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Automated and human proofs in general mathematics: An initial comparison
 Logic for Programming, Artificial Intelligence, and Reasoning (LPAR18), Lecture Notes in Computer Science
, 2012
"... Abstract. Firstorder translations of large mathematical repositories allow discovery of new proofs by automated reasoning systems. Large amounts of available mathematical knowledge can be reused by combined AI/ATP systems, possibly in unexpected ways. But automated systems can be also more easi ..."
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Abstract. Firstorder translations of large mathematical repositories allow discovery of new proofs by automated reasoning systems. Large amounts of available mathematical knowledge can be reused by combined AI/ATP systems, possibly in unexpected ways. But automated systems can be also more easily misled by irrelevant knowledge in this setting, and finding deeper proofs is typically more difficult. Both largetheory AI/ATP methods, and translation and datamining techniques of large formal corpora, have significantly developed recently, providing enough data for an initial comparison of the proofs written by mathematicians and the proofs found automatically. This paper describes such an initial experiment and comparison conducted over the 50000 mathematical theorems from the Mizar Mathematical Library.
Automated Proof Compression by Invention of New Definitions
"... Stateoftheart automated theorem provers (ATPs) are today able to solve relatively complicated mathematical problems. But as ATPs become stronger and more used by mathematicians, the length and human unreadability of the automatically found proofs become a serious problem for the ATP users. One re ..."
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Stateoftheart automated theorem provers (ATPs) are today able to solve relatively complicated mathematical problems. But as ATPs become stronger and more used by mathematicians, the length and human unreadability of the automatically found proofs become a serious problem for the ATP users. One remedy is automated proof compression by invention of new definitions. We propose a new algorithm for automated compression of arbitrary sets of terms (like mathematical proofs) by invention of new definitions, using a heuristics based on substitution trees. The algorithm has been implemented and tested on a number of automatically found proofs. The results of the tests are included. 1 Introduction, motivation, and related work Stateoftheart automated theorem provers (ATPs) are today able to solve relatively complicated mathematical problems [McC97], [PS08], and are becoming a standard part of interactive theorem provers and verification tools [MP08], [Urb08]. But as ATPs become stronger and more used by mathematicians, understanding and refactoring the automatically found proofs becomes more and more important.
Automated theorem proving in quasigroup and loop theory
 NORTHERN MICHIGAN UNIVERSITY, MARQUETTE, MI 49855 USA
"... We survey all known results in the area of quasigroup and loop theory to have been obtained with the assistance of automated theorem provers. We provide both informal and formal descriptions of selected problems, and compare the performance of selected stateofthe art first order theorem provers on ..."
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We survey all known results in the area of quasigroup and loop theory to have been obtained with the assistance of automated theorem provers. We provide both informal and formal descriptions of selected problems, and compare the performance of selected stateofthe art first order theorem provers on them. Our analysis yields some surprising results, e.g., the theorem prover most often used by loop theorists does not necessarily yield the best performance.
Using Automated Theorem Provers in Nonassociative Algebra
"... We present a case study on how mathematicians use automated theorem provers to solve open problems in (nonassociative) algebra. 1 ..."
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We present a case study on how mathematicians use automated theorem provers to solve open problems in (nonassociative) algebra. 1
MULTIOUTPUT RANKING FOR AUTOMATED REASONING
"... The following full text is a preprint version which may differ from the publisher's version. ..."
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The following full text is a preprint version which may differ from the publisher's version.