Does submodularity property hold for the trace of a positive-definite hermitian matrix?

I.e., does given any real symmetric positive-definite matrices $X,A,B$ $$ tr~X^{-1} + tr~(X+A+B)^{-1} \leq tr~(X+A)^{-1} + tr~(X+B)^{-1} $$ hold?