Consider the following premises. For all x_12, x_12 will sleep or x_12 will make tea. For all x_12, if x_12 makes tea, then x_12 is writing a letter. There is at least one x_12 for which if x_12 sleeps, then x_12 is not running. For all x_12, x_12 will go running. Can we infer the following from them? There is at least one x_12 for which x_12 will write a letter.
 From the fact that there is at least one x_12 for which if x_12 sleeps, then x_12 is not running, and that for all x_12, x_12 will go running we can infer that there is at least one x_12 for which x_12 will not sleep. From the fact that for all x_12, x_12 will sleep or x_12 will make tea, and that there is at least one x_12 for which x_12 will not sleep we can infer that there is at least one x_12 for which x_12 will make tea. Finally, from the fact that for all x_12, if x_12 makes tea, then x_12 is writing a letter, and that there is at least one x_12 for which x_12 will make tea we can infer that there is at least one x_12 for which x_12 will write a letter. Therefore, the answer is yes.