External Analogy in Inductive Theorem Proving

This paper investigates analogy-driven proof plan construction in inductive theorem proving. Given a proof plan of a source theorem, we identify constraints of second-order mappings that enable a replay of the source plan to produce a similar plan for the target theorem. In addition, the analogical replay is controlled by justifications that have to be satisfied in the target. Our analogy procedure, ABALONE, is implemented on top of the proof planner, CLaM. Employing analogy has extended the problem solving horizon of CLaM: with analogy, some theorems could be proved that CLAM could not prove automatically.

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