ANTIGONE: algorithms for coNTinuous/Integer global optimization of nonlinear equations. This manuscript introduces ANTIGONE, Algorithms for coNTinuous/Integer Global Optimization of Nonlinear Equations, a general mixed-integer nonlinear global optimization framework. ANTIGONE is the evolution of the Global Mixed-Integer Quadratic Optimizer, GloMIQO, to general nonconvex terms. The purpose of this paper is to show how the extensible structure of ANTIGONE realizes our previously-proposed mixed-integer quadratically-constrained quadratic program and mixed-integer signomial optimization computational frameworks. To demonstrate the capacity of ANTIGONE, this paper presents computational results on a test suite of 2,571 problems from standard libraries and the open literature; we compare ANTIGONE to other state-of-the-art global optimization solvers.