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_1, x_1 will play tennis if and only if x_1 is a scientist. For all x_1, if x_1 plays tennis, then x_1 is curious. There is at least one x_1 for which x_1 is not a scientist. For all x_1, x_1 will play tennis if and only if x_1 is curious.
For all x_1, if x_1 plays tennis, then x_1 is a scientist can be inferred via the universal biconditional elimination rule. For all x_1, if x_1 plays tennis, then x_1 is curious can be inferred via the universal biconditional elimination rule. For all x_1, if x_1 were a scientist, then x_1 is playing tennis can be inferred via the universal biconditional elimination rule. For all x_1, if x_1 were curious, then x_1 is playing tennis can be inferred via the universal biconditional elimination rule. There is at least one x_1 for which x_1 will not play tennis can be inferred via the existential biconditional elimination rule.