Consider the following premises. For all x_8, if x_8 were a carpenter, then x_8 is a sailor. There is at least one x_8 for which x_8 is a carpenter if and only if x_8 will play a game. For all x_8, x_8 will not play a game. For all x_8, if x_8 were a sailor, then x_8 is a carpenter. 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 x_8 is not a sailor.
 From the fact that there is at least one x_8 for which x_8 is a carpenter if and only if x_8 will play a game, and that for all x_8, x_8 will not play a game we can infer that there is at least one x_8 for which x_8 is not a carpenter via existential biconditional elimination. From the fact that for all x_8, if x_8 were a sailor, then x_8 is a carpenter, and that for all x_8, if x_8 were a carpenter, then x_8 is a sailor we can infer that for all x_8, x_8 is a sailor if and only if x_8 is a carpenter via universal biconditional introduction. Finally, from the fact that for all x_8, x_8 is a sailor if and only if x_8 is a carpenter, and that there is at least one x_8 for which x_8 is not a carpenter we can infer that there is at least one x_8 for which x_8 is not a sailor via existential biconditional elimination. Therefore, the answer is yes.