%--------------------------------------------------------------------------
% File     : ROB004-1 : TPTP v9.0.0. Released v1.0.0.
% Domain   : Robbins Algebra
% Problem  : c = -d, c + d=d, and c + c=c => Boolean
% Version  : [Win90] (equality) axioms.
% English  : If there exist c, d such that c = -d, c+d=d, and c+c=c, 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 2.3 [Win90]

% Status   : Unsatisfiable
% Rating   : 0.18 v9.0.0, 0.14 v8.2.0, 0.17 v8.1.0, 0.20 v7.5.0, 0.17 v7.4.0, 0.26 v7.3.0, 0.21 v7.1.0, 0.11 v6.4.0, 0.16 v6.3.0, 0.12 v6.2.0, 0.07 v6.1.0, 0.19 v6.0.0, 0.33 v5.5.0, 0.37 v5.4.0, 0.20 v5.3.0, 0.08 v5.2.0, 0.14 v5.1.0, 0.13 v5.0.0, 0.07 v4.1.0, 0.00 v3.4.0, 0.12 v3.3.0, 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.38 v2.0.0
% Syntax   : Number of clauses     :    7 (   7 unt;   0 nHn;   4 RR)
%            Number of literals    :    7 (   7 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    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :    7 (   0 sgn)
% 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(negate_d_is_c,hypothesis,
    negate(d) = c ).

cnf(c_plus_d_is_d,hypothesis,
    add(c,d) = d ).

cnf(c_plus_c_is_c,hypothesis,
    add(c,c) = c ).

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

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