The discipline of automated theorem proving encompasses techniques which allow us to find a justification of a logical statement expressing an assertion in some domain of knowledge. Beside obvious importance for mathematics, many of the tasks traditionally associated with human…

We consider a nonlinear mathematical program, with twice continuously differentiable functions., If a point x$ sb0$ does not satisfy a certain Second Order Sufficient Condition (SOS) for optimality (that does not require any constraint qualification, see, e.g., BEN-ISRAEL, BEN-TAL and…