Completion of a join of reloids

I proved true the following conjecture:

Theorem $\mathrm{Compl} \left( \bigcup^{\mathsf{RLD}} R \right) = \bigcup ^{\mathsf{RLD}} \langle \mathrm{Compl} \rangle R$ for every set $R$ of reloids.

The following conjecture remains open:

Conjecture $\mathrm{Compl}\,f \cap^{\mathsf{RLD}} \mathrm{Compl}\,g =\mathrm{Compl} (f \cap^{\mathsf{RLD}} g)$ for every reloids $f$ and $g$.

See here for definitions and proofs.