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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 55 (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.
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 &qu ..."
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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
Experiments in the Heuristic Use of Past Proof Experience
 Proc. CADE13
, 1996
"... Problems stemming from the study of logic calculi in connection with an inference rule called "condensed detachment" are widely acknowledged as prominent test sets for automated deduction systems and their search guiding heuristics. It is in the light of these problems that we demonstrate ..."
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Cited by 16 (4 self)
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Problems stemming from the study of logic calculi in connection with an inference rule called "condensed detachment" are widely acknowledged as prominent test sets for automated deduction systems and their search guiding heuristics. It is in the light of these problems that we demonstrate the power of heuristics that make use of past proof experience with numerous experiments. We present two such heuristics. The first heuristic attempts to reenact a proof of a proof problem found in the past in a flexible way in order to find a proof of a similar problem. The second heuristic employs "features" in connection with past proof experience to prune the search space. Both these heuristics not only allow for substantial speedups, but also make it possible to prove problems that were out of reach when using socalled basic heuristics. Moreover, a combination of these two heuristics can further increase performance. We compare our results with the results the creators of Otter obtained with t...
Combining Hilbert Style and Semantic Reasoning in a Resolution Framework
 In Proc. CADE15, LNAI 1421
, 1998
"... Many nonclassical logics can be axiomatized by means of Hilbert Systems. Reasoning in Hilbert Systems, however, is extremely inefficient. Most inference methods therefore use the semantics of a logic in one kind or another to get more efficiency. In this paper a combination of Hilbert style and sem ..."
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Many nonclassical logics can be axiomatized by means of Hilbert Systems. Reasoning in Hilbert Systems, however, is extremely inefficient. Most inference methods therefore use the semantics of a logic in one kind or another to get more efficiency. In this paper a combination of Hilbert style and semantic reasoning is proposed. It is particularly tailored for cases where either the semantics of some operators is not known, or it is secondorder, or it is just too complicated to handle, or flexibility in experimenting with different versions of a logic is required. Firstorder predicate logic is used as a metalogic for combining the Hilbert part with the semantics part. Reasoning is done in a (theory) resolution framework. The basic method is applicable to many different (monotonic propositional) nonclassical logics. It can, however, be improved by treating particular formulae in a special way, as rewrite rules, as theory unification or t...
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 ...
Application of Automated Deduction to the Search for Single Axioms for Exponent Groups
 in Logic Programming and Automated Reasoning
, 1995
"... We present new results in axiomatic group theory obtained by using automated deduction programs. The results include single axioms, some with the identity and others without, for groups of exponents 3, 4, 5, and 7, and a general form for single axioms for groups of odd exponent. The results were obt ..."
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We present new results in axiomatic group theory obtained by using automated deduction programs. The results include single axioms, some with the identity and others without, for groups of exponents 3, 4, 5, and 7, and a general form for single axioms for groups of odd exponent. The results were obtained by using the programs in three separate ways: as a symbolic calculator, to search for proofs, and to search for counterexamples. We also touch on relations between logic programmingand automated reasoning. 1 Introduction A group of exponent n is a group in which for all elements x, x n is the identity e. Groups of exponent 2, xx = e, are also called Boolean groups. A single axiom for an equational theory is an equality from which the entire theory can be derived by equational reasoning. We are concerned with single axioms for groups of exponent n, n 2. B. H. Neumann [6, p.83] gives a general form for single axioms for certain subvarieties of groups, including exponent groups. The a...
The power of combining resonance with heat
 J. Automated Reasoning
, 1996
"... In this article, I present experimental evidence of the value of combining two strategies each of which has proved powerful in various contexts. The resonance strategy gives preference (for directing a program’s reasoning) to equations or formulas that have the same shape (ignoring variables) as one ..."
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Cited by 6 (5 self)
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In this article, I present experimental evidence of the value of combining two strategies each of which has proved powerful in various contexts. The resonance strategy gives preference (for directing a program’s reasoning) to equations or formulas that have the same shape (ignoring variables) as one of the patterns supplied by the researcher to be used as a resonator. The hot list strategy rearranges the order in which conclusions are drawn, the rearranging caused by immediately visiting and, depending on the value of the heat parameter, even immediately revisiting a set of input statements chosen by the researcher; the chosen statements are used to complete applications of inference rules rather than to initiate them. Combining these two strategies often enables an automated reasoning program to attack deep questions and hard problems with far more effectiveness than using either alone. The use of this combination in the context of cursory proof checking produced most unexpected and satisfying results, as I show here. I present the material (including commentary) in the spirit of excerpts from an experimenter’s notebook, thus meeting the frequent request to illustrate how a researcher can make wise choices from among the numerous options offered by McCune’s automated reasoning program OTTER. I include challenges and topics for research and, to aid the researcher, in the Appendix a sample input
Computer Support for the Development and Investigation of Logics
, 1996
"... The development and investigation of applicationoriented logics comprises many aspects and problems. For a few of them some computer support is possible which frees the investigator from sometimes quite complex computations. This paper gives an overview about some developments in this area. In par ..."
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Cited by 5 (0 self)
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The development and investigation of applicationoriented logics comprises many aspects and problems. For a few of them some computer support is possible which frees the investigator from sometimes quite complex computations. This paper gives an overview about some developments in this area. In particular, we consider the correspondences between axiomatic and semantic specifications of a logic and the problem of finding one from the other by means of automated theorem provers and quantifier elimination algorithms. Other topics adressed in this paper are reasoning in Hilbert systems, the investigation of the expressiveness of a logic and the axiomatizability of semantic conditions. For the technical details of the methods and the proofs I refer to the original papers.