%------------------------------------------------------------------------------
% File     : ph_p2 : Dyckhoff's benchmark formulae (1997)
% Domain   : Syntactic
% Problem  : Cook pigeon-hole problem
% Version  : Especial.
%            Problem formulation : Prop. Non-Clausal. Intuit. Valid  Size 2
% English  : Suppose there are N holes and N+1 pigeons to put in the
%            holes. Every pigeon is in a hole and no hole contains more
%            than one pigeon. Prove that this is impossible. The size is
%            the number of pigeons.
%            LHS(N) => RHS(N) with 
%            LHS(N) = &&_{p=1..N+1} (||_{h=1,..N} o(p,h) )
%            RHS(N) = ||_{h=1..N, p1=1..{N+1}, p2={p1+1}..{N+1}} s(p1,p2,h)
%            with s(p1,p2,h) = o(p1,h) & o(p2,h)

% Refs     : [Dyc97] Roy Dyckhoff. Some benchmark formulae for
%                    intuitionistic propositional logic. At
%                    http://www.dcs.st-and.ac.uk/~rd/logic/marks.html
%          : [CR79]  Cook & Reckhow (1979), The Relative Efficiency of
%                    Propositional Proof Systems, Journal of Symbolic
%                    Logic 44, pp.36-50.

% Source   : [Dyc97]
% Names    : 

% Status   : Theorem
% Rating   : 0.00 v 1.0
% Syntax   : Number of formulae    :    4 (   0 unit)
%            Number of atoms       :   18 (   0 equality)
%            Maximal formula depth :    7 (   3 average)
%            Number of connectives :   14 (   0 ~  ;   8  |;   6  &)
%                                         (   0 <=>;   0 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :    6 (   6 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 ph_p.002.p 
%------------------------------------------------------------------------------

f((

% axiom1, axiom.
(( o11 v o12 ))

 & 

% axiom2, axiom.
(( o21 v o22 ))

 & 

% axiom3, axiom.
(( o31 v o32 ))

  ->

% conjecture_name, conjecture.
(( ( o11 & o21 ) v ( ( o11 & o31 ) v ( ( o21 & o31 ) v ( ( o12 & o22 ) v ( ( o12 & o32 ) v ( o22 & o32 ) ) ) ) ) ))

)).

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