Consider the following premises. For all x_5, x_5 will take a plane. For all x_5, x_5 will not take a plane. There is at least one x_5 for which if x_5 were a sailor, then x_5 is a carpenter. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_5 for which x_5 is a carpenter.
 From the fact that for all x_5, x_5 will take a plane we can infer that for all x_5, x_5 will take a plane or x_5 is a sailor via universal addition. From the fact that for all x_5, x_5 will take a plane or x_5 is a sailor, and that for all x_5, x_5 will not take a plane we can infer that for all x_5, x_5 is a sailor via universal disjunctive syllogism. Finally, from the fact that there is at least one x_5 for which if x_5 were a sailor, then x_5 is a carpenter, and that for all x_5, x_5 is a sailor we can infer that there is at least one x_5 for which x_5 is a carpenter via existential modus ponens. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.