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% File     : SYN007+1.005 : TPTP v8.2.0. Released v2.0.0.
% Domain   : Syntactic
% Problem  : Pelletier Problem 71
% Version  : Especial.
%            Theorem formulation : For N = SIZE.
% English  : Clausal forms of statements of the form :
%            (p1 <-> (p2 <->...(pN <-> (p1 <-> (p2 <->...<-> pN)...)

% Refs     : [Pel86] Pelletier (1986), Seventy-five Problems for Testing Au
%          : [Urq87] Urquart (1987), Hard Problems for Resolution
% Source   : [Pel86]
% Names    : Pelletier 71 [Pel86]

% Status   : Theorem
% Rating   : ? v2.0.0
% Syntax   :

% Comments : The number of distinct letters in U-N is N. The number of
%            occurrences of sentence letters in 2N. The number of clauses
%            goes up dramatically as N increases, but I don't think it
%            shows that the problems are dramatically more difficult as N
%            increases. Rather, it's that the awkward clause form
%            representation comes to the fore most dramatically with
%            embedded biconditionals. On all other measures of complexity,
%            one should say that the problems increase linearly in
%            difficulty. Urquhart says that the proof size of any resolution
%            system increases exponentially with increase in N.
%          : This problem can also be done in terms of graphs, as described
%            in [Pel86] Problem 74.
%          : tptp2X: -ftptp -s5 SYN007+1.g
% Bugfixes : v2.1.0 - Replaced by a new SOTA size.
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