The problem I'm working on is: Prove that indirect proof is a tautologically valid method of proof. That is, show that if P1,...,Pn, S is TT-contradictory, then ~S is a tautological consequence of P1,...,Pn. What I have done so far is set up a TT with P1 to Pn being my premises, and S being P1^P2^...^Pn. A TT-contradictory means that there's a false P in every row going across, so that S is never true. So then I set up another TT with P1 to Pn, and made ~S be (~P1 or ~P2 or ... or ~Pn). So now ~S is always true, because there's always going to be at least one P that is false in every row, by definition of a TT-contradictory. Is this all I have to do??? I'm really stuck on this question, I feel like it should be harder than that. Can anybody help me?