central_binom_prime_mask_weighted_upper

Exact expanded first-order arithmetic statement

forall n C b c d f l. (exists pc_le_central_weight_positive. pc_le_central_weight_positive + (1) = (n)) -> (((exists bcf_lt_gap_pc_central_weight_value_out_of_range. bcf_lt_gap_pc_central_weight_value_out_of_range + S (n + n) = n) /\ C = 0) \/ ((exists bcf_le_gap_pc_central_weight_value_in_range. bcf_le_gap_pc_central_weight_value_in_range + (n) = n + n) /\ (exists bcf_row_code_code_pc_central_weight_value bcf_row_code_scale_pc_central_weight_value bcf_row_scale_code_pc_central_weight_value bcf_row_scale_scale_pc_central_weight_value bcf_row_code_pc_central_weight_value bcf_row_scale_pc_central_weight_value. ((forall bcf_row_index_pc_central_weight_value_table. (exists bcf_lt_gap_pc_central_weight_value_table_row_bound. bcf_lt_gap_pc_central_weight_value_table_row_bound + S (bcf_row_index_pc_central_weight_value_table) = S (n + n)) -> exists bcf_row_code_pc_central_weight_value_table bcf_row_scale_pc_central_weight_value_table. ((((exists bcf_height_pc_central_weight_value_table_decoded_row_code. bcf_height_pc_central_weight_value_table_decoded_row_code + S (bcf_row_code_pc_central_weight_value_table) = S ((S (bcf_row_index_pc_central_weight_value_table)) * bcf_row_code_scale_pc_central_weight_value)) /\ exists bcf_quotient_pc_central_weight_value_table_decoded_row_code. bcf_row_code_code_pc_central_weight_value = bcf_quotient_pc_central_weight_value_table_decoded_row_code * S ((S (bcf_row_index_pc_central_weight_value_table)) * bcf_row_code_scale_pc_central_weight_value) + (bcf_row_code_pc_central_weight_value_table))) /\ ((((exists bcf_height_pc_central_weight_value_table_decoded_row_scale. bcf_height_pc_central_weight_value_table_decoded_row_scale + S (bcf_row_scale_pc_central_weight_value_table) = S ((S (bcf_row_index_pc_central_weight_value_table)) * bcf_row_scale_scale_pc_central_weight_value)) /\ exists bcf_quotient_pc_central_weight_value_table_decoded_row_scale. bcf_row_scale_code_pc_central_weight_value = bcf_quotient_pc_central_weight_value_table_decoded_row_scale * S ((S (bcf_row_index_pc_central_weight_value_table)) * bcf_row_scale_scale_pc_central_weight_value) + (bcf_row_scale_pc_central_weight_value_table))) /\ ((bcf_row_index_pc_central_weight_value_table = 0 /\ (forall bcf_index_pc_central_weight_value_table_zero_row. (exists bcf_lt_gap_pc_central_weight_value_table_zero_row_bound. bcf_lt_gap_pc_central_weight_value_table_zero_row_bound + S (bcf_index_pc_central_weight_value_table_zero_row) = S (n + n)) -> exists bcf_value_pc_central_weight_value_table_zero_row. ((((exists bcf_height_pc_central_weight_value_table_zero_row_entry. bcf_height_pc_central_weight_value_table_zero_row_entry + S (bcf_value_pc_central_weight_value_table_zero_row) = S ((S (bcf_index_pc_central_weight_value_table_zero_row)) * bcf_row_scale_pc_central_weight_value_table)) /\ exists bcf_quotient_pc_central_weight_value_table_zero_row_entry. bcf_row_code_pc_central_weight_value_table = bcf_quotient_pc_central_weight_value_table_zero_row_entry * S ((S (bcf_index_pc_central_weight_value_table_zero_row)) * bcf_row_scale_pc_central_weight_value_table) + (bcf_value_pc_central_weight_value_table_zero_row))) /\ ((bcf_index_pc_central_weight_value_table_zero_row = 0 /\ bcf_value_pc_central_weight_value_table_zero_row = 1) \/ exists bcf_predecessor_pc_central_weight_value_table_zero_row. bcf_index_pc_central_weight_value_table_zero_row = S bcf_predecessor_pc_central_weight_value_table_zero_row /\ bcf_value_pc_central_weight_value_table_zero_row = 0)))) \/ exists bcf_predecessor_pc_central_weight_value_table bcf_previous_code_pc_central_weight_value_table bcf_previous_scale_pc_central_weight_value_table. bcf_row_index_pc_central_weight_value_table = S bcf_predecessor_pc_central_weight_value_table /\ ((((exists bcf_height_pc_central_weight_value_table_decoded_previous_code. bcf_height_pc_central_weight_value_table_decoded_previous_code + S (bcf_previous_code_pc_central_weight_value_table) = S ((S (bcf_predecessor_pc_central_weight_value_table)) * bcf_row_code_scale_pc_central_weight_value)) /\ exists bcf_quotient_pc_central_weight_value_table_decoded_previous_code. bcf_row_code_code_pc_central_weight_value = bcf_quotient_pc_central_weight_value_table_decoded_previous_code * S ((S (bcf_predecessor_pc_central_weight_value_table)) * bcf_row_code_scale_pc_central_weight_value) + (bcf_previous_code_pc_central_weight_value_table))) /\ ((((exists bcf_height_pc_central_weight_value_table_decoded_previous_scale. bcf_height_pc_central_weight_value_table_decoded_previous_scale + S (bcf_previous_scale_pc_central_weight_value_table) = S ((S (bcf_predecessor_pc_central_weight_value_table)) * bcf_row_scale_scale_pc_central_weight_value)) /\ exists bcf_quotient_pc_central_weight_value_table_decoded_previous_scale. bcf_row_scale_code_pc_central_weight_value = bcf_quotient_pc_central_weight_value_table_decoded_previous_scale * S ((S (bcf_predecessor_pc_central_weight_value_table)) * bcf_row_scale_scale_pc_central_weight_value) + (bcf_previous_scale_pc_central_weight_value_table))) /\ (forall bcf_index_pc_central_weight_value_table_row_step. (exists bcf_lt_gap_pc_central_weight_value_table_row_step_bound. bcf_lt_gap_pc_central_weight_value_table_row_step_bound + S (bcf_index_pc_central_weight_value_table_row_step) = S (n + n)) -> exists bcf_value_pc_central_weight_value_table_row_step. ((((exists bcf_height_pc_central_weight_value_table_row_step_entry. bcf_height_pc_central_weight_value_table_row_step_entry + S (bcf_value_pc_central_weight_value_table_row_step) = S ((S (bcf_index_pc_central_weight_value_table_row_step)) * bcf_row_scale_pc_central_weight_value_table)) /\ exists bcf_quotient_pc_central_weight_value_table_row_step_entry. bcf_row_code_pc_central_weight_value_table = bcf_quotient_pc_central_weight_value_table_row_step_entry * S ((S (bcf_index_pc_central_weight_value_table_row_step)) * bcf_row_scale_pc_central_weight_value_table) + (bcf_value_pc_central_weight_value_table_row_step))) /\ ((bcf_index_pc_central_weight_value_table_row_step = 0 /\ bcf_value_pc_central_weight_value_table_row_step = 1) \/ exists bcf_predecessor_pc_central_weight_value_table_row_step bcf_left_pc_central_weight_value_table_row_step bcf_right_pc_central_weight_value_table_row_step. bcf_index_pc_central_weight_value_table_row_step = S bcf_predecessor_pc_central_weight_value_table_row_step /\ ((((exists bcf_height_pc_central_weight_value_table_row_step_previous_left. bcf_height_pc_central_weight_value_table_row_step_previous_left + S (bcf_left_pc_central_weight_value_table_row_step) = S ((S (bcf_predecessor_pc_central_weight_value_table_row_step)) * bcf_previous_scale_pc_central_weight_value_table)) /\ exists bcf_quotient_pc_central_weight_value_table_row_step_previous_left. bcf_previous_code_pc_central_weight_value_table = bcf_quotient_pc_central_weight_value_table_row_step_previous_left * S ((S (bcf_predecessor_pc_central_weight_value_table_row_step)) * bcf_previous_scale_pc_central_weight_value_table) + (bcf_left_pc_central_weight_value_table_row_step))) /\ ((((exists bcf_height_pc_central_weight_value_table_row_step_previous_right. bcf_height_pc_central_weight_value_table_row_step_previous_right + S (bcf_right_pc_central_weight_value_table_row_step) = S ((S (S (bcf_predecessor_pc_central_weight_value_table_row_step))) * bcf_previous_scale_pc_central_weight_value_table)) /\ exists bcf_quotient_pc_central_weight_value_table_row_step_previous_right. bcf_previous_code_pc_central_weight_value_table = bcf_quotient_pc_central_weight_value_table_row_step_previous_right * S ((S (S (bcf_predecessor_pc_central_weight_value_table_row_step))) * bcf_previous_scale_pc_central_weight_value_table) + (bcf_right_pc_central_weight_value_table_row_step))) /\ bcf_value_pc_central_weight_value_table_row_step = bcf_left_pc_central_weight_value_table_row_step + bcf_right_pc_central_weight_value_table_row_step))))))))))) /\ ((((exists bcf_height_pc_central_weight_value_decoded_row_code. bcf_height_pc_central_weight_value_decoded_row_code + S (bcf_row_code_pc_central_weight_value) = S ((S (n + n)) * bcf_row_code_scale_pc_central_weight_value)) /\ exists bcf_quotient_pc_central_weight_value_decoded_row_code. bcf_row_code_code_pc_central_weight_value = bcf_quotient_pc_central_weight_value_decoded_row_code * S ((S (n + n)) * bcf_row_code_scale_pc_central_weight_value) + (bcf_row_code_pc_central_weight_value))) /\ ((((exists bcf_height_pc_central_weight_value_decoded_row_scale. bcf_height_pc_central_weight_value_decoded_row_scale + S (bcf_row_scale_pc_central_weight_value) = S ((S (n + n)) * bcf_row_scale_scale_pc_central_weight_value)) /\ exists bcf_quotient_pc_central_weight_value_decoded_row_scale. bcf_row_scale_code_pc_central_weight_value = bcf_quotient_pc_central_weight_value_decoded_row_scale * S ((S (n + n)) * bcf_row_scale_scale_pc_central_weight_value) + (bcf_row_scale_pc_central_weight_value))) /\ (((exists bcf_height_pc_central_weight_value_decoded_value. bcf_height_pc_central_weight_value_decoded_value + S (C) = S ((S (n)) * bcf_row_scale_pc_central_weight_value)) /\ exists bcf_quotient_pc_central_weight_value_decoded_value. bcf_row_code_pc_central_weight_value = bcf_quotient_pc_central_weight_value_decoded_value * S ((S (n)) * bcf_row_scale_pc_central_weight_value) + (C))))))))) -> (forall bpr_prefix_index_pc_central_weight_factors. (exists bpr_gap_pc_central_weight_factors_bound. bpr_gap_pc_central_weight_factors_bound + S (bpr_prefix_index_pc_central_weight_factors) = l) -> exists bpr_prefix_value_pc_central_weight_factors. ((((exists bpr_height_pc_central_weight_factors_decoded. bpr_height_pc_central_weight_factors_decoded + S (bpr_prefix_value_pc_central_weight_factors) = S ((S (bpr_prefix_index_pc_central_weight_factors)) * c)) /\ exists bpr_quotient_pc_central_weight_factors_decoded. b = bpr_quotient_pc_central_weight_factors_decoded * S ((S (bpr_prefix_index_pc_central_weight_factors)) * c) + (bpr_prefix_value_pc_central_weight_factors))) /\ (((((~(S (bpr_prefix_index_pc_central_weight_factors) = 1) /\ forall bpr_left_pc_central_weight_factors_choice_prime bpr_right_pc_central_weight_factors_choice_prime. S (bpr_prefix_index_pc_central_weight_factors) = bpr_left_pc_central_weight_factors_choice_prime * bpr_right_pc_central_weight_factors_choice_prime -> bpr_left_pc_central_weight_factors_choice_prime = 1 \/ bpr_right_pc_central_weight_factors_choice_prime = 1)) /\ exists bpr_choice_exponent_pc_central_weight_factors_choice. ((((exists bpr_le_gap_pc_central_weight_factors_choice_valuation_selected_bound. bpr_le_gap_pc_central_weight_factors_choice_valuation_selected_bound + (bpr_choice_exponent_pc_central_weight_factors_choice) = (C)) /\ (exists bpr_power_value_pc_central_weight_factors_choice_valuation_selected. ((exists bpr_power_code_pc_central_weight_factors_choice_valuation_selected_power bpr_power_scale_pc_central_weight_factors_choice_valuation_selected_power. ((forall bpr_power_index_pc_central_weight_factors_choice_valuation_selected_power. (exists bpr_gap_pc_central_weight_factors_choice_valuation_selected_power_repeat_bound. bpr_gap_pc_central_weight_factors_choice_valuation_selected_power_repeat_bound + S (bpr_power_index_pc_central_weight_factors_choice_valuation_selected_power) = bpr_choice_exponent_pc_central_weight_factors_choice) -> (((exists bpr_height_pc_central_weight_factors_choice_valuation_selected_power_repeat_entry. bpr_height_pc_central_weight_factors_choice_valuation_selected_power_repeat_entry + S (S (bpr_prefix_index_pc_central_weight_factors)) = S ((S (bpr_power_index_pc_central_weight_factors_choice_valuation_selected_power)) * bpr_power_scale_pc_central_weight_factors_choice_valuation_selected_power)) /\ exists bpr_quotient_pc_central_weight_factors_choice_valuation_selected_power_repeat_entry. bpr_power_code_pc_central_weight_factors_choice_valuation_selected_power = bpr_quotient_pc_central_weight_factors_choice_valuation_selected_power_repeat_entry * S ((S (bpr_power_index_pc_central_weight_factors_choice_valuation_selected_power)) * bpr_power_scale_pc_central_weight_factors_choice_valuation_selected_power) + (S (bpr_prefix_index_pc_central_weight_factors))))) /\ (exists ff_u_pc_central_weight_factors_choice_valuation_selected_power_product ff_v_pc_central_weight_factors_choice_valuation_selected_power_product. ((((exists ff_h_pc_central_weight_factors_choice_valuation_selected_power_product_start. ff_h_pc_central_weight_factors_choice_valuation_selected_power_product_start + S (1) = S ((S (0)) * ff_v_pc_central_weight_factors_choice_valuation_selected_power_product)) /\ exists ff_q_pc_central_weight_factors_choice_valuation_selected_power_product_start. ff_u_pc_central_weight_factors_choice_valuation_selected_power_product = ff_q_pc_central_weight_factors_choice_valuation_selected_power_product_start * S ((S (0)) * ff_v_pc_central_weight_factors_choice_valuation_selected_power_product) + (1))) /\ ((((exists ff_h_pc_central_weight_factors_choice_valuation_selected_power_product_terminal. ff_h_pc_central_weight_factors_choice_valuation_selected_power_product_terminal + S (bpr_power_value_pc_central_weight_factors_choice_valuation_selected) = S ((S (bpr_choice_exponent_pc_central_weight_factors_choice)) * ff_v_pc_central_weight_factors_choice_valuation_selected_power_product)) /\ exists ff_q_pc_central_weight_factors_choice_valuation_selected_power_product_terminal. ff_u_pc_central_weight_factors_choice_valuation_selected_power_product = ff_q_pc_central_weight_factors_choice_valuation_selected_power_product_terminal * S ((S (bpr_choice_exponent_pc_central_weight_factors_choice)) * ff_v_pc_central_weight_factors_choice_valuation_selected_power_product) + (bpr_power_value_pc_central_weight_factors_choice_valuation_selected))) /\ forall ff_i_pc_central_weight_factors_choice_valuation_selected_power_product. (exists ff_lt_pc_central_weight_factors_choice_valuation_selected_power_product_bound. ff_lt_pc_central_weight_factors_choice_valuation_selected_power_product_bound + S ff_i_pc_central_weight_factors_choice_valuation_selected_power_product = bpr_choice_exponent_pc_central_weight_factors_choice) -> exists ff_p_pc_central_weight_factors_choice_valuation_selected_power_product ff_r_pc_central_weight_factors_choice_valuation_selected_power_product ff_s_pc_central_weight_factors_choice_valuation_selected_power_product. ((((exists ff_h_pc_central_weight_factors_choice_valuation_selected_power_product_factor. ff_h_pc_central_weight_factors_choice_valuation_selected_power_product_factor + S (ff_p_pc_central_weight_factors_choice_valuation_selected_power_product) = S ((S (ff_i_pc_central_weight_factors_choice_valuation_selected_power_product)) * bpr_power_scale_pc_central_weight_factors_choice_valuation_selected_power)) /\ exists ff_q_pc_central_weight_factors_choice_valuation_selected_power_product_factor. bpr_power_code_pc_central_weight_factors_choice_valuation_selected_power = ff_q_pc_central_weight_factors_choice_valuation_selected_power_product_factor * S ((S (ff_i_pc_central_weight_factors_choice_valuation_selected_power_product)) * bpr_power_scale_pc_central_weight_factors_choice_valuation_selected_power) + (ff_p_pc_central_weight_factors_choice_valuation_selected_power_product))) /\ ((((exists ff_h_pc_central_weight_factors_choice_valuation_selected_power_product_partial. ff_h_pc_central_weight_factors_choice_valuation_selected_power_product_partial + S (ff_r_pc_central_weight_factors_choice_valuation_selected_power_product) = S ((S (ff_i_pc_central_weight_factors_choice_valuation_selected_power_product)) * ff_v_pc_central_weight_factors_choice_valuation_selected_power_product)) /\ exists ff_q_pc_central_weight_factors_choice_valuation_selected_power_product_partial. ff_u_pc_central_weight_factors_choice_valuation_selected_power_product = ff_q_pc_central_weight_factors_choice_valuation_selected_power_product_partial * S ((S (ff_i_pc_central_weight_factors_choice_valuation_selected_power_product)) * ff_v_pc_central_weight_factors_choice_valuation_selected_power_product) + (ff_r_pc_central_weight_factors_choice_valuation_selected_power_product))) /\ ((((exists ff_h_pc_central_weight_factors_choice_valuation_selected_power_product_successor. ff_h_pc_central_weight_factors_choice_valuation_selected_power_product_successor + S (ff_s_pc_central_weight_factors_choice_valuation_selected_power_product) = S ((S (S ff_i_pc_central_weight_factors_choice_valuation_selected_power_product)) * ff_v_pc_central_weight_factors_choice_valuation_selected_power_product)) /\ exists ff_q_pc_central_weight_factors_choice_valuation_selected_power_product_successor. ff_u_pc_central_weight_factors_choice_valuation_selected_power_product = ff_q_pc_central_weight_factors_choice_valuation_selected_power_product_successor * S ((S (S ff_i_pc_central_weight_factors_choice_valuation_selected_power_product)) * ff_v_pc_central_weight_factors_choice_valuation_selected_power_product) + (ff_s_pc_central_weight_factors_choice_valuation_selected_power_product))) /\ ff_s_pc_central_weight_factors_choice_valuation_selected_power_product = ff_r_pc_central_weight_factors_choice_valuation_selected_power_product * ff_p_pc_central_weight_factors_choice_valuation_selected_power_product)))))))) /\ (exists bpr_divides_quotient_pc_central_weight_factors_choice_valuation_selected_divides. C = (bpr_power_value_pc_central_weight_factors_choice_valuation_selected) * bpr_divides_quotient_pc_central_weight_factors_choice_valuation_selected_divides)))) /\ forall bpr_valuation_candidate_pc_central_weight_factors_choice_valuation. (exists bpr_le_gap_pc_central_weight_factors_choice_valuation_candidate_bound. bpr_le_gap_pc_central_weight_factors_choice_valuation_candidate_bound + (bpr_valuation_candidate_pc_central_weight_factors_choice_valuation) = (C)) -> (exists bpr_power_value_pc_central_weight_factors_choice_valuation_candidate. ((exists bpr_power_code_pc_central_weight_factors_choice_valuation_candidate_power bpr_power_scale_pc_central_weight_factors_choice_valuation_candidate_power. ((forall bpr_power_index_pc_central_weight_factors_choice_valuation_candidate_power. (exists bpr_gap_pc_central_weight_factors_choice_valuation_candidate_power_repeat_bound. bpr_gap_pc_central_weight_factors_choice_valuation_candidate_power_repeat_bound + S (bpr_power_index_pc_central_weight_factors_choice_valuation_candidate_power) = bpr_valuation_candidate_pc_central_weight_factors_choice_valuation) -> (((exists bpr_height_pc_central_weight_factors_choice_valuation_candidate_power_repeat_entry. bpr_height_pc_central_weight_factors_choice_valuation_candidate_power_repeat_entry + S (S (bpr_prefix_index_pc_central_weight_factors)) = S ((S (bpr_power_index_pc_central_weight_factors_choice_valuation_candidate_power)) * bpr_power_scale_pc_central_weight_factors_choice_valuation_candidate_power)) /\ exists bpr_quotient_pc_central_weight_factors_choice_valuation_candidate_power_repeat_entry. bpr_power_code_pc_central_weight_factors_choice_valuation_candidate_power = bpr_quotient_pc_central_weight_factors_choice_valuation_candidate_power_repeat_entry * S ((S (bpr_power_index_pc_central_weight_factors_choice_valuation_candidate_power)) * bpr_power_scale_pc_central_weight_factors_choice_valuation_candidate_power) + (S (bpr_prefix_index_pc_central_weight_factors))))) /\ (exists ff_u_pc_central_weight_factors_choice_valuation_candidate_power_product ff_v_pc_central_weight_factors_choice_valuation_candidate_power_product. ((((exists ff_h_pc_central_weight_factors_choice_valuation_candidate_power_product_start. ff_h_pc_central_weight_factors_choice_valuation_candidate_power_product_start + S (1) = S ((S (0)) * ff_v_pc_central_weight_factors_choice_valuation_candidate_power_product)) /\ exists ff_q_pc_central_weight_factors_choice_valuation_candidate_power_product_start. ff_u_pc_central_weight_factors_choice_valuation_candidate_power_product = ff_q_pc_central_weight_factors_choice_valuation_candidate_power_product_start * S ((S (0)) * ff_v_pc_central_weight_factors_choice_valuation_candidate_power_product) + (1))) /\ ((((exists ff_h_pc_central_weight_factors_choice_valuation_candidate_power_product_terminal. ff_h_pc_central_weight_factors_choice_valuation_candidate_power_product_terminal + S (bpr_power_value_pc_central_weight_factors_choice_valuation_candidate) = S ((S (bpr_valuation_candidate_pc_central_weight_factors_choice_valuation)) * ff_v_pc_central_weight_factors_choice_valuation_candidate_power_product)) /\ exists ff_q_pc_central_weight_factors_choice_valuation_candidate_power_product_terminal. ff_u_pc_central_weight_factors_choice_valuation_candidate_power_product = ff_q_pc_central_weight_factors_choice_valuation_candidate_power_product_terminal * S ((S (bpr_valuation_candidate_pc_central_weight_factors_choice_valuation)) * ff_v_pc_central_weight_factors_choice_valuation_candidate_power_product) + (bpr_power_value_pc_central_weight_factors_choice_valuation_candidate))) /\ forall ff_i_pc_central_weight_factors_choice_valuation_candidate_power_product. (exists ff_lt_pc_central_weight_factors_choice_valuation_candidate_power_product_bound. ff_lt_pc_central_weight_factors_choice_valuation_candidate_power_product_bound + S ff_i_pc_central_weight_factors_choice_valuation_candidate_power_product = bpr_valuation_candidate_pc_central_weight_factors_choice_valuation) -> exists ff_p_pc_central_weight_factors_choice_valuation_candidate_power_product ff_r_pc_central_weight_factors_choice_valuation_candidate_power_product ff_s_pc_central_weight_factors_choice_valuation_candidate_power_product. ((((exists ff_h_pc_central_weight_factors_choice_valuation_candidate_power_product_factor. ff_h_pc_central_weight_factors_choice_valuation_candidate_power_product_factor + S (ff_p_pc_central_weight_factors_choice_valuation_candidate_power_product) = S ((S (ff_i_pc_central_weight_factors_choice_valuation_candidate_power_product)) * bpr_power_scale_pc_central_weight_factors_choice_valuation_candidate_power)) /\ exists ff_q_pc_central_weight_factors_choice_valuation_candidate_power_product_factor. bpr_power_code_pc_central_weight_factors_choice_valuation_candidate_power = ff_q_pc_central_weight_factors_choice_valuation_candidate_power_product_factor * S ((S (ff_i_pc_central_weight_factors_choice_valuation_candidate_power_product)) * bpr_power_scale_pc_central_weight_factors_choice_valuation_candidate_power) + (ff_p_pc_central_weight_factors_choice_valuation_candidate_power_product))) /\ ((((exists ff_h_pc_central_weight_factors_choice_valuation_candidate_power_product_partial. ff_h_pc_central_weight_factors_choice_valuation_candidate_power_product_partial + S (ff_r_pc_central_weight_factors_choice_valuation_candidate_power_product) = S ((S (ff_i_pc_central_weight_factors_choice_valuation_candidate_power_product)) * ff_v_pc_central_weight_factors_choice_valuation_candidate_power_product)) /\ exists ff_q_pc_central_weight_factors_choice_valuation_candidate_power_product_partial. ff_u_pc_central_weight_factors_choice_valuation_candidate_power_product = ff_q_pc_central_weight_factors_choice_valuation_candidate_power_product_partial * S ((S (ff_i_pc_central_weight_factors_choice_valuation_candidate_power_product)) * ff_v_pc_central_weight_factors_choice_valuation_candidate_power_product) + (ff_r_pc_central_weight_factors_choice_valuation_candidate_power_product))) /\ ((((exists ff_h_pc_central_weight_factors_choice_valuation_candidate_power_product_successor. ff_h_pc_central_weight_factors_choice_valuation_candidate_power_product_successor + S (ff_s_pc_central_weight_factors_choice_valuation_candidate_power_product) = S ((S (S ff_i_pc_central_weight_factors_choice_valuation_candidate_power_product)) * ff_v_pc_central_weight_factors_choice_valuation_candidate_power_product)) /\ exists ff_q_pc_central_weight_factors_choice_valuation_candidate_power_product_successor. ff_u_pc_central_weight_factors_choice_valuation_candidate_power_product = ff_q_pc_central_weight_factors_choice_valuation_candidate_power_product_successor * S ((S (S ff_i_pc_central_weight_factors_choice_valuation_candidate_power_product)) * ff_v_pc_central_weight_factors_choice_valuation_candidate_power_product) + (ff_s_pc_central_weight_factors_choice_valuation_candidate_power_product))) /\ ff_s_pc_central_weight_factors_choice_valuation_candidate_power_product = ff_r_pc_central_weight_factors_choice_valuation_candidate_power_product * ff_p_pc_central_weight_factors_choice_valuation_candidate_power_product)))))))) /\ (exists bpr_divides_quotient_pc_central_weight_factors_choice_valuation_candidate_divides. C = (bpr_power_value_pc_central_weight_factors_choice_valuation_candidate) * bpr_divides_quotient_pc_central_weight_factors_choice_valuation_candidate_divides))) -> (exists bpr_le_gap_pc_central_weight_factors_choice_valuation_candidate_below. bpr_le_gap_pc_central_weight_factors_choice_valuation_candidate_below + (bpr_valuation_candidate_pc_central_weight_factors_choice_valuation) = (bpr_choice_exponent_pc_central_weight_factors_choice))) /\ (exists bpr_power_code_pc_central_weight_factors_choice_power bpr_power_scale_pc_central_weight_factors_choice_power. ((forall bpr_power_index_pc_central_weight_factors_choice_power. (exists bpr_gap_pc_central_weight_factors_choice_power_repeat_bound. bpr_gap_pc_central_weight_factors_choice_power_repeat_bound + S (bpr_power_index_pc_central_weight_factors_choice_power) = bpr_choice_exponent_pc_central_weight_factors_choice) -> (((exists bpr_height_pc_central_weight_factors_choice_power_repeat_entry. bpr_height_pc_central_weight_factors_choice_power_repeat_entry + S (S (bpr_prefix_index_pc_central_weight_factors)) = S ((S (bpr_power_index_pc_central_weight_factors_choice_power)) * bpr_power_scale_pc_central_weight_factors_choice_power)) /\ exists bpr_quotient_pc_central_weight_factors_choice_power_repeat_entry. bpr_power_code_pc_central_weight_factors_choice_power = bpr_quotient_pc_central_weight_factors_choice_power_repeat_entry * S ((S (bpr_power_index_pc_central_weight_factors_choice_power)) * bpr_power_scale_pc_central_weight_factors_choice_power) + (S (bpr_prefix_index_pc_central_weight_factors))))) /\ (exists ff_u_pc_central_weight_factors_choice_power_product ff_v_pc_central_weight_factors_choice_power_product. ((((exists ff_h_pc_central_weight_factors_choice_power_product_start. ff_h_pc_central_weight_factors_choice_power_product_start + S (1) = S ((S (0)) * ff_v_pc_central_weight_factors_choice_power_product)) /\ exists ff_q_pc_central_weight_factors_choice_power_product_start. ff_u_pc_central_weight_factors_choice_power_product = ff_q_pc_central_weight_factors_choice_power_product_start * S ((S (0)) * ff_v_pc_central_weight_factors_choice_power_product) + (1))) /\ ((((exists ff_h_pc_central_weight_factors_choice_power_product_terminal. ff_h_pc_central_weight_factors_choice_power_product_terminal + S (bpr_prefix_value_pc_central_weight_factors) = S ((S (bpr_choice_exponent_pc_central_weight_factors_choice)) * ff_v_pc_central_weight_factors_choice_power_product)) /\ exists ff_q_pc_central_weight_factors_choice_power_product_terminal. ff_u_pc_central_weight_factors_choice_power_product = ff_q_pc_central_weight_factors_choice_power_product_terminal * S ((S (bpr_choice_exponent_pc_central_weight_factors_choice)) * ff_v_pc_central_weight_factors_choice_power_product) + (bpr_prefix_value_pc_central_weight_factors))) /\ forall ff_i_pc_central_weight_factors_choice_power_product. (exists ff_lt_pc_central_weight_factors_choice_power_product_bound. ff_lt_pc_central_weight_factors_choice_power_product_bound + S ff_i_pc_central_weight_factors_choice_power_product = bpr_choice_exponent_pc_central_weight_factors_choice) -> exists ff_p_pc_central_weight_factors_choice_power_product ff_r_pc_central_weight_factors_choice_power_product ff_s_pc_central_weight_factors_choice_power_product. ((((exists ff_h_pc_central_weight_factors_choice_power_product_factor. ff_h_pc_central_weight_factors_choice_power_product_factor + S (ff_p_pc_central_weight_factors_choice_power_product) = S ((S (ff_i_pc_central_weight_factors_choice_power_product)) * bpr_power_scale_pc_central_weight_factors_choice_power)) /\ exists ff_q_pc_central_weight_factors_choice_power_product_factor. bpr_power_code_pc_central_weight_factors_choice_power = ff_q_pc_central_weight_factors_choice_power_product_factor * S ((S (ff_i_pc_central_weight_factors_choice_power_product)) * bpr_power_scale_pc_central_weight_factors_choice_power) + (ff_p_pc_central_weight_factors_choice_power_product))) /\ ((((exists ff_h_pc_central_weight_factors_choice_power_product_partial. ff_h_pc_central_weight_factors_choice_power_product_partial + S (ff_r_pc_central_weight_factors_choice_power_product) = S ((S (ff_i_pc_central_weight_factors_choice_power_product)) * ff_v_pc_central_weight_factors_choice_power_product)) /\ exists ff_q_pc_central_weight_factors_choice_power_product_partial. ff_u_pc_central_weight_factors_choice_power_product = ff_q_pc_central_weight_factors_choice_power_product_partial * S ((S (ff_i_pc_central_weight_factors_choice_power_product)) * ff_v_pc_central_weight_factors_choice_power_product) + (ff_r_pc_central_weight_factors_choice_power_product))) /\ ((((exists ff_h_pc_central_weight_factors_choice_power_product_successor. ff_h_pc_central_weight_factors_choice_power_product_successor + S (ff_s_pc_central_weight_factors_choice_power_product) = S ((S (S ff_i_pc_central_weight_factors_choice_power_product)) * ff_v_pc_central_weight_factors_choice_power_product)) /\ exists ff_q_pc_central_weight_factors_choice_power_product_successor. ff_u_pc_central_weight_factors_choice_power_product = ff_q_pc_central_weight_factors_choice_power_product_successor * S ((S (S ff_i_pc_central_weight_factors_choice_power_product)) * ff_v_pc_central_weight_factors_choice_power_product) + (ff_s_pc_central_weight_factors_choice_power_product))) /\ ff_s_pc_central_weight_factors_choice_power_product = ff_r_pc_central_weight_factors_choice_power_product * ff_p_pc_central_weight_factors_choice_power_product)))))))))) \/ (~((~(S (bpr_prefix_index_pc_central_weight_factors) = 1) /\ forall bpr_left_pc_central_weight_factors_choice_prime bpr_right_pc_central_weight_factors_choice_prime. S (bpr_prefix_index_pc_central_weight_factors) = bpr_left_pc_central_weight_factors_choice_prime * bpr_right_pc_central_weight_factors_choice_prime -> bpr_left_pc_central_weight_factors_choice_prime = 1 \/ bpr_right_pc_central_weight_factors_choice_prime = 1)) /\ bpr_prefix_value_pc_central_weight_factors = 1))))) -> (forall pc_index_central_weight_mask. (exists pc_lt_central_weight_mask_bound. pc_lt_central_weight_mask_bound + S (pc_index_central_weight_mask) = (l)) -> exists pc_bit_central_weight_mask. (((exists fs_h_pc_central_weight_mask_entry. fs_h_pc_central_weight_mask_entry + S (pc_bit_central_weight_mask) = S ((S (pc_index_central_weight_mask)) * f)) /\ exists fs_q_pc_central_weight_mask_entry. d = fs_q_pc_central_weight_mask_entry * S ((S (pc_index_central_weight_mask)) * f) + (pc_bit_central_weight_mask))) /\ (((((~(S (pc_index_central_weight_mask) = 1) /\ forall bpr_left_pc_central_weight_mask_choice_prime bpr_right_pc_central_weight_mask_choice_prime. S (pc_index_central_weight_mask) = bpr_left_pc_central_weight_mask_choice_prime * bpr_right_pc_central_weight_mask_choice_prime -> bpr_left_pc_central_weight_mask_choice_prime = 1 \/ bpr_right_pc_central_weight_mask_choice_prime = 1)) /\ pc_bit_central_weight_mask = 1) \/ (~((~(S (pc_index_central_weight_mask) = 1) /\ forall bpr_left_pc_central_weight_mask_choice_prime bpr_right_pc_central_weight_mask_choice_prime. S (pc_index_central_weight_mask) = bpr_left_pc_central_weight_mask_choice_prime * bpr_right_pc_central_weight_mask_choice_prime -> bpr_left_pc_central_weight_mask_choice_prime = 1 \/ bpr_right_pc_central_weight_mask_choice_prime = 1)) /\ pc_bit_central_weight_mask = 0)))) -> (forall pc_index_central_weight_result pc_factor_central_weight_result pc_bit_central_weight_result. (exists pc_lt_central_weight_result_index. pc_lt_central_weight_result_index + S (pc_index_central_weight_result) = (l)) -> (((exists fs_h_pc_central_weight_result_factor. fs_h_pc_central_weight_result_factor + S (pc_factor_central_weight_result) = S ((S (pc_index_central_weight_result)) * c)) /\ exists fs_q_pc_central_weight_result_factor. b = fs_q_pc_central_weight_result_factor * S ((S (pc_index_central_weight_result)) * c) + (pc_factor_central_weight_result))) -> (((exists fs_h_pc_central_weight_result_bit. fs_h_pc_central_weight_result_bit + S (pc_bit_central_weight_result) = S ((S (pc_index_central_weight_result)) * f)) /\ exists fs_q_pc_central_weight_result_bit. d = fs_q_pc_central_weight_result_bit * S ((S (pc_index_central_weight_result)) * f) + (pc_bit_central_weight_result))) -> ((pc_bit_central_weight_result = 0 /\ (pc_factor_central_weight_result = 1)) \/ (pc_bit_central_weight_result = 1 /\ (exists pc_le_central_weight_result_one. pc_le_central_weight_result_one + (pc_factor_central_weight_result) = (n + n)))))