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The Finite-Universe Method

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State

To prove invalidity: build a small universe (one or two members) where universals become conjunctions, existentials become disjunctions — then find an assignment with true premises and a false conclusion.

Show

A two-member world is a truth-table row for predicate logic.

Watch for

This proves invalidity only. Proofs certify validity; models certify invalidity; between them, the system is complete.