Consider the following premises. If Jennifer climbs a mountain, then John is listening to a song. For all z, z will not listen to a song. If Elisabeth cooks, then it is late. Jennifer is climbing a mountain if and only if Elisabeth is cooking. If it is late, then Elisabeth is cooking. Can we infer the following from them? If we can, name the inference rule being used: It is late.
 From the fact that if Elisabeth cooks, then it is late, and that if it is late, then Elisabeth is cooking we can infer that Elisabeth is cooking if and only if it is late via biconditional introduction. From the fact that for all z, z will not listen to a song we can infer that John is not listening to a song via universal instantiation. From the fact that if Jennifer climbs a mountain, then John is listening to a song, and that John is not listening to a song we can infer that Jennifer is not climbing a mountain via modus tollens. From the fact that Jennifer is climbing a mountain if and only if Elisabeth is cooking, and that Jennifer is not climbing a mountain we can infer that Elisabeth is not cooking via biconditional elimination. Finally, from the fact that Elisabeth is cooking if and only if it is late, and that Elisabeth is not cooking we can infer that it is not late via biconditional elimination, which contradicts that It is late. Therefore, the answer is no.