Consider the following premises. For all x_6, if x_6 were curious, then x_6 is climbing a mountain. For all x_6, x_6 is curious. There is at least one x_6 for which if x_6 goes running, then x_6 is not listening to a song. For all x_6, x_6 will listen to a song. 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 will not go running.
 From the fact that for all x_6, if x_6 were curious, then x_6 is climbing a mountain, and that for all x_6, x_6 is curious we can infer that for all x_6, x_6 will climb a mountain via universal modus ponens. From the fact that for all x_6, x_6 will listen to a song, and that for all x_6, x_6 will climb a mountain we can infer that for all x_6, x_6 will listen to a song and x_6 will climb a mountain via universal conjunction. From the fact that for all x_6, x_6 will listen to a song and x_6 will climb a mountain we can infer that for all x_6, x_6 will listen to a song via universal simplification. Finally, from the fact that there is at least one x_6 for which if x_6 goes running, then x_6 is not listening to a song, and that for all x_6, x_6 will listen to a song we can infer that there is at least one x_6 for which x_6 will not go running via existential modus tollens. Therefore, the answer is yes.