This is slightly adapted from John Ioannidis's original, which can be found at http://www.netfunny.com/rhf/jokes/90q4/burnher.html
Monty Python and the Holy Grail
Scene 5: 'Burn the witch!'
(abridged)
BEDEVERE: Quiet! Quiet! Quiet!
Quiet! There are ways of telling whether she is a witch.
CROWD: Tell us! Tell us!... BEDEVERE: Tell me. What do you do with witches? CROWD: Burn! Burn them up! Burn!... 

BEDEVERE: And what do you burn
apart from witches?
VILLAGER #1: More witches! VILLAGER #2: Wood! BEDEVERE: So, why do witches burn? VILLAGER #3: B... 'cause they're made of... wood? BEDEVERE: Good! Heh heh. 
[3] ∀x, ISMADEOFWOOD(x) ⇒ BURNS(x) 
BEDEVERE: So, how do we tell
whether she is made of wood?
VILLAGER #1: Build a bridge out of her. BEDEVERE: Ah, but can you not also make bridges out of stone? VILLAGER #1: Oh, yeah. BEDEVERE: Does wood sink in water? VILLAGER #2: No, it floats! It floats! CROWD: The pond! Throw her into the pond! 
[4] ∀x, FLOATS(x) ⇒ ISMADEOFWOOD(x) 
BEDEVERE: What also floats in
water?
VILLAGER #3: Uh, very small rocks! ARTHUR: A duck! CROWD: Oooh. 
[5] FLOATS(DUCK) 
BEDEVERE: Exactly. So,
logically...
VILLAGER #1: If... she... weighs... the same as a duck,... she's made of wood. BEDEVERE: And therefore? CROWD: A witch! A witch!... 
[6] ∀x,y FLOATS(x) ∧ SAMEWEIGHT(x,y) ⇒
FLOATS(y) 
VILLAGER #4: Here is a duck.
Use this duck.
DUCK: [quack quack quack] BEDEVERE: Very good. We shall use my largest scales. BEDEVERE: Right. Remove the supports! [whop] [clunk] [creak] CROWD: A witch! A witch! A witch! WITCH: It's a fair cop. CROWD: Burn her! Burn her! Burn her! Burn! Burn!... 
and, by experiment,

First, we reduce [1] through [7] to Conjunctive Normal Form
From:  We get: 

[1] BURNS(x) ∧ WOMAN(x) ⇒ WITCH(x) 
[9] ¬BURNS(x) ∨ ¬WOMAN(x) ∨ WITCH(x) 
[2] WOMAN(GIRL) 

[3] ∀x, ISMADEOFWOOD(x) ⇒ BURNS(x) 
[10] ¬ISMADEOFWOOD(x) ∨ BURNS(x) 
[4] ∀x, FLOATS(x) ⇒ ISMADEOFWOOD(x) 
[11] ¬FLOATS(x) ∨ ISMADEOFWOOD(x) 
[5] FLOATS(DUCK) 

[6] ∀x,y FLOATS(x) ∧ SAMEWEIGHT(x,y) ⇒ FLOATS(y) 
¬(FLOATS(x) ∧ SAMEWEIGHT(x,y)) ∨ FLOATS(y)  that
is,

[7] SAMEWEIGHT(DUCK,GIRL) 

To prove: WITCH(GIRL) 
So add:

Now we'll try to resolve these statements to a NIL.
Using:  Conclude: 

[12] ¬FLOATS(x) ∨ ¬SAMEWEIGHT(x, y) ∨ FLOATS(y) 
Substituting DUCK and GIRL for
x and y gives:

[14] ¬ 
[15] ¬FLOATS(DUCK) ∨ FLOATS(GIRL) 
[15] ¬FLOATS(DUCK) ∨ FLOATS(GIRL) 
[16] FLOATS(GIRL) 
[11] ¬FLOATS(x) ∨ ISMADEOFWOOD(x) 
Substituting GIRL for x gives:

[17] ¬FLOATS(GIRL) ∨ ISMADEOFWOOD(GIRL) 
[18] ISMADEOFWOOD(GIRL) 
[10] ¬ISMADEOFWOOD(x) ∨ BURNS(x) 
Substituting GIRL for x gives:

[19] ¬ISMADEOFWOOD(GIRL) ∨ BURNS(GIRL) 
[20] BURNS(GIRL) 
[9] ¬BURNS(x) ∨ ¬WOMAN(x) ∨ WITCH(x) 
Substituting GIRL for x gives:

[20] BURNS(GIRL) 
[22] ¬WOMAN(GIRL) ∨ WITCH(GIRL) 
[22] ¬WOMAN(GIRL) ∨ WITCH(GIRL) 
[23] WITCH(GIRL) 
[23] WITCH(GIRL) 
NIL 
which proves, once and for all, that the villagers were right and the girl was indeed a witch! BURN HER! 