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_6, if x_6 plays tennis, then x_6 is not excited. For all x_6, x_6 is a scientist if and only if x_6 will play a game. For all x_6, x_6 is excited. For all x_6, x_6 is a scientist if and only if x_6 will play tennis.
For all x_6, x_6 will not play tennis can be inferred via the universal modus tollens rule. For all x_6, if x_6 were a scientist, then x_6 is playing a game can be inferred via the universal biconditional elimination rule. For all x_6, if x_6 were a scientist, then x_6 is playing tennis can be inferred via the universal biconditional elimination rule. For all x_6, if x_6 plays a game, then x_6 is a scientist can be inferred via the universal biconditional elimination rule. For all x_6, if x_6 plays tennis, then x_6 is a scientist can be inferred via the universal biconditional elimination rule.