Consider the following premises. For all x_11, if x_11 reads a book, then x_11 is not a bartender. For all x_11, x_11 is a soldier. For all x_11, x_11 will read a book. For all x_11, x_11 is a bartender. Can we infer the following from them? If we can, name the inference rule being used: For all x_11, x_11 will write a letter.
 From the fact that for all x_11, x_11 will read a book, and that for all x_11, x_11 is a soldier we can infer that for all x_11, x_11 will read a book and x_11 is a soldier via universal conjunction. From the fact that for all x_11, if x_11 reads a book, then x_11 is not a bartender, and that for all x_11, x_11 is a bartender we can infer that for all x_11, x_11 will not read a book via universal modus tollens. From the fact that for all x_11, x_11 will read a book and x_11 is a soldier we can infer that for all x_11, x_11 will read a book via universal simplification. From the fact that for all x_11, x_11 will read a book we can infer that for all x_11, x_11 will read a book or x_11 will write a letter via universal addition. Finally, from the fact that for all x_11, x_11 will read a book or x_11 will write a letter, and that for all x_11, x_11 will not read a book we can infer that for all x_11, x_11 will write a letter via universal disjunctive syllogism. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.