An ATP of a Relational Proof System for Order of Magnitude Reasoning with Negligibility, Non-closeness and Distance

We introduce an Automatic Theorem Prover (ATP) of a dual tableau system for a relational logic for order of magnitude qualitative reasoning, which allows us to deal with relations such as negligibility, non-closeness and distance. Dual tableau systems are validity checkers that can serve as a tool for verification of a variety of tasks in order of magnitude reasoning, such as the use of qualitative sum of some classes of numbers. In the design of our ATP, we have introduced some heuristics, such as the so called phantom variables, which improve the efficiency of the selection of variables used un the proof.