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  1. The argument presupposes that which is to be proved.
  2. The word "refute" means "prove sth to be wrong".

In the first sentence, the phrase "to be" seems to have a meaning of future. However, in the second sentence, the phrase "to be" just seems to explain current status rather than having a meaning of future. This subtle difference makes me confused about how to understand the phrase. What does "to be" exactly mean?

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Think of "to be" in this context as short for "to become". In the first example, the argument will become proven true. In the second example, the argument will become proven wrong. The statements aren't about the actual state or conditions being argued about. They refer to future recognition of correctness or incorrectness resulting from the proof. In both cases, "to be" refers to the future.

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