TPTP Problem File: SYO350^5.p
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% File : SYO350^5 : TPTP v8.2.0. Released v4.0.0.
% Domain : Syntactic
% Problem : TPS problem E1FUNC
% Version : Especial.
% English : Example from [Ben99] p.115.
% Refs : [Ben99] Benzmueller (1999), Equality and Extensionality in Hig
% : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source : [Bro09]
% Names : tps_0067 [Bro09]
% : E1FUNC [TPS]
% Status : Theorem
% Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.09 v7.5.0, 0.00 v6.2.0, 0.29 v6.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.40 v5.3.0, 0.60 v4.1.0, 0.67 v4.0.1, 1.00 v4.0.0
% Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% Number of atoms : 3 ( 1 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 6 ( 0 ~; 0 |; 0 &; 4 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 4 ( 3 usr; 0 con; 1-2 aty)
% Number of variables : 1 ( 0 ^; 1 !; 0 ?; 1 :)
% SPC : TH0_THM_EQU_NAR
% Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% project in the Department of Mathematical Sciences at Carnegie
% Mellon University. Distributed under the Creative Commons copyleft
% license: http://creativecommons.org/licenses/by-sa/3.0/
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thf(g,type,
g: $i > $i ).
thf(p,type,
p: ( $i > $i ) > $o ).
thf(f,type,
f: $i > $i ).
thf(cE1FUNC,conjecture,
( ! [X: $i] :
( ( f @ X )
= ( g @ X ) )
=> ( ( p @ f )
=> ( p @ g ) ) ) ).
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