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GRP004-0.ax
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GRP004-0.ax
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%--------------------------------------------------------------------------
% File : GRP004-0 : TPTP v7.0.0. Released v1.0.0.
% Domain : Group Theory
% Axioms : Group theory (equality) axioms
% Version : [MOW76] (equality) axioms :
% Reduced > Complete.
% English :
% Refs : [MOW76] McCharen et al. (1976), Problems and Experiments for a
% : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr
% Source : [ANL]
% Names :
% Status : Satisfiable
% Syntax : Number of clauses : 3 ( 0 non-Horn; 3 unit; 0 RR)
% Number of atoms : 3 ( 3 equality)
% Maximal clause size : 1 ( 1 average)
% Number of predicates : 1 ( 0 propositional; 2-2 arity)
% Number of functors : 3 ( 1 constant; 0-2 arity)
% Number of variables : 5 ( 0 singleton)
% Maximal term depth : 3 ( 2 average)
% SPC :
% Comments : [MOW76] also contains redundant right_identity and
% right_inverse axioms.
% : These axioms are also used in [Wos88] p.186, also with
% right_identity and right_inverse.
%--------------------------------------------------------------------------
%----For any x and y in the group x*y is also in the group. No clause
%----is needed here since this is an instance of reflexivity
%----There exists an identity element
cnf(left_identity,axiom,
( multiply(identity,X) = X )).
%----For any x in the group, there exists an element y such that x*y = y*x
%----= identity.
cnf(left_inverse,axiom,
( multiply(inverse(X),X) = identity )).
%----The operation '*' is associative
cnf(associativity,axiom,
( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )).
%--------------------------------------------------------------------------