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Do combinatory logic bases need a function of 3 variables?

All the known bases of combinatory logic, such as $\{S,K\}$, or $\{K,W,B,C\}$, have one or more combinators using 3 variables: \begin{align*} S ={} & \lambda x\lambda y\lambda z. x z(y z), \\ B ={}...
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