Should I break up with her?

I few months ago I went shopping, after I went to visit a friend. I called my girlfriend to say that I was at my friend's, she didn't like the idea of me telling her that I went shopping and then going to see my friend. So she decided to go out without telling me, just to get back at me. I called her and she said that she was at her girlfriend's place.
She sounded vague and rude and put the phone down on me. I didn't bother. She got home around 12am and came to the bed drinking tea in a huge mug I never saw before. I asked her were did you get that mug, she said she bought it, then I said that it looks old so she was lying, she then confessed that she got it from her parents home that evening, and that she didn't go to see her friend as she had said earlier.
I caught her lying but I didn't judge her, but she started to cry saying that I would probably have lost all the trust in her.
I comforted her and said to not worried about it.

A few months later her father came to visit, I made him a coffee and served it on that same mug, he started to complain about how big the mug was, so I told him your daughter bought it from your house, he replied that he never seen that mug before and that it was impossible for it to came from his house.

Later that evening I told her what her dad said, she didn't said anything about it and walked away, later I asked her if she had really brought it from her parents house, she just said yes and no further comment. Knowing how she always waits for people to accuse her and then play the victim, I decided to not confront her about it, I remained calm and silent, but now I'm planning to break up with her.

She tried her hardest to cover up the fact that in that day she went to see some secret person till late, and that person gave her the mug. The fact that she made up all this stories to cover up where she really was and that after getting caught not telling me the truth, is enough for me to assume that she was messing about.
Should I break up with her?
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