Consider the following premises. For all x_5, x_5 will read a book. For all x_5, if x_5 reads a book, then x_5 is listening to a song. For all x_5, x_5 will listen to a song if and only if x_5 is a politician. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_5 for which x_5 will not listen to a song.
 From the fact that for all x_5, x_5 will read a book we can infer that for all x_5, x_5 will read a book or x_5 is a politician via universal addition. From the fact that for all x_5, x_5 will listen to a song if and only if x_5 is a politician we can infer that for all x_5, if x_5 were a politician, then x_5 is listening to a song via universal biconditional elimination. Finally, from the fact that for all x_5, if x_5 reads a book, then x_5 is listening to a song, that for all x_5, if x_5 were a politician, then x_5 is listening to a song, and that for all x_5, x_5 will read a book or x_5 is a politician we can infer that for all x_5, x_5 will listen to a song via universal disjunction elimination, which contradicts that There is at least one x_5 for which x_5 will not listen to a song. Therefore, the answer is no.