%--------------------------------------------------------------------------
% File     : GRP084-1 : TPTP v9.0.0. Bugfixed v2.7.0.
% Domain   : Group Theory (Abelian)
% Problem  : Single axiom for Abelian group theory, in product and inverse
% Version  : [McC93] (equality) axioms.
% English  : This is a single axiom for Abelian group theory, in terms
%            of product and inverse.

% Refs     : [Neu81] Neumann (1981), Another Single Law for Groups
%          : [LW92]  Lusk & Wos (1992), Benchmark Problems in Which Equalit
%          : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr
% Source   : [McC93]
% Names    : GT6 [LW92]
%          : Axiom 2.4 [McC93]

% Status   : Unsatisfiable
% Rating   : 0.73 v9.0.0, 0.60 v8.2.0, 0.75 v8.1.0, 0.74 v7.5.0, 0.76 v7.4.0, 0.71 v7.3.0, 0.62 v7.2.0, 0.67 v7.1.0, 0.55 v7.0.0, 0.62 v6.4.0, 0.64 v6.3.0, 0.50 v6.2.0, 0.70 v6.1.0, 0.73 v6.0.0, 0.71 v5.5.0, 0.75 v5.4.0, 0.89 v5.3.0, 0.90 v5.2.0, 0.88 v5.1.0, 0.89 v5.0.0, 0.90 v4.1.0, 0.89 v4.0.1, 0.88 v4.0.0, 0.71 v3.7.0, 0.86 v3.4.0, 0.83 v3.3.0, 0.78 v3.2.0, 0.67 v3.1.0, 0.80 v2.7.0
% Syntax   : Number of clauses     :    2 (   1 unt;   0 nHn;   1 RR)
%            Number of literals    :    5 (   5 equ;   4 neg)
%            Maximal clause size   :    4 (   2 avg)
%            Maximal term depth    :   10 (   2 avg)
%            Number of predicates  :    1 (   0 usr;   0 prp; 2-2 aty)
%            Number of functors    :   11 (  11 usr;   9 con; 0-2 aty)
%            Number of variables   :    6 (   0 sgn)
% SPC      : CNF_UNS_RFO_PEQ_NUE

% Comments :
% Bugfixes : v2.7.0 - Grounded conjecture
%--------------------------------------------------------------------------
cnf(single_axiom,axiom,
    multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(Y,X))),multiply(inverse(multiply(Z,U)),multiply(Z,inverse(multiply(multiply(V,inverse(W)),inverse(U))))))),W) = V ).

cnf(prove_these_axioms,negated_conjecture,
    ( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
    | multiply(multiply(inverse(b2),b2),a2) != a2
    | multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
    | multiply(a4,b4) != multiply(b4,a4) ) ).

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