# How to prove a Double CNF SAT is in NP [duplicate]

So I've been stuck trying to figure this problem out for a while. I've looked on wikis and all over stack exchange but I'm really stumped. This isn't my best subject, so any sort of explanation would be AMAZING.

The Double CNF SAT problem is given a Boolean formula in CNF determine if it
is satisfiable with every clause having at least two literals that are true.
Show that Double CNF SAT is in NP.


I'm really not confident in these SAT, NP problems. I know that NP is the class that consists of problems "verifiable" in polynomial times. So is my goal to show that a double CNF SAT can be verified in polynomial time? If so, how would I do this? How am I supposed to verify it in polynomial time. Is it just a generic solution?

Thanks for any contributions/help

## marked as duplicate by D.W.♦, Nicholas Mancuso, Juho, David Richerby, Luke MathiesonMay 6 '15 at 9:09

In answer to your comment; yes, you can simply iterate through the clauses. If I had given you a certificate like $$(y\lor w\lor u)\land(x\lor y\lor \overline{u}\lor z); x=T, y=T, z=F, w=T, u=F$$ could you quickly (in time polynomial in the length of the certificate) verify that (1) the CNF expression is satisfied by the assignments and (2) every clause has at least two literals that are true? Bet you could and could see that this verification is always possible. From that, one can conclude that DOUBLE CNF SAT is indeed in NP.