Finite orthodox locally idempotent semigroups having no finite basis of biidentities

A finitely generated existence variety of orthodox locally idempotent semigroups is constructed which has no finite basis of biidentities within the class of all orthodox semigroups. In addition, ordinary semigroup identities valid in this existence variety also cannot be finitely based. This yields examples of finite orthodox locally idempotent semigroups having both no finite basis of biidentities and also no finite basis of identities in the usual sense.