all_bad_prime_even_valuations_strip_represented_prime

Exact expanded first-order arithmetic statement

forall q n. ((~(q = 1) /\ forall frm_prime_left_ftsp_q frm_prime_right_ftsp_q. q = frm_prime_left_ftsp_q * frm_prime_right_ftsp_q -> frm_prime_left_ftsp_q = 1 \/ frm_prime_right_ftsp_q = 1)) -> (exists ftsc_first_ftsp_good_prime ftsc_second_ftsp_good_prime. (q) = ftsc_first_ftsp_good_prime * ftsc_first_ftsp_good_prime + ftsc_second_ftsp_good_prime * ftsc_second_ftsp_good_prime) -> ~(n = 0) -> (forall ftsp_bad_prime_parity_good_product ftsp_bad_exponent_parity_good_product. ((~(ftsp_bad_prime_parity_good_product = 1) /\ forall frm_prime_left_ftsp_parity_good_product_prime frm_prime_right_ftsp_parity_good_product_prime. ftsp_bad_prime_parity_good_product = frm_prime_left_ftsp_parity_good_product_prime * frm_prime_right_ftsp_parity_good_product_prime -> frm_prime_left_ftsp_parity_good_product_prime = 1 \/ frm_prime_right_ftsp_parity_good_product_prime = 1)) -> (exists ftsc_four_three_ftsp_parity_good_product_three. (ftsp_bad_prime_parity_good_product) = 4 * ftsc_four_three_ftsp_parity_good_product_three + 3) -> (((exists bpv_gap_ftsp_parity_good_product_valuation_exponent_bound. bpv_gap_ftsp_parity_good_product_valuation_exponent_bound + ftsp_bad_exponent_parity_good_product = (n * q)) /\ (exists bpv_result_ftsp_parity_good_product_valuation_selected. ((exists ff_b_ftsp_parity_good_product_valuation_selected_power ff_c_ftsp_parity_good_product_valuation_selected_power. ((forall ff_i_ftsp_parity_good_product_valuation_selected_power_repeat. (exists ff_lt_ftsp_parity_good_product_valuation_selected_power_repeat_bound. ff_lt_ftsp_parity_good_product_valuation_selected_power_repeat_bound + S ff_i_ftsp_parity_good_product_valuation_selected_power_repeat = ftsp_bad_exponent_parity_good_product) -> (((exists ff_h_ftsp_parity_good_product_valuation_selected_power_repeat_decoded. ff_h_ftsp_parity_good_product_valuation_selected_power_repeat_decoded + S (ftsp_bad_prime_parity_good_product) = S ((S (ff_i_ftsp_parity_good_product_valuation_selected_power_repeat)) * ff_c_ftsp_parity_good_product_valuation_selected_power)) /\ exists ff_q_ftsp_parity_good_product_valuation_selected_power_repeat_decoded. ff_b_ftsp_parity_good_product_valuation_selected_power = ff_q_ftsp_parity_good_product_valuation_selected_power_repeat_decoded * S ((S (ff_i_ftsp_parity_good_product_valuation_selected_power_repeat)) * ff_c_ftsp_parity_good_product_valuation_selected_power) + (ftsp_bad_prime_parity_good_product)))) /\ (exists ff_u_ftsp_parity_good_product_valuation_selected_power_product ff_v_ftsp_parity_good_product_valuation_selected_power_product. ((((exists ff_h_ftsp_parity_good_product_valuation_selected_power_product_start. ff_h_ftsp_parity_good_product_valuation_selected_power_product_start + S (1) = S ((S (0)) * ff_v_ftsp_parity_good_product_valuation_selected_power_product)) /\ exists ff_q_ftsp_parity_good_product_valuation_selected_power_product_start. ff_u_ftsp_parity_good_product_valuation_selected_power_product = ff_q_ftsp_parity_good_product_valuation_selected_power_product_start * S ((S (0)) * ff_v_ftsp_parity_good_product_valuation_selected_power_product) + (1))) /\ ((((exists ff_h_ftsp_parity_good_product_valuation_selected_power_product_terminal. ff_h_ftsp_parity_good_product_valuation_selected_power_product_terminal + S (bpv_result_ftsp_parity_good_product_valuation_selected) = S ((S (ftsp_bad_exponent_parity_good_product)) * ff_v_ftsp_parity_good_product_valuation_selected_power_product)) /\ exists ff_q_ftsp_parity_good_product_valuation_selected_power_product_terminal. ff_u_ftsp_parity_good_product_valuation_selected_power_product = ff_q_ftsp_parity_good_product_valuation_selected_power_product_terminal * S ((S (ftsp_bad_exponent_parity_good_product)) * ff_v_ftsp_parity_good_product_valuation_selected_power_product) + (bpv_result_ftsp_parity_good_product_valuation_selected))) /\ forall ff_i_ftsp_parity_good_product_valuation_selected_power_product. (exists ff_lt_ftsp_parity_good_product_valuation_selected_power_product_bound. ff_lt_ftsp_parity_good_product_valuation_selected_power_product_bound + S ff_i_ftsp_parity_good_product_valuation_selected_power_product = ftsp_bad_exponent_parity_good_product) -> exists ff_p_ftsp_parity_good_product_valuation_selected_power_product ff_r_ftsp_parity_good_product_valuation_selected_power_product ff_s_ftsp_parity_good_product_valuation_selected_power_product. ((((exists ff_h_ftsp_parity_good_product_valuation_selected_power_product_factor. ff_h_ftsp_parity_good_product_valuation_selected_power_product_factor + S (ff_p_ftsp_parity_good_product_valuation_selected_power_product) = S ((S (ff_i_ftsp_parity_good_product_valuation_selected_power_product)) * ff_c_ftsp_parity_good_product_valuation_selected_power)) /\ exists ff_q_ftsp_parity_good_product_valuation_selected_power_product_factor. ff_b_ftsp_parity_good_product_valuation_selected_power = ff_q_ftsp_parity_good_product_valuation_selected_power_product_factor * S ((S (ff_i_ftsp_parity_good_product_valuation_selected_power_product)) * ff_c_ftsp_parity_good_product_valuation_selected_power) + (ff_p_ftsp_parity_good_product_valuation_selected_power_product))) /\ ((((exists ff_h_ftsp_parity_good_product_valuation_selected_power_product_partial. ff_h_ftsp_parity_good_product_valuation_selected_power_product_partial + S (ff_r_ftsp_parity_good_product_valuation_selected_power_product) = S ((S (ff_i_ftsp_parity_good_product_valuation_selected_power_product)) * ff_v_ftsp_parity_good_product_valuation_selected_power_product)) /\ exists ff_q_ftsp_parity_good_product_valuation_selected_power_product_partial. ff_u_ftsp_parity_good_product_valuation_selected_power_product = ff_q_ftsp_parity_good_product_valuation_selected_power_product_partial * S ((S (ff_i_ftsp_parity_good_product_valuation_selected_power_product)) * ff_v_ftsp_parity_good_product_valuation_selected_power_product) + (ff_r_ftsp_parity_good_product_valuation_selected_power_product))) /\ ((((exists ff_h_ftsp_parity_good_product_valuation_selected_power_product_successor. ff_h_ftsp_parity_good_product_valuation_selected_power_product_successor + S (ff_s_ftsp_parity_good_product_valuation_selected_power_product) = S ((S (S ff_i_ftsp_parity_good_product_valuation_selected_power_product)) * ff_v_ftsp_parity_good_product_valuation_selected_power_product)) /\ exists ff_q_ftsp_parity_good_product_valuation_selected_power_product_successor. ff_u_ftsp_parity_good_product_valuation_selected_power_product = ff_q_ftsp_parity_good_product_valuation_selected_power_product_successor * S ((S (S ff_i_ftsp_parity_good_product_valuation_selected_power_product)) * ff_v_ftsp_parity_good_product_valuation_selected_power_product) + (ff_s_ftsp_parity_good_product_valuation_selected_power_product))) /\ ff_s_ftsp_parity_good_product_valuation_selected_power_product = ff_r_ftsp_parity_good_product_valuation_selected_power_product * ff_p_ftsp_parity_good_product_valuation_selected_power_product)))))))) /\ (exists bpv_factor_ftsp_parity_good_product_valuation_selected_divides. (n * q) = bpv_result_ftsp_parity_good_product_valuation_selected * bpv_factor_ftsp_parity_good_product_valuation_selected_divides)))) /\ forall bpv_candidate_ftsp_parity_good_product_valuation. (exists bpv_gap_ftsp_parity_good_product_valuation_candidate_bound. bpv_gap_ftsp_parity_good_product_valuation_candidate_bound + bpv_candidate_ftsp_parity_good_product_valuation = (n * q)) -> (exists bpv_result_ftsp_parity_good_product_valuation_candidate. ((exists ff_b_ftsp_parity_good_product_valuation_candidate_power ff_c_ftsp_parity_good_product_valuation_candidate_power. ((forall ff_i_ftsp_parity_good_product_valuation_candidate_power_repeat. (exists ff_lt_ftsp_parity_good_product_valuation_candidate_power_repeat_bound. ff_lt_ftsp_parity_good_product_valuation_candidate_power_repeat_bound + S ff_i_ftsp_parity_good_product_valuation_candidate_power_repeat = bpv_candidate_ftsp_parity_good_product_valuation) -> (((exists ff_h_ftsp_parity_good_product_valuation_candidate_power_repeat_decoded. ff_h_ftsp_parity_good_product_valuation_candidate_power_repeat_decoded + S (ftsp_bad_prime_parity_good_product) = S ((S (ff_i_ftsp_parity_good_product_valuation_candidate_power_repeat)) * ff_c_ftsp_parity_good_product_valuation_candidate_power)) /\ exists ff_q_ftsp_parity_good_product_valuation_candidate_power_repeat_decoded. ff_b_ftsp_parity_good_product_valuation_candidate_power = ff_q_ftsp_parity_good_product_valuation_candidate_power_repeat_decoded * S ((S (ff_i_ftsp_parity_good_product_valuation_candidate_power_repeat)) * ff_c_ftsp_parity_good_product_valuation_candidate_power) + (ftsp_bad_prime_parity_good_product)))) /\ (exists ff_u_ftsp_parity_good_product_valuation_candidate_power_product ff_v_ftsp_parity_good_product_valuation_candidate_power_product. ((((exists ff_h_ftsp_parity_good_product_valuation_candidate_power_product_start. ff_h_ftsp_parity_good_product_valuation_candidate_power_product_start + S (1) = S ((S (0)) * ff_v_ftsp_parity_good_product_valuation_candidate_power_product)) /\ exists ff_q_ftsp_parity_good_product_valuation_candidate_power_product_start. ff_u_ftsp_parity_good_product_valuation_candidate_power_product = ff_q_ftsp_parity_good_product_valuation_candidate_power_product_start * S ((S (0)) * ff_v_ftsp_parity_good_product_valuation_candidate_power_product) + (1))) /\ ((((exists ff_h_ftsp_parity_good_product_valuation_candidate_power_product_terminal. ff_h_ftsp_parity_good_product_valuation_candidate_power_product_terminal + S (bpv_result_ftsp_parity_good_product_valuation_candidate) = S ((S (bpv_candidate_ftsp_parity_good_product_valuation)) * ff_v_ftsp_parity_good_product_valuation_candidate_power_product)) /\ exists ff_q_ftsp_parity_good_product_valuation_candidate_power_product_terminal. ff_u_ftsp_parity_good_product_valuation_candidate_power_product = ff_q_ftsp_parity_good_product_valuation_candidate_power_product_terminal * S ((S (bpv_candidate_ftsp_parity_good_product_valuation)) * ff_v_ftsp_parity_good_product_valuation_candidate_power_product) + (bpv_result_ftsp_parity_good_product_valuation_candidate))) /\ forall ff_i_ftsp_parity_good_product_valuation_candidate_power_product. (exists ff_lt_ftsp_parity_good_product_valuation_candidate_power_product_bound. ff_lt_ftsp_parity_good_product_valuation_candidate_power_product_bound + S ff_i_ftsp_parity_good_product_valuation_candidate_power_product = bpv_candidate_ftsp_parity_good_product_valuation) -> exists ff_p_ftsp_parity_good_product_valuation_candidate_power_product ff_r_ftsp_parity_good_product_valuation_candidate_power_product ff_s_ftsp_parity_good_product_valuation_candidate_power_product. ((((exists ff_h_ftsp_parity_good_product_valuation_candidate_power_product_factor. ff_h_ftsp_parity_good_product_valuation_candidate_power_product_factor + S (ff_p_ftsp_parity_good_product_valuation_candidate_power_product) = S ((S (ff_i_ftsp_parity_good_product_valuation_candidate_power_product)) * ff_c_ftsp_parity_good_product_valuation_candidate_power)) /\ exists ff_q_ftsp_parity_good_product_valuation_candidate_power_product_factor. ff_b_ftsp_parity_good_product_valuation_candidate_power = ff_q_ftsp_parity_good_product_valuation_candidate_power_product_factor * S ((S (ff_i_ftsp_parity_good_product_valuation_candidate_power_product)) * ff_c_ftsp_parity_good_product_valuation_candidate_power) + (ff_p_ftsp_parity_good_product_valuation_candidate_power_product))) /\ ((((exists ff_h_ftsp_parity_good_product_valuation_candidate_power_product_partial. ff_h_ftsp_parity_good_product_valuation_candidate_power_product_partial + S (ff_r_ftsp_parity_good_product_valuation_candidate_power_product) = S ((S (ff_i_ftsp_parity_good_product_valuation_candidate_power_product)) * ff_v_ftsp_parity_good_product_valuation_candidate_power_product)) /\ exists ff_q_ftsp_parity_good_product_valuation_candidate_power_product_partial. ff_u_ftsp_parity_good_product_valuation_candidate_power_product = ff_q_ftsp_parity_good_product_valuation_candidate_power_product_partial * S ((S (ff_i_ftsp_parity_good_product_valuation_candidate_power_product)) * ff_v_ftsp_parity_good_product_valuation_candidate_power_product) + (ff_r_ftsp_parity_good_product_valuation_candidate_power_product))) /\ ((((exists ff_h_ftsp_parity_good_product_valuation_candidate_power_product_successor. ff_h_ftsp_parity_good_product_valuation_candidate_power_product_successor + S (ff_s_ftsp_parity_good_product_valuation_candidate_power_product) = S ((S (S ff_i_ftsp_parity_good_product_valuation_candidate_power_product)) * ff_v_ftsp_parity_good_product_valuation_candidate_power_product)) /\ exists ff_q_ftsp_parity_good_product_valuation_candidate_power_product_successor. ff_u_ftsp_parity_good_product_valuation_candidate_power_product = ff_q_ftsp_parity_good_product_valuation_candidate_power_product_successor * S ((S (S ff_i_ftsp_parity_good_product_valuation_candidate_power_product)) * ff_v_ftsp_parity_good_product_valuation_candidate_power_product) + (ff_s_ftsp_parity_good_product_valuation_candidate_power_product))) /\ ff_s_ftsp_parity_good_product_valuation_candidate_power_product = ff_r_ftsp_parity_good_product_valuation_candidate_power_product * ff_p_ftsp_parity_good_product_valuation_candidate_power_product)))))))) /\ (exists bpv_factor_ftsp_parity_good_product_valuation_candidate_divides. (n * q) = bpv_result_ftsp_parity_good_product_valuation_candidate * bpv_factor_ftsp_parity_good_product_valuation_candidate_divides))) -> (exists bpv_gap_ftsp_parity_good_product_valuation_maximal. bpv_gap_ftsp_parity_good_product_valuation_maximal + bpv_candidate_ftsp_parity_good_product_valuation = ftsp_bad_exponent_parity_good_product)) -> exists ftsp_bad_half_parity_good_product. ftsp_bad_exponent_parity_good_product = ftsp_bad_half_parity_good_product + ftsp_bad_half_parity_good_product) -> (forall ftsp_bad_prime_parity_source ftsp_bad_exponent_parity_source. ((~(ftsp_bad_prime_parity_source = 1) /\ forall frm_prime_left_ftsp_parity_source_prime frm_prime_right_ftsp_parity_source_prime. ftsp_bad_prime_parity_source = frm_prime_left_ftsp_parity_source_prime * frm_prime_right_ftsp_parity_source_prime -> frm_prime_left_ftsp_parity_source_prime = 1 \/ frm_prime_right_ftsp_parity_source_prime = 1)) -> (exists ftsc_four_three_ftsp_parity_source_three. (ftsp_bad_prime_parity_source) = 4 * ftsc_four_three_ftsp_parity_source_three + 3) -> (((exists bpv_gap_ftsp_parity_source_valuation_exponent_bound. bpv_gap_ftsp_parity_source_valuation_exponent_bound + ftsp_bad_exponent_parity_source = (n)) /\ (exists bpv_result_ftsp_parity_source_valuation_selected. ((exists ff_b_ftsp_parity_source_valuation_selected_power ff_c_ftsp_parity_source_valuation_selected_power. ((forall ff_i_ftsp_parity_source_valuation_selected_power_repeat. (exists ff_lt_ftsp_parity_source_valuation_selected_power_repeat_bound. ff_lt_ftsp_parity_source_valuation_selected_power_repeat_bound + S ff_i_ftsp_parity_source_valuation_selected_power_repeat = ftsp_bad_exponent_parity_source) -> (((exists ff_h_ftsp_parity_source_valuation_selected_power_repeat_decoded. ff_h_ftsp_parity_source_valuation_selected_power_repeat_decoded + S (ftsp_bad_prime_parity_source) = S ((S (ff_i_ftsp_parity_source_valuation_selected_power_repeat)) * ff_c_ftsp_parity_source_valuation_selected_power)) /\ exists ff_q_ftsp_parity_source_valuation_selected_power_repeat_decoded. ff_b_ftsp_parity_source_valuation_selected_power = ff_q_ftsp_parity_source_valuation_selected_power_repeat_decoded * S ((S (ff_i_ftsp_parity_source_valuation_selected_power_repeat)) * ff_c_ftsp_parity_source_valuation_selected_power) + (ftsp_bad_prime_parity_source)))) /\ (exists ff_u_ftsp_parity_source_valuation_selected_power_product ff_v_ftsp_parity_source_valuation_selected_power_product. ((((exists ff_h_ftsp_parity_source_valuation_selected_power_product_start. ff_h_ftsp_parity_source_valuation_selected_power_product_start + S (1) = S ((S (0)) * ff_v_ftsp_parity_source_valuation_selected_power_product)) /\ exists ff_q_ftsp_parity_source_valuation_selected_power_product_start. ff_u_ftsp_parity_source_valuation_selected_power_product = ff_q_ftsp_parity_source_valuation_selected_power_product_start * S ((S (0)) * ff_v_ftsp_parity_source_valuation_selected_power_product) + (1))) /\ ((((exists ff_h_ftsp_parity_source_valuation_selected_power_product_terminal. ff_h_ftsp_parity_source_valuation_selected_power_product_terminal + S (bpv_result_ftsp_parity_source_valuation_selected) = S ((S (ftsp_bad_exponent_parity_source)) * ff_v_ftsp_parity_source_valuation_selected_power_product)) /\ exists ff_q_ftsp_parity_source_valuation_selected_power_product_terminal. ff_u_ftsp_parity_source_valuation_selected_power_product = ff_q_ftsp_parity_source_valuation_selected_power_product_terminal * S ((S (ftsp_bad_exponent_parity_source)) * ff_v_ftsp_parity_source_valuation_selected_power_product) + (bpv_result_ftsp_parity_source_valuation_selected))) /\ forall ff_i_ftsp_parity_source_valuation_selected_power_product. (exists ff_lt_ftsp_parity_source_valuation_selected_power_product_bound. ff_lt_ftsp_parity_source_valuation_selected_power_product_bound + S ff_i_ftsp_parity_source_valuation_selected_power_product = ftsp_bad_exponent_parity_source) -> exists ff_p_ftsp_parity_source_valuation_selected_power_product ff_r_ftsp_parity_source_valuation_selected_power_product ff_s_ftsp_parity_source_valuation_selected_power_product. ((((exists ff_h_ftsp_parity_source_valuation_selected_power_product_factor. ff_h_ftsp_parity_source_valuation_selected_power_product_factor + S (ff_p_ftsp_parity_source_valuation_selected_power_product) = S ((S (ff_i_ftsp_parity_source_valuation_selected_power_product)) * ff_c_ftsp_parity_source_valuation_selected_power)) /\ exists ff_q_ftsp_parity_source_valuation_selected_power_product_factor. ff_b_ftsp_parity_source_valuation_selected_power = ff_q_ftsp_parity_source_valuation_selected_power_product_factor * S ((S (ff_i_ftsp_parity_source_valuation_selected_power_product)) * ff_c_ftsp_parity_source_valuation_selected_power) + (ff_p_ftsp_parity_source_valuation_selected_power_product))) /\ ((((exists ff_h_ftsp_parity_source_valuation_selected_power_product_partial. ff_h_ftsp_parity_source_valuation_selected_power_product_partial + S (ff_r_ftsp_parity_source_valuation_selected_power_product) = S ((S (ff_i_ftsp_parity_source_valuation_selected_power_product)) * ff_v_ftsp_parity_source_valuation_selected_power_product)) /\ exists ff_q_ftsp_parity_source_valuation_selected_power_product_partial. ff_u_ftsp_parity_source_valuation_selected_power_product = ff_q_ftsp_parity_source_valuation_selected_power_product_partial * S ((S (ff_i_ftsp_parity_source_valuation_selected_power_product)) * ff_v_ftsp_parity_source_valuation_selected_power_product) + (ff_r_ftsp_parity_source_valuation_selected_power_product))) /\ ((((exists ff_h_ftsp_parity_source_valuation_selected_power_product_successor. ff_h_ftsp_parity_source_valuation_selected_power_product_successor + S (ff_s_ftsp_parity_source_valuation_selected_power_product) = S ((S (S ff_i_ftsp_parity_source_valuation_selected_power_product)) * ff_v_ftsp_parity_source_valuation_selected_power_product)) /\ exists ff_q_ftsp_parity_source_valuation_selected_power_product_successor. ff_u_ftsp_parity_source_valuation_selected_power_product = ff_q_ftsp_parity_source_valuation_selected_power_product_successor * S ((S (S ff_i_ftsp_parity_source_valuation_selected_power_product)) * ff_v_ftsp_parity_source_valuation_selected_power_product) + (ff_s_ftsp_parity_source_valuation_selected_power_product))) /\ ff_s_ftsp_parity_source_valuation_selected_power_product = ff_r_ftsp_parity_source_valuation_selected_power_product * ff_p_ftsp_parity_source_valuation_selected_power_product)))))))) /\ (exists bpv_factor_ftsp_parity_source_valuation_selected_divides. (n) = bpv_result_ftsp_parity_source_valuation_selected * bpv_factor_ftsp_parity_source_valuation_selected_divides)))) /\ forall bpv_candidate_ftsp_parity_source_valuation. (exists bpv_gap_ftsp_parity_source_valuation_candidate_bound. bpv_gap_ftsp_parity_source_valuation_candidate_bound + bpv_candidate_ftsp_parity_source_valuation = (n)) -> (exists bpv_result_ftsp_parity_source_valuation_candidate. ((exists ff_b_ftsp_parity_source_valuation_candidate_power ff_c_ftsp_parity_source_valuation_candidate_power. ((forall ff_i_ftsp_parity_source_valuation_candidate_power_repeat. (exists ff_lt_ftsp_parity_source_valuation_candidate_power_repeat_bound. ff_lt_ftsp_parity_source_valuation_candidate_power_repeat_bound + S ff_i_ftsp_parity_source_valuation_candidate_power_repeat = bpv_candidate_ftsp_parity_source_valuation) -> (((exists ff_h_ftsp_parity_source_valuation_candidate_power_repeat_decoded. ff_h_ftsp_parity_source_valuation_candidate_power_repeat_decoded + S (ftsp_bad_prime_parity_source) = S ((S (ff_i_ftsp_parity_source_valuation_candidate_power_repeat)) * ff_c_ftsp_parity_source_valuation_candidate_power)) /\ exists ff_q_ftsp_parity_source_valuation_candidate_power_repeat_decoded. ff_b_ftsp_parity_source_valuation_candidate_power = ff_q_ftsp_parity_source_valuation_candidate_power_repeat_decoded * S ((S (ff_i_ftsp_parity_source_valuation_candidate_power_repeat)) * ff_c_ftsp_parity_source_valuation_candidate_power) + (ftsp_bad_prime_parity_source)))) /\ (exists ff_u_ftsp_parity_source_valuation_candidate_power_product ff_v_ftsp_parity_source_valuation_candidate_power_product. ((((exists ff_h_ftsp_parity_source_valuation_candidate_power_product_start. ff_h_ftsp_parity_source_valuation_candidate_power_product_start + S (1) = S ((S (0)) * ff_v_ftsp_parity_source_valuation_candidate_power_product)) /\ exists ff_q_ftsp_parity_source_valuation_candidate_power_product_start. ff_u_ftsp_parity_source_valuation_candidate_power_product = ff_q_ftsp_parity_source_valuation_candidate_power_product_start * S ((S (0)) * ff_v_ftsp_parity_source_valuation_candidate_power_product) + (1))) /\ ((((exists ff_h_ftsp_parity_source_valuation_candidate_power_product_terminal. ff_h_ftsp_parity_source_valuation_candidate_power_product_terminal + S (bpv_result_ftsp_parity_source_valuation_candidate) = S ((S (bpv_candidate_ftsp_parity_source_valuation)) * ff_v_ftsp_parity_source_valuation_candidate_power_product)) /\ exists ff_q_ftsp_parity_source_valuation_candidate_power_product_terminal. ff_u_ftsp_parity_source_valuation_candidate_power_product = ff_q_ftsp_parity_source_valuation_candidate_power_product_terminal * S ((S (bpv_candidate_ftsp_parity_source_valuation)) * ff_v_ftsp_parity_source_valuation_candidate_power_product) + (bpv_result_ftsp_parity_source_valuation_candidate))) /\ forall ff_i_ftsp_parity_source_valuation_candidate_power_product. (exists ff_lt_ftsp_parity_source_valuation_candidate_power_product_bound. ff_lt_ftsp_parity_source_valuation_candidate_power_product_bound + S ff_i_ftsp_parity_source_valuation_candidate_power_product = bpv_candidate_ftsp_parity_source_valuation) -> exists ff_p_ftsp_parity_source_valuation_candidate_power_product ff_r_ftsp_parity_source_valuation_candidate_power_product ff_s_ftsp_parity_source_valuation_candidate_power_product. ((((exists ff_h_ftsp_parity_source_valuation_candidate_power_product_factor. ff_h_ftsp_parity_source_valuation_candidate_power_product_factor + S (ff_p_ftsp_parity_source_valuation_candidate_power_product) = S ((S (ff_i_ftsp_parity_source_valuation_candidate_power_product)) * ff_c_ftsp_parity_source_valuation_candidate_power)) /\ exists ff_q_ftsp_parity_source_valuation_candidate_power_product_factor. ff_b_ftsp_parity_source_valuation_candidate_power = ff_q_ftsp_parity_source_valuation_candidate_power_product_factor * S ((S (ff_i_ftsp_parity_source_valuation_candidate_power_product)) * ff_c_ftsp_parity_source_valuation_candidate_power) + (ff_p_ftsp_parity_source_valuation_candidate_power_product))) /\ ((((exists ff_h_ftsp_parity_source_valuation_candidate_power_product_partial. ff_h_ftsp_parity_source_valuation_candidate_power_product_partial + S (ff_r_ftsp_parity_source_valuation_candidate_power_product) = S ((S (ff_i_ftsp_parity_source_valuation_candidate_power_product)) * ff_v_ftsp_parity_source_valuation_candidate_power_product)) /\ exists ff_q_ftsp_parity_source_valuation_candidate_power_product_partial. ff_u_ftsp_parity_source_valuation_candidate_power_product = ff_q_ftsp_parity_source_valuation_candidate_power_product_partial * S ((S (ff_i_ftsp_parity_source_valuation_candidate_power_product)) * ff_v_ftsp_parity_source_valuation_candidate_power_product) + (ff_r_ftsp_parity_source_valuation_candidate_power_product))) /\ ((((exists ff_h_ftsp_parity_source_valuation_candidate_power_product_successor. ff_h_ftsp_parity_source_valuation_candidate_power_product_successor + S (ff_s_ftsp_parity_source_valuation_candidate_power_product) = S ((S (S ff_i_ftsp_parity_source_valuation_candidate_power_product)) * ff_v_ftsp_parity_source_valuation_candidate_power_product)) /\ exists ff_q_ftsp_parity_source_valuation_candidate_power_product_successor. ff_u_ftsp_parity_source_valuation_candidate_power_product = ff_q_ftsp_parity_source_valuation_candidate_power_product_successor * S ((S (S ff_i_ftsp_parity_source_valuation_candidate_power_product)) * ff_v_ftsp_parity_source_valuation_candidate_power_product) + (ff_s_ftsp_parity_source_valuation_candidate_power_product))) /\ ff_s_ftsp_parity_source_valuation_candidate_power_product = ff_r_ftsp_parity_source_valuation_candidate_power_product * ff_p_ftsp_parity_source_valuation_candidate_power_product)))))))) /\ (exists bpv_factor_ftsp_parity_source_valuation_candidate_divides. (n) = bpv_result_ftsp_parity_source_valuation_candidate * bpv_factor_ftsp_parity_source_valuation_candidate_divides))) -> (exists bpv_gap_ftsp_parity_source_valuation_maximal. bpv_gap_ftsp_parity_source_valuation_maximal + bpv_candidate_ftsp_parity_source_valuation = ftsp_bad_exponent_parity_source)) -> exists ftsp_bad_half_parity_source. ftsp_bad_exponent_parity_source = ftsp_bad_half_parity_source + ftsp_bad_half_parity_source)