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, if x_10 were a musician, then x_10 is playing squash. For all x_10, if x_10 were a soldier, then x_10 is playing a game. For all x_10, if x_10 plays squash, then x_10 is a musician. For all x_10, x_10 will not play squash. For all x_10, if x_10 plays a game, then x_10 is a musician. For all x_10, if x_10 were a musician, then x_10 is playing a game.
For all x_10, x_10 is not a musician can be inferred via the universal modus tollens rule. For all x_10, if x_10 were a soldier, then x_10 is a musician can be inferred via the universal transitivity rule. For all x_10, if x_10 plays squash, then x_10 is playing a game can be inferred via the universal transitivity rule. For all x_10, if x_10 plays a game, then x_10 is playing squash can be inferred via the universal transitivity rule. For all x_10, x_10 is a musician if and only if x_10 will play squash can be inferred via the universal biconditional introduction rule. For all x_10, x_10 will play squash if and only if x_10 is a musician can be inferred via the universal biconditional introduction rule. For all x_10, x_10 will play a game if and only if x_10 is a musician can be inferred via the universal biconditional introduction rule. For all x_10, x_10 is a musician if and only if x_10 will play a game can be inferred via the universal biconditional introduction rule.