Consider the following premises. For all x_8, if x_8 were a nurse, then x_8 is a soldier. There is at least one x_8 for which x_8 is a nurse or x_8 will not climb a mountain. For all x_8, if x_8 were a writer, then x_8 is climbing a mountain. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_8 for which if x_8 were a writer, then x_8 is a soldier.
 From the fact that there is at least one x_8 for which x_8 is a nurse or x_8 will not climb a mountain we can infer that there is at least one x_8 for which if x_8 climbs a mountain, then x_8 is a nurse via existential rewriting. From the fact that there is at least one x_8 for which if x_8 climbs a mountain, then x_8 is a nurse, and that for all x_8, if x_8 were a nurse, then x_8 is a soldier we can infer that there is at least one x_8 for which if x_8 climbs a mountain, then x_8 is a soldier via existential transitivity. Finally, from the fact that for all x_8, if x_8 were a writer, then x_8 is climbing a mountain, and that there is at least one x_8 for which if x_8 climbs a mountain, then x_8 is a soldier we can infer that there is at least one x_8 for which if x_8 were a writer, then x_8 is a soldier via existential transitivity. Therefore, the answer is yes.