Consider the following premises. For all x_10, x_10 is curious if and only if x_10 will listen to a song. William is not listening to a song. If William listens to a song, then William is curious. Can we infer the following from them? If we can, name the inference rule being used: William is curious.
 From the fact that for all x_10, x_10 is curious if and only if x_10 will listen to a song we can infer that for all x_10, if x_10 were curious, then x_10 is listening to a song via universal biconditional elimination. From the fact that for all x_10, if x_10 were curious, then x_10 is listening to a song we can infer that if William were curious, then William is listening to a song via universal instantiation. From the fact that if William were curious, then William is listening to a song, and that if William listens to a song, then William is curious we can infer that William is curious if and only if William is listening to a song via biconditional introduction. Finally, from the fact that William is curious if and only if William is listening to a song, and that William is not listening to a song we can infer that William is not curious via biconditional elimination, which contradicts that William is curious. Therefore, the answer is no.