demonstrate/prove

Question: Mobile phones emit microwave radio emissions. Researchers are questioning whether exposure to these radio
waves might lead to brain cancer. So far, the data are not conclusive. The scientific evidence does not enable us to say with certainly that mobile phones are categorically safe. On the other hand,
current research has not yet ____ clear adverse effect associated with the prolonged use of mobile phones.
To fill in the gap, which is correct: prove or demonstrate?

I thought it's 'demonstrate', but the correct answer the test gives is 'prove'. After checking the Oxford dictionary, I don't know which of them is more suitable. Please tell me.