Consider the following premises. For all x_8, if x_8 writes a letter, then x_8 is playing squash. There is at least one x_8 for which x_8 will play squash if and only if x_8 will write a letter. For all x_8, if x_8 plays squash, then x_8 is making tea. For all x_8, x_8 will not make tea. Can we infer the following from them? There is at least one x_8 for which x_8 will not write a letter.
 From the fact that for all x_8, if x_8 plays squash, then x_8 is making tea, and that for all x_8, x_8 will not make tea we can infer that for all x_8, x_8 will not play squash. From the fact that there is at least one x_8 for which x_8 will play squash if and only if x_8 will write a letter we can infer that there is at least one x_8 for which if x_8 plays squash, then x_8 is writing a letter. From the fact that there is at least one x_8 for which if x_8 plays squash, then x_8 is writing a letter, and that for all x_8, if x_8 writes a letter, then x_8 is playing squash we can infer that there is at least one x_8 for which x_8 will play squash if and only if x_8 will write a letter. Finally, from the fact that there is at least one x_8 for which x_8 will play squash if and only if x_8 will write a letter, and that for all x_8, x_8 will not play squash we can infer that there is at least one x_8 for which x_8 will not write a letter. Therefore, the answer is yes.