FactorParitySign(n,z)

exists mv_factor_code_bottomlayer mv_factor_scale_bottomlayer mv_factor_count_bottomlayer. (((~((n) = 0) /\ ((exists ff_u_fsat_bottomlayerfactorization_product ff_v_fsat_bottomlayerfactorization_product. ((((exists ff_h_fsat_bottomlayerfactorization_product_start. ff_h_fsat_bottomlayerfactorization_product_start + S (1) = S ((S (0)) * ff_v_fsat_bottomlayerfactorization_product)) /\ exists ff_q_fsat_bottomlayerfactorization_product_start. ff_u_fsat_bottomlayerfactorization_product = ff_q_fsat_bottomlayerfactorization_product_start * S ((S (0)) * ff_v_fsat_bottomlayerfactorization_product) + (1))) /\ ((((exists ff_h_fsat_bottomlayerfactorization_product_terminal. ff_h_fsat_bottomlayerfactorization_product_terminal + S ((n)) = S ((S (mv_factor_count_bottomlayer)) * ff_v_fsat_bottomlayerfactorization_product)) /\ exists ff_q_fsat_bottomlayerfactorization_product_terminal. ff_u_fsat_bottomlayerfactorization_product = ff_q_fsat_bottomlayerfactorization_product_terminal * S ((S (mv_factor_count_bottomlayer)) * ff_v_fsat_bottomlayerfactorization_product) + ((n)))) /\ forall ff_i_fsat_bottomlayerfactorization_product. (exists ff_lt_fsat_bottomlayerfactorization_product_bound. ff_lt_fsat_bottomlayerfactorization_product_bound + S ff_i_fsat_bottomlayerfactorization_product = mv_factor_count_bottomlayer) -> exists ff_p_fsat_bottomlayerfactorization_product ff_r_fsat_bottomlayerfactorization_product ff_s_fsat_bottomlayerfactorization_product. ((((exists ff_h_fsat_bottomlayerfactorization_product_factor. ff_h_fsat_bottomlayerfactorization_product_factor + S (ff_p_fsat_bottomlayerfactorization_product) = S ((S (ff_i_fsat_bottomlayerfactorization_product)) * mv_factor_scale_bottomlayer)) /\ exists ff_q_fsat_bottomlayerfactorization_product_factor. mv_factor_code_bottomlayer = ff_q_fsat_bottomlayerfactorization_product_factor * S ((S (ff_i_fsat_bottomlayerfactorization_product)) * mv_factor_scale_bottomlayer) + (ff_p_fsat_bottomlayerfactorization_product))) /\ ((((exists ff_h_fsat_bottomlayerfactorization_product_partial. ff_h_fsat_bottomlayerfactorization_product_partial + S (ff_r_fsat_bottomlayerfactorization_product) = S ((S (ff_i_fsat_bottomlayerfactorization_product)) * ff_v_fsat_bottomlayerfactorization_product)) /\ exists ff_q_fsat_bottomlayerfactorization_product_partial. ff_u_fsat_bottomlayerfactorization_product = ff_q_fsat_bottomlayerfactorization_product_partial * S ((S (ff_i_fsat_bottomlayerfactorization_product)) * ff_v_fsat_bottomlayerfactorization_product) + (ff_r_fsat_bottomlayerfactorization_product))) /\ ((((exists ff_h_fsat_bottomlayerfactorization_product_successor. ff_h_fsat_bottomlayerfactorization_product_successor + S (ff_s_fsat_bottomlayerfactorization_product) = S ((S (S ff_i_fsat_bottomlayerfactorization_product)) * ff_v_fsat_bottomlayerfactorization_product)) /\ exists ff_q_fsat_bottomlayerfactorization_product_successor. ff_u_fsat_bottomlayerfactorization_product = ff_q_fsat_bottomlayerfactorization_product_successor * S ((S (S ff_i_fsat_bottomlayerfactorization_product)) * ff_v_fsat_bottomlayerfactorization_product) + (ff_s_fsat_bottomlayerfactorization_product))) /\ ff_s_fsat_bottomlayerfactorization_product = ff_r_fsat_bottomlayerfactorization_product * ff_p_fsat_bottomlayerfactorization_product)))))) /\ (forall ftsf_index_fsat_bottomlayerfactorization_primes. (exists ftsf_gap_fsat_bottomlayerfactorization_primes_bound. ftsf_gap_fsat_bottomlayerfactorization_primes_bound + S ftsf_index_fsat_bottomlayerfactorization_primes = (mv_factor_count_bottomlayer)) -> exists ftsf_factor_fsat_bottomlayerfactorization_primes. ((((exists ff_h_ftsf_fsat_bottomlayerfactorization_primes_entry. ff_h_ftsf_fsat_bottomlayerfactorization_primes_entry + S (ftsf_factor_fsat_bottomlayerfactorization_primes) = S ((S (ftsf_index_fsat_bottomlayerfactorization_primes)) * mv_factor_scale_bottomlayer)) /\ exists ff_q_ftsf_fsat_bottomlayerfactorization_primes_entry. mv_factor_code_bottomlayer = ff_q_ftsf_fsat_bottomlayerfactorization_primes_entry * S ((S (ftsf_index_fsat_bottomlayerfactorization_primes)) * mv_factor_scale_bottomlayer) + (ftsf_factor_fsat_bottomlayerfactorization_primes))) /\ ((~(ftsf_factor_fsat_bottomlayerfactorization_primes = 1) /\ forall frm_prime_left_ftsf_fsat_bottomlayerfactorization_primes_prime frm_prime_right_ftsf_fsat_bottomlayerfactorization_primes_prime. ftsf_factor_fsat_bottomlayerfactorization_primes = frm_prime_left_ftsf_fsat_bottomlayerfactorization_primes_prime * frm_prime_right_ftsf_fsat_bottomlayerfactorization_primes_prime -> frm_prime_left_ftsf_fsat_bottomlayerfactorization_primes_prime = 1 \/ frm_prime_right_ftsf_fsat_bottomlayerfactorization_primes_prime = 1))))))) /\ ((((exists mv_even_half_bottomlayerparityeven. (mv_factor_count_bottomlayer) = 2 * mv_even_half_bottomlayerparityeven) /\ (((z)) = 2))) \/ (((exists mv_odd_half_bottomlayerparityodd. (mv_factor_count_bottomlayer) = 2 * mv_odd_half_bottomlayerparityodd + 1) /\ (((z)) = 1)))))

The unchanged native kernel never receives this surface symbol. Binder-safe expansion produces only its existing first-order syntax.