Consider the following premises. For all x_1, if x_1 were a writer, then x_1 is a poet. There is at least one x_1 for which if x_1 were a carpenter, then x_1 is a poet. For all x_1, x_1 is a carpenter. Can we infer the following from them? If we can, name the inference rule being used: For all x_1, x_1 is not a poet.
 From the fact that for all x_1, x_1 is a carpenter we can infer that for all x_1, x_1 is a carpenter or x_1 is a writer via universal addition. Finally, from the fact that there is at least one x_1 for which if x_1 were a carpenter, then x_1 is a poet, that for all x_1, if x_1 were a writer, then x_1 is a poet, and that for all x_1, x_1 is a carpenter or x_1 is a writer we can infer that there is at least one x_1 for which x_1 is a poet via existential disjunction elimination, which contradicts that For all x_1, x_1 is not a poet. Therefore, the answer is no.