## Otter: The CADE-13 Competition Incarnations (1997)

Venue: | JOURNAL OF AUTOMATED REASONING |

Citations: | 44 - 3 self |

### BibTeX

@ARTICLE{McCune97otter:the,

author = {William McCune and Larry Wos},

title = {Otter: The CADE-13 Competition Incarnations},

journal = {JOURNAL OF AUTOMATED REASONING},

year = {1997},

volume = {18},

pages = {211--220}

}

### Years of Citing Articles

### OpenURL

### Abstract

This article discusses the two incarnations of Otter entered in the CADE-13 Automated Theorem Proving Competition. Also presented are some historical background, a summary of applications that have led to new results in mathematics and logic, and a general discussion of Otter.

### Citations

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- Otter
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Citation Context ...cs and logic, and a general discussion of Otter. Key words: Automated theorem proving, competition, Otter, automated reasoning, equational deduction, paramodulation, resolution. 1. Introduction Otter =-=[17, 19]-=- is an automated deduction system for first-order logic with equality. Two versions of Otter were entered in the CADE-13 Automated Theorem Proving System Competition, and the main purpose of this arti... |

95 | A Davis-Putnam program and its application to finite first-order model seach: Quasigroup existence problems
- McCune
- 1994
(Show Context)
Citation Context ...ter Optimization) , by John Slaney, Lusk, and McCune, which is a parallel version of Otter; FDB [1] (Formula DataBase), by Overbeek and Ralph Butler, which is a unification and indexing toolkit; MACE =-=[16]-=- (Models And CounterExamples) , by McCune, which searches for finite models; and EQP [18] (EQuational Prover), by McCune, a program for equational logic, which incorporates associative-commutative uni... |

77 |
Efficiency and completeness of the set of support strategy in theorem proving
- wos, Robinson, et al.
- 1965
(Show Context)
Citation Context ...d mainly of two programs. PG1 (Program 1), designed by Dan Carson, George Robinson, and Wos in 1963, had the unit preference strategy [37]; experimentation with PG1 led to the set of support strategy =-=[39]-=- and demodulation [40]. The program RG1 [38], designed by George Robinson and Wos in 1967, had binary resolution, factoring, paramodulation, demodulation, and the set of support strategy. The second g... |

36 |
The concept of demodulation in theorem proving
- wos, Robinson, et al.
- 1967
(Show Context)
Citation Context ...ms. PG1 (Program 1), designed by Dan Carson, George Robinson, and Wos in 1963, had the unit preference strategy [37]; experimentation with PG1 led to the set of support strategy [39] and demodulation =-=[40]-=-. The program RG1 [38], designed by George Robinson and Wos in 1967, had binary resolution, factoring, paramodulation, demodulation, and the set of support strategy. The second generation, started by ... |

32 |
Complexity and related enhancements for automated theorem-proving programs
- McCharen, Overbeek, et al.
- 1976
(Show Context)
Citation Context ...ng, paramodulation, demodulation, and the set of support strategy. The second generation, started by Ross Overbeek in 1970, was based on the NIUTP (Northern Illinois University Theorem Prover) series =-=[10, 11]-=-, Supported by the Mathematical, Information, and Computational Sciences Division subprogram of the Office of Computational and Technology Research, U.S. Department of Energy, under Contract W-31-109-... |

32 |
Single axioms for groups and Abelian groups with various operations
- McCune
- 1993
(Show Context)
Citation Context ...ogic final.tex; 22/11/1996; 11:29; no v.; p.2 OTTER 3 [23, 33], logic calculi with condensed detachment [25], single axioms for group calculi [12, 15], single axioms for group theory and subvarieties =-=[14, 24, 4, 2, 5]-=-, single axioms for ternary Boolean algebra [27], equational theorems about cubic curves [26], single axioms for lattice-like algebras [20], self-dual bases for groups and for lattices [21], implicati... |

27 |
The unit preference strategy in theorem proving
- Wos, Carson, et al.
- 1964
(Show Context)
Citation Context ...computer programs have been written. The first generation consisted mainly of two programs. PG1 (Program 1), designed by Dan Carson, George Robinson, and Wos in 1963, had the unit preference strategy =-=[37]-=-; experimentation with PG1 led to the set of support strategy [39] and demodulation [40]. The program RG1 [38], designed by George Robinson and Wos in 1967, had binary resolution, factoring, paramodul... |

27 | Automated Deduction in Equational Logic and Cubic Curves
- McCune, Padmanabhan
- 1996
(Show Context)
Citation Context ...) [30], equational theorems about cubic curves (with Padmanabhan) [29], single axioms for lattice-like algebras (with Padmanabhan) [22], self-dual bases for groups and for lattices (with Padmanabhan) =-=[23]-=-, implicational axioms for groups and Abelian groups (with A. D. Sands) [24], Robbins algebra (with S. Winker) [44, 20, 34], Moufang loops [23] and (Kunen) [7, 8], illiative combinatory logic (T. Jech... |

24 |
Problems and experiments for and with automated theorem proving programs
- McCharen, Overbeek, et al.
- 1976
(Show Context)
Citation Context ...ng, paramodulation, demodulation, and the set of support strategy. The second generation, started by Ross Overbeek in 1970, was based on the NIUTP (Northern Illinois University Theorem Prover) series =-=[10, 11]-=-, Supported by the Mathematical, Information, and Computational Sciences Division subprogram of the Office of Computational and Technology Research, U.S. Department of Energy, under Contract W-31-109-... |

24 | Basic test problems: A practical evaluation of some paramodulation strategies
- McCune
- 1996
(Show Context)
Citation Context ...r; FDB [1] (Formula DataBase), by Overbeek and Ralph Butler, which is a unification and indexing toolkit; MACE [16] (Models And CounterExamples) , by McCune, which searches for finite models; and EQP =-=[18]-=- (EQuational Prover), by McCune, a program for equational logic, which incorporates associative-commutative unification. Aside from effective inference rules and strategies for proving theorems, speed... |

23 | Experiments in automated deduction with condensed detachment
- McCune, Wos
- 1992
(Show Context)
Citation Context ...mples of such results are the existence of fixed point combinators in fragments of combinatory logic final.tex; 22/11/1996; 11:29; no v.; p.2 OTTER 3 [23, 33], logic calculi with condensed detachment =-=[25]-=-, single axioms for group calculi [12, 15], single axioms for group theory and subvarieties [14, 24, 4, 2, 5], single axioms for ternary Boolean algebra [27], equational theorems about cubic curves [2... |

22 |
Single axioms for groups
- Kunen
- 1992
(Show Context)
Citation Context ...ogic final.tex; 22/11/1996; 11:29; no v.; p.2 OTTER 3 [23, 33], logic calculi with condensed detachment [25], single axioms for group calculi [12, 15], single axioms for group theory and subvarieties =-=[14, 24, 4, 2, 5]-=-, single axioms for ternary Boolean algebra [27], equational theorems about cubic curves [26], single axioms for lattice-like algebras [20], self-dual bases for groups and for lattices [21], implicati... |

20 |
Experiments with discrimination tree indexing and path indexing for term retrieval
- McCune
- 1992
(Show Context)
Citation Context .... The functionality of AURA and ITP, especially the inference and search methods, was quite useful in practice, so Otter retained most of it. However, low-level algorithms such as indexing techniques =-=[13]-=- were improved, resulting in sharp speedups over ITP. Major releases of Otter occurred at CADE-9 in May 1988 (version 0.9), in January 1989 (version 1), in March 1990 (version 2), and in January 1994 ... |

20 |
Generation and verification of finite models and counterexamples using an automated theorem prover answering two open questions
- Winker
- 1982
(Show Context)
Citation Context ...sulting resolution and weighting. The result was the first practical set of programs in that their use led to answers to several open questions in equivalential calculus [41], ternary Boolean algebra =-=[30]-=- and semigroups [32]. The third generation of Argonne theorem provers, started in 1980 by Overbeek, Lusk, and McCune, consisted mostly of the LMA [9] (Logic Machine Architecture), a toolkit (written i... |

16 |
algebra: Conditions that make a near-Boolean algebra Boolean
- Robbins
- 1990
(Show Context)
Citation Context ...orems about cubic curves [26], single axioms for lattice-like algebras [20], self-dual bases for groups and for lattices [21], implicational axioms for groups and Abelian groups [22], Robbins algebra =-=[18, 31]-=-, Moufang loops [21, 6, 7], illiative combinatory logic [3], and proofs with particular properties [34, 35, 36]. 2. Architecture Otter reads an input file containing a set of formulas and some control... |

16 |
Automated reasoning contributes to mathematics and logic
- Wos, Winker, et al.
- 1990
(Show Context)
Citation Context ...th Padmanabhan) [22], self-dual bases for groups and for lattices (with Padmanabhan) [23], implicational axioms for groups and Abelian groups (with A. D. Sands) [24], Robbins algebra (with S. Winker) =-=[44, 20, 34]-=-, Moufang loops [23] and (Kunen) [7, 8], illiative combinatory logic (T. Jech) [4], and proofs with particular properties [37, 38, 39]. 2. Architecture Otter reads an input file containing a set of cl... |

15 |
Otter: An Automated Deduction
- McCune
- 1997
(Show Context)
Citation Context ...4, 24, 4, 2, 5], single axioms for ternary Boolean algebra [27], equational theorems about cubic curves [26], single axioms for lattice-like algebras [20], self-dual bases for groups and for lattices =-=[21]-=-, implicational axioms for groups and Abelian groups [22], Robbins algebra [18, 31], Moufang loops [21, 6, 7], illiative combinatory logic [3], and proofs with particular properties [34, 35, 36]. 2. A... |

14 | Single axioms for odd exponent groups
- Hart, Kunen
- 1995
(Show Context)
Citation Context ...ogic final.tex; 22/11/1996; 11:29; no v.; p.2 OTTER 3 [23, 33], logic calculi with condensed detachment [25], single axioms for group calculi [12, 15], single axioms for group theory and subvarieties =-=[14, 24, 4, 2, 5]-=-, single axioms for ternary Boolean algebra [27], equational theorems about cubic curves [26], single axioms for lattice-like algebras [20], self-dual bases for groups and for lattices [21], implicati... |

14 | Searching for Circles of Pure Proofs
- Wos
- 1995
(Show Context)
Citation Context ... for lattices [21], implicational axioms for groups and Abelian groups [22], Robbins algebra [18, 31], Moufang loops [21, 6, 7], illiative combinatory logic [3], and proofs with particular properties =-=[34, 35, 36]-=-. 2. Architecture Otter reads an input file containing a set of formulas and some control information. The set of formulas represents the theory and denial of the conclusion (all proofs are by contrad... |

13 |
Reference Manual for the Environmental Theorem Prover: An Incarnation of AURA, Argonne National Laboratory report ANL-88-2
- Smith
- 1988
(Show Context)
Citation Context ...mputational and Technology Research, U.S. Department of Energy, under Contract W-31-109-Eng-38. 2 WILLIAM McCUNE and LARRY WOS which evolved into AURA (AUtomated Reasoning Assistant) and its variants =-=[28]-=-, with contributions from Brian Smith, Rusty Lusk, Bob Veroff, Steve Winker, and Wos. The NIUTP/AURA generation (written mostly in IBM assembly language, with some PL/1) included the first high-perfor... |

13 |
Paramodulation and set of support
- Wos, Robinson
- 1968
(Show Context)
Citation Context ...esigned by Dan Carson, George Robinson, and Wos in 1963, had the unit preference strategy [37]; experimentation with PG1 led to the set of support strategy [39] and demodulation [40]. The program RG1 =-=[38]-=-, designed by George Robinson and Wos in 1967, had binary resolution, factoring, paramodulation, demodulation, and the set of support strategy. The second generation, started by Ross Overbeek in 1970,... |

12 | Automated reasoning about cubic curves
- Padmanabhan, McCune
- 1995
(Show Context)
Citation Context ...5], single axioms for group calculi [12, 15], single axioms for group theory and subvarieties [14, 24, 4, 2, 5], single axioms for ternary Boolean algebra [27], equational theorems about cubic curves =-=[26]-=-, single axioms for lattice-like algebras [20], self-dual bases for groups and for lattices [21], implicational axioms for groups and Abelian groups [22], Robbins algebra [18, 31], Moufang loops [21, ... |

12 |
A new use of an automated reasoning assistant: Open questions in equivalential calculus and the study of infinite domains
- Wos, Winker, et al.
- 1984
(Show Context)
Citation Context ...ion, and it introduced unit-resulting resolution and weighting. The result was the first practical set of programs in that their use led to answers to several open questions in equivalential calculus =-=[41]-=-, ternary Boolean algebra [30] and semigroups [32]. The third generation of Argonne theorem provers, started in 1980 by Overbeek, Lusk, and McCune, consisted mostly of the LMA [9] (Logic Machine Archi... |

11 |
Experiments with ROO, a Parallel Automated Deduction System
- Lusk, McCune
- 1992
(Show Context)
Citation Context ... our research on inference rules and search strategies. The program was later named Otter (Organized theorem-proving techniques for effective research). Other members of the fourth generation are ROO =-=[8]-=- (Radical Otter Optimization) , by John Slaney, Lusk, and McCune, which is a parallel version of Otter; FDB [1] (Formula DataBase), by Overbeek and Ralph Butler, which is a unification and indexing to... |

11 |
Automated discovery of new axiomatizations of the left group and right group calculi
- McCune
- 1992
(Show Context)
Citation Context ...e of fixed point combinators in fragments of combinatory logic final.tex; 22/11/1996; 11:29; no v.; p.2 OTTER 3 [23, 33], logic calculi with condensed detachment [25], single axioms for group calculi =-=[12, 15]-=-, single axioms for group theory and subvarieties [14, 24, 4, 2, 5], single axioms for ternary Boolean algebra [27], equational theorems about cubic curves [26], single axioms for lattice-like algebra... |

11 | Single identities for lattice theory and for weakly associative lattices
- McCune, Padmanabhan
- 1996
(Show Context)
Citation Context ...single axioms for group theory and subvarieties [14, 24, 4, 2, 5], single axioms for ternary Boolean algebra [27], equational theorems about cubic curves [26], single axioms for lattice-like algebras =-=[20]-=-, self-dual bases for groups and for lattices [21], implicational axioms for groups and Abelian groups [22], Robbins algebra [18, 31], Moufang loops [21, 6, 7], illiative combinatory logic [3], and pr... |

11 |
The Results - of the CADE-13
- Sutcliffe, Suttner
- 1997
(Show Context)
Citation Context ...es, and a weakness not evident is propositional unsatisfiability. 5. Conclusion One of the most important features of the results can be seen in the tables of runtimes for each system on each theorem =-=[29]-=-. Most of the theorems on which the top finishers failed were proved easily by at least one system. Each of the unit equality theorems was proved by at least one system, and 45 of 50 were proved in le... |

10 |
Moufang quasigroups
- Kunen
- 1996
(Show Context)
Citation Context ... [26], single axioms for lattice-like algebras [20], self-dual bases for groups and for lattices [21], implicational axioms for groups and Abelian groups [22], Robbins algebra [18, 31], Moufang loops =-=[21, 6, 7]-=-, illiative combinatory logic [3], and proofs with particular properties [34, 35, 36]. 2. Architecture Otter reads an input file containing a set of formulas and some control information. The set of f... |

10 |
Logic machine architecture: kernel functions
- Lusk, McCune, et al.
- 1982
(Show Context)
Citation Context ...ivalential calculus [41], ternary Boolean algebra [30] and semigroups [32]. The third generation of Argonne theorem provers, started in 1980 by Overbeek, Lusk, and McCune, consisted mostly of the LMA =-=[9]-=- (Logic Machine Architecture), a toolkit (written in Pascal) for building deduction systems, and ITP (Interactive Theorem Prover), constructed with LMA. The functionality of ITP was similar to that of... |

9 | Single Identities for Ternary Boolean Algebras
- Padmanabhan, McCune
- 1995
(Show Context)
Citation Context ...], logic calculi with condensed detachment [25], single axioms for group calculi [12, 15], single axioms for group theory and subvarieties [14, 24, 4, 2, 5], single axioms for ternary Boolean algebra =-=[27]-=-, equational theorems about cubic curves [26], single axioms for lattice-like algebras [20], self-dual bases for groups and for lattices [21], implicational axioms for groups and Abelian groups [22], ... |

8 | Experiments in a System of Combinatory Logic
- Jech, ‘‘OTTER
- 1995
(Show Context)
Citation Context ...gebras [20], self-dual bases for groups and for lattices [21], implicational axioms for groups and Abelian groups [22], Robbins algebra [18, 31], Moufang loops [21, 6, 7], illiative combinatory logic =-=[3]-=-, and proofs with particular properties [34, 35, 36]. 2. Architecture Otter reads an input file containing a set of formulas and some control information. The set of formulas represents the theory and... |

8 |
The absence and the presence of fixed point combinators
- McCune, Wos
- 1991
(Show Context)
Citation Context ...y new results have been obtained with its use. Examples of such results are the existence of fixed point combinators in fragments of combinatory logic final.tex; 22/11/1996; 11:29; no v.; p.2 OTTER 3 =-=[23, 33]-=-, logic calculi with condensed detachment [25], single axioms for group calculi [12, 15], single axioms for group theory and subvarieties [14, 24, 4, 2, 5], single axioms for ternary Boolean algebra [... |

8 | Applications of automated deduction to the search for single axioms for exponent groups
- McCune, Wos
- 1992
(Show Context)
Citation Context |

8 |
The kernel strategy and its use for the study of combinatory logic
- Wos
- 1993
(Show Context)
Citation Context ...y new results have been obtained with its use. Examples of such results are the existence of fixed point combinators in fragments of combinatory logic final.tex; 22/11/1996; 11:29; no v.; p.2 OTTER 3 =-=[23, 33]-=-, logic calculi with condensed detachment [25], single axioms for group calculi [12, 15], single axioms for group theory and subvarieties [14, 24, 4, 2, 5], single axioms for ternary Boolean algebra [... |

7 | The Shortest Single Axioms for Groups of Exponent 4
- Kunen
- 1995
(Show Context)
Citation Context |

6 | The power of combining resonance with heat
- Wos
- 1996
(Show Context)
Citation Context ... for lattices [21], implicational axioms for groups and Abelian groups [22], Robbins algebra [18, 31], Moufang loops [21, 6, 7], illiative combinatory logic [3], and proofs with particular properties =-=[34, 35, 36]-=-. 2. Architecture Otter reads an input file containing a set of formulas and some control information. The set of formulas represents the theory and denial of the conclusion (all proofs are by contrad... |

5 |
Paths to high-performance automated theorem proving
- Butler, Lusk, et al.
- 1986
(Show Context)
Citation Context ... that environments were omitted. The motivations for LMA and ITP were sound software engineering and portability. Several experimental theorem provers based on technology for compiling logic programs =-=[1]-=- were also part of the third generation. Otter [19] is a member of the fourth generation. We started writing code for a new theorem prover in June 1987, and by December of that year it had developed i... |

5 |
A New Class of Automated Theorem-Proving Algorithms
- Overbeek
- 1974
(Show Context)
Citation Context ..., designed by George Robinson and Wos in 1967, had binary resolution, factoring, paramodulation, demodulation, and the set of support strategy. The second generation, started by Ross Overbeek in 1970 =-=[28]-=-, was based on the NIUTP (Northern Illinois University Theorem Prover) series [12, 13], which Supported by the Mathematical, Information, and Computational Sciences Division subprogram of the Office o... |

4 |
Formula databases for high-performance resolution/paramodulation systems
- Butler, Overbeek
- 1994
(Show Context)
Citation Context ...oving techniques for effective research). Other members of the fourth generation are ROO [8] (Radical Otter Optimization) , by John Slaney, Lusk, and McCune, which is a parallel version of Otter; FDB =-=[1]-=- (Formula DataBase), by Overbeek and Ralph Butler, which is a unification and indexing toolkit; MACE [16] (Models And CounterExamples) , by McCune, which searches for finite models; and EQP [18] (EQua... |

3 |
Single axioms for the left group and right group calculi
- McCune
- 1993
(Show Context)
Citation Context ...e of fixed point combinators in fragments of combinatory logic final.tex; 22/11/1996; 11:29; no v.; p.2 OTTER 3 [23, 33], logic calculi with condensed detachment [25], single axioms for group calculi =-=[12, 15]-=-, single axioms for group theory and subvarieties [14, 24, 4, 2, 5], single axioms for ternary Boolean algebra [27], equational theorems about cubic curves [26], single axioms for lattice-like algebra... |

3 | Computer and Human Reasoning: Single Implicative Axioms for Groups and for Abelian Groups
- McCune, Sands
- 1996
(Show Context)
Citation Context ...a [27], equational theorems about cubic curves [26], single axioms for lattice-like algebras [20], self-dual bases for groups and for lattices [21], implicational axioms for groups and Abelian groups =-=[22]-=-, Robbins algebra [18, 31], Moufang loops [21, 6, 7], illiative combinatory logic [3], and proofs with particular properties [34, 35, 36]. 2. Architecture Otter reads an input file containing a set of... |

3 |
involutions: A computer solution to an open problem
- Semigroups
- 1981
(Show Context)
Citation Context ...nd weighting. The result was the first practical set of programs in that their use led to answers to several open questions in equivalential calculus [41], ternary Boolean algebra [30] and semigroups =-=[32]-=-. The third generation of Argonne theorem provers, started in 1980 by Overbeek, Lusk, and McCune, consisted mostly of the LMA [9] (Logic Machine Architecture), a toolkit (written in Pascal) for buildi... |

2 |
and the Moufang identity problem
- Otter
- 1996
(Show Context)
Citation Context ... for lattices [21], implicational axioms for groups and Abelian groups [22], Robbins algebra [18, 31], Moufang loops [21, 6, 7], illiative combinatory logic [3], and proofs with particular properties =-=[34, 35, 36]-=-. 2. Architecture Otter reads an input file containing a set of formulas and some control information. The set of formulas represents the theory and denial of the conclusion (all proofs are by contrad... |

1 |
A tutorial on the construction of high-performance resolution /paramodulation systems
- Butler, Overbeek
- 1990
(Show Context)
Citation Context ...iques for effective research) in May 1988. Other members of the fourth generation are ROO [9] (Radical Otter Optimization), by John Slaney, Lusk, and McCune, which is a parallel version of Otter; FDB =-=[2]-=- (Formula DataBase), by Overbeek and Ralph Butler, which is a unification and indexing toolkit; MACE [18] (Models And CounterExamples), by McCune, which searches for finite models; and EQP [20] (EQuat... |

1 |
ITP at Argonne National Laboratory
- Lusk, McCune, et al.
- 1986
(Show Context)
Citation Context ...e theorem provers, started in 1980 by Overbeek, Lusk, and McCune, consisted mostly of the LMA [10] (Logic Machine Architecture) , a toolkit (written in Pascal) for building deduction systems, and ITP =-=[11]-=- (Interactive Theorem Prover), constructed with LMA. The functionality of ITP was similar to that of AURA, except that environments were omitted. The motivations for LMA and ITP were sound software en... |

1 |
CADE-13 ATP system competition results. http://www.cs.jcu.edu.au/ftp/users/GSutcliffe/Competition/Results.html
- Sutcliffe, Suttner
- 1996
(Show Context)
Citation Context ...weakness not evident is, of course, propositional satisfiability. 5. Conclusion One of the most important features of the results can be seen in the tables of runtimes for each system on each theorem =-=[32]-=-. Most of the theorems on which the top finishers failed were proved easily by at least one system. Each of the unit equality theorems was proved by at least one system, and 45 of 50 were proved in le... |

1 |
The power of combining reasonance with heat
- Wos
- 1996
(Show Context)
Citation Context ... groups (with A. D. Sands) [24], Robbins algebra (with S. Winker) [44, 20, 34], Moufang loops [23] and (Kunen) [7, 8], illiative combinatory logic (T. Jech) [4], and proofs with particular properties =-=[37, 38, 39]-=-. 2. Architecture Otter reads an input file containing a set of clauses and some control information. The set of clauses represents the theory and denial of the conclusion (all proofs are by contradic... |