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The numerical results $M_{X_{L,+}}=3.95\\pm0.09\\,\\rm{GeV}$ and $M_{X_{H,+}}=5.00\\pm0.10\\,\\rm{GeV}$ disfavor assigning the $X(4140)$ to be the $J^{PC}=1^{++}$ diquark-antidiquark type $cs\\bar{c}\\bar{s}$ tetraquark state. Moreover, we obtain the masses of the $J^{PC}=1^{+-}$ diquark-antidiquark type $cs\\bar{c}\\bar{s}$ tetraquark states as a byproduct. 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The numerical results $M_{X_{L,+}}=3.95\\pm0.09\\,\\rm{GeV}$ and $M_{X_{H,+}}=5.00\\pm0.10\\,\\rm{GeV}$ disfavor assigning the $X(4140)$ to be the $J^{PC}=1^{++}$ diquark-antidiquark type $cs\\bar{c}\\bar{s}$ tetraquark state. Moreover, we obtain the masses of the $J^{PC}=1^{+-}$ diquark-antidiquark type $cs\\bar{c}\\bar{s}$ tetraquark states as a byproduct. 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