This paper introduces a new method for performing time-frame expansion based on writing the number of time frames in terms of powers of two. In the proposed method, the behavior of a circuit for t time frames, where 0≤t0, 21, 22,...,2(log n-1) times and combining them. This formulation of the problem makes it possible to prune the search space quickly when the problem is infeasible. To show the advantage of this method, we have used it to model the state justification problem and solve the problem using a SAT-solver. Experimental results show several orders of magnitude speedup for some non-trivial infeasible problems. Furthermore, in most cases the CPU time requirement grows linearly in terms of the number of time frames.