%--------------------------------------------------------------------------
% File     : GRP545-1 : TPTP v8.2.0. Released v2.6.0.
% Domain   : Group Theory (Abelian)
% Problem  : Axiom for Abelian group theory, in division and identity, part 1
% Version  : [McC93] (equality) axioms.
% English  :

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

% Status   : Unsatisfiable
% Rating   : 0.00 v7.4.0, 0.04 v7.3.0, 0.00 v2.6.0
% Syntax   : Number of clauses     :    5 (   5 unt;   0 nHn;   1 RR)
%            Number of literals    :    5 (   5 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    1 (   0 usr;   0 prp; 2-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :    7 (   0 sgn)
% SPC      : CNF_UNS_RFO_PEQ_UEQ

% Comments : A UEQ part of GRP094-1
%--------------------------------------------------------------------------
cnf(single_axiom,axiom,
    divide(divide(identity,divide(A,B)),divide(divide(B,C),A)) = C ).

cnf(multiply,axiom,
    multiply(A,B) = divide(A,divide(identity,B)) ).

cnf(inverse,axiom,
    inverse(A) = divide(identity,A) ).

cnf(identity,axiom,
    identity = divide(A,A) ).

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

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