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