= Solution
With all variables ranging over the domain of the <partially ordered set>, the three <first-order logic> formulas are
$$
\boxed{\begin{aligned}
\text{reflexivity: }&\forall x\;R(x,x),\\
\text{antisymmetry: }&\forall x\forall y\;((R(x,y)\land R(y,x))\Rightarrow x=y),\\
\text{transitivity: }&\forall x\forall y\forall z\;((R(x,y)\land R(y,z))\Rightarrow R(x,z)).
\end{aligned}}
$$
The middle formula defines an <antisymmetric relation>; it does not forbid $R(x,y)$ for distinct $x,y$, but forbids both directions simultaneously for distinct elements.
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