Open Answer Set Programming (OASP) can be seen as a framework to represent tightly integrated combined knowledge bases of ontologies and rules that are not necessarily DL-safe. The framework makes the open-domain assumption and has a rule-based syntax supporting negation under a stable model semantics. Although decidability of different fragments of OASP has been identified, reasoning and effective algorithms remained largely unexplored. In this paper, we describe an algorithm for satisfiability checking of the fragment of simple Conceptual Logic Programs and provide a BProlog implementation. To the best of our knowledge, this is the first implementation of a (fragment) of a framework that can tightly integrate ontologies and non-DL-safe rules under an expressive nonmonotonic semantics.