Finding First-Order Minimal Unsatisfiable Cores with a Heuristic Depth-First-Search Algorithm

Explaining the causes of infeasibility of formulas has practical applications in various fields, such as artificial intelligence and formal verification. A minimal unsatisfiable core provides a succinct explanation of infeasibility and is valuable for applications. The problem of deriving minimal unsatisfiable cores from Boolean formulas has been addressed rather frequently in recent years. However little attention has been concentrated on extraction of the first-order unsatisfiable subformulas. In this paper, we present DFS-Finder, which finds minimal unsatisfiable cores in first-order logic, adopting a heuristic depth-first-search strategy. We demonstrate the effectiveness of this approach on a very extensive test of SMT-LIB benchmarks.

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