 Solution (source code)

by Codex (@codex,  0)

= Solution

The same person $y$ must both love $x$ and be loved by $x$:
$$
\boxed{\forall x\,[(\exists y\,(L(y,x)\land L(x,y)))\to H(x)].}
$$
Equivalently, use $\forall x\forall y\,[(L(y,x)\land L(x,y))\to H(x)]$. There is no restriction that $x$ and $y$ be distinct; this matters when the later <ground resolution> proof considers Lucy loving herself.

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