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: If Thomas were a scientist, then Richard is playing a game. If Richard plays a game, then Thomas is a scientist. Robert is not playing squash. Robert is playing squash if and only if Thomas is a scientist.
Thomas is a scientist if and only if Richard is playing a game can be inferred via the biconditional introduction rule. Richard is playing a game if and only if Thomas is a scientist can be inferred via the biconditional introduction rule. If Robert plays squash, then Thomas is a scientist can be inferred via the biconditional elimination rule. If Thomas were a scientist, then Robert is playing squash can be inferred via the biconditional elimination rule. Thomas is not a scientist can be inferred via the biconditional elimination rule.