Consider the following premises. For all x_10, x_10 will work if and only if x_10 is bored. For all x_10, if x_10 were excited, then x_10 is bored. For all x_10, x_10 will cook. For all x_10, x_10 will work or x_10 is excited. Can we infer the following from them? If we can, name the inference rule being used: Barbara is cooking.
 From the fact that for all x_10, x_10 will work if and only if x_10 is bored we can infer that for all x_10, if x_10 works, then x_10 is bored via universal biconditional elimination. From the fact that for all x_10, if x_10 works, then x_10 is bored, that for all x_10, if x_10 were excited, then x_10 is bored, and that for all x_10, x_10 will work or x_10 is excited we can infer that for all x_10, x_10 is bored via universal disjunction elimination. From the fact that for all x_10, x_10 is bored, and that for all x_10, x_10 will cook we can infer that for all x_10, x_10 is bored and x_10 will cook via universal conjunction. From the fact that for all x_10, x_10 is bored and x_10 will cook we can infer that Barbara is bored and Barbara is cooking via universal instantiation. Finally, from the fact that Barbara is bored and Barbara is cooking we can infer that Barbara is cooking via simplification. Therefore, the answer is yes.