Evenness via Fixed-Point-Free Involution

Prompt (Question • Data • Logic)

Question.
Given a finite set U = {a,b,c,d}, is |U| even?
Data.
Universe U of 4 distinct elements.
Logic (Second-Order).
Decide evenness via the SOL formula:
∃f: U→U. (∀x. f(f(x)) = x) ∧ (∀x. f(x) ≠ x)
i.e., a fixed-point-free involution that pairs elements into 2-cycles.

Answer

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Reason Why

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Checks (at least 5)

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