Mobius(n,z)

((~(((n)) = 0)) /\ ((((exists mv_square_prime_bottomlayersquare. ((~((mv_square_prime_bottomlayersquare) = 1) /\ forall pvs_left_bottomlayersquareprime pvs_right_bottomlayersquareprime. (mv_square_prime_bottomlayersquare) = pvs_left_bottomlayersquareprime * pvs_right_bottomlayersquareprime -> pvs_left_bottomlayersquareprime = 1 \/ pvs_right_bottomlayersquareprime = 1) /\ (exists pvs_factor_bottomlayersquaredivisor. ((n)) = (mv_square_prime_bottomlayersquare * mv_square_prime_bottomlayersquare) * pvs_factor_bottomlayersquaredivisor))) /\ (((z)) = 0))) \/ (((((~(((n)) = 0)) /\ (forall sfd_prime_bottomlayersquarefree. (~((sfd_prime_bottomlayersquarefree) = 1) /\ forall pvs_left_bottomlayersquarefreedomain pvs_right_bottomlayersquarefreedomain. (sfd_prime_bottomlayersquarefree) = pvs_left_bottomlayersquarefreedomain * pvs_right_bottomlayersquarefreedomain -> pvs_left_bottomlayersquarefreedomain = 1 \/ pvs_right_bottomlayersquarefreedomain = 1) -> (exists pvs_le_gap_bottomlayersquarefreebound. pvs_le_gap_bottomlayersquarefreebound + (sfd_prime_bottomlayersquarefree) = ((n))) -> ~(exists pvs_factor_bottomlayersquarefreesquare. ((n)) = (sfd_prime_bottomlayersquarefree * sfd_prime_bottomlayersquarefree) * pvs_factor_bottomlayersquarefreesquare)))) /\ (exists mv_factor_code_bottomlayerfactors mv_factor_scale_bottomlayerfactors mv_factor_count_bottomlayerfactors. (((~((n) = 0) /\ ((exists ff_u_fsat_bottomlayerfactorsfactorization_product ff_v_fsat_bottomlayerfactorsfactorization_product. ((((exists ff_h_fsat_bottomlayerfactorsfactorization_product_start. ff_h_fsat_bottomlayerfactorsfactorization_product_start + S (1) = S ((S (0)) * ff_v_fsat_bottomlayerfactorsfactorization_product)) /\ exists ff_q_fsat_bottomlayerfactorsfactorization_product_start. ff_u_fsat_bottomlayerfactorsfactorization_product = ff_q_fsat_bottomlayerfactorsfactorization_product_start * S ((S (0)) * ff_v_fsat_bottomlayerfactorsfactorization_product) + (1))) /\ ((((exists ff_h_fsat_bottomlayerfactorsfactorization_product_terminal. ff_h_fsat_bottomlayerfactorsfactorization_product_terminal + S ((n)) = S ((S (mv_factor_count_bottomlayerfactors)) * ff_v_fsat_bottomlayerfactorsfactorization_product)) /\ exists ff_q_fsat_bottomlayerfactorsfactorization_product_terminal. ff_u_fsat_bottomlayerfactorsfactorization_product = ff_q_fsat_bottomlayerfactorsfactorization_product_terminal * S ((S (mv_factor_count_bottomlayerfactors)) * ff_v_fsat_bottomlayerfactorsfactorization_product) + ((n)))) /\ forall ff_i_fsat_bottomlayerfactorsfactorization_product. (exists ff_lt_fsat_bottomlayerfactorsfactorization_product_bound. ff_lt_fsat_bottomlayerfactorsfactorization_product_bound + S ff_i_fsat_bottomlayerfactorsfactorization_product = mv_factor_count_bottomlayerfactors) -> exists ff_p_fsat_bottomlayerfactorsfactorization_product ff_r_fsat_bottomlayerfactorsfactorization_product ff_s_fsat_bottomlayerfactorsfactorization_product. ((((exists ff_h_fsat_bottomlayerfactorsfactorization_product_factor. ff_h_fsat_bottomlayerfactorsfactorization_product_factor + S (ff_p_fsat_bottomlayerfactorsfactorization_product) = S ((S (ff_i_fsat_bottomlayerfactorsfactorization_product)) * mv_factor_scale_bottomlayerfactors)) /\ exists ff_q_fsat_bottomlayerfactorsfactorization_product_factor. mv_factor_code_bottomlayerfactors = ff_q_fsat_bottomlayerfactorsfactorization_product_factor * S ((S (ff_i_fsat_bottomlayerfactorsfactorization_product)) * mv_factor_scale_bottomlayerfactors) + (ff_p_fsat_bottomlayerfactorsfactorization_product))) /\ ((((exists ff_h_fsat_bottomlayerfactorsfactorization_product_partial. ff_h_fsat_bottomlayerfactorsfactorization_product_partial + S (ff_r_fsat_bottomlayerfactorsfactorization_product) = S ((S (ff_i_fsat_bottomlayerfactorsfactorization_product)) * ff_v_fsat_bottomlayerfactorsfactorization_product)) /\ exists ff_q_fsat_bottomlayerfactorsfactorization_product_partial. ff_u_fsat_bottomlayerfactorsfactorization_product = ff_q_fsat_bottomlayerfactorsfactorization_product_partial * S ((S (ff_i_fsat_bottomlayerfactorsfactorization_product)) * ff_v_fsat_bottomlayerfactorsfactorization_product) + (ff_r_fsat_bottomlayerfactorsfactorization_product))) /\ ((((exists ff_h_fsat_bottomlayerfactorsfactorization_product_successor. ff_h_fsat_bottomlayerfactorsfactorization_product_successor + S (ff_s_fsat_bottomlayerfactorsfactorization_product) = S ((S (S ff_i_fsat_bottomlayerfactorsfactorization_product)) * ff_v_fsat_bottomlayerfactorsfactorization_product)) /\ exists ff_q_fsat_bottomlayerfactorsfactorization_product_successor. ff_u_fsat_bottomlayerfactorsfactorization_product = ff_q_fsat_bottomlayerfactorsfactorization_product_successor * S ((S (S ff_i_fsat_bottomlayerfactorsfactorization_product)) * ff_v_fsat_bottomlayerfactorsfactorization_product) + (ff_s_fsat_bottomlayerfactorsfactorization_product))) /\ ff_s_fsat_bottomlayerfactorsfactorization_product = ff_r_fsat_bottomlayerfactorsfactorization_product * ff_p_fsat_bottomlayerfactorsfactorization_product)))))) /\ (forall ftsf_index_fsat_bottomlayerfactorsfactorization_primes. (exists ftsf_gap_fsat_bottomlayerfactorsfactorization_primes_bound. ftsf_gap_fsat_bottomlayerfactorsfactorization_primes_bound + S ftsf_index_fsat_bottomlayerfactorsfactorization_primes = (mv_factor_count_bottomlayerfactors)) -> exists ftsf_factor_fsat_bottomlayerfactorsfactorization_primes. ((((exists ff_h_ftsf_fsat_bottomlayerfactorsfactorization_primes_entry. ff_h_ftsf_fsat_bottomlayerfactorsfactorization_primes_entry + S (ftsf_factor_fsat_bottomlayerfactorsfactorization_primes) = S ((S (ftsf_index_fsat_bottomlayerfactorsfactorization_primes)) * mv_factor_scale_bottomlayerfactors)) /\ exists ff_q_ftsf_fsat_bottomlayerfactorsfactorization_primes_entry. mv_factor_code_bottomlayerfactors = ff_q_ftsf_fsat_bottomlayerfactorsfactorization_primes_entry * S ((S (ftsf_index_fsat_bottomlayerfactorsfactorization_primes)) * mv_factor_scale_bottomlayerfactors) + (ftsf_factor_fsat_bottomlayerfactorsfactorization_primes))) /\ ((~(ftsf_factor_fsat_bottomlayerfactorsfactorization_primes = 1) /\ forall frm_prime_left_ftsf_fsat_bottomlayerfactorsfactorization_primes_prime frm_prime_right_ftsf_fsat_bottomlayerfactorsfactorization_primes_prime. ftsf_factor_fsat_bottomlayerfactorsfactorization_primes = frm_prime_left_ftsf_fsat_bottomlayerfactorsfactorization_primes_prime * frm_prime_right_ftsf_fsat_bottomlayerfactorsfactorization_primes_prime -> frm_prime_left_ftsf_fsat_bottomlayerfactorsfactorization_primes_prime = 1 \/ frm_prime_right_ftsf_fsat_bottomlayerfactorsfactorization_primes_prime = 1))))))) /\ ((((exists mv_even_half_bottomlayerfactorsparityeven. (mv_factor_count_bottomlayerfactors) = 2 * mv_even_half_bottomlayerfactorsparityeven) /\ (((z)) = 2))) \/ (((exists mv_odd_half_bottomlayerfactorsparityodd. (mv_factor_count_bottomlayerfactors) = 2 * mv_odd_half_bottomlayerfactorsparityodd + 1) /\ (((z)) = 1))))))))))

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