Consider the following premises. For all x, x is a poet if and only if x will read a book. Robert is a poet if and only if Robert is reading a book. Robert is not reading a book. Can we infer the following from them? If we can, name the inference rule being used: Robert is a poet.
 From the fact that for all x, x is a poet if and only if x will read a book we can infer that Robert is a poet if and only if Robert is reading a book via universal instantiation. From the fact that Robert is a poet if and only if Robert is reading a book we can infer that if Robert were a poet, then Robert is reading a book via biconditional elimination. From the fact that Robert is a poet if and only if Robert is reading a book we can infer that if Robert reads a book, then Robert is a poet via biconditional elimination. From the fact that if Robert reads a book, then Robert is a poet, and that if Robert were a poet, then Robert is reading a book we can infer that Robert is reading a book if and only if Robert is a poet via biconditional introduction. Finally, from the fact that Robert is reading a book if and only if Robert is a poet, and that Robert is not reading a book we can infer that Robert is not a poet via biconditional elimination, which contradicts that Robert is a poet. Therefore, the answer is no.