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A correct proof (a proof which is indistinguishable from previously sent proof) can be tagged as wrong by the ideal functionality here if the adversary sends no witness.

And, let's say P is a party which has does not have a witness, it can send an arbitrary string. And this proof might get accepted if the adversary has knowledge of the witness.

This functionality according to me does not capture completeness and soundness! Am I missing something?

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    $\begingroup$ Why do you think soundness is not preserved? Proofs are accepted iff a witness has been presented for the statement. Since witnesses by definition do not exist for statements not in the language, only true statements can have valid proofs. $\endgroup$ – Maeher Oct 21 '19 at 13:02
  • $\begingroup$ Yes. The proofs are sound. But does it capture correctness? $\endgroup$ – Severus Oct 21 '19 at 20:00

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