Overview 3 T A P is a tableau-based theorem prover for many-valued rst-order logics with sorts (in the two-valued version with equality); it is implemented in Prolog. This paper gives an overview of the system with a special focus on the new features of 3 T A P Version 4.0, including: eecient completion-based equality reasoning , methods for handling redundant axiom sets, utilization of pragmat...