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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
fitelson.org Presented @ Berkeley 03/21/03 Branden Fitelson Recent Results Obtained Via Automated Reasoning 3
, 2003
"... Equational Bases for BA in + and n II • In 1979, Steve Winker, a student visiting Argonne, learned of the Robbins problem from Joel Berman. He and Larry Wos began to attack the problem. • Larry Wos suggested looking for properties that force Robbins algebras to be Boolean. Winker [52] ingeniously fo ..."
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Equational Bases for BA in + and n II • In 1979, Steve Winker, a student visiting Argonne, learned of the Robbins problem from Joel Berman. He and Larry Wos began to attack the problem. • Larry Wos suggested looking for properties that force Robbins algebras to be Boolean. Winker [52] ingeniously found several such conditions (both “hand” and automated reasoning), including the following two relatively weak ones: 1. ∃c∃d(c + d = c) 2. ∃c∃d(n(c + d) = n(c)) • In 1996, Bill McCune [22] used an Argonne TP (EQP [21], a cousin of OTTER [20]) to prove that all Robbins algebras satisfy Winker’s (2), above. • This solved the longstanding Robbins problem. But, the machine proof of Winker’s condition was not very easy for a human to follow or understand. • Since McCune’s discovery, several people (including myself [7]) have tried, in various ways, to make the EQP (and OTTER) proofs easier to digest [3]. fitelson.org Presented @ Berkeley 03/21/03