Learn English – “has been studied” versus “has studied”

Without any other context, (b) is the best option. "The atmosphere has been proved to extend several hundred kilometers above the Earth" does the best job of providing the necessary context within the sentence.

"The atmosphere proves to extend several hundred kilometers above the Earth" would sound better if it were preceded by a statement like "When measured using radio-scattering technology".

"The atmosphere is proved to extend several hundred kilometers above the Earth" would sound better if it were preceded by a statement like "In the work of Professor Braun".

In this context, any of the three choices would have essentially the same meaning. The writer is trying to define what it means to "benefit" from work performed by someone else for purposes of the legal principle under discussion. His point appears to be that from a contract law point of view, the recipient "benefits" if he gets the service that he asked for, regardless of whether that service really does him any good.

(I presume the point he is building toward is that the recipient must live up to his part of the contract -- paying the agreed price or whatever he said he would do -- even if the service turns out to not provide the benefit he expected. This makes sense to me. If, say, you hire a taxi to take you to your friend's house, and when you get there you discover that your friend is not home, you might well say that this was a wasted trip and that you did not get anything of value from it. But it's not the cab driver's fault that you didn't call ahead or make arrangements. He performed exactly the service you asked him to perform, and so you owe him the agreed-upon fare for the trip.)

So the tense of the benefit doesn't really matter here. Technically, "is benefitted" means that he is getting the benefit right now. "Was benefitted" means that he got the benefit in the past. "Has benefitted" means that he got the benefit over a period of time. Etc. But whether the benefit was in the past, the present, or was not expected to be realized until the future, the point here is that the benefit does or does not happen, not when it might happen.