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11 Introduction 1

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OTTER is a resolution-style theorem-proving program for first-order logic with equality. OTTER includes the inference rules binary resolution, hyperresolution, URresolution, and binary paramodulation. Some of its other abilities and features are conversion from first-order formulas to clauses, forward and back subsumption, factoring, weighting, answer literals, term ordering, forward and back demodulation, evaluable functions and predicates, Knuth-Bendix completion, and the hints strategy. OTTER is coded in ANSI C, is free, and is portable to many different kinds of computer. 1. Renumber variables. * 2. Output new_cl. 3. Demodulate new_cl (including $ evaluation). * 4. Orient equalities. * 5. Apply unit deletion. 6. Merge identical literals (leftmost copy is kept). * 7. Apply factor-simplification. * 8. Discard new_cl and exit if too many literals or variables. 9. Discard new_cl and exit if new_cl is a tautology. * 10. Discard new_cl and exit if new_cl is too 'heavy'. * 11. Sort literals. * 12. Discard new_cl and exit if new_cl is subsumed by any clause in usable, sos, or passive (forward subsumption). 13. Integrate new_cl and append it to sos. * 14. Output kept clause. * 17. Print the proof if a refutation has been found. * 18. Try to make new_cl into a demodulator.