multinomial_empty_carry_count

Exact expanded first-order arithmetic statement

forall p b c e. (exists mkm_total_empty_carries mkm_sb_empty_carries mkm_sc_empty_carries mkm_cb_empty_carries mkm_cc_empty_carries. (((((exists fs_h_mkm_empty_carries_trace_start. fs_h_mkm_empty_carries_trace_start + S (0) = S ((S (0)) * mkm_sc_empty_carries)) /\ exists fs_q_mkm_empty_carries_trace_start. mkm_sb_empty_carries = fs_q_mkm_empty_carries_trace_start * S ((S (0)) * mkm_sc_empty_carries) + (0))) /\ ((((exists fs_h_mkm_empty_carries_trace_terminal. fs_h_mkm_empty_carries_trace_terminal + S (mkm_total_empty_carries) = S ((S (0)) * mkm_sc_empty_carries)) /\ exists fs_q_mkm_empty_carries_trace_terminal. mkm_sb_empty_carries = fs_q_mkm_empty_carries_trace_terminal * S ((S (0)) * mkm_sc_empty_carries) + (mkm_total_empty_carries))) /\ forall fs_i_mkm_empty_carries_trace_steps. (exists fs_lt_mkm_empty_carries_trace_steps_bound. fs_lt_mkm_empty_carries_trace_steps_bound + S fs_i_mkm_empty_carries_trace_steps = 0) -> exists fs_a_mkm_empty_carries_trace_steps fs_r_mkm_empty_carries_trace_steps fs_s_mkm_empty_carries_trace_steps. ((((exists fs_h_mkm_empty_carries_trace_steps_summand. fs_h_mkm_empty_carries_trace_steps_summand + S (fs_a_mkm_empty_carries_trace_steps) = S ((S (fs_i_mkm_empty_carries_trace_steps)) * c)) /\ exists fs_q_mkm_empty_carries_trace_steps_summand. b = fs_q_mkm_empty_carries_trace_steps_summand * S ((S (fs_i_mkm_empty_carries_trace_steps)) * c) + (fs_a_mkm_empty_carries_trace_steps))) /\ ((((exists fs_h_mkm_empty_carries_trace_steps_partial. fs_h_mkm_empty_carries_trace_steps_partial + S (fs_r_mkm_empty_carries_trace_steps) = S ((S (fs_i_mkm_empty_carries_trace_steps)) * mkm_sc_empty_carries)) /\ exists fs_q_mkm_empty_carries_trace_steps_partial. mkm_sb_empty_carries = fs_q_mkm_empty_carries_trace_steps_partial * S ((S (fs_i_mkm_empty_carries_trace_steps)) * mkm_sc_empty_carries) + (fs_r_mkm_empty_carries_trace_steps))) /\ ((((exists fs_h_mkm_empty_carries_trace_steps_successor. fs_h_mkm_empty_carries_trace_steps_successor + S (fs_s_mkm_empty_carries_trace_steps) = S ((S (S fs_i_mkm_empty_carries_trace_steps)) * mkm_sc_empty_carries)) /\ exists fs_q_mkm_empty_carries_trace_steps_successor. mkm_sb_empty_carries = fs_q_mkm_empty_carries_trace_steps_successor * S ((S (S fs_i_mkm_empty_carries_trace_steps)) * mkm_sc_empty_carries) + (fs_s_mkm_empty_carries_trace_steps))) /\ fs_s_mkm_empty_carries_trace_steps = fs_r_mkm_empty_carries_trace_steps + fs_a_mkm_empty_carries_trace_steps)))))) /\ ((forall mkm_index_empty_carries_rows. (exists mkm_lt_empty_carries_rows_bound. mkm_lt_empty_carries_rows_bound + S (mkm_index_empty_carries_rows) = (0)) -> (exists mkm_value_empty_carries_rows_point mkm_partial_empty_carries_rows_point mkm_count_empty_carries_rows_point. (((exists fs_h_mkm_empty_carries_rows_point_source. fs_h_mkm_empty_carries_rows_point_source + S (mkm_value_empty_carries_rows_point) = S ((S (mkm_index_empty_carries_rows)) * c)) /\ exists fs_q_mkm_empty_carries_rows_point_source. b = fs_q_mkm_empty_carries_rows_point_source * S ((S (mkm_index_empty_carries_rows)) * c) + (mkm_value_empty_carries_rows_point))) /\ ((((exists fs_h_mkm_empty_carries_rows_point_partial. fs_h_mkm_empty_carries_rows_point_partial + S (mkm_partial_empty_carries_rows_point) = S ((S (mkm_index_empty_carries_rows)) * mkm_sc_empty_carries)) /\ exists fs_q_mkm_empty_carries_rows_point_partial. mkm_sb_empty_carries = fs_q_mkm_empty_carries_rows_point_partial * S ((S (mkm_index_empty_carries_rows)) * mkm_sc_empty_carries) + (mkm_partial_empty_carries_rows_point))) /\ ((((exists fs_h_mkm_empty_carries_rows_point_stored. fs_h_mkm_empty_carries_rows_point_stored + S (mkm_count_empty_carries_rows_point) = S ((S (mkm_index_empty_carries_rows)) * mkm_cc_empty_carries)) /\ exists fs_q_mkm_empty_carries_rows_point_stored. mkm_cb_empty_carries = fs_q_mkm_empty_carries_rows_point_stored * S ((S (mkm_index_empty_carries_rows)) * mkm_cc_empty_carries) + (mkm_count_empty_carries_rows_point))) /\ (exists mkm_lb_empty_carries_rows_point_binary mkm_lc_empty_carries_rows_point_binary mkm_rb_empty_carries_rows_point_binary mkm_rc_empty_carries_rows_point_binary mkm_tb_empty_carries_rows_point_binary mkm_tc_empty_carries_rows_point_binary mkm_cb_empty_carries_rows_point_binary mkm_cc_empty_carries_rows_point_binary. (forall bls_index_mkm_empty_carries_rows_point_binary_left. (exists bls_gap_mkm_empty_carries_rows_point_binary_left_bound. bls_gap_mkm_empty_carries_rows_point_binary_left_bound + S (bls_index_mkm_empty_carries_rows_point_binary_left) = (mkm_partial_empty_carries_rows_point + mkm_value_empty_carries_rows_point)) -> exists bls_power_mkm_empty_carries_rows_point_binary_left bls_quotient_mkm_empty_carries_rows_point_binary_left bls_remainder_mkm_empty_carries_rows_point_binary_left. ((exists bpvi_b_bls_mkm_empty_carries_rows_point_binary_left_power bpvi_c_bls_mkm_empty_carries_rows_point_binary_left_power. ((forall bpvi_i_bls_mkm_empty_carries_rows_point_binary_left_power. (exists bpvi_repeat_gap_bls_mkm_empty_carries_rows_point_binary_left_power. bpvi_repeat_gap_bls_mkm_empty_carries_rows_point_binary_left_power + S bpvi_i_bls_mkm_empty_carries_rows_point_binary_left_power = S bls_index_mkm_empty_carries_rows_point_binary_left) -> (((exists bpvi_h_bls_mkm_empty_carries_rows_point_binary_left_power_repeat. bpvi_h_bls_mkm_empty_carries_rows_point_binary_left_power_repeat + S (p) = S ((S (bpvi_i_bls_mkm_empty_carries_rows_point_binary_left_power)) * bpvi_c_bls_mkm_empty_carries_rows_point_binary_left_power)) /\ exists bpvi_q_bls_mkm_empty_carries_rows_point_binary_left_power_repeat. bpvi_b_bls_mkm_empty_carries_rows_point_binary_left_power = bpvi_q_bls_mkm_empty_carries_rows_point_binary_left_power_repeat * S ((S (bpvi_i_bls_mkm_empty_carries_rows_point_binary_left_power)) * bpvi_c_bls_mkm_empty_carries_rows_point_binary_left_power) + (p)))) /\ (exists bpvi_u_bls_mkm_empty_carries_rows_point_binary_left_power bpvi_v_bls_mkm_empty_carries_rows_point_binary_left_power. ((((exists bpvi_h_bls_mkm_empty_carries_rows_point_binary_left_power_start. bpvi_h_bls_mkm_empty_carries_rows_point_binary_left_power_start + S (1) = S ((S (0)) * bpvi_v_bls_mkm_empty_carries_rows_point_binary_left_power)) /\ exists bpvi_q_bls_mkm_empty_carries_rows_point_binary_left_power_start. bpvi_u_bls_mkm_empty_carries_rows_point_binary_left_power = bpvi_q_bls_mkm_empty_carries_rows_point_binary_left_power_start * S ((S (0)) * bpvi_v_bls_mkm_empty_carries_rows_point_binary_left_power) + (1))) /\ ((((exists bpvi_h_bls_mkm_empty_carries_rows_point_binary_left_power_terminal. bpvi_h_bls_mkm_empty_carries_rows_point_binary_left_power_terminal + S (bls_power_mkm_empty_carries_rows_point_binary_left) = S ((S (S bls_index_mkm_empty_carries_rows_point_binary_left)) * bpvi_v_bls_mkm_empty_carries_rows_point_binary_left_power)) /\ exists bpvi_q_bls_mkm_empty_carries_rows_point_binary_left_power_terminal. bpvi_u_bls_mkm_empty_carries_rows_point_binary_left_power = bpvi_q_bls_mkm_empty_carries_rows_point_binary_left_power_terminal * S ((S (S bls_index_mkm_empty_carries_rows_point_binary_left)) * bpvi_v_bls_mkm_empty_carries_rows_point_binary_left_power) + (bls_power_mkm_empty_carries_rows_point_binary_left))) /\ forall bpvi_j_bls_mkm_empty_carries_rows_point_binary_left_power. (exists bpvi_product_gap_bls_mkm_empty_carries_rows_point_binary_left_power. bpvi_product_gap_bls_mkm_empty_carries_rows_point_binary_left_power + S bpvi_j_bls_mkm_empty_carries_rows_point_binary_left_power = S bls_index_mkm_empty_carries_rows_point_binary_left) -> exists bpvi_factor_bls_mkm_empty_carries_rows_point_binary_left_power bpvi_partial_bls_mkm_empty_carries_rows_point_binary_left_power bpvi_successor_bls_mkm_empty_carries_rows_point_binary_left_power. ((((exists bpvi_h_bls_mkm_empty_carries_rows_point_binary_left_power_factor. bpvi_h_bls_mkm_empty_carries_rows_point_binary_left_power_factor + S (bpvi_factor_bls_mkm_empty_carries_rows_point_binary_left_power) = S ((S (bpvi_j_bls_mkm_empty_carries_rows_point_binary_left_power)) * bpvi_c_bls_mkm_empty_carries_rows_point_binary_left_power)) /\ exists bpvi_q_bls_mkm_empty_carries_rows_point_binary_left_power_factor. bpvi_b_bls_mkm_empty_carries_rows_point_binary_left_power = bpvi_q_bls_mkm_empty_carries_rows_point_binary_left_power_factor * S ((S (bpvi_j_bls_mkm_empty_carries_rows_point_binary_left_power)) * bpvi_c_bls_mkm_empty_carries_rows_point_binary_left_power) + (bpvi_factor_bls_mkm_empty_carries_rows_point_binary_left_power))) /\ ((((exists bpvi_h_bls_mkm_empty_carries_rows_point_binary_left_power_partial. bpvi_h_bls_mkm_empty_carries_rows_point_binary_left_power_partial + S (bpvi_partial_bls_mkm_empty_carries_rows_point_binary_left_power) = S ((S (bpvi_j_bls_mkm_empty_carries_rows_point_binary_left_power)) * bpvi_v_bls_mkm_empty_carries_rows_point_binary_left_power)) /\ exists bpvi_q_bls_mkm_empty_carries_rows_point_binary_left_power_partial. bpvi_u_bls_mkm_empty_carries_rows_point_binary_left_power = bpvi_q_bls_mkm_empty_carries_rows_point_binary_left_power_partial * S ((S (bpvi_j_bls_mkm_empty_carries_rows_point_binary_left_power)) * bpvi_v_bls_mkm_empty_carries_rows_point_binary_left_power) + (bpvi_partial_bls_mkm_empty_carries_rows_point_binary_left_power))) /\ ((((exists bpvi_h_bls_mkm_empty_carries_rows_point_binary_left_power_successor. bpvi_h_bls_mkm_empty_carries_rows_point_binary_left_power_successor + S (bpvi_successor_bls_mkm_empty_carries_rows_point_binary_left_power) = S ((S (S bpvi_j_bls_mkm_empty_carries_rows_point_binary_left_power)) * bpvi_v_bls_mkm_empty_carries_rows_point_binary_left_power)) /\ exists bpvi_q_bls_mkm_empty_carries_rows_point_binary_left_power_successor. bpvi_u_bls_mkm_empty_carries_rows_point_binary_left_power = bpvi_q_bls_mkm_empty_carries_rows_point_binary_left_power_successor * S ((S (S bpvi_j_bls_mkm_empty_carries_rows_point_binary_left_power)) * bpvi_v_bls_mkm_empty_carries_rows_point_binary_left_power) + (bpvi_successor_bls_mkm_empty_carries_rows_point_binary_left_power))) /\ bpvi_successor_bls_mkm_empty_carries_rows_point_binary_left_power = bpvi_partial_bls_mkm_empty_carries_rows_point_binary_left_power * bpvi_factor_bls_mkm_empty_carries_rows_point_binary_left_power)))))))) /\ ((((exists ff_h_bls_mkm_empty_carries_rows_point_binary_left_quotient_entry. ff_h_bls_mkm_empty_carries_rows_point_binary_left_quotient_entry + S (bls_quotient_mkm_empty_carries_rows_point_binary_left) = S ((S (bls_index_mkm_empty_carries_rows_point_binary_left)) * mkm_lc_empty_carries_rows_point_binary)) /\ exists ff_q_bls_mkm_empty_carries_rows_point_binary_left_quotient_entry. mkm_lb_empty_carries_rows_point_binary = ff_q_bls_mkm_empty_carries_rows_point_binary_left_quotient_entry * S ((S (bls_index_mkm_empty_carries_rows_point_binary_left)) * mkm_lc_empty_carries_rows_point_binary) + (bls_quotient_mkm_empty_carries_rows_point_binary_left))) /\ ((mkm_partial_empty_carries_rows_point = bls_power_mkm_empty_carries_rows_point_binary_left * bls_quotient_mkm_empty_carries_rows_point_binary_left + bls_remainder_mkm_empty_carries_rows_point_binary_left /\ exists bls_remainder_gap_mkm_empty_carries_rows_point_binary_left_division. bls_remainder_gap_mkm_empty_carries_rows_point_binary_left_division + S (bls_remainder_mkm_empty_carries_rows_point_binary_left) = bls_power_mkm_empty_carries_rows_point_binary_left))))) /\ ((forall bls_index_mkm_empty_carries_rows_point_binary_right. (exists bls_gap_mkm_empty_carries_rows_point_binary_right_bound. bls_gap_mkm_empty_carries_rows_point_binary_right_bound + S (bls_index_mkm_empty_carries_rows_point_binary_right) = (mkm_partial_empty_carries_rows_point + mkm_value_empty_carries_rows_point)) -> exists bls_power_mkm_empty_carries_rows_point_binary_right bls_quotient_mkm_empty_carries_rows_point_binary_right bls_remainder_mkm_empty_carries_rows_point_binary_right. ((exists bpvi_b_bls_mkm_empty_carries_rows_point_binary_right_power bpvi_c_bls_mkm_empty_carries_rows_point_binary_right_power. ((forall bpvi_i_bls_mkm_empty_carries_rows_point_binary_right_power. (exists bpvi_repeat_gap_bls_mkm_empty_carries_rows_point_binary_right_power. bpvi_repeat_gap_bls_mkm_empty_carries_rows_point_binary_right_power + S bpvi_i_bls_mkm_empty_carries_rows_point_binary_right_power = S bls_index_mkm_empty_carries_rows_point_binary_right) -> (((exists bpvi_h_bls_mkm_empty_carries_rows_point_binary_right_power_repeat. bpvi_h_bls_mkm_empty_carries_rows_point_binary_right_power_repeat + S (p) = S ((S (bpvi_i_bls_mkm_empty_carries_rows_point_binary_right_power)) * bpvi_c_bls_mkm_empty_carries_rows_point_binary_right_power)) /\ exists bpvi_q_bls_mkm_empty_carries_rows_point_binary_right_power_repeat. bpvi_b_bls_mkm_empty_carries_rows_point_binary_right_power = bpvi_q_bls_mkm_empty_carries_rows_point_binary_right_power_repeat * S ((S (bpvi_i_bls_mkm_empty_carries_rows_point_binary_right_power)) * bpvi_c_bls_mkm_empty_carries_rows_point_binary_right_power) + (p)))) /\ (exists bpvi_u_bls_mkm_empty_carries_rows_point_binary_right_power bpvi_v_bls_mkm_empty_carries_rows_point_binary_right_power. ((((exists bpvi_h_bls_mkm_empty_carries_rows_point_binary_right_power_start. bpvi_h_bls_mkm_empty_carries_rows_point_binary_right_power_start + S (1) = S ((S (0)) * bpvi_v_bls_mkm_empty_carries_rows_point_binary_right_power)) /\ exists bpvi_q_bls_mkm_empty_carries_rows_point_binary_right_power_start. bpvi_u_bls_mkm_empty_carries_rows_point_binary_right_power = bpvi_q_bls_mkm_empty_carries_rows_point_binary_right_power_start * S ((S (0)) * bpvi_v_bls_mkm_empty_carries_rows_point_binary_right_power) + (1))) /\ ((((exists bpvi_h_bls_mkm_empty_carries_rows_point_binary_right_power_terminal. bpvi_h_bls_mkm_empty_carries_rows_point_binary_right_power_terminal + S (bls_power_mkm_empty_carries_rows_point_binary_right) = S ((S (S bls_index_mkm_empty_carries_rows_point_binary_right)) * bpvi_v_bls_mkm_empty_carries_rows_point_binary_right_power)) /\ exists bpvi_q_bls_mkm_empty_carries_rows_point_binary_right_power_terminal. bpvi_u_bls_mkm_empty_carries_rows_point_binary_right_power = bpvi_q_bls_mkm_empty_carries_rows_point_binary_right_power_terminal * S ((S (S bls_index_mkm_empty_carries_rows_point_binary_right)) * bpvi_v_bls_mkm_empty_carries_rows_point_binary_right_power) + (bls_power_mkm_empty_carries_rows_point_binary_right))) /\ forall bpvi_j_bls_mkm_empty_carries_rows_point_binary_right_power. (exists bpvi_product_gap_bls_mkm_empty_carries_rows_point_binary_right_power. bpvi_product_gap_bls_mkm_empty_carries_rows_point_binary_right_power + S bpvi_j_bls_mkm_empty_carries_rows_point_binary_right_power = S bls_index_mkm_empty_carries_rows_point_binary_right) -> exists bpvi_factor_bls_mkm_empty_carries_rows_point_binary_right_power bpvi_partial_bls_mkm_empty_carries_rows_point_binary_right_power bpvi_successor_bls_mkm_empty_carries_rows_point_binary_right_power. ((((exists bpvi_h_bls_mkm_empty_carries_rows_point_binary_right_power_factor. bpvi_h_bls_mkm_empty_carries_rows_point_binary_right_power_factor + S (bpvi_factor_bls_mkm_empty_carries_rows_point_binary_right_power) = S ((S (bpvi_j_bls_mkm_empty_carries_rows_point_binary_right_power)) * bpvi_c_bls_mkm_empty_carries_rows_point_binary_right_power)) /\ exists bpvi_q_bls_mkm_empty_carries_rows_point_binary_right_power_factor. bpvi_b_bls_mkm_empty_carries_rows_point_binary_right_power = bpvi_q_bls_mkm_empty_carries_rows_point_binary_right_power_factor * S ((S (bpvi_j_bls_mkm_empty_carries_rows_point_binary_right_power)) * bpvi_c_bls_mkm_empty_carries_rows_point_binary_right_power) + (bpvi_factor_bls_mkm_empty_carries_rows_point_binary_right_power))) /\ ((((exists bpvi_h_bls_mkm_empty_carries_rows_point_binary_right_power_partial. bpvi_h_bls_mkm_empty_carries_rows_point_binary_right_power_partial + S (bpvi_partial_bls_mkm_empty_carries_rows_point_binary_right_power) = S ((S (bpvi_j_bls_mkm_empty_carries_rows_point_binary_right_power)) * bpvi_v_bls_mkm_empty_carries_rows_point_binary_right_power)) /\ exists bpvi_q_bls_mkm_empty_carries_rows_point_binary_right_power_partial. bpvi_u_bls_mkm_empty_carries_rows_point_binary_right_power = bpvi_q_bls_mkm_empty_carries_rows_point_binary_right_power_partial * S ((S (bpvi_j_bls_mkm_empty_carries_rows_point_binary_right_power)) * bpvi_v_bls_mkm_empty_carries_rows_point_binary_right_power) + (bpvi_partial_bls_mkm_empty_carries_rows_point_binary_right_power))) /\ ((((exists bpvi_h_bls_mkm_empty_carries_rows_point_binary_right_power_successor. bpvi_h_bls_mkm_empty_carries_rows_point_binary_right_power_successor + S (bpvi_successor_bls_mkm_empty_carries_rows_point_binary_right_power) = S ((S (S bpvi_j_bls_mkm_empty_carries_rows_point_binary_right_power)) * bpvi_v_bls_mkm_empty_carries_rows_point_binary_right_power)) /\ exists bpvi_q_bls_mkm_empty_carries_rows_point_binary_right_power_successor. bpvi_u_bls_mkm_empty_carries_rows_point_binary_right_power = bpvi_q_bls_mkm_empty_carries_rows_point_binary_right_power_successor * S ((S (S bpvi_j_bls_mkm_empty_carries_rows_point_binary_right_power)) * bpvi_v_bls_mkm_empty_carries_rows_point_binary_right_power) + (bpvi_successor_bls_mkm_empty_carries_rows_point_binary_right_power))) /\ bpvi_successor_bls_mkm_empty_carries_rows_point_binary_right_power = bpvi_partial_bls_mkm_empty_carries_rows_point_binary_right_power * bpvi_factor_bls_mkm_empty_carries_rows_point_binary_right_power)))))))) /\ ((((exists ff_h_bls_mkm_empty_carries_rows_point_binary_right_quotient_entry. ff_h_bls_mkm_empty_carries_rows_point_binary_right_quotient_entry + S (bls_quotient_mkm_empty_carries_rows_point_binary_right) = S ((S (bls_index_mkm_empty_carries_rows_point_binary_right)) * mkm_rc_empty_carries_rows_point_binary)) /\ exists ff_q_bls_mkm_empty_carries_rows_point_binary_right_quotient_entry. mkm_rb_empty_carries_rows_point_binary = ff_q_bls_mkm_empty_carries_rows_point_binary_right_quotient_entry * S ((S (bls_index_mkm_empty_carries_rows_point_binary_right)) * mkm_rc_empty_carries_rows_point_binary) + (bls_quotient_mkm_empty_carries_rows_point_binary_right))) /\ ((mkm_value_empty_carries_rows_point = bls_power_mkm_empty_carries_rows_point_binary_right * bls_quotient_mkm_empty_carries_rows_point_binary_right + bls_remainder_mkm_empty_carries_rows_point_binary_right /\ exists bls_remainder_gap_mkm_empty_carries_rows_point_binary_right_division. bls_remainder_gap_mkm_empty_carries_rows_point_binary_right_division + S (bls_remainder_mkm_empty_carries_rows_point_binary_right) = bls_power_mkm_empty_carries_rows_point_binary_right))))) /\ ((forall bls_index_mkm_empty_carries_rows_point_binary_total. (exists bls_gap_mkm_empty_carries_rows_point_binary_total_bound. bls_gap_mkm_empty_carries_rows_point_binary_total_bound + S (bls_index_mkm_empty_carries_rows_point_binary_total) = (mkm_partial_empty_carries_rows_point + mkm_value_empty_carries_rows_point)) -> exists bls_power_mkm_empty_carries_rows_point_binary_total bls_quotient_mkm_empty_carries_rows_point_binary_total bls_remainder_mkm_empty_carries_rows_point_binary_total. ((exists bpvi_b_bls_mkm_empty_carries_rows_point_binary_total_power bpvi_c_bls_mkm_empty_carries_rows_point_binary_total_power. ((forall bpvi_i_bls_mkm_empty_carries_rows_point_binary_total_power. (exists bpvi_repeat_gap_bls_mkm_empty_carries_rows_point_binary_total_power. bpvi_repeat_gap_bls_mkm_empty_carries_rows_point_binary_total_power + S bpvi_i_bls_mkm_empty_carries_rows_point_binary_total_power = S bls_index_mkm_empty_carries_rows_point_binary_total) -> (((exists bpvi_h_bls_mkm_empty_carries_rows_point_binary_total_power_repeat. bpvi_h_bls_mkm_empty_carries_rows_point_binary_total_power_repeat + S (p) = S ((S (bpvi_i_bls_mkm_empty_carries_rows_point_binary_total_power)) * bpvi_c_bls_mkm_empty_carries_rows_point_binary_total_power)) /\ exists bpvi_q_bls_mkm_empty_carries_rows_point_binary_total_power_repeat. bpvi_b_bls_mkm_empty_carries_rows_point_binary_total_power = bpvi_q_bls_mkm_empty_carries_rows_point_binary_total_power_repeat * S ((S (bpvi_i_bls_mkm_empty_carries_rows_point_binary_total_power)) * bpvi_c_bls_mkm_empty_carries_rows_point_binary_total_power) + (p)))) /\ (exists bpvi_u_bls_mkm_empty_carries_rows_point_binary_total_power bpvi_v_bls_mkm_empty_carries_rows_point_binary_total_power. ((((exists bpvi_h_bls_mkm_empty_carries_rows_point_binary_total_power_start. bpvi_h_bls_mkm_empty_carries_rows_point_binary_total_power_start + S (1) = S ((S (0)) * bpvi_v_bls_mkm_empty_carries_rows_point_binary_total_power)) /\ exists bpvi_q_bls_mkm_empty_carries_rows_point_binary_total_power_start. bpvi_u_bls_mkm_empty_carries_rows_point_binary_total_power = bpvi_q_bls_mkm_empty_carries_rows_point_binary_total_power_start * S ((S (0)) * bpvi_v_bls_mkm_empty_carries_rows_point_binary_total_power) + (1))) /\ ((((exists bpvi_h_bls_mkm_empty_carries_rows_point_binary_total_power_terminal. bpvi_h_bls_mkm_empty_carries_rows_point_binary_total_power_terminal + S (bls_power_mkm_empty_carries_rows_point_binary_total) = S ((S (S bls_index_mkm_empty_carries_rows_point_binary_total)) * bpvi_v_bls_mkm_empty_carries_rows_point_binary_total_power)) /\ exists bpvi_q_bls_mkm_empty_carries_rows_point_binary_total_power_terminal. bpvi_u_bls_mkm_empty_carries_rows_point_binary_total_power = bpvi_q_bls_mkm_empty_carries_rows_point_binary_total_power_terminal * S ((S (S bls_index_mkm_empty_carries_rows_point_binary_total)) * bpvi_v_bls_mkm_empty_carries_rows_point_binary_total_power) + (bls_power_mkm_empty_carries_rows_point_binary_total))) /\ forall bpvi_j_bls_mkm_empty_carries_rows_point_binary_total_power. (exists bpvi_product_gap_bls_mkm_empty_carries_rows_point_binary_total_power. bpvi_product_gap_bls_mkm_empty_carries_rows_point_binary_total_power + S bpvi_j_bls_mkm_empty_carries_rows_point_binary_total_power = S bls_index_mkm_empty_carries_rows_point_binary_total) -> exists bpvi_factor_bls_mkm_empty_carries_rows_point_binary_total_power bpvi_partial_bls_mkm_empty_carries_rows_point_binary_total_power bpvi_successor_bls_mkm_empty_carries_rows_point_binary_total_power. ((((exists bpvi_h_bls_mkm_empty_carries_rows_point_binary_total_power_factor. bpvi_h_bls_mkm_empty_carries_rows_point_binary_total_power_factor + S (bpvi_factor_bls_mkm_empty_carries_rows_point_binary_total_power) = S ((S (bpvi_j_bls_mkm_empty_carries_rows_point_binary_total_power)) * bpvi_c_bls_mkm_empty_carries_rows_point_binary_total_power)) /\ exists bpvi_q_bls_mkm_empty_carries_rows_point_binary_total_power_factor. bpvi_b_bls_mkm_empty_carries_rows_point_binary_total_power = bpvi_q_bls_mkm_empty_carries_rows_point_binary_total_power_factor * S ((S (bpvi_j_bls_mkm_empty_carries_rows_point_binary_total_power)) * bpvi_c_bls_mkm_empty_carries_rows_point_binary_total_power) + (bpvi_factor_bls_mkm_empty_carries_rows_point_binary_total_power))) /\ ((((exists bpvi_h_bls_mkm_empty_carries_rows_point_binary_total_power_partial. bpvi_h_bls_mkm_empty_carries_rows_point_binary_total_power_partial + S (bpvi_partial_bls_mkm_empty_carries_rows_point_binary_total_power) = S ((S (bpvi_j_bls_mkm_empty_carries_rows_point_binary_total_power)) * bpvi_v_bls_mkm_empty_carries_rows_point_binary_total_power)) /\ exists bpvi_q_bls_mkm_empty_carries_rows_point_binary_total_power_partial. bpvi_u_bls_mkm_empty_carries_rows_point_binary_total_power = bpvi_q_bls_mkm_empty_carries_rows_point_binary_total_power_partial * S ((S (bpvi_j_bls_mkm_empty_carries_rows_point_binary_total_power)) * bpvi_v_bls_mkm_empty_carries_rows_point_binary_total_power) + (bpvi_partial_bls_mkm_empty_carries_rows_point_binary_total_power))) /\ ((((exists bpvi_h_bls_mkm_empty_carries_rows_point_binary_total_power_successor. bpvi_h_bls_mkm_empty_carries_rows_point_binary_total_power_successor + S (bpvi_successor_bls_mkm_empty_carries_rows_point_binary_total_power) = S ((S (S bpvi_j_bls_mkm_empty_carries_rows_point_binary_total_power)) * bpvi_v_bls_mkm_empty_carries_rows_point_binary_total_power)) /\ exists bpvi_q_bls_mkm_empty_carries_rows_point_binary_total_power_successor. bpvi_u_bls_mkm_empty_carries_rows_point_binary_total_power = bpvi_q_bls_mkm_empty_carries_rows_point_binary_total_power_successor * S ((S (S bpvi_j_bls_mkm_empty_carries_rows_point_binary_total_power)) * bpvi_v_bls_mkm_empty_carries_rows_point_binary_total_power) + (bpvi_successor_bls_mkm_empty_carries_rows_point_binary_total_power))) /\ bpvi_successor_bls_mkm_empty_carries_rows_point_binary_total_power = bpvi_partial_bls_mkm_empty_carries_rows_point_binary_total_power * bpvi_factor_bls_mkm_empty_carries_rows_point_binary_total_power)))))))) /\ ((((exists ff_h_bls_mkm_empty_carries_rows_point_binary_total_quotient_entry. ff_h_bls_mkm_empty_carries_rows_point_binary_total_quotient_entry + S (bls_quotient_mkm_empty_carries_rows_point_binary_total) = S ((S (bls_index_mkm_empty_carries_rows_point_binary_total)) * mkm_tc_empty_carries_rows_point_binary)) /\ exists ff_q_bls_mkm_empty_carries_rows_point_binary_total_quotient_entry. mkm_tb_empty_carries_rows_point_binary = ff_q_bls_mkm_empty_carries_rows_point_binary_total_quotient_entry * S ((S (bls_index_mkm_empty_carries_rows_point_binary_total)) * mkm_tc_empty_carries_rows_point_binary) + (bls_quotient_mkm_empty_carries_rows_point_binary_total))) /\ ((mkm_partial_empty_carries_rows_point + mkm_value_empty_carries_rows_point = bls_power_mkm_empty_carries_rows_point_binary_total * bls_quotient_mkm_empty_carries_rows_point_binary_total + bls_remainder_mkm_empty_carries_rows_point_binary_total /\ exists bls_remainder_gap_mkm_empty_carries_rows_point_binary_total_division. bls_remainder_gap_mkm_empty_carries_rows_point_binary_total_division + S (bls_remainder_mkm_empty_carries_rows_point_binary_total) = bls_power_mkm_empty_carries_rows_point_binary_total))))) /\ ((forall kmc_index_mkm_empty_carries_rows_point_binary_carries. (exists bcf_lt_gap_mkm_empty_carries_rows_point_binary_carries_bound. bcf_lt_gap_mkm_empty_carries_rows_point_binary_carries_bound + S (kmc_index_mkm_empty_carries_rows_point_binary_carries) = mkm_partial_empty_carries_rows_point + mkm_value_empty_carries_rows_point) -> exists kmc_left_mkm_empty_carries_rows_point_binary_carries kmc_right_mkm_empty_carries_rows_point_binary_carries kmc_total_mkm_empty_carries_rows_point_binary_carries kmc_bit_mkm_empty_carries_rows_point_binary_carries. (((exists fs_h_mkm_empty_carries_rows_point_binary_carries_left. fs_h_mkm_empty_carries_rows_point_binary_carries_left + S (kmc_left_mkm_empty_carries_rows_point_binary_carries) = S ((S (kmc_index_mkm_empty_carries_rows_point_binary_carries)) * mkm_lc_empty_carries_rows_point_binary)) /\ exists fs_q_mkm_empty_carries_rows_point_binary_carries_left. mkm_lb_empty_carries_rows_point_binary = fs_q_mkm_empty_carries_rows_point_binary_carries_left * S ((S (kmc_index_mkm_empty_carries_rows_point_binary_carries)) * mkm_lc_empty_carries_rows_point_binary) + (kmc_left_mkm_empty_carries_rows_point_binary_carries))) /\ ((((exists fs_h_mkm_empty_carries_rows_point_binary_carries_right. fs_h_mkm_empty_carries_rows_point_binary_carries_right + S (kmc_right_mkm_empty_carries_rows_point_binary_carries) = S ((S (kmc_index_mkm_empty_carries_rows_point_binary_carries)) * mkm_rc_empty_carries_rows_point_binary)) /\ exists fs_q_mkm_empty_carries_rows_point_binary_carries_right. mkm_rb_empty_carries_rows_point_binary = fs_q_mkm_empty_carries_rows_point_binary_carries_right * S ((S (kmc_index_mkm_empty_carries_rows_point_binary_carries)) * mkm_rc_empty_carries_rows_point_binary) + (kmc_right_mkm_empty_carries_rows_point_binary_carries))) /\ ((((exists fs_h_mkm_empty_carries_rows_point_binary_carries_total. fs_h_mkm_empty_carries_rows_point_binary_carries_total + S (kmc_total_mkm_empty_carries_rows_point_binary_carries) = S ((S (kmc_index_mkm_empty_carries_rows_point_binary_carries)) * mkm_tc_empty_carries_rows_point_binary)) /\ exists fs_q_mkm_empty_carries_rows_point_binary_carries_total. mkm_tb_empty_carries_rows_point_binary = fs_q_mkm_empty_carries_rows_point_binary_carries_total * S ((S (kmc_index_mkm_empty_carries_rows_point_binary_carries)) * mkm_tc_empty_carries_rows_point_binary) + (kmc_total_mkm_empty_carries_rows_point_binary_carries))) /\ ((((exists fs_h_mkm_empty_carries_rows_point_binary_carries_bit. fs_h_mkm_empty_carries_rows_point_binary_carries_bit + S (kmc_bit_mkm_empty_carries_rows_point_binary_carries) = S ((S (kmc_index_mkm_empty_carries_rows_point_binary_carries)) * mkm_cc_empty_carries_rows_point_binary)) /\ exists fs_q_mkm_empty_carries_rows_point_binary_carries_bit. mkm_cb_empty_carries_rows_point_binary = fs_q_mkm_empty_carries_rows_point_binary_carries_bit * S ((S (kmc_index_mkm_empty_carries_rows_point_binary_carries)) * mkm_cc_empty_carries_rows_point_binary) + (kmc_bit_mkm_empty_carries_rows_point_binary_carries))) /\ (((kmc_bit_mkm_empty_carries_rows_point_binary_carries = 0 /\ kmc_total_mkm_empty_carries_rows_point_binary_carries = kmc_left_mkm_empty_carries_rows_point_binary_carries + kmc_right_mkm_empty_carries_rows_point_binary_carries) \/ (kmc_bit_mkm_empty_carries_rows_point_binary_carries = 1 /\ kmc_total_mkm_empty_carries_rows_point_binary_carries = S (kmc_left_mkm_empty_carries_rows_point_binary_carries + kmc_right_mkm_empty_carries_rows_point_binary_carries)))))))) /\ (((exists ff_u_mkm_empty_carries_rows_point_binary_count_sum ff_v_mkm_empty_carries_rows_point_binary_count_sum. ((((exists ff_h_mkm_empty_carries_rows_point_binary_count_sum_start. ff_h_mkm_empty_carries_rows_point_binary_count_sum_start + S (0) = S ((S (0)) * ff_v_mkm_empty_carries_rows_point_binary_count_sum)) /\ exists ff_q_mkm_empty_carries_rows_point_binary_count_sum_start. ff_u_mkm_empty_carries_rows_point_binary_count_sum = ff_q_mkm_empty_carries_rows_point_binary_count_sum_start * S ((S (0)) * ff_v_mkm_empty_carries_rows_point_binary_count_sum) + (0))) /\ ((((exists ff_h_mkm_empty_carries_rows_point_binary_count_sum_terminal. ff_h_mkm_empty_carries_rows_point_binary_count_sum_terminal + S ((mkm_count_empty_carries_rows_point)) = S ((S ((mkm_partial_empty_carries_rows_point + mkm_value_empty_carries_rows_point))) * ff_v_mkm_empty_carries_rows_point_binary_count_sum)) /\ exists ff_q_mkm_empty_carries_rows_point_binary_count_sum_terminal. ff_u_mkm_empty_carries_rows_point_binary_count_sum = ff_q_mkm_empty_carries_rows_point_binary_count_sum_terminal * S ((S ((mkm_partial_empty_carries_rows_point + mkm_value_empty_carries_rows_point))) * ff_v_mkm_empty_carries_rows_point_binary_count_sum) + ((mkm_count_empty_carries_rows_point)))) /\ forall ff_i_mkm_empty_carries_rows_point_binary_count_sum. (exists ff_lt_mkm_empty_carries_rows_point_binary_count_sum_bound. ff_lt_mkm_empty_carries_rows_point_binary_count_sum_bound + S ff_i_mkm_empty_carries_rows_point_binary_count_sum = (mkm_partial_empty_carries_rows_point + mkm_value_empty_carries_rows_point)) -> exists ff_a_mkm_empty_carries_rows_point_binary_count_sum ff_r_mkm_empty_carries_rows_point_binary_count_sum ff_s_mkm_empty_carries_rows_point_binary_count_sum. ((((exists ff_h_mkm_empty_carries_rows_point_binary_count_sum_summand. ff_h_mkm_empty_carries_rows_point_binary_count_sum_summand + S (ff_a_mkm_empty_carries_rows_point_binary_count_sum) = S ((S (ff_i_mkm_empty_carries_rows_point_binary_count_sum)) * mkm_cc_empty_carries_rows_point_binary)) /\ exists ff_q_mkm_empty_carries_rows_point_binary_count_sum_summand. mkm_cb_empty_carries_rows_point_binary = ff_q_mkm_empty_carries_rows_point_binary_count_sum_summand * S ((S (ff_i_mkm_empty_carries_rows_point_binary_count_sum)) * mkm_cc_empty_carries_rows_point_binary) + (ff_a_mkm_empty_carries_rows_point_binary_count_sum))) /\ ((((exists ff_h_mkm_empty_carries_rows_point_binary_count_sum_partial. ff_h_mkm_empty_carries_rows_point_binary_count_sum_partial + S (ff_r_mkm_empty_carries_rows_point_binary_count_sum) = S ((S (ff_i_mkm_empty_carries_rows_point_binary_count_sum)) * ff_v_mkm_empty_carries_rows_point_binary_count_sum)) /\ exists ff_q_mkm_empty_carries_rows_point_binary_count_sum_partial. ff_u_mkm_empty_carries_rows_point_binary_count_sum = ff_q_mkm_empty_carries_rows_point_binary_count_sum_partial * S ((S (ff_i_mkm_empty_carries_rows_point_binary_count_sum)) * ff_v_mkm_empty_carries_rows_point_binary_count_sum) + (ff_r_mkm_empty_carries_rows_point_binary_count_sum))) /\ ((((exists ff_h_mkm_empty_carries_rows_point_binary_count_sum_successor. ff_h_mkm_empty_carries_rows_point_binary_count_sum_successor + S (ff_s_mkm_empty_carries_rows_point_binary_count_sum) = S ((S (S ff_i_mkm_empty_carries_rows_point_binary_count_sum)) * ff_v_mkm_empty_carries_rows_point_binary_count_sum)) /\ exists ff_q_mkm_empty_carries_rows_point_binary_count_sum_successor. ff_u_mkm_empty_carries_rows_point_binary_count_sum = ff_q_mkm_empty_carries_rows_point_binary_count_sum_successor * S ((S (S ff_i_mkm_empty_carries_rows_point_binary_count_sum)) * ff_v_mkm_empty_carries_rows_point_binary_count_sum) + (ff_s_mkm_empty_carries_rows_point_binary_count_sum))) /\ ff_s_mkm_empty_carries_rows_point_binary_count_sum = ff_r_mkm_empty_carries_rows_point_binary_count_sum + ff_a_mkm_empty_carries_rows_point_binary_count_sum)))))) /\ (forall ff_i_mkm_empty_carries_rows_point_binary_count_bits. (exists ff_lt_mkm_empty_carries_rows_point_binary_count_bits_bound. ff_lt_mkm_empty_carries_rows_point_binary_count_bits_bound + S ff_i_mkm_empty_carries_rows_point_binary_count_bits = (mkm_partial_empty_carries_rows_point + mkm_value_empty_carries_rows_point)) -> exists ff_bit_mkm_empty_carries_rows_point_binary_count_bits. ((((exists ff_h_mkm_empty_carries_rows_point_binary_count_bits_decoded. ff_h_mkm_empty_carries_rows_point_binary_count_bits_decoded + S (ff_bit_mkm_empty_carries_rows_point_binary_count_bits) = S ((S (ff_i_mkm_empty_carries_rows_point_binary_count_bits)) * mkm_cc_empty_carries_rows_point_binary)) /\ exists ff_q_mkm_empty_carries_rows_point_binary_count_bits_decoded. mkm_cb_empty_carries_rows_point_binary = ff_q_mkm_empty_carries_rows_point_binary_count_bits_decoded * S ((S (ff_i_mkm_empty_carries_rows_point_binary_count_bits)) * mkm_cc_empty_carries_rows_point_binary) + (ff_bit_mkm_empty_carries_rows_point_binary_count_bits))) /\ (ff_bit_mkm_empty_carries_rows_point_binary_count_bits = 0 \/ ff_bit_mkm_empty_carries_rows_point_binary_count_bits = 1))))))))))))) /\ (exists fs_u_mkm_empty_carries_count fs_v_mkm_empty_carries_count. ((((exists fs_h_mkm_empty_carries_count_body_start. fs_h_mkm_empty_carries_count_body_start + S (0) = S ((S (0)) * fs_v_mkm_empty_carries_count)) /\ exists fs_q_mkm_empty_carries_count_body_start. fs_u_mkm_empty_carries_count = fs_q_mkm_empty_carries_count_body_start * S ((S (0)) * fs_v_mkm_empty_carries_count) + (0))) /\ ((((exists fs_h_mkm_empty_carries_count_body_terminal. fs_h_mkm_empty_carries_count_body_terminal + S (e) = S ((S (0)) * fs_v_mkm_empty_carries_count)) /\ exists fs_q_mkm_empty_carries_count_body_terminal. fs_u_mkm_empty_carries_count = fs_q_mkm_empty_carries_count_body_terminal * S ((S (0)) * fs_v_mkm_empty_carries_count) + (e))) /\ forall fs_i_mkm_empty_carries_count_body_steps. (exists fs_lt_mkm_empty_carries_count_body_steps_bound. fs_lt_mkm_empty_carries_count_body_steps_bound + S fs_i_mkm_empty_carries_count_body_steps = 0) -> exists fs_a_mkm_empty_carries_count_body_steps fs_r_mkm_empty_carries_count_body_steps fs_s_mkm_empty_carries_count_body_steps. ((((exists fs_h_mkm_empty_carries_count_body_steps_summand. fs_h_mkm_empty_carries_count_body_steps_summand + S (fs_a_mkm_empty_carries_count_body_steps) = S ((S (fs_i_mkm_empty_carries_count_body_steps)) * mkm_cc_empty_carries)) /\ exists fs_q_mkm_empty_carries_count_body_steps_summand. mkm_cb_empty_carries = fs_q_mkm_empty_carries_count_body_steps_summand * S ((S (fs_i_mkm_empty_carries_count_body_steps)) * mkm_cc_empty_carries) + (fs_a_mkm_empty_carries_count_body_steps))) /\ ((((exists fs_h_mkm_empty_carries_count_body_steps_partial. fs_h_mkm_empty_carries_count_body_steps_partial + S (fs_r_mkm_empty_carries_count_body_steps) = S ((S (fs_i_mkm_empty_carries_count_body_steps)) * fs_v_mkm_empty_carries_count)) /\ exists fs_q_mkm_empty_carries_count_body_steps_partial. fs_u_mkm_empty_carries_count = fs_q_mkm_empty_carries_count_body_steps_partial * S ((S (fs_i_mkm_empty_carries_count_body_steps)) * fs_v_mkm_empty_carries_count) + (fs_r_mkm_empty_carries_count_body_steps))) /\ ((((exists fs_h_mkm_empty_carries_count_body_steps_successor. fs_h_mkm_empty_carries_count_body_steps_successor + S (fs_s_mkm_empty_carries_count_body_steps) = S ((S (S fs_i_mkm_empty_carries_count_body_steps)) * fs_v_mkm_empty_carries_count)) /\ exists fs_q_mkm_empty_carries_count_body_steps_successor. fs_u_mkm_empty_carries_count = fs_q_mkm_empty_carries_count_body_steps_successor * S ((S (S fs_i_mkm_empty_carries_count_body_steps)) * fs_v_mkm_empty_carries_count) + (fs_s_mkm_empty_carries_count_body_steps))) /\ fs_s_mkm_empty_carries_count_body_steps = fs_r_mkm_empty_carries_count_body_steps + fs_a_mkm_empty_carries_count_body_steps)))))))) -> e = 0