Eulerian Path via ∃ edge-order

Prompt (Question • Data • Logic)

Question.
Does the directed graph G=(V,E) admit an Eulerian path (a trail using every arc exactly once)?
Data.
V = {a,b,c,d,e,f}
E = { a→b, b→c, c→d, d→a, a→e }   (f is isolated)
Logic (Second-Order).
∃ order : {0..|E|-1} → E (bijection) s.t. head(order[i]) = tail(order[i+1]).
This quantifies over a total order of edges — a genuine second-order witness.

Answer

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Reason Why

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Checks (at least 5)

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Diagnostics

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