Consider a certain formal system with only axiom **Excluded Middle** -$EM$

[![enter image description here][1]][1]

and 18 inference rules:

9 implicative ruules (clearly not independent)

[![enter image description here][2]][2]

and 9 tautological rules:

[![enter image description here][3]][3]

If we have substitution at hands as well but we are restricted no to use conditional proof. 

>Is this particular system complete? 

I always believed that the system is complete. 
But once I decided to prove or disprove completeness I stuck.
I neither can find any reference neither nor can proof completeness.

If someone is familiar with  this system I would be grateful to have some reference or proof. 

  [1]: https://i.sstatic.net/o5WuK.png
  [2]: https://i.sstatic.net/6nGnu.png
  [3]: https://i.sstatic.net/fUZCG.png