Given a linear system of inequalities $Ax \geq b$, I would ideally like to compute the irredundant set for those set of inequalities. I know how to do so mathematically, but I was wondering if there is a function implemented in CPLEX which the user can access and obtain the required irredundant set. When solving a LP using CPLEX, the solver seems to eliminate redundant inequalities as the first step, so I am wondering if it is possible for the user to access the pruned set (even if it is not the irredundant set). If it is possible, can someone please tell me how.
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 cluster, as well.
If you are Linux user you can find LRS in standard repositories. Anyway, open sources (in C) are available for "manual" building.