Consider the following premises. Patricia is not a bartender. For all x_13, x_13 is a bartender. Can we infer the following from them? If we can, name the inference rule being used: Patricia is excited or it is overcast.
 From the fact that for all x_13, x_13 is a bartender we can infer that for all x_13, x_13 is a bartender or x_13 is excited via universal addition. From the fact that for all x_13, x_13 is a bartender or x_13 is excited we can infer that Patricia is a bartender or Patricia is excited via universal instantiation. From the fact that Patricia is a bartender or Patricia is excited, and that Patricia is not a bartender we can infer that Patricia is excited via disjunctive syllogism. Finally, from the fact that Patricia is excited we can infer that Patricia is excited or it is overcast via addition. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.