Consider the following premises. For all x_7, x_7 is not an astronaut or x_7 will sleep. For all x_7, x_7 is an astronaut. For all x_7, x_7 is not an artist. For all x_7, x_7 is sad if and only if x_7 is an artist. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_7 for which x_7 will not sleep.
 From the fact that for all x_7, x_7 is an astronaut we can infer that for all x_7, x_7 is an astronaut or x_7 is sad via universal addition. From the fact that for all x_7, x_7 is sad if and only if x_7 is an artist, and that for all x_7, x_7 is not an artist we can infer that for all x_7, x_7 is not sad via universal biconditional elimination. From the fact that for all x_7, x_7 is an astronaut or x_7 is sad, and that for all x_7, x_7 is not an astronaut or x_7 will sleep we can infer that for all x_7, x_7 is sad or x_7 will sleep via universal resolution. Finally, from the fact that for all x_7, x_7 is sad or x_7 will sleep, and that for all x_7, x_7 is not sad we can infer that for all x_7, x_7 will sleep via universal disjunctive syllogism, which contradicts that There is at least one x_7 for which x_7 will not sleep. Therefore, the answer is no.