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33
Otter: The CADE13 Competition Incarnations
 JOURNAL OF AUTOMATED REASONING
, 1997
"... This article discusses the two incarnations of Otter entered in the CADE13 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. ..."
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Cited by 50 (3 self)
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This article discusses the two incarnations of Otter entered in the CADE13 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.
Experiments with DiscriminationTree Indexing and Path Indexing for Term Retrieval
 JOURNAL OF AUTOMATED REASONING
, 1990
"... This article addresses the problem of indexing and retrieving firstorder predicate calculus terms in the context of automated deduction programs. The four retrieval operations of concern are to find variants, generalizations, instances, and terms that unify with a given term. Discriminationtree ..."
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Cited by 47 (0 self)
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This article addresses the problem of indexing and retrieving firstorder predicate calculus terms in the context of automated deduction programs. The four retrieval operations of concern are to find variants, generalizations, instances, and terms that unify with a given term. Discriminationtree indexing is reviewed, and several variations are presented. The pathindexing method is also reviewed. Experiments were conducted on large sets of terms to determine how the properties of the terms affect the performance of the two indexing methods. Results of the experiments are presented.
Solving Open Questions and Other Challenge Problems Using Proof Sketches
, 2001
"... . In this article, we describe a set of procedures and strategies for searching for proofs in logical systems based on the inference rule condensed detachment. The procedures and strategies rely on the derivation of proof sketchessequences of formulas that are used as hints to guide the search for ..."
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Cited by 29 (14 self)
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. In this article, we describe a set of procedures and strategies for searching for proofs in logical systems based on the inference rule condensed detachment. The procedures and strategies rely on the derivation of proof sketchessequences of formulas that are used as hints to guide the search for sound proofs. In the simplest case, a proof sketch consists of a subproofkey lemmas to prove, for exampleand the proof is completed by lling in the missing steps. In the more general case, a proof sketch consists of a sequence of formulas sucient to nd a proof, but it may include formulas that are not provable in the current theory. We nd that even in this more general case, proof sketches can provide valuable guidance in nding sound proofs. Proof sketches have been used successfully for numerous problems coming from a variety of problem areas. We have, for example, used proof sketches to nd several new twoaxiom systems for Boolean algebra using the Sheer stroke. Keywords: proof sk...
Searching for Circles of Pure Proofs
, 1995
"... hen given a set of properties or conditions (say, three) that are claimed to be equivalent, the claim e s can be verified by supplying what we call a circle of proofs. In the case in point, one proves th econd property or condition from the first, the third from the second, and the first from the ..."
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Cited by 14 (9 self)
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hen given a set of properties or conditions (say, three) that are claimed to be equivalent, the claim e s can be verified by supplying what we call a circle of proofs. In the case in point, one proves th econd property or condition from the first, the third from the second, and the first from the third. If r s the proof that 1 implies 2 does not rely on 3, then we say that the proof is pure with respect to 3, o imply say the proof is pure. If one can renumber the three properties or conditions in such a way that t one can find a circle of three pure proofstechnically, each proof pure with respect to the condition hat is neither the hypothesis nor the conclusionthen we say that a circle of pure proofs has been n s found. Here we study the specific question of the existence of a circle of pure proofs for the thirtee hortest single axioms for equivalential calculus, subject to the requirement that condensed detachment t be used as the rule of inference. For an indication of ...
A Heterogeneous Parallel Deduction System
 In Proc. FGCS'92 Workshop W3
, 1992
"... This paper describes the architecture, implementation and performance, of a heterogeneous parallel deduction system (HPDS). The HPDS uses multiple deduction components, each of which attempts to find a refutation of the same input set, but using different deduction formats. The components cooperate ..."
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This paper describes the architecture, implementation and performance, of a heterogeneous parallel deduction system (HPDS). The HPDS uses multiple deduction components, each of which attempts to find a refutation of the same input set, but using different deduction formats. The components cooperate by distributing clauses they generate to other components. The HPDS has been implemented in PrologDLinda. PrologDLinda provides appropriate data transfer and synchronisation facilities for implementing parallel deduction systems. The performance of the HPDS has been investigated. Parallel Deduction Systems A parallel deduction system is one in which multiple deduction components run in parallel on separate processors. This is distinct from those deduction systems which run multiple deduction components alternately, such as the unit preference system [Wos, Carlson & Robinson#G.A.,#1964], and those which are only conceptually parallel systems. Parallel deduction systems can be categorised ...
A Shortest 2Basis for Boolean Algebra in Terms of the Sheffer Stroke
 J. Automated Reasoning
, 2003
"... In this article, we present a short 2basis for Boolean algebra in terms of the Sheffer stroke and prove that no such 2basis can be shorter. We also prove that the new 2basis is unique (for its length) up to applications of commutativity. Our proof of the 2basis was found by using the method of p ..."
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Cited by 9 (6 self)
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In this article, we present a short 2basis for Boolean algebra in terms of the Sheffer stroke and prove that no such 2basis can be shorter. We also prove that the new 2basis is unique (for its length) up to applications of commutativity. Our proof of the 2basis was found by using the method of proof sketches and relied on the use of an automated reasoning program.
Automated Reasoning and Bledsoe's Dream for the Field
"... In one sense, this article is a personal tribute to Woody Bledsoe. As such, the style will in general be that of private correspondence. However, since this article is also a compendium of experiments with an automated reasoning program, researchers interested in automated reasoning, mathematics, an ..."
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In one sense, this article is a personal tribute to Woody Bledsoe. As such, the style will in general be that of private correspondence. However, since this article is also a compendium of experiments with an automated reasoning program, researchers interested in automated reasoning, mathematics, and logic will find pertinent material here. The results of those experiments strongly suggest that research frequently benefits greatly from the use of an automated reasoning program. As evidence, I select from those results some proofs that are better than one can find in the literature, and focus on some theorems that, until now, had never been proved with an automated reasoning program, theorems that Hilbert, Church, and various logicians thought significant. To add spice to the article, I present challenges for reasoning programs, including questions that are still open. 1 This work was supported by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Depa...