%--------------------------------------------------------------------------
% File     : ROB027-1 : TPTP v8.2.0. Released v1.2.0.
% Domain   : Robbins Algebra
% Problem  : -(-c) = c => Boolean
% Version  : [Win90] (equality) axioms.
%            Theorem formulation : Denies Huntington's axiom.
% English  : If there are elements c and d such that c+d=d, then the
%            algebra is Boolean.

% Refs     : [HMT71] Henkin et al. (1971), Cylindrical Algebras
%          : [Win90] Winker (1990), Robbins Algebra: Conditions that make a
%          : [Wos94] Wos (1994), Two Challenge Problems
% Source   : [Wos94]
% Names    : - [Wos94]

% Status   : Open
% Rating   : 1.00 v2.0.0
% Syntax   : Number of clauses     :    5 (   5 unt;   0 nHn;   2 RR)
%            Number of literals    :    5 (   5 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    1 (   0 usr;   0 prp; 2-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :    7 (   0 sgn)
% SPC      : CNF_OPN_RFO_PEQ_UEQ

% Comments : Commutativity, associativity, and Huntington's axiom
%            axiomatize Boolean algebra.
%--------------------------------------------------------------------------
%----Include axioms for Robbins algebra
include('Axioms/ROB001-0.ax').
%--------------------------------------------------------------------------
cnf(double_negation,hypothesis,
    negate(negate(c)) = c ).

cnf(prove_huntingtons_axiom,negated_conjecture,
    add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) != b ).

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