Seventy-five problems for testing automatic theorem provers
Journal of Automated Reasoning
First-order logic and automated theorem proving (2nd ed.)
First-order logic and automated theorem proving (2nd ed.)
JELIA '96 Proceedings of the European Workshop on Logics in Artificial Intelligence
KI '97 Proceedings of the 21st Annual German Conference on Artificial Intelligence: Advances in Artificial Intelligence
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Several syntactic methods have been constructed to automate theorem proving in first-order logic. The positive (negative) hyper-resolution and the clause tableaux were combined in a single calculus called hyper tableaux in [1]. In this paper we propose a new calculus called hyperS tableaux which overcomes substantial drawbacks of hyper tableaux. Contrast to hyper tableaux, hyperS tableaux are entirely automated and heuristic. We prove the soundness and the completeness of hyperS tableaux. HyperS tableaux are applied in the theorem prover Sofia, which additionally provides useful tools for clause set generation (based on justificational tableaux) and for tableau simplification (based on redundancy), and advantageous heuristics as well. An additional feature is the support of the so-called parametrized theorems, which makes the prover able to give compound answers.