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## Lightweight relevance filtering for machine-generated resolution problems (2006)

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Venue: | In ESCoR: Empirically Successful Computerized Reasoning |

Citations: | 50 - 9 self |

### Citations

1106 |
A machine-oriented logic based on the resolution principle.
- Robinson
- 1965
(Show Context)
Citation Context ...hen the amount of redundancy is extreme, especially if we can relax the requirement for completeness. The relevance problem dates back to the earliest days of resolution. As first defined by Robinson =-=[Rob65]-=-, a literal is pure if it is not unifiable with a complementary literal in any other clause. Clauses containing pure literals can be removed without affecting consistency. This process is a form of re... |

480 | The inductive approach to verifying cryptographic protocols.
- Paulson
- 1998
(Show Context)
Citation Context ...ange of difficulties, from easy to impossible. The following table breaks down the 285 problems according to their domain. The O-notation problems involve arithmetic. domain number security protocols =-=[12,14]-=- 124 set theory and Zorn’s lemma 48 O-notation [2] 39 combinatory logic [11] 24 Tarski’s fixedpoint theorem 23 propositional logic 24 UNITY formalism 3 In this paper, the term “problem size” means “nu... |

225 |
The design and implementation of Vampire.
- Riazanov, Voronkov
- 2002
(Show Context)
Citation Context ...fer to them as automatic theorem provers or ATPs. (This term includes clausal tableau provers, but not SAT solvers, decision procedures etc.) Our experiments mainly use E [20], SPASS [25] and Vampire =-=[17]-=-. Interactive theorem provers allow proofs to be constructed by natural chains of reasoning, generally in a rich formalism such as higher-order logic, but their automation tends to be limited to rewri... |

177 | Resolution theorem proving.
- Bachmair, Ganzinger
(Show Context)
Citation Context ...iltering through a series of graphs (Sect. 5). Finally, we present brief conclusions (Sect. 6). 2 Background Resolution theorem provers work by deriving a contradiction from a supplied set of clauses =-=[BG01]-=-. Each clause is a disjunction of literals (atomic formulae and their negations) and the set of clauses is interpreted as a conjunction. Clause form can be difficult to read, and the proofs that are f... |

159 |
The TPTP Problem Library: CNF Release v1.2.1.
- Sutcliffe, Suttner
- 1998
(Show Context)
Citation Context ...econds, while the higher time limit allows proof attempts on 100 variants of the problem. A combination of RedAx and Vampire found the first-ever automatic proofs of four theorems in the TPTP library =-=[24]-=-. We were unaware of this work when undertaking ours, and could not have applied such an approach to problems containing thousands of clauses. However, RedAx demonstrates the power of simple means. Of... |

107 | Spass: Combining superposition, sorts and splitting. Handbook of automated reasoning
- Weidenbach
- 1999
(Show Context)
Citation Context ...matic theorem provers or ATPs. (This term includes clausal tableau provers, but not SAT solvers, decision procedures etc.) Our experiments mainly use E versions 0.9 and 0.91dev001 [Sch04], SPASS V2.2 =-=[Wei01]-=- and Vampire 8 [RV01a]. 1 Interactive theorem provers allow proofs to be constructed by natural chains of reasoning, generally in a rich formalism such as higher-order logic, but their automation tend... |

94 |
Efficiency and completeness of the set of support strategy in theorem proving.
- Wos, Carson, et al.
- 1965
(Show Context)
Citation Context ...as set, and instead to define relevance with respect to the provided conjecture clauses. The simplest way of doing this is to enable the Set of Support option, if it is available. Wos’s SOS heuristic =-=[WRC65]-=-, which dates from 1965, ensures that all inference rule applications involve at least one clause derived from a conjecture clause. It prevents inferences among the axioms and makes the search goal-di... |

62 | Relations between Secrets: Two Formal Analyses of the Yahalom Protocol,
- Paulson, C
- 2001
(Show Context)
Citation Context ...ange of difficulties, from easy to impossible. The following table breaks down the 285 problems according to their domain. The O-notation problems involve arithmetic. domain number security protocols =-=[12,14]-=- 124 set theory and Zorn’s lemma 48 O-notation [2] 39 combinatory logic [11] 24 Tarski’s fixedpoint theorem 23 propositional logic 24 UNITY formalism 3 In this paper, the term “problem size” means “nu... |

51 | A generic tableau prover and its integration with Isabelle
- Paulson
- 1999
(Show Context)
Citation Context ...osen by the user, translated into clause form. A small problem, which typically comprised over 1300 axiom clauses, included the theorems that were provided by default to Isabelle’s classical reasoner =-=[11,13]-=-. A large problem, which typically comprised 2500 clauses, also included the theorems that were provided by default to Isabelle’s rewriter. Even our small problems looked rather large to a resolution ... |

45 | System description: E 0.81.
- Schulz
- 2004
(Show Context)
Citation Context ...efer to them as automatic theorem provers or ATPs. (This term includes clausal tableau provers, but not SAT solvers, decision procedures etc.) Our experiments mainly use E versions 0.9 and 0.91dev001 =-=[Sch04]-=-, SPASS V2.2 [Wei01] and Vampire 8 [RV01a]. 1 Interactive theorem provers allow proofs to be constructed by natural chains of reasoning, generally in a rich formalism such as higher-order logic, but t... |

40 |
Vampire 1.1 (system description
- Riazanov, Voronkov
- 2001
(Show Context)
Citation Context ...or ATPs. (This term includes clausal tableau provers, but not SAT solvers, decision procedures etc.) Our experiments mainly use E versions 0.9 and 0.91dev001 [Sch04], SPASS V2.2 [Wei01] and Vampire 8 =-=[RV01a]-=-. 1 Interactive theorem provers allow proofs to be constructed by natural chains of reasoning, generally in a rich formalism such as higher-order logic, but their automation tends to be limited to rew... |

31 | Integrating automated and interactive theorem proving
- Ahrendt, Beckert, et al.
- 1998
(Show Context)
Citation Context ...dAx demonstrates the power of simple means. Of previous work, the most pertinent is the integration between the Karlsruhe Interactive Verifier (KIV) and the tableau prover 3TAP, by Ahrendt and others =-=[1]-=-. Reif and Schellhorn [16] present a component of that integration: an algorithm for removing irrelevant axioms. It relies on analysing the structure of the theory in which the conjecture is posed. Sp... |

31 | Experiments on supporting interactive proof using resolution.
- Meng, Paulson
- 2004
(Show Context)
Citation Context ...type(τ) → order(list(τ))] says if the argument of list is a member of class type, then the resulting type of lists belong to class order. For more information, we refer readers to our previous papers =-=[8,10]-=-. Although the arity and class inclusion clauses typically number over one thousand, they pose no difficulties for modern ATPs. They are Horn clauses that contain only monadic (unary) predicates, whic... |

31 | Theorem proving in large theories, in:
- Reif, Schellhorn
- 1998
(Show Context)
Citation Context ...ant axioms. Of previous work, the most pertinent is the integration between the Karlsruhe Interactive Verifier (KIV) and the tableau prover 3TAP, by Ahrendt and others [ABH + 98]. Reif and Schellhorn =-=[RS98]-=- present a component of that integration: an algorithm for removing redundant axioms. It relies on analysing the structure of the theory in which the conjecture is posed. Specifically, their method is... |

30 | L.C.: Automation for interactive proof: First prototype.
- Meng, Quigley, et al.
- 2006
(Show Context)
Citation Context ...edsproblems are not merely huge but may be presented to the automatic prover by the dozen, with its heuristics set to their defaults and with a small time limit. Our integration of Isabelle with ATPs =-=[MQP06]-=- generates small or large problems, depending on whether or not rewrite rules are included. A small problem occupies 200 kilobytes and comprises over 1300 clauses; a large problem occupies about 450 k... |

29 | Generic automatic proof tools
- Paulson
- 1997
(Show Context)
Citation Context ... performs deep searches in a fashion inspired by tableau provers. Even ten years ago, using early predecessors of these tools, Isabelle users could automatically prove theorems like this set equality =-=[Pau97]-=-: � � � (Ai ∪ Bi) = Ai i∈I i∈I � � � ∪ Set theory problems, and the combinatory logic examples presented in that paper, remain difficult for automatic theorem provers. When we first got our link-up wo... |

20 | Translating higher-order problems to first-order clauses.
- Meng, Paulson
- 2006
(Show Context)
Citation Context ...e experiments described in this paper now numbers 285 problems; a second set of 151 problems is chiefly intended for evaluating different ways of translating higher-order logic into first-order logic =-=[9]-=-, but we have also used this set to investigate relevance filtering. In choosing our problems, we were mainly interested in their difficulty as indicated by the length of the existing manual proof. We... |

17 | Formalizing O notation in Isabelle/HOL
- Avigad, Donnelly
- 2004
(Show Context)
Citation Context ...lowing table breaks down the 285 problems according to their domain. The O-notation problems involve arithmetic. domain number security protocols [12,14] 124 set theory and Zorn’s lemma 48 O-notation =-=[2]-=- 39 combinatory logic [11] 24 Tarski’s fixedpoint theorem 23 propositional logic 24 UNITY formalism 3 In this paper, the term “problem size” means “number of axiom clauses in the problem.” We later re... |

10 |
de Nivelle. Automatic proof construction in type theory using resolution
- Bezem, Hendriks, et al.
- 2002
(Show Context)
Citation Context ...wer of ATPs without requiring them to become experts on ATPs. We have implemented a linkup between ATPs and the interactive prover Isabelle. Of the many differences between our project and other work =-=[5,21]-=-, a crucial one is that Isabelle already provides excellent automation. By typing auto, the Isabelle user causes approximately 2000 previously-proved theorems to be used as rewriting rules and for for... |

7 |
2001℄, Resolution theorem proving, in A. Robinson and A. Voronkov, eds, `Handbook of Automated Reasoning', Vol
- Ba, Ganzinger
(Show Context)
Citation Context ...present empirical results as series of graphs. Finally, we present brief conclusions (Sect. 6). 2 Background Resolution theorem provers work by deriving a contradiction from a supplied set of clauses =-=[3]-=-. Each clause is a disjunction of literals (atomic formulae and their negations) and the set of clauses is interpreted as a conjunction. Clause form can be difficult to read, and the proofs that are f... |

5 | Proving Harder Theorems by Axiom Reduction.
- Sutcliffe, Dvorsky
- 2003
(Show Context)
Citation Context ...enoted by α. We devoted some time to identifying prover settings to help ATPs cope with huge problems. Above all, we have struggled to find ways to filter out irrelevant axioms. Sutcliffe and Dvorsky =-=[22]-=- propose a remarkably simple idea. Given a problem involving n axiom clauses, their RedAx (“reduce axioms”) tool systematically generates its 2 n subsets. Heuristic criteria are used to remove “heavy”... |

4 |
Abstraction-based relevancy testing for model elimination, in:
- Fuchs, Fuchs
- 1999
(Show Context)
Citation Context ...ithout actually running proofs: yet more Perl scripts compare the new problems with the reduced ones, reporting any missing axioms. The abstraction-based relevancy testing approach of Fuchs and Fuchs =-=[FF99]-=- is specifically designed for model elimination (or connection tableau) provers. It is not clear how to modify this approach for use with saturation provers, which are the type we use almost exclusive... |

2 |
and Adnan Yahya. A relevance restriction strategy for automated deduction
- Plaisted
(Show Context)
Citation Context ...nce classes of clauses. We confess that we were not able to derive any ideas from this highly mathematical paper. 4.1 Plaisted and Yahya’s Strategy Plaisted and Yahya’s relevance restriction strategy =-=[PY03]-=- introduces the concept of relevance distance between two clauses, reflecting how closely two clauses are related. Simply put, the idea is to start with the conjecture clauses and to identify a set R1... |

1 | Automated Deduction— A Basis for Applications, volume II. Systems and Implementation Techniques - Schmitt - 1998 |