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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 44 (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 43 (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.
33 Basic Test Problems: A Practical Evaluation of Some Paramodulation Strategies
, 1996
"... Introduction Many researchers who study the theoretical aspects of inference systems believe that if inference rule A is complete and more restrictive than inference rule B, then the use of A will lead more quickly to proofs than will the use of B. The literature contains statements of the sort "ou ..."
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Cited by 24 (5 self)
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Introduction Many researchers who study the theoretical aspects of inference systems believe that if inference rule A is complete and more restrictive than inference rule B, then the use of A will lead more quickly to proofs than will the use of B. The literature contains statements of the sort "our rule is complete and it heavily prunes the search space; therefore it is efficient". 2 These positions are highly questionable and indicate that the authors have little or no experience with the practical use of automated inference systems. Restrictive rules (1) can block short, easytofind proofs, (2) can block proofs involving simple clauses, the type of clause on which many practical searches focus, (3) can require weakening of redundancy control such as subsumption and demodulation, and (4) can require the use of complex checks in deciding whether such rules should be applied. The only way to determ
Automated reasoning: Real uses and . . .
"... An automated reasoning program has provided invaluable assistance in answering certain previously open questions in mathematics and in formal logic. These questions would not have been answered, at least by those who obtained the results, were it not for the program's contribution. Others have used ..."
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An automated reasoning program has provided invaluable assistance in answering certain previously open questions in mathematics and in formal logic. These questions would not have been answered, at least by those who obtained the results, were it not for the program's contribution. Others have used such a program to design logic circuits, many of which proved superior (with respect to transistor count) to the existing designs, and to validate the design of other circuits. These successes establish the value of an automated reasoning program for research and suggest the value for practical applications. We thus conclude that the field of automated reasoning is on the verge of becoming one of the more significant branches of computer science. Further, we conclude that the field has already advanced from stage 1, that of potential usefulness, to stage 2, that of actual usefulness. To pass to stage 3, that of wide acceptance and use, requires, among other things, easy access to an automated reasoning program and an understanding of the various aspects of automated reasoning. In fact, an automated reasoning program is available that is portable and can be run on relatively inexpensive machines. Moreover, a system exists for producing a reasoning program tailored to given specifications. As for the requirement of understanding the aspects of automated reasoning, much research remainsâ€”research aided by access to a reasoning program. A large obstacle has thus been removed, permitting many to experiment with and find uses for a computer program that can be relied upon as a most valuable automated reasoning assistant.
New Implementation Framework for SaturationBased Reasoning
, 2006
"... Abstract. The saturationbased reasoning methods are among the most theoretically developed ones and are used by most of the stateoftheart firstorder logic reasoners. In the last decade there was a sharp increase in performance of such systems, which I attribute to the use of advanced calculi an ..."
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Abstract. The saturationbased reasoning methods are among the most theoretically developed ones and are used by most of the stateoftheart firstorder logic reasoners. In the last decade there was a sharp increase in performance of such systems, which I attribute to the use of advanced calculi and the intensified research in implementation techniques. However, nowadays we are witnessing a slowdown in performance progress, which may be considered as a sign that the saturationbased technology is reaching its inherent limits. The position I am trying to put forward in this paper is that such scepticism is premature and a sharp improvement in performance may potentially be reached by adopting new architectural principles for saturation. The toplevel algorithms and corresponding designs used in the stateoftheart saturationbased theorem provers have (at least) two inherent drawbacks: the insufficient flexibility of the used inference selection mechanisms and the lack of means for intelligent prioritising of search directions. In this position paper I analyse these drawbacks and present two ideas on how they could be overcome. In particular, I propose a flexible lowcost highprecision mechanism for inference selection, intended to overcome problems associated with the currently used instances of clause selectionbased procedures. I also outline a method for intelligent prioritising of search directions, based on probing the search space by exploring generalised search directions. I discuss some technical issues related to implementation of the proposed architectural principles and outline possible solutions. 1