Does Protagoras refute himself?

Classical Quarterly 45 (02):333- (1995)
Protagoras believes that all beliefs are true. Since Protagoras' belief that all beliefs are true is itself a belief, it follows from Protagoras' belief that all beliefs are true that Protagoras' belief is true. But what about the belief that Protagoras' belief is false? Doesn't it follow, by parallel reasoning and not at all trivially, that if all beliefs are true and there is a belief that Protagoras' belief is false, then Protagoras' belief is false?
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James Haden (1984). Did Plato Refute Protagoras? History of Philosophy Quarterly 1 (3):225 - 240.

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