Consider the following premises. For all x_7, if x_7 writes a letter, then x_7 is playing squash. For all x_7, x_7 is fast or x_7 will write a letter. There is at least one x_7 for which x_7 is not fast or x_7 will play tennis. For all x_7, x_7 will not play squash. Can we infer the following from them? There is at least one x_7 for which x_7 will play tennis.
 From the fact that for all x_7, x_7 is fast or x_7 will write a letter, and that there is at least one x_7 for which x_7 is not fast or x_7 will play tennis we can infer that there is at least one x_7 for which x_7 will write a letter or x_7 will play tennis. From the fact that for all x_7, if x_7 writes a letter, then x_7 is playing squash, and that for all x_7, x_7 will not play squash we can infer that for all x_7, x_7 will not write a letter. Finally, from the fact that there is at least one x_7 for which x_7 will write a letter or x_7 will play tennis, and that for all x_7, x_7 will not write a letter we can infer that there is at least one x_7 for which x_7 will play tennis. Therefore, the answer is yes.