Consider the following premises. For all x_12, x_12 will work. For all x_12, if x_12 writes a letter, then x_12 is running. For all x_12, x_12 will go running if and only if x_12 will write a letter. There is at least one x_12 for which if x_12 writes a letter, then x_12 is not working. Can we infer the following from them? For all x_12, x_12 will go running.
 From the fact that for all x_12, x_12 will go running if and only if x_12 will write a letter we can infer that for all x_12, if x_12 goes running, then x_12 is writing a letter. From the fact that there is at least one x_12 for which if x_12 writes a letter, then x_12 is not working, and that for all x_12, x_12 will work we can infer that there is at least one x_12 for which x_12 will not write a letter. From the fact that for all x_12, if x_12 goes running, then x_12 is writing a letter, and that for all x_12, if x_12 writes a letter, then x_12 is running we can infer that for all x_12, x_12 will go running if and only if x_12 will write a letter. Finally, from the fact that for all x_12, x_12 will go running if and only if x_12 will write a letter, and that there is at least one x_12 for which x_12 will not write a letter we can infer that there is at least one x_12 for which x_12 will not go running, which contradicts that For all x_12, x_12 will go running. Therefore, the answer is no.