Unleash the full power of the Mapping Method (Graphs and Systems of Boolean Equations by E.A. Mironchik) (P-34 with xj,yj,zj,wj ; j=1,.,5 for five conditional equations)

Consider following system

System is a bit harder to treat vs P-34 itself (brackets contain only xj,yj,zj )
in other words 3 digits keys configuration. Why I believe it's worth to analyze ?
P-34 may be solved in a couple of minutes just scanning through {X} bitmask table and calculating sum of solutions  for each row of {X}.
Four variables in brackets result  bitmask approach failure to generate
simple (y,z) systems for each row in {X}. Thus it clearly demonstrates
an advantage of "Graph&&Mapping method"  idea by Helen Mironchick

(x1=>x2)^(x2=>x3)^(x3=>x4)^(x4=>x5)=1

(¬x1+y1+z1+w1)^(x1+¬y1+z1+w1)^(x1+y1+¬z1+w1)^(x1+y1+z1+¬w1)=1
(¬x2+y2+z2+w2)^(x2+¬y2+z2+w2)^(x2+y2+¬z2+w2)^(x2+y2+z2+¬w2)=1  
(¬x3+y3+z3+w3)^(x3+¬y3+z3+w3)^(x3+y3+¬z3+w3)^(x3+y3+z3+¬w3)=1
(¬x4+y4+z4+w4)^(x4+¬y4+z4+w4)^(x4+y4+¬z4+w4)^(x4+y4+z4+¬w4)=1
(¬x5+y5+z5+w4)^(x5+¬y5+z5+w4)^(x5+y5+¬z5+w4)^(x5+y5+z5+¬w5)=1

            Convert system as follows

(x1=>x2)^(¬x1+y1+z1+w1)^(x1+¬y1+z1+w1)^(x1+y1+¬z1+w1)^(x1+y1+z1+¬w1)=1

(x2=>x3)^(¬x2+y2+z2+w2)^(x2+¬y2+z2+w2)^(x2+y2+¬z2+w2)^(x2+y2+z2+¬w2)=1  

(x3=>x4)^(¬x3+y3+z3+w3)^(x3+¬y3+z3+w3)^(x3+y3+¬z3+w3)^(x3+y3+z3+¬w3)=1

(x4=>x5)^(¬x4+y4+z4+w4)^(x4+¬y4+z4+w4)^(x4+y4+¬z4+w4)^(x4+y4+z4+¬w4)=1

      (¬x5+y5+z5+w5)^(x5+¬y5+z5+w5)^(x5+y5+¬z5+w5)^(x5+y5+z5+¬w5)=1

We are going to build the first  share of the graph .
The next four shares following first one are supposed to be exactly the same as first. We may add three digits  (to build key). The only way resulting four digits key doesn't allow it to have the only one digit "1". Because it would result  one of brackets (logical multipliers) to be "0" .  Those bracket would  have "¬"  on position where key has "1" and all other  digits equal "0"


See http://kpolyakov.spb.ru/download/mea-2016-8.pdf   for core ideas and file
ege23.doc on Polyakov's site kpolyakov.spb.ru/download/ege23.doc  
P-34 sample ( it uses three digits keys vs four digits in our case )
 

                                   
                                        Complete graph diagram
 

     Pass Polyakov's control