Consider the following premises. For all x_11, if x_11 were fast, then x_11 is listening to a song. For all x_11, if x_11 were an office clerk, then x_11 is listening to a song. For all x_11, x_11 is a sailor and x_11 is a soldier. For all x_11, x_11 is not a musician or x_11 is an office clerk. For all x_11, x_11 is a musician. Can we infer the following from them? If we can, name the inference rule being used: For all x_11, x_11 is a sailor and x_11 will listen to a song.
 From the fact that for all x_11, x_11 is a sailor and x_11 is a soldier we can infer that for all x_11, x_11 is a sailor via universal simplification. From the fact that for all x_11, x_11 is a musician we can infer that for all x_11, x_11 is a musician or x_11 is fast via universal addition. From the fact that for all x_11, x_11 is a musician or x_11 is fast, and that for all x_11, x_11 is not a musician or x_11 is an office clerk we can infer that for all x_11, x_11 is fast or x_11 is an office clerk via universal resolution. From the fact that for all x_11, if x_11 were fast, then x_11 is listening to a song, that for all x_11, if x_11 were an office clerk, then x_11 is listening to a song, and that for all x_11, x_11 is fast or x_11 is an office clerk we can infer that for all x_11, x_11 will listen to a song via universal disjunction elimination. Finally, from the fact that for all x_11, x_11 is a sailor, and that for all x_11, x_11 will listen to a song we can infer that for all x_11, x_11 is a sailor and x_11 will listen to a song via universal conjunction. Therefore, the answer is yes.