Consider the following premises. If Mary were a scientist, then it is snowing. If Susan were a lawyer, then Mary is a scientist. If it snows, then it is cloudy. If it is cloudy, then Susan is a lawyer. Can we infer the following from them? If we can, name the inference rule being used: The fact that it is cloudy does not imply that Mary is a scientist.
 From the fact that if Mary were a scientist, then it is snowing, and that if it snows, then it is cloudy we can infer that if Mary were a scientist, then it is cloudy via transitivity. Finally, from the fact that if it is cloudy, then Susan is a lawyer, and that if Susan were a lawyer, then Mary is a scientist we can infer that if it is cloudy, then Mary is a scientist via transitivity, which contradicts that The fact that it is cloudy does not imply that Mary is a scientist. Therefore, the answer is no.