You can simply say "We are terminating your employment." However, that generally means that you cannot demand back relocation, bonuses, stocks, etc. and you're going to have to cough up equivalent severance to everybody else--otherwise you're staring at a discrimination lawsuit.
In which case fire them with no reason. If however you waive that choice and offer a specific reason then you probably should make the chosen reason true unless you want to be sued for wrongful dismissal.
Giving an invalid reason that is unsupported by facts is generally a strong place for a lawyer to assert "wrongful termination" and invoke those laws.
They gave a reason: performance and the girl mentioned to have 0 sales + 3 opportunities.
I wouldn't bet a penny on that lawsuit to win.
Not closing a deal in your first month of sales is not exactly unheard of or even uncommon.
Either way, WT lawsuits don't generally "win or lose". They settle.