Existence of a non-discrete Tychonoff P-space in ZF

Determine whether there exists a non-discrete Tychonoff (completely regular Hausdorff) P-space in the Zermelo–Fraenkel set theory without the Axiom of Choice (ZF).

Background

The paper studies the existence and construction of crowded zero-dimensional Hausdorff P-spaces under various weak choice principles and in symmetric/permutation models. While many related problems are addressed, the classical question of obtaining a non-discrete Tychonoff P-space in ZF remains unresolved. The authors cite prior work of Keremedis, Olfati, and Wajch and emphasize that, to the best of their knowledge, this specific problem has not been solved.