The most common and most likely answer to this crossword clue is the 8 plus 2 plus 8 letter word REDUCTIO AD ABSURDUM
I've seen this crossword clue in The Times
R
E
D
U
C
T
I
O
A
D
A
B
S
U
R
D
U
M
Buddy explains!

The straight part
We know that "proof of falsehood" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case proof of falsehood = reductio ad absurdum.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.