%--------------------------------------------------------------------------
% File     : GRP011-4 : TPTP v8.2.0. Released v1.0.0.
% Domain   : Group Theory
% Problem  : Left cancellation
% Version  : [Wos65] (equality) axioms : Incomplete.
% English  :

% Refs     : [Wos65] Wos (1965), Unpublished Note
%          : [Pel86] Pelletier (1986), Seventy-five Problems for Testing Au
% Source   : [Pel86]
% Names    : Pelletier 63 [Pel86]

% Status   : Unsatisfiable
% Rating   : 0.14 v8.2.0, 0.17 v8.1.0, 0.20 v7.5.0, 0.17 v7.4.0, 0.22 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, 0.06 v6.0.0, 0.24 v5.5.0, 0.21 v5.4.0, 0.00 v5.2.0, 0.07 v5.1.0, 0.13 v5.0.0, 0.07 v4.1.0, 0.09 v4.0.1, 0.07 v4.0.0, 0.08 v3.7.0, 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.25 v2.0.0
% Syntax   : Number of clauses     :    5 (   5 unt;   0 nHn;   2 RR)
%            Number of literals    :    5 (   5 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    3 (   1 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   :    5 (   0 sgn)
% SPC      : CNF_UNS_RFO_PEQ_UEQ

% Comments : [Pel86] says "... problems, published I think, by Larry Wos
%            (but I cannot locate where)."
%--------------------------------------------------------------------------
%----The operation '*' is associative
cnf(associativity,axiom,
    multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ).

%----There exists an identity element
cnf(left_identity,axiom,
    multiply(identity,X) = X ).

cnf(left_inverse,axiom,
    multiply(inverse(X),X) = identity ).

cnf(product_equality,hypothesis,
    multiply(b,c) = multiply(d,c) ).

cnf(prove_left_cancellation,negated_conjecture,
    b != d ).

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