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Recursively defined linked data structures embedded in a pointer-based heapand their properties are naturally expressed in pure first-order logic withleast fixpoint definitions (FO+lfp) with background theories. Such logics,unlike pure first-order logic, do not admit even complete procedures. In thispaper, we undertake a novel approach for synthesizing inductive hypotheses toprove validity in this logic. The idea is to utilize several kinds of finitefirst-order models as counterexamples that capture the non-provability andinvalidity of formulas to guide the search for inductive hypotheses. Weimplement our procedures and evaluate them extensively over theorems involvingheap data structures that require inductive proofs and demonstrate theeffectiveness of our methodology.

Model-Guided Synthesis of Inductive Lemmas for FOL with Least Fixpoints