(VAR x y z)
(RULES
not(x) -> xor(x,true)
or(x,y) -> xor(and(x,y),xor(x,y))
implies(x,y) -> xor(and(x,y),xor(x,true))
and(x,true) -> x
and(x,false) -> false
and(x,x) -> x
xor(x,false) -> x
xor(x,x) -> false
and(xor(x,y),z) -> xor(and(x,z),and(y,z))
)
(COMMENT Example 4.20 (Boolean Ring) in \cite{SK90})