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_10, x_10 will sleep if and only if x_10 will play a game. Barbara is playing a game. If Michael cooks, then Barbara is sleeping.
There is at least one x for which x will play a game can be inferred via the existential generalization rule. For all x_10, if x_10 sleeps, then x_10 is playing a game can be inferred via the universal biconditional elimination rule. For all x_10, if x_10 plays a game, then x_10 is sleeping can be inferred via the universal biconditional elimination rule.