%--------------------------------------------------------------------------
% File     : GRP502-1 : TPTP v9.0.0. Released v2.6.0.
% Domain   : Group Theory
% Problem  : Axiom for group theory, in double division and inverse, part 1
% Version  : [McC93] (equality) axioms.
% English  :

% Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr
% Source   : [TPTP]
% Names    :

% Status   : Unsatisfiable
% Rating   : 0.23 v8.2.0, 0.25 v7.5.0, 0.29 v7.4.0, 0.35 v7.3.0, 0.32 v7.1.0, 0.22 v7.0.0, 0.26 v6.4.0, 0.32 v6.3.0, 0.29 v6.1.0, 0.38 v6.0.0, 0.52 v5.5.0, 0.53 v5.4.0, 0.40 v5.3.0, 0.33 v5.2.0, 0.36 v5.1.0, 0.40 v5.0.0, 0.43 v4.1.0, 0.36 v4.0.0, 0.31 v3.7.0, 0.11 v3.4.0, 0.12 v3.3.0, 0.14 v3.1.0, 0.11 v2.7.0, 0.09 v2.6.0
% Syntax   : Number of clauses     :    3 (   3 unt;   0 nHn;   1 RR)
%            Number of literals    :    3 (   3 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    1 (   0 usr;   0 prp; 2-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :    6 (   0 sgn)
% SPC      : CNF_UNS_RFO_PEQ_UEQ

% Comments : A UEQ part of GRP083-1
%--------------------------------------------------------------------------
cnf(single_axiom,axiom,
    double_divide(double_divide(A,inverse(double_divide(B,C))),double_divide(inverse(B),inverse(double_divide(D,double_divide(A,D))))) = C ).

cnf(multiply,axiom,
    multiply(A,B) = inverse(double_divide(B,A)) ).

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

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