Blowing Mind Epistemic Paradox

This is an old, one but it's rational nutshell. No one has solved it up today.
This one reminds of the Socrates's one, when the philosopher said: "All I know that I know nothing".

The paradox is told usually logical, with epistemic and modal operators:

Alphabet:
p, q – is certain propositions that are either true, or false
K – modal operator for knowledge; means "Kp = a person knows p" or "p is known"
♦ - modal operator for possibility; means "♦p = p is possible"

Axioms:
1. Kp → p
2. K(p & q) → (Kp & Kq)
3. p → ♦Kp

2nd is easy, it means to distribute the operator K, so it's algebraic;
1st is "if we know p, then p must be true" (otherwise, this isn't knowledge)
3rd is an epistemic principle means "if there's a true knowledge, it's possible for us to find it".

Then let's try to entail something from a phrase

p & ~Kp

which means "there's a knowledge, yet we don't know it. It's a coherent statement, since we still don't know every true facts. Applying 3:

♦K(p & ~Kp)

and then use 2:

♦(Kp & K~Kp)

transforming K~Kp into ~Kp using 1:

♦(Kp & ~Kp)

that reads: "it's possible to know and not to know p at the same time".

Later changes won't bring results, because the sequence and logic behind these proof is correct.