con_n.002.ljt

%------------------------------------------------------------------------------
% File     : con_n2 : Dyckhoff's benchmark formulae (1997)
% Domain   : Syntactic
% Problem  : Formulae requiring many contractions
% Version  : Especial.
%            Problem formulation : Inuit. Invalid.   Size 2
% English  : ((&&_{i=1..N} p(i) | ~~p(1)=>f | ||_{i=2..N} (p(i)=>f))=>f)=>f

% Refs     : [Dyc97] Roy Dyckhoff. Some benchmark formulae for
%                    intuitionistic propositional logic. At
%                    http://www.dcs.st-and.ac.uk/~rd/logic/marks.html
%          : [Fr88]  T. Franzen, Algorithmic Aspects of intuitionistic
%                    propositional logic, SICS Research Report R87010B,
%                    1988.
%          : [Fr89]  T. Franzen, Algorithmic Aspects of intuitionistic
%                    propositional logic II, SICS Research Report
%                    R-89/89006, 1989.
% Source   : [Dyc97]
% Names    : 

% Status   : Non-Theorem
% Rating   : 0.60 v 1.0
% Syntax   : Number of formulae    :    2 (   1 unit)
%            Number of atoms       :    8 (   0 equality)
%            Maximal formula depth :    7 (   4 average)
%            Number of connectives :    8 (   2 ~  ;   2  |;   1  &)
%                                         (   0 <=>;   3 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :    3 (   3 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 : "proof in LJ needs n contractions" [Dyc97]
%          : tptp2X -f ljt con_n.002.p 
%------------------------------------------------------------------------------

f((

% axiom1, axiom.
(( ( ( p1 & p2 ) v ( ( ( ~ ( ~ p1 ) ) -> f ) v ( p2 -> f ) ) ) -> f ))

  ->

% conjecture_name, conjecture.
(f)

)).

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