Consider the following premises. It is not snowing or Mary is sad. It is snowing or Charles is a bartender. If Charles were a bartender, then Mary is bored. For all x_10, x_10 is bored or x_10 is not sad. Can we infer the following from them? If we can, name the inference rule being used: Mary is not bored.
 From the fact that for all x_10, x_10 is bored or x_10 is not sad we can infer that for all x_10, if x_10 were sad, then x_10 is bored via universal rewriting. From the fact that for all x_10, if x_10 were sad, then x_10 is bored we can infer that if Mary were sad, then Mary is bored via universal instantiation. From the fact that it is snowing or Charles is a bartender, and that it is not snowing or Mary is sad we can infer that Charles is a bartender or Mary is sad via resolution. Finally, from the fact that if Charles were a bartender, then Mary is bored, that if Mary were sad, then Mary is bored, and that Charles is a bartender or Mary is sad we can infer that Mary is bored via disjunction elimination, which contradicts that Mary is not bored. Therefore, the answer is no.