## TPTP Problem File: ROB023-1.p

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```%--------------------------------------------------------------------------
% File     : ROB023-1 : TPTP v7.5.0. Released v1.0.0.
% Domain   : Robbins Algebra
% Problem  : X + X=X => Boolean
% Version  : [Win90] (equality) axioms.
% English  : If for all X X + X = X then the algebra is Boolean.

% Refs     : [HMT71] Henkin et al. (1971), Cylindrical Algebras
%          : [Win90] Winker (1990), Robbins Algebra: Conditions that make a
%          : [LM92]  Lusk & McCune (1992), Experiments with ROO, a Parallel
%          : [McC92] McCune (1992), Email to G. Sutcliffe
% Source   : [McC92]
% Names    : Robbins [LM92]

% Status   : Unsatisfiable
% Rating   : 0.30 v7.5.0, 0.21 v7.4.0, 0.26 v7.3.0, 0.21 v7.1.0, 0.11 v7.0.0, 0.16 v6.4.0, 0.21 v6.3.0, 0.24 v6.2.0, 0.21 v6.1.0, 0.19 v6.0.0, 0.38 v5.5.0, 0.32 v5.4.0, 0.13 v5.3.0, 0.08 v5.2.0, 0.14 v5.1.0, 0.13 v5.0.0, 0.14 v4.1.0, 0.09 v4.0.1, 0.14 v4.0.0, 0.15 v3.7.0, 0.11 v3.4.0, 0.12 v3.3.0, 0.00 v2.2.1, 0.44 v2.2.0, 0.43 v2.1.0, 0.38 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(x_plus_x_is_x,hypothesis,
( add(X,X) = X )).

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

%--------------------------------------------------------------------------
```