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Contrails cannot evaporate because the temperature in the layers of the atmosphere when the planes flight is about -50ºC. They eventually dissipate, but very slowly because the atmosphere in those layers has very low pressure and wind is weak.

Barrels filled with water are used in flight tests to check the plane performance with different weight distribution, pumping the water between the barrels. Source

Anyway, it is impossible to prove that there is not a conspiracy for massive spraying the atmosphere. In case there is, you must try harder to prove it. Until them, by the Occam´s razor principle I will believe that there is no conspiracy at all