%------------------------------------------------------------------------------
% File     : kk_n10 : Dyckhoff's benchmark formulae (1997)
% Domain   : Syntactic
% Problem  : Formulae of Korn & Kreitz
% Version  : Especial.
%            Problem formulation : Inuit. Invalid.   Size 10
% 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   : 0.80 v 1.0
% Syntax   : Number of formulae    :   13 (   1 unit)
%            Number of atoms       :   36 (   0 equality)
%            Maximal formula depth :    5 (   4 average)
%            Number of connectives :   45 (  22 ~  ;   0  |;   0  &)
%                                         (   0 <=>;  23 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   23 (  23 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.010.p 
%------------------------------------------------------------------------------

f((

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

 & 

% axiom2, axiom.
(( ( ( ~ ( ~ b10 ) ) -> b0 ) -> a10 ))

 & 

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

 & 

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

 & 

% axiom5, axiom.
(( ( ( ~ ( ~ b2 ) ) -> a3 ) -> a2 ))

 & 

% axiom6, axiom.
(( ( ( ~ ( ~ b3 ) ) -> a4 ) -> a3 ))

 & 

% axiom7, axiom.
(( ( ( ~ ( ~ b4 ) ) -> a5 ) -> a4 ))

 & 

% axiom8, axiom.
(( ( ( ~ ( ~ b5 ) ) -> a6 ) -> a5 ))

 & 

% axiom9, axiom.
(( ( ( ~ ( ~ b6 ) ) -> a7 ) -> a6 ))

 & 

% axiom10, axiom.
(( ( ( ~ ( ~ b7 ) ) -> a8 ) -> a7 ))

 & 

% axiom11, axiom.
(( ( ( ~ ( ~ b8 ) ) -> a9 ) -> a8 ))

 & 

% axiom12, axiom.
(( ( ( ~ ( ~ b9 ) ) -> a10 ) -> a9 ))

  ->

% conjecture_name, conjecture.
(f)

)).

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