 Solution

Index the coins so that $c_1$ is smallest and $c_n$ largest. Choose $s_1$ as the initial stack and $s_2$ as the destination, assuming $k\ge 2$. The static predicate facts describing size areNo size comparison with $g$ is needed: moving onto empty ground will have a separate action schema. The initial STRIPS state isUnder the closed-world assumption, all other ground ground atoms are false. In particular, the initial state contains just one predicate fact naming the top of each stack. The predicate $\mathrm{OnTop}$ names the immediate support, not every coin farther below.

An explicit positive conjunctive goal is the following set of required ground atoms:A state succeeds when it contains $G_{\mathrm{goal}}$. The static predicate facts in $S_{\mathrm{size}}$ persist automatically. Starting from $I$, the planning state invariants proved below make this goal exactly the desired completed stack on $s_2$ with all other stacks empty. If any new stack is acceptable, the choice of $s_2$ loses no generality because the initially empty stacks are interchangeable.