Consider the following premises. If it is sunny, then it is raining. If Elisabeth were an astronaut, then it is snowing. If Elisabeth takes a plane, then it is sunny. If it rains, then it is cold. Elisabeth is taking a plane or Elisabeth is an astronaut. If it snows, then it is cold. Can we infer the following from them? If we can, name the inference rule being used: It is not cold.
 From the fact that if Elisabeth were an astronaut, then it is snowing, and that if it snows, then it is cold we can infer that if Elisabeth were an astronaut, then it is cold via transitivity. From the fact that if Elisabeth takes a plane, then it is sunny, and that if it is sunny, then it is raining we can infer that if Elisabeth takes a plane, then it is raining via transitivity. From the fact that if Elisabeth takes a plane, then it is raining, and that if it rains, then it is cold we can infer that if Elisabeth takes a plane, then it is cold via transitivity. Finally, from the fact that if Elisabeth takes a plane, then it is cold, that if Elisabeth were an astronaut, then it is cold, and that Elisabeth is taking a plane or Elisabeth is an astronaut we can infer that it is cold via disjunction elimination, which contradicts that It is not cold. Therefore, the answer is no.