%--------------------------------------------------------------------------
% File     : GRP505-1 : TPTP v9.0.0. Released v2.6.0.
% Domain   : Group Theory (Abelian)
% Problem  : Axiom for Abelian group theory, in product and inverse, part 1
% Version  : [McC93] (equality) axioms.
% English  :

% 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   : [TPTP]
% Names    :

% Status   : Unsatisfiable
% Rating   : 0.64 v9.0.0, 0.73 v8.2.0, 0.71 v8.1.0, 0.65 v7.5.0, 0.67 v7.4.0, 0.74 v7.3.0, 0.68 v7.1.0, 0.61 v7.0.0, 0.58 v6.4.0, 0.63 v6.3.0, 0.59 v6.2.0, 0.57 v6.1.0, 0.69 v6.0.0, 0.76 v5.5.0, 0.79 v5.4.0, 0.80 v5.3.0, 0.75 v5.2.0, 0.79 v5.1.0, 0.80 v5.0.0, 0.79 v4.1.0, 0.73 v4.0.1, 0.71 v4.0.0, 0.69 v3.7.0, 0.56 v3.4.0, 0.50 v3.3.0, 0.57 v3.2.0, 0.50 v3.1.0, 0.44 v2.7.0, 0.64 v2.6.0
% Syntax   : Number of clauses     :    2 (   2 unt;   0 nHn;   1 RR)
%            Number of literals    :    2 (   2 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :   10 (   3 avg)
%            Number of predicates  :    1 (   0 usr;   0 prp; 2-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :    6 (   0 sgn)
% SPC      : CNF_UNS_RFO_PEQ_UEQ

% Comments : A UEQ part of GRP084-1
%--------------------------------------------------------------------------
cnf(single_axiom,axiom,
    multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(B,A))),multiply(inverse(multiply(C,D)),multiply(C,inverse(multiply(multiply(E,inverse(F)),inverse(D))))))),F) = E ).

cnf(prove_these_axioms_1,negated_conjecture,
    multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ).

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