Seventy-five problems for testing automatic theorem provers
Journal of Automated Reasoning
ACM SIGACT News
An introduction to mathematical logic and type theory: to truth through proof
An introduction to mathematical logic and type theory: to truth through proof
Efficient unification of quantified terms
Journal of Logic Programming
Lecture notes in computer science on Foundations of logic and functional programming
MUSCADET: an automatic theorem proving system using knowledge and metaknowledge in mathematics
Artificial Intelligence
A resolution rule for well-formed formulae
Theoretical Computer Science
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
An Efficient Unification Algorithm
ACM Transactions on Programming Languages and Systems (TOPLAS)
Introduction to Mathematical Theory of Computation
Introduction to Mathematical Theory of Computation
Symbolic Logic and Mechanical Theorem Proving
Symbolic Logic and Mechanical Theorem Proving
Proceedings of the 7th International Conference on Automated Deduction
A Natural Deduction Automated Theorem Proving System
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
Semantically Guided First-Order Theorem Proving using Hyper-Linking
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
Transforming Matings into Natural Deduction Proofs
Proceedings of the 5th Conference on Automated Deduction
An Intuitionistic Predicate Logic Theorem Prover
An Intuitionistic Predicate Logic Theorem Prover
Computation: finite and infinite machines
Computation: finite and infinite machines
The equality axioms are not independent
ACM SIGACT News
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A natural deduction system was adapted from Gentzen system. It enables valid wffs to be deduced in a very ‘natural’ way. One need not transform a formula into other normal forms. Robinson’s unification algorithm is used to handle clausal formulas. Algorithms for eliminating and introducing quantifiers without Skolemization are presented, and unification theorems for them are proved. A natural deduction automated theorem prover based on the algorithms was implemented. The rules for quantifiers are controlled by the algorithms. The Andrews challenge and the halting problem were proved by the system.