In previous work, we presented a symbolic execution method which starts with a concrete model of the program but progressively abstracts away details only when these are known to be irrelevant using interpolation. In this paper, we extend the technique to handle unbounded loops. The central idea is to progressively discover the strongest invariants through a process of loop unrolling. The key feature of this technique, called the minimax algorithm, is intelligent backtracking which directs the search for the next invariant. We then present an analysis of the main differences between our symbolic execution method and mainstream techniques mainly based on abstract refinement (CEGAR). Finally, we evaluate our technique against available state-of-the-art systems.