolution,[],[f416,f162]) ).
fof(f560,plain,
! [X0,X1] :
( v3_membered(sK11(powerset(X0),X1))
| element(powerset(X0),powerset(X1))
| ~ v4_membered(X0) ),
inference(resolution,[],[f416,f161]) ).
fof(f1097,plain,
! [X0] :
( ~ in(sK10(sK3,sK4),sK5(X0))
| ~ empty(X0)
| ~ in(sK5(X0),sK10(sK3,empty_set)) ),
inference(resolution,[],[f1089,f195]) ).
fof(f1099,plain,
! [X0] :
( ~ empty(X0)
| element(sK5(X0),powerset(the_carrier(sK3)))
| ~ element(sK5(X0),sK10(sK3,empty_set))
| empty(sK10(sK3,empty_set)) ),
inference(resolution,[],[f1093,f175]) ).
fof(f1093,plain,
! [X0] :
( ~ in(sK5(X0),sK10(sK3,empty_set))
| ~ empty(X0)
| element(sK5(X0),powerset(the_carrier(sK3))) ),
inference(resolution,[],[f1089,f707]) ).
fof(f1092,plain,
! [X0] :
( ~ in(sK5(X0),sK10(sK3,empty_set))
| ~ empty(X0)
| empty(sK5(X0))
| ~ element(powerset(the_carrier(sK3)),sK5(X0)) ),
inference(resolution,[],[f1089,f706]) ).
fof(f1089,plain,
! [X0] :
( in(sK5(X0),sK10(sK3,sK4))
| ~ in(sK5(X0),sK10(sK3,empty_set))
| ~ empty(X0) ),
inference(subsumption_resolution,[],[f1088,f132]) ).
fof(f1088,plain,
! [X0] :
( ~ in(sK5(X0),sK10(sK3,empty_set))
| ~ topological_space(sK3)
| in(sK5(X0),sK10(sK3,sK4))
| ~ empty(X0) ),
inference(subsumption_resolution,[],[f1080,f133]) ).
fof(f1080,plain,
! [X0] :
( ~ in(sK5(X0),sK10(sK3,empty_set))
| ~ top_str(sK3)
| ~ topological_space(sK3)
| in(sK5(X0),sK10(sK3,sK4))
| ~ empty(X0) ),
inference(resolution,[],[f694,f761]) ).
fof(f1087,plain,
! [X2,X0,X1] :
( ~ in(set_difference(cast_as_carrier_subset(X0),X1),sK10(X2,empty_set))
| ~ top_str(X2)
| ~ topological_space(X2)
| in(X1,sK10(X0,powerset(the_carrier(X2))))
| ~ in(X1,powerset(the_carrier(X0)))
| ~ element(powerset(the_carrier(X2)),powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(resolution,[],[f694,f198]) ).
fof(f1086,plain,
! [X0,X1] :
( ~ in(sK11(X0,powerset(the_carrier(X1))),sK10(X1,empty_set))
| ~ top_str(X1)
| ~ topological_space(X1)
| element(X0,powerset(powerset(the_carrier(X1)))) ),
inference(resolution,[],[f694,f200]) ).
fof(f1084,plain,
! [X0,X1] :
( ~ in(X0,sK10(X1,empty_set))
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ in(powerset(the_carrier(X1)),X0) ),
inference(resolution,[],[f694,f195]) ).
fof(f1083,plain,
! [X0,X1] :
( ~ in(X0,sK10(X1,empty_set))
| ~ top_str(X1)
| ~ topological_space(X1)
| element(X0,powerset(the_carrier(X1))) ),
inference(resolution,[],[f694,f409]) ).
fof(f1082,plain,
! [X0,X1] :
( ~ in(X0,sK10(X1,empty_set))
| ~ top_str(X1)
| ~ topological_space(X1)
| empty(X0)
| ~ element(powerset(the_carrier(X1)),X0) ),
inference(resolution,[],[f694,f407]) ).
fof(f1081,plain,
! [X0] :
( ~ in(powerset(the_carrier(sK3)),sK10(X0,empty_set))
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ in(powerset(the_carrier(X0)),sK10(sK3,sK4)) ),
inference(resolution,[],[f694,f708]) ).
fof(f694,plain,
! [X0,X1] :
( in(X0,powerset(the_carrier(X1)))
| ~ in(X0,sK10(X1,empty_set))
| ~ top_str(X1)
| ~ topological_space(X1) ),
inference(resolution,[],[f196,f246]) ).
fof(f559,plain,
! [X0,X1] :
( v2_membered(sK11(powerset(X0),X1))
| element(powerset(X0),powerset(X1))
| ~ v4_membered(X0) ),
inference(resolution,[],[f416,f160]) ).
fof(f558,plain,
! [X0,X1] :
( v1_membered(sK11(powerset(X0),X1))
| element(powerset(X0),powerset(X1))
| ~ v4_membered(X0) ),
inference(resolution,[],[f416,f159]) ).
fof(f557,plain,
! [X0,X1] :
( sP0(sK11(powerset(X0),X1))
| element(powerset(X0),powerset(X1))
| ~ v5_membered(X0) ),
inference(resolution,[],[f416,f150]) ).
fof(f1069,plain,
! [X0] :
( element(sK10(sK3,sK4),powerset(X0))
| ~ element(powerset(the_carrier(sK3)),sK11(sK10(sK3,sK4),X0))
| empty(sK11(sK10(sK3,sK4),X0)) ),
inference(resolution,[],[f712,f488]) ).
fof(f712,plain,
! [X0] :
( element(sK11(sK10(sK3,sK4),X0),powerset(the_carrier(sK3)))
| element(sK10(sK3,sK4),powerset(X0)) ),
inference(resolution,[],[f707,f199]) ).
fof(f623,plain,
! [X0] :
( ~ element(sK4,set_difference(cast_as_carrier_subset(sK3),sK5(X0)))
| empty(set_difference(cast_as_carrier_subset(sK3),sK5(X0)))
| ~ empty(X0) ),
inference(resolution,[],[f621,f407]) ).
fof(f517,plain,
! [X0] :
( ~ element(powerset(the_carrier(sK3)),sK5(X0))
| empty(sK5(X0))
| ~ element(X0,powerset(powerset(the_carrier(sK3)))) ),
inference(resolution,[],[f488,f135]) ).
fof(f1054,plain,
! [X0] :
( in(sK11(sK10(sK3,sK10(sK3,sK4)),X0),powerset(the_carrier(sK3)))
| element(sK10(sK3,sK10(sK3,sK4)),powerset(X0)) ),
inference(resolution,[],[f1048,f199]) ).
fof(f1053,plain,
! [X0,X1] :
( in(set_difference(cast_as_carrier_subset(X0),X1),powerset(the_carrier(sK3)))
| ~ in(X1,sK10(X0,sK10(sK3,sK10(sK3,sK4))))
| ~ element(sK10(sK3,sK10(sK3,sK4)),powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(resolution,[],[f1048,f197]) ).
fof(f1052,plain,
! [X0] :
( in(X0,powerset(the_carrier(sK3)))
| ~ element(X0,sK10(sK3,sK10(sK3,sK4)))
| empty(sK10(sK3,sK10(sK3,sK4))) ),
inference(resolution,[],[f1048,f175]) ).
fof(f1048,plain,
! [X0] :
( ~ in(X0,sK10(sK3,sK10(sK3,sK4)))
| in(X0,powerset(the_carrier(sK3))) ),
inference(subsumption_resolution,[],[f1047,f132]) ).
fof(f1047,plain,
! [X0] :
( ~ in(X0,sK10(sK3,sK10(sK3,sK4)))
| in(X0,powerset(the_carrier(sK3)))
| ~ topological_space(sK3) ),
inference(subsumption_resolution,[],[f1033,f133]) ).
fof(f1033,plain,
! [X0] :
( ~ in(X0,sK10(sK3,sK10(sK3,sK4)))
| in(X0,powerset(the_carrier(sK3)))
| ~ top_str(sK3)
| ~ topological_space(sK3) ),
inference(resolution,[],[f1030,f196]) ).
fof(f931,plain,
! [X0] :
( ~ empty(X0)
| empty_set = sK8(sK8(sK8(sK8(sK8(sK8(X0)))))) ),
inference(resolution,[],[f582,f250]) ).
fof(f925,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ empty(X0)
| sK8(X1) = sK8(sK8(sK8(X0))) ),
inference(resolution,[],[f570,f250]) ).
fof(f513,plain,
! [X0] :
( ~ element(powerset(the_carrier(X0)),cast_as_carrier_subset(X0))
| empty(cast_as_carrier_subset(X0))
| ~ one_sorted_str(X0) ),
inference(resolution,[],[f488,f142]) ).
fof(f982,plain,
! [X0] :
( ~ in(sK10(sK3,sK4),sK5(X0))
| ~ element(sK5(X0),powerset(the_carrier(sK3)))
| ~ empty(X0) ),
inference(resolution,[],[f971,f195]) ).
fof(f993,plain,
! [X0] :
( ~ element(sK10(sK3,sK4),sK5(X0))
| ~ empty(X0)
| empty(sK5(X0)) ),
inference(resolution,[],[f990,f488]) ).
fof(f990,plain,
! [X0] :
( element(sK5(X0),sK10(sK3,sK4))
| ~ empty(X0) ),
inference(subsumption_resolution,[],[f984,f418]) ).
fof(f984,plain,
! [X0] :
( ~ empty(X0)
| element(sK5(X0),sK10(sK3,sK4))
| ~ element(X0,powerset(powerset(the_carrier(sK3)))) ),
inference(resolution,[],[f981,f135]) ).
fof(f991,plain,
! [X0] :
( ~ empty(X0)
| element(sK5(X0),sK10(sK3,sK4)) ),
inference(global_subsumption,[],[f173,f176,f132,f133,f138,f203,f204,f205,f206,f207,f208,f209,f210,f139,f174,f143,f144,f145,f146,f147,f148,f149,f152,f153,f154,f155,f156,f157,f158,f163,f167,f172,f211,f216,f217,f218,f212,f219,f220,f134,f221,f213,f222,f223,f224,f214,f225,f226,f227,f215,f228,f141,f229,f230,f151,f232,f233,f246,f184,f202,f185,f186,f187,f188,f189,f190,f191,f192,f193,f194,f195,f140,f177,f250,f178,f252,f253,f254,f255,f256,f251,f263,f264,f259,f265,f179,f180,f181,f182,f183,f201,f260,f142,f150,f291,f292,f159,f320,f294,f322,f337,f160,f347,f338,f339,f340,f341,f293,f321,f346,f348,f349,f350,f161,f358,f357,f351,f352,f162,f364,f363,f164,f370,f369,f165,f378,f377,f166,f384,f383,f168,f390,f389,f169,f398,f170,f404,f397,f403,f175,f409,f290,f318,f343,f354,f199,f418,f419,f360,f366,f374,f380,f386,f394,f200,f455,f456,f457,f458,f461,f470,f471,f472,f400,f407,f487,f274,f135,f500,f501,f502,f504,f505,f507,f411,f412,f413,f414,f415,f488,f513,f517,f512,f519,f521,f280,f171,f553,f416,f555,f557,f558,f559,f560,f561,f562,f563,f564,f565,f566,f567,f417,f568,f490,f531,f498,f499,f136,f614,f622,f619,f620,f621,f623,f624,f627,f625,f629,f616,f617,f137,f503,f506,f508,f196,f691,f692,f694,f701,f697,f698,f700,f710,f707,f711,f712,f708,f713,f715,f716,f706,f728,f197,f734,f735,f736,f739,f740,f741,f542,f543,f544,f545,f546,f547,f548,f549,f550,f551,f198,f756,f757,f552,f454,f747,f748,f742,f920,f921,f923,f749,f750,f751,f907,f570,f925,f582,f931,f761,f745,f971,f980,f982,f981,f990,f988]) ).
fof(f988,plain,
! [X0] :
( ~ empty(X0)
| element(sK5(X0),sK10(sK3,sK4))
| ~ empty(sK5(X0)) ),
inference(resolution,[],[f981,f418]) ).
fof(f981,plain,
! [X0] :
( ~ element(sK5(X0),powerset(the_carrier(sK3)))
| ~ empty(X0)
| element(sK5(X0),sK10(sK3,sK4)) ),
inference(resolution,[],[f971,f409]) ).
fof(f980,plain,
! [X0] :
( ~ empty(X0)
| ~ element(sK5(X0),powerset(the_carrier(sK3)))
| empty(sK5(X0))
| ~ element(sK10(sK3,sK4),sK5(X0)) ),
inference(resolution,[],[f971,f407]) ).
fof(f971,plain,
! [X0] :
( in(sK5(X0),sK10(sK3,sK4))
| ~ empty(X0)
| ~ element(sK5(X0),powerset(the_carrier(sK3))) ),
inference(subsumption_resolution,[],[f970,f139]) ).
fof(f970,plain,
! [X0] :
( in(sK5(X0),sK10(sK3,sK4))
| ~ empty(X0)
| ~ element(sK5(X0),powerset(the_carrier(sK3)))
| empty(powerset(the_carrier(sK3))) ),
inference(resolution,[],[f761,f175]) ).
fof(f761,plain,
! [X0] :
( ~ in(sK5(X0),powerset(the_carrier(sK3)))
| in(sK5(X0),sK10(sK3,sK4))
| ~ empty(X0) ),
inference(subsumption_resolution,[],[f760,f132]) ).
fof(f760,plain,
! [X0] :
( in(sK5(X0),sK10(sK3,sK4))
| ~ in(sK5(X0),powerset(the_carrier(sK3)))
| ~ topological_space(sK3)
| ~ empty(X0) ),
inference(subsumption_resolution,[],[f759,f133]) ).
fof(f759,plain,
! [X0] :
( in(sK5(X0),sK10(sK3,sK4))
| ~ in(sK5(X0),powerset(the_carrier(sK3)))
| ~ top_str(sK3)
| ~ topological_space(sK3)
| ~ empty(X0) ),
inference(subsumption_resolution,[],[f752,f134]) ).
fof(f752,plain,
! [X0] :
( in(sK5(X0),sK10(sK3,sK4))
| ~ in(sK5(X0),powerset(the_carrier(sK3)))
| ~ element(sK4,powerset(powerset(the_carrier(sK3))))
| ~ top_str(sK3)
| ~ topological_space(sK3)
| ~ empty(X0) ),
inference(resolution,[],[f198,f621]) ).
fof(f582,plain,
! [X0] :
( ~ empty(X0)
| empty_set = sK8(sK8(sK8(sK8(sK8(X0))))) ),
inference(resolution,[],[f531,f250]) ).
fof(f570,plain,
! [X0,X1] :
( ~ empty(X1)
| sK8(sK8(sK8(X0))) = X1
| ~ empty(X0) ),
inference(resolution,[],[f490,f250]) ).
fof(f907,plain,
! [X0,X1] :
( ~ empty(sK11(X0,powerset(X1)))
| element(X0,powerset(powerset(X1))) ),
inference(subsumption_resolution,[],[f905,f139]) ).
fof(f905,plain,
! [X0,X1] :
( element(X0,powerset(powerset(X1)))
| empty(powerset(X1))
| ~ empty(sK11(X0,powerset(X1))) ),
inference(resolution,[],[f454,f418]) ).
fof(f751,plain,
! [X0] :
( v1_membered(sK7(X0))
| ~ top_str(X0)
| ~ v5_membered(the_carrier(X0))
| ~ topological_space(X0) ),
inference(resolution,[],[f542,f145]) ).
fof(f750,plain,
! [X0] :
( v2_membered(sK7(X0))
| ~ top_str(X0)
| ~ v5_membered(the_carrier(X0))
| ~ topological_space(X0) ),
inference(resolution,[],[f542,f146]) ).
fof(f749,plain,
! [X0] :
( v3_membered(sK7(X0))
| ~ top_str(X0)
| ~ v5_membered(the_carrier(X0))
| ~ topological_space(X0) ),
inference(resolution,[],[f542,f147]) ).
fof(f921,plain,
! [X2,X3,X0,X1] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ~ empty(X1)
| ~ in(X2,sK10(X3,sK10(X0,X1)))
| ~ element(sK10(X0,X1),powerset(powerset(the_carrier(X3))))
| ~ top_str(X3)
| ~ topological_space(X3) ),
inference(resolution,[],[f742,f197]) ).
fof(f920,plain,
! [X2,X0,X1] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ~ empty(X1)
| ~ element(X2,sK10(X0,X1))
| empty(sK10(X0,X1)) ),
inference(resolution,[],[f742,f175]) ).
fof(f742,plain,
! [X2,X0,X1] :
( ~ in(X0,sK10(X1,X2))
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ empty(X2) ),
inference(subsumption_resolution,[],[f737,f418]) ).
fof(f737,plain,
! [X2,X0,X1] :
( ~ in(X0,sK10(X1,X2))
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ empty(X2) ),
inference(resolution,[],[f197,f202]) ).
fof(f748,plain,
! [X0] :
( v4_membered(sK7(X0))
| ~ top_str(X0)
| ~ v5_membered(the_carrier(X0))
| ~ topological_space(X0) ),
inference(resolution,[],[f542,f148]) ).
fof(f747,plain,
! [X0] :
( v5_membered(sK7(X0))
| ~ top_str(X0)
| ~ v5_membered(the_carrier(X0))
| ~ topological_space(X0) ),
inference(resolution,[],[f542,f149]) ).
fof(f454,plain,
! [X0,X1] :
( ~ element(sK11(X0,X1),X1)
| element(X0,powerset(X1))
| empty(X1) ),
inference(resolution,[],[f200,f175]) ).
fof(f552,plain,
! [X0] :
( v1_membered(sK7(X0))
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ v1_membered(the_carrier(X0)) ),
inference(resolution,[],[f171,f170]) ).
fof(f757,plain,
! [X0,X1] :
( in(X0,sK10(X1,powerset(the_carrier(sK3))))
| ~ in(X0,powerset(the_carrier(X1)))
| ~ element(powerset(the_carrier(sK3)),powerset(powerset(the_carrier(X1))))
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ in(set_difference(cast_as_carrier_subset(X1),X0),sK10(sK3,sK4)) ),
inference(resolution,[],[f198,f700]) ).
fof(f551,plain,
! [X0] :
( v2_membered(sK7(X0))
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ v2_membered(the_carrier(X0)) ),
inference(resolution,[],[f171,f169]) ).
fof(f550,plain,
! [X0] :
( v1_membered(sK7(X0))
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ v2_membered(the_carrier(X0)) ),
inference(resolution,[],[f171,f168]) ).
fof(f549,plain,
! [X0] :
( v3_membered(sK7(X0))
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ v3_membered(the_carrier(X0)) ),
inference(resolution,[],[f171,f166]) ).
fof(f548,plain,
! [X0] :
( v2_membered(sK7(X0))
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ v3_membered(the_carrier(X0)) ),
inference(resolution,[],[f171,f165]) ).
fof(f547,plain,
! [X0] :
( v1_membered(sK7(X0))
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ v3_membered(the_carrier(X0)) ),
inference(resolution,[],[f171,f164]) ).
fof(f546,plain,
! [X0] :
( v4_membered(sK7(X0))
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ v4_membered(the_carrier(X0)) ),
inference(resolution,[],[f171,f162]) ).
fof(f545,plain,
! [X0] :
( v3_membered(sK7(X0))
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ v4_membered(the_carrier(X0)) ),
inference(resolution,[],[f171,f161]) ).
fof(f544,plain,
! [X0] :
( v2_membered(sK7(X0))
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ v4_membered(the_carrier(X0)) ),
inference(resolution,[],[f171,f160]) ).
fof(f543,plain,
! [X0] :
( v1_membered(sK7(X0))
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ v4_membered(the_carrier(X0)) ),
inference(resolution,[],[f171,f159]) ).
fof(f542,plain,
! [X0] :
( sP0(sK7(X0))
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ v5_membered(the_carrier(X0)) ),
inference(resolution,[],[f171,f150]) ).
fof(f741,plain,
! [X2,X0,X1] :
( ~ in(X0,sK10(X1,sK11(set_difference(cast_as_carrier_subset(X1),X0),X2)))
| ~ element(sK11(set_difference(cast_as_carrier_subset(X1),X0),X2),powerset(powerset(the_carrier(X1))))
| ~ top_str(X1)
| ~ topological_space(X1)
| element(set_difference(cast_as_carrier_subset(X1),X0),powerset(X2)) ),
inference(resolution,[],[f197,f417]) ).
fof(f740,plain,
! [X0,X1] :
( ~ in(X0,sK10(X1,sK10(sK3,sK4)))
| ~ element(sK10(sK3,sK4),powerset(powerset(the_carrier(X1))))
| ~ top_str(X1)
| ~ topological_space(X1)
| element(set_difference(cast_as_carrier_subset(X1),X0),powerset(the_carrier(sK3))) ),
inference(resolution,[],[f197,f707]) ).
fof(f739,plain,
! [X0,X1] :
( ~ in(X0,sK10(X1,sK10(sK3,sK4)))
| ~ element(sK10(sK3,sK4),powerset(powerset(the_carrier(X1))))
| ~ top_str(X1)
| ~ topological_space(X1)
| empty(set_difference(cast_as_carrier_subset(X1),X0))
| ~ element(powerset(the_carrier(sK3)),set_difference(cast_as_carrier_subset(X1),X0)) ),
inference(resolution,[],[f197,f706]) ).
fof(f734,plain,
! [X2,X0,X1] :
( ~ in(X0,sK10(X1,X2))
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ top_str(X1)
| ~ topological_space(X1)
| empty(set_difference(cast_as_carrier_subset(X1),X0))
| ~ element(X2,set_difference(cast_as_carrier_subset(X1),X0)) ),
inference(resolution,[],[f197,f407]) ).
fof(f728,plain,
! [X0] :
( empty(sK11(sK10(sK3,sK4),X0))
| ~ element(powerset(the_carrier(sK3)),sK11(sK10(sK3,sK4),X0))
| element(sK10(sK3,sK4),powerset(X0)) ),
inference(resolution,[],[f706,f199]) ).
fof(f706,plain,
! [X0] :
( ~ in(X0,sK10(sK3,sK4))
| empty(X0)
| ~ element(powerset(the_carrier(sK3)),X0) ),
inference(resolution,[],[f700,f407]) ).
fof(f716,plain,
( ~ element(powerset(the_carrier(sK3)),sK10(sK3,sK4))
| empty(sK10(sK3,sK4)) ),
inference(resolution,[],[f715,f175]) ).
fof(f715,plain,
~ in(powerset(the_carrier(sK3)),sK10(sK3,sK4)),
inference(duplicate_literal_removal,[],[f714]) ).
fof(f714,plain,
( ~ in(powerset(the_carrier(sK3)),sK10(sK3,sK4))
| ~ in(powerset(the_carrier(sK3)),sK10(sK3,sK4)) ),
inference(resolution,[],[f708,f700]) ).
fof(f713,plain,
! [X0] :
( ~ in(X0,sK10(sK3,sK4))
| ~ element(powerset(the_carrier(sK3)),X0)
| empty(X0) ),
inference(resolution,[],[f708,f175]) ).
fof(f708,plain,
! [X0] :
( ~ in(powerset(the_carrier(sK3)),X0)
| ~ in(X0,sK10(sK3,sK4)) ),
inference(resolution,[],[f700,f195]) ).
fof(f711,plain,
! [X0] :
( element(X0,powerset(the_carrier(sK3)))
| ~ element(X0,sK10(sK3,sK4))
| empty(sK10(sK3,sK4)) ),
inference(resolution,[],[f707,f175]) ).
fof(f707,plain,
! [X0] :
( ~ in(X0,sK10(sK3,sK4))
| element(X0,powerset(the_carrier(sK3))) ),
inference(resolution,[],[f700,f409]) ).
fof(f698,plain,
! [X2,X0,X1] :
( ~ in(X0,sK10(X1,sK11(powerset(powerset(the_carrier(X1))),X2)))
| in(X0,powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ topological_space(X1)
| element(powerset(powerset(the_carrier(X1))),powerset(X2)) ),
inference(resolution,[],[f196,f416]) ).
fof(f692,plain,
! [X0,X1] :
( ~ in(X0,sK10(X1,powerset(the_carrier(X1))))
| in(X0,powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ topological_space(X1) ),
inference(resolution,[],[f196,f455]) ).
fof(f691,plain,
! [X2,X0,X1] :
( ~ in(X0,sK10(X1,X2))
| in(X0,powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ empty(X2) ),
inference(resolution,[],[f196,f418]) ).
fof(f508,plain,
! [X0] :
( ~ element(X0,powerset(powerset(the_carrier(sK3))))
| v1_membered(sK5(X0))
| ~ v1_membered(the_carrier(sK3)) ),
inference(resolution,[],[f135,f170]) ).
fof(f506,plain,
! [X0] :
( ~ element(X0,powerset(powerset(the_carrier(sK3))))
| v1_membered(sK5(X0))
| ~ v2_membered(the_carrier(sK3)) ),
inference(resolution,[],[f135,f168]) ).
fof(f503,plain,
! [X0] :
( ~ element(X0,powerset(powerset(the_carrier(sK3))))
| v1_membered(sK5(X0))
| ~ v3_membered(the_carrier(sK3)) ),
inference(resolution,[],[f135,f164]) ).
fof(f617,plain,
( in(sK5(sK4),sK4)
| in(set_difference(cast_as_carrier_subset(sK3),sK5(sK4)),sK4) ),
inference(resolution,[],[f136,f134]) ).
fof(f616,plain,
( in(sK5(empty_set),empty_set)
| in(set_difference(cast_as_carrier_subset(sK3),sK5(empty_set)),sK4) ),
inference(resolution,[],[f136,f246]) ).
fof(f629,plain,
! [X0] :
( ~ empty(X0)
| ~ element(sK4,set_difference(cast_as_carrier_subset(sK3),sK5(X0)))
| empty(set_difference(cast_as_carrier_subset(sK3),sK5(X0))) ),
inference(resolution,[],[f625,f175]) ).
fof(f625,plain,
! [X0] :
( ~ in(sK4,set_difference(cast_as_carrier_subset(sK3),sK5(X0)))
| ~ empty(X0) ),
inference(resolution,[],[f621,f195]) ).
fof(f627,plain,
! [X0] :
( ~ empty(X0)
| ~ element(sK4,set_difference(cast_as_carrier_subset(sK3),sK5(X0)))
| empty(set_difference(cast_as_carrier_subset(sK3),sK5(X0))) ),
inference(resolution,[],[f624,f488]) ).
fof(f624,plain,
! [X0] :
( element(set_difference(cast_as_carrier_subset(sK3),sK5(X0)),sK4)
| ~ empty(X0) ),
inference(resolution,[],[f621,f409]) ).
fof(f621,plain,
! [X0] :
( in(set_difference(cast_as_carrier_subset(sK3),sK5(X0)),sK4)
| ~ empty(X0) ),
inference(subsumption_resolution,[],[f613,f202]) ).
fof(f613,plain,
! [X0] :
( in(sK5(X0),X0)
| in(set_difference(cast_as_carrier_subset(sK3),sK5(X0)),sK4)
| ~ empty(X0) ),
inference(resolution,[],[f136,f418]) ).
fof(f620,plain,
! [X0] :
( in(sK5(sK11(powerset(powerset(the_carrier(sK3))),X0)),sK11(powerset(powerset(the_carrier(sK3))),X0))
| in(set_difference(cast_as_carrier_subset(sK3),sK5(sK11(powerset(powerset(the_carrier(sK3))),X0))),sK4)
| element(powerset(powerset(the_carrier(sK3))),powerset(X0)) ),
inference(resolution,[],[f136,f416]) ).
fof(f136,plain,
! [X2] :
( ~ element(X2,powerset(powerset(the_carrier(sK3))))
| in(sK5(X2),X2)
| in(set_difference(cast_as_carrier_subset(sK3),sK5(X2)),sK4) ),
inference(cnf_transformation,[],[f105]) ).
fof(f499,plain,
! [X0] :
( ~ element(X0,powerset(powerset(the_carrier(sK3))))
| v1_membered(sK5(X0))
| ~ v4_membered(the_carrier(sK3)) ),
inference(resolution,[],[f135,f159]) ).
fof(f498,plain,
! [X0] :
( ~ element(X0,powerset(powerset(the_carrier(sK3))))
| sP0(sK5(X0))
| ~ v5_membered(the_carrier(sK3)) ),
inference(resolution,[],[f135,f150]) ).
fof(f531,plain,
! [X0] :
( ~ empty(X0)
| empty_set = sK8(sK8(sK8(sK8(X0)))) ),
inference(resolution,[],[f280,f250]) ).
fof(f490,plain,
! [X0,X1] :
( ~ empty(X1)
| sK8(sK8(X1)) = X0
| ~ empty(X0) ),
inference(resolution,[],[f274,f250]) ).
fof(f568,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ element(X0,sK11(X0,X1))
| empty(sK11(X0,X1)) ),
inference(resolution,[],[f417,f175]) ).
fof(f417,plain,
! [X0,X1] :
( ~ in(X0,sK11(X0,X1))
| element(X0,powerset(X1)) ),
inference(resolution,[],[f199,f195]) ).
fof(f555,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ element(X0,sK11(X0,X1))
| empty(sK11(X0,X1)) ),
inference(resolution,[],[f416,f488]) ).
fof(f416,plain,
! [X0,X1] :
( element(sK11(X0,X1),X0)
| element(X0,powerset(X1)) ),
inference(resolution,[],[f199,f409]) ).
fof(f171,plain,
! [X0] :
( element(sK7(X0),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f112]) ).
fof(f112,plain,
! [X0] :
( element(sK7(X0),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f82,f111]) ).
fof(f111,plain,
! [X0] :
( ? [X1] : element(X1,powerset(the_carrier(X0)))
=> element(sK7(X0),powerset(the_carrier(X0))) ),
introduced(choice_axiom,[]) ).
fof(f82,plain,
! [X0] :
( ? [X1] : element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(flattening,[],[f81]) ).
fof(f81,plain,
! [X0] :
( ? [X1] : element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(ennf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ? [X1] : element(X1,powerset(the_carrier(X0))) ),
inference(pure_predicate_removal,[],[f24]) ).
fof(f24,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ? [X1] :
( closed_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc6_pre_topc) ).
fof(f280,plain,
! [X0] :
( ~ empty(X0)
| empty_set = sK8(sK8(sK8(X0))) ),
inference(resolution,[],[f260,f250]) ).
fof(f521,plain,
! [X0] :
( ~ element(powerset(X0),sK6(X0))
| empty(X0) ),
inference(subsumption_resolution,[],[f518,f141]) ).
fof(f518,plain,
! [X0] :
( ~ element(powerset(X0),sK6(X0))
| empty(sK6(X0))
| empty(X0) ),
inference(resolution,[],[f488,f140]) ).
fof(f519,plain,
! [X0] :
( ~ element(X0,sK8(X0))
| empty(sK8(X0)) ),
inference(resolution,[],[f488,f172]) ).
fof(f512,plain,
! [X0] :
( ~ element(powerset(X0),X0)
| empty(X0) ),
inference(resolution,[],[f488,f455]) ).
fof(f488,plain,
! [X0,X1] :
( ~ element(X1,X0)
| ~ element(X0,X1)
| empty(X1) ),
inference(subsumption_resolution,[],[f486,f177]) ).
fof(f486,plain,
! [X0,X1] :
( empty(X0)
| ~ element(X1,X0)
| ~ element(X0,X1)
| empty(X1) ),
inference(resolution,[],[f407,f175]) ).
fof(f415,plain,
! [X0] :
( v1_membered(cast_as_carrier_subset(X0))
| ~ one_sorted_str(X0)
| ~ v5_membered(the_carrier(X0)) ),
inference(resolution,[],[f290,f145]) ).
fof(f414,plain,
! [X0] :
( v2_membered(cast_as_carrier_subset(X0))
| ~ one_sorted_str(X0)
| ~ v5_membered(the_carrier(X0)) ),
inference(resolution,[],[f290,f146]) ).
fof(f413,plain,
! [X0] :
( v3_membered(cast_as_carrier_subset(X0))
| ~ one_sorted_str(X0)
| ~ v5_membered(the_carrier(X0)) ),
inference(resolution,[],[f290,f147]) ).
fof(f412,plain,
! [X0] :
( v4_membered(cast_as_carrier_subset(X0))
| ~ one_sorted_str(X0)
| ~ v5_membered(the_carrier(X0)) ),
inference(resolution,[],[f290,f148]) ).
fof(f411,plain,
! [X0] :
( v5_membered(cast_as_carrier_subset(X0))
| ~ one_sorted_str(X0)
| ~ v5_membered(the_carrier(X0)) ),
inference(resolution,[],[f290,f149]) ).
fof(f507,plain,
! [X0] :
( ~ element(X0,powerset(powerset(the_carrier(sK3))))
| v2_membered(sK5(X0))
| ~ v2_membered(the_carrier(sK3)) ),
inference(resolution,[],[f135,f169]) ).
fof(f505,plain,
! [X0] :
( ~ element(X0,powerset(powerset(the_carrier(sK3))))
| v3_membered(sK5(X0))
| ~ v3_membered(the_carrier(sK3)) ),
inference(resolution,[],[f135,f166]) ).
fof(f504,plain,
! [X0] :
( ~ element(X0,powerset(powerset(the_carrier(sK3))))
| v2_membered(sK5(X0))
| ~ v3_membered(the_carrier(sK3)) ),
inference(resolution,[],[f135,f165]) ).
fof(f502,plain,
! [X0] :
( ~ element(X0,powerset(powerset(the_carrier(sK3))))
| v4_membered(sK5(X0))
| ~ v4_membered(the_carrier(sK3)) ),
inference(resolution,[],[f135,f162]) ).
fof(f501,plain,
! [X0] :
( ~ element(X0,powerset(powerset(the_carrier(sK3))))
| v3_membered(sK5(X0))
| ~ v4_membered(the_carrier(sK3)) ),
inference(resolution,[],[f135,f161]) ).
fof(f500,plain,
! [X0] :
( ~ element(X0,powerset(powerset(the_carrier(sK3))))
| v2_membered(sK5(X0))
| ~ v4_membered(the_carrier(sK3)) ),
inference(resolution,[],[f135,f160]) ).
fof(f135,plain,
! [X2] :
( element(sK5(X2),powerset(the_carrier(sK3)))
| ~ element(X2,powerset(powerset(the_carrier(sK3)))) ),
inference(cnf_transformation,[],[f105]) ).
fof(f274,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ empty(X0)
| sK8(X1) = X0 ),
inference(resolution,[],[f201,f250]) ).
fof(f407,plain,
! [X0,X1] :
( ~ in(X1,X0)
| empty(X1)
| ~ element(X0,X1) ),
inference(resolution,[],[f175,f195]) ).
fof(f400,plain,
! [X0] :
( v1_membered(cast_as_carrier_subset(X0))
| ~ v1_membered(the_carrier(X0))
| ~ one_sorted_str(X0) ),
inference(resolution,[],[f170,f142]) ).
fof(f472,plain,
! [X0] :
( v1_membered(X0)
| ~ v5_membered(X0) ),
inference(resolution,[],[f456,f145]) ).
fof(f471,plain,
! [X0] :
( v2_membered(X0)
| ~ v5_membered(X0) ),
inference(resolution,[],[f456,f146]) ).
fof(f470,plain,
! [X0] :
( v3_membered(X0)
| ~ v5_membered(X0) ),
inference(resolution,[],[f456,f147]) ).
fof(f461,plain,
! [X0] :
( v1_membered(X0)
| ~ v3_membered(X0) ),
inference(resolution,[],[f455,f164]) ).
fof(f458,plain,
! [X0] :
( v2_membered(X0)
| ~ v4_membered(X0) ),
inference(resolution,[],[f455,f160]) ).
fof(f457,plain,
! [X0] :
( v1_membered(X0)
| ~ v4_membered(X0) ),
inference(resolution,[],[f455,f159]) ).
fof(f456,plain,
! [X0] :
( sP0(X0)
| ~ v5_membered(X0) ),
inference(resolution,[],[f455,f150]) ).
fof(f455,plain,
! [X0] : element(X0,powerset(X0)),
inference(duplicate_literal_removal,[],[f453]) ).
fof(f453,plain,
! [X0] :
( element(X0,powerset(X0))
| element(X0,powerset(X0)) ),
inference(resolution,[],[f200,f199]) ).
fof(f394,plain,
! [X0] :
( v2_membered(cast_as_carrier_subset(X0))
| ~ v2_membered(the_carrier(X0))
| ~ one_sorted_str(X0) ),
inference(resolution,[],[f169,f142]) ).
fof(f386,plain,
! [X0] :
( v1_membered(cast_as_carrier_subset(X0))
| ~ v2_membered(the_carrier(X0))
| ~ one_sorted_str(X0) ),
inference(resolution,[],[f168,f142]) ).
fof(f380,plain,
! [X0] :
( v3_membered(cast_as_carrier_subset(X0))
| ~ v3_membered(the_carrier(X0))
| ~ one_sorted_str(X0) ),
inference(resolution,[],[f166,f142]) ).
fof(f374,plain,
! [X0] :
( v2_membered(cast_as_carrier_subset(X0))
| ~ v3_membered(the_carrier(X0))
| ~ one_sorted_str(X0) ),
inference(resolution,[],[f165,f142]) ).
fof(f366,plain,
! [X0] :
( v1_membered(cast_as_carrier_subset(X0))
| ~ v3_membered(the_carrier(X0))
| ~ one_sorted_str(X0) ),
inference(resolution,[],[f164,f142]) ).
fof(f360,plain,
! [X0] :
( v4_membered(cast_as_carrier_subset(X0))
| ~ v4_membered(the_carrier(X0))
| ~ one_sorted_str(X0) ),
inference(resolution,[],[f162,f142]) ).
fof(f419,plain,
! [X0,X1] :
( ~ empty(X0)
| sP0(X0)
| ~ v5_membered(X1) ),
inference(resolution,[],[f418,f150]) ).
fof(f418,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ empty(X0) ),
inference(resolution,[],[f199,f202]) ).
fof(f354,plain,
! [X0] :
( v3_membered(cast_as_carrier_subset(X0))
| ~ v4_membered(the_carrier(X0))
| ~ one_sorted_str(X0) ),
inference(resolution,[],[f161,f142]) ).
fof(f343,plain,
! [X0] :
( v2_membered(cast_as_carrier_subset(X0))
| ~ v4_membered(the_carrier(X0))
| ~ one_sorted_str(X0) ),
inference(resolution,[],[f160,f142]) ).
fof(f318,plain,
! [X0] :
( v1_membered(cast_as_carrier_subset(X0))
| ~ v4_membered(the_carrier(X0))
| ~ one_sorted_str(X0) ),
inference(resolution,[],[f159,f142]) ).
fof(f290,plain,
! [X0] :
( sP0(cast_as_carrier_subset(X0))
| ~ v5_membered(the_carrier(X0))
| ~ one_sorted_str(X0) ),
inference(resolution,[],[f150,f142]) ).
fof(f409,plain,
! [X0,X1] :
( ~ in(X1,X0)
| element(X1,X0) ),
inference(subsumption_resolution,[],[f176,f202]) ).
fof(f175,plain,
! [X0,X1] :
( in(X1,X0)
| ~ element(X1,X0)
| empty(X0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f117,plain,
! [X0,X1] :
( ( ( ( element(X1,X0)
| ~ empty(X1) )
& ( empty(X1)
| ~ element(X1,X0) ) )
| ~ empty(X0) )
& ( ( ( element(X1,X0)
| ~ in(X1,X0) )
& ( in(X1,X0)
| ~ element(X1,X0) ) )
| empty(X0) ) ),
inference(nnf_transformation,[],[f83]) ).
fof(f83,plain,
! [X0,X1] :
( ( ( element(X1,X0)
<=> empty(X1) )
| ~ empty(X0) )
& ( ( element(X1,X0)
<=> in(X1,X0) )
| empty(X0) ) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0,X1] :
( ( empty(X0)
=> ( element(X1,X0)
<=> empty(X1) ) )
& ( ~ empty(X0)
=> ( element(X1,X0)
<=> in(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_subset_1) ).
fof(f403,plain,
! [X0] :
( v1_membered(sK6(X0))
| ~ v1_membered(X0)
| empty(X0) ),
inference(resolution,[],[f170,f140]) ).
fof(f397,plain,
! [X0] :
( v2_membered(sK6(X0))
| ~ v2_membered(X0)
| empty(X0) ),
inference(resolution,[],[f169,f140]) ).
fof(f404,plain,
! [X0] :
( v1_membered(sK8(powerset(X0)))
| ~ v1_membered(X0) ),
inference(resolution,[],[f170,f172]) ).
fof(f170,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| v1_membered(X1)
| ~ v1_membered(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0] :
( ! [X1] :
( v1_membered(X1)
| ~ element(X1,powerset(X0)) )
| ~ v1_membered(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0] :
( v1_membered(X0)
=> ! [X1] :
( element(X1,powerset(X0))
=> v1_membered(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc16_membered) ).
fof(f398,plain,
! [X0] :
( v2_membered(sK8(powerset(X0)))
| ~ v2_membered(X0) ),
inference(resolution,[],[f169,f172]) ).
fof(f169,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| v2_membered(X1)
| ~ v2_membered(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0] :
( ! [X1] :
( ( v2_membered(X1)
& v1_membered(X1) )
| ~ element(X1,powerset(X0)) )
| ~ v2_membered(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,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(f389,plain,
! [X0] :
( v1_membered(sK6(X0))
| ~ v2_membered(X0)
| empty(X0) ),
inference(resolution,[],[f168,f140]) ).
fof(f390,plain,
! [X0] :
( v1_membered(sK8(powerset(X0)))
| ~ v2_membered(X0) ),
inference(resolution,[],[f168,f172]) ).
fof(f168,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| v1_membered(X1)
| ~ v2_membered(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f383,plain,
! [X0] :
( v3_membered(sK6(X0))
| ~ v3_membered(X0)
| empty(X0) ),
inference(resolution,[],[f166,f140]) ).
fof(f384,plain,
! [X0] :
( v3_membered(sK8(powerset(X0)))
| ~ v3_membered(X0) ),
inference(resolution,[],[f166,f172]) ).
fof(f166,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| v3_membered(X1)
| ~ v3_membered(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0] :
( ! [X1] :
( ( v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1) )
| ~ element(X1,powerset(X0)) )
| ~ v3_membered(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,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(f377,plain,
! [X0] :
( v2_membered(sK6(X0))
| ~ v3_membered(X0)
| empty(X0) ),
inference(resolution,[],[f165,f140]) ).
fof(f378,plain,
! [X0] :
( v2_membered(sK8(powerset(X0)))
| ~ v3_membered(X0) ),
inference(resolution,[],[f165,f172]) ).
fof(f165,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| v2_membered(X1)
| ~ v3_membered(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f369,plain,
! [X0] :
( v1_membered(sK6(X0))
| ~ v3_membered(X0)
| empty(X0) ),
inference(resolution,[],[f164,f140]) ).
fof(f370,plain,
! [X0] :
( v1_membered(sK8(powerset(X0)))
| ~ v3_membered(X0) ),
inference(resolution,[],[f164,f172]) ).
fof(f164,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| v1_membered(X1)
| ~ v3_membered(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f363,plain,
! [X0] :
( v4_membered(sK6(X0))
| ~ v4_membered(X0)
| empty(X0) ),
inference(resolution,[],[f162,f140]) ).
fof(f364,plain,
! [X0] :
( v4_membered(sK8(powerset(X0)))
| ~ v4_membered(X0) ),
inference(resolution,[],[f162,f172]) ).
fof(f162,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| v4_membered(X1)
| ~ v4_membered(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,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,[],[f16]) ).
fof(f16,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(f352,plain,
! [X0] :
( v1_membered(sK6(X0))
| empty(X0)
| ~ v5_membered(X0) ),
inference(resolution,[],[f293,f145]) ).
fof(f351,plain,
! [X0] :
( v2_membered(sK6(X0))
| empty(X0)
| ~ v5_membered(X0) ),
inference(resolution,[],[f293,f146]) ).
fof(f357,plain,
! [X0] :
( v3_membered(sK6(X0))
| ~ v4_membered(X0)
| empty(X0) ),
inference(resolution,[],[f161,f140]) ).
fof(f358,plain,
! [X0] :
( v3_membered(sK8(powerset(X0)))
| ~ v4_membered(X0) ),
inference(resolution,[],[f161,f172]) ).
fof(f161,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| v3_membered(X1)
| ~ v4_membered(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f350,plain,
! [X0] :
( v3_membered(sK6(X0))
| empty(X0)
| ~ v5_membered(X0) ),
inference(resolution,[],[f293,f147]) ).
fof(f349,plain,
! [X0] :
( v4_membered(sK6(X0))
| empty(X0)
| ~ v5_membered(X0) ),
inference(resolution,[],[f293,f148]) ).
fof(f348,plain,
! [X0] :
( v5_membered(sK6(X0))
| empty(X0)
| ~ v5_membered(X0) ),
inference(resolution,[],[f293,f149]) ).
fof(f346,plain,
! [X0] :
( v2_membered(sK6(X0))
| ~ v4_membered(X0)
| empty(X0) ),
inference(resolution,[],[f160,f140]) ).
fof(f321,plain,
! [X0] :
( v1_membered(sK6(X0))
| ~ v4_membered(X0)
| empty(X0) ),
inference(resolution,[],[f159,f140]) ).
fof(f293,plain,
! [X0] :
( sP0(sK6(X0))
| ~ v5_membered(X0)
| empty(X0) ),
inference(resolution,[],[f150,f140]) ).
fof(f341,plain,
! [X0] :
( v1_membered(sK8(powerset(X0)))
| ~ v5_membered(X0) ),
inference(resolution,[],[f294,f145]) ).
fof(f340,plain,
! [X0] :
( v2_membered(sK8(powerset(X0)))
| ~ v5_membered(X0) ),
inference(resolution,[],[f294,f146]) ).
fof(f339,plain,
! [X0] :
( v3_membered(sK8(powerset(X0)))
| ~ v5_membered(X0) ),
inference(resolution,[],[f294,f147]) ).
fof(f338,plain,
! [X0] :
( v4_membered(sK8(powerset(X0)))
| ~ v5_membered(X0) ),
inference(resolution,[],[f294,f148]) ).
fof(f347,plain,
! [X0] :
( v2_membered(sK8(powerset(X0)))
| ~ v4_membered(X0) ),
inference(resolution,[],[f160,f172]) ).
fof(f160,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| v2_membered(X1)
| ~ v4_membered(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f337,plain,
! [X0] :
( v5_membered(sK8(powerset(X0)))
| ~ v5_membered(X0) ),
inference(resolution,[],[f294,f149]) ).
fof(f322,plain,
! [X0] :
( v1_membered(sK8(powerset(X0)))
| ~ v4_membered(X0) ),
inference(resolution,[],[f159,f172]) ).
fof(f294,plain,
! [X0] :
( sP0(sK8(powerset(X0)))
| ~ v5_membered(X0) ),
inference(resolution,[],[f150,f172]) ).
fof(f320,plain,
( v1_membered(sK4)
| ~ v4_membered(powerset(the_carrier(sK3))) ),
inference(resolution,[],[f159,f134]) ).
fof(f159,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| v1_membered(X1)
| ~ v4_membered(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f292,plain,
( sP0(sK4)
| ~ v5_membered(powerset(the_carrier(sK3))) ),
inference(resolution,[],[f150,f134]) ).
fof(f291,plain,
! [X0] :
( sP0(empty_set)
| ~ v5_membered(X0) ),
inference(resolution,[],[f150,f246]) ).
fof(f150,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| sP0(X1)
| ~ v5_membered(X0) ),
inference(cnf_transformation,[],[f96]) ).
fof(f96,plain,
! [X0] :
( ! [X1] :
( sP0(X1)
| ~ element(X1,powerset(X0)) )
| ~ v5_membered(X0) ),
inference(definition_folding,[],[f71,f95]) ).
fof(f95,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(f71,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,[],[f17]) ).
fof(f17,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(f142,plain,
! [X0] :
( element(cast_as_carrier_subset(X0),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0] :
( element(cast_as_carrier_subset(X0),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0] :
( one_sorted_str(X0)
=> element(cast_as_carrier_subset(X0),powerset(the_carrier(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_pre_topc) ).
fof(f260,plain,
! [X0] :
( ~ empty(X0)
| empty_set = sK8(sK8(X0)) ),
inference(resolution,[],[f251,f250]) ).
fof(f201,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f93,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f47]) ).
fof(f47,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(f183,plain,
! [X0,X1] :
( v5_membered(set_difference(X1,X0))
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f119]) ).
fof(f119,plain,
! [X0,X1] :
( ( v5_membered(set_difference(X1,X0))
& v4_membered(set_difference(X1,X0))
& v3_membered(set_difference(X1,X0))
& v2_membered(set_difference(X1,X0))
& v1_membered(set_difference(X1,X0)) )
| ~ sP2(X0,X1) ),
inference(rectify,[],[f118]) ).
fof(f118,plain,
! [X1,X0] :
( ( v5_membered(set_difference(X0,X1))
& v4_membered(set_difference(X0,X1))
& v3_membered(set_difference(X0,X1))
& v2_membered(set_difference(X0,X1))
& v1_membered(set_difference(X0,X1)) )
| ~ sP2(X1,X0) ),
inference(nnf_transformation,[],[f99]) ).
fof(f99,plain,
! [X1,X0] :
( ( v5_membered(set_difference(X0,X1))
& v4_membered(set_difference(X0,X1))
& v3_membered(set_difference(X0,X1))
& v2_membered(set_difference(X0,X1))
& v1_membered(set_difference(X0,X1)) )
| ~ sP2(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f182,plain,
! [X0,X1] :
( v4_membered(set_difference(X1,X0))
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f119]) ).
fof(f181,plain,
! [X0,X1] :
( v3_membered(set_difference(X1,X0))
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f119]) ).
fof(f180,plain,
! [X0,X1] :
( v2_membered(set_difference(X1,X0))
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f119]) ).
fof(f179,plain,
! [X0,X1] :
( v1_membered(set_difference(X1,X0))
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f119]) ).
fof(f265,plain,
element(empty_set,empty_set),
inference(superposition,[],[f172,f259]) ).
fof(f259,plain,
empty_set = sK8(empty_set),
inference(resolution,[],[f251,f138]) ).
fof(f264,plain,
empty_set = sK8(empty_set),
inference(forward_demodulation,[],[f262,f232]) ).
fof(f262,plain,
empty_set = sK8(sK13),
inference(resolution,[],[f251,f204]) ).
fof(f263,plain,
empty_set = sK8(empty_set),
inference(forward_demodulation,[],[f261,f233]) ).
fof(f261,plain,
! [X0] : empty_set = sK8(sK9(X0)),
inference(resolution,[],[f251,f174]) ).
fof(f251,plain,
! [X0] :
( ~ empty(X0)
| empty_set = sK8(X0) ),
inference(resolution,[],[f250,f151]) ).
fof(f256,plain,
! [X0] :
( v5_membered(sK8(X0))
| ~ empty(X0) ),
inference(resolution,[],[f250,f211]) ).
fof(f255,plain,
! [X0] :
( v4_membered(sK8(X0))
| ~ empty(X0) ),
inference(resolution,[],[f250,f212]) ).
fof(f254,plain,
! [X0] :
( v3_membered(sK8(X0))
| ~ empty(X0) ),
inference(resolution,[],[f250,f213]) ).
fof(f253,plain,
! [X0] :
( v2_membered(sK8(X0))
| ~ empty(X0) ),
inference(resolution,[],[f250,f214]) ).
fof(f252,plain,
! [X0] :
( v1_membered(sK8(X0))
| ~ empty(X0) ),
inference(resolution,[],[f250,f215]) ).
fof(f178,plain,
! [X0,X1] :
( element(X1,X0)
| ~ empty(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f250,plain,
! [X0] :
( empty(sK8(X0))
| ~ empty(X0) ),
inference(resolution,[],[f177,f172]) ).
fof(f177,plain,
! [X0,X1] :
( ~ element(X1,X0)
| empty(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f140,plain,
! [X0] :
( element(sK6(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f107,plain,
! [X0] :
( ( ~ empty(sK6(X0))
& element(sK6(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f67,f106]) ).
fof(f106,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( ~ empty(sK6(X0))
& element(sK6(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f67,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f195,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f194,plain,
! [X0,X1] :
( v1_membered(set_difference(X0,X1))
| ~ v1_membered(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0,X1] :
( v1_membered(set_difference(X0,X1))
| ~ v1_membered(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0,X1] :
( v1_membered(X0)
=> v1_membered(set_difference(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc37_membered) ).
fof(f193,plain,
! [X0,X1] :
( v2_membered(set_difference(X0,X1))
| ~ v2_membered(X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f87,plain,
! [X0,X1] :
( ( v2_membered(set_difference(X0,X1))
& v1_membered(set_difference(X0,X1)) )
| ~ v2_membered(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0,X1] :
( v2_membered(X0)
=> ( v2_membered(set_difference(X0,X1))
& v1_membered(set_difference(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc38_membered) ).
fof(f192,plain,
! [X0,X1] :
( v1_membered(set_difference(X0,X1))
| ~ v2_membered(X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f191,plain,
! [X0,X1] :
( v3_membered(set_difference(X0,X1))
| ~ v3_membered(X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0,X1] :
( ( v3_membered(set_difference(X0,X1))
& v2_membered(set_difference(X0,X1))
& v1_membered(set_difference(X0,X1)) )
| ~ v3_membered(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0,X1] :
( v3_membered(X0)
=> ( v3_membered(set_difference(X0,X1))
& v2_membered(set_difference(X0,X1))
& v1_membered(set_difference(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc39_membered) ).
fof(f190,plain,
! [X0,X1] :
( v2_membered(set_difference(X0,X1))
| ~ v3_membered(X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f189,plain,
! [X0,X1] :
( v1_membered(set_difference(X0,X1))
| ~ v3_membered(X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f188,plain,
! [X0,X1] :
( v4_membered(set_difference(X0,X1))
| ~ v4_membered(X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
! [X0,X1] :
( ( v4_membered(set_difference(X0,X1))
& v3_membered(set_difference(X0,X1))
& v2_membered(set_difference(X0,X1))
& v1_membered(set_difference(X0,X1)) )
| ~ v4_membered(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0,X1] :
( v4_membered(X0)
=> ( v4_membered(set_difference(X0,X1))
& v3_membered(set_difference(X0,X1))
& v2_membered(set_difference(X0,X1))
& v1_membered(set_difference(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc40_membered) ).
fof(f187,plain,
! [X0,X1] :
( v3_membered(set_difference(X0,X1))
| ~ v4_membered(X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f186,plain,
! [X0,X1] :
( v2_membered(set_difference(X0,X1))
| ~ v4_membered(X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f185,plain,
! [X0,X1] :
( v1_membered(set_difference(X0,X1))
| ~ v4_membered(X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f202,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f94]) ).
fof(f94,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f46]) ).
fof(f46,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f184,plain,
! [X0,X1] :
( sP2(X1,X0)
| ~ v5_membered(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f100,plain,
! [X0,X1] :
( sP2(X1,X0)
| ~ v5_membered(X0) ),
inference(definition_folding,[],[f84,f99]) ).
fof(f84,plain,
! [X0,X1] :
( ( v5_membered(set_difference(X0,X1))
& v4_membered(set_difference(X0,X1))
& v3_membered(set_difference(X0,X1))
& v2_membered(set_difference(X0,X1))
& v1_membered(set_difference(X0,X1)) )
| ~ v5_membered(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0,X1] :
( v5_membered(X0)
=> ( v5_membered(set_difference(X0,X1))
& v4_membered(set_difference(X0,X1))
& v3_membered(set_difference(X0,X1))
& v2_membered(set_difference(X0,X1))
& v1_membered(set_difference(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc41_membered) ).
fof(f246,plain,
! [X0] : element(empty_set,powerset(X0)),
inference(forward_demodulation,[],[f173,f233]) ).
fof(f233,plain,
! [X0] : empty_set = sK9(X0),
inference(resolution,[],[f151,f174]) ).
fof(f232,plain,
empty_set = sK13,
inference(resolution,[],[f151,f204]) ).
fof(f151,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f230,plain,
! [X0] : v1_membered(sK9(X0)),
inference(resolution,[],[f215,f174]) ).
fof(f229,plain,
v1_membered(sK13),
inference(resolution,[],[f215,f204]) ).
fof(f141,plain,
! [X0] :
( ~ empty(sK6(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f228,plain,
v1_membered(empty_set),
inference(resolution,[],[f215,f138]) ).
fof(f215,plain,
! [X0] :
( ~ empty(X0)
| v1_membered(X0) ),
inference(resolution,[],[f157,f152]) ).
fof(f227,plain,
! [X0] : v2_membered(sK9(X0)),
inference(resolution,[],[f214,f174]) ).
fof(f226,plain,
v2_membered(sK13),
inference(resolution,[],[f214,f204]) ).
fof(f225,plain,
v2_membered(empty_set),
inference(resolution,[],[f214,f138]) ).
fof(f214,plain,
! [X0] :
( ~ empty(X0)
| v2_membered(X0) ),
inference(resolution,[],[f157,f153]) ).
fof(f224,plain,
! [X0] : v3_membered(sK9(X0)),
inference(resolution,[],[f213,f174]) ).
fof(f223,plain,
v3_membered(sK13),
inference(resolution,[],[f213,f204]) ).
fof(f222,plain,
v3_membered(empty_set),
inference(resolution,[],[f213,f138]) ).
fof(f213,plain,
! [X0] :
( ~ empty(X0)
| v3_membered(X0) ),
inference(resolution,[],[f157,f154]) ).
fof(f221,plain,
! [X0] : v4_membered(sK9(X0)),
inference(resolution,[],[f212,f174]) ).
fof(f220,plain,
v4_membered(sK13),
inference(resolution,[],[f212,f204]) ).
fof(f219,plain,
v4_membered(empty_set),
inference(resolution,[],[f212,f138]) ).
fof(f212,plain,
! [X0] :
( ~ empty(X0)
| v4_membered(X0) ),
inference(resolution,[],[f157,f155]) ).
fof(f218,plain,
! [X0] : v5_membered(sK9(X0)),
inference(resolution,[],[f211,f174]) ).
fof(f217,plain,
v5_membered(sK13),
inference(resolution,[],[f211,f204]) ).
fof(f216,plain,
v5_membered(empty_set),
inference(resolution,[],[f211,f138]) ).
fof(f211,plain,
! [X0] :
( ~ empty(X0)
| v5_membered(X0) ),
inference(resolution,[],[f157,f156]) ).
fof(f172,plain,
! [X0] : element(sK8(X0),X0),
inference(cnf_transformation,[],[f114]) ).
fof(f114,plain,
! [X0] : element(sK8(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f40,f113]) ).
fof(f113,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK8(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f40,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f167,plain,
! [X0] :
( v1_membered(X0)
| ~ v2_membered(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
! [X0] :
( v1_membered(X0)
| ~ v2_membered(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( v2_membered(X0)
=> v1_membered(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_membered) ).
fof(f163,plain,
! [X0] :
( v2_membered(X0)
| ~ v3_membered(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0] :
( v2_membered(X0)
| ~ v3_membered(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( v3_membered(X0)
=> v2_membered(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_membered) ).
fof(f158,plain,
! [X0] :
( v3_membered(X0)
| ~ v4_membered(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
! [X0] :
( v3_membered(X0)
| ~ v4_membered(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( v4_membered(X0)
=> v3_membered(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_membered) ).
fof(f157,plain,
! [X0] :
( sP1(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f98]) ).
fof(f98,plain,
! [X0] :
( sP1(X0)
| ~ empty(X0) ),
inference(definition_folding,[],[f73,f97]) ).
fof(f97,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(f73,plain,
! [X0] :
( ( v5_membered(X0)
& v4_membered(X0)
& v3_membered(X0)
& v2_membered(X0)
& v1_membered(X0) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,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(f156,plain,
! [X0] :
( ~ sP1(X0)
| v5_membered(X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f110,plain,
! [X0] :
( ( v5_membered(X0)
& v4_membered(X0)
& v3_membered(X0)
& v2_membered(X0)
& v1_membered(X0) )
| ~ sP1(X0) ),
inference(nnf_transformation,[],[f97]) ).
fof(f155,plain,
! [X0] :
( ~ sP1(X0)
| v4_membered(X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f154,plain,
! [X0] :
( ~ sP1(X0)
| v3_membered(X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f153,plain,
! [X0] :
( ~ sP1(X0)
| v2_membered(X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f152,plain,
! [X0] :
( ~ sP1(X0)
| v1_membered(X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f149,plain,
! [X0] :
( ~ sP0(X0)
| v5_membered(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f109,plain,
! [X0] :
( ( v5_membered(X0)
& v4_membered(X0)
& v3_membered(X0)
& v2_membered(X0)
& v1_membered(X0) )
| ~ sP0(X0) ),
inference(rectify,[],[f108]) ).
fof(f108,plain,
! [X1] :
( ( v5_membered(X1)
& v4_membered(X1)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1) )
| ~ sP0(X1) ),
inference(nnf_transformation,[],[f95]) ).
fof(f148,plain,
! [X0] :
( ~ sP0(X0)
| v4_membered(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f147,plain,
! [X0] :
( ~ sP0(X0)
| v3_membered(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f146,plain,
! [X0] :
( ~ sP0(X0)
| v2_membered(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f145,plain,
! [X0] :
( ~ sP0(X0)
| v1_membered(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f144,plain,
! [X0] :
( v4_membered(X0)
| ~ v5_membered(X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0] :
( v4_membered(X0)
| ~ v5_membered(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( v5_membered(X0)
=> v4_membered(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_membered) ).
fof(f143,plain,
! [X0] :
( one_sorted_str(X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0] :
( one_sorted_str(X0)
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0] :
( top_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
fof(f174,plain,
! [X0] : empty(sK9(X0)),
inference(cnf_transformation,[],[f116]) ).
fof(f116,plain,
! [X0] :
( empty(sK9(X0))
& element(sK9(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f26,f115]) ).
fof(f115,plain,
! [X0] :
( ? [X1] :
( empty(X1)
& element(X1,powerset(X0)) )
=> ( empty(sK9(X0))
& element(sK9(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f26,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f139,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f210,plain,
v5_membered(sK14),
inference(cnf_transformation,[],[f131]) ).
fof(f131,plain,
( v5_membered(sK14)
& v4_membered(sK14)
& v3_membered(sK14)
& v2_membered(sK14)
& v1_membered(sK14)
& ~ empty(sK14) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f7,f130]) ).
fof(f130,plain,
( ? [X0] :
( v5_membered(X0)
& v4_membered(X0)
& v3_membered(X0)
& v2_membered(X0)
& v1_membered(X0)
& ~ empty(X0) )
=> ( v5_membered(sK14)
& v4_membered(sK14)
& v3_membered(sK14)
& v2_membered(sK14)
& v1_membered(sK14)
& ~ empty(sK14) ) ),
introduced(choice_axiom,[]) ).
fof(f7,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(f209,plain,
v4_membered(sK14),
inference(cnf_transformation,[],[f131]) ).
fof(f208,plain,
v3_membered(sK14),
inference(cnf_transformation,[],[f131]) ).
fof(f207,plain,
v2_membered(sK14),
inference(cnf_transformation,[],[f131]) ).
fof(f206,plain,
v1_membered(sK14),
inference(cnf_transformation,[],[f131]) ).
fof(f205,plain,
~ empty(sK14),
inference(cnf_transformation,[],[f131]) ).
fof(f204,plain,
empty(sK13),
inference(cnf_transformation,[],[f129]) ).
fof(f129,plain,
empty(sK13),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f43,f128]) ).
fof(f128,plain,
( ? [X0] : empty(X0)
=> empty(sK13) ),
introduced(choice_axiom,[]) ).
fof(f43,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f203,plain,
~ empty(sK12),
inference(cnf_transformation,[],[f127]) ).
fof(f127,plain,
~ empty(sK12),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f44,f126]) ).
fof(f126,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK12) ),
introduced(choice_axiom,[]) ).
fof(f44,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f138,plain,
empty(empty_set),
inference(cnf_transformation,[],[f41]) ).
fof(f41,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f176,plain,
! [X0,X1] :
( element(X1,X0)
| ~ in(X1,X0)
| empty(X0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f173,plain,
! [X0] : element(sK9(X0),powerset(X0)),
inference(cnf_transformation,[],[f116]) ).
fof(f1460,plain,
( ~ spl15_42
| spl15_43 ),
inference(avatar_contradiction_clause,[],[f1459]) ).
fof(f1459,plain,
( $false
| ~ spl15_42
| spl15_43 ),
inference(subsumption_resolution,[],[f1455,f1030]) ).
fof(f1455,plain,
( ~ element(sK10(sK3,sK4),powerset(powerset(the_carrier(sK3))))
| ~ spl15_42
| spl15_43 ),
inference(resolution,[],[f1453,f135]) ).
fof(f1453,plain,
( ~ element(sK5(sK10(sK3,sK4)),powerset(the_carrier(sK3)))
| ~ spl15_42
| spl15_43 ),
inference(subsumption_resolution,[],[f1450,f139]) ).
fof(f1450,plain,
( ~ element(sK5(sK10(sK3,sK4)),powerset(the_carrier(sK3)))
| empty(powerset(the_carrier(sK3)))
| ~ spl15_42
| spl15_43 ),
inference(resolution,[],[f1447,f175]) ).
fof(f1447,plain,
( ~ in(sK5(sK10(sK3,sK4)),powerset(the_carrier(sK3)))
| ~ spl15_42
| spl15_43 ),
inference(subsumption_resolution,[],[f1446,f132]) ).
fof(f1446,plain,
( ~ in(sK5(sK10(sK3,sK4)),powerset(the_carrier(sK3)))
| ~ topological_space(sK3)
| ~ spl15_42
| spl15_43 ),
inference(subsumption_resolution,[],[f1445,f133]) ).
fof(f1445,plain,
( ~ in(sK5(sK10(sK3,sK4)),powerset(the_carrier(sK3)))
| ~ top_str(sK3)
| ~ topological_space(sK3)
| ~ spl15_42
| spl15_43 ),
inference(subsumption_resolution,[],[f1444,f134]) ).
fof(f1444,plain,
( ~ in(sK5(sK10(sK3,sK4)),powerset(the_carrier(sK3)))
| ~ element(sK4,powerset(powerset(the_carrier(sK3))))
| ~ top_str(sK3)
| ~ topological_space(sK3)
| ~ spl15_42
| spl15_43 ),
inference(subsumption_resolution,[],[f1443,f1429]) ).
fof(f1429,plain,
( ~ in(sK5(sK10(sK3,sK4)),sK10(sK3,sK4))
| spl15_43 ),
inference(avatar_component_clause,[],[f1428]) ).
fof(f1431,plain,
( spl15_42
| spl15_43 ),
inference(avatar_split_clause,[],[f1032,f1428,f1424]) ).
fof(f1395,plain,
( ~ spl15_40
| spl15_41
| ~ spl15_39 ),
inference(avatar_split_clause,[],[f1339,f1314,f1392,f1388]) ).
fof(f1388,plain,
( spl15_40
<=> element(powerset(the_carrier(sK3)),sK5(powerset(the_carrier(sK3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_40])]) ).
fof(f1392,plain,
( spl15_41
<=> empty(sK5(powerset(the_carrier(sK3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_41])]) ).
fof(f1314,plain,
( spl15_39
<=> in(sK5(powerset(the_carrier(sK3))),powerset(the_carrier(sK3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_39])]) ).
fof(f1339,plain,
( empty(sK5(powerset(the_carrier(sK3))))
| ~ element(powerset(the_carrier(sK3)),sK5(powerset(the_carrier(sK3))))
| ~ spl15_39 ),
inference(resolution,[],[f1316,f407]) ).
fof(f1316,plain,
( in(sK5(powerset(the_carrier(sK3))),powerset(the_carrier(sK3)))
| ~ spl15_39 ),
inference(avatar_component_clause,[],[f1314]) ).
fof(f1366,plain,
( ~ spl15_38
| ~ spl15_39 ),
inference(avatar_contradiction_clause,[],[f1365]) ).
fof(f1365,plain,
( $false
| ~ spl15_38
| ~ spl15_39 ),
inference(subsumption_resolution,[],[f1364,f455]) ).
fof(f1364,plain,
( ~ element(powerset(the_carrier(sK3)),powerset(powerset(the_carrier(sK3))))
| ~ spl15_38
| ~ spl15_39 ),
inference(subsumption_resolution,[],[f1358,f1316]) ).
fof(f1358,plain,
( ~ in(sK5(powerset(the_carrier(sK3))),powerset(the_carrier(sK3)))
| ~ element(powerset(the_carrier(sK3)),powerset(powerset(the_carrier(sK3))))
| ~ spl15_38 ),
inference(resolution,[],[f1312,f137]) ).
fof(f1312,plain,
( in(set_difference(cast_as_carrier_subset(sK3),sK5(powerset(the_carrier(sK3)))),sK4)
| ~ spl15_38 ),
inference(avatar_component_clause,[],[f1310]) ).
fof(f1310,plain,
( spl15_38
<=> in(set_difference(cast_as_carrier_subset(sK3),sK5(powerset(the_carrier(sK3)))),sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_38])]) ).
fof(f1337,plain,
spl15_39,
inference(avatar_contradiction_clause,[],[f1336]) ).
fof(f1336,plain,
( $false
| spl15_39 ),
inference(subsumption_resolution,[],[f1332,f455]) ).
fof(f1332,plain,
( ~ element(powerset(the_carrier(sK3)),powerset(powerset(the_carrier(sK3))))
| spl15_39 ),
inference(resolution,[],[f1323,f135]) ).
fof(f1323,plain,
( ~ element(sK5(powerset(the_carrier(sK3))),powerset(the_carrier(sK3)))
| spl15_39 ),
inference(subsumption_resolution,[],[f1320,f139]) ).
fof(f1320,plain,
( ~ element(sK5(powerset(the_carrier(sK3))),powerset(the_carrier(sK3)))
| empty(powerset(the_carrier(sK3)))
| spl15_39 ),
inference(resolution,[],[f1315,f175]) ).
fof(f1315,plain,
( ~ in(sK5(powerset(the_carrier(sK3))),powerset(the_carrier(sK3)))
| spl15_39 ),
inference(avatar_component_clause,[],[f1314]) ).
fof(f1317,plain,
( spl15_38
| spl15_39 ),
inference(avatar_split_clause,[],[f614,f1314,f1310]) ).
fof(f1184,plain,
( spl15_36
| spl15_37 ),
inference(avatar_split_clause,[],[f619,f1181,f1177]) ).
fof(f1177,plain,
( spl15_36
<=> in(set_difference(cast_as_carrier_subset(sK3),sK5(sK8(powerset(powerset(the_carrier(sK3)))))),sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_36])]) ).
fof(f1181,plain,
( spl15_37
<=> in(sK5(sK8(powerset(powerset(the_carrier(sK3))))),sK8(powerset(powerset(the_carrier(sK3))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_37])]) ).
fof(f1170,plain,
( spl15_1
| spl15_35 ),
inference(avatar_split_clause,[],[f1135,f1168,f296]) ).
fof(f296,plain,
( spl15_1
<=> ! [X0] : ~ v5_membered(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_1])]) ).
fof(f1168,plain,
( spl15_35
<=> ! [X0,X1] :
( ~ topological_space(X0)
| sP0(sK10(X0,X1))
| ~ top_str(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_35])]) ).
fof(f1133,plain,
( spl15_33
| ~ spl15_34
| spl15_32 ),
inference(avatar_split_clause,[],[f1120,f1106,f1130,f1126]) ).
fof(f1126,plain,
( spl15_33
<=> empty(sK6(powerset(the_carrier(sK3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_33])]) ).
fof(f1130,plain,
( spl15_34
<=> element(sK5(sK6(powerset(the_carrier(sK3)))),sK6(powerset(the_carrier(sK3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_34])]) ).
fof(f1106,plain,
( spl15_32
<=> in(sK5(sK6(powerset(the_carrier(sK3)))),sK6(powerset(the_carrier(sK3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_32])]) ).
fof(f1120,plain,
( ~ element(sK5(sK6(powerset(the_carrier(sK3)))),sK6(powerset(the_carrier(sK3))))
| empty(sK6(powerset(the_carrier(sK3))))
| spl15_32 ),
inference(resolution,[],[f1107,f175]) ).
fof(f1107,plain,
( ~ in(sK5(sK6(powerset(the_carrier(sK3)))),sK6(powerset(the_carrier(sK3))))
| spl15_32 ),
inference(avatar_component_clause,[],[f1106]) ).
fof(f1109,plain,
( spl15_31
| spl15_32 ),
inference(avatar_split_clause,[],[f622,f1106,f1102]) ).
fof(f918,plain,
( ~ spl15_29
| spl15_30
| ~ spl15_12 ),
inference(avatar_split_clause,[],[f819,f631,f915,f911]) ).
fof(f911,plain,
( spl15_29
<=> element(sK4,set_difference(cast_as_carrier_subset(sK3),sK5(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_29])]) ).
fof(f915,plain,
( spl15_30
<=> empty(set_difference(cast_as_carrier_subset(sK3),sK5(empty_set))) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_30])]) ).
fof(f631,plain,
( spl15_12
<=> in(set_difference(cast_as_carrier_subset(sK3),sK5(empty_set)),sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_12])]) ).
fof(f819,plain,
( empty(set_difference(cast_as_carrier_subset(sK3),sK5(empty_set)))
| ~ element(sK4,set_difference(cast_as_carrier_subset(sK3),sK5(empty_set)))
| ~ spl15_12 ),
inference(resolution,[],[f633,f407]) ).
fof(f633,plain,
( in(set_difference(cast_as_carrier_subset(sK3),sK5(empty_set)),sK4)
| ~ spl15_12 ),
inference(avatar_component_clause,[],[f631]) ).
fof(f899,plain,
( ~ spl15_27
| spl15_28
| ~ spl15_15 ),
inference(avatar_split_clause,[],[f861,f652,f896,f892]) ).
fof(f892,plain,
( spl15_27
<=> element(sK4,sK5(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_27])]) ).
fof(f896,plain,
( spl15_28
<=> empty(sK5(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_28])]) ).
fof(f652,plain,
( spl15_15
<=> in(sK5(sK4),sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_15])]) ).
fof(f861,plain,
( empty(sK5(sK4))
| ~ element(sK4,sK5(sK4))
| ~ spl15_15 ),
inference(resolution,[],[f654,f407]) ).
fof(f654,plain,
( in(sK5(sK4),sK4)
| ~ spl15_15 ),
inference(avatar_component_clause,[],[f652]) ).
fof(f860,plain,
spl15_25,
inference(avatar_contradiction_clause,[],[f859]) ).
fof(f859,plain,
( $false
| spl15_25 ),
inference(subsumption_resolution,[],[f856,f134]) ).
fof(f856,plain,
( ~ element(sK4,powerset(powerset(the_carrier(sK3))))
| spl15_25 ),
inference(resolution,[],[f853,f135]) ).
fof(f853,plain,
( ~ element(sK5(sK4),powerset(the_carrier(sK3)))
| spl15_25 ),
inference(subsumption_resolution,[],[f852,f139]) ).
fof(f852,plain,
( ~ element(sK5(sK4),powerset(the_carrier(sK3)))
| empty(powerset(the_carrier(sK3)))
| spl15_25 ),
inference(resolution,[],[f845,f175]) ).
fof(f845,plain,
( ~ in(sK5(sK4),powerset(the_carrier(sK3)))
| spl15_25 ),
inference(avatar_component_clause,[],[f843]) ).
fof(f843,plain,
( spl15_25
<=> in(sK5(sK4),powerset(the_carrier(sK3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_25])]) ).
fof(f850,plain,
( ~ spl15_25
| spl15_26
| ~ spl15_14 ),
inference(avatar_split_clause,[],[f767,f648,f847,f843]) ).
fof(f847,plain,
( spl15_26
<=> in(sK5(sK4),sK10(sK3,sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_26])]) ).
fof(f648,plain,
( spl15_14
<=> in(set_difference(cast_as_carrier_subset(sK3),sK5(sK4)),sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_14])]) ).
fof(f767,plain,
( in(sK5(sK4),sK10(sK3,sK4))
| ~ in(sK5(sK4),powerset(the_carrier(sK3)))
| ~ spl15_14 ),
inference(subsumption_resolution,[],[f766,f132]) ).
fof(f766,plain,
( in(sK5(sK4),sK10(sK3,sK4))
| ~ in(sK5(sK4),powerset(the_carrier(sK3)))
| ~ topological_space(sK3)
| ~ spl15_14 ),
inference(subsumption_resolution,[],[f765,f133]) ).
fof(f765,plain,
( in(sK5(sK4),sK10(sK3,sK4))
| ~ in(sK5(sK4),powerset(the_carrier(sK3)))
| ~ top_str(sK3)
| ~ topological_space(sK3)
| ~ spl15_14 ),
inference(subsumption_resolution,[],[f754,f134]) ).
fof(f754,plain,
( in(sK5(sK4),sK10(sK3,sK4))
| ~ in(sK5(sK4),powerset(the_carrier(sK3)))
| ~ element(sK4,powerset(powerset(the_carrier(sK3))))
| ~ top_str(sK3)
| ~ topological_space(sK3)
| ~ spl15_14 ),
inference(resolution,[],[f198,f650]) ).
fof(f650,plain,
( in(set_difference(cast_as_carrier_subset(sK3),sK5(sK4)),sK4)
| ~ spl15_14 ),
inference(avatar_component_clause,[],[f648]) ).
fof(f838,plain,
( ~ spl15_23
| spl15_24
| ~ spl15_21 ),
inference(avatar_split_clause,[],[f794,f769,f835,f831]) ).
fof(f831,plain,
( spl15_23
<=> element(powerset(the_carrier(sK3)),sK5(empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_23])]) ).
fof(f835,plain,
( spl15_24
<=> empty(sK5(empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_24])]) ).
fof(f769,plain,
( spl15_21
<=> in(sK5(empty_set),powerset(the_carrier(sK3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_21])]) ).
fof(f794,plain,
( empty(sK5(empty_set))
| ~ element(powerset(the_carrier(sK3)),sK5(empty_set))
| ~ spl15_21 ),
inference(resolution,[],[f770,f407]) ).
fof(f770,plain,
( in(sK5(empty_set),powerset(the_carrier(sK3)))
| ~ spl15_21 ),
inference(avatar_component_clause,[],[f769]) ).
fof(f792,plain,
~ spl15_13,
inference(avatar_contradiction_clause,[],[f791]) ).
fof(f791,plain,
( $false
| ~ spl15_13 ),
inference(subsumption_resolution,[],[f790,f138]) ).
fof(f790,plain,
( ~ empty(empty_set)
| ~ spl15_13 ),
inference(resolution,[],[f637,f202]) ).
fof(f637,plain,
( in(sK5(empty_set),empty_set)
| ~ spl15_13 ),
inference(avatar_component_clause,[],[f635]) ).
fof(f635,plain,
( spl15_13
<=> in(sK5(empty_set),empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_13])]) ).
fof(f786,plain,
spl15_21,
inference(avatar_contradiction_clause,[],[f785]) ).
fof(f785,plain,
( $false
| spl15_21 ),
inference(subsumption_resolution,[],[f782,f246]) ).
fof(f782,plain,
( ~ element(empty_set,powerset(powerset(the_carrier(sK3))))
| spl15_21 ),
inference(resolution,[],[f779,f135]) ).
fof(f779,plain,
( ~ element(sK5(empty_set),powerset(the_carrier(sK3)))
| spl15_21 ),
inference(subsumption_resolution,[],[f778,f139]) ).
fof(f778,plain,
( ~ element(sK5(empty_set),powerset(the_carrier(sK3)))
| empty(powerset(the_carrier(sK3)))
| spl15_21 ),
inference(resolution,[],[f771,f175]) ).
fof(f771,plain,
( ~ in(sK5(empty_set),powerset(the_carrier(sK3)))
| spl15_21 ),
inference(avatar_component_clause,[],[f769]) ).
fof(f776,plain,
( ~ spl15_21
| spl15_22
| ~ spl15_12 ),
inference(avatar_split_clause,[],[f764,f631,f773,f769]) ).
fof(f773,plain,
( spl15_22
<=> in(sK5(empty_set),sK10(sK3,sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_22])]) ).
fof(f764,plain,
( in(sK5(empty_set),sK10(sK3,sK4))
| ~ in(sK5(empty_set),powerset(the_carrier(sK3)))
| ~ spl15_12 ),
inference(subsumption_resolution,[],[f763,f132]) ).
fof(f763,plain,
( in(sK5(empty_set),sK10(sK3,sK4))
| ~ in(sK5(empty_set),powerset(the_carrier(sK3)))
| ~ topological_space(sK3)
| ~ spl15_12 ),
inference(subsumption_resolution,[],[f762,f133]) ).
fof(f762,plain,
( in(sK5(empty_set),sK10(sK3,sK4))
| ~ in(sK5(empty_set),powerset(the_carrier(sK3)))
| ~ top_str(sK3)
| ~ topological_space(sK3)
| ~ spl15_12 ),
inference(subsumption_resolution,[],[f753,f134]) ).
fof(f753,plain,
( in(sK5(empty_set),sK10(sK3,sK4))
| ~ in(sK5(empty_set),powerset(the_carrier(sK3)))
| ~ element(sK4,powerset(powerset(the_carrier(sK3))))
| ~ top_str(sK3)
| ~ topological_space(sK3)
| ~ spl15_12 ),
inference(resolution,[],[f198,f633]) ).
fof(f725,plain,
( spl15_19
| ~ spl15_20 ),
inference(avatar_split_clause,[],[f716,f722,f718]) ).
fof(f718,plain,
( spl15_19
<=> empty(sK10(sK3,sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_19])]) ).
fof(f722,plain,
( spl15_20
<=> element(powerset(the_carrier(sK3)),sK10(sK3,sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_20])]) ).
fof(f690,plain,
( ~ spl15_18
| spl15_11 ),
inference(avatar_split_clause,[],[f508,f609,f687]) ).
fof(f687,plain,
( spl15_18
<=> v1_membered(the_carrier(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_18])]) ).
fof(f609,plain,
( spl15_11
<=> ! [X0] :
( ~ element(X0,powerset(powerset(the_carrier(sK3))))
| v1_membered(sK5(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_11])]) ).
fof(f682,plain,
( ~ spl15_17
| spl15_11 ),
inference(avatar_split_clause,[],[f506,f609,f679]) ).
fof(f679,plain,
( spl15_17
<=> v2_membered(the_carrier(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_17])]) ).
fof(f675,plain,
( ~ spl15_16
| spl15_11 ),
inference(avatar_split_clause,[],[f503,f609,f672]) ).
fof(f672,plain,
( spl15_16
<=> v3_membered(the_carrier(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_16])]) ).
fof(f655,plain,
( spl15_14
| spl15_15 ),
inference(avatar_split_clause,[],[f617,f652,f648]) ).
fof(f638,plain,
( spl15_12
| spl15_13 ),
inference(avatar_split_clause,[],[f616,f635,f631]) ).
fof(f611,plain,
( ~ spl15_10
| spl15_11 ),
inference(avatar_split_clause,[],[f499,f609,f605]) ).
fof(f605,plain,
( spl15_10
<=> v4_membered(the_carrier(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_10])]) ).
fof(f603,plain,
( ~ spl15_8
| spl15_9 ),
inference(avatar_split_clause,[],[f498,f601,f597]) ).
fof(f597,plain,
( spl15_8
<=> v5_membered(the_carrier(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_8])]) ).
fof(f601,plain,
( spl15_9
<=> ! [X0] :
( ~ element(X0,powerset(powerset(the_carrier(sK3))))
| sP0(sK5(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_9])]) ).
fof(f446,plain,
~ spl15_1,
inference(avatar_contradiction_clause,[],[f436]) ).
fof(f436,plain,
( $false
| ~ spl15_1 ),
inference(resolution,[],[f297,f216]) ).
fof(f297,plain,
( ! [X0] : ~ v5_membered(X0)
| ~ spl15_1 ),
inference(avatar_component_clause,[],[f296]) ).
fof(f445,plain,
~ spl15_1,
inference(avatar_contradiction_clause,[],[f440]) ).
fof(f440,plain,
( $false
| ~ spl15_1 ),
inference(resolution,[],[f297,f218]) ).
fof(f444,plain,
~ spl15_1,
inference(avatar_contradiction_clause,[],[f441]) ).
fof(f441,plain,
( $false
| ~ spl15_1 ),
inference(resolution,[],[f297,f217]) ).
fof(f443,plain,
~ spl15_1,
inference(avatar_contradiction_clause,[],[f442]) ).
fof(f442,plain,
( $false
| ~ spl15_1 ),
inference(resolution,[],[f297,f210]) ).
fof(f434,plain,
( spl15_1
| spl15_7 ),
inference(avatar_split_clause,[],[f419,f432,f296]) ).
fof(f432,plain,
( spl15_7
<=> ! [X0] :
( ~ empty(X0)
| sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_7])]) ).
fof(f331,plain,
( ~ spl15_5
| spl15_6 ),
inference(avatar_split_clause,[],[f320,f328,f324]) ).
fof(f324,plain,
( spl15_5
<=> v4_membered(powerset(the_carrier(sK3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_5])]) ).
fof(f328,plain,
( spl15_6
<=> v1_membered(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_6])]) ).
fof(f316,plain,
( ~ spl15_3
| spl15_4 ),
inference(avatar_split_clause,[],[f292,f313,f309]) ).
fof(f309,plain,
( spl15_3
<=> v5_membered(powerset(the_carrier(sK3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_3])]) ).
fof(f313,plain,
( spl15_4
<=> sP0(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_4])]) ).
fof(f302,plain,
( spl15_1
| spl15_2 ),
inference(avatar_split_clause,[],[f291,f299,f296]) ).
fof(f299,plain,
( spl15_2
<=> sP0(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_2])]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : SEU311+1 : TPTP v8.1.2. Released v3.3.0.
% 0.02/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.31 % Computer : n012.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Mon Apr 29 20:56:11 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.16/0.31 % (22713)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.33 % (22716)WARNING: value z3 for option sas not known
% 0.16/0.33 % (22720)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)
% 0.16/0.33 % (22717)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.33 % (22715)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.33 % (22719)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)
% 0.16/0.33 % (22714)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.33 % (22718)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)
% 0.16/0.33 % (22716)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)
% 0.16/0.33 TRYING [1]
% 0.16/0.34 TRYING [2]
% 0.16/0.34 TRYING [3]
% 0.16/0.34 TRYING [1]
% 0.16/0.34 TRYING [4]
% 0.16/0.34 TRYING [2]
% 0.16/0.36 TRYING [5]
% 0.16/0.36 TRYING [3]
% 0.16/0.37 % (22716)First to succeed.
% 0.16/0.38 TRYING [1]
% 0.16/0.38 TRYING [2]
% 0.16/0.38 TRYING [3]
% 0.16/0.38 % (22716)Refutation found. Thanks to Tanya!
% 0.16/0.38 % SZS status Theorem for theBenchmark
% 0.16/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.39 % (22716)------------------------------
% 0.16/0.39 % (22716)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.16/0.39 % (22716)Termination reason: Refutation
% 0.16/0.39
% 0.16/0.39 % (22716)Memory used [KB]: 1404
% 0.16/0.39 % (22716)Time elapsed: 0.053 s
% 0.16/0.39 % (22716)Instructions burned: 96 (million)
% 0.16/0.39 % (22716)------------------------------
% 0.16/0.39 % (22716)------------------------------
% 0.16/0.39 % (22713)Success in time 0.071 s
%------------------------------------------------------------------------------