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