Zheng–Sun's revised generalized Kriesell conjecture for non-regular graphs

Let $t>0$. A graph is non-regular if its vertex degrees are not all equal, and a minimally $t$-tough graph is a $t$-tough graph whose toughness decreases after deleting any edge. Zheng–Sun's revised conjecture. Every non-regular minimally $t$-tough graph has a vertex of degree $\lceil 2t\rceil$. The paper states that this revised conjecture fails for small graphs, since one of the counterexamples to the generalized conjecture is non-regular.