Equality of total inner and outer quasi-local masses

Let $(M^3,g,h)$ be asymptotically flat with total ADM mass $m_{ADM}$. Define the total inner mass $m_{inner}^{total}$ and total outer mass $m_{outer}^{total}$ as the suprema of the corresponding inner and outer masses over all outer-minimising surfaces. The total quasi-local mass conjecture. Then

$$m_{inner}^{total}=m_{outer}^{total}=m_{ADM}.$$

This conjecture would show that the interval-valued total quasi-local mass collapses to the ADM mass in the asymptotically flat setting. The supplied text gives no resolution evidence.