The four-dimensional numerical non-vanishing conjecture

Let $(X,B)$ be a log minimal model with $\dim(X)=4$, and let $C$ be a very general curve in $X$. Four-dimensional numerical non-vanishing conjecture. If $(K+B)\cdot C>0$ for very general curves $C\subset X$, then $(K+B)^4>0$. This condition is presented as equivalent to the four-dimensional case of the Log Abundance Conjecture, using the main theorem for log minimal models whose log canonical divisor has nef dimension at most $3$. The source does not state a resolution of this equivalent formulation.