An Improved Propositional Approach to First-Order Theorem Proving

Ordered semantic hyper-linking (OSHL) is a theorem prover for first-order logic that generates models and uses them to instantiate first-order clauses to ground clauses, and applies a propositional prover to these ground clauses. OSHL-U extends OSHL with rules for unit clauses and with heuristics. The unit rules in OHSL-U are designed to minimize the use of blind instantiation to generate ground instances of input clauses. OSHL-U demonstrates significantly improved performance over OSHL on the TPTP problem set, and also performs better than OSHL with semantics and OSHL with replacement rules and definition detection on set theory problems. Despite its propositional approach, OSHL-U also obtains more than half of the problems that Otter solves with the auto flag on the TPTP problem set in 30 seconds, and has comparable or superior performance on several groups of TPTP problems. This is especially interesting because OSHL-U has no special rules for equality axioms. This is the first time, to our knowledge, that a propositional style prover, not performing unifications between non ground literals, has demonstrated performance comparable to that of a resolution prover on groups of TPTP problems that are not near-propositional in structure. These results suggest that a propositional prover may be superior on some classes of problems, particularly non-Horn problems, to provers based on the resolution-unification and model elimination paradigms.