Variable elimination and chaining in a resolution-based prover for inequalities

A modified resolution procedure is described which has been designed to prove theorems about general linear inequalities. This prover uses "variable elimination", and a modified form of inequality chaining (in which chaining is allowed only on so called "shielding terms"), and a decision procedure for proving ground inequality theorems. These techniques and others help to avoid the explicit use of certain axioms, such as the transitivity and interpolation axioms for inequalities, in order to reduce the size of the search space and to speed up proofs. Several examples are given along with results from a computer implementation. In particular this program has proved some difficult theorems such as: The sum of two continuous functions is continuous.