I have the following problem:
We are given an instance of the 3-SAT problem. Is there a satisfying assignment s.t. at least two literals are satisfied in each clause?
The question is:
Is the problem NP-complete?
The question might sound stupid, but I couldn't figure it out by myself.
I searched the web and in books but didn't find anything.
I also tried to reduce 3-SAT to it, but without success.
(I have to admit that I didn't spent much time to do it since it is not my main research focus; this is just a question that came to my mind while working on another problem. I am interested in the answer because if it turns out to be NP-complete it could help me in a future problem.)
Thanks in advance for your answers! Every answer or comment is welcome.