TPTP Problem File: SET646^3.p
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% File : SET646^3 : TPTP v8.2.0. Released v3.6.0.
% Domain : Set Theory
% Problem : If x is in X and y is in Y then {<x,y>} is from X to Y.
% Version : [BS+08] axioms.
% English :
% Refs : [BS+05] Benzmueller et al. (2005), Can a Higher-Order and a Fi
% : [BS+08] Benzmueller et al. (2008), Combined Reasoning by Autom
% : [Ben08] Benzmueller (2008), Email to Geoff Sutcliffe
% Source : [Ben08]
% Names :
% Status : Theorem
% Rating : 0.20 v8.2.0, 0.31 v8.1.0, 0.09 v7.5.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v3.7.0
% Syntax : Number of formulae : 71 ( 35 unt; 35 typ; 35 def)
% Number of atoms : 91 ( 43 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 130 ( 8 ~; 5 |; 18 &; 89 @)
% ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 212 ( 212 >; 0 *; 0 +; 0 <<)
% Number of symbols : 41 ( 38 usr; 5 con; 0-4 aty)
% Number of variables : 111 ( 82 ^; 21 !; 8 ?; 111 :)
% SPC : TH0_THM_EQU_NAR
% Comments :
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%----Include basic set theory definitions
include('Axioms/SET008^0.ax').
%----Include definitions for relations
include('Axioms/SET008^2.ax').
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thf(thm,conjecture,
! [X: $i,Y: $i] :
( sub_rel @ ( pair_rel @ X @ Y )
@ ( cartesian_product
@ ^ [X: $i] : $true
@ ^ [X: $i] : $true ) ) ).
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