VKontakte P-31 Задача 23 as of 24.05.17

Total Records of {x} :-

15 (x1->y1=1 produces 3*Z4 )  + 16 (x1->y1=0 produces 2^4 {x3,x4,x5,x6} ) = 31
  Z4 = 2^4 - K4 ; K4 =  11 => Z4 = 5 

I follow Konstanin Polyakov's article  http://kpolyakov.spb.ru/download/inf-2014-12a.pdf
published in December of 2014 / ИНФОРМАТИКА with identifiers ZJ and KJ

Total Records of {y} :- 5*5 = 25 (K3^2)
First two equations generate  31*25 = 775 corteges

***************************************************************************************
When (x1->x2=0) then number of records {y} which might satisfy first equation
is one solution of (x1->x2) multiplied by  2^4=16 total number corteges {x3,x4,x5,x6}
*************************************************************************************** 

******************************************************************
Calculate number of corteges to remove due to (x2->y2)^(x3->y3)=0
****************************************************************** 

Case 1.

A = x1->x2 True
B = x3->x4->x5->x6  False

x1 x2                 
-----                  
0  0                   
0  1 =>                  
1  1 =>                   
1  0

x3  x4  x5   x6     x3->x4->x5->x6=0  Z4 = K3 = 5; 3(x3) leading 1.

----------------------
1=> 1    1   0
0   1    1   0              
1=> 1    0   0    
0   0    1   0
1=> 0    0   0

Entries from x2 in table bellow

y1->y2 ->  y3 = 1  K3 = 5
----------------------
1   0<=x2   1
0   0<=x2   1
1   1       1  
0   1       1    
1   0<=x2   0  

Entries from x3 in table bellow

y1->y2 ->  y3 = 1  K3 = 5
----------------------
1   0       1
0   0       1
1   1       1  
0   1       1    
1   0       0<=x3      

y4->y5-> y6 = 1  K3 = 5
--------------------
1   0     1
0   0     1                
1   1     1      
0   1     1  
1   0     0

2*3*5 generated via x1->x2
3*1*1 generated via x3->x4->x5->x6
Total 30+3 = 33
************************************************************** 

Case 2. 
A = x1->x2 False
B = x3->x4->x5->x6  False
x1 x2
------
1  0
y1->y2 ->  y3 = 1  K3 = 5
----------------------
1   0       1
0   0       1
1   1       1  
0   1       1    
1   0       0<=x3     
x3  x4  x5   x6     x3->x4->x5->x6=0  Z4 = K3 = 5; 3(x3) leading 1.
----------------------
1=> 1    1   0
0   1    1   0              
1=> 1    0   0    
0   0    1   0
1=> 0    0   0

Total 3*1*1 = 3 generated via x3->x4->x5->x6 = 0
***************************************************************
Case 3. 
A = x1->x2 False
B = x3->x4->x5->x6  True
x1 x2
-------
1   0
 
y1->y2 ->  y3 = 1  K3 = 5
----------------------
1   0       1
0   0       1
1   1       1  
0   1       1    
1   0       0 <= x3 
x3 -> x4 -> x5  -> x6  = 1  K4=11  ; 5(x3) leading 1
-----------------------------
0     0     0      0
0     0     0      1
0     0     1      1
0     1     0      0
0     1     0      1
0     1     1      1
1=>   0     0      1
1=>   0     1      1
1=>   1     0      0
1=>   1     0      1
1=>   1     1      1

Total 5*1*1=5 generated via x3->x4->x5-x6 =1


******************************************************
Result = 33 +3 +5 = 41
******************************************************


Now remind
y4->y5-> y6 = 1  K3 = 5
--------------------
1   0     1
0   0     1                
1   1     1      
0   1     1  
1   0     0 
************************************* 
So for all three cases considered
*************************************
Final result is 41*5 = 205 ( {x},{y} stays in line as cortege detected to remove )
Thus answer 775 - 205 = 570 
References
1.  http://kpolyakov.spb.ru/download/inf-2014-12a.pdf