Consider the following premises. For all x_10, if x_10 works, then x_10 is a carpenter. For all x_10, if x_10 works, then x_10 is bored. For all x_10, x_10 is not bored. There is at least one x_10 for which x_10 is a carpenter if and only if x_10 will work. Can we infer the following from them? There is at least one x_10 for which x_10 is not a carpenter.
 From the fact that there is at least one x_10 for which x_10 is a carpenter if and only if x_10 will work we can infer that there is at least one x_10 for which if x_10 were a carpenter, then x_10 is working. From the fact that there is at least one x_10 for which if x_10 were a carpenter, then x_10 is working, and that for all x_10, if x_10 works, then x_10 is a carpenter we can infer that there is at least one x_10 for which x_10 is a carpenter if and only if x_10 will work. From the fact that for all x_10, if x_10 works, then x_10 is bored, and that for all x_10, x_10 is not bored we can infer that for all x_10, x_10 will not work. Finally, from the fact that there is at least one x_10 for which x_10 is a carpenter if and only if x_10 will work, and that for all x_10, x_10 will not work we can infer that there is at least one x_10 for which x_10 is not a carpenter. Therefore, the answer is yes.