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: Joseph is playing a game. For all x_8, if x_8 plays a game, then x_8 is a carpenter. For all x_8, if x_8 were a carpenter, then x_8 is playing a game.
There is at least one x for which x will play a game can be inferred via the existential generalization rule. For all x_8, x_8 will play a game if and only if x_8 is a carpenter can be inferred via the universal biconditional introduction rule. For all x_8, x_8 is a carpenter if and only if x_8 will play a game can be inferred via the universal biconditional introduction rule.