Consider the following premises. For all x_15, x_15 will cook if and only if x_15 is a taxi driver. For all x_15, x_15 is a taxi driver if and only if x_15 will make tea. For all x_15, x_15 is bored if and only if x_15 will cook. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_15 for which the fact that x_15 were bored does not imply that x_15 is making tea.
 From the fact that for all x_15, x_15 is a taxi driver if and only if x_15 will make tea we can infer that for all x_15, if x_15 were a taxi driver, then x_15 is making tea via universal biconditional elimination. From the fact that for all x_15, x_15 will cook if and only if x_15 is a taxi driver we can infer that for all x_15, if x_15 cooks, then x_15 is a taxi driver via universal biconditional elimination. From the fact that for all x_15, x_15 is bored if and only if x_15 will cook we can infer that for all x_15, if x_15 were bored, then x_15 is cooking via universal biconditional elimination. From the fact that for all x_15, if x_15 cooks, then x_15 is a taxi driver, and that for all x_15, if x_15 were a taxi driver, then x_15 is making tea we can infer that for all x_15, if x_15 cooks, then x_15 is making tea via universal transitivity. Finally, from the fact that for all x_15, if x_15 were bored, then x_15 is cooking, and that for all x_15, if x_15 cooks, then x_15 is making tea we can infer that for all x_15, if x_15 were bored, then x_15 is making tea via universal transitivity, which contradicts that There is at least one x_15 for which the fact that x_15 were bored does not imply that x_15 is making tea. Therefore, the answer is no.