Consider the following premises. For all x_1, if x_1 writes a letter, then x_1 is running. For all x_1, x_1 is a sailor if and only if x_1 will go running. For all x_1, x_1 is not a sailor. For all x_1, if x_1 goes running, then x_1 is writing a letter. Can we infer the following from them? For all x_1, x_1 will not write a letter.
 From the fact that for all x_1, x_1 is a sailor if and only if x_1 will go running, and that for all x_1, x_1 is not a sailor we can infer that for all x_1, x_1 will not go running. From the fact that for all x_1, if x_1 goes running, then x_1 is writing a letter, and that for all x_1, if x_1 writes a letter, then x_1 is running we can infer that for all x_1, x_1 will go running if and only if x_1 will write a letter. Finally, from the fact that for all x_1, x_1 will go running if and only if x_1 will write a letter, and that for all x_1, x_1 will not go running we can infer that for all x_1, x_1 will not write a letter. Therefore, the answer is yes.