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: For all x_13, x_13 will play tennis if and only if x_13 is curious. For all x_13, x_13 is not poor. For all x_13, x_13 is excited if and only if x_13 will play tennis. There is at least one x_13 for which x_13 is poor if and only if x_13 is curious.
For all x_13, if x_13 plays tennis, then x_13 is curious can be inferred via the universal biconditional elimination rule. For all x_13, if x_13 were excited, then x_13 is playing tennis can be inferred via the universal biconditional elimination rule. There is at least one x_13 for which if x_13 were poor, then x_13 is curious can be inferred via the existential biconditional elimination rule. For all x_13, if x_13 were curious, then x_13 is playing tennis can be inferred via the universal biconditional elimination rule. For all x_13, if x_13 plays tennis, then x_13 is excited can be inferred via the universal biconditional elimination rule. There is at least one x_13 for which if x_13 were curious, then x_13 is poor can be inferred via the existential biconditional elimination rule. There is at least one x_13 for which x_13 is not curious can be inferred via the existential biconditional elimination rule.