TPTP Problem File: SYO024^1.p
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% File : SYO024^1 : TPTP v9.0.0. Released v3.7.0.
% Domain : Syntactic
% Problem : De Morgan by connectives and Leibnitz
% Version : Especial.
% English :
% Refs : [BB05] Benzmueller & Brown (2005), A Structured Set of Higher
% : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% Source : [Ben09]
% Names : Example 20d [BB05]
% Status : Theorem
% : Without Boolean extensionality : CounterSatisfiable
% : Without functional extensionality : CounterSatisfiable
% Rating : 0.25 v9.0.0, 0.30 v8.2.0, 0.54 v8.1.0, 0.36 v7.5.0, 0.29 v7.4.0, 0.33 v7.2.0, 0.12 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, 0.20 v5.3.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0, 0.33 v3.7.0
% Syntax : Number of formulae : 3 ( 1 unt; 1 typ; 1 def)
% Number of atoms : 4 ( 1 equ; 1 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 10 ( 3 ~; 1 |; 1 &; 4 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 3 ( 1 usr; 1 con; 0-2 aty)
% Number of variables : 5 ( 4 ^; 1 !; 0 ?; 5 :)
% SPC : TH0_THM_EQU_NAR
% Comments :
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thf(leibeq_decl,type,
leibeq: ( $o > $o > $o ) > ( $o > $o > $o ) > $o ).
thf(leibeq,definition,
( leibeq
= ( ^ [X: $o > $o > $o,Y: $o > $o > $o] :
! [P: ( $o > $o > $o ) > $o] :
( ( P @ X )
=> ( P @ Y ) ) ) ) ).
thf(conj,conjecture,
( leibeq @ (&)
@ ^ [X: $o,Y: $o] :
~ ( ~ X
| ~ Y ) ) ).
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