Consider the following premises. For all x_17, x_17 will listen to a song if and only if x_17 is fast. For all x_17, if x_17 were a carpenter, then x_17 is not reading a book. For all x_17, if x_17 listens to a song, then x_17 is fast. For all x_17, x_17 is a carpenter if and only if x_17 is fast. There is at least one x_17 for which x_17 will read a book. Can we infer the following from them? If we can, name the inference rule being used: For all x_17, x_17 will listen to a song.
 From the fact that for all x_17, if x_17 were a carpenter, then x_17 is not reading a book, and that there is at least one x_17 for which x_17 will read a book we can infer that there is at least one x_17 for which x_17 is not a carpenter via existential modus tollens. From the fact that for all x_17, x_17 is a carpenter if and only if x_17 is fast, and that there is at least one x_17 for which x_17 is not a carpenter we can infer that there is at least one x_17 for which x_17 is not fast via existential biconditional elimination. From the fact that for all x_17, x_17 will listen to a song if and only if x_17 is fast we can infer that for all x_17, if x_17 were fast, then x_17 is listening to a song via universal biconditional elimination. From the fact that for all x_17, if x_17 listens to a song, then x_17 is fast, and that for all x_17, if x_17 were fast, then x_17 is listening to a song we can infer that for all x_17, x_17 will listen to a song if and only if x_17 is fast via universal biconditional introduction. Finally, from the fact that for all x_17, x_17 will listen to a song if and only if x_17 is fast, and that there is at least one x_17 for which x_17 is not fast we can infer that there is at least one x_17 for which x_17 will not listen to a song via existential biconditional elimination, which contradicts that For all x_17, x_17 will listen to a song. Therefore, the answer is no.