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What practical consequence follows from semidecidability?

  • A.Only propositional encodings may be used in practice
  • B.A prover may run indefinitely without reporting failure
  • C.No theorem in first order logic can ever be proved
  • D.Every first order question must be answered eventually somehow

Answer: B

A user who has waited an hour cannot tell whether the conjecture is false or the proof is merely long, which is why provers report timeouts rather than negative answers. Theorems are provable and questions are often answered, and propositional encodings are one response among several. Knowing that a negative result is unobtainable, rather than merely slow, changes how a tool's output must be interpreted.

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