## Integrating a SAT Solver with an LCF-style Theorem Prover (2005)

Venue: | Proceedings of the Third International Workshop on Pragmatical Aspects of Decision Procedures in Automated Reasoning (PDPAR 2005 |

Citations: | 6 - 1 self |

### BibTeX

@INPROCEEDINGS{Weber05integratinga,

author = {Tjark Weber},

title = {Integrating a SAT Solver with an LCF-style Theorem Prover},

booktitle = {Proceedings of the Third International Workshop on Pragmatical Aspects of Decision Procedures in Automated Reasoning (PDPAR 2005},

year = {2005}

}

### OpenURL

### Abstract

This paper describes the integration of a leading SAT solver with Isabelle/HOL, a popular interactive theorem prover. The SAT solver generates resolution-style proofs for (instances of) propositional tautologies. These proofs are verified by the theorem prover. The presented approach significantly improves Isabelle’s performance on propositional problems, and furthermore exhibits counterexamples for unprovable conjectures. 1

### Citations

215 |
CVC Lite: A new implementation of the cooperating validity checker
- Barrett, Berezin
- 2004
(Show Context)
Citation Context ...spropositional tautologies, but it avoids difficult translation issues, and uses a SAT solver, rather than a first-order prover. A custom-built SAT solver has been integrated with the CVC Lite system =-=[3]-=- by Clark Barrett et al. [4]. While this solver produces proofs that can be checked independently, our work shows that it is possible to integrate an existing, highly efficient solver with an LCF-styl... |

200 |
Melham, editors. Introduction to HOL: A Theorem Proving Environment for Higher Order Logic
- Gordon, F
- 1993
(Show Context)
Citation Context ...ificantly improves Isabelle’s performance on propositional problems, and furthermore exhibits counterexamples for unprovable conjectures. 1 Introduction Interactive theorem provers like PVS [19], HOL =-=[10]-=- or Isabelle [20] traditionally support rich specification logics. Proof search and automation for these logics however is difficult, and proving a non-trivial theorem usually requires manual guidance... |

80 | A SAT based approach for solving formulas over boolean and linear mathematical propositions
- Audemard, Bertoli, et al.
- 2002
(Show Context)
Citation Context ...ent to produce a proof object in a theorem prover, no custom-built solver is necessary. Other applications of SAT solvers in the context of theorem proving include SAT-based decision procedures (e.g. =-=[2, 23]-=-), as well as SAT-based model generation techniques (e.g. [1, 26]). These applications again require involved translations, and a correctly implemented SAT solver is usually taken for granted. 5 Concl... |

44 | Integrating Gandalf and HOL
- Hurd
- 1999
(Show Context)
Citation Context ... bug in the SAT solver could ultimately lead to an inconsistency in HOL 4. Perhaps closer related to our work is the integration of automated firstorder provers, recently further explored by Joe Hurd =-=[12, 13]-=- and Jia Meng [15, 16]. Proofs found by the automated system are either verified by the interactive prover immediately [12], or translated into a proof script that can be executed later [16]. The main... |

40 |
T.: SATLIB: An online resource for research on
- Hoos, Stützle
- 2000
(Show Context)
Citation Context ...ms occur in practice, has thereby improved considerably. However, Isabelle’s performance is still not sufficient for problems with thousands of clauses, like some of those found in the SATLIB library =-=[11]-=-. Their sheer size currently does not permit an efficient treatment in Isabelle/HOL. Further work is necessary to investigate if this issue can be resolved by relatively minor optimizations to Isabell... |

34 | An LCF-Style Interface between HOL and First-Order Logic
- Hurd
- 2002
(Show Context)
Citation Context ... bug in the SAT solver could ultimately lead to an inconsistency in HOL 4. Perhaps closer related to our work is the integration of automated firstorder provers, recently further explored by Joe Hurd =-=[12, 13]-=- and Jia Meng [15, 16]. Proofs found by the automated system are either verified by the interactive prover immediately [12], or translated into a proof script that can be executed later [16]. The main... |

25 | From LCF to HOL: a short history
- Gordon
- 2000
(Show Context)
Citation Context ... goes back at least to the early nineties [14]. However, to ensure that a potential bug in the automated prover does not render the whole system unsound, theorems in Isabelle, like in other LCF-style =-=[8]-=- provers, can be derived only through a set of core inference rules. Therefore it is not sufficient for the automated prover to return whether a formula is provable, but it must also generate the ∗ Th... |

13 | A proof-producing boolean search engine
- Barrett, Berezin
- 2003
(Show Context)
Citation Context ...but it avoids difficult translation issues, and uses a SAT solver, rather than a first-order prover. A custom-built SAT solver has been integrated with the CVC Lite system [3] by Clark Barrett et al. =-=[4]-=-. While this solver produces proofs that can be checked independently, our work shows that it is possible to integrate an existing, highly efficient solver with an LCF-style prover: the information pr... |

3 |
HolSatLib documentation, version 1.0b
- Gordon
- 2001
(Show Context)
Citation Context ...should be relatively simple [27], but despite some work in this direction [7], zChaff, to our knowledge, is currently the only proof-generating SAT solver that is publicly available. 3sHOL level, cf. =-=[9]-=-). Quantified subformulas of φ are treated as atomic. Note that it is not sufficient to convert φ into an equivalent formula φ ′ in CNF. Rather, we have to prove this equivalence inside Isabelle/HOL. ... |

2 |
Efficient SAT-based bounded model checking for software verification
- Ashar, Ganai, et al.
- 2004
(Show Context)
Citation Context ...t solver is necessary. Other applications of SAT solvers in the context of theorem proving include SAT-based decision procedures (e.g. [2, 23]), as well as SAT-based model generation techniques (e.g. =-=[1, 26]-=-). These applications again require involved translations, and a correctly implemented SAT solver is usually taken for granted. 5 Conclusions and Future Work Our results show that the zChaff-based tac... |