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I would like to know if there is a point $(a, b, p, q, x, y) \in [0,1]^6$ satisfying the following collection of inequalities. $b \ge a$ $q \ge p$ $y \ge x$ $a \ge p \ge a^2$ $b \ge q \ge b^2$ $p \ge ...

Let $n_1, n_2 \geq 1$ be known integer constants. Suppose that we have the following system of $n$ polynomial inequalities for which we know that there exists a feasible solution $(p_1, p_2) \in (0,1)...