Consider the following premises. For all x_7, if x_7 were a doctor, then x_7 is reading a book. For all x_7, x_7 is a doctor or x_7 is a server. For all x_7, x_7 is a bartender. For all x_7, x_7 is a server if and only if x_7 will read a book. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_7 for which either x_7 is a bartender or x_7 will read a book are not true.
 From the fact that for all x_7, x_7 is a server if and only if x_7 will read a book we can infer that for all x_7, if x_7 were a server, then x_7 is reading a book via universal biconditional elimination. From the fact that for all x_7, if x_7 were a doctor, then x_7 is reading a book, that for all x_7, if x_7 were a server, then x_7 is reading a book, and that for all x_7, x_7 is a doctor or x_7 is a server we can infer that for all x_7, x_7 will read a book via universal disjunction elimination. Finally, from the fact that for all x_7, x_7 is a bartender, and that for all x_7, x_7 will read a book we can infer that for all x_7, x_7 is a bartender and x_7 will read a book via universal conjunction, which contradicts that There is at least one x_7 for which either x_7 is a bartender or x_7 will read a book are not true. Therefore, the answer is no.