#-------------------------------------------------------------
# Equational specification of a group. This specification does have
# models, i.e. it cannot be refuted (and the prover will note this). 
#
# It uses only unit clauses in infix-equational notation.
#

# There exists a right-neutral element (0).
f(X,0)=X.

# For each X, there is a right inverse element i(X).
f(X,i(X))=0.

# f is associative.
f(f(X,Y),Z)=f(X,f(Y,Z)).

# Possible Hypothesis: Right inverse is also left inverse
# <- f(i(a),a) = 0.

# A nother possible hypothesis: Multiplication with inverse element is
# commutative. 
# ~f(a,i(a)) = f(i(a),a).