Consider the following premises. There is at least one x_7 for which if x_7 sleeps, then x_7 is listening to a song. For all x_7, x_7 will sleep or x_7 will write a letter. For all x_7, x_7 is a poet. For all x_7, if x_7 writes a letter, then x_7 is 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_7 for which x_7 will listen to a song and x_7 is a poet.
 From the fact that there is at least one x_7 for which if x_7 sleeps, then x_7 is listening to a song, that for all x_7, if x_7 writes a letter, then x_7 is listening to a song, and that for all x_7, x_7 will sleep or x_7 will write a letter we can infer that there is at least one x_7 for which x_7 will listen to a song via existential disjunction elimination. Finally, from the fact that there is at least one x_7 for which x_7 will listen to a song, and that for all x_7, x_7 is a poet we can infer that there is at least one x_7 for which x_7 will listen to a song and x_7 is a poet via existential conjunction. Therefore, the answer is yes.