Mapping method as it works at nowdays or another lesson been taught from Helen Mironchick regarding technique of solving the systems of equations in boolean variables

System usually treated via bitmasks tables
concatenation. In particular case could hardly be
solved as it happens with fourth equation kind of
x6^y6^z6=0


(x1=>x2)^(x2=>x3)^(x3=>x4)^(x4=>x5)^(x5=>x6)=1
(y1=>y2)^(y2=>y3)^(y3=>y4)^(y4=>y5)^(y5=>y6)=1
(z1=>z2)^(z2=>z3)^(z3=>z4)^(z4=>z5)^(z5=>z6)=1
(x6=>y6)=>z6=1

(x1=>x2)^(x2=>x3)^(x3=>x4)^(x4=>x5)^(x5=>x6)=1
(y1=>y2)^(y2=>y3)^(y3=>y4)^(y4=>y5)^(y5=>y6)=1
(z1=>z2)^(z2=>z3)^(z3=>z4)^(z4=>z5)^(z5=>z6)=1
(x1=>y1)=>z1=1

Получаем x1,y1,z1 обратным проходом (6,1)

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