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Redirecting Proofs by Contradiction

16 pagesPublished: May 27, 2013

Abstract

This paper presents an algorithm that redirects proofs by contradiction. The input is a refutation graph, as produced by an automatic theorem prover (e.g., E, SPASS, Vampire, Z3); the output is a direct proof expressed in natural deduction extended with case analyses and nested subproofs. The algorithm is implemented in Isabelle’s Sledgehammer, where it enhances the legibility of machine-generated proofs.

Keyphrases: automatic theorem provers, direct proofs, Isabelle/HOL, proof assistants, resolution, Sledgehammer

In: Jasmin Christian Blanchette and Josef Urban (editors). PxTP 2013. Third International Workshop on Proof Exchange for Theorem Proving, vol 14, pages 11--26

Links:
BibTeX entry
@inproceedings{PxTP2013:Redirecting_Proofs_by_Contradiction,
  author    = {Jasmin Christian Blanchette},
  title     = {Redirecting Proofs by Contradiction},
  booktitle = {PxTP 2013. Third International Workshop on Proof Exchange for Theorem Proving},
  editor    = {Jasmin Christian Blanchette and Josef Urban},
  series    = {EPiC Series in Computing},
  volume    = {14},
  pages     = {11--26},
  year      = {2013},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {https://easychair.org/publications/paper/d6nT},
  doi       = {10.29007/wm8b}}
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