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