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Why may a clause be used more than once in a single proof?

  • A.Proof procedures cache clauses for efficiency reasons
  • B.Each use consumes a different literal of the clause
  • C.The clause is copied into the knowledge base each time
  • D.It is universally quantified so any number of instances hold

Answer: D

Because the clause holds for every instantiation, distinct instances may be used at different points in the same derivation, with fresh variables each time. That is exactly why standardising apart must be repeated per use rather than done once. Caching, literal consumption and copying are implementation matters. A premise that is a universally quantified statement is an inexhaustible resource, which is a genuine difference from a propositional premise.

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