TPTP Problem File: SYN391^4.p
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% File : SYN391^4 : TPTP v7.4.0. Released v4.0.0.
% Domain : Logic Calculi (Intuitionistic logic)
% Problem : Pelletier 9
% Version : [Goe33] axioms.
% English :
% Refs : [Goe33] Goedel (1933), An Interpretation of the Intuitionistic
% : [Gol06] Goldblatt (2006), Mathematical Modal Logic: A View of
% : [ROK06] Raths et al. (2006), The ILTP Problem Library for Intu
% : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% : [BP10] Benzmueller & Paulson (2009), Exploring Properties of
% Source : [Ben09]
% Names :
% Status : Theorem
% Rating : 0.29 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.57 v6.1.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.40 v5.3.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% Syntax : Number of formulae : 44 ( 0 unit; 22 type; 19 defn)
% Number of atoms : 140 ( 19 equality; 48 variable)
% Maximal formula depth : 11 ( 5 average)
% Number of connectives : 83 ( 3 ~; 1 |; 2 &; 75 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% ( 0 ~|; 0 ~&)
% Number of type conns : 97 ( 97 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 22 :; 0 =)
% Number of variables : 40 ( 1 sgn; 7 !; 2 ?; 31 ^)
% ( 40 :; 0 !>; 0 ?*)
% ( 0 @-; 0 @+)
% SPC : TH0_THM_EQU_NAR
% Comments : This is an ILTP problem embedded in TH0
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include('Axioms/LCL010^0.ax').
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thf(p1_type,type,(
p1: $i > $o )).
thf(p2_type,type,(
p2: $i > $o )).
thf(pel9,conjecture,
( ivalid @ ( iimplies @ ( iand @ ( ior @ ( iatom @ p1 ) @ ( iatom @ p2 ) ) @ ( iand @ ( ior @ ( inot @ ( iatom @ p1 ) ) @ ( iatom @ p2 ) ) @ ( ior @ ( iatom @ p1 ) @ ( inot @ ( iatom @ p2 ) ) ) ) ) @ ( inot @ ( ior @ ( inot @ ( iatom @ p1 ) ) @ ( inot @ ( iatom @ p2 ) ) ) ) ) )).
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