While model checking safety of infinite-state systems by inferring state invariants has steadily improved recently, most verification tools still rely on a technique based on bounded model checking to detect safety violations. In particular, the current techniques typically analyze executions by unfolding transitions one step at a time, and the slow growth of execution length prevents detection of deep counterexamples before the tool reaches its limits on computations. We propose a novel model-checking algorithm that is capable of both proving unbounded safety and finding long counterexamples. The idea is to use Craig interpolation to guide the creation of symbolic abstractions of exponentially longer sequences of transitions. Our experimental analysis shows that on unsafe benchmarks with deep counterexamples our implementation can detect faulty executions that are at least an order of magnitude longer than those detectable by the state-of-the-art tools.