Takahashi's infinitude conjecture for indecomposable totally reflexive modules

Let $R$ be a non-Gorenstein local ring, and suppose that there is a nonfree totally reflexive $R$-module. The Takahashi conjecture. There are infinitely many isomorphism classes of indecomposable totally reflexive $R$-modules. This proposes that a non-Gorenstein local ring admitting a nonfree totally reflexive module cannot have only finitely many isomorphism classes of indecomposable totally reflexive modules; the source gives no resolution of the conjecture.