In recent years, the inductive, incremental verification algorithm IC3 had a major impact on hardware model checking. Also with respect to software model checking, a number of adaptations of Boolean IC3 and combinations with CEGAR and ART-based techniques have been developed. However, most of them exploit the peculiarities of software programs, such as the explicit representation of control flow, only to a limited extent. In this paper, we propose a technique that supports this explicit representation in the form of control flow automata, and integrates it with symbolic reasoning about the data state space of the program. It thus provides a true lifting of IC3 from hardware to software model checking. By evaluating the approach on a number of case studies using a prototypical implementation, we demonstrate that our method shows promising results.