Consider the following premises. For all x_5, if x_5 were bored, then x_5 is a politician. For all x_5, x_5 is a scientist or x_5 is bored. For all x_5, x_5 is an artist. For all x_5, if x_5 were a scientist, then x_5 is listening to a song. For all x_5, if x_5 listens to a song, then x_5 is a politician. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, x_5 is a politician and x_5 is an artist.
 From the fact that for all x_5, if x_5 were a scientist, then x_5 is listening to a song, and that for all x_5, if x_5 listens to a song, then x_5 is a politician we can infer that for all x_5, if x_5 were a scientist, then x_5 is a politician via universal transitivity. From the fact that for all x_5, if x_5 were a scientist, then x_5 is a politician, that for all x_5, if x_5 were bored, then x_5 is a politician, and that for all x_5, x_5 is a scientist or x_5 is bored we can infer that for all x_5, x_5 is a politician via universal disjunction elimination. Finally, from the fact that for all x_5, x_5 is a politician, and that for all x_5, x_5 is an artist we can infer that for all x_5, x_5 is a politician and x_5 is an artist via universal conjunction. Therefore, the answer is yes.