I recommend you to try very powerful utility LRS, http://cgm.cs.mcgill.ca/~avis/C/lrs.html.
It is an open source application (a set of applications) to handle polyhedrals. B.t.w. one of LRS applications, called redund "removes redundant inequalities from an H-representation" (from description) - seems that what you need. There are parallel (MPI-based) versions for clusters and multiprocessor computers, as well.
If you are Linux user you can find LRS in standard repositories. Anyway, open sources (in C) are available for "manual" buildingbuilt.