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We give an affirmative answer to a problem of Conlon, Fox and Sudakov by proving that, for every fixed \\(s\\ge4\\), \\[\n  f^{(4)}_{s,s+1}(n)=(\\log n)^{o(1)} . \\] The key input is a new \\(3\\)-uniform estimate: for every fixed \\(s\\ge3\\), \\(f^{(3)}_{s,s+1}(n)=O(\\frac{\\log n}{\\log\\log n})\\). This improves the logarithmic upper bound of Dudek and Mubayi. 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