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No, #2 is the correct meaning. #1 is nonsense, as it is vacuously satisfied for any statement in any theory: one of the two algorithms ""return YES"" and ""return NO"" always works. I do not see any ambiguity in the formulation, it clearly starts with an existential quantifier, and in any case, there is a link to decidability (logic) which explains it in detail. You just have to read carefully. —  J. "