Conjectures can always be proven true.
true or false

If it's false then it can't be proven true

basically if you start with a crazy wrong conjecture, then it can't be proven true

a conjecture is a guess based on incomplete information
some examples are when you have some special cases and assume they are true for all cases

example:
this rectangle is 4 by 16
this square is 8 by 8
they have the same area
therfor I think that all squares have the same area as rectangles
(that's obviously false)
so you can't prove that true