Consider the following premises. There is at least one x for which if x were a nurse, then x is running. For all x, x will listen to a song or x is a nurse. For all x, if x goes running, then x is listening to a song. For all x, if x listens to a song, then x is running. Can we infer the following from them? If we can, name the inference rule being used: For all x, x will not go running.
 From the fact that for all x, if x listens to a song, then x is running, and that for all x, if x goes running, then x is listening to a song we can infer that for all x, x will listen to a song if and only if x will go running via universal biconditional introduction. From the fact that for all x, x will listen to a song if and only if x will go running we can infer that for all x, if x listens to a song, then x is running via universal biconditional elimination. Finally, from the fact that for all x, if x listens to a song, then x is running, that there is at least one x for which if x were a nurse, then x is running, and that for all x, x will listen to a song or x is a nurse we can infer that there is at least one x for which x will go running via existential disjunction elimination, which contradicts that For all x, x will not go running. Therefore, the answer is no.