TPTP Problem File: SET756+4.p
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%--------------------------------------------------------------------------
% File : SET756+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% Domain : Set Theory (Mappings)
% Problem : Inverse image of union equals the union of inverse images
% Version : [Pas99] axioms.
% English :
% Refs : [Pas99] Pastre (1999), Email to G. Sutcliffe
% Source : [Pas99]
% Names :
% Status : Theorem
% Rating : 0.79 v9.0.0, 0.78 v8.2.0, 0.81 v8.1.0, 0.72 v7.5.0, 0.78 v7.4.0, 0.70 v7.3.0, 0.72 v7.1.0, 0.65 v7.0.0, 0.73 v6.3.0, 0.75 v6.2.0, 0.72 v6.1.0, 0.77 v6.0.0, 0.78 v5.5.0, 0.89 v5.4.0, 0.93 v5.2.0, 0.95 v5.0.0, 0.96 v3.7.0, 0.95 v3.3.0, 0.93 v3.2.0, 0.91 v3.1.0, 0.89 v2.7.0, 0.83 v2.6.0, 0.86 v2.5.0, 0.88 v2.4.0, 0.75 v2.3.0, 0.67 v2.2.1
% Syntax : Number of formulae : 29 ( 1 unt; 0 def)
% Number of atoms : 132 ( 6 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 105 ( 2 ~; 2 |; 52 &)
% ( 30 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 9 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 15 usr; 0 prp; 2-6 aty)
% Number of functors : 15 ( 15 usr; 1 con; 0-5 aty)
% Number of variables : 138 ( 129 !; 9 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments :
% Bugfixes : v2.2.1 - Bugfixes in SET006+1.ax.
%--------------------------------------------------------------------------
%----Include set theory definitions
include('Axioms/SET006+0.ax').
%----Include mappings axioms
include('Axioms/SET006+1.ax').
%--------------------------------------------------------------------------
fof(thIIa06,conjecture,
! [F,A,B,X,Y] :
( ( maps(F,A,B)
& subset(X,B)
& subset(Y,B) )
=> equal_set(inverse_image2(F,union(X,Y)),union(inverse_image2(F,X),inverse_image2(F,Y))) ) ).
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