Consider the following premises. For all x_15, x_15 will play squash or x_15 will not drink water. There is at least one x_15 for which x_15 will sleep if and only if x_15 will play squash. For all x_15, x_15 is a bartender. For all x_15, if x_15 were a bartender, then x_15 is drinking water. Can we infer the following from them? If we can, name the inference rule being used: For all x_15, x_15 will not sleep.
 From the fact that for all x_15, x_15 will play squash or x_15 will not drink water we can infer that for all x_15, if x_15 drinks water, then x_15 is playing squash via universal rewriting. From the fact that for all x_15, if x_15 were a bartender, then x_15 is drinking water, and that for all x_15, if x_15 drinks water, then x_15 is playing squash we can infer that for all x_15, if x_15 were a bartender, then x_15 is playing squash via universal transitivity. From the fact that for all x_15, if x_15 were a bartender, then x_15 is playing squash, and that for all x_15, x_15 is a bartender we can infer that for all x_15, x_15 will play squash via universal modus ponens. From the fact that there is at least one x_15 for which x_15 will sleep if and only if x_15 will play squash we can infer that there is at least one x_15 for which if x_15 plays squash, then x_15 is sleeping via existential biconditional elimination. Finally, from the fact that there is at least one x_15 for which if x_15 plays squash, then x_15 is sleeping, and that for all x_15, x_15 will play squash we can infer that there is at least one x_15 for which x_15 will sleep via existential modus ponens, which contradicts that For all x_15, x_15 will not sleep. Therefore, the answer is no.