Consider the following premises. For all x_8, x_8 is happy or x_8 is a sailor. For all x_8, if x_8 were happy, then x_8 is bored. For all x_8, if x_8 were a sailor, then x_8 is bored. For all x_8, x_8 is an astronaut if and only if x_8 is bored. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_8 for which x_8 is not an astronaut.
 From the fact that for all x_8, if x_8 were happy, then x_8 is bored, that for all x_8, if x_8 were a sailor, then x_8 is bored, and that for all x_8, x_8 is happy or x_8 is a sailor we can infer that for all x_8, x_8 is bored via universal disjunction elimination. From the fact that for all x_8, x_8 is an astronaut if and only if x_8 is bored we can infer that for all x_8, if x_8 were bored, then x_8 is an astronaut via universal biconditional elimination. Finally, from the fact that for all x_8, if x_8 were bored, then x_8 is an astronaut, and that for all x_8, x_8 is bored we can infer that for all x_8, x_8 is an astronaut via universal modus ponens, which contradicts that There is at least one x_8 for which x_8 is not an astronaut. Therefore, the answer is no.