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Why must clause selection be fair in a saturating prover?

  • A.Otherwise the prover would use too much memory
  • B.Otherwise the clauses would be derived in the wrong order
  • C.Otherwise subsumption could not be applied correctly
  • D.Otherwise some clause might never be selected and a proof missed

Answer: D

A heuristic that always prefers short clauses might postpone a long one indefinitely, losing completeness, so a fairness mechanism such as alternating with age is required. Memory, ordering and subsumption are separate concerns. That an aggressive heuristic can destroy completeness unless deliberately tempered is a lesson that applies to any priority driven search, and the remedy is always some form of guaranteed eventual selection.

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