TPTP Problem File: SET724^4.p
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% File : SET724^4 : TPTP v9.0.0. Released v3.6.0.
% Domain : Set Theory
% Problem : If GoF = HoF and F is surjective, then G = H
% 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 : 0.00 v8.2.0, 0.15 v8.1.0, 0.18 v7.5.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.40 v5.3.0, 0.60 v4.1.0, 0.33 v3.7.0
% Syntax : Number of formulae : 17 ( 8 unt; 8 typ; 8 def)
% Number of atoms : 28 ( 15 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 36 ( 0 ~; 0 |; 4 &; 28 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 49 ( 49 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 10 usr; 2 con; 0-3 aty)
% Number of variables : 29 ( 16 ^; 10 !; 3 ?; 29 :)
% SPC : TH0_THM_EQU_NAR
% Comments :
%------------------------------------------------------------------------------
%----Include definitions for functions
include('Axioms/SET008^1.ax').
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thf(thm,conjecture,
! [F: $i > $i,G: $i > $i,H: $i > $i] :
( ( ( ( fun_composition @ F @ G )
= ( fun_composition @ F @ H ) )
& ( fun_surjective @ F ) )
=> ( G = H ) ) ).
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