On the consistency of Chisholm's axioms of epistemic logic

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In the opening chapters of (Chisholm, 1977) and (Chisholm, 1982), Chisholm sketches an account of some basic concepts of epistemic justification in terms of the relation `P is more reasonable than Q' (suppressing references to epistemic agents and moments of time since they are not relevant for my purposes here), where P and Q are (roughly) propositional attitudes logically built from the primitives `believing p' and `withholding p', for any proposition p. In particular, Chisholm gives several axioms for the logic of this relation. My purpose here is to prove that these axioms are inconsistent.