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#### The search efficiency of theorem proving strategies: an analytical comparison

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##### Fulltext (public)

MPI-I-94-233.pdf

(Any fulltext), 343KB

##### Supplementary Material (public)

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##### Citation

Plaisted, D.(1994). *The search efficiency of theorem proving
strategies: an analytical comparison* (MPI-I-94-233). Saarbrücken: Max-Planck-Institut für Informatik.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0014-B5B4-8

##### Abstract

We analyze the search efficiency of a number of common refutational
theorem proving strategies for first-order logic. Search efficiency
is concerned with the total number of proofs and partial proofs
generated, rather than with the sizes of the proofs. We show that
most common strategies produce search spaces of exponential size even
on simple sets of clauses, or else are not sensitive to the goal.
However, clause linking, which uses a reduction to propositional
calculus, has behavior that is more favorable in some respects, a
property that it shares with methods that cache subgoals. A strategy
which is of interest for term-rewriting based theorem proving is the
A-ordering strategy, and we discuss it in some detail. We show some
advantages of A-ordering over other strategies, which may help to
explain its efficiency in practice. We also point out some of its
combinatorial inefficiencies, especially in relation to
goal-sensitivity and irrelevant clauses. In addition, SLD-resolution,
which is of importance for Prolog implementation, has combinatorial
inefficiencies; this may suggest basing Prolog implementations on a
different theorem proving strategy.