Algebra of predicates {D(k)} (Helen Mironchick ) versus Advanced Implication usage by Natalya Konina regarding problem 132 from ege18.doc

Original task

Solution bellow differs from the original one proposed by Helen Mironchick
to address question of Anastasia Stepanenko, however it is still based on algebra of {D(k)} ( see [1] ) .

Solution itself

D(A) v ¬D(24)^¬D(36) ≡1
D(24)≡ D(2^3)^D(3)
D(36)≡ D(3^2)^D(2^2)

¬D(24)^¬D(36)≡(¬D(2^3) v ¬D(3))^(¬D(3^2) v ¬D(2^2))≡
¬D(2^3)^¬D(3^2) v ¬D(2^3)^¬D(2^2) v ¬D(3)^¬D(3^2) v ¬D(3)^¬D(2^2)

Due to
¬D(3)^¬D(3^2)≡ ¬D(3)
¬D(2^3)^¬D(2^2)≡ ¬D(2^2)

Getting
¬D(2^3)^¬D(3^2) v ¬D(2^2) v ¬D(3) v ¬D(3)^¬D(2^2)≡ ¬D(2^3)^¬D(3^2) v ¬D(2^2) v ¬D(3)
because  ¬D(3) absorbs ¬D(3)^¬D(2^2)

Per De Morgan rules

¬D(2^3)^¬D(3^2) v ¬D(2^2) v ¬D(3)≡ ¬(D(2^3)vD(3^2) v ¬(D(2^2)^D(3))
¬(D(2^3)vD(3^2) v ¬(D(2^2)^D(3))≡ ¬(D(8) v D(9)) v ¬D(12)

Finally we obtain
D(А) v ¬(D(8) v D(9)) v ¬D(12) ≡1
Hence  A(min)=12

You might want to compare it with solution provided in
http://kpolyakov.spb.ru/download/ege18del.pdf 
for the task 132

References
1. E.A. Mironchick ALGEBRA OF PREDICATES AND RELATED GEOMETRIC MODELS CREATION IN REGARDS OF UNIFIED STATE EXAM IN INFORMATICS (RUSSIAN EGE) , Informatics in school #3 2019