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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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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 concerning the Automated Search for Elegant Proofs
 Technical Memorandum ANL/MCSTM221, Mathematics and Computer Science Division, Argonne National Laboratory
, 1997
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Experiments with the Hot List Strategy
 Technical Memorandum ANL/MCSTM232, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne
, 1997
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Communications of the ACM (to appear 1997) Also Preprint ANL/MCSP6550397 Programs That Offer Fast, Flawless, Logical Reasoning*
"... Sherlock Holmes and Mr. Spock of Star Trek could reason logically and flawlessly, always. Some people you know have that ability, sometimes. Unfortunately, without perfect reasoning, diverse problems arise: � Bugs in computer programs. If a sort program places Sun before Intel, more than disappointm ..."
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Sherlock Holmes and Mr. Spock of Star Trek could reason logically and flawlessly, always. Some people you know have that ability, sometimes. Unfortunately, without perfect reasoning, diverse problems arise: � Bugs in computer programs. If a sort program places Sun before Intel, more than disappointment is experienced. � Flaws in chip design. One Pentium chip became famous because of a flaw. � Errors in mathematical proofs. Papers having a title of the form ‘‘On an Error by MacLane’ ’ are well remembered, but not with pleasure (at least by MacLane). How can the likelihood of the various cited disasters be reduced? One answer is automated reasoning. (For further information on automated reasoning at Argonne National Laboratory, see
Universitaet Leipzig
"... Throughout the twentieth century, the worlds of logic and mathematics were well aware of Hilbert’s twentythree problems and the challenge they offered. Although not known until very recently, there existed yet one more challenge offered by Hilbert, his twentyfourth problem. This problem focuses on ..."
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Throughout the twentieth century, the worlds of logic and mathematics were well aware of Hilbert’s twentythree problems and the challenge they offered. Although not known until very recently, there existed yet one more challenge offered by Hilbert, his twentyfourth problem. This problem focuses on finding simpler proofs, on the criteria for measuring simplicity, and on the ‘‘development of a theory of the method of proof in mathematics in general’’. Of the three themes of Hilbert’s twentyfourth problem, the first two are central to this article. We visit various areas of logic, showing that some of the studies of the masters are indeed strongly connected to this newly discovered problem. We also demonstrate that the use of an automated reasoning program (specifically, W. McCune’s OTTER) enables one to address this challenging problem. We offer questions that remain unanswered.