Consider the following premises. For all x_7, x_7 will write a letter or x_7 is a janitor. For all x_7, x_7 is an artist if and only if x_7 is an astronaut. For all x_7, x_7 is not an artist. For all x_7, x_7 will write a letter if and only if x_7 is an astronaut. Can we infer the following from them? There is at least one x_7 for which x_7 is not a janitor.
 From the fact that for all x_7, x_7 is an artist if and only if x_7 is an astronaut, and that for all x_7, x_7 is not an artist we can infer that for all x_7, x_7 is not an astronaut. From the fact that for all x_7, x_7 will write a letter if and only if x_7 is an astronaut, and that for all x_7, x_7 is not an astronaut we can infer that for all x_7, x_7 will not write a letter. Finally, from the fact that for all x_7, x_7 will write a letter or x_7 is a janitor, and that for all x_7, x_7 will not write a letter we can infer that for all x_7, x_7 is a janitor, which contradicts that There is at least one x_7 for which x_7 is not a janitor. Therefore, the answer is no.