Consider the following premises. For all x_15, x_15 will not play squash. For all x_15, x_15 will play squash or x_15 will not drink water. Karen is curious if and only if it is cold. For all x_15, x_15 will drink water if and only if x_15 is curious. Can we infer the following from them? If we can, name the inference rule being used: It is not cold.
 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 drinks water, then x_15 is playing squash, and that for all x_15, x_15 will not play squash we can infer that for all x_15, x_15 will not drink water via universal modus tollens. From the fact that for all x_15, x_15 will drink water if and only if x_15 is curious, and that for all x_15, x_15 will not drink water we can infer that for all x_15, x_15 is not curious via universal biconditional elimination. From the fact that for all x_15, x_15 is not curious we can infer that Karen is not curious via universal instantiation. Finally, from the fact that Karen is curious if and only if it is cold, and that Karen is not curious we can infer that it is not cold via biconditional elimination. Therefore, the answer is yes.