%--------------------------------------------------------------------------
% File     : GRP008-1 : TPTP v7.2.0. Released v2.2.0.
% Domain   : Group Theory (Cancellative semigroups)
% Axioms   : Cancellative semigroups axioms
% Version  : [MP96] (equality) axioms.
% English  :

% Refs     : [McC98] McCune (1998), Email to G. Sutcliffe
%          : [MP96]  McCune & Padmanabhan (1996), Automated Deduction in Eq
% Source   : [McC98]
% Names    :

% Status   : Satisfiable
% Syntax   : Number of clauses    :    2 (   0 non-Horn;   0 unit;   2 RR)
%            Number of atoms      :    4 (   4 equality)
%            Maximal clause size  :    2 (   2 average)
%            Number of predicates :    1 (   0 propositional; 2-2 arity)
%            Number of functors   :    1 (   0 constant; 2-2 arity)
%            Number of variables  :    6 (   0 singleton)
%            Maximal term depth   :    2 (   2 average)
% SPC      : 

% Comments : Requires GRP008-0.ax
%--------------------------------------------------------------------------
%----Left and right cancellation:
cnf(right_cancellation,axiom,
    ( multiply(A,B) != multiply(C,B)
    | A = C )).

cnf(left_cancellation,axiom,
    ( multiply(A,B) != multiply(A,C)
    | B = C )).

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