Consider the following premises. For all x_5, if x_5 reads a book, then x_5 is a server. For all x_5, x_5 will listen to a song or x_5 will read a book. For all x_5, if x_5 were a server, then x_5 is making tea. For all x_5, if x_5 listens to a song, then x_5 is making tea. For all x_5, x_5 will cook. 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 either x_5 will cook or x_5 will make tea are not true.
 From the fact that for all x_5, if x_5 reads a book, then x_5 is a server, and that for all x_5, if x_5 were a server, then x_5 is making tea we can infer that for all x_5, if x_5 reads a book, then x_5 is making tea via universal transitivity. From the fact that for all x_5, if x_5 listens to a song, then x_5 is making tea, that for all x_5, if x_5 reads a book, then x_5 is making tea, and that for all x_5, x_5 will listen to a song or x_5 will read a book we can infer that for all x_5, x_5 will make tea via universal disjunction elimination. Finally, from the fact that for all x_5, x_5 will cook, and that for all x_5, x_5 will make tea we can infer that for all x_5, x_5 will cook and x_5 will make tea via universal conjunction, which contradicts that There is at least one x_5 for which either x_5 will cook or x_5 will make tea are not true. Therefore, the answer is no.