Consider the following premises. For all x_6, x_6 is fast or x_6 is a sailor. For all x_6, if x_6 were fast, then x_6 is playing squash. There is at least one x_6 for which if x_6 plays squash, then x_6 is a writer. For all x_6, if x_6 were a police officer, then x_6 is a writer. For all x_6, if x_6 were a sailor, then x_6 is a police officer. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_6 for which x_6 is a writer.
 From the fact that for all x_6, if x_6 were a sailor, then x_6 is a police officer, and that for all x_6, if x_6 were a police officer, then x_6 is a writer we can infer that for all x_6, if x_6 were a sailor, then x_6 is a writer via universal transitivity. From the fact that for all x_6, if x_6 were fast, then x_6 is playing squash, and that there is at least one x_6 for which if x_6 plays squash, then x_6 is a writer we can infer that there is at least one x_6 for which if x_6 were fast, then x_6 is a writer via existential transitivity. Finally, from the fact that there is at least one x_6 for which if x_6 were fast, then x_6 is a writer, that for all x_6, if x_6 were a sailor, then x_6 is a writer, and that for all x_6, x_6 is fast or x_6 is a sailor we can infer that there is at least one x_6 for which x_6 is a writer via existential disjunction elimination. Therefore, the answer is yes.