Solution of Assignment #T6854 Yandex Tutor of the Unified State Examination Informatics 2020

Original task
See https://yandex.ru/tutor/subject/problem/?problem_id=T8654

 ¬(x1≡x2)∨¬(x3≡x4)∨¬(x5≡x6)=1
 ¬(x5≡x6)∨¬(x7≡x8)∨¬(x9≡x10)=1
 ¬(x9≡x10)∨¬(x11≡x12)∨¬(x13≡x14)=1
 ¬((x1∧x5)≡(x9∧x13))=1

Convert to equivalent system
 (x1⊕x2)∨(x3⊕x4)∨(x5⊕x6)=1
 (x5⊕x6)∨(x7⊕x8)∨(x9⊕x10)=1
 (x9⊕x10)∨(x11⊕x12)∨(x13⊕x14)=1
 (x1∧x5)⊕(x9∧x13)=1

Introduce variables z1,z2, . . , z7 as follows
  z1=x1⊕x2
  z2=x3⊕x4
  z3=x5⊕x6
  z4=x7⊕x8
  z5=x9⊕x10
  z6=x11⊕x12
  z7=x13⊕x14

Consider system (1)
   z1+z2+z3=1
   z3+z4+z5=1
   z5+z6+z7=1

Then, subtract the number of false solutions from the total number of solutions. The total number of solutions is obviously 89*2^7, each zj from the tuple {z1, z2, . , z7} which is a solution to system (1) implies a multiplication by 2
Proceed as follows
z1 = x1⊕x2
z3 = x5⊕x6
z5 = x9⊕x10
z7 = x13⊕x14
Thus, constructing the diagram {x1x5, x9x13} by assumption
(x1^x5=x9^x13) = 1 we get the number 10 by which we should multiply 2^3,
since z1,z3,z5,z7 give exactly 10 false options. Remaining z2,z4,z6 give 2*2*2 = 2^3 combinations. The total number of false solutions is 89*2^3*10.

Control for number of false solutions

  Control for number of total solutions  

   Finally double check obtained result