Consider the following premises. For all x_7, x_7 will cook or x_7 will not drink water. For all x_7, x_7 is a nurse if and only if x_7 will drink water. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_7 for which the fact that x_7 were a nurse does not imply that x_7 is cooking.
 From the fact that for all x_7, x_7 is a nurse if and only if x_7 will drink water we can infer that for all x_7, if x_7 were a nurse, then x_7 is drinking water via universal biconditional elimination. From the fact that for all x_7, x_7 will cook or x_7 will not drink water we can infer that for all x_7, if x_7 drinks water, then x_7 is cooking via universal rewriting. Finally, from the fact that for all x_7, if x_7 were a nurse, then x_7 is drinking water, and that for all x_7, if x_7 drinks water, then x_7 is cooking we can infer that for all x_7, if x_7 were a nurse, then x_7 is cooking via universal transitivity, which contradicts that There is at least one x_7 for which the fact that x_7 were a nurse does not imply that x_7 is cooking. Therefore, the answer is no.