Consider the following premises. Sarah is playing squash or it is not raining. Sarah is not playing squash. Sarah is playing squash if and only if it is cloudy. If it is cloudy, then it is raining. Can we infer the following from them? If we can, name the inference rule being used: It is raining.
 From the fact that Sarah is playing squash if and only if it is cloudy we can infer that if Sarah plays squash, then it is cloudy via biconditional elimination. From the fact that if Sarah plays squash, then it is cloudy, and that if it is cloudy, then it is raining we can infer that if Sarah plays squash, then it is raining via transitivity. From the fact that Sarah is playing squash or it is not raining we can infer that if it rains, then Sarah is playing squash via rewriting. From the fact that if it rains, then Sarah is playing squash, and that if Sarah plays squash, then it is raining we can infer that it is raining if and only if Sarah is playing squash via biconditional introduction. Finally, from the fact that it is raining if and only if Sarah is playing squash, and that Sarah is not playing squash we can infer that it is not raining via biconditional elimination, which contradicts that It is raining. Therefore, the answer is no.