Consider the following premises. For all x_12, if x_12 were a writer, then x_12 is a bartender. For all x_12, x_12 is a writer. There is at least one x_12 for which x_12 is not a bartender. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_12 for which x_12 is curious or x_12 will drive a car.
 From the fact that for all x_12, if x_12 were a writer, then x_12 is a bartender, and that for all x_12, x_12 is a writer we can infer that for all x_12, x_12 is a bartender via universal modus ponens. From the fact that for all x_12, x_12 is a bartender we can infer that for all x_12, x_12 is a bartender or x_12 is curious via universal addition. From the fact that for all x_12, x_12 is a bartender or x_12 is curious, and that there is at least one x_12 for which x_12 is not a bartender we can infer that there is at least one x_12 for which x_12 is curious via existential disjunctive syllogism. Finally, from the fact that there is at least one x_12 for which x_12 is curious we can infer that there is at least one x_12 for which x_12 is curious or x_12 will drive a car via existential addition. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.