Answer Set Programming (ASP) is a powerful paradigm of logic programming for non-monotonic reasoning. However, the restriction of “grounded range-restricted function-free normal programs” for ASP has been the defining limitation of ASP and its capability since its conception. Moreover, current state of ASP solvers has been characterized by the inherent “bottom-up” evaluation strategy. However, recent progress of Coinductive Logic Programming (co-LP) has allowed the development of a new type of ASP solver with top-down query-based goal-driven evaluation strategy. In this paper we present this novel approach to solving predicate answer set programs with co-LP. Our method eliminates the need for grounding, allows functions, and effectively handles a large class of predicate answer set programs including possibly infinite ones.