## Uniform Strategies: The CADE-11 Theorem Proving Contest (1993)

Venue: | Journal of Automated Reasoning |

Citations: | 4 - 0 self |

### BibTeX

@ARTICLE{Lusk93uniformstrategies:,

author = {Ewing L. Lusk and William W. Mccune},

title = {Uniform Strategies: The CADE-11 Theorem Proving Contest},

journal = {Journal of Automated Reasoning},

year = {1993},

volume = {11},

pages = {31733--1}

}

### OpenURL

### Abstract

. At CADE-10 Ross Overbeek proposed a two-part contest to stimulate and reward work in automated theorem proving. The first part consists of seven theorems to be proved with resolution, and the second part of equational theorems. Our theorem provers Otter and its parallel child Roo proved all of the resolution theorems and half of the equational theorems. This paper represents a family of entries in the contest. Key Words. Automated theorem proving, resolution, paramodulation, Knuth-Bendix completion, strategy. 1 Introduction The Conference on Automated Deduction (CADE) has been for nearly twenty years a meeting where both theoreticians and practitioners present their work. Feeling perhaps that the conference was becoming dominated by the theoreticians, Ross Overbeek proposed at CADE-10 in 1990 a contest to stimulate work on the implementation and use of automated theorem-proving systems. The challenge was to prove a set of theorems, and do so with a uniform approach. That is, one w...

### Citations

65 |
Otter 2.0 users guide
- McCune
- 1990
(Show Context)
Citation Context ...c inference components, and the other represented by a set of ten problems designed to test equality-based systems. This paper describes the results of our preparation to enter the contest with Otter =-=[6, 7]-=- and Roo [1, 2], two systems developed at Argonne National Laboratory. Roo is a parallel version of Otter but has such different behavior in some cases that we treat them as separate entries. We enter... |

33 |
Complexity and related enhancements for automated theorem proving programs
- McCharen, Overbeek, et al.
- 1976
(Show Context)
Citation Context ...on. Although not explicitly stated in the contest rules, we believe that demodulation is permitted, but that paramodulation is not. This has been the traditional approach when using the P-formulation =-=[5, 4]-=-, and we have followed it. Theorem 1. x 2 = e groups are commutative, stated in the P-formulation. Theorem 2. The commutator theorem: if a group has the property x 3 = e, then [[x; y]; y] = e, where [... |

25 |
Problems and Experiments for and with Automated TheoremProving Programs
- McCharen, Overbeek, et al.
- 1976
(Show Context)
Citation Context ...on. Although not explicitly stated in the contest rules, we believe that demodulation is permitted, but that paramodulation is not. This has been the traditional approach when using the P-formulation =-=[5, 4]-=-, and we have followed it. Theorem 1. x 2 = e groups are commutative, stated in the P-formulation. Theorem 2. The commutator theorem: if a group has the property x 3 = e, then [[x; y]; y] = e, where [... |

24 | Experiments in automated deduction with condensed detachment
- McCune, Wos
- 1992
(Show Context)
Citation Context ... The formula i(i(i(x; y); z); i(i(z; x); i(u; x))) implies the formula i(i(x; y); i(i(y; z); i(x; z))) by condensed detachment. We refer to this theorem as Imp4, and it is CD-67 of the problem set in =-=[9]-=-. Theorem 6. The formula i(i(x; y); i(i(z; x); i(z; y))) is a theorem in the many-valued sentential calculus. This is theorem CD-57 in [9]. Theorem 7. The formula i(i(x; y); i(n(y); n(x))) is a theore... |

13 | Reference manual for the environmental theorem prover: An incarnation of AURA - Smith - 1988 |

12 |
Experiments with ROO, a Parallel Automated Deduction System
- Lusk, McCune
- 1992
(Show Context)
Citation Context ...ponents, and the other represented by a set of ten problems designed to test equality-based systems. This paper describes the results of our preparation to enter the contest with Otter [6, 7] and Roo =-=[1, 2]-=-, two systems developed at Argonne National Laboratory. Roo is a parallel version of Otter but has such different behavior in some cases that we treat them as separate entries. We entered each of them... |

10 |
Roo: A parallel theorem prover
- Lusk, McCune, et al.
- 1992
(Show Context)
Citation Context ...ponents, and the other represented by a set of ten problems designed to test equality-based systems. This paper describes the results of our preparation to enter the contest with Otter [6, 7] and Roo =-=[1, 2]-=-, two systems developed at Argonne National Laboratory. Roo is a parallel version of Otter but has such different behavior in some cases that we treat them as separate entries. We entered each of them... |

10 | The automated reasoning system ITP - Lusk, Overbeek - 1984 |

8 |
What's New in Otter 2.2
- McCune
- 1991
(Show Context)
Citation Context ...c inference components, and the other represented by a set of ten problems designed to test equality-based systems. This paper describes the results of our preparation to enter the contest with Otter =-=[6, 7]-=- and Roo [1, 2], two systems developed at Argonne National Laboratory. Roo is a parallel version of Otter but has such different behavior in some cases that we treat them as separate entries. We enter... |

8 |
The absence and the presence of fixed point combinators
- McCune, Wos
- 1991
(Show Context)
Citation Context .... The fragment fB,Wg of combinatory logic contains fixed point combinators.sThis theorem is much more difficult than EQ-6, and the strategy above that works for EQ-6 fails for EQ-8. The kernel method =-=[8]-=-, which was developed for this type of problem, finds a proof of EQ-8 within a few seconds. Theorems EQ-9 and EQ-10. On Moufang identities in nonassociative rings (EQ-9), and on right alternative nona... |

5 |
Automatic proofs of equality problems in Overbeek's competition
- Zhang
(Show Context)
Citation Context ...ings in which x 3 = x are commutative. Theorem EQ-8. The fragment fB,Wg of combinatory logic contains fixed point combinators. Theorems EQ-9. On three Moufang identities and nonassociative rings. See =-=[11]-=- for a statement of the theorem. Theorems EQ-10. On right alternative nonassociative rings. As far as we know, this is still an open problem. See [11] for a statement of the theorem. 3 Results Otter a... |

1 |
The absence and the presence of point combinators
- McCune, Wos
- 1991
(Show Context)
Citation Context ...EQ-8. The fragment fB,Wg of combinatory logic containssxed point combinators. This theorem is much more dicult than EQ-6, and the strategy above that works for EQ-6 fails for EQ-8. The kernel method =-=[8]-=-, which was developed for this type of problem,snds a proof of EQ-8 within a few seconds. Theorems EQ-9 and EQ-10. On Moufang identities in nonassociative rings (EQ-9), and on right alternative nonass... |