Consider the following premises. For all x, x will not read a book or x is an electrician. There is at least one x for which x will read a book or x will climb a mountain. For all x, if x were an electrician, then x is listening to a song. For all x, if x climbs a mountain, then x is listening to a song. For all x, if x listens to a song, then x is sad. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x for which x is sad.
 From the fact that there is at least one x for which x will read a book or x will climb a mountain, and that for all x, x will not read a book or x is an electrician we can infer that there is at least one x for which x will climb a mountain or x is an electrician via existential resolution. From the fact that for all x, if x climbs a mountain, then x is listening to a song, that for all x, if x were an electrician, then x is listening to a song, and that there is at least one x for which x will climb a mountain or x is an electrician we can infer that there is at least one x for which x will listen to a song via existential disjunction elimination. Finally, from the fact that for all x, if x listens to a song, then x is sad, and that there is at least one x for which x will listen to a song we can infer that there is at least one x for which x is sad via existential modus ponens. Therefore, the answer is yes.