Consider the following premises. For all x_2, x_2 is not a lawyer. There is at least one x_2 for which if x_2 were a writer, then x_2 is a lawyer. For all x_2, if x_2 plays squash, then x_2 is a writer. Can we infer the following from them? If we can, name the inference rule being used: For all x_2, x_2 will play squash.
 From the fact that for all x_2, if x_2 plays squash, then x_2 is a writer, and that there is at least one x_2 for which if x_2 were a writer, then x_2 is a lawyer we can infer that there is at least one x_2 for which if x_2 plays squash, then x_2 is a lawyer via existential transitivity. Finally, from the fact that there is at least one x_2 for which if x_2 plays squash, then x_2 is a lawyer, and that for all x_2, x_2 is not a lawyer we can infer that there is at least one x_2 for which x_2 will not play squash via existential modus tollens, which contradicts that For all x_2, x_2 will play squash. Therefore, the answer is no.