The dibinary-algebra extension-monad conjecture for the beta reduct

Let $cmathbb{A}=(A;\beta,cdelta)$ be a dibinary algebra with two binary operations satisfying

$$cdelta(x,cbeta(y,z))=cbeta(cdelta(x,y),cdelta(x,z))$$

and

$$cdelta(cbeta(x,y),z)=cbeta(cdelta(x,z),cdelta(y,z)).$$

Its $cbeta$ reduct is the algebra obtained by retaining only $cbeta$; write the corresponding extension monads for $cmathbb{A}$ and its $cbeta$ reduct.

Dibinary extension-monad conjecture. The extension monad of $cmathbb{A}$ has the same underlying set as the extension monad of its $cbeta$ reduct.

The source presents this as a proposed extension of the preceding ring-versus-additive-reduct property to dibinary distributive algebras. The supplied text does not state whether it has been resolved.