Consider the following premises. For all x_10, x_10 is a poet. For all y_2, y_2 will cook. Can we infer the following from them? If we can, name the inference rule being used: For all y_2, either y_2 is a poet or y_2 will cook are not true.
 From the fact that for all x_10, x_10 is a poet we can infer that Barbara is a poet via universal instantiation. From the fact that Barbara is a poet we can infer that there is at least one y_2 for which y_2 is a poet via existential generalization. Finally, from the fact that there is at least one y_2 for which y_2 is a poet, and that for all y_2, y_2 will cook we can infer that some poets will cook via existential conjunction, which contradicts that For all y_2, either y_2 is a poet or y_2 will cook are not true. Therefore, the answer is no.