Consider the following premises. For all x_7, if x_7 were bored, then x_7 is reading a book. For all x_7, x_7 is a nurse or x_7 is bored. For all x_7, x_7 is a bartender. For all x_7, if x_7 were sad, then x_7 is reading a book. For all x_7, x_7 is not a nurse or x_7 is sad. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_7 for which x_7 is not a bartender.
 From the fact that for all x_7, x_7 is a nurse or x_7 is bored, and that for all x_7, x_7 is not a nurse or x_7 is sad we can infer that for all x_7, x_7 is bored or x_7 is sad via universal resolution. From the fact that for all x_7, if x_7 were bored, then x_7 is reading a book, that for all x_7, if x_7 were sad, then x_7 is reading a book, and that for all x_7, x_7 is bored or x_7 is sad we can infer that for all x_7, x_7 will read a book via universal disjunction elimination. From the fact that for all x_7, x_7 will read a book, and that for all x_7, x_7 is a bartender we can infer that for all x_7, x_7 will read a book and x_7 is a bartender via universal conjunction. Finally, from the fact that for all x_7, x_7 will read a book and x_7 is a bartender we can infer that for all x_7, x_7 will read a book via universal simplification, which contradicts that There is at least one x_7 for which x_7 is not a bartender. Therefore, the answer is no.