Consider the following premises. For all x_4, if x_4 goes running, then x_4 is not writing a letter. For all x_4, x_4 will write a letter. For all x_4, x_4 will go running. Can we infer the following from them? For all x_4, x_4 is an astronaut.
 From the fact that for all x_4, if x_4 goes running, then x_4 is not writing a letter, and that for all x_4, x_4 will write a letter we can infer that for all x_4, x_4 will not go running. From the fact that for all x_4, x_4 will go running we can infer that for all x_4, x_4 will go running or x_4 is an astronaut. Finally, from the fact that for all x_4, x_4 will go running or x_4 is an astronaut, and that for all x_4, x_4 will not go running we can infer that for all x_4, x_4 is an astronaut. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.