disapprove, disprove

Disapprove or disapprove means to find unacceptable or wrong; to reject or condemn--
I'm sure your parents would disapprove of that behavior if they knew about it.
You didn't spend much time on that project; your teacher will disapprove.

Disprove or disprove means to show or demonstrate that something is false or wrong; to refute--
One way to disprove the theory is to demonstrate that the reverse or opposite is true.
An intelligent person would not attempt to prove or disprove religious claims.

Now that you know that, you can say--
"Many of us disapprove of  claims of meeting extra-terrestrials, but they are impossible to disprove."

Note--"disapprove"may be mean the same as "not approve"--
Your parents would not approve of that behavior.
"Not approve" may also mean to refuse a request or application--
The DMV did not approve his application for a permit.