## Using a SAT solver as a fast decision procedure for propositional logic in an LCF-style theorem prover (2005)

Venue: | In Proc. of 18th Int. Conf. on the Theorem Proving in Higher Order Logics |

Citations: | 6 - 1 self |

### BibTeX

@TECHREPORT{Weber05usinga,

author = {Tjark Weber},

title = {Using a SAT solver as a fast decision procedure for propositional logic in an LCF-style theorem prover},

institution = {In Proc. of 18th Int. Conf. on the Theorem Proving in Higher Order Logics},

year = {2005}

}

### OpenURL

### Abstract

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

1206 | Chaff: Engineering an efficient SAT solver
- Moskewicz, Madigan, et al.
- 2001
(Show Context)
Citation Context ...approach feasible in practice. Hence the performance of an interactive prover on propositional problems may be of significant practical importance. In this paper we describe the integration of zChaff =-=[15]-=-, a leading SAT solver, with the Isabelle/HOL [16] prover. We show that using zChaff to prove theorems of propositional logic dramatically improves Isabelle’s performance on this class of formulas. Fu... |

795 |
Isabelle/HOL: A Proof Assistant for Higher-Order Logic, volume 2283
- Nipkow, Paulson, et al.
- 2002
(Show Context)
Citation Context ...ce of an interactive prover on propositional problems may be of significant practical importance. In this paper we describe the integration of zChaff [15], a leading SAT solver, with the Isabelle/HOL =-=[16]-=- prover. We show that using zChaff to prove theorems of propositional logic dramatically improves Isabelle’s performance on this class of formulas. Furthermore, while Isabelle’s previous decision proc... |

571 | PVS: A Prototype Verification System
- Owre, Rushby, et al.
- 1992
(Show Context)
Citation Context ...roach significantly improves Isabelle’s performance on propositional problems, and furthermore exhibits counterexamples for unprovable conjectures. 1 Introduction Interactive theorem provers like PVS =-=[17]-=-, HOL [8] or Isabelle [18] traditionally support rich specification logics. Proof search and automation for these logics however is difficult, and proving a non-trivial theorem usually requires manual... |

202 |
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 [17], HOL =-=[8]-=- or Isabelle [18] 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... |

175 |
Isabelle: A Generic Theorem Prover, volume 828
- Paulson
(Show Context)
Citation Context ...es Isabelle’s performance on propositional problems, and furthermore exhibits counterexamples for unprovable conjectures. 1 Introduction Interactive theorem provers like PVS [17], HOL [8] or Isabelle =-=[18]-=- 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 by an expert use... |

81 | A SAT Based Approach for Solving Formulas over Boolean and Linear Mathematical Propositions
- Audemard, Bertoli, et al.
- 2002
(Show Context)
Citation Context ...tion issues, and uses a SAT solver, rather than a first-order prover. Other applications of SAT solvers in the context of theorem proving include SAT-based decision procedures for richer logics (e.g. =-=[2, 21]-=-), as well as SATbased model generation techniques (e.g. [1, 24]). These applications again require involved translations, and a correctly implemented SAT solver is usually taken for granted. 5 Conclu... |

43 | 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 first-order provers, recently further explored by Joe Hurd =-=[10, 11]-=- and Jia Meng [13, 14]. Proofs found by the automated system are either verified by the interactive prover immediately [10], or translated into a proof script that can be executed later [14]. The main... |

41 |
Satlib: An online resource for research on
- Hoos, Stutzle
- 2000
(Show Context)
Citation Context ...improved considerably. However, it is also important to note that Isabelle’s performance is still not sufficient for problems with thousands of clauses, like some of those found in the SATLIB library =-=[9]-=-. While zChaff and other recent SAT solvers may well be able to decide these problems in practice, their sheer size currently does not permit an efficient treatment in Isabelle/HOL. Further work is ne... |

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 first-order provers, recently further explored by Joe Hurd =-=[10, 11]-=- and Jia Meng [13, 14]. Proofs found by the automated system are either verified by the interactive prover immediately [10], or translated into a proof script that can be executed later [14]. The main... |

28 | Experiments on supporting interactive proof using resolution
- Meng, Paulson
- 2004
(Show Context)
Citation Context ...could ultimately lead to an inconsistency in HOL 4. Perhaps closer related to our work is the integration of automated first-order provers, recently further explored by Joe Hurd [10, 11] and Jia Meng =-=[13, 14]-=-. Proofs found by the automated system are either verified by the interactive prover immediately [10], or translated into a proof script that can be executed later [14]. The main focus of their work h... |

26 | From LCF to HOL: A Short History
- Gordon
- 2000
(Show Context)
Citation Context ...sion procedures are often based on complex algorithms. To ensure that a potential bug in the decision procedure does not render the whole prover unsound, theorems in Isabelle, like in other LCF-style =-=[6]-=- provers, can be derived only through a set of core inference rules. Therefore it is not sufficient for a decision procedure to return whether a formula is provable, but the decision procedure must al... |

13 | Integrating a first-order automatic prover in the HOL environment
- Kumar, Kropf, et al.
- 1991
(Show Context)
Citation Context ...e prover, only changes to its interface – which should happen much more rarely than changes to the algorithm – still require maintenance. This is an idea that goes back at least to the early nineties =-=[12]-=-. Formal verification is an important application area of interactive theorem proving. Problems in verification can often be reduced to Boolean satisfiability (SAT), and recent SAT solver advances hav... |

5 | Integration of interactive and automatic provers
- Meng
(Show Context)
Citation Context ...could ultimately lead to an inconsistency in HOL 4. Perhaps closer related to our work is the integration of automated first-order provers, recently further explored by Joe Hurd [10, 11] and Jia Meng =-=[13, 14]-=-. Proofs found by the automated system are either verified by the interactive prover immediately [10], or translated into a proof script that can be executed later [14]. The main focus of their work h... |

3 |
HolSatLib documentation, version 1.0b
- Gordon
- 2001
(Show Context)
Citation Context ...time, at which point a definite answer can already be displayed to the user – a feature that is particularly useful in our interactive setting. 4 Related Work Michael Gordon has implemented HolSatLib =-=[7]-=-, a library which is now part of the HOL 4 theorem prover. This library provides functions to convert HOL 4 terms into CNF, and to analyze them using a SAT solver. In the case of unsatisfiability howe... |

2 |
Efficient SAT-based bounded model checking for software verification
- Ashar, Ganai, et al.
- 2004
(Show Context)
Citation Context ...over. Other applications of SAT solvers in the context of theorem proving include SAT-based decision procedures for richer logics (e.g. [2, 21]), as well as SATbased model generation techniques (e.g. =-=[1, 24]-=-). 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... |