None of us have read this book ( correct the sentence )

None of us have read this book ( correct the sentence )

not one of us does read this book!!
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"Does" because none is a shorter form of 'no one' or 'not one'.
If you substitute in "not one" for "none", you'll find that "not one of us does" makes more sense than "not one of us do".

But this is formal English, most people say "do", only editors and pedants will put none as singular.