Consider the following premises. For all x_8, if x_8 were a musician, then x_8 is playing a game. For all x_8, if x_8 plays a game, then x_8 is reading a book. For all x_8, x_8 will play a game if and only if x_8 is a musician. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_8 for which the fact that x_8 were a musician does not imply that x_8 is reading a book.
 From the fact that for all x_8, x_8 will play a game if and only if x_8 is a musician we can infer that for all x_8, if x_8 plays a game, then x_8 is a musician via universal biconditional elimination. From the fact that for all x_8, if x_8 were a musician, then x_8 is playing a game, and that for all x_8, if x_8 plays a game, then x_8 is a musician we can infer that for all x_8, x_8 is a musician if and only if x_8 will play a game via universal biconditional introduction. From the fact that for all x_8, x_8 is a musician if and only if x_8 will play a game we can infer that for all x_8, if x_8 were a musician, then x_8 is playing a game via universal biconditional elimination. Finally, from the fact that for all x_8, if x_8 were a musician, then x_8 is playing a game, and that for all x_8, if x_8 plays a game, then x_8 is reading a book we can infer that for all x_8, if x_8 were a musician, then x_8 is reading a book via universal transitivity, which contradicts that There is at least one x_8 for which the fact that x_8 were a musician does not imply that x_8 is reading a book. Therefore, the answer is no.