Ruling on eating from the university canteen if the plates are not washed seven times after having been licked by dogs

Praise be to Allah.

Firstly: 

Muslims narrated in his Saheeh (279) that Abu Hurayrah (may Allah be pleased with him) said: The Messenger of Allah (sa) said: “The purification of the vessel of one of you, if a dog licks it, is to wash it seven times, the first time with dust.” 

An-Nawawi (may Allah have mercy on him) said: This clearly supports the view of ash-Shaafa‘i (may Allah be pleased with him) and others who say that dogs are najis (impure), because purification is only needed in the case of impurity.

End quote from Sharh Muslim

For more information please see the answers to questions no. 2453 and 46314 

Once it is established that the saliva of dogs is impure (najis) and that the vessels that the dogs have licked cannot be purified except by washing them in the manner described in the hadeeth, then what you have to do is advise the canteen workers and emphasise to them that they have to make sure that the plates are not left where the dogs can reach them. If it so happens that they forget some of them or neglect to protect them from being licked by the dogs, then they must be washed seven times, the first time with dust. 

If they respond to your advice and requests, then there is nothing wrong with you eating in their canteen; if they do not respond then do not eat anything from these plates of theirs. 

And Allah knows best.