The corner-tetrahedra lower-bound conjecture for triangulations of prisms

Let an $m$-prism be triangulated using $t$ corner tetrahedra. Corner-tetrahedra conjecture. Such a triangulation has at least

$$\max\{3m-t,2.5m\}$$

tetrahedra, and therefore at least

$$\max\{8m-4t,6m\}$$

interior triangles. The claim is presented as a possible improvement under the paper's assumption about triangulating boundary prisms, and no proof or resolution is given in the supplied text.