TPTP Problem File: SET817+4.p
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%------------------------------------------------------------------------------
% File : SET817+4 : TPTP v9.0.0. Released v3.2.0.
% Domain : Set Theory (Order relations)
% Problem : The product of a nonempty set of ordinals is an ordinal
% Version : [Pas05] axioms.
% English :
% Refs : [Pas05] Pastre (2005), Email to G. Sutcliffe
% Source : [Pas05]
% Names :
% Status : Theorem
% Rating : 0.91 v9.0.0, 0.89 v8.2.0, 0.92 v8.1.0, 0.89 v7.5.0, 0.91 v7.4.0, 0.93 v7.1.0, 0.91 v7.0.0, 0.97 v6.4.0, 0.96 v6.2.0, 0.88 v6.1.0, 0.97 v6.0.0, 0.96 v5.5.0, 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
% Syntax : Number of formulae : 23 ( 1 unt; 0 def)
% Number of atoms : 76 ( 4 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 56 ( 3 ~; 3 |; 19 &)
% ( 17 <=>; 14 =>; 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 : 64 ( 60 !; 4 ?)
% 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(thI3,axiom,
! [A,B,C] :
( ( subset(A,B)
& subset(B,C) )
=> subset(A,C) ) ).
fof(set_product,axiom,
! [X] :
( set(X)
=> set(product(X)) ) ).
fof(thI42,axiom,
! [A,X] :
( member(X,A)
=> subset(product(A),X) ) ).
fof(thV21,conjecture,
! [A] :
( ( subset(A,on)
& set(A)
& ? [X] : member(X,A) )
=> member(product(A),on) ) ).
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