What can be inferred from the following premises in a single inference step (ignoring inferences that add new predicates or constants)? Name the inference rule being used: There is at least one x_5 for which if x_5 were a doctor, then x_5 is curious. For all x_5, x_5 is happy or x_5 is a doctor. For all x_5, if x_5 were happy, then x_5 is curious. For all x_5, if x_5 were curious, then x_5 is happy.
There is at least one x_5 for which if x_5 were a doctor, then x_5 is happy can be inferred via the existential transitivity rule. There is at least one x_5 for which x_5 is curious can be inferred via the existential disjunction elimination rule. For all x_5, x_5 is happy if and only if x_5 is curious can be inferred via the universal biconditional introduction rule. For all x_5, x_5 is curious if and only if x_5 is happy can be inferred via the universal biconditional introduction rule.