Consider the following premises. Karen is running or Susan is not a janitor. Susan is a janitor or it is cold. If it is cold, then Karen is running. Can we infer the following from them? Karen is running or John is a carpenter.
 From the fact that Karen is running or Susan is not a janitor we can infer that if Susan were a janitor, then Karen is running. From the fact that if Susan were a janitor, then Karen is running, that if it is cold, then Karen is running, and that Susan is a janitor or it is cold we can infer that Karen is running. Finally, from the fact that Karen is running we can infer that Karen is running or John is a carpenter. Therefore, the answer is yes.