Consider the following premises. There is at least one x_6 for which if x_6 writes a letter, then x_6 is playing tennis. For all x_6, x_6 will drink water or x_6 will play tennis. For all x_6, if x_6 drinks water, then x_6 is writing a letter. For all x_6, if x_6 plays tennis, then x_6 is writing a letter. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, x_6 will not write a letter.
 From the fact that there is at least one x_6 for which if x_6 writes a letter, then x_6 is playing tennis, and that for all x_6, if x_6 plays tennis, then x_6 is writing a letter we can infer that there is at least one x_6 for which x_6 will write a letter if and only if x_6 will play tennis via existential biconditional introduction. From the fact that there is at least one x_6 for which x_6 will write a letter if and only if x_6 will play tennis we can infer that there is at least one x_6 for which if x_6 plays tennis, then x_6 is writing a letter via existential biconditional elimination. Finally, from the fact that for all x_6, if x_6 drinks water, then x_6 is writing a letter, that there is at least one x_6 for which if x_6 plays tennis, then x_6 is writing a letter, and that for all x_6, x_6 will drink water or x_6 will play tennis we can infer that there is at least one x_6 for which x_6 will write a letter via existential disjunction elimination, which contradicts that For all x_6, x_6 will not write a letter. Therefore, the answer is no.