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 Charles goes running, then it is cold. If it is cold, then William is making tea. Robert is taking a plane if and only if Charles is running. Mary is not writing a letter. William is making tea if and only if Mary is writing a letter.
If Charles goes running, then William is making tea can be inferred via the transitivity rule. If Robert takes a plane, then Charles is running can be inferred via the biconditional elimination rule. If William makes tea, then Mary is writing a letter can be inferred via the biconditional elimination rule. If Charles goes running, then Robert is taking a plane can be inferred via the biconditional elimination rule. If Mary writes a letter, then William is making tea can be inferred via the biconditional elimination rule. William is not making tea can be inferred via the biconditional elimination rule.