Consider the following premises. For all x_5, if x_5 sleeps, then x_5 is running. For all x_5, if x_5 goes running, then x_5 is a sailor. For all x_5, if x_5 were a sailor, then x_5 is listening to a song. There is at least one x_5 for which x_5 will not listen to a song. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, x_5 will sleep.
 From the fact that for all x_5, if x_5 sleeps, then x_5 is running, and that for all x_5, if x_5 goes running, then x_5 is a sailor we can infer that for all x_5, if x_5 sleeps, then x_5 is a sailor via universal transitivity. From the fact that for all x_5, if x_5 sleeps, then x_5 is a sailor, and that for all x_5, if x_5 were a sailor, then x_5 is listening to a song we can infer that for all x_5, if x_5 sleeps, then x_5 is listening to a song via universal transitivity. Finally, from the fact that for all x_5, if x_5 sleeps, then x_5 is listening to a song, and that there is at least one x_5 for which x_5 will not listen to a song we can infer that there is at least one x_5 for which x_5 will not sleep via existential modus tollens, which contradicts that For all x_5, x_5 will sleep. Therefore, the answer is no.