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We show that the 42-element monoid of all partial order preserving andextensive injections on the 4-element chain is not contained in any varietygenerated by a finitely based finite $\mathcal{R}$-trivial semigroup. Thisprovides unified proofs for several known facts and leads to a bunch of newresults on the Finite Basis Problem for finite $\mathcal{R}$- and$\mathcal{J}$-trivial semigroups.

Catalan monoids inherently nonfinitely based relative to finite $\mathcal{R}$-trivial semigroups