TPTP Problem File: ROB002-1.p

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%--------------------------------------------------------------------------
% File     : ROB002-1 : TPTP v7.5.0. Released v1.0.0.
% Domain   : Robbins Algebra
% Problem  : --X = X => Boolean
% Version  : [Win90] (equality) axioms.
% English  : If --X = X then the algebra is Boolean.

% Refs     : [HMT71] Henkin et al. (1971), Cylindrical Algebras
%          : [Win90] Winker (1990), Robbins Algebra: Conditions that make a
% Source   : [Win90]
% Names    : Lemma 2.1 [Win90]

% Status   : Unsatisfiable
% Rating   : 0.00 v7.4.0, 0.04 v7.3.0, 0.00 v6.1.0, 0.06 v6.0.0, 0.24 v5.5.0, 0.21 v5.4.0, 0.07 v5.3.0, 0.00 v5.2.0, 0.07 v5.1.0, 0.13 v5.0.0, 0.07 v4.1.0, 0.09 v4.0.1, 0.07 v4.0.0, 0.08 v3.7.0, 0.00 v2.2.1, 0.11 v2.2.0, 0.14 v2.1.0, 0.13 v2.0.0
% Syntax   : Number of clauses     :    5 (   0 non-Horn;   5 unit;   1 RR)
%            Number of atoms       :    5 (   5 equality)
%            Maximal clause size   :    1 (   1 average)
%            Number of predicates  :    1 (   0 propositional; 2-2 arity)
%            Number of functors    :    4 (   2 constant; 0-2 arity)
%            Number of variables   :    8 (   0 singleton)
%            Maximal term depth    :    6 (   3 average)
% SPC      : CNF_UNS_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(X)) = X )).

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

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