We describe and evaluate a novel optimization-based off-line path planning algorithm for mobile robots based on the Counterexample-Guided Inductive Optimization (CEGIO) technique. CEGIO iteratively employs counterexamples generated from Boolean Satisfiability (SAT) and Satisfiability Modulo Theories (SMT) solvers, in order to guide the optimization process and to ensure global optimization. This paper marks the first application of CEGIO for planning mobile robot path. In particular, CEGIO has been successfully applied to obtain optimal two-dimensional paths for autonomous mobile robots using off-the-shelf SAT and SMT solvers.