Consider the following premises. For all x, if x works, then x is climbing a mountain. If Elisabeth climbs a mountain, then Elisabeth is working. Elisabeth is working. Can we infer the following from them? If we can, name the inference rule being used: Elisabeth is not climbing a mountain.
 From the fact that for all x, if x works, then x is climbing a mountain we can infer that if Elisabeth works, then Elisabeth is climbing a mountain via universal instantiation. From the fact that if Elisabeth climbs a mountain, then Elisabeth is working, and that if Elisabeth works, then Elisabeth is climbing a mountain we can infer that Elisabeth is climbing a mountain if and only if Elisabeth is working via biconditional introduction. From the fact that Elisabeth is climbing a mountain if and only if Elisabeth is working we can infer that if Elisabeth works, then Elisabeth is climbing a mountain via biconditional elimination. Finally, from the fact that if Elisabeth works, then Elisabeth is climbing a mountain, and that Elisabeth is working we can infer that Elisabeth is climbing a mountain via modus ponens, which contradicts that Elisabeth is not climbing a mountain. Therefore, the answer is no.