prime_exponent_entries_restore_prime_power

Exact expanded first-order arithmetic statement

forall n u p k P pb pc eb ec vb vc l. (~((p) = 1) /\ forall pvs_left_restore_domain pvs_right_restore_domain. (p) = pvs_left_restore_domain * pvs_right_restore_domain -> pvs_left_restore_domain = 1 \/ pvs_right_restore_domain = 1) -> ~(u = 0) -> n = P * u -> (exists pa_b_pvs_restore_power pa_c_pvs_restore_power. ((forall pa_i_pvs_restore_power_repeat. (exists pa_lt_pvs_restore_power_repeat_bound. pa_lt_pvs_restore_power_repeat_bound + S pa_i_pvs_restore_power_repeat = k) -> (((exists pa_h_pvs_restore_power_repeat_decoded. pa_h_pvs_restore_power_repeat_decoded + S (p) = S ((S (pa_i_pvs_restore_power_repeat)) * pa_c_pvs_restore_power)) /\ exists pa_q_pvs_restore_power_repeat_decoded. pa_b_pvs_restore_power = pa_q_pvs_restore_power_repeat_decoded * S ((S (pa_i_pvs_restore_power_repeat)) * pa_c_pvs_restore_power) + (p)))) /\ (exists pa_u_pvs_restore_power_product pa_v_pvs_restore_power_product. ((((exists pa_h_pvs_restore_power_product_start. pa_h_pvs_restore_power_product_start + S (1) = S ((S (0)) * pa_v_pvs_restore_power_product)) /\ exists pa_q_pvs_restore_power_product_start. pa_u_pvs_restore_power_product = pa_q_pvs_restore_power_product_start * S ((S (0)) * pa_v_pvs_restore_power_product) + (1))) /\ ((((exists pa_h_pvs_restore_power_product_terminal. pa_h_pvs_restore_power_product_terminal + S (P) = S ((S (k)) * pa_v_pvs_restore_power_product)) /\ exists pa_q_pvs_restore_power_product_terminal. pa_u_pvs_restore_power_product = pa_q_pvs_restore_power_product_terminal * S ((S (k)) * pa_v_pvs_restore_power_product) + (P))) /\ forall pa_i_pvs_restore_power_product. (exists pa_lt_pvs_restore_power_product_bound. pa_lt_pvs_restore_power_product_bound + S pa_i_pvs_restore_power_product = k) -> exists pa_p_pvs_restore_power_product pa_r_pvs_restore_power_product pa_s_pvs_restore_power_product. ((((exists pa_h_pvs_restore_power_product_factor. pa_h_pvs_restore_power_product_factor + S (pa_p_pvs_restore_power_product) = S ((S (pa_i_pvs_restore_power_product)) * pa_c_pvs_restore_power)) /\ exists pa_q_pvs_restore_power_product_factor. pa_b_pvs_restore_power = pa_q_pvs_restore_power_product_factor * S ((S (pa_i_pvs_restore_power_product)) * pa_c_pvs_restore_power) + (pa_p_pvs_restore_power_product))) /\ ((((exists pa_h_pvs_restore_power_product_partial. pa_h_pvs_restore_power_product_partial + S (pa_r_pvs_restore_power_product) = S ((S (pa_i_pvs_restore_power_product)) * pa_v_pvs_restore_power_product)) /\ exists pa_q_pvs_restore_power_product_partial. pa_u_pvs_restore_power_product = pa_q_pvs_restore_power_product_partial * S ((S (pa_i_pvs_restore_power_product)) * pa_v_pvs_restore_power_product) + (pa_r_pvs_restore_power_product))) /\ ((((exists pa_h_pvs_restore_power_product_successor. pa_h_pvs_restore_power_product_successor + S (pa_s_pvs_restore_power_product) = S ((S (S pa_i_pvs_restore_power_product)) * pa_v_pvs_restore_power_product)) /\ exists pa_q_pvs_restore_power_product_successor. pa_u_pvs_restore_power_product = pa_q_pvs_restore_power_product_successor * S ((S (S pa_i_pvs_restore_power_product)) * pa_v_pvs_restore_power_product) + (pa_s_pvs_restore_power_product))) /\ pa_s_pvs_restore_power_product = pa_r_pvs_restore_power_product * pa_p_pvs_restore_power_product)))))))) -> ~(exists pvs_factor_restore_fresh. (u) = (p) * pvs_factor_restore_fresh) -> (forall pvs_index_restore_source. (exists pvs_gap_restore_sourceindex. pvs_gap_restore_sourceindex + S (pvs_index_restore_source) = (l)) -> exists pvs_prime_restore_source pvs_exponent_restore_source pvs_power_restore_source. (((((exists ff_h_pvs_restore_sourceprime. ff_h_pvs_restore_sourceprime + S (pvs_prime_restore_source) = S ((S (pvs_index_restore_source)) * pc)) /\ exists ff_q_pvs_restore_sourceprime. pb = ff_q_pvs_restore_sourceprime * S ((S (pvs_index_restore_source)) * pc) + (pvs_prime_restore_source))) /\ (((((exists ff_h_pvs_restore_sourceexponent. ff_h_pvs_restore_sourceexponent + S (pvs_exponent_restore_source) = S ((S (pvs_index_restore_source)) * ec)) /\ exists ff_q_pvs_restore_sourceexponent. eb = ff_q_pvs_restore_sourceexponent * S ((S (pvs_index_restore_source)) * ec) + (pvs_exponent_restore_source))) /\ (((((exists ff_h_pvs_restore_sourcepower. ff_h_pvs_restore_sourcepower + S (pvs_power_restore_source) = S ((S (pvs_index_restore_source)) * vc)) /\ exists ff_q_pvs_restore_sourcepower. vb = ff_q_pvs_restore_sourcepower * S ((S (pvs_index_restore_source)) * vc) + (pvs_power_restore_source))) /\ (((~((pvs_prime_restore_source) = 1) /\ forall pvs_left_restore_sourcedomain pvs_right_restore_sourcedomain. (pvs_prime_restore_source) = pvs_left_restore_sourcedomain * pvs_right_restore_sourcedomain -> pvs_left_restore_sourcedomain = 1 \/ pvs_right_restore_sourcedomain = 1) /\ (((~(pvs_exponent_restore_source = 0)) /\ (((((exists bpd_gap_pvs_restore_sourcevaluation_selected_bound. bpd_gap_pvs_restore_sourcevaluation_selected_bound + (pvs_exponent_restore_source) = (u)) /\ (exists bpvi_result_pvs_restore_sourcevaluation_selected. ((exists bpvi_b_pvs_restore_sourcevaluation_selected_power bpvi_c_pvs_restore_sourcevaluation_selected_power. ((forall bpvi_i_pvs_restore_sourcevaluation_selected_power. (exists bpvi_repeat_gap_pvs_restore_sourcevaluation_selected_power. bpvi_repeat_gap_pvs_restore_sourcevaluation_selected_power + S bpvi_i_pvs_restore_sourcevaluation_selected_power = pvs_exponent_restore_source) -> (((exists bpvi_h_pvs_restore_sourcevaluation_selected_power_repeat. bpvi_h_pvs_restore_sourcevaluation_selected_power_repeat + S (pvs_prime_restore_source) = S ((S (bpvi_i_pvs_restore_sourcevaluation_selected_power)) * bpvi_c_pvs_restore_sourcevaluation_selected_power)) /\ exists bpvi_q_pvs_restore_sourcevaluation_selected_power_repeat. bpvi_b_pvs_restore_sourcevaluation_selected_power = bpvi_q_pvs_restore_sourcevaluation_selected_power_repeat * S ((S (bpvi_i_pvs_restore_sourcevaluation_selected_power)) * bpvi_c_pvs_restore_sourcevaluation_selected_power) + (pvs_prime_restore_source)))) /\ (exists bpvi_u_pvs_restore_sourcevaluation_selected_power bpvi_v_pvs_restore_sourcevaluation_selected_power. ((((exists bpvi_h_pvs_restore_sourcevaluation_selected_power_start. bpvi_h_pvs_restore_sourcevaluation_selected_power_start + S (1) = S ((S (0)) * bpvi_v_pvs_restore_sourcevaluation_selected_power)) /\ exists bpvi_q_pvs_restore_sourcevaluation_selected_power_start. bpvi_u_pvs_restore_sourcevaluation_selected_power = bpvi_q_pvs_restore_sourcevaluation_selected_power_start * S ((S (0)) * bpvi_v_pvs_restore_sourcevaluation_selected_power) + (1))) /\ ((((exists bpvi_h_pvs_restore_sourcevaluation_selected_power_terminal. bpvi_h_pvs_restore_sourcevaluation_selected_power_terminal + S (bpvi_result_pvs_restore_sourcevaluation_selected) = S ((S (pvs_exponent_restore_source)) * bpvi_v_pvs_restore_sourcevaluation_selected_power)) /\ exists bpvi_q_pvs_restore_sourcevaluation_selected_power_terminal. bpvi_u_pvs_restore_sourcevaluation_selected_power = bpvi_q_pvs_restore_sourcevaluation_selected_power_terminal * S ((S (pvs_exponent_restore_source)) * bpvi_v_pvs_restore_sourcevaluation_selected_power) + (bpvi_result_pvs_restore_sourcevaluation_selected))) /\ forall bpvi_j_pvs_restore_sourcevaluation_selected_power. (exists bpvi_product_gap_pvs_restore_sourcevaluation_selected_power. bpvi_product_gap_pvs_restore_sourcevaluation_selected_power + S bpvi_j_pvs_restore_sourcevaluation_selected_power = pvs_exponent_restore_source) -> exists bpvi_factor_pvs_restore_sourcevaluation_selected_power bpvi_partial_pvs_restore_sourcevaluation_selected_power bpvi_successor_pvs_restore_sourcevaluation_selected_power. ((((exists bpvi_h_pvs_restore_sourcevaluation_selected_power_factor. bpvi_h_pvs_restore_sourcevaluation_selected_power_factor + S (bpvi_factor_pvs_restore_sourcevaluation_selected_power) = S ((S (bpvi_j_pvs_restore_sourcevaluation_selected_power)) * bpvi_c_pvs_restore_sourcevaluation_selected_power)) /\ exists bpvi_q_pvs_restore_sourcevaluation_selected_power_factor. bpvi_b_pvs_restore_sourcevaluation_selected_power = bpvi_q_pvs_restore_sourcevaluation_selected_power_factor * S ((S (bpvi_j_pvs_restore_sourcevaluation_selected_power)) * bpvi_c_pvs_restore_sourcevaluation_selected_power) + (bpvi_factor_pvs_restore_sourcevaluation_selected_power))) /\ ((((exists bpvi_h_pvs_restore_sourcevaluation_selected_power_partial. bpvi_h_pvs_restore_sourcevaluation_selected_power_partial + S (bpvi_partial_pvs_restore_sourcevaluation_selected_power) = S ((S (bpvi_j_pvs_restore_sourcevaluation_selected_power)) * bpvi_v_pvs_restore_sourcevaluation_selected_power)) /\ exists bpvi_q_pvs_restore_sourcevaluation_selected_power_partial. bpvi_u_pvs_restore_sourcevaluation_selected_power = bpvi_q_pvs_restore_sourcevaluation_selected_power_partial * S ((S (bpvi_j_pvs_restore_sourcevaluation_selected_power)) * bpvi_v_pvs_restore_sourcevaluation_selected_power) + (bpvi_partial_pvs_restore_sourcevaluation_selected_power))) /\ ((((exists bpvi_h_pvs_restore_sourcevaluation_selected_power_successor. bpvi_h_pvs_restore_sourcevaluation_selected_power_successor + S (bpvi_successor_pvs_restore_sourcevaluation_selected_power) = S ((S (S bpvi_j_pvs_restore_sourcevaluation_selected_power)) * bpvi_v_pvs_restore_sourcevaluation_selected_power)) /\ exists bpvi_q_pvs_restore_sourcevaluation_selected_power_successor. bpvi_u_pvs_restore_sourcevaluation_selected_power = bpvi_q_pvs_restore_sourcevaluation_selected_power_successor * S ((S (S bpvi_j_pvs_restore_sourcevaluation_selected_power)) * bpvi_v_pvs_restore_sourcevaluation_selected_power) + (bpvi_successor_pvs_restore_sourcevaluation_selected_power))) /\ bpvi_successor_pvs_restore_sourcevaluation_selected_power = bpvi_partial_pvs_restore_sourcevaluation_selected_power * bpvi_factor_pvs_restore_sourcevaluation_selected_power)))))))) /\ exists bpvi_divisor_factor_pvs_restore_sourcevaluation_selected. u = bpvi_result_pvs_restore_sourcevaluation_selected * bpvi_divisor_factor_pvs_restore_sourcevaluation_selected))) /\ forall bpd_candidate_pvs_restore_sourcevaluation. (exists bpd_gap_pvs_restore_sourcevaluation_candidate_bound. bpd_gap_pvs_restore_sourcevaluation_candidate_bound + (bpd_candidate_pvs_restore_sourcevaluation) = (u)) -> (exists bpvi_result_pvs_restore_sourcevaluation_candidate. ((exists bpvi_b_pvs_restore_sourcevaluation_candidate_power bpvi_c_pvs_restore_sourcevaluation_candidate_power. ((forall bpvi_i_pvs_restore_sourcevaluation_candidate_power. (exists bpvi_repeat_gap_pvs_restore_sourcevaluation_candidate_power. bpvi_repeat_gap_pvs_restore_sourcevaluation_candidate_power + S bpvi_i_pvs_restore_sourcevaluation_candidate_power = bpd_candidate_pvs_restore_sourcevaluation) -> (((exists bpvi_h_pvs_restore_sourcevaluation_candidate_power_repeat. bpvi_h_pvs_restore_sourcevaluation_candidate_power_repeat + S (pvs_prime_restore_source) = S ((S (bpvi_i_pvs_restore_sourcevaluation_candidate_power)) * bpvi_c_pvs_restore_sourcevaluation_candidate_power)) /\ exists bpvi_q_pvs_restore_sourcevaluation_candidate_power_repeat. bpvi_b_pvs_restore_sourcevaluation_candidate_power = bpvi_q_pvs_restore_sourcevaluation_candidate_power_repeat * S ((S (bpvi_i_pvs_restore_sourcevaluation_candidate_power)) * bpvi_c_pvs_restore_sourcevaluation_candidate_power) + (pvs_prime_restore_source)))) /\ (exists bpvi_u_pvs_restore_sourcevaluation_candidate_power bpvi_v_pvs_restore_sourcevaluation_candidate_power. ((((exists bpvi_h_pvs_restore_sourcevaluation_candidate_power_start. bpvi_h_pvs_restore_sourcevaluation_candidate_power_start + S (1) = S ((S (0)) * bpvi_v_pvs_restore_sourcevaluation_candidate_power)) /\ exists bpvi_q_pvs_restore_sourcevaluation_candidate_power_start. bpvi_u_pvs_restore_sourcevaluation_candidate_power = bpvi_q_pvs_restore_sourcevaluation_candidate_power_start * S ((S (0)) * bpvi_v_pvs_restore_sourcevaluation_candidate_power) + (1))) /\ ((((exists bpvi_h_pvs_restore_sourcevaluation_candidate_power_terminal. bpvi_h_pvs_restore_sourcevaluation_candidate_power_terminal + S (bpvi_result_pvs_restore_sourcevaluation_candidate) = S ((S (bpd_candidate_pvs_restore_sourcevaluation)) * bpvi_v_pvs_restore_sourcevaluation_candidate_power)) /\ exists bpvi_q_pvs_restore_sourcevaluation_candidate_power_terminal. bpvi_u_pvs_restore_sourcevaluation_candidate_power = bpvi_q_pvs_restore_sourcevaluation_candidate_power_terminal * S ((S (bpd_candidate_pvs_restore_sourcevaluation)) * bpvi_v_pvs_restore_sourcevaluation_candidate_power) + (bpvi_result_pvs_restore_sourcevaluation_candidate))) /\ forall bpvi_j_pvs_restore_sourcevaluation_candidate_power. (exists bpvi_product_gap_pvs_restore_sourcevaluation_candidate_power. bpvi_product_gap_pvs_restore_sourcevaluation_candidate_power + S bpvi_j_pvs_restore_sourcevaluation_candidate_power = bpd_candidate_pvs_restore_sourcevaluation) -> exists bpvi_factor_pvs_restore_sourcevaluation_candidate_power bpvi_partial_pvs_restore_sourcevaluation_candidate_power bpvi_successor_pvs_restore_sourcevaluation_candidate_power. ((((exists bpvi_h_pvs_restore_sourcevaluation_candidate_power_factor. bpvi_h_pvs_restore_sourcevaluation_candidate_power_factor + S (bpvi_factor_pvs_restore_sourcevaluation_candidate_power) = S ((S (bpvi_j_pvs_restore_sourcevaluation_candidate_power)) * bpvi_c_pvs_restore_sourcevaluation_candidate_power)) /\ exists bpvi_q_pvs_restore_sourcevaluation_candidate_power_factor. bpvi_b_pvs_restore_sourcevaluation_candidate_power = bpvi_q_pvs_restore_sourcevaluation_candidate_power_factor * S ((S (bpvi_j_pvs_restore_sourcevaluation_candidate_power)) * bpvi_c_pvs_restore_sourcevaluation_candidate_power) + (bpvi_factor_pvs_restore_sourcevaluation_candidate_power))) /\ ((((exists bpvi_h_pvs_restore_sourcevaluation_candidate_power_partial. bpvi_h_pvs_restore_sourcevaluation_candidate_power_partial + S (bpvi_partial_pvs_restore_sourcevaluation_candidate_power) = S ((S (bpvi_j_pvs_restore_sourcevaluation_candidate_power)) * bpvi_v_pvs_restore_sourcevaluation_candidate_power)) /\ exists bpvi_q_pvs_restore_sourcevaluation_candidate_power_partial. bpvi_u_pvs_restore_sourcevaluation_candidate_power = bpvi_q_pvs_restore_sourcevaluation_candidate_power_partial * S ((S (bpvi_j_pvs_restore_sourcevaluation_candidate_power)) * bpvi_v_pvs_restore_sourcevaluation_candidate_power) + (bpvi_partial_pvs_restore_sourcevaluation_candidate_power))) /\ ((((exists bpvi_h_pvs_restore_sourcevaluation_candidate_power_successor. bpvi_h_pvs_restore_sourcevaluation_candidate_power_successor + S (bpvi_successor_pvs_restore_sourcevaluation_candidate_power) = S ((S (S bpvi_j_pvs_restore_sourcevaluation_candidate_power)) * bpvi_v_pvs_restore_sourcevaluation_candidate_power)) /\ exists bpvi_q_pvs_restore_sourcevaluation_candidate_power_successor. bpvi_u_pvs_restore_sourcevaluation_candidate_power = bpvi_q_pvs_restore_sourcevaluation_candidate_power_successor * S ((S (S bpvi_j_pvs_restore_sourcevaluation_candidate_power)) * bpvi_v_pvs_restore_sourcevaluation_candidate_power) + (bpvi_successor_pvs_restore_sourcevaluation_candidate_power))) /\ bpvi_successor_pvs_restore_sourcevaluation_candidate_power = bpvi_partial_pvs_restore_sourcevaluation_candidate_power * bpvi_factor_pvs_restore_sourcevaluation_candidate_power)))))))) /\ exists bpvi_divisor_factor_pvs_restore_sourcevaluation_candidate. u = bpvi_result_pvs_restore_sourcevaluation_candidate * bpvi_divisor_factor_pvs_restore_sourcevaluation_candidate)) -> (exists bpd_gap_pvs_restore_sourcevaluation_maximal. bpd_gap_pvs_restore_sourcevaluation_maximal + (bpd_candidate_pvs_restore_sourcevaluation) = (pvs_exponent_restore_source))) /\ (exists pa_b_pvs_restore_sourcevalue pa_c_pvs_restore_sourcevalue. ((forall pa_i_pvs_restore_sourcevalue_repeat. (exists pa_lt_pvs_restore_sourcevalue_repeat_bound. pa_lt_pvs_restore_sourcevalue_repeat_bound + S pa_i_pvs_restore_sourcevalue_repeat = pvs_exponent_restore_source) -> (((exists pa_h_pvs_restore_sourcevalue_repeat_decoded. pa_h_pvs_restore_sourcevalue_repeat_decoded + S (pvs_prime_restore_source) = S ((S (pa_i_pvs_restore_sourcevalue_repeat)) * pa_c_pvs_restore_sourcevalue)) /\ exists pa_q_pvs_restore_sourcevalue_repeat_decoded. pa_b_pvs_restore_sourcevalue = pa_q_pvs_restore_sourcevalue_repeat_decoded * S ((S (pa_i_pvs_restore_sourcevalue_repeat)) * pa_c_pvs_restore_sourcevalue) + (pvs_prime_restore_source)))) /\ (exists pa_u_pvs_restore_sourcevalue_product pa_v_pvs_restore_sourcevalue_product. ((((exists pa_h_pvs_restore_sourcevalue_product_start. pa_h_pvs_restore_sourcevalue_product_start + S (1) = S ((S (0)) * pa_v_pvs_restore_sourcevalue_product)) /\ exists pa_q_pvs_restore_sourcevalue_product_start. pa_u_pvs_restore_sourcevalue_product = pa_q_pvs_restore_sourcevalue_product_start * S ((S (0)) * pa_v_pvs_restore_sourcevalue_product) + (1))) /\ ((((exists pa_h_pvs_restore_sourcevalue_product_terminal. pa_h_pvs_restore_sourcevalue_product_terminal + S (pvs_power_restore_source) = S ((S (pvs_exponent_restore_source)) * pa_v_pvs_restore_sourcevalue_product)) /\ exists pa_q_pvs_restore_sourcevalue_product_terminal. pa_u_pvs_restore_sourcevalue_product = pa_q_pvs_restore_sourcevalue_product_terminal * S ((S (pvs_exponent_restore_source)) * pa_v_pvs_restore_sourcevalue_product) + (pvs_power_restore_source))) /\ forall pa_i_pvs_restore_sourcevalue_product. (exists pa_lt_pvs_restore_sourcevalue_product_bound. pa_lt_pvs_restore_sourcevalue_product_bound + S pa_i_pvs_restore_sourcevalue_product = pvs_exponent_restore_source) -> exists pa_p_pvs_restore_sourcevalue_product pa_r_pvs_restore_sourcevalue_product pa_s_pvs_restore_sourcevalue_product. ((((exists pa_h_pvs_restore_sourcevalue_product_factor. pa_h_pvs_restore_sourcevalue_product_factor + S (pa_p_pvs_restore_sourcevalue_product) = S ((S (pa_i_pvs_restore_sourcevalue_product)) * pa_c_pvs_restore_sourcevalue)) /\ exists pa_q_pvs_restore_sourcevalue_product_factor. pa_b_pvs_restore_sourcevalue = pa_q_pvs_restore_sourcevalue_product_factor * S ((S (pa_i_pvs_restore_sourcevalue_product)) * pa_c_pvs_restore_sourcevalue) + (pa_p_pvs_restore_sourcevalue_product))) /\ ((((exists pa_h_pvs_restore_sourcevalue_product_partial. pa_h_pvs_restore_sourcevalue_product_partial + S (pa_r_pvs_restore_sourcevalue_product) = S ((S (pa_i_pvs_restore_sourcevalue_product)) * pa_v_pvs_restore_sourcevalue_product)) /\ exists pa_q_pvs_restore_sourcevalue_product_partial. pa_u_pvs_restore_sourcevalue_product = pa_q_pvs_restore_sourcevalue_product_partial * S ((S (pa_i_pvs_restore_sourcevalue_product)) * pa_v_pvs_restore_sourcevalue_product) + (pa_r_pvs_restore_sourcevalue_product))) /\ ((((exists pa_h_pvs_restore_sourcevalue_product_successor. pa_h_pvs_restore_sourcevalue_product_successor + S (pa_s_pvs_restore_sourcevalue_product) = S ((S (S pa_i_pvs_restore_sourcevalue_product)) * pa_v_pvs_restore_sourcevalue_product)) /\ exists pa_q_pvs_restore_sourcevalue_product_successor. pa_u_pvs_restore_sourcevalue_product = pa_q_pvs_restore_sourcevalue_product_successor * S ((S (S pa_i_pvs_restore_sourcevalue_product)) * pa_v_pvs_restore_sourcevalue_product) + (pa_s_pvs_restore_sourcevalue_product))) /\ pa_s_pvs_restore_sourcevalue_product = pa_r_pvs_restore_sourcevalue_product * pa_p_pvs_restore_sourcevalue_product))))))))))))))))))))) -> (forall pvs_index_restore_target. (exists pvs_gap_restore_targetindex. pvs_gap_restore_targetindex + S (pvs_index_restore_target) = (l)) -> exists pvs_prime_restore_target pvs_exponent_restore_target pvs_power_restore_target. (((((exists ff_h_pvs_restore_targetprime. ff_h_pvs_restore_targetprime + S (pvs_prime_restore_target) = S ((S (pvs_index_restore_target)) * pc)) /\ exists ff_q_pvs_restore_targetprime. pb = ff_q_pvs_restore_targetprime * S ((S (pvs_index_restore_target)) * pc) + (pvs_prime_restore_target))) /\ (((((exists ff_h_pvs_restore_targetexponent. ff_h_pvs_restore_targetexponent + S (pvs_exponent_restore_target) = S ((S (pvs_index_restore_target)) * ec)) /\ exists ff_q_pvs_restore_targetexponent. eb = ff_q_pvs_restore_targetexponent * S ((S (pvs_index_restore_target)) * ec) + (pvs_exponent_restore_target))) /\ (((((exists ff_h_pvs_restore_targetpower. ff_h_pvs_restore_targetpower + S (pvs_power_restore_target) = S ((S (pvs_index_restore_target)) * vc)) /\ exists ff_q_pvs_restore_targetpower. vb = ff_q_pvs_restore_targetpower * S ((S (pvs_index_restore_target)) * vc) + (pvs_power_restore_target))) /\ (((~((pvs_prime_restore_target) = 1) /\ forall pvs_left_restore_targetdomain pvs_right_restore_targetdomain. (pvs_prime_restore_target) = pvs_left_restore_targetdomain * pvs_right_restore_targetdomain -> pvs_left_restore_targetdomain = 1 \/ pvs_right_restore_targetdomain = 1) /\ (((~(pvs_exponent_restore_target = 0)) /\ (((((exists bpd_gap_pvs_restore_targetvaluation_selected_bound. bpd_gap_pvs_restore_targetvaluation_selected_bound + (pvs_exponent_restore_target) = (n)) /\ (exists bpvi_result_pvs_restore_targetvaluation_selected. ((exists bpvi_b_pvs_restore_targetvaluation_selected_power bpvi_c_pvs_restore_targetvaluation_selected_power. ((forall bpvi_i_pvs_restore_targetvaluation_selected_power. (exists bpvi_repeat_gap_pvs_restore_targetvaluation_selected_power. bpvi_repeat_gap_pvs_restore_targetvaluation_selected_power + S bpvi_i_pvs_restore_targetvaluation_selected_power = pvs_exponent_restore_target) -> (((exists bpvi_h_pvs_restore_targetvaluation_selected_power_repeat. bpvi_h_pvs_restore_targetvaluation_selected_power_repeat + S (pvs_prime_restore_target) = S ((S (bpvi_i_pvs_restore_targetvaluation_selected_power)) * bpvi_c_pvs_restore_targetvaluation_selected_power)) /\ exists bpvi_q_pvs_restore_targetvaluation_selected_power_repeat. bpvi_b_pvs_restore_targetvaluation_selected_power = bpvi_q_pvs_restore_targetvaluation_selected_power_repeat * S ((S (bpvi_i_pvs_restore_targetvaluation_selected_power)) * bpvi_c_pvs_restore_targetvaluation_selected_power) + (pvs_prime_restore_target)))) /\ (exists bpvi_u_pvs_restore_targetvaluation_selected_power bpvi_v_pvs_restore_targetvaluation_selected_power. ((((exists bpvi_h_pvs_restore_targetvaluation_selected_power_start. bpvi_h_pvs_restore_targetvaluation_selected_power_start + S (1) = S ((S (0)) * bpvi_v_pvs_restore_targetvaluation_selected_power)) /\ exists bpvi_q_pvs_restore_targetvaluation_selected_power_start. bpvi_u_pvs_restore_targetvaluation_selected_power = bpvi_q_pvs_restore_targetvaluation_selected_power_start * S ((S (0)) * bpvi_v_pvs_restore_targetvaluation_selected_power) + (1))) /\ ((((exists bpvi_h_pvs_restore_targetvaluation_selected_power_terminal. bpvi_h_pvs_restore_targetvaluation_selected_power_terminal + S (bpvi_result_pvs_restore_targetvaluation_selected) = S ((S (pvs_exponent_restore_target)) * bpvi_v_pvs_restore_targetvaluation_selected_power)) /\ exists bpvi_q_pvs_restore_targetvaluation_selected_power_terminal. bpvi_u_pvs_restore_targetvaluation_selected_power = bpvi_q_pvs_restore_targetvaluation_selected_power_terminal * S ((S (pvs_exponent_restore_target)) * bpvi_v_pvs_restore_targetvaluation_selected_power) + (bpvi_result_pvs_restore_targetvaluation_selected))) /\ forall bpvi_j_pvs_restore_targetvaluation_selected_power. (exists bpvi_product_gap_pvs_restore_targetvaluation_selected_power. bpvi_product_gap_pvs_restore_targetvaluation_selected_power + S bpvi_j_pvs_restore_targetvaluation_selected_power = pvs_exponent_restore_target) -> exists bpvi_factor_pvs_restore_targetvaluation_selected_power bpvi_partial_pvs_restore_targetvaluation_selected_power bpvi_successor_pvs_restore_targetvaluation_selected_power. ((((exists bpvi_h_pvs_restore_targetvaluation_selected_power_factor. bpvi_h_pvs_restore_targetvaluation_selected_power_factor + S (bpvi_factor_pvs_restore_targetvaluation_selected_power) = S ((S (bpvi_j_pvs_restore_targetvaluation_selected_power)) * bpvi_c_pvs_restore_targetvaluation_selected_power)) /\ exists bpvi_q_pvs_restore_targetvaluation_selected_power_factor. bpvi_b_pvs_restore_targetvaluation_selected_power = bpvi_q_pvs_restore_targetvaluation_selected_power_factor * S ((S (bpvi_j_pvs_restore_targetvaluation_selected_power)) * bpvi_c_pvs_restore_targetvaluation_selected_power) + (bpvi_factor_pvs_restore_targetvaluation_selected_power))) /\ ((((exists bpvi_h_pvs_restore_targetvaluation_selected_power_partial. bpvi_h_pvs_restore_targetvaluation_selected_power_partial + S (bpvi_partial_pvs_restore_targetvaluation_selected_power) = S ((S (bpvi_j_pvs_restore_targetvaluation_selected_power)) * bpvi_v_pvs_restore_targetvaluation_selected_power)) /\ exists bpvi_q_pvs_restore_targetvaluation_selected_power_partial. bpvi_u_pvs_restore_targetvaluation_selected_power = bpvi_q_pvs_restore_targetvaluation_selected_power_partial * S ((S (bpvi_j_pvs_restore_targetvaluation_selected_power)) * bpvi_v_pvs_restore_targetvaluation_selected_power) + (bpvi_partial_pvs_restore_targetvaluation_selected_power))) /\ ((((exists bpvi_h_pvs_restore_targetvaluation_selected_power_successor. bpvi_h_pvs_restore_targetvaluation_selected_power_successor + S (bpvi_successor_pvs_restore_targetvaluation_selected_power) = S ((S (S bpvi_j_pvs_restore_targetvaluation_selected_power)) * bpvi_v_pvs_restore_targetvaluation_selected_power)) /\ exists bpvi_q_pvs_restore_targetvaluation_selected_power_successor. bpvi_u_pvs_restore_targetvaluation_selected_power = bpvi_q_pvs_restore_targetvaluation_selected_power_successor * S ((S (S bpvi_j_pvs_restore_targetvaluation_selected_power)) * bpvi_v_pvs_restore_targetvaluation_selected_power) + (bpvi_successor_pvs_restore_targetvaluation_selected_power))) /\ bpvi_successor_pvs_restore_targetvaluation_selected_power = bpvi_partial_pvs_restore_targetvaluation_selected_power * bpvi_factor_pvs_restore_targetvaluation_selected_power)))))))) /\ exists bpvi_divisor_factor_pvs_restore_targetvaluation_selected. n = bpvi_result_pvs_restore_targetvaluation_selected * bpvi_divisor_factor_pvs_restore_targetvaluation_selected))) /\ forall bpd_candidate_pvs_restore_targetvaluation. (exists bpd_gap_pvs_restore_targetvaluation_candidate_bound. bpd_gap_pvs_restore_targetvaluation_candidate_bound + (bpd_candidate_pvs_restore_targetvaluation) = (n)) -> (exists bpvi_result_pvs_restore_targetvaluation_candidate. ((exists bpvi_b_pvs_restore_targetvaluation_candidate_power bpvi_c_pvs_restore_targetvaluation_candidate_power. ((forall bpvi_i_pvs_restore_targetvaluation_candidate_power. (exists bpvi_repeat_gap_pvs_restore_targetvaluation_candidate_power. bpvi_repeat_gap_pvs_restore_targetvaluation_candidate_power + S bpvi_i_pvs_restore_targetvaluation_candidate_power = bpd_candidate_pvs_restore_targetvaluation) -> (((exists bpvi_h_pvs_restore_targetvaluation_candidate_power_repeat. bpvi_h_pvs_restore_targetvaluation_candidate_power_repeat + S (pvs_prime_restore_target) = S ((S (bpvi_i_pvs_restore_targetvaluation_candidate_power)) * bpvi_c_pvs_restore_targetvaluation_candidate_power)) /\ exists bpvi_q_pvs_restore_targetvaluation_candidate_power_repeat. bpvi_b_pvs_restore_targetvaluation_candidate_power = bpvi_q_pvs_restore_targetvaluation_candidate_power_repeat * S ((S (bpvi_i_pvs_restore_targetvaluation_candidate_power)) * bpvi_c_pvs_restore_targetvaluation_candidate_power) + (pvs_prime_restore_target)))) /\ (exists bpvi_u_pvs_restore_targetvaluation_candidate_power bpvi_v_pvs_restore_targetvaluation_candidate_power. ((((exists bpvi_h_pvs_restore_targetvaluation_candidate_power_start. bpvi_h_pvs_restore_targetvaluation_candidate_power_start + S (1) = S ((S (0)) * bpvi_v_pvs_restore_targetvaluation_candidate_power)) /\ exists bpvi_q_pvs_restore_targetvaluation_candidate_power_start. bpvi_u_pvs_restore_targetvaluation_candidate_power = bpvi_q_pvs_restore_targetvaluation_candidate_power_start * S ((S (0)) * bpvi_v_pvs_restore_targetvaluation_candidate_power) + (1))) /\ ((((exists bpvi_h_pvs_restore_targetvaluation_candidate_power_terminal. bpvi_h_pvs_restore_targetvaluation_candidate_power_terminal + S (bpvi_result_pvs_restore_targetvaluation_candidate) = S ((S (bpd_candidate_pvs_restore_targetvaluation)) * bpvi_v_pvs_restore_targetvaluation_candidate_power)) /\ exists bpvi_q_pvs_restore_targetvaluation_candidate_power_terminal. bpvi_u_pvs_restore_targetvaluation_candidate_power = bpvi_q_pvs_restore_targetvaluation_candidate_power_terminal * S ((S (bpd_candidate_pvs_restore_targetvaluation)) * bpvi_v_pvs_restore_targetvaluation_candidate_power) + (bpvi_result_pvs_restore_targetvaluation_candidate))) /\ forall bpvi_j_pvs_restore_targetvaluation_candidate_power. (exists bpvi_product_gap_pvs_restore_targetvaluation_candidate_power. bpvi_product_gap_pvs_restore_targetvaluation_candidate_power + S bpvi_j_pvs_restore_targetvaluation_candidate_power = bpd_candidate_pvs_restore_targetvaluation) -> exists bpvi_factor_pvs_restore_targetvaluation_candidate_power bpvi_partial_pvs_restore_targetvaluation_candidate_power bpvi_successor_pvs_restore_targetvaluation_candidate_power. ((((exists bpvi_h_pvs_restore_targetvaluation_candidate_power_factor. bpvi_h_pvs_restore_targetvaluation_candidate_power_factor + S (bpvi_factor_pvs_restore_targetvaluation_candidate_power) = S ((S (bpvi_j_pvs_restore_targetvaluation_candidate_power)) * bpvi_c_pvs_restore_targetvaluation_candidate_power)) /\ exists bpvi_q_pvs_restore_targetvaluation_candidate_power_factor. bpvi_b_pvs_restore_targetvaluation_candidate_power = bpvi_q_pvs_restore_targetvaluation_candidate_power_factor * S ((S (bpvi_j_pvs_restore_targetvaluation_candidate_power)) * bpvi_c_pvs_restore_targetvaluation_candidate_power) + (bpvi_factor_pvs_restore_targetvaluation_candidate_power))) /\ ((((exists bpvi_h_pvs_restore_targetvaluation_candidate_power_partial. bpvi_h_pvs_restore_targetvaluation_candidate_power_partial + S (bpvi_partial_pvs_restore_targetvaluation_candidate_power) = S ((S (bpvi_j_pvs_restore_targetvaluation_candidate_power)) * bpvi_v_pvs_restore_targetvaluation_candidate_power)) /\ exists bpvi_q_pvs_restore_targetvaluation_candidate_power_partial. bpvi_u_pvs_restore_targetvaluation_candidate_power = bpvi_q_pvs_restore_targetvaluation_candidate_power_partial * S ((S (bpvi_j_pvs_restore_targetvaluation_candidate_power)) * bpvi_v_pvs_restore_targetvaluation_candidate_power) + (bpvi_partial_pvs_restore_targetvaluation_candidate_power))) /\ ((((exists bpvi_h_pvs_restore_targetvaluation_candidate_power_successor. bpvi_h_pvs_restore_targetvaluation_candidate_power_successor + S (bpvi_successor_pvs_restore_targetvaluation_candidate_power) = S ((S (S bpvi_j_pvs_restore_targetvaluation_candidate_power)) * bpvi_v_pvs_restore_targetvaluation_candidate_power)) /\ exists bpvi_q_pvs_restore_targetvaluation_candidate_power_successor. bpvi_u_pvs_restore_targetvaluation_candidate_power = bpvi_q_pvs_restore_targetvaluation_candidate_power_successor * S ((S (S bpvi_j_pvs_restore_targetvaluation_candidate_power)) * bpvi_v_pvs_restore_targetvaluation_candidate_power) + (bpvi_successor_pvs_restore_targetvaluation_candidate_power))) /\ bpvi_successor_pvs_restore_targetvaluation_candidate_power = bpvi_partial_pvs_restore_targetvaluation_candidate_power * bpvi_factor_pvs_restore_targetvaluation_candidate_power)))))))) /\ exists bpvi_divisor_factor_pvs_restore_targetvaluation_candidate. n = bpvi_result_pvs_restore_targetvaluation_candidate * bpvi_divisor_factor_pvs_restore_targetvaluation_candidate)) -> (exists bpd_gap_pvs_restore_targetvaluation_maximal. bpd_gap_pvs_restore_targetvaluation_maximal + (bpd_candidate_pvs_restore_targetvaluation) = (pvs_exponent_restore_target))) /\ (exists pa_b_pvs_restore_targetvalue pa_c_pvs_restore_targetvalue. ((forall pa_i_pvs_restore_targetvalue_repeat. (exists pa_lt_pvs_restore_targetvalue_repeat_bound. pa_lt_pvs_restore_targetvalue_repeat_bound + S pa_i_pvs_restore_targetvalue_repeat = pvs_exponent_restore_target) -> (((exists pa_h_pvs_restore_targetvalue_repeat_decoded. pa_h_pvs_restore_targetvalue_repeat_decoded + S (pvs_prime_restore_target) = S ((S (pa_i_pvs_restore_targetvalue_repeat)) * pa_c_pvs_restore_targetvalue)) /\ exists pa_q_pvs_restore_targetvalue_repeat_decoded. pa_b_pvs_restore_targetvalue = pa_q_pvs_restore_targetvalue_repeat_decoded * S ((S (pa_i_pvs_restore_targetvalue_repeat)) * pa_c_pvs_restore_targetvalue) + (pvs_prime_restore_target)))) /\ (exists pa_u_pvs_restore_targetvalue_product pa_v_pvs_restore_targetvalue_product. ((((exists pa_h_pvs_restore_targetvalue_product_start. pa_h_pvs_restore_targetvalue_product_start + S (1) = S ((S (0)) * pa_v_pvs_restore_targetvalue_product)) /\ exists pa_q_pvs_restore_targetvalue_product_start. pa_u_pvs_restore_targetvalue_product = pa_q_pvs_restore_targetvalue_product_start * S ((S (0)) * pa_v_pvs_restore_targetvalue_product) + (1))) /\ ((((exists pa_h_pvs_restore_targetvalue_product_terminal. pa_h_pvs_restore_targetvalue_product_terminal + S (pvs_power_restore_target) = S ((S (pvs_exponent_restore_target)) * pa_v_pvs_restore_targetvalue_product)) /\ exists pa_q_pvs_restore_targetvalue_product_terminal. pa_u_pvs_restore_targetvalue_product = pa_q_pvs_restore_targetvalue_product_terminal * S ((S (pvs_exponent_restore_target)) * pa_v_pvs_restore_targetvalue_product) + (pvs_power_restore_target))) /\ forall pa_i_pvs_restore_targetvalue_product. (exists pa_lt_pvs_restore_targetvalue_product_bound. pa_lt_pvs_restore_targetvalue_product_bound + S pa_i_pvs_restore_targetvalue_product = pvs_exponent_restore_target) -> exists pa_p_pvs_restore_targetvalue_product pa_r_pvs_restore_targetvalue_product pa_s_pvs_restore_targetvalue_product. ((((exists pa_h_pvs_restore_targetvalue_product_factor. pa_h_pvs_restore_targetvalue_product_factor + S (pa_p_pvs_restore_targetvalue_product) = S ((S (pa_i_pvs_restore_targetvalue_product)) * pa_c_pvs_restore_targetvalue)) /\ exists pa_q_pvs_restore_targetvalue_product_factor. pa_b_pvs_restore_targetvalue = pa_q_pvs_restore_targetvalue_product_factor * S ((S (pa_i_pvs_restore_targetvalue_product)) * pa_c_pvs_restore_targetvalue) + (pa_p_pvs_restore_targetvalue_product))) /\ ((((exists pa_h_pvs_restore_targetvalue_product_partial. pa_h_pvs_restore_targetvalue_product_partial + S (pa_r_pvs_restore_targetvalue_product) = S ((S (pa_i_pvs_restore_targetvalue_product)) * pa_v_pvs_restore_targetvalue_product)) /\ exists pa_q_pvs_restore_targetvalue_product_partial. pa_u_pvs_restore_targetvalue_product = pa_q_pvs_restore_targetvalue_product_partial * S ((S (pa_i_pvs_restore_targetvalue_product)) * pa_v_pvs_restore_targetvalue_product) + (pa_r_pvs_restore_targetvalue_product))) /\ ((((exists pa_h_pvs_restore_targetvalue_product_successor. pa_h_pvs_restore_targetvalue_product_successor + S (pa_s_pvs_restore_targetvalue_product) = S ((S (S pa_i_pvs_restore_targetvalue_product)) * pa_v_pvs_restore_targetvalue_product)) /\ exists pa_q_pvs_restore_targetvalue_product_successor. pa_u_pvs_restore_targetvalue_product = pa_q_pvs_restore_targetvalue_product_successor * S ((S (S pa_i_pvs_restore_targetvalue_product)) * pa_v_pvs_restore_targetvalue_product) + (pa_s_pvs_restore_targetvalue_product))) /\ pa_s_pvs_restore_targetvalue_product = pa_r_pvs_restore_targetvalue_product * pa_p_pvs_restore_targetvalue_product)))))))))))))))))))))