%--------------------------------------------------------------------------
% File     : ROB031-1 : TPTP v8.2.0. Released v3.1.0.
% Domain   : Robbins Algebra
% Problem  : Robbins => Exists absorbed within negation element
% 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     : [Win90] Winker (1990), Robbins Algebra: Conditions that make a
%          : [Loe04] Loechner (2004), Email to Geoff Sutcliffe
% Source   : [Loe04]
% Names    : (3) [Loe04]

% Status   : Unsatisfiable
% Rating   : 1.00 v3.1.0
% Syntax   : Number of clauses     :    4 (   4 unt;   0 nHn;   1 RR)
%            Number of literals    :    4 (   4 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    :    2 (   2 usr;   0 con; 1-2 aty)
%            Number of variables   :    9 (   1 sgn)
% SPC      : CNF_UNS_RFO_PEQ_UEQ

% Comments :
%--------------------------------------------------------------------------
%----Include axioms for Robbins algebra
include('Axioms/ROB001-0.ax').
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cnf(prove_absorption_within_negation,negated_conjecture,
    negate(add(A,B)) != negate(B) ).

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