Ernst, Fitelson, Harris, and Wos [A
concise axiomatization of RM_{→},
Bulletin of the Section of Logic
(University of Lódź), vol. 30 (2001), pp. 191194] discovered two threebases for the implicational fragment of
Dunn's system RMingle, {CCpqCCqrCpr, CpCCpqq,
CCCCCpqrCqprr} and
{CCpqCCqrCpr, CpCCpqq, CCCpCCCqprqrr}.
Each of their bases has a total
length of 31 (counting occurrences of sentential variables and of the
connective). Wos later asks [as Open Question OQ29.RM in L. Wos and G. Pieper, Automated Reasoning and the Discovery of Missing and Elegant Proofs, Rinton Press, Paramus, 2003] if there exists an equivalent twobase, and [as Open Question OQ30.RM] if there exists a single axiom for this system. 

ANSWER TO OQ29.RM
CCCCpqqrCCrsCps 

© Dolph Ulrich, 2007 Entrance page  Home page  Twentysix open questions  Single axioms for:

BCI 
4 subsystems of BCI 
monothetic BCI 
Cpure R 
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Cpure
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