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We also use the same method to deal with $4$-folds, and prove that for a smooth projective irregular $4$-fold $X$ with $K_X\\equiv 0$ and an ample divisor $L$ on $X$, $|mL+P|$ gives a birational map for all $m\\geq 5$ and all $P\\in \\text{Pic}^0(X)$. 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