Consider the following premises. For all x_13, x_13 will drink water if and only if x_13 is excited. For all x_13, if x_13 plays squash, then x_13 is drinking water. For all x_13, x_13 will play squash if and only if x_13 is excited. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_13 for which the fact that x_13 were excited does not imply that x_13 is drinking water.
 From the fact that for all x_13, x_13 will play squash if and only if x_13 is excited we can infer that for all x_13, if x_13 were excited, then x_13 is playing squash via universal biconditional elimination. From the fact that for all x_13, if x_13 were excited, then x_13 is playing squash, and that for all x_13, if x_13 plays squash, then x_13 is drinking water we can infer that for all x_13, if x_13 were excited, then x_13 is drinking water via universal transitivity. From the fact that for all x_13, x_13 will drink water if and only if x_13 is excited we can infer that for all x_13, if x_13 drinks water, then x_13 is excited via universal biconditional elimination. From the fact that for all x_13, if x_13 drinks water, then x_13 is excited, and that for all x_13, if x_13 were excited, then x_13 is drinking water we can infer that for all x_13, x_13 will drink water if and only if x_13 is excited via universal biconditional introduction. Finally, from the fact that for all x_13, x_13 will drink water if and only if x_13 is excited we can infer that for all x_13, if x_13 were excited, then x_13 is drinking water via universal biconditional elimination, which contradicts that There is at least one x_13 for which the fact that x_13 were excited does not imply that x_13 is drinking water. Therefore, the answer is no.