kk_n.002.ljt

%------------------------------------------------------------------------------
% File     : kk_n2 : Dyckhoff's benchmark formulae (1997)
% Domain   : Syntactic
% Problem  : Formulae of Korn & Kreitz
% Version  : Especial.
%            Problem formulation : Inuit. Invalid.   Size 2
% English  : (A & B(N) & C(N)) => f with
%            A = (a(0) => f), B(N) = (~~b(N) => b(0) => a(N)),
%            C(N) = (&&_{i=1..n} ((~~b(i-1) => a(i)) => a(i-1))),

% Refs     : [Dyc97] Roy Dyckhoff. Some benchmark formulae for
%                    intuitionistic propositional logic. At
%                    http://www.dcs.st-and.ac.uk/~rd/logic/marks.html
%          : [KK97]  D. Korn & C. Kreitz, A constructively adequate
%                    refutation system for intuitionistic logic,
%                    position paper at Tableaux'97, available at
%                    http://www.cs.uni-potsdam.de/ti/kreitz/PDF/
% Source   : [Dyc97]
% Names    : 

% Status   : Non-Theorem
% Rating   : 0.40 v 1.0
% Syntax   : Number of formulae    :    5 (   1 unit)
%            Number of atoms       :   12 (   0 equality)
%            Maximal formula depth :    5 (   3 average)
%            Number of connectives :   13 (   6 ~  ;   0  |;   0  &)
%                                         (   0 <=>;   7 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :    7 (   7 propositional; 0-0 arity)
%            Number of functors    :    0 (   0 constant; --- arity)
%            Number of variables   :    0 (   0 singleton;   0 !;   0 ?)
%            Maximal term depth    :    0 (   0 average)

% Comments : 
%          : tptp2X -f ljt kk_n.002.p 
%------------------------------------------------------------------------------

f((

% axiom1, axiom.
(( a0 -> f ))

 & 

% axiom2, axiom.
(( ( ( ~ ( ~ b2 ) ) -> b0 ) -> a2 ))

 & 

% axiom3, axiom.
(( ( ( ~ ( ~ b0 ) ) -> a1 ) -> a0 ))

 & 

% axiom4, axiom.
(( ( ( ~ ( ~ b1 ) ) -> a2 ) -> a1 ))

  ->

% conjecture_name, conjecture.
(f)

)).

%------------------------------------------------------------------------------