Consider the structure $(\mathbb{R};+)$. Now, I know that it's equational theory can be generated by the commutative and associative equations. I also know that the commutative and associative equations are independent of each other. My question is this. Suppose we have a set $S$ of equations that generate the equational theory of addition. Suppose also that $S$ has cardinality greater than or equal to $3$. Must it be the case that $S$ has at least one redundant axiom?
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