Consider the following premises. For all x_11, x_11 will listen to a song and x_11 is happy. For all x_11, x_11 is a musician or x_11 is sad. There is at least one x_11 for which x_11 is not a musician or x_11 will work. For all x_11, if x_11 were sad, then x_11 is not listening 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_11 for which x_11 will work.
 From the fact that for all x_11, x_11 is a musician or x_11 is sad, and that there is at least one x_11 for which x_11 is not a musician or x_11 will work we can infer that there is at least one x_11 for which x_11 is sad or x_11 will work via existential resolution. From the fact that for all x_11, x_11 will listen to a song and x_11 is happy we can infer that for all x_11, x_11 will listen to a song via universal simplification. From the fact that for all x_11, if x_11 were sad, then x_11 is not listening to a song, and that for all x_11, x_11 will listen to a song we can infer that for all x_11, x_11 is not sad via universal modus tollens. Finally, from the fact that there is at least one x_11 for which x_11 is sad or x_11 will work, and that for all x_11, x_11 is not sad we can infer that there is at least one x_11 for which x_11 will work via existential disjunctive syllogism. Therefore, the answer is yes.