Abstract
A system for parallel proofs is proposed. This system proves the inconsistency of formulas in the disjunctive-normal-forms. The system is a meta-system of Horn clauses (meta-rules) of a meta-predicate Prov which represents a clause. A parallelism other than or-parallelism and the reduction of proving procedures with or-parallelism are shown. The efficiency is quantitatively shown for a simple case by estimating the complexity with or-parallelism defined by the number of matching steps needed for the proof. A feature of the system is that any set of clauses can be represented as one meta-rule by using the disjunctive-normal-form. This fact shows new approaches to the parallelism and the use of lemmas. The soundness and the completeness of the system are proved.
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