It's a paradox! Maybe?

Logic Level 3

Consider the following story:

You have the ability to go back in time. So you decide to go back and kill your grandfather when he was born, but this means that your father will never be born since his father (your grandfather) was killed immediately after he was born, meaning that you would also not exist since your father never existed, which means that you never existed in the first place to go back in time and kill your grandfather.

Is the story above a paradox or not?

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