Consider the following premises. For all x_4, if x_4 listens to a song, then x_4 is a bartender. For all x_4, if x_4 were a bartender, then x_4 is curious. For all x_4, if x_4 were curious, then x_4 is listening to a song. Linda is not listening to a song. Can we infer the following from them? If we can, name the inference rule being used: Linda is a bartender.
 From the fact that for all x_4, if x_4 were a bartender, then x_4 is curious, and that for all x_4, if x_4 were curious, then x_4 is listening to a song we can infer that for all x_4, if x_4 were a bartender, then x_4 is listening to a song via universal transitivity. From the fact that for all x_4, if x_4 were a bartender, then x_4 is listening to a song, and that for all x_4, if x_4 listens to a song, then x_4 is a bartender we can infer that for all x_4, x_4 is a bartender if and only if x_4 will listen to a song via universal biconditional introduction. From the fact that for all x_4, x_4 is a bartender if and only if x_4 will listen to a song we can infer that Linda is a bartender if and only if Linda is listening to a song via universal instantiation. Finally, from the fact that Linda is a bartender if and only if Linda is listening to a song, and that Linda is not listening to a song we can infer that Linda is not a bartender via biconditional elimination, which contradicts that Linda is a bartender. Therefore, the answer is no.