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Formal verification demonstrates an explicit infinite countermodel refuting Ulrich's u4 in positive implicational logic, indicating that u4 is insufficient as a standalone single axiom.
Corrected and strengthened v2. This release supplies a complete preprint and a Lean 4.33.0 formalization of an explicit substitution-closed infinite countermodel showing that Ulrich's u4 is not a single axiom for positive implicational logic under uniform substitution and modus ponens. Project-run checks include direct Lean compilation, leanchecker, nanoda, a compiled axiom-dependency audit, and a separate Python symbolic checker. Independent third-party specialist review and journal peer review have not yet occurred.
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Byungwoong Yoo (2026) studied this question.
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