Solution of one system of equations in boolean variables having style like x1 => x2 => ... =>x6=1 && y1 => y2 => ... =>y6 =1 && x1 => y1 via Mapping method

Original system looks like :-

x1 => x2 => x3 => x4 => x5 => x6 =1
y1 => y2 => y3 => y4 => y5 => y6 =1
x1 => y1 =1


Down here we follow approach originally developed in
http://www.loiro.ru/files/news/news_943_etodotobrajeniya-mea-2013-10.pdf


Build basic diagram and define function F( ) to apply Mapping method
suggested  by E. Mironchick

   Now calculate number of solutions of equation
   x1 => x2 => x2 => x3 => x4 => x5 => x6 =1  starting with  x1=1
     

    Calculate  number of solutions of equation
    y1 => y2 => y3 => y4 => y5 => y6 =1  starting with y1=0

   So, we intent to calculate number  of {x},{y} corteges breaking
   third equation and afterwards deduct amount been obtained  from 43^2

     

  Keeping in mind

 

   
 Thus final answer is : -   Count = 43^2 - 21*22 = 1387