Consider the following premises. It is cloudy if and only if Susan is curious. If it rains, then it is cloudy. If Susan were curious, then it is late. Can we infer the following from them? If we can, name the inference rule being used: The fact that it rains does not imply that it is late.
 From the fact that it is cloudy if and only if Susan is curious we can infer that if it is cloudy, then Susan is curious via biconditional elimination. From the fact that if it is cloudy, then Susan is curious, and that if Susan were curious, then it is late we can infer that if it is cloudy, then it is late via transitivity. Finally, from the fact that if it rains, then it is cloudy, and that if it is cloudy, then it is late we can infer that if it rains, then it is late via transitivity, which contradicts that The fact that it rains does not imply that it is late. Therefore, the answer is no.