Absence of belief does not require proof of absence.
There seems to be a general mix-up with 'proof' and 'evidence'. Contrary to misguided belief, they are not the same thing. The only real proofs are mathematical ones, anyway. In math, after the system has been formed, deductive reasoning (rather than inductive or empirical) is applied to accepted premises, and a conclusion can be formed. A deductive argument is always either true or false, and its conclusion is always a bi-conditional statement. If all premises of a deductive argument are true, then the conclusion will be true as well. But for the deductive argument to be valid, all conclusion must be necessarily true. Here are three examples of deductive arguments.
1. A quadrilateral has four sides. (True)
2. A square has four sides. (True)
3. Therefore, a square is a quadrilateral. (True)
In bi-conditional form: A square is a quadrilateral if and only if it has four sides. (If I recall correctly, for a bi-conditional to be true, the inverse, converse, and contrapostive of the bi-conditional must be true as well.)
1. Sarah is a girl. (True)
2. All girls like boys. (False)
3. Sarah likes boys. (False)
Though it is possible for Sarah to still like boys, it isn't necessarily true, and therefore this is a fallacious argument.
1. All men have moobs. (False)
2. All people with extra chest blubber wear bras. (False)
3. All men wear bras. (False)
I'm sure you can see the problem with this one for yourself.
An example of a mathematical proof would be one of the many out there for the Pythagorean Theorem. Here's one we had to prove in math yesterday. From my book:
James Abram Garfield, the twentieth president of the United States, discovered a proof of the Pythagoren Theorem in 1876. His proof involved the fact that a trapezoid can be formed from two congruent right triangles and an isosceles right triangle. Use the diagram at the right to write a paragraph proof showing that a2 + b2 = c2.
What I did was set up the area of the trapezoid using 1/2h(b1 + b2) equal to the area of the three triangles added together. Basically:
1/2(a+b)(a+b) = 1/2ab + 1/2c2 + 1/2ab (Substitution)
1/2(a2 + 2ab + b2) = ab + 1/2c2 (Simplify)
a2 + 2ab + b2 = 2ab + c2 (Multiply both sides by 2)
a2 + b2 = c2 (Subtract 2ab from both sides)
That's a proof. Evidence for the Pythagorean Theorem would be pointing out that with all the variations you've tried with angle measures and side lengths of a right triangle, you always seem to get a2 + b2 = c2. Clearly you haven't tried every combination, and though evidence is helpful, it isn't in upon itself proof.
I'm not asking for proof of mythological creatures, but some evidence (your word, I'm sorry, means nothing to me) would be much appreciated. I mean, if you don't have any evidence, why should I give your (extraordinary) claim any more credence than I would any other random assertion? I was going to use magic, extraordinary healing, and astrology as examples of 'random assertions', but I forgot you probably believe in them too...