The cake is a liar! Part 3

Alan, Ben, Chris, Dave, Emma and Frank are eating a big cake. After eating, there was one slice left, and they decided to leave it for Gabe but someone ate it! Gabe knows that FOUR people are telling ONE lie, but all other statements are true:

Alan said: It wasn't Ben, It wasn't Dave, It wasn't Emma.
Ben said: It wasn't Alan, It wasn't Chris, It wasn't Emma.
Chris said: It wasn't Ben, It wasn't Frank, It wasn't Emma.
Dave said: It wasn't Alan, It wasn't Frank, It wasn't Chris.
Emma said: It wasn't Chris, It wasn't Dave, It wasn't Frank.
Frank said: It wasn't Chris It wasn't Dave It wasn't Alan.

Who ate the cake?

Also, please check Part 1, Part 2 and Part 4.