  Several tools have been developed to enhance automation of theorem proving in
the 2D plane. However, in 3D, only a few approaches have been studied, and to
our knowledge, nothing has been done in higher dimensions. In this paper, we
present a few examples of incidence geometry theorems in dimensions 3, 4, and
5. We then prove them with the help of a combinatorial prover based on matroid
theory applied to geometry.
