positive_determinant_matrix_data_from_nonzero

Exact expanded first-order arithmetic statement

forall ab ac bb bc d p n. ~(d = 0) -> (exists mdr_b_nondegenerate_value mdr_c_nondegenerate_value mdr_l_nondegenerate_value mdr_i_nondegenerate_value. ((forall mdr_i_nondegenerate_valueh. (exists mdr_gap_nondegenerate_valuehi. mdr_gap_nondegenerate_valuehi + S (mdr_i_nondegenerate_valueh) = (mdr_l_nondegenerate_value)) -> exists mdr_d_nondegenerate_valueh mdr_pb_nondegenerate_valueh mdr_pc_nondegenerate_valueh mdr_nb_nondegenerate_valueh mdr_nc_nondegenerate_valueh mdr_p_nondegenerate_valueh mdr_n_nondegenerate_valueh. ((exists mdr_z_nondegenerate_valuehr. ((exists mdr_a_nondegenerate_valuehrc mdr_b_nondegenerate_valuehrc mdr_c_nondegenerate_valuehrc mdr_e_nondegenerate_valuehrc mdr_f_nondegenerate_valuehrc. ((mdr_a_nondegenerate_valuehrc = ((mdr_d_nondegenerate_valueh) + (mdr_pb_nondegenerate_valueh)) * S ((mdr_d_nondegenerate_valueh) + (mdr_pb_nondegenerate_valueh)) + ((mdr_pb_nondegenerate_valueh) + (mdr_pb_nondegenerate_valueh))) /\ ((mdr_b_nondegenerate_valuehrc = ((mdr_pc_nondegenerate_valueh) + (mdr_nb_nondegenerate_valueh)) * S ((mdr_pc_nondegenerate_valueh) + (mdr_nb_nondegenerate_valueh)) + ((mdr_nb_nondegenerate_valueh) + (mdr_nb_nondegenerate_valueh))) /\ ((mdr_c_nondegenerate_valuehrc = ((mdr_a_nondegenerate_valuehrc) + (mdr_b_nondegenerate_valuehrc)) * S ((mdr_a_nondegenerate_valuehrc) + (mdr_b_nondegenerate_valuehrc)) + ((mdr_b_nondegenerate_valuehrc) + (mdr_b_nondegenerate_valuehrc))) /\ ((mdr_e_nondegenerate_valuehrc = ((mdr_p_nondegenerate_valueh) + (mdr_n_nondegenerate_valueh)) * S ((mdr_p_nondegenerate_valueh) + (mdr_n_nondegenerate_valueh)) + ((mdr_n_nondegenerate_valueh) + (mdr_n_nondegenerate_valueh))) /\ ((mdr_f_nondegenerate_valuehrc = ((mdr_nc_nondegenerate_valueh) + (mdr_e_nondegenerate_valuehrc)) * S ((mdr_nc_nondegenerate_valueh) + (mdr_e_nondegenerate_valuehrc)) + ((mdr_e_nondegenerate_valuehrc) + (mdr_e_nondegenerate_valuehrc))) /\ ((mdr_z_nondegenerate_valuehr) = ((mdr_c_nondegenerate_valuehrc) + (mdr_f_nondegenerate_valuehrc)) * S ((mdr_c_nondegenerate_valuehrc) + (mdr_f_nondegenerate_valuehrc)) + ((mdr_f_nondegenerate_valuehrc) + (mdr_f_nondegenerate_valuehrc))))))))) /\ (((exists ff_h_mdr_nondegenerate_valuehrb. ff_h_mdr_nondegenerate_valuehrb + S (mdr_z_nondegenerate_valuehr) = S ((S (mdr_i_nondegenerate_valueh)) * mdr_c_nondegenerate_value)) /\ exists ff_q_mdr_nondegenerate_valuehrb. mdr_b_nondegenerate_value = ff_q_mdr_nondegenerate_valuehrb * S ((S (mdr_i_nondegenerate_valueh)) * mdr_c_nondegenerate_value) + (mdr_z_nondegenerate_valuehr))))) /\ (((((mdr_d_nondegenerate_valueh) = 0) /\ (((mdr_p_nondegenerate_valueh) = 1) /\ ((mdr_n_nondegenerate_valueh) = 0))) \/ exists mdr_q_nondegenerate_valuehs mdr_eb_nondegenerate_valuehs mdr_ec_nondegenerate_valuehs mdr_fb_nondegenerate_valuehs mdr_fc_nondegenerate_valuehs. (((mdr_d_nondegenerate_valueh) = S (mdr_q_nondegenerate_valuehs)) /\ ((forall mdr_j_nondegenerate_valuehsc. (exists mdr_gap_nondegenerate_valuehscj. mdr_gap_nondegenerate_valuehscj + S (mdr_j_nondegenerate_valuehsc) = (S (mdr_q_nondegenerate_valuehs))) -> exists mdr_i_nondegenerate_valuehsc mdr_up_nondegenerate_valuehsc mdr_us_nondegenerate_valuehsc mdr_un_nondegenerate_valuehsc mdr_ut_nondegenerate_valuehsc mdr_p_nondegenerate_valuehsc mdr_n_nondegenerate_valuehsc. ((exists mdr_gap_nondegenerate_valuehsci. mdr_gap_nondegenerate_valuehsci + S (mdr_i_nondegenerate_valuehsc) = (mdr_i_nondegenerate_valueh)) /\ ((exists mdr_z_nondegenerate_valuehscr. ((exists mdr_a_nondegenerate_valuehscrc mdr_b_nondegenerate_valuehscrc mdr_c_nondegenerate_valuehscrc mdr_e_nondegenerate_valuehscrc mdr_f_nondegenerate_valuehscrc. ((mdr_a_nondegenerate_valuehscrc = ((mdr_q_nondegenerate_valuehs) + (mdr_up_nondegenerate_valuehsc)) * S ((mdr_q_nondegenerate_valuehs) + (mdr_up_nondegenerate_valuehsc)) + ((mdr_up_nondegenerate_valuehsc) + (mdr_up_nondegenerate_valuehsc))) /\ ((mdr_b_nondegenerate_valuehscrc = ((mdr_us_nondegenerate_valuehsc) + (mdr_un_nondegenerate_valuehsc)) * S ((mdr_us_nondegenerate_valuehsc) + (mdr_un_nondegenerate_valuehsc)) + ((mdr_un_nondegenerate_valuehsc) + (mdr_un_nondegenerate_valuehsc))) /\ ((mdr_c_nondegenerate_valuehscrc = ((mdr_a_nondegenerate_valuehscrc) + (mdr_b_nondegenerate_valuehscrc)) * S ((mdr_a_nondegenerate_valuehscrc) + (mdr_b_nondegenerate_valuehscrc)) + ((mdr_b_nondegenerate_valuehscrc) + (mdr_b_nondegenerate_valuehscrc))) /\ ((mdr_e_nondegenerate_valuehscrc = ((mdr_p_nondegenerate_valuehsc) + (mdr_n_nondegenerate_valuehsc)) * S ((mdr_p_nondegenerate_valuehsc) + (mdr_n_nondegenerate_valuehsc)) + ((mdr_n_nondegenerate_valuehsc) + (mdr_n_nondegenerate_valuehsc))) /\ ((mdr_f_nondegenerate_valuehscrc = ((mdr_ut_nondegenerate_valuehsc) + (mdr_e_nondegenerate_valuehscrc)) * S ((mdr_ut_nondegenerate_valuehsc) + (mdr_e_nondegenerate_valuehscrc)) + ((mdr_e_nondegenerate_valuehscrc) + (mdr_e_nondegenerate_valuehscrc))) /\ ((mdr_z_nondegenerate_valuehscr) = ((mdr_c_nondegenerate_valuehscrc) + (mdr_f_nondegenerate_valuehscrc)) * S ((mdr_c_nondegenerate_valuehscrc) + (mdr_f_nondegenerate_valuehscrc)) + ((mdr_f_nondegenerate_valuehscrc) + (mdr_f_nondegenerate_valuehscrc))))))))) /\ (((exists ff_h_mdr_nondegenerate_valuehscrb. ff_h_mdr_nondegenerate_valuehscrb + S (mdr_z_nondegenerate_valuehscr) = S ((S (mdr_i_nondegenerate_valuehsc)) * mdr_c_nondegenerate_value)) /\ exists ff_q_mdr_nondegenerate_valuehscrb. mdr_b_nondegenerate_value = ff_q_mdr_nondegenerate_valuehscrb * S ((S (mdr_i_nondegenerate_valuehsc)) * mdr_c_nondegenerate_value) + (mdr_z_nondegenerate_valuehscr))))) /\ ((((forall ff_index_mdm_prefix_mdr_nondegenerate_valuehscm_positive. (exists ff_gap_mdm_lt_mdr_nondegenerate_valuehscm_positive_index_bound. ff_gap_mdm_lt_mdr_nondegenerate_valuehscm_positive_index_bound + S (ff_index_mdm_prefix_mdr_nondegenerate_valuehscm_positive) = ((mdr_q_nondegenerate_valuehs) * (mdr_q_nondegenerate_valuehs))) -> exists ff_row_mdm_prefix_mdr_nondegenerate_valuehscm_positive ff_column_mdm_prefix_mdr_nondegenerate_valuehscm_positive ff_value_mdm_prefix_mdr_nondegenerate_valuehscm_positive. (ff_index_mdm_prefix_mdr_nondegenerate_valuehscm_positive = (mdr_q_nondegenerate_valuehs) * ff_row_mdm_prefix_mdr_nondegenerate_valuehscm_positive + ff_column_mdm_prefix_mdr_nondegenerate_valuehscm_positive /\ ((exists ff_gap_mdm_lt_mdr_nondegenerate_valuehscm_positive_column_bound. ff_gap_mdm_lt_mdr_nondegenerate_valuehscm_positive_column_bound + S (ff_column_mdm_prefix_mdr_nondegenerate_valuehscm_positive) = (mdr_q_nondegenerate_valuehs)) /\ ((exists ff_row_mdm_cell_mdr_nondegenerate_valuehscm_positive_cell ff_column_mdm_cell_mdr_nondegenerate_valuehscm_positive_cell. (((((exists ff_gap_mdm_lt_mdr_nondegenerate_valuehscm_positive_cell_row_before. ff_gap_mdm_lt_mdr_nondegenerate_valuehscm_positive_cell_row_before + S (ff_row_mdm_prefix_mdr_nondegenerate_valuehscm_positive) = (0)) /\ ff_row_mdm_cell_mdr_nondegenerate_valuehscm_positive_cell = ff_row_mdm_prefix_mdr_nondegenerate_valuehscm_positive) \/ ((exists ff_gap_mdm_le_mdr_nondegenerate_valuehscm_positive_cell_row_after. ff_gap_mdm_le_mdr_nondegenerate_valuehscm_positive_cell_row_after + (0) = (ff_row_mdm_prefix_mdr_nondegenerate_valuehscm_positive)) /\ ff_row_mdm_cell_mdr_nondegenerate_valuehscm_positive_cell = S ff_row_mdm_prefix_mdr_nondegenerate_valuehscm_positive))) /\ (((((exists ff_gap_mdm_lt_mdr_nondegenerate_valuehscm_positive_cell_column_before. ff_gap_mdm_lt_mdr_nondegenerate_valuehscm_positive_cell_column_before + S (ff_column_mdm_prefix_mdr_nondegenerate_valuehscm_positive) = (mdr_j_nondegenerate_valuehsc)) /\ ff_column_mdm_cell_mdr_nondegenerate_valuehscm_positive_cell = ff_column_mdm_prefix_mdr_nondegenerate_valuehscm_positive) \/ ((exists ff_gap_mdm_le_mdr_nondegenerate_valuehscm_positive_cell_column_after. ff_gap_mdm_le_mdr_nondegenerate_valuehscm_positive_cell_column_after + (mdr_j_nondegenerate_valuehsc) = (ff_column_mdm_prefix_mdr_nondegenerate_valuehscm_positive)) /\ ff_column_mdm_cell_mdr_nondegenerate_valuehscm_positive_cell = S ff_column_mdm_prefix_mdr_nondegenerate_valuehscm_positive))) /\ (((exists ff_h_mdm_mdr_nondegenerate_valuehscm_positive_cell_source. ff_h_mdm_mdr_nondegenerate_valuehscm_positive_cell_source + S (ff_value_mdm_prefix_mdr_nondegenerate_valuehscm_positive) = S ((S ((ff_row_mdm_cell_mdr_nondegenerate_valuehscm_positive_cell) * (S (mdr_q_nondegenerate_valuehs)) + (ff_column_mdm_cell_mdr_nondegenerate_valuehscm_positive_cell))) * mdr_pc_nondegenerate_valueh)) /\ exists ff_q_mdm_mdr_nondegenerate_valuehscm_positive_cell_source. mdr_pb_nondegenerate_valueh = ff_q_mdm_mdr_nondegenerate_valuehscm_positive_cell_source * S ((S ((ff_row_mdm_cell_mdr_nondegenerate_valuehscm_positive_cell) * (S (mdr_q_nondegenerate_valuehs)) + (ff_column_mdm_cell_mdr_nondegenerate_valuehscm_positive_cell))) * mdr_pc_nondegenerate_valueh) + (ff_value_mdm_prefix_mdr_nondegenerate_valuehscm_positive)))))) /\ (((exists ff_h_mdm_mdr_nondegenerate_valuehscm_positive_target. ff_h_mdm_mdr_nondegenerate_valuehscm_positive_target + S (ff_value_mdm_prefix_mdr_nondegenerate_valuehscm_positive) = S ((S (ff_index_mdm_prefix_mdr_nondegenerate_valuehscm_positive)) * mdr_us_nondegenerate_valuehsc)) /\ exists ff_q_mdm_mdr_nondegenerate_valuehscm_positive_target. mdr_up_nondegenerate_valuehsc = ff_q_mdm_mdr_nondegenerate_valuehscm_positive_target * S ((S (ff_index_mdm_prefix_mdr_nondegenerate_valuehscm_positive)) * mdr_us_nondegenerate_valuehsc) + (ff_value_mdm_prefix_mdr_nondegenerate_valuehscm_positive))))))) /\ (forall ff_index_mdm_prefix_mdr_nondegenerate_valuehscm_negative. (exists ff_gap_mdm_lt_mdr_nondegenerate_valuehscm_negative_index_bound. ff_gap_mdm_lt_mdr_nondegenerate_valuehscm_negative_index_bound + S (ff_index_mdm_prefix_mdr_nondegenerate_valuehscm_negative) = ((mdr_q_nondegenerate_valuehs) * (mdr_q_nondegenerate_valuehs))) -> exists ff_row_mdm_prefix_mdr_nondegenerate_valuehscm_negative ff_column_mdm_prefix_mdr_nondegenerate_valuehscm_negative ff_value_mdm_prefix_mdr_nondegenerate_valuehscm_negative. (ff_index_mdm_prefix_mdr_nondegenerate_valuehscm_negative = (mdr_q_nondegenerate_valuehs) * ff_row_mdm_prefix_mdr_nondegenerate_valuehscm_negative + ff_column_mdm_prefix_mdr_nondegenerate_valuehscm_negative /\ ((exists ff_gap_mdm_lt_mdr_nondegenerate_valuehscm_negative_column_bound. ff_gap_mdm_lt_mdr_nondegenerate_valuehscm_negative_column_bound + S (ff_column_mdm_prefix_mdr_nondegenerate_valuehscm_negative) = (mdr_q_nondegenerate_valuehs)) /\ ((exists ff_row_mdm_cell_mdr_nondegenerate_valuehscm_negative_cell ff_column_mdm_cell_mdr_nondegenerate_valuehscm_negative_cell. (((((exists ff_gap_mdm_lt_mdr_nondegenerate_valuehscm_negative_cell_row_before. ff_gap_mdm_lt_mdr_nondegenerate_valuehscm_negative_cell_row_before + S (ff_row_mdm_prefix_mdr_nondegenerate_valuehscm_negative) = (0)) /\ ff_row_mdm_cell_mdr_nondegenerate_valuehscm_negative_cell = ff_row_mdm_prefix_mdr_nondegenerate_valuehscm_negative) \/ ((exists ff_gap_mdm_le_mdr_nondegenerate_valuehscm_negative_cell_row_after. ff_gap_mdm_le_mdr_nondegenerate_valuehscm_negative_cell_row_after + (0) = (ff_row_mdm_prefix_mdr_nondegenerate_valuehscm_negative)) /\ ff_row_mdm_cell_mdr_nondegenerate_valuehscm_negative_cell = S ff_row_mdm_prefix_mdr_nondegenerate_valuehscm_negative))) /\ (((((exists ff_gap_mdm_lt_mdr_nondegenerate_valuehscm_negative_cell_column_before. ff_gap_mdm_lt_mdr_nondegenerate_valuehscm_negative_cell_column_before + S (ff_column_mdm_prefix_mdr_nondegenerate_valuehscm_negative) = (mdr_j_nondegenerate_valuehsc)) /\ ff_column_mdm_cell_mdr_nondegenerate_valuehscm_negative_cell = ff_column_mdm_prefix_mdr_nondegenerate_valuehscm_negative) \/ ((exists ff_gap_mdm_le_mdr_nondegenerate_valuehscm_negative_cell_column_after. ff_gap_mdm_le_mdr_nondegenerate_valuehscm_negative_cell_column_after + (mdr_j_nondegenerate_valuehsc) = (ff_column_mdm_prefix_mdr_nondegenerate_valuehscm_negative)) /\ ff_column_mdm_cell_mdr_nondegenerate_valuehscm_negative_cell = S ff_column_mdm_prefix_mdr_nondegenerate_valuehscm_negative))) /\ (((exists ff_h_mdm_mdr_nondegenerate_valuehscm_negative_cell_source. ff_h_mdm_mdr_nondegenerate_valuehscm_negative_cell_source + S (ff_value_mdm_prefix_mdr_nondegenerate_valuehscm_negative) = S ((S ((ff_row_mdm_cell_mdr_nondegenerate_valuehscm_negative_cell) * (S (mdr_q_nondegenerate_valuehs)) + (ff_column_mdm_cell_mdr_nondegenerate_valuehscm_negative_cell))) * mdr_nc_nondegenerate_valueh)) /\ exists ff_q_mdm_mdr_nondegenerate_valuehscm_negative_cell_source. mdr_nb_nondegenerate_valueh = ff_q_mdm_mdr_nondegenerate_valuehscm_negative_cell_source * S ((S ((ff_row_mdm_cell_mdr_nondegenerate_valuehscm_negative_cell) * (S (mdr_q_nondegenerate_valuehs)) + (ff_column_mdm_cell_mdr_nondegenerate_valuehscm_negative_cell))) * mdr_nc_nondegenerate_valueh) + (ff_value_mdm_prefix_mdr_nondegenerate_valuehscm_negative)))))) /\ (((exists ff_h_mdm_mdr_nondegenerate_valuehscm_negative_target. ff_h_mdm_mdr_nondegenerate_valuehscm_negative_target + S (ff_value_mdm_prefix_mdr_nondegenerate_valuehscm_negative) = S ((S (ff_index_mdm_prefix_mdr_nondegenerate_valuehscm_negative)) * mdr_ut_nondegenerate_valuehsc)) /\ exists ff_q_mdm_mdr_nondegenerate_valuehscm_negative_target. mdr_un_nondegenerate_valuehsc = ff_q_mdm_mdr_nondegenerate_valuehscm_negative_target * S ((S (ff_index_mdm_prefix_mdr_nondegenerate_valuehscm_negative)) * mdr_ut_nondegenerate_valuehsc) + (ff_value_mdm_prefix_mdr_nondegenerate_valuehscm_negative))))))))) /\ ((((exists ff_h_mdr_nondegenerate_valuehscp. ff_h_mdr_nondegenerate_valuehscp + S (mdr_p_nondegenerate_valuehsc) = S ((S (mdr_j_nondegenerate_valuehsc)) * mdr_ec_nondegenerate_valuehs)) /\ exists ff_q_mdr_nondegenerate_valuehscp. mdr_eb_nondegenerate_valuehs = ff_q_mdr_nondegenerate_valuehscp * S ((S (mdr_j_nondegenerate_valuehsc)) * mdr_ec_nondegenerate_valuehs) + (mdr_p_nondegenerate_valuehsc))) /\ (((exists ff_h_mdr_nondegenerate_valuehscn. ff_h_mdr_nondegenerate_valuehscn + S (mdr_n_nondegenerate_valuehsc) = S ((S (mdr_j_nondegenerate_valuehsc)) * mdr_fc_nondegenerate_valuehs)) /\ exists ff_q_mdr_nondegenerate_valuehscn. mdr_fb_nondegenerate_valuehs = ff_q_mdr_nondegenerate_valuehscn * S ((S (mdr_j_nondegenerate_valuehsc)) * mdr_fc_nondegenerate_valuehs) + (mdr_n_nondegenerate_valuehsc)))))))) /\ (exists ff_ub_mce_fold_mdr_nondegenerate_valuehsf ff_uc_mce_fold_mdr_nondegenerate_valuehsf ff_vb_mce_fold_mdr_nondegenerate_valuehsf ff_vc_mce_fold_mdr_nondegenerate_valuehsf. ((forall ff_index_mce_alternating_mdr_nondegenerate_valuehsf_prefix. (exists ff_gap_mce_mdr_nondegenerate_valuehsf_prefix_index. ff_gap_mce_mdr_nondegenerate_valuehsf_prefix_index + S (ff_index_mce_alternating_mdr_nondegenerate_valuehsf_prefix) = (S (mdr_q_nondegenerate_valuehs))) -> exists ff_ap_mce_alternating_mdr_nondegenerate_valuehsf_prefix ff_an_mce_alternating_mdr_nondegenerate_valuehsf_prefix ff_bp_mce_alternating_mdr_nondegenerate_valuehsf_prefix ff_bn_mce_alternating_mdr_nondegenerate_valuehsf_prefix ff_p_mce_alternating_mdr_nondegenerate_valuehsf_prefix ff_n_mce_alternating_mdr_nondegenerate_valuehsf_prefix. ((((exists ff_h_mce_mdr_nondegenerate_valuehsf_prefix_ap. ff_h_mce_mdr_nondegenerate_valuehsf_prefix_ap + S (ff_ap_mce_alternating_mdr_nondegenerate_valuehsf_prefix) = S ((S (ff_index_mce_alternating_mdr_nondegenerate_valuehsf_prefix)) * mdr_pc_nondegenerate_valueh)) /\ exists ff_q_mce_mdr_nondegenerate_valuehsf_prefix_ap. mdr_pb_nondegenerate_valueh = ff_q_mce_mdr_nondegenerate_valuehsf_prefix_ap * S ((S (ff_index_mce_alternating_mdr_nondegenerate_valuehsf_prefix)) * mdr_pc_nondegenerate_valueh) + (ff_ap_mce_alternating_mdr_nondegenerate_valuehsf_prefix))) /\ ((((exists ff_h_mce_mdr_nondegenerate_valuehsf_prefix_an. ff_h_mce_mdr_nondegenerate_valuehsf_prefix_an + S (ff_an_mce_alternating_mdr_nondegenerate_valuehsf_prefix) = S ((S (ff_index_mce_alternating_mdr_nondegenerate_valuehsf_prefix)) * mdr_nc_nondegenerate_valueh)) /\ exists ff_q_mce_mdr_nondegenerate_valuehsf_prefix_an. mdr_nb_nondegenerate_valueh = ff_q_mce_mdr_nondegenerate_valuehsf_prefix_an * S ((S (ff_index_mce_alternating_mdr_nondegenerate_valuehsf_prefix)) * mdr_nc_nondegenerate_valueh) + (ff_an_mce_alternating_mdr_nondegenerate_valuehsf_prefix))) /\ ((((exists ff_h_mce_mdr_nondegenerate_valuehsf_prefix_bp. ff_h_mce_mdr_nondegenerate_valuehsf_prefix_bp + S (ff_bp_mce_alternating_mdr_nondegenerate_valuehsf_prefix) = S ((S (ff_index_mce_alternating_mdr_nondegenerate_valuehsf_prefix)) * mdr_ec_nondegenerate_valuehs)) /\ exists ff_q_mce_mdr_nondegenerate_valuehsf_prefix_bp. mdr_eb_nondegenerate_valuehs = ff_q_mce_mdr_nondegenerate_valuehsf_prefix_bp * S ((S (ff_index_mce_alternating_mdr_nondegenerate_valuehsf_prefix)) * mdr_ec_nondegenerate_valuehs) + (ff_bp_mce_alternating_mdr_nondegenerate_valuehsf_prefix))) /\ ((((exists ff_h_mce_mdr_nondegenerate_valuehsf_prefix_bn. ff_h_mce_mdr_nondegenerate_valuehsf_prefix_bn + S (ff_bn_mce_alternating_mdr_nondegenerate_valuehsf_prefix) = S ((S (ff_index_mce_alternating_mdr_nondegenerate_valuehsf_prefix)) * mdr_fc_nondegenerate_valuehs)) /\ exists ff_q_mce_mdr_nondegenerate_valuehsf_prefix_bn. mdr_fb_nondegenerate_valuehs = ff_q_mce_mdr_nondegenerate_valuehsf_prefix_bn * S ((S (ff_index_mce_alternating_mdr_nondegenerate_valuehsf_prefix)) * mdr_fc_nondegenerate_valuehs) + (ff_bn_mce_alternating_mdr_nondegenerate_valuehsf_prefix))) /\ ((((exists ff_h_mce_mdr_nondegenerate_valuehsf_prefix_positive. ff_h_mce_mdr_nondegenerate_valuehsf_prefix_positive + S (ff_p_mce_alternating_mdr_nondegenerate_valuehsf_prefix) = S ((S (ff_index_mce_alternating_mdr_nondegenerate_valuehsf_prefix)) * ff_uc_mce_fold_mdr_nondegenerate_valuehsf)) /\ exists ff_q_mce_mdr_nondegenerate_valuehsf_prefix_positive. ff_ub_mce_fold_mdr_nondegenerate_valuehsf = ff_q_mce_mdr_nondegenerate_valuehsf_prefix_positive * S ((S (ff_index_mce_alternating_mdr_nondegenerate_valuehsf_prefix)) * ff_uc_mce_fold_mdr_nondegenerate_valuehsf) + (ff_p_mce_alternating_mdr_nondegenerate_valuehsf_prefix))) /\ ((((exists ff_h_mce_mdr_nondegenerate_valuehsf_prefix_negative. ff_h_mce_mdr_nondegenerate_valuehsf_prefix_negative + S (ff_n_mce_alternating_mdr_nondegenerate_valuehsf_prefix) = S ((S (ff_index_mce_alternating_mdr_nondegenerate_valuehsf_prefix)) * ff_vc_mce_fold_mdr_nondegenerate_valuehsf)) /\ exists ff_q_mce_mdr_nondegenerate_valuehsf_prefix_negative. ff_vb_mce_fold_mdr_nondegenerate_valuehsf = ff_q_mce_mdr_nondegenerate_valuehsf_prefix_negative * S ((S (ff_index_mce_alternating_mdr_nondegenerate_valuehsf_prefix)) * ff_vc_mce_fold_mdr_nondegenerate_valuehsf) + (ff_n_mce_alternating_mdr_nondegenerate_valuehsf_prefix))) /\ (((exists ff_even_mce_term_mdr_nondegenerate_valuehsf_prefix_term. ff_index_mce_alternating_mdr_nondegenerate_valuehsf_prefix = 2 * ff_even_mce_term_mdr_nondegenerate_valuehsf_prefix_term) /\ (ff_p_mce_alternating_mdr_nondegenerate_valuehsf_prefix = (ff_ap_mce_alternating_mdr_nondegenerate_valuehsf_prefix) * (ff_bp_mce_alternating_mdr_nondegenerate_valuehsf_prefix) + (ff_an_mce_alternating_mdr_nondegenerate_valuehsf_prefix) * (ff_bn_mce_alternating_mdr_nondegenerate_valuehsf_prefix) /\ ff_n_mce_alternating_mdr_nondegenerate_valuehsf_prefix = (ff_ap_mce_alternating_mdr_nondegenerate_valuehsf_prefix) * (ff_bn_mce_alternating_mdr_nondegenerate_valuehsf_prefix) + (ff_an_mce_alternating_mdr_nondegenerate_valuehsf_prefix) * (ff_bp_mce_alternating_mdr_nondegenerate_valuehsf_prefix))) \/ ((exists ff_odd_mce_term_mdr_nondegenerate_valuehsf_prefix_term. ff_index_mce_alternating_mdr_nondegenerate_valuehsf_prefix = 2 * ff_odd_mce_term_mdr_nondegenerate_valuehsf_prefix_term + 1) /\ (ff_p_mce_alternating_mdr_nondegenerate_valuehsf_prefix = (ff_ap_mce_alternating_mdr_nondegenerate_valuehsf_prefix) * (ff_bn_mce_alternating_mdr_nondegenerate_valuehsf_prefix) + (ff_an_mce_alternating_mdr_nondegenerate_valuehsf_prefix) * (ff_bp_mce_alternating_mdr_nondegenerate_valuehsf_prefix) /\ ff_n_mce_alternating_mdr_nondegenerate_valuehsf_prefix = (ff_ap_mce_alternating_mdr_nondegenerate_valuehsf_prefix) * (ff_bp_mce_alternating_mdr_nondegenerate_valuehsf_prefix) + (ff_an_mce_alternating_mdr_nondegenerate_valuehsf_prefix) * (ff_bn_mce_alternating_mdr_nondegenerate_valuehsf_prefix))))))))))) /\ ((exists ff_u_mce_mdr_nondegenerate_valuehsf_positive ff_v_mce_mdr_nondegenerate_valuehsf_positive. ((((exists ff_h_mce_mdr_nondegenerate_valuehsf_positive_start. ff_h_mce_mdr_nondegenerate_valuehsf_positive_start + S (0) = S ((S (0)) * ff_v_mce_mdr_nondegenerate_valuehsf_positive)) /\ exists ff_q_mce_mdr_nondegenerate_valuehsf_positive_start. ff_u_mce_mdr_nondegenerate_valuehsf_positive = ff_q_mce_mdr_nondegenerate_valuehsf_positive_start * S ((S (0)) * ff_v_mce_mdr_nondegenerate_valuehsf_positive) + (0))) /\ ((((exists ff_h_mce_mdr_nondegenerate_valuehsf_positive_terminal. ff_h_mce_mdr_nondegenerate_valuehsf_positive_terminal + S (mdr_p_nondegenerate_valueh) = S ((S ((S (mdr_q_nondegenerate_valuehs)))) * ff_v_mce_mdr_nondegenerate_valuehsf_positive)) /\ exists ff_q_mce_mdr_nondegenerate_valuehsf_positive_terminal. ff_u_mce_mdr_nondegenerate_valuehsf_positive = ff_q_mce_mdr_nondegenerate_valuehsf_positive_terminal * S ((S ((S (mdr_q_nondegenerate_valuehs)))) * ff_v_mce_mdr_nondegenerate_valuehsf_positive) + (mdr_p_nondegenerate_valueh))) /\ forall ff_i_mce_mdr_nondegenerate_valuehsf_positive. (exists ff_lt_mce_mdr_nondegenerate_valuehsf_positive_bound. ff_lt_mce_mdr_nondegenerate_valuehsf_positive_bound + S ff_i_mce_mdr_nondegenerate_valuehsf_positive = (S (mdr_q_nondegenerate_valuehs))) -> exists ff_a_mce_mdr_nondegenerate_valuehsf_positive ff_r_mce_mdr_nondegenerate_valuehsf_positive ff_s_mce_mdr_nondegenerate_valuehsf_positive. ((((exists ff_h_mce_mdr_nondegenerate_valuehsf_positive_summand. ff_h_mce_mdr_nondegenerate_valuehsf_positive_summand + S (ff_a_mce_mdr_nondegenerate_valuehsf_positive) = S ((S (ff_i_mce_mdr_nondegenerate_valuehsf_positive)) * ff_uc_mce_fold_mdr_nondegenerate_valuehsf)) /\ exists ff_q_mce_mdr_nondegenerate_valuehsf_positive_summand. ff_ub_mce_fold_mdr_nondegenerate_valuehsf = ff_q_mce_mdr_nondegenerate_valuehsf_positive_summand * S ((S (ff_i_mce_mdr_nondegenerate_valuehsf_positive)) * ff_uc_mce_fold_mdr_nondegenerate_valuehsf) + (ff_a_mce_mdr_nondegenerate_valuehsf_positive))) /\ ((((exists ff_h_mce_mdr_nondegenerate_valuehsf_positive_partial. ff_h_mce_mdr_nondegenerate_valuehsf_positive_partial + S (ff_r_mce_mdr_nondegenerate_valuehsf_positive) = S ((S (ff_i_mce_mdr_nondegenerate_valuehsf_positive)) * ff_v_mce_mdr_nondegenerate_valuehsf_positive)) /\ exists ff_q_mce_mdr_nondegenerate_valuehsf_positive_partial. ff_u_mce_mdr_nondegenerate_valuehsf_positive = ff_q_mce_mdr_nondegenerate_valuehsf_positive_partial * S ((S (ff_i_mce_mdr_nondegenerate_valuehsf_positive)) * ff_v_mce_mdr_nondegenerate_valuehsf_positive) + (ff_r_mce_mdr_nondegenerate_valuehsf_positive))) /\ ((((exists ff_h_mce_mdr_nondegenerate_valuehsf_positive_successor. ff_h_mce_mdr_nondegenerate_valuehsf_positive_successor + S (ff_s_mce_mdr_nondegenerate_valuehsf_positive) = S ((S (S ff_i_mce_mdr_nondegenerate_valuehsf_positive)) * ff_v_mce_mdr_nondegenerate_valuehsf_positive)) /\ exists ff_q_mce_mdr_nondegenerate_valuehsf_positive_successor. ff_u_mce_mdr_nondegenerate_valuehsf_positive = ff_q_mce_mdr_nondegenerate_valuehsf_positive_successor * S ((S (S ff_i_mce_mdr_nondegenerate_valuehsf_positive)) * ff_v_mce_mdr_nondegenerate_valuehsf_positive) + (ff_s_mce_mdr_nondegenerate_valuehsf_positive))) /\ ff_s_mce_mdr_nondegenerate_valuehsf_positive = ff_r_mce_mdr_nondegenerate_valuehsf_positive + ff_a_mce_mdr_nondegenerate_valuehsf_positive)))))) /\ (exists ff_u_mce_mdr_nondegenerate_valuehsf_negative ff_v_mce_mdr_nondegenerate_valuehsf_negative. ((((exists ff_h_mce_mdr_nondegenerate_valuehsf_negative_start. ff_h_mce_mdr_nondegenerate_valuehsf_negative_start + S (0) = S ((S (0)) * ff_v_mce_mdr_nondegenerate_valuehsf_negative)) /\ exists ff_q_mce_mdr_nondegenerate_valuehsf_negative_start. ff_u_mce_mdr_nondegenerate_valuehsf_negative = ff_q_mce_mdr_nondegenerate_valuehsf_negative_start * S ((S (0)) * ff_v_mce_mdr_nondegenerate_valuehsf_negative) + (0))) /\ ((((exists ff_h_mce_mdr_nondegenerate_valuehsf_negative_terminal. ff_h_mce_mdr_nondegenerate_valuehsf_negative_terminal + S (mdr_n_nondegenerate_valueh) = S ((S ((S (mdr_q_nondegenerate_valuehs)))) * ff_v_mce_mdr_nondegenerate_valuehsf_negative)) /\ exists ff_q_mce_mdr_nondegenerate_valuehsf_negative_terminal. ff_u_mce_mdr_nondegenerate_valuehsf_negative = ff_q_mce_mdr_nondegenerate_valuehsf_negative_terminal * S ((S ((S (mdr_q_nondegenerate_valuehs)))) * ff_v_mce_mdr_nondegenerate_valuehsf_negative) + (mdr_n_nondegenerate_valueh))) /\ forall ff_i_mce_mdr_nondegenerate_valuehsf_negative. (exists ff_lt_mce_mdr_nondegenerate_valuehsf_negative_bound. ff_lt_mce_mdr_nondegenerate_valuehsf_negative_bound + S ff_i_mce_mdr_nondegenerate_valuehsf_negative = (S (mdr_q_nondegenerate_valuehs))) -> exists ff_a_mce_mdr_nondegenerate_valuehsf_negative ff_r_mce_mdr_nondegenerate_valuehsf_negative ff_s_mce_mdr_nondegenerate_valuehsf_negative. ((((exists ff_h_mce_mdr_nondegenerate_valuehsf_negative_summand. ff_h_mce_mdr_nondegenerate_valuehsf_negative_summand + S (ff_a_mce_mdr_nondegenerate_valuehsf_negative) = S ((S (ff_i_mce_mdr_nondegenerate_valuehsf_negative)) * ff_vc_mce_fold_mdr_nondegenerate_valuehsf)) /\ exists ff_q_mce_mdr_nondegenerate_valuehsf_negative_summand. ff_vb_mce_fold_mdr_nondegenerate_valuehsf = ff_q_mce_mdr_nondegenerate_valuehsf_negative_summand * S ((S (ff_i_mce_mdr_nondegenerate_valuehsf_negative)) * ff_vc_mce_fold_mdr_nondegenerate_valuehsf) + (ff_a_mce_mdr_nondegenerate_valuehsf_negative))) /\ ((((exists ff_h_mce_mdr_nondegenerate_valuehsf_negative_partial. ff_h_mce_mdr_nondegenerate_valuehsf_negative_partial + S (ff_r_mce_mdr_nondegenerate_valuehsf_negative) = S ((S (ff_i_mce_mdr_nondegenerate_valuehsf_negative)) * ff_v_mce_mdr_nondegenerate_valuehsf_negative)) /\ exists ff_q_mce_mdr_nondegenerate_valuehsf_negative_partial. ff_u_mce_mdr_nondegenerate_valuehsf_negative = ff_q_mce_mdr_nondegenerate_valuehsf_negative_partial * S ((S (ff_i_mce_mdr_nondegenerate_valuehsf_negative)) * ff_v_mce_mdr_nondegenerate_valuehsf_negative) + (ff_r_mce_mdr_nondegenerate_valuehsf_negative))) /\ ((((exists ff_h_mce_mdr_nondegenerate_valuehsf_negative_successor. ff_h_mce_mdr_nondegenerate_valuehsf_negative_successor + S (ff_s_mce_mdr_nondegenerate_valuehsf_negative) = S ((S (S ff_i_mce_mdr_nondegenerate_valuehsf_negative)) * ff_v_mce_mdr_nondegenerate_valuehsf_negative)) /\ exists ff_q_mce_mdr_nondegenerate_valuehsf_negative_successor. ff_u_mce_mdr_nondegenerate_valuehsf_negative = ff_q_mce_mdr_nondegenerate_valuehsf_negative_successor * S ((S (S ff_i_mce_mdr_nondegenerate_valuehsf_negative)) * ff_v_mce_mdr_nondegenerate_valuehsf_negative) + (ff_s_mce_mdr_nondegenerate_valuehsf_negative))) /\ ff_s_mce_mdr_nondegenerate_valuehsf_negative = ff_r_mce_mdr_nondegenerate_valuehsf_negative + ff_a_mce_mdr_nondegenerate_valuehsf_negative))))))))))))))) /\ ((exists mdr_gap_nondegenerate_valuei. mdr_gap_nondegenerate_valuei + S (mdr_i_nondegenerate_value) = (mdr_l_nondegenerate_value)) /\ (exists mdr_z_nondegenerate_valuer. ((exists mdr_a_nondegenerate_valuerc mdr_b_nondegenerate_valuerc mdr_c_nondegenerate_valuerc mdr_e_nondegenerate_valuerc mdr_f_nondegenerate_valuerc. ((mdr_a_nondegenerate_valuerc = ((d) + (ab)) * S ((d) + (ab)) + ((ab) + (ab))) /\ ((mdr_b_nondegenerate_valuerc = ((ac) + (bb)) * S ((ac) + (bb)) + ((bb) + (bb))) /\ ((mdr_c_nondegenerate_valuerc = ((mdr_a_nondegenerate_valuerc) + (mdr_b_nondegenerate_valuerc)) * S ((mdr_a_nondegenerate_valuerc) + (mdr_b_nondegenerate_valuerc)) + ((mdr_b_nondegenerate_valuerc) + (mdr_b_nondegenerate_valuerc))) /\ ((mdr_e_nondegenerate_valuerc = ((p) + (n)) * S ((p) + (n)) + ((n) + (n))) /\ ((mdr_f_nondegenerate_valuerc = ((bc) + (mdr_e_nondegenerate_valuerc)) * S ((bc) + (mdr_e_nondegenerate_valuerc)) + ((mdr_e_nondegenerate_valuerc) + (mdr_e_nondegenerate_valuerc))) /\ ((mdr_z_nondegenerate_valuer) = ((mdr_c_nondegenerate_valuerc) + (mdr_f_nondegenerate_valuerc)) * S ((mdr_c_nondegenerate_valuerc) + (mdr_f_nondegenerate_valuerc)) + ((mdr_f_nondegenerate_valuerc) + (mdr_f_nondegenerate_valuerc))))))))) /\ (((exists ff_h_mdr_nondegenerate_valuerb. ff_h_mdr_nondegenerate_valuerb + S (mdr_z_nondegenerate_valuer) = S ((S (mdr_i_nondegenerate_value)) * mdr_c_nondegenerate_value)) /\ exists ff_q_mdr_nondegenerate_valuerb. mdr_b_nondegenerate_value = ff_q_mdr_nondegenerate_valuerb * S ((S (mdr_i_nondegenerate_value)) * mdr_c_nondegenerate_value) + (mdr_z_nondegenerate_valuer)))))))) -> ~(p = n) -> exists D. (((~(d = 0)) /\ ((~(D = 0)) /\ (exists mdr_p_nondegenerate_dataabsolute mdr_n_nondegenerate_dataabsolute. ((exists mdr_b_nondegenerate_dataabsoluteevaluation mdr_c_nondegenerate_dataabsoluteevaluation mdr_l_nondegenerate_dataabsoluteevaluation mdr_i_nondegenerate_dataabsoluteevaluation. ((forall mdr_i_nondegenerate_dataabsoluteevaluationh. (exists mdr_gap_nondegenerate_dataabsoluteevaluationhi. mdr_gap_nondegenerate_dataabsoluteevaluationhi + S (mdr_i_nondegenerate_dataabsoluteevaluationh) = (mdr_l_nondegenerate_dataabsoluteevaluation)) -> exists mdr_d_nondegenerate_dataabsoluteevaluationh mdr_pb_nondegenerate_dataabsoluteevaluationh mdr_pc_nondegenerate_dataabsoluteevaluationh mdr_nb_nondegenerate_dataabsoluteevaluationh mdr_nc_nondegenerate_dataabsoluteevaluationh mdr_p_nondegenerate_dataabsoluteevaluationh mdr_n_nondegenerate_dataabsoluteevaluationh. ((exists mdr_z_nondegenerate_dataabsoluteevaluationhr. ((exists mdr_a_nondegenerate_dataabsoluteevaluationhrc mdr_b_nondegenerate_dataabsoluteevaluationhrc mdr_c_nondegenerate_dataabsoluteevaluationhrc mdr_e_nondegenerate_dataabsoluteevaluationhrc mdr_f_nondegenerate_dataabsoluteevaluationhrc. ((mdr_a_nondegenerate_dataabsoluteevaluationhrc = ((mdr_d_nondegenerate_dataabsoluteevaluationh) + (mdr_pb_nondegenerate_dataabsoluteevaluationh)) * S ((mdr_d_nondegenerate_dataabsoluteevaluationh) + (mdr_pb_nondegenerate_dataabsoluteevaluationh)) + ((mdr_pb_nondegenerate_dataabsoluteevaluationh) + (mdr_pb_nondegenerate_dataabsoluteevaluationh))) /\ ((mdr_b_nondegenerate_dataabsoluteevaluationhrc = ((mdr_pc_nondegenerate_dataabsoluteevaluationh) + (mdr_nb_nondegenerate_dataabsoluteevaluationh)) * S ((mdr_pc_nondegenerate_dataabsoluteevaluationh) + (mdr_nb_nondegenerate_dataabsoluteevaluationh)) + ((mdr_nb_nondegenerate_dataabsoluteevaluationh) + (mdr_nb_nondegenerate_dataabsoluteevaluationh))) /\ ((mdr_c_nondegenerate_dataabsoluteevaluationhrc = ((mdr_a_nondegenerate_dataabsoluteevaluationhrc) + (mdr_b_nondegenerate_dataabsoluteevaluationhrc)) * S ((mdr_a_nondegenerate_dataabsoluteevaluationhrc) + (mdr_b_nondegenerate_dataabsoluteevaluationhrc)) + ((mdr_b_nondegenerate_dataabsoluteevaluationhrc) + (mdr_b_nondegenerate_dataabsoluteevaluationhrc))) /\ ((mdr_e_nondegenerate_dataabsoluteevaluationhrc = ((mdr_p_nondegenerate_dataabsoluteevaluationh) + (mdr_n_nondegenerate_dataabsoluteevaluationh)) * S ((mdr_p_nondegenerate_dataabsoluteevaluationh) + (mdr_n_nondegenerate_dataabsoluteevaluationh)) + ((mdr_n_nondegenerate_dataabsoluteevaluationh) + (mdr_n_nondegenerate_dataabsoluteevaluationh))) /\ ((mdr_f_nondegenerate_dataabsoluteevaluationhrc = ((mdr_nc_nondegenerate_dataabsoluteevaluationh) + (mdr_e_nondegenerate_dataabsoluteevaluationhrc)) * S ((mdr_nc_nondegenerate_dataabsoluteevaluationh) + (mdr_e_nondegenerate_dataabsoluteevaluationhrc)) + ((mdr_e_nondegenerate_dataabsoluteevaluationhrc) + (mdr_e_nondegenerate_dataabsoluteevaluationhrc))) /\ ((mdr_z_nondegenerate_dataabsoluteevaluationhr) = ((mdr_c_nondegenerate_dataabsoluteevaluationhrc) + (mdr_f_nondegenerate_dataabsoluteevaluationhrc)) * S ((mdr_c_nondegenerate_dataabsoluteevaluationhrc) + (mdr_f_nondegenerate_dataabsoluteevaluationhrc)) + ((mdr_f_nondegenerate_dataabsoluteevaluationhrc) + (mdr_f_nondegenerate_dataabsoluteevaluationhrc))))))))) /\ (((exists ff_h_mdr_nondegenerate_dataabsoluteevaluationhrb. ff_h_mdr_nondegenerate_dataabsoluteevaluationhrb + S (mdr_z_nondegenerate_dataabsoluteevaluationhr) = S ((S (mdr_i_nondegenerate_dataabsoluteevaluationh)) * mdr_c_nondegenerate_dataabsoluteevaluation)) /\ exists ff_q_mdr_nondegenerate_dataabsoluteevaluationhrb. mdr_b_nondegenerate_dataabsoluteevaluation = ff_q_mdr_nondegenerate_dataabsoluteevaluationhrb * S ((S (mdr_i_nondegenerate_dataabsoluteevaluationh)) * mdr_c_nondegenerate_dataabsoluteevaluation) + (mdr_z_nondegenerate_dataabsoluteevaluationhr))))) /\ (((((mdr_d_nondegenerate_dataabsoluteevaluationh) = 0) /\ (((mdr_p_nondegenerate_dataabsoluteevaluationh) = 1) /\ ((mdr_n_nondegenerate_dataabsoluteevaluationh) = 0))) \/ exists mdr_q_nondegenerate_dataabsoluteevaluationhs mdr_eb_nondegenerate_dataabsoluteevaluationhs mdr_ec_nondegenerate_dataabsoluteevaluationhs mdr_fb_nondegenerate_dataabsoluteevaluationhs mdr_fc_nondegenerate_dataabsoluteevaluationhs. (((mdr_d_nondegenerate_dataabsoluteevaluationh) = S (mdr_q_nondegenerate_dataabsoluteevaluationhs)) /\ ((forall mdr_j_nondegenerate_dataabsoluteevaluationhsc. (exists mdr_gap_nondegenerate_dataabsoluteevaluationhscj. mdr_gap_nondegenerate_dataabsoluteevaluationhscj + S (mdr_j_nondegenerate_dataabsoluteevaluationhsc) = (S (mdr_q_nondegenerate_dataabsoluteevaluationhs))) -> exists mdr_i_nondegenerate_dataabsoluteevaluationhsc mdr_up_nondegenerate_dataabsoluteevaluationhsc mdr_us_nondegenerate_dataabsoluteevaluationhsc mdr_un_nondegenerate_dataabsoluteevaluationhsc mdr_ut_nondegenerate_dataabsoluteevaluationhsc mdr_p_nondegenerate_dataabsoluteevaluationhsc mdr_n_nondegenerate_dataabsoluteevaluationhsc. ((exists mdr_gap_nondegenerate_dataabsoluteevaluationhsci. mdr_gap_nondegenerate_dataabsoluteevaluationhsci + S (mdr_i_nondegenerate_dataabsoluteevaluationhsc) = (mdr_i_nondegenerate_dataabsoluteevaluationh)) /\ ((exists mdr_z_nondegenerate_dataabsoluteevaluationhscr. ((exists mdr_a_nondegenerate_dataabsoluteevaluationhscrc mdr_b_nondegenerate_dataabsoluteevaluationhscrc mdr_c_nondegenerate_dataabsoluteevaluationhscrc mdr_e_nondegenerate_dataabsoluteevaluationhscrc mdr_f_nondegenerate_dataabsoluteevaluationhscrc. ((mdr_a_nondegenerate_dataabsoluteevaluationhscrc = ((mdr_q_nondegenerate_dataabsoluteevaluationhs) + (mdr_up_nondegenerate_dataabsoluteevaluationhsc)) * S ((mdr_q_nondegenerate_dataabsoluteevaluationhs) + (mdr_up_nondegenerate_dataabsoluteevaluationhsc)) + ((mdr_up_nondegenerate_dataabsoluteevaluationhsc) + (mdr_up_nondegenerate_dataabsoluteevaluationhsc))) /\ ((mdr_b_nondegenerate_dataabsoluteevaluationhscrc = ((mdr_us_nondegenerate_dataabsoluteevaluationhsc) + (mdr_un_nondegenerate_dataabsoluteevaluationhsc)) * S ((mdr_us_nondegenerate_dataabsoluteevaluationhsc) + (mdr_un_nondegenerate_dataabsoluteevaluationhsc)) + ((mdr_un_nondegenerate_dataabsoluteevaluationhsc) + (mdr_un_nondegenerate_dataabsoluteevaluationhsc))) /\ ((mdr_c_nondegenerate_dataabsoluteevaluationhscrc = ((mdr_a_nondegenerate_dataabsoluteevaluationhscrc) + (mdr_b_nondegenerate_dataabsoluteevaluationhscrc)) * S ((mdr_a_nondegenerate_dataabsoluteevaluationhscrc) + (mdr_b_nondegenerate_dataabsoluteevaluationhscrc)) + ((mdr_b_nondegenerate_dataabsoluteevaluationhscrc) + (mdr_b_nondegenerate_dataabsoluteevaluationhscrc))) /\ ((mdr_e_nondegenerate_dataabsoluteevaluationhscrc = ((mdr_p_nondegenerate_dataabsoluteevaluationhsc) + (mdr_n_nondegenerate_dataabsoluteevaluationhsc)) * S ((mdr_p_nondegenerate_dataabsoluteevaluationhsc) + (mdr_n_nondegenerate_dataabsoluteevaluationhsc)) + ((mdr_n_nondegenerate_dataabsoluteevaluationhsc) + (mdr_n_nondegenerate_dataabsoluteevaluationhsc))) /\ ((mdr_f_nondegenerate_dataabsoluteevaluationhscrc = ((mdr_ut_nondegenerate_dataabsoluteevaluationhsc) + (mdr_e_nondegenerate_dataabsoluteevaluationhscrc)) * S ((mdr_ut_nondegenerate_dataabsoluteevaluationhsc) + (mdr_e_nondegenerate_dataabsoluteevaluationhscrc)) + ((mdr_e_nondegenerate_dataabsoluteevaluationhscrc) + (mdr_e_nondegenerate_dataabsoluteevaluationhscrc))) /\ ((mdr_z_nondegenerate_dataabsoluteevaluationhscr) = ((mdr_c_nondegenerate_dataabsoluteevaluationhscrc) + (mdr_f_nondegenerate_dataabsoluteevaluationhscrc)) * S ((mdr_c_nondegenerate_dataabsoluteevaluationhscrc) + (mdr_f_nondegenerate_dataabsoluteevaluationhscrc)) + ((mdr_f_nondegenerate_dataabsoluteevaluationhscrc) + (mdr_f_nondegenerate_dataabsoluteevaluationhscrc))))))))) /\ (((exists ff_h_mdr_nondegenerate_dataabsoluteevaluationhscrb. ff_h_mdr_nondegenerate_dataabsoluteevaluationhscrb + S (mdr_z_nondegenerate_dataabsoluteevaluationhscr) = S ((S (mdr_i_nondegenerate_dataabsoluteevaluationhsc)) * mdr_c_nondegenerate_dataabsoluteevaluation)) /\ exists ff_q_mdr_nondegenerate_dataabsoluteevaluationhscrb. mdr_b_nondegenerate_dataabsoluteevaluation = ff_q_mdr_nondegenerate_dataabsoluteevaluationhscrb * S ((S (mdr_i_nondegenerate_dataabsoluteevaluationhsc)) * mdr_c_nondegenerate_dataabsoluteevaluation) + (mdr_z_nondegenerate_dataabsoluteevaluationhscr))))) /\ ((((forall ff_index_mdm_prefix_mdr_nondegenerate_dataabsoluteevaluationhscm_positive. (exists ff_gap_mdm_lt_mdr_nondegenerate_dataabsoluteevaluationhscm_positive_index_bound. ff_gap_mdm_lt_mdr_nondegenerate_dataabsoluteevaluationhscm_positive_index_bound + S (ff_index_mdm_prefix_mdr_nondegenerate_dataabsoluteevaluationhscm_positive) = ((mdr_q_nondegenerate_dataabsoluteevaluationhs) * (mdr_q_nondegenerate_dataabsoluteevaluationhs))) -> exists ff_row_mdm_prefix_mdr_nondegenerate_dataabsoluteevaluationhscm_positive ff_column_mdm_prefix_mdr_nondegenerate_dataabsoluteevaluationhscm_positive ff_value_mdm_prefix_mdr_nondegenerate_dataabsoluteevaluationhscm_positive. (ff_index_mdm_prefix_mdr_nondegenerate_dataabsoluteevaluationhscm_positive = (mdr_q_nondegenerate_dataabsoluteevaluationhs) * ff_row_mdm_prefix_mdr_nondegenerate_dataabsoluteevaluationhscm_positive + ff_column_mdm_prefix_mdr_nondegenerate_dataabsoluteevaluationhscm_positive /\ ((exists ff_gap_mdm_lt_mdr_nondegenerate_dataabsoluteevaluationhscm_positive_column_bound. ff_gap_mdm_lt_mdr_nondegenerate_dataabsoluteevaluationhscm_positive_column_bound + S (ff_column_mdm_prefix_mdr_nondegenerate_dataabsoluteevaluationhscm_positive) = (mdr_q_nondegenerate_dataabsoluteevaluationhs)) /\ ((exists ff_row_mdm_cell_mdr_nondegenerate_dataabsoluteevaluationhscm_positive_cell ff_column_mdm_cell_mdr_nondegenerate_dataabsoluteevaluationhscm_positive_cell. (((((exists ff_gap_mdm_lt_mdr_nondegenerate_dataabsoluteevaluationhscm_positive_cell_row_before. ff_gap_mdm_lt_mdr_nondegenerate_dataabsoluteevaluationhscm_positive_cell_row_before + S (ff_row_mdm_prefix_mdr_nondegenerate_dataabsoluteevaluationhscm_positive) = (0)) /\ ff_row_mdm_cell_mdr_nondegenerate_dataabsoluteevaluationhscm_positive_cell = ff_row_mdm_prefix_mdr_nondegenerate_dataabsoluteevaluationhscm_positive) \/ ((exists ff_gap_mdm_le_mdr_nondegenerate_dataabsoluteevaluationhscm_positive_cell_row_after. ff_gap_mdm_le_mdr_nondegenerate_dataabsoluteevaluationhscm_positive_cell_row_after + (0) = (ff_row_mdm_prefix_mdr_nondegenerate_dataabsoluteevaluationhscm_positive)) /\ ff_row_mdm_cell_mdr_nondegenerate_dataabsoluteevaluationhscm_positive_cell = S ff_row_mdm_prefix_mdr_nondegenerate_dataabsoluteevaluationhscm_positive))) /\ (((((exists ff_gap_mdm_lt_mdr_nondegenerate_dataabsoluteevaluationhscm_positive_cell_column_before. ff_gap_mdm_lt_mdr_nondegenerate_dataabsoluteevaluationhscm_positive_cell_column_before + S (ff_column_mdm_prefix_mdr_nondegenerate_dataabsoluteevaluationhscm_positive) = (mdr_j_nondegenerate_dataabsoluteevaluationhsc)) /\ ff_column_mdm_cell_mdr_nondegenerate_dataabsoluteevaluationhscm_positive_cell = ff_column_mdm_prefix_mdr_nondegenerate_dataabsoluteevaluationhscm_positive) \/ ((exists ff_gap_mdm_le_mdr_nondegenerate_dataabsoluteevaluationhscm_positive_cell_column_after. ff_gap_mdm_le_mdr_nondegenerate_dataabsoluteevaluationhscm_positive_cell_column_after + (mdr_j_nondegenerate_dataabsoluteevaluationhsc) = (ff_column_mdm_prefix_mdr_nondegenerate_dataabsoluteevaluationhscm_positive)) /\ ff_column_mdm_cell_mdr_nondegenerate_dataabsoluteevaluationhscm_positive_cell = S ff_column_mdm_prefix_mdr_nondegenerate_dataabsoluteevaluationhscm_positive))) /\ (((exists ff_h_mdm_mdr_nondegenerate_dataabsoluteevaluationhscm_positive_cell_source. ff_h_mdm_mdr_nondegenerate_dataabsoluteevaluationhscm_positive_cell_source + S (ff_value_mdm_prefix_mdr_nondegenerate_dataabsoluteevaluationhscm_positive) = S ((S ((ff_row_mdm_cell_mdr_nondegenerate_dataabsoluteevaluationhscm_positive_cell) * (S (mdr_q_nondegenerate_dataabsoluteevaluationhs)) + (ff_column_mdm_cell_mdr_nondegenerate_dataabsoluteevaluationhscm_positive_cell))) * mdr_pc_nondegenerate_dataabsoluteevaluationh)) /\ exists ff_q_mdm_mdr_nondegenerate_dataabsoluteevaluationhscm_positive_cell_source. mdr_pb_nondegenerate_dataabsoluteevaluationh = ff_q_mdm_mdr_nondegenerate_dataabsoluteevaluationhscm_positive_cell_source * S ((S ((ff_row_mdm_cell_mdr_nondegenerate_dataabsoluteevaluationhscm_positive_cell) * (S (mdr_q_nondegenerate_dataabsoluteevaluationhs)) + (ff_column_mdm_cell_mdr_nondegenerate_dataabsoluteevaluationhscm_positive_cell))) * mdr_pc_nondegenerate_dataabsoluteevaluationh) + (ff_value_mdm_prefix_mdr_nondegenerate_dataabsoluteevaluationhscm_positive)))))) /\ (((exists ff_h_mdm_mdr_nondegenerate_dataabsoluteevaluationhscm_positive_target. ff_h_mdm_mdr_nondegenerate_dataabsoluteevaluationhscm_positive_target + S (ff_value_mdm_prefix_mdr_nondegenerate_dataabsoluteevaluationhscm_positive) = S ((S (ff_index_mdm_prefix_mdr_nondegenerate_dataabsoluteevaluationhscm_positive)) * mdr_us_nondegenerate_dataabsoluteevaluationhsc)) /\ exists ff_q_mdm_mdr_nondegenerate_dataabsoluteevaluationhscm_positive_target. mdr_up_nondegenerate_dataabsoluteevaluationhsc = ff_q_mdm_mdr_nondegenerate_dataabsoluteevaluationhscm_positive_target * S ((S (ff_index_mdm_prefix_mdr_nondegenerate_dataabsoluteevaluationhscm_positive)) * mdr_us_nondegenerate_dataabsoluteevaluationhsc) + (ff_value_mdm_prefix_mdr_nondegenerate_dataabsoluteevaluationhscm_positive))))))) /\ (forall ff_index_mdm_prefix_mdr_nondegenerate_dataabsoluteevaluationhscm_negative. (exists ff_gap_mdm_lt_mdr_nondegenerate_dataabsoluteevaluationhscm_negative_index_bound. ff_gap_mdm_lt_mdr_nondegenerate_dataabsoluteevaluationhscm_negative_index_bound + S (ff_index_mdm_prefix_mdr_nondegenerate_dataabsoluteevaluationhscm_negative) = ((mdr_q_nondegenerate_dataabsoluteevaluationhs) * (mdr_q_nondegenerate_dataabsoluteevaluationhs))) -> exists ff_row_mdm_prefix_mdr_nondegenerate_dataabsoluteevaluationhscm_negative ff_column_mdm_prefix_mdr_nondegenerate_dataabsoluteevaluationhscm_negative ff_value_mdm_prefix_mdr_nondegenerate_dataabsoluteevaluationhscm_negative. (ff_index_mdm_prefix_mdr_nondegenerate_dataabsoluteevaluationhscm_negative = (mdr_q_nondegenerate_dataabsoluteevaluationhs) * ff_row_mdm_prefix_mdr_nondegenerate_dataabsoluteevaluationhscm_negative + ff_column_mdm_prefix_mdr_nondegenerate_dataabsoluteevaluationhscm_negative /\ ((exists ff_gap_mdm_lt_mdr_nondegenerate_dataabsoluteevaluationhscm_negative_column_bound. ff_gap_mdm_lt_mdr_nondegenerate_dataabsoluteevaluationhscm_negative_column_bound + S (ff_column_mdm_prefix_mdr_nondegenerate_dataabsoluteevaluationhscm_negative) = (mdr_q_nondegenerate_dataabsoluteevaluationhs)) /\ ((exists ff_row_mdm_cell_mdr_nondegenerate_dataabsoluteevaluationhscm_negative_cell ff_column_mdm_cell_mdr_nondegenerate_dataabsoluteevaluationhscm_negative_cell. (((((exists ff_gap_mdm_lt_mdr_nondegenerate_dataabsoluteevaluationhscm_negative_cell_row_before. ff_gap_mdm_lt_mdr_nondegenerate_dataabsoluteevaluationhscm_negative_cell_row_before + S (ff_row_mdm_prefix_mdr_nondegenerate_dataabsoluteevaluationhscm_negative) = (0)) /\ ff_row_mdm_cell_mdr_nondegenerate_dataabsoluteevaluationhscm_negative_cell = ff_row_mdm_prefix_mdr_nondegenerate_dataabsoluteevaluationhscm_negative) \/ ((exists ff_gap_mdm_le_mdr_nondegenerate_dataabsoluteevaluationhscm_negative_cell_row_after. ff_gap_mdm_le_mdr_nondegenerate_dataabsoluteevaluationhscm_negative_cell_row_after + (0) = (ff_row_mdm_prefix_mdr_nondegenerate_dataabsoluteevaluationhscm_negative)) /\ ff_row_mdm_cell_mdr_nondegenerate_dataabsoluteevaluationhscm_negative_cell = S ff_row_mdm_prefix_mdr_nondegenerate_dataabsoluteevaluationhscm_negative))) /\ (((((exists ff_gap_mdm_lt_mdr_nondegenerate_dataabsoluteevaluationhscm_negative_cell_column_before. ff_gap_mdm_lt_mdr_nondegenerate_dataabsoluteevaluationhscm_negative_cell_column_before + S (ff_column_mdm_prefix_mdr_nondegenerate_dataabsoluteevaluationhscm_negative) = (mdr_j_nondegenerate_dataabsoluteevaluationhsc)) /\ ff_column_mdm_cell_mdr_nondegenerate_dataabsoluteevaluationhscm_negative_cell = ff_column_mdm_prefix_mdr_nondegenerate_dataabsoluteevaluationhscm_negative) \/ ((exists ff_gap_mdm_le_mdr_nondegenerate_dataabsoluteevaluationhscm_negative_cell_column_after. ff_gap_mdm_le_mdr_nondegenerate_dataabsoluteevaluationhscm_negative_cell_column_after + (mdr_j_nondegenerate_dataabsoluteevaluationhsc) = (ff_column_mdm_prefix_mdr_nondegenerate_dataabsoluteevaluationhscm_negative)) /\ ff_column_mdm_cell_mdr_nondegenerate_dataabsoluteevaluationhscm_negative_cell = S ff_column_mdm_prefix_mdr_nondegenerate_dataabsoluteevaluationhscm_negative))) /\ (((exists ff_h_mdm_mdr_nondegenerate_dataabsoluteevaluationhscm_negative_cell_source. ff_h_mdm_mdr_nondegenerate_dataabsoluteevaluationhscm_negative_cell_source + S (ff_value_mdm_prefix_mdr_nondegenerate_dataabsoluteevaluationhscm_negative) = S ((S ((ff_row_mdm_cell_mdr_nondegenerate_dataabsoluteevaluationhscm_negative_cell) * (S (mdr_q_nondegenerate_dataabsoluteevaluationhs)) + (ff_column_mdm_cell_mdr_nondegenerate_dataabsoluteevaluationhscm_negative_cell))) * mdr_nc_nondegenerate_dataabsoluteevaluationh)) /\ exists ff_q_mdm_mdr_nondegenerate_dataabsoluteevaluationhscm_negative_cell_source. mdr_nb_nondegenerate_dataabsoluteevaluationh = ff_q_mdm_mdr_nondegenerate_dataabsoluteevaluationhscm_negative_cell_source * S ((S ((ff_row_mdm_cell_mdr_nondegenerate_dataabsoluteevaluationhscm_negative_cell) * (S (mdr_q_nondegenerate_dataabsoluteevaluationhs)) + (ff_column_mdm_cell_mdr_nondegenerate_dataabsoluteevaluationhscm_negative_cell))) * mdr_nc_nondegenerate_dataabsoluteevaluationh) + (ff_value_mdm_prefix_mdr_nondegenerate_dataabsoluteevaluationhscm_negative)))))) /\ (((exists ff_h_mdm_mdr_nondegenerate_dataabsoluteevaluationhscm_negative_target. ff_h_mdm_mdr_nondegenerate_dataabsoluteevaluationhscm_negative_target + S (ff_value_mdm_prefix_mdr_nondegenerate_dataabsoluteevaluationhscm_negative) = S ((S (ff_index_mdm_prefix_mdr_nondegenerate_dataabsoluteevaluationhscm_negative)) * mdr_ut_nondegenerate_dataabsoluteevaluationhsc)) /\ exists ff_q_mdm_mdr_nondegenerate_dataabsoluteevaluationhscm_negative_target. mdr_un_nondegenerate_dataabsoluteevaluationhsc = ff_q_mdm_mdr_nondegenerate_dataabsoluteevaluationhscm_negative_target * S ((S (ff_index_mdm_prefix_mdr_nondegenerate_dataabsoluteevaluationhscm_negative)) * mdr_ut_nondegenerate_dataabsoluteevaluationhsc) + (ff_value_mdm_prefix_mdr_nondegenerate_dataabsoluteevaluationhscm_negative))))))))) /\ ((((exists ff_h_mdr_nondegenerate_dataabsoluteevaluationhscp. ff_h_mdr_nondegenerate_dataabsoluteevaluationhscp + S (mdr_p_nondegenerate_dataabsoluteevaluationhsc) = S ((S (mdr_j_nondegenerate_dataabsoluteevaluationhsc)) * mdr_ec_nondegenerate_dataabsoluteevaluationhs)) /\ exists ff_q_mdr_nondegenerate_dataabsoluteevaluationhscp. mdr_eb_nondegenerate_dataabsoluteevaluationhs = ff_q_mdr_nondegenerate_dataabsoluteevaluationhscp * S ((S (mdr_j_nondegenerate_dataabsoluteevaluationhsc)) * mdr_ec_nondegenerate_dataabsoluteevaluationhs) + (mdr_p_nondegenerate_dataabsoluteevaluationhsc))) /\ (((exists ff_h_mdr_nondegenerate_dataabsoluteevaluationhscn. ff_h_mdr_nondegenerate_dataabsoluteevaluationhscn + S (mdr_n_nondegenerate_dataabsoluteevaluationhsc) = S ((S (mdr_j_nondegenerate_dataabsoluteevaluationhsc)) * mdr_fc_nondegenerate_dataabsoluteevaluationhs)) /\ exists ff_q_mdr_nondegenerate_dataabsoluteevaluationhscn. mdr_fb_nondegenerate_dataabsoluteevaluationhs = ff_q_mdr_nondegenerate_dataabsoluteevaluationhscn * S ((S (mdr_j_nondegenerate_dataabsoluteevaluationhsc)) * mdr_fc_nondegenerate_dataabsoluteevaluationhs) + (mdr_n_nondegenerate_dataabsoluteevaluationhsc)))))))) /\ (exists ff_ub_mce_fold_mdr_nondegenerate_dataabsoluteevaluationhsf ff_uc_mce_fold_mdr_nondegenerate_dataabsoluteevaluationhsf ff_vb_mce_fold_mdr_nondegenerate_dataabsoluteevaluationhsf ff_vc_mce_fold_mdr_nondegenerate_dataabsoluteevaluationhsf. ((forall ff_index_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix. (exists ff_gap_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix_index. ff_gap_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix_index + S (ff_index_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix) = (S (mdr_q_nondegenerate_dataabsoluteevaluationhs))) -> exists ff_ap_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix ff_an_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix ff_bp_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix ff_bn_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix ff_p_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix ff_n_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix. ((((exists ff_h_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix_ap. ff_h_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix_ap + S (ff_ap_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix) = S ((S (ff_index_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix)) * mdr_pc_nondegenerate_dataabsoluteevaluationh)) /\ exists ff_q_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix_ap. mdr_pb_nondegenerate_dataabsoluteevaluationh = ff_q_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix_ap * S ((S (ff_index_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix)) * mdr_pc_nondegenerate_dataabsoluteevaluationh) + (ff_ap_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix))) /\ ((((exists ff_h_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix_an. ff_h_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix_an + S (ff_an_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix) = S ((S (ff_index_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix)) * mdr_nc_nondegenerate_dataabsoluteevaluationh)) /\ exists ff_q_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix_an. mdr_nb_nondegenerate_dataabsoluteevaluationh = ff_q_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix_an * S ((S (ff_index_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix)) * mdr_nc_nondegenerate_dataabsoluteevaluationh) + (ff_an_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix))) /\ ((((exists ff_h_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix_bp. ff_h_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix_bp + S (ff_bp_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix) = S ((S (ff_index_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix)) * mdr_ec_nondegenerate_dataabsoluteevaluationhs)) /\ exists ff_q_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix_bp. mdr_eb_nondegenerate_dataabsoluteevaluationhs = ff_q_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix_bp * S ((S (ff_index_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix)) * mdr_ec_nondegenerate_dataabsoluteevaluationhs) + (ff_bp_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix))) /\ ((((exists ff_h_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix_bn. ff_h_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix_bn + S (ff_bn_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix) = S ((S (ff_index_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix)) * mdr_fc_nondegenerate_dataabsoluteevaluationhs)) /\ exists ff_q_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix_bn. mdr_fb_nondegenerate_dataabsoluteevaluationhs = ff_q_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix_bn * S ((S (ff_index_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix)) * mdr_fc_nondegenerate_dataabsoluteevaluationhs) + (ff_bn_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix))) /\ ((((exists ff_h_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix_positive. ff_h_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix_positive + S (ff_p_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix) = S ((S (ff_index_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix)) * ff_uc_mce_fold_mdr_nondegenerate_dataabsoluteevaluationhsf)) /\ exists ff_q_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix_positive. ff_ub_mce_fold_mdr_nondegenerate_dataabsoluteevaluationhsf = ff_q_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix_positive * S ((S (ff_index_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix)) * ff_uc_mce_fold_mdr_nondegenerate_dataabsoluteevaluationhsf) + (ff_p_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix))) /\ ((((exists ff_h_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix_negative. ff_h_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix_negative + S (ff_n_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix) = S ((S (ff_index_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix)) * ff_vc_mce_fold_mdr_nondegenerate_dataabsoluteevaluationhsf)) /\ exists ff_q_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix_negative. ff_vb_mce_fold_mdr_nondegenerate_dataabsoluteevaluationhsf = ff_q_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix_negative * S ((S (ff_index_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix)) * ff_vc_mce_fold_mdr_nondegenerate_dataabsoluteevaluationhsf) + (ff_n_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix))) /\ (((exists ff_even_mce_term_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix_term. ff_index_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix = 2 * ff_even_mce_term_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix_term) /\ (ff_p_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix = (ff_ap_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix) * (ff_bp_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix) + (ff_an_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix) * (ff_bn_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix) /\ ff_n_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix = (ff_ap_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix) * (ff_bn_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix) + (ff_an_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix) * (ff_bp_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix))) \/ ((exists ff_odd_mce_term_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix_term. ff_index_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix = 2 * ff_odd_mce_term_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix_term + 1) /\ (ff_p_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix = (ff_ap_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix) * (ff_bn_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix) + (ff_an_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix) * (ff_bp_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix) /\ ff_n_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix = (ff_ap_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix) * (ff_bp_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix) + (ff_an_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix) * (ff_bn_mce_alternating_mdr_nondegenerate_dataabsoluteevaluationhsf_prefix))))))))))) /\ ((exists ff_u_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive ff_v_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive. ((((exists ff_h_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive_start. ff_h_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive_start + S (0) = S ((S (0)) * ff_v_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive)) /\ exists ff_q_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive_start. ff_u_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive = ff_q_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive_start * S ((S (0)) * ff_v_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive) + (0))) /\ ((((exists ff_h_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive_terminal. ff_h_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive_terminal + S (mdr_p_nondegenerate_dataabsoluteevaluationh) = S ((S ((S (mdr_q_nondegenerate_dataabsoluteevaluationhs)))) * ff_v_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive)) /\ exists ff_q_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive_terminal. ff_u_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive = ff_q_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive_terminal * S ((S ((S (mdr_q_nondegenerate_dataabsoluteevaluationhs)))) * ff_v_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive) + (mdr_p_nondegenerate_dataabsoluteevaluationh))) /\ forall ff_i_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive. (exists ff_lt_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive_bound. ff_lt_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive_bound + S ff_i_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive = (S (mdr_q_nondegenerate_dataabsoluteevaluationhs))) -> exists ff_a_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive ff_r_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive ff_s_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive. ((((exists ff_h_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive_summand. ff_h_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive_summand + S (ff_a_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive) = S ((S (ff_i_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive)) * ff_uc_mce_fold_mdr_nondegenerate_dataabsoluteevaluationhsf)) /\ exists ff_q_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive_summand. ff_ub_mce_fold_mdr_nondegenerate_dataabsoluteevaluationhsf = ff_q_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive_summand * S ((S (ff_i_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive)) * ff_uc_mce_fold_mdr_nondegenerate_dataabsoluteevaluationhsf) + (ff_a_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive))) /\ ((((exists ff_h_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive_partial. ff_h_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive_partial + S (ff_r_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive) = S ((S (ff_i_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive)) * ff_v_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive)) /\ exists ff_q_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive_partial. ff_u_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive = ff_q_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive_partial * S ((S (ff_i_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive)) * ff_v_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive) + (ff_r_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive))) /\ ((((exists ff_h_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive_successor. ff_h_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive_successor + S (ff_s_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive) = S ((S (S ff_i_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive)) * ff_v_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive)) /\ exists ff_q_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive_successor. ff_u_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive = ff_q_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive_successor * S ((S (S ff_i_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive)) * ff_v_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive) + (ff_s_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive))) /\ ff_s_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive = ff_r_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive + ff_a_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_positive)))))) /\ (exists ff_u_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative ff_v_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative. ((((exists ff_h_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative_start. ff_h_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative_start + S (0) = S ((S (0)) * ff_v_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative)) /\ exists ff_q_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative_start. ff_u_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative = ff_q_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative_start * S ((S (0)) * ff_v_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative) + (0))) /\ ((((exists ff_h_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative_terminal. ff_h_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative_terminal + S (mdr_n_nondegenerate_dataabsoluteevaluationh) = S ((S ((S (mdr_q_nondegenerate_dataabsoluteevaluationhs)))) * ff_v_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative)) /\ exists ff_q_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative_terminal. ff_u_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative = ff_q_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative_terminal * S ((S ((S (mdr_q_nondegenerate_dataabsoluteevaluationhs)))) * ff_v_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative) + (mdr_n_nondegenerate_dataabsoluteevaluationh))) /\ forall ff_i_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative. (exists ff_lt_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative_bound. ff_lt_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative_bound + S ff_i_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative = (S (mdr_q_nondegenerate_dataabsoluteevaluationhs))) -> exists ff_a_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative ff_r_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative ff_s_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative. ((((exists ff_h_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative_summand. ff_h_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative_summand + S (ff_a_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative) = S ((S (ff_i_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative)) * ff_vc_mce_fold_mdr_nondegenerate_dataabsoluteevaluationhsf)) /\ exists ff_q_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative_summand. ff_vb_mce_fold_mdr_nondegenerate_dataabsoluteevaluationhsf = ff_q_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative_summand * S ((S (ff_i_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative)) * ff_vc_mce_fold_mdr_nondegenerate_dataabsoluteevaluationhsf) + (ff_a_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative))) /\ ((((exists ff_h_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative_partial. ff_h_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative_partial + S (ff_r_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative) = S ((S (ff_i_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative)) * ff_v_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative)) /\ exists ff_q_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative_partial. ff_u_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative = ff_q_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative_partial * S ((S (ff_i_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative)) * ff_v_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative) + (ff_r_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative))) /\ ((((exists ff_h_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative_successor. ff_h_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative_successor + S (ff_s_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative) = S ((S (S ff_i_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative)) * ff_v_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative)) /\ exists ff_q_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative_successor. ff_u_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative = ff_q_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative_successor * S ((S (S ff_i_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative)) * ff_v_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative) + (ff_s_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative))) /\ ff_s_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative = ff_r_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative + ff_a_mce_mdr_nondegenerate_dataabsoluteevaluationhsf_negative))))))))))))))) /\ ((exists mdr_gap_nondegenerate_dataabsoluteevaluationi. mdr_gap_nondegenerate_dataabsoluteevaluationi + S (mdr_i_nondegenerate_dataabsoluteevaluation) = (mdr_l_nondegenerate_dataabsoluteevaluation)) /\ (exists mdr_z_nondegenerate_dataabsoluteevaluationr. ((exists mdr_a_nondegenerate_dataabsoluteevaluationrc mdr_b_nondegenerate_dataabsoluteevaluationrc mdr_c_nondegenerate_dataabsoluteevaluationrc mdr_e_nondegenerate_dataabsoluteevaluationrc mdr_f_nondegenerate_dataabsoluteevaluationrc. ((mdr_a_nondegenerate_dataabsoluteevaluationrc = ((d) + (ab)) * S ((d) + (ab)) + ((ab) + (ab))) /\ ((mdr_b_nondegenerate_dataabsoluteevaluationrc = ((ac) + (bb)) * S ((ac) + (bb)) + ((bb) + (bb))) /\ ((mdr_c_nondegenerate_dataabsoluteevaluationrc = ((mdr_a_nondegenerate_dataabsoluteevaluationrc) + (mdr_b_nondegenerate_dataabsoluteevaluationrc)) * S ((mdr_a_nondegenerate_dataabsoluteevaluationrc) + (mdr_b_nondegenerate_dataabsoluteevaluationrc)) + ((mdr_b_nondegenerate_dataabsoluteevaluationrc) + (mdr_b_nondegenerate_dataabsoluteevaluationrc))) /\ ((mdr_e_nondegenerate_dataabsoluteevaluationrc = ((mdr_p_nondegenerate_dataabsolute) + (mdr_n_nondegenerate_dataabsolute)) * S ((mdr_p_nondegenerate_dataabsolute) + (mdr_n_nondegenerate_dataabsolute)) + ((mdr_n_nondegenerate_dataabsolute) + (mdr_n_nondegenerate_dataabsolute))) /\ ((mdr_f_nondegenerate_dataabsoluteevaluationrc = ((bc) + (mdr_e_nondegenerate_dataabsoluteevaluationrc)) * S ((bc) + (mdr_e_nondegenerate_dataabsoluteevaluationrc)) + ((mdr_e_nondegenerate_dataabsoluteevaluationrc) + (mdr_e_nondegenerate_dataabsoluteevaluationrc))) /\ ((mdr_z_nondegenerate_dataabsoluteevaluationr) = ((mdr_c_nondegenerate_dataabsoluteevaluationrc) + (mdr_f_nondegenerate_dataabsoluteevaluationrc)) * S ((mdr_c_nondegenerate_dataabsoluteevaluationrc) + (mdr_f_nondegenerate_dataabsoluteevaluationrc)) + ((mdr_f_nondegenerate_dataabsoluteevaluationrc) + (mdr_f_nondegenerate_dataabsoluteevaluationrc))))))))) /\ (((exists ff_h_mdr_nondegenerate_dataabsoluteevaluationrb. ff_h_mdr_nondegenerate_dataabsoluteevaluationrb + S (mdr_z_nondegenerate_dataabsoluteevaluationr) = S ((S (mdr_i_nondegenerate_dataabsoluteevaluation)) * mdr_c_nondegenerate_dataabsoluteevaluation)) /\ exists ff_q_mdr_nondegenerate_dataabsoluteevaluationrb. mdr_b_nondegenerate_dataabsoluteevaluation = ff_q_mdr_nondegenerate_dataabsoluteevaluationrb * S ((S (mdr_i_nondegenerate_dataabsoluteevaluation)) * mdr_c_nondegenerate_dataabsoluteevaluation) + (mdr_z_nondegenerate_dataabsoluteevaluationr)))))))) /\ (((mdr_p_nondegenerate_dataabsolute) = (mdr_n_nondegenerate_dataabsolute) + (D)) \/ ((mdr_n_nondegenerate_dataabsolute) = (mdr_p_nondegenerate_dataabsolute) + (D))))))))