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Case studies of Z-module reasoning: Proving benchmark theorems from ring theory


A new method, called Z-module reasoning, was formulated for proving and discovering theorems from ring theory. In a case study, the ZMR system designed to implement this method was used to prove the benchmark x 3 ring theorem from associative ring theory. The system proved the theorem quite efficiently. The system was then used to prove the x 4 ring theorem from associative ring theory. Again, a proof was produced easily. These proofs, together with the successes in proving other difficult theorems from ring theory suggest that the Z-module reasoning method is useful for solving a class of problems relying on equality reasoning. This paper illustrates the Z-module reasoning method, and analyzes the computer proof of the x 3 ring theorem.

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This reasearch was supported in part by the Applied Mathematical Sciences subprogram of the office of Energy Research, U.S. Department of Energy, under contract W-31-109-Eng-38.

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Wang, T. Case studies of Z-module reasoning: Proving benchmark theorems from ring theory. J Autom Reasoning 3, 437–451 (1987).

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Key words

  • Automated theorem proving
  • Z-module reasoning
  • equality reasoning
  • ide-paramodulation
  • pseudo-Gaussian elimination
  • ring theory