A ternary self-distributive algebra is an algebra $(X,t)$ that satisfies the identity $$t(u,v,t(x,y,z))=t(t(u,v,x),t(u,v,y),t(u,v,z)).$$

Is the equational theory of the variety of ternary self-distributive algebras decidable? If so, then when are two terms equivalent in the variety of ternary self-distributive algebras. It may be easier to prove the decidability of this variety if one assumes strong large cardinal hypotheses.