Consider the following premises. For all x_10, if x_10 climbs a mountain, then x_10 is a poet. For all x_10, x_10 will climb a mountain. There is at least one x_10 for which if x_10 were a poet, then x_10 is a soldier. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_10 for which x_10 is a soldier or x_10 is an astronaut.
 From the fact that for all x_10, if x_10 climbs a mountain, then x_10 is a poet, and that for all x_10, x_10 will climb a mountain we can infer that for all x_10, x_10 is a poet via universal modus ponens. From the fact that there is at least one x_10 for which if x_10 were a poet, then x_10 is a soldier, and that for all x_10, x_10 is a poet we can infer that there is at least one x_10 for which x_10 is a soldier via existential modus ponens. Finally, from the fact that there is at least one x_10 for which x_10 is a soldier we can infer that there is at least one x_10 for which x_10 is a soldier or x_10 is an astronaut via existential addition. Therefore, the answer is yes.