Does [Tverberg's theorem](http://en.wikipedia.org/wiki/Tverberg's_theorem) hold  for CAT(0) spaces of covering dimension $d<\infty$: 

Is it true that for any $d$-dimensional $CAT(0)$-space $X$ and a subset $E\subset X$ of cardinality $(d + 1)(r - 1) + 1$, there exists a point $x\in X$ and a partition of $E$ into $r$ subsets $E_1,...,E_r$, such that $x$ belongs to the intersection of closed convex hulls of the subsets $E_i$?