Consider the following premises. For all x_10, if x_10 reads a book, then x_10 is writing a letter. For all x_10, if x_10 were a janitor, then x_10 is reading a book. For all x_10, x_10 will play squash. For all x_10, if x_10 writes a letter, then x_10 is not playing squash. For all x_10, if x_10 were a sailor, then x_10 is a janitor. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_10 for which x_10 is a sailor.
 From the fact that for all x_10, if x_10 writes a letter, then x_10 is not playing squash, and that for all x_10, x_10 will play squash we can infer that for all x_10, x_10 will not write a letter via universal modus tollens. From the fact that for all x_10, if x_10 were a sailor, then x_10 is a janitor, and that for all x_10, if x_10 were a janitor, then x_10 is reading a book we can infer that for all x_10, if x_10 were a sailor, then x_10 is reading a book via universal transitivity. From the fact that for all x_10, if x_10 reads a book, then x_10 is writing a letter, and that for all x_10, x_10 will not write a letter we can infer that for all x_10, x_10 will not read a book via universal modus tollens. Finally, from the fact that for all x_10, if x_10 were a sailor, then x_10 is reading a book, and that for all x_10, x_10 will not read a book we can infer that for all x_10, x_10 is not a sailor via universal modus tollens, which contradicts that There is at least one x_10 for which x_10 is a sailor. Therefore, the answer is no.