In WL 12.2, AxiomaticTheory@"RingAxioms" returns 1-sided distributivity.
But 2-sided distributivity characterizes a ring.
Why does RingAxioms behave this way?
It seems that a new theory (say NearRingAxioms) could treat 1-sided distributivity so that RingAxioms could treat 2-sided distributivity. Nevertheless, there's undoubtedly a good reason that RingAxioms uses 1-sided distributivity.