How Do You Know Humpty Dumpty Was An Egg?
The story of Humpty Dumpty, upon further chewing, is very revealing as to the insufficiency of many Charedi 'proofs' for Torah - not out of ignorance of Torah.

Humpty Dumpty began as a spoken riddle to children...and children were originally to deduce that Humpty D. is an egg. Only now, b'zman hazeh, is it again oral, but now merely a rhyme because Humpty's eggness is ALREADY common knowledge after almost two centuries of being published in picture books of nursery rhymes for children (first printed in 1810 - much too early for Charedi memory...). It is an assumption, though an understandable one, to first think of it as something one reads and then applies an oral understanding to; but say it to yourself as you say it to a child - as a riddle - and it makes perfect sense that it used to be just that - an oral riddle.

It's actually a potential proof for the critics! Their general position is that Torah laws, narratives and histories were oral and written fragments that co-existed and co-evolved within and between different 'communities', ultimately becoming fossilized in one state or another, in one 'community' or another - and within the regnant (surviving), Jewish community, BOTH torahs are now, due to our sins, written.
Critics claim material (A) became text, material (B) stayed oral and was written later, etc, IOW, material changes form and evolves over time in different contexts, and is interpreted accordingly. And here with Humpty Dumpty you have exactly that; it was an oral 'tradition', a riddle, which then becomes widely known via being printed with images (now no longer a riddle, but a rhyme), and then becomes oral again, repeated without reference to the picture, in our day and setting. Only in the aftermath of this long history can a kiruv rabbi come and ask with astounding sincerity "But how do you know Humpty Dumpty was an egg?"....

Sources;
I. Opie and P. Opie, The Oxford Dictionary of Nursery Rhymes (Oxford: Oxford University Press, 1951, 2nd edn., 1997), pp. 213-5.

http://en.wikipedia.org/wiki/Humpty_dumpty