Consider the following premises. For all x_11, if x_11 goes running, then x_11 is sleeping. If Jessica sleeps, then Michael is playing squash. If Michael plays squash, then Jessica is excited. For all x_11, if x_11 were excited, then x_11 is running. Can we infer the following from them? If we can, name the inference rule being used: If is not true that Jessica is excited if and only if Jessica is sleeping.
 From the fact that for all x_11, if x_11 were excited, then x_11 is running, and that for all x_11, if x_11 goes running, then x_11 is sleeping we can infer that for all x_11, if x_11 were excited, then x_11 is sleeping via universal transitivity. From the fact that for all x_11, if x_11 were excited, then x_11 is sleeping we can infer that if Jessica were excited, then Jessica is sleeping via universal instantiation. From the fact that if Jessica sleeps, then Michael is playing squash, and that if Michael plays squash, then Jessica is excited we can infer that if Jessica sleeps, then Jessica is excited via transitivity. Finally, from the fact that if Jessica were excited, then Jessica is sleeping, and that if Jessica sleeps, then Jessica is excited we can infer that Jessica is excited if and only if Jessica is sleeping via biconditional introduction, which contradicts that If is not true that Jessica is excited if and only if Jessica is sleeping. Therefore, the answer is no.