Embodiments of the present invention provide methods and apparatuses for verifying the functionality of a circuit. The system can determine a lower-bound-distance (LBD) value, such that the LBD value is associated with an LBD abstract model of the CUV which does not satisfy a property. The system can use an abstraction-refinement technique to determine whether the CUV satisfies the property. The system can determine an upper-bound-distance value for an abstract model which is being used in the abstraction-refinement technique, and can determine whether the LBD value is greater than or equal to the upper-bound-distance value. If so, the system can conclude that the abstract model does not satisfy the property, and hence, the system can decide not to perform reachability analysis on the abstract model that is currently being used in the abstraction-refinement technique.