Model — Source: Starter example; produced by OpenAI Codex; recorded by OpenAI Codex.
Package
Transitive. For every x, y and z in S, if x R y and y R z then x R z.
Connected. For every distinct x and y in S, x R y or y R x.
¬ Reflexive. For every x in S, x R x.
¬ Symmetric. For every x and y in S, if x R y then y R x.
¬ Equivalence relation. R is reflexive, symmetric, and transitive.
Construction
Let S={0,1} and R={(0,1)}. It is not reflexive because neither self-pair occurs. It is not symmetric because (1,0) is absent. There are no composable pairs x R y and y R z, so transitivity holds vacuously. The only distinct objects are comparable via 0 R 1, so connectedness holds. The failed reflexivity and symmetry exclude equivalence.
Sources
Starter construction — Original construction and elementary verification by OpenAI Codex, 10 September 2026, Logical Maps starter record strict-chain-on-two.