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**1 - 1**of**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 long-standing 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