TPTP Problem File: SYO363^5.p
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% File : SYO363^5 : TPTP v8.2.0. Released v4.0.0.
% Domain : Syntactic
% Problem : TPS problem EDEC2
% Version : Especial.
% English : EDEC from [Ben99], using Primeq in the antecedent instead of
% Leibeq.
% Refs : [Ben99] Benzmueller (1999), Equality and Extensionality in Hig
% : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source : [Bro09]
% Names : tps_0469 [Bro09]
% : EDEC2 [TPS]
% : EDEC [Ben99]
% Status : Theorem
% Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.09 v7.5.0, 0.00 v7.4.0, 0.11 v7.3.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v6.1.0, 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 : 6 ( 0 unt; 5 typ; 0 def)
% Number of atoms : 2 ( 2 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 13 ( 0 ~; 0 |; 1 &; 10 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 4 usr; 0 con; 1-2 aty)
% Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% 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/
% : Polymorphic definitions expanded.
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thf(a_type,type,
a: $tType ).
thf(j,type,
j: a > a ).
thf(g,type,
g: ( a > a ) > a > a ).
thf(h,type,
h: a > a ).
thf(f,type,
f: ( a > a ) > a > a ).
thf(cEDEC2_pme,conjecture,
( ( ! [X: a > a,Y: a] :
( ( f @ X @ Y )
= ( g @ X @ Y ) )
& ! [Z: a] :
( ( h @ Z )
= ( j @ Z ) ) )
=> ! [Xq: ( a > a ) > $o] :
( ( Xq @ ( f @ h ) )
=> ( Xq @ ( g @ j ) ) ) ) ).
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