A system and method for deciding the satisfiability of a non-linear real decision problem is disclosed. Linear and non-linear constraints associated with the problem are separated. The feasibility of the linear constraints is determined using a linear solver. The feasibility of the non-linear constraints is determined using a non-linear solver which employs interval constraint propagation. The interval solutions obtained from the non-linear solver are validated using the linear solver. If the solutions cannot be validated, linear constraints are learned to refine a search space associated with the problem. The learned constraints and the non-linear constraints are iteratively solved using the non-linear solver until either a feasible solution is obtained or no solution is possible.