The first is very formal, but acceptable. The seccond and third are incorrect. The fourth is possible, but would be far more natural as She is the girl to beat.
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Anonymous 99% of English people will say "She is the girl to rely on" even though it is not grammatically correct.Who says it is not correct?
Amir OghlowWhen I say "She is the girl to beat."Does it mean "She is the girl who is beaten or who is going to be beaten"?Neither. It means that she is the girl whom we should attempt to beat.
Amir OghlowAre they natural?Yes. Of course, I don't know what you think they mean.
fivejedjonWho says ir is not correct?I don't know who says that, but I think Anon means that an active infinitive (to beat) is used even though the meaning is passive. In other words, the girl does not rely on anything in the sentence. Others rely, or should rely, on her. CalifJim once gave an excellent example of this grammatical phenomenon with his s