Productive use of failure in inductive proof

@article{Ireland1996ProductiveUO,
  title={Productive use of failure in inductive proof},
  author={Andrew Ireland},
  journal={Journal of Automated Reasoning},
  year={1996},
  volume={16},
  pages={79-111}
}
Proof by mathematical induction gives rise to various kinds of eureka steps, e.g., missing lemmata and generalization. Most inductive theorem provers rely upon user intervention in supplying the required eureka steps. In contrast, we present a novel theorem-proving architecture for supporting the automatic discovery of eureka steps. We build upon rippling, a search control heuristic designed for inductive reasoning. We show how the failure if rippling can be used in bridging gaps in the search… CONTINUE READING
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