Consider the following premises. There is at least one x_7 for which x_7 will work if and only if x_7 will make tea. For all x_7, if x_7 makes tea, then x_7 is not writing a letter. For all x_7, x_7 will write a letter. Can we infer the following from them? For all x_7, x_7 will work.
 From the fact that for all x_7, if x_7 makes tea, then x_7 is not writing a letter, and that for all x_7, x_7 will write a letter we can infer that for all x_7, x_7 will not make tea. From the fact that there is at least one x_7 for which x_7 will work if and only if x_7 will make tea we can infer that there is at least one x_7 for which if x_7 works, then x_7 is making tea. Finally, from the fact that there is at least one x_7 for which if x_7 works, then x_7 is making tea, and that for all x_7, x_7 will not make tea we can infer that there is at least one x_7 for which x_7 will not work, which contradicts that For all x_7, x_7 will work. Therefore, the answer is no.