%--------------------------------------------------------------------------
% File     : ALG010-1 : TPTP v4.0.1. Released v2.5.0.
% Domain   : General Algebra (Quasivarieties)
% Problem  : Prove J follows from HBCK
% Version  : [EF+02] axioms.
% English  : Axioms for the quasivariety HBCK are given below. Show that
%            equation J follows.

% Refs     : [MP96]  McCune & Padmanabhan (1996), Automated Deduction in Equ
%          : [EF+02] Ernst et al. (2002), More First-order Test Problems in
% Source   : [EF+02]
% Names    : hbck [EF+02]

% Status   : Unsatisfiable
% Rating   : 1.00 v2.5.0
% Syntax   : Number of clauses     :    8 (   0 non-Horn;   7 unit;   2 RR)
%            Number of atoms       :   10 (  10 equality)
%            Maximal clause size   :    3 (   1 average)
%            Number of predicates  :    1 (   0 propositional; 2-2 arity)
%            Number of functors    :    4 (   3 constant; 0-2 arity)
%            Number of variables   :   14 (   1 singleton)
%            Maximal term depth    :    5 (   2 average)

% Comments : This result has been known for some time by a model-theoretic
%            argument. The first  1storder proof was found by Veroff in 2002.
%--------------------------------------------------------------------------
%----M3
cnf(m3,axiom,
    ( multiply(A,one) = one )).

%----M4
cnf(m4,axiom,
    ( multiply(one,A) = A )).

%----M5
cnf(m5,axiom,
    ( multiply(multiply(A,B),multiply(multiply(C,A),multiply(C,B))) = one )).

%----M7
cnf(m7,axiom,
    ( multiply(A,B) != one
    | multiply(B,A) != one
    | A = B )).

%----M8
cnf(m8,axiom,
    ( multiply(A,A) = one )).

%----M9
cnf(m9,axiom,
    ( multiply(A,multiply(B,C)) = multiply(B,multiply(A,C)) )).

%----H
cnf(h,axiom,
    ( multiply(multiply(A,B),multiply(A,C)) = multiply(multiply(B,A),multiply(B,C)) )).

%----Denial of J
cnf(prove_j,negated_conjecture,
    (  multiply(multiply(multiply(multiply(a,b),b),a),a) != multiply(multiply(multiply(multiply(b,a),a),b),b) )).

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