A computer implemented cover process is disclosed for use in program analysis and verification techniques where existential quantifier elimination is not possible. The cover process allows an accurate assessment of the viability of a theory. Where a theory can be described using quantifier-free formulas, it can be shown that the program analysis and verification techniques using cover are not only sound (i.e., an indication of validity is reliable), but also precise (i.e., and indication of an error is reliable).