  Recently, FO(C), the integration of C-Log with classical logic, was
introduced as a knowledge representation language. Up to this point, no systems
exist that perform inference on FO(C), and very little is known about
properties of inference in FO(C). In this paper, we study both of the above
problems. We define normal forms for FO(C), one of which corresponds to FO(ID).
We define transformations between these normal forms, and show that, using
these transformations, several inference tasks for FO(C) can be reduced to
inference tasks for FO(ID), for which solvers exist. We implemented a prototype
of this transformation, and thus present the first system to perform inference
in FO(C). We also provide results about the complexity of reasoning in FO(C).
