Finite representation property conjecture for relation algebra reduct signatures

Let a Relation Algebra reduct signature $\tau$ be a sub-signature of the Relation Algebra language, and let the finite representation property mean that every finite member of its representation class has a finite representation.

Finite representation property conjecture. The signature $\tau$ has the finite representation property if and only if

$$\{-,;\} \not\subseteq \tau \not\supseteq \{\cdot,;\}.$$

Equivalently, the finite representation property fails exactly when the reduct signature contains both negation and composition, or both meet and composition. The conjecture seeks to classify which Relation Algebra reduct languages have finite representations for all their finite representable members; the supplied text does not state whether it has been resolved.