TPTP Problem File: LCL579^2.p
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%------------------------------------------------------------------------------
% File : LCL579^2 : TPTP v8.2.0. Released v5.1.0.
% Domain : Logical Calculi
% Problem : Leibniz-equality definition means it's an equivalence
% Version : Especial.
% English :
% Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source : [Bro09]
% Names : tps_0085 [Bro09]
% : THM76A [TPS]
% Status : Theorem
% Rating : 0.00 v8.1.0, 0.08 v7.4.0, 0.00 v6.2.0, 0.17 v6.1.0, 0.00 v6.0.0, 0.17 v5.5.0, 0.20 v5.4.0, 0.25 v5.3.0, 0.50 v5.2.0, 0.25 v5.1.0
% Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% Number of atoms : 0 ( 0 equ; 0 cnn)
% Maximal formula atoms : 0 ( 0 avg)
% Number of connectives : 7 ( 0 ~; 0 |; 0 &; 4 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of symbols : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 2 ( 0 ^; 2 !; 0 ?; 2 :)
% SPC : TH0_THM_NEQ_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/
% : This theorem has two proofs.
% :
% : Renamed from SYO254^5
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thf(cY,type,
cY: $i ).
thf(cX,type,
cX: $i ).
thf(cTHM76A,conjecture,
( ! [P: $i > $o] :
( ( P @ cY )
=> ( P @ cX ) )
=> ! [R: $i > $o] :
( ( R @ cX )
=> ( R @ cY ) ) ) ).
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