Consider the following premises. Sarah is not bored. For all x_1, if x_1 were bored, then x_1 is a mechanic. For all x_1, x_1 is bored or x_1 is not a mechanic. Can we infer the following from them? If we can, name the inference rule being used: Sarah is a mechanic.
 From the fact that for all x_1, x_1 is bored or x_1 is not a mechanic we can infer that for all x_1, if x_1 were a mechanic, then x_1 is bored via universal rewriting. From the fact that for all x_1, if x_1 were a mechanic, then x_1 is bored, and that for all x_1, if x_1 were bored, then x_1 is a mechanic we can infer that for all x_1, x_1 is a mechanic if and only if x_1 is bored via universal biconditional introduction. From the fact that for all x_1, x_1 is a mechanic if and only if x_1 is bored we can infer that Sarah is a mechanic if and only if Sarah is bored via universal instantiation. Finally, from the fact that Sarah is a mechanic if and only if Sarah is bored, and that Sarah is not bored we can infer that Sarah is not a mechanic via biconditional elimination, which contradicts that Sarah is a mechanic. Therefore, the answer is no.