Consider the following premises. For all x_4, if x_4 were a carpenter, then x_4 is working. For all x_4, x_4 will not cook or x_4 will write a letter. For all x_4, x_4 will take a plane or x_4 will cook. For all x_4, x_4 will not take a plane or x_4 is a carpenter. There is at least one x_4 for which if x_4 writes a letter, then x_4 is working. Can we infer the following from them? There is at least one x_4 for which x_4 will work.
 From the fact that for all x_4, x_4 will take a plane or x_4 will cook, and that for all x_4, x_4 will not take a plane or x_4 is a carpenter we can infer that for all x_4, x_4 will cook or x_4 is a carpenter. From the fact that for all x_4, x_4 will cook or x_4 is a carpenter, and that for all x_4, x_4 will not cook or x_4 will write a letter we can infer that for all x_4, x_4 is a carpenter or x_4 will write a letter. Finally, from the fact that for all x_4, if x_4 were a carpenter, then x_4 is working, that there is at least one x_4 for which if x_4 writes a letter, then x_4 is working, and that for all x_4, x_4 is a carpenter or x_4 will write a letter we can infer that there is at least one x_4 for which x_4 will work. Therefore, the answer is yes.