Seventy-five problems for testing automatic theorem provers
Journal of Automated Reasoning
A PROLOG technology theorem prover: implementation by an extended PROLOG compiler
Proc. of the 8th international conference on Automated deduction
Principles of artificial intelligence
Principles of artificial intelligence
An introduction to mathematical logic and type theory: to truth through proof
An introduction to mathematical logic and type theory: to truth through proof
On connections and higher-order logic
Journal of Automated Reasoning
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
Efficiency and Completeness of the Set of Support Strategy in Theorem Proving
Journal of the ACM (JACM)
A Proof Procedure Using Connection Graphs
Journal of the ACM (JACM)
Theorem Proving via General Matings
Journal of the ACM (JACM)
Symbolic Logic and Mechanical Theorem Proving
Symbolic Logic and Mechanical Theorem Proving
The TPS Theorem Proving System
Proceedings of the 9th International Conference on Automated Deduction
Presenting Intuitive Deductions via Symmetric Simplification
Proceedings of the 10th International Conference on Automated Deduction
Transforming Matings into Natural Deduction Proofs
Proceedings of the 5th Conference on Automated Deduction
On the Comparative Complexity of Resolution and the Connection Method
On the Comparative Complexity of Resolution and the Connection Method
Automated theorem proving: A logical basis (Fundamental studies in computer science)
Automated theorem proving: A logical basis (Fundamental studies in computer science)
Towards an advanced implementation of the connection method
IJCAI'83 Proceedings of the Eighth international joint conference on Artificial intelligence - Volume 2
Some necessary conditions for a master chess program
IJCAI'73 Proceedings of the 3rd international joint conference on Artificial intelligence
On the dynamic increase of multiplicities in matrix proof methods for classical higher-order logic
TABLEAUX'05 Proceedings of the 14th international conference on Automated Reasoning with Analytic Tableaux and Related Methods
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The mating paradigm for automated theorem provers was proposed by Andrews to avoid some of the shortcomings in resolution. It facilitates automated deduction in higher-order and non-classical logics. Moreover, there are procedures which translate back and forth between refutations by the mating method and proofs in a natural deduction system. We describe a search procedure, called path-focused duplication, for finding refutations by the mating method. This procedure, which is a complete strategy for the mating method, addresses two crucial issues (inadequately handled in current implementations) that arise in the search for refutations: when and how to expand the search space. It focuses on a particular path that seems to cause an impasse in the search and expands the search space relative to this path in a way that allows the search to immediately resolve the impasse. The search space grows and shrinks dynamically to respond to the requirements that have arisen or have been met in the search process, thus avoiding an explosion in the size of the search space. We have implemented a prototype of this procedure and have been able to easily solve many problems that an earlier program found difficult.