%--------------------------------------------------------------------------
% File     : GRP008-1 : TPTP v9.0.0. 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 unt;   0 nHn;   2 RR)
%            Number of literals    :    4 (   4 equ;   2 neg)
%            Maximal clause size   :    2 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    1 (   0 usr;   0 prp; 2-2 aty)
%            Number of functors    :    1 (   1 usr;   0 con; 2-2 aty)
%            Number of variables   :    6 (   0 sgn)
% 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 ) ).

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