Consider the following premises. For all x_8, x_8 is not a carpenter. David is a carpenter. Can we infer the following from them? If we can, name the inference rule being used: John is happy.
 From the fact that for all x_8, x_8 is not a carpenter we can infer that David is not a carpenter via universal instantiation. From the fact that David is a carpenter we can infer that David is a carpenter or John is happy via addition. Finally, from the fact that David is a carpenter or John is happy, and that David is not a carpenter we can infer that John is happy via disjunctive syllogism. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.