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273-282, Paris UNESCO House, 1959. , "A Simplified Format for the Model Elimination TheoremProving Procedure", J. ACM, Vol. 16, No. 3, pp. 349-363, July 1969. , 'Refinement Theorems in Resolution Theory", Proc. IRIA Syrup. Automatic Demonstration, Versailles, France, 1968, Springer-Verlag, New York, pp. 163-190, 1970. , "Non-Horn Clause Logic Programming Without Contrapositires", Journal of Automated Reasoning, Vot. 4, Nov. 3, September 1988. , "A Semantically Guided Deductive System for Automatic Theorem Proving", I E E E Transaction on Computers, Vol.

The input clauses to the modified problem reduction format are given as Horn-like clauses. For each clause C, only one Horn-like clause H C will be needed; the clause heads of the input clauses must be a positive literal (for 18 clauses containing positive literals) or F A L S E (for all-negative clauses). The modified problem reduction format has an inference rule for each input clause plus the a s s u m p t i o n a x i o m s and the case analysis rule. If S is a set of Horn-like clauses, we obtain a set of inference rules from S for the modified problem reduction format as follows: For each Horn-like clause L : - L x , L~ .

1 l J Figure 1: System architecture input formula with others that anticipate inferences of the proof process itself. Currently our preprocessing module consists of five independent submodules: tautology reduction, restricted unit resolution, subsumption reduction, purity reduction, and isolated connection reduction. For a detailed description consult [16]. The inference machine, the sequential version as well as the parallel one, is realized as an abstract machine. Hence the formula must be compiled into abstract machine code.

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