Consider the following premises. For all x_11, if x_11 drinks water, then x_11 is playing squash. For all x_11, x_11 will play a game. There is at least one x_11 for which if x_11 reads a book, then x_11 is playing squash. For all x_11, if x_11 plays a game, then x_11 is drinking water. For all x_11, if x_11 plays squash, then x_11 is drinking water. Can we infer the following from them? If we can, name the inference rule being used: For all x_11, x_11 will not play squash.
 From the fact that for all x_11, if x_11 plays squash, then x_11 is drinking water, and that for all x_11, if x_11 drinks water, then x_11 is playing squash we can infer that for all x_11, x_11 will play squash if and only if x_11 will drink water via universal biconditional introduction. From the fact that for all x_11, x_11 will play a game we can infer that for all x_11, x_11 will play a game or x_11 will read a book via universal addition. From the fact that for all x_11, x_11 will play squash if and only if x_11 will drink water we can infer that for all x_11, if x_11 drinks water, then x_11 is playing squash via universal biconditional elimination. From the fact that for all x_11, if x_11 plays a game, then x_11 is drinking water, and that for all x_11, if x_11 drinks water, then x_11 is playing squash we can infer that for all x_11, if x_11 plays a game, then x_11 is playing squash via universal transitivity. Finally, from the fact that for all x_11, if x_11 plays a game, then x_11 is playing squash, that there is at least one x_11 for which if x_11 reads a book, then x_11 is playing squash, and that for all x_11, x_11 will play a game or x_11 will read a book we can infer that there is at least one x_11 for which x_11 will play squash via existential disjunction elimination, which contradicts that For all x_11, x_11 will not play squash. Therefore, the answer is no.