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