Refutation of a 'concrete' Rauszer Boolean Algebra Generated by a Preorder

From the 11 equations tested, we refute 13 artifacts: 1. condition for an existential quantifier ∃ … on Boolean 2. a quantifier ∃ as closure operator on B, for which every open element is closed; 3. the interior operator on abstract topological Boolean algebra; 4. the kernel of homomorphism from Heyting algebra into another as filter; 5. deductive systems and filters as equivalent; 6. the atomic definition of p ≤ ∃p in Halmos algebra; 7. ‘concrete’ Rauszer Boolean algebra; 8. two conditions for the definition of filter (and Heyting algebra using the filter); 9. De Morgan algebra as Kleene algebra; 10. equivalences of symmetrical Heyting algebras; 11. equivalences in Heyting algebras; 12. intuitionistic implication of intuitionistic logic; and 13. theorem and proposition of Nelson algebras. As result, the following seven areas are non tautologous fragments of the universal logic VŁ4: 1. Topological Boolean algebra; 2. Heyting algebra; 3. Intuitionistic logic; 4. Halmos algebra; 5. Rauszer algebra; 6. Kleene algebra; and 7. Nelson algebra.