Unification algorithms for eliminating and introducing quantifiers in natural deduction automated theorem proving

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.