TPTP Problem File: SET812+4.p
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%------------------------------------------------------------------------------
% File : SET812+4 : TPTP v8.2.0. Released v3.2.0.
% Domain : Set Theory (Order relations)
% Problem : An ordinal A is equal to its intersection with its power-set
% Version : [Pas05] axioms.
% English :
% Refs : [Pas05] Pastre (2005), Email to G. Sutcliffe
% Source : [Pas05]
% Names :
% Status : Theorem
% Rating : 0.47 v8.1.0, 0.50 v7.4.0, 0.43 v7.3.0, 0.38 v7.2.0, 0.34 v7.1.0, 0.35 v7.0.0, 0.47 v6.4.0, 0.46 v6.3.0, 0.50 v6.2.0, 0.52 v6.1.0, 0.57 v6.0.0, 0.65 v5.5.0, 0.67 v5.4.0, 0.71 v5.3.0, 0.74 v5.2.0, 0.65 v5.1.0, 0.67 v5.0.0, 0.71 v4.1.0, 0.65 v4.0.0, 0.67 v3.7.0, 0.70 v3.5.0, 0.74 v3.4.0, 0.89 v3.3.0, 0.64 v3.2.0
% Syntax : Number of formulae : 20 ( 1 unt; 0 def)
% Number of atoms : 67 ( 4 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 50 ( 3 ~; 3 |; 16 &)
% ( 17 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 0 prp; 1-3 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 57 ( 54 !; 3 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments :
%------------------------------------------------------------------------------
%----Include set theory definitions
include('Axioms/SET006+0.ax').
%----Include ordinal numbers axioms
include('Axioms/SET006+4.ax').
%------------------------------------------------------------------------------
fof(thV10,conjecture,
! [A] :
( member(A,on)
=> equal_set(A,intersection(A,power_set(A))) ) ).
%------------------------------------------------------------------------------