Consider the following premises. For all x_12, x_12 will climb a mountain and x_12 is a carpenter. For all x_12, x_12 will make tea. There is at least one x_12 for which if x_12 makes tea, then x_12 is running. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_12 for which x_12 will go running and x_12 will climb a mountain.
 From the fact that for all x_12, x_12 will climb a mountain and x_12 is a carpenter we can infer that for all x_12, x_12 will climb a mountain via universal simplification. From the fact that there is at least one x_12 for which if x_12 makes tea, then x_12 is running, and that for all x_12, x_12 will make tea we can infer that there is at least one x_12 for which x_12 will go running via existential modus ponens. Finally, from the fact that there is at least one x_12 for which x_12 will go running, and that for all x_12, x_12 will climb a mountain we can infer that there is at least one x_12 for which x_12 will go running and x_12 will climb a mountain via existential conjunction. Therefore, the answer is yes.