Consider the following premises. If it snows, then Sarah is cooking. It is raining or James is not fast. If Sarah cooks, then James is fast. Can we infer the following from them? The fact that it snows does not imply that it is raining.
 From the fact that it is raining or James is not fast we can infer that if James were fast, then it is raining. From the fact that if Sarah cooks, then James is fast, and that if James were fast, then it is raining we can infer that if Sarah cooks, then it is raining. Finally, from the fact that if it snows, then Sarah is cooking, and that if Sarah cooks, then it is raining we can infer that if it snows, then it is raining, which contradicts that The fact that it snows does not imply that it is raining. Therefore, the answer is no.