Consider the following premises. There is at least one x_11 for which if x_11 were an artist, then x_11 is listening to a song. For all x_11, if x_11 reads a book, then x_11 is listening to a song. For all x_11, x_11 will read a book or x_11 is a bartender. For all x_11, if x_11 were a bartender, then x_11 is an artist. 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 listen to a song or x_11 will take a plane.
 From the fact that for all x_11, if x_11 were a bartender, then x_11 is an artist, and that there is at least one x_11 for which if x_11 were an artist, then x_11 is listening to a song we can infer that there is at least one x_11 for which if x_11 were a bartender, then x_11 is listening to a song via existential transitivity. From the fact that for all x_11, if x_11 reads a book, then x_11 is listening to a song, that there is at least one x_11 for which if x_11 were a bartender, then x_11 is listening to a song, and that for all x_11, x_11 will read a book or x_11 is a bartender we can infer that there is at least one x_11 for which x_11 will listen to a song via existential disjunction elimination. Finally, from the fact that there is at least one x_11 for which x_11 will listen to a song we can infer that there is at least one x_11 for which x_11 will listen to a song or x_11 will take a plane via existential addition. Therefore, the answer is yes.