Consider the following premises. p -> t. w. p_14 -> t. w -> p_14. p_14 -> w. Can we infer ~t from them? If possible, name the inference rules being used at each step.
 From p_14 -> w, w -> p_14 we can infer p_14 <-> w via biconditional introduction. From p_14 <-> w we can infer w -> p_14 via biconditional elimination. From w -> p_14, p_14 -> t we can infer w -> t via transitivity. From w we can infer w or p via addition. Finally, from w -> t, p -> t, w or p we can infer t via disjunction elimination, which contradicts ~t. Therefore, the answer is no.