apply iter successor
apply iter add zero
apply match add indices_to_match=[0,1]
apply match multiply indices_to_match=[0,1]
apply specialize successor zero index_to_specialize=0
apply specialize successor one index_to_specialize=0
apply specialize successor two index_to_specialize=0
apply specialize successor three index_to_specialize=0
apply specialize successor four index_to_specialize=0
apply specialize successor five index_to_specialize=0
apply iter multiply one
apply specialize multiply three index_to_specialize=0
apply specialize power three index_to_specialize=0
apply exists multiply indices_to_quantify=[0]
apply size divides indices_to_quantify=[0]
apply compose tau tau output_to_input_map={0:0}
apply exists double indices_to_quantify=[0]
apply negation is_even
apply exists square indices_to_quantify=[0]
apply exists add indices_to_quantify=[0]
apply negation leq
apply negation eq
apply compose ne leq shared_vars={0:0,1:1}
apply negation lt
apply match divides indices_to_match=[0,1]
apply specialize eq zero index_to_specialize=0
apply negation eq_zero
apply forall gt_zero divides_self indices_to_map={0:0} indices_to_quantify=[0]
apply specialize divides zero index_to_specialize=1
apply forall gt_zero is_divisor_of_zero indices_to_map={0:0} indices_to_quantify=[0]
apply compose divides gt_zero shared_vars={1:0}
apply implication divides_and_multiple_gt_zero leq
apply compose multiply add output_to_input_map={0:0}
apply compose multiply product_add output_to_input_map={0:2}
apply compose divides divides shared_vars={0:0}
apply compose sum_two_products divides output_to_input_map={0:1}
apply forall divides_both_numbers divides_sum_two_products indices_to_map={0:4,1:1,2:3} indices_to_quantify=[0,1,2,3,4]
apply compose divides divides shared_vars={0:1,1:0}
apply implication divides_each_other eq
apply negation divides
apply specialize tau two index_to_specialize=1
apply compose is_prime is_square shared_vars={0:0}
apply compose is_prime is_even shared_vars={0:0}
apply nonexistence is_prime_square
apply compose product_add eq output_to_input_map={0:0}
apply compose eq_product_add lt shared_vars={0:1,2:0}
apply specialize add one index_to_specialize=0
apply compose double add_one output_to_input_map={0:0}
apply compose double add output_to_input_map={0:0}
apply compose double add_with_doubled_summand output_to_input_map={0:1}
apply exists sum_of_doubles indices_to_quantify=[0,1]
apply equivalence is_sum_of_evens is_even
apply compose double_add_one add output_to_input_map={0:0}
apply compose double_add_one add_with_doubled_incr_summand output_to_input_map={0:1}
apply exists sum_of_doubles_incr indices_to_quantify=[0,1]
apply equivalence is_sum_of_odds is_even
apply compose double_add_one add_with_doubled_summand output_to_input_map={0:1}
apply exists sum_of_even_odd indices_to_quantify=[0,1]
apply equivalence is_sum_of_even_odd is_odd
apply compose power add output_to_input_map={0:0}
apply compose power power_add output_to_input_map={0:2}
apply compose sum_two_powers eq output_to_input_map={0:0}
apply compose power eq_sum_two_powers output_to_input_map={0:4}
apply match power_eq_sum_two_powers indices_to_match=[1,3,5]
apply specialize gt one index_to_specialize=1
apply specialize gt two index_to_specialize=1
apply specialize gt five index_to_specialize=1
apply compose gt_two power_eq_sum_two_powers_match_exp shared_vars={0:1}
apply compose fermats_last_thm_false_zzz gt_zero shared_vars={0:0}
apply compose fermats_last_thm_false_zz gt_zero shared_vars={2:0}
apply compose fermats_last_thm_false_z gt_zero shared_vars={3:0}
apply nonexistence fermats_last_thm_false
apply specialize add two index_to_specialize=0
apply compose add_two is_prime output_to_input_map={0:0}
apply compose is_prime is_prime_minus_two shared_vars={0:0}
apply compose gt is_twin_prime shared_vars={0:0}
apply exists is_twin_prime_gt indices_to_quantify=[0]
apply forall exists_is_twin_prime_gt indices_to_quantify=[0]
apply compose double lt output_to_input_map={0:1}
apply compose gt double_gt shared_vars={0:1,1:0}
apply compose is_prime gt_and_lt_double shared_vars={0:0}
apply exists is_prime_gt_and_lt_double indices_to_quantify=[0]
apply forall gt_one bertrand_postulate_q indices_to_map={0:0} indices_to_quantify=[0]
apply compose gt is_prime shared_vars={0:0}
apply exists is_prime_gt indices_to_quantify=[0]
apply forall exists_is_prime_gt indices_to_quantify=[0]
apply exists gt indices_to_quantify=[0]
apply forall exists_gt indices_to_quantify=[0]
apply compose add eq output_to_input_map={0:0}
apply compose is_prime eq_sum shared_vars={0:0}
apply compose is_prime eq_sum_first_summand_prime shared_vars={0:1}
apply exists eq_sum_of_primes indices_to_quantify=[0,1]
apply compose gt_two is_even shared_vars={0:0}
apply forall gt_two_even goldbach_strong_q indices_to_map={0:0} indices_to_quantify=[0]
apply compose add_one square output_to_input_map={0:0}
apply compose add_one_square lt output_to_input_map={0:1}
apply compose square gt output_to_input_map={0:1}
apply compose square_lt add_one_square_gt shared_vars={0:0,1:1}
apply compose is_prime square_lt_and_add_one_square_gt shared_vars={0:1}
apply exists is_prime_gt_square_and_lt_add_one_square indices_to_quantify=[0]
apply forall gt_zero legendre_conjecture_q indices_to_map={0:0} indices_to_quantify=[0]
apply compose add add output_to_input_map={0:0}
apply compose add_three_numbers eq output_to_input_map={0:0}
apply compose is_prime eq_sum_three_numbers shared_vars={0:0}
apply compose is_prime eq_sum_three_numbers_prime_summand1 shared_vars={0:1}
apply compose is_prime eq_sum_three_numbers_prime_summand1_prime_summand2 shared_vars={0:2}
apply exists eq_sum_three_primes indices_to_quantify=[0,1,2]
apply forall gt_five goldbach_weak_q indices_to_map={0:0} indices_to_quantify=[0]
apply exists product_add indices_to_quantify=[0]
apply compose power is_mod output_to_input_map={0:2}
apply match is_mod_power indices_to_match=[0,3]
apply match is_mod_power_matched_base_res indices_to_match=[1,2]
apply forall is_prime is_mod_power_matched_base_res_pwr_mod indices_to_map={0:1} indices_to_quantify=[0,1]
apply specialize power four index_to_specialize=1
apply compose fourth_power eq_sum_three_numbers output_to_input_map={0:0}
apply compose fourth_power eq_sum_three_numbers_fourth_power_summand1 output_to_input_map={0:1}
apply compose fourth_power eq_sum_three_numbers_fourth_power_summand1_fourth_power_summand2 output_to_input_map={0:2}
apply compose fourth_power eq_sum_three_numbers_fourth_power_summand1_fourth_power_summand2_fourth_power_summand3 output_to_input_map={0:3}
apply compose sum_of_fourth_powers_equals_fourth_power_zzzz gt_zero shared_vars={0:0}
apply compose sum_of_fourth_powers_equals_fourth_power_zzz gt_zero shared_vars={1:0}
apply compose sum_of_fourth_powers_equals_fourth_power_zz gt_zero shared_vars={2:0}
apply compose sum_of_fourth_powers_equals_fourth_power_z gt_zero shared_vars={3:0}
apply nonexistence sum_of_fourth_powers_equals_fourth_power
apply specialize eq two index_to_specialize=0
apply equivalence is_even_prime eq_two
apply compose is_even is_square shared_vars={0:0}
apply specialize divides four index_to_specialize=0
apply equivalence divis_by_four is_even_square
apply compose is_square gt_zero shared_vars={0:0}
apply compose tau is_odd output_to_input_map={0:0}
apply equivalence is_nonzero_square odd_number_divisors
apply compose double multiply output_to_input_map={0:0}
apply compose multiply_with_doubled_factor eq output_to_input_map={0:0}
apply forall eq_product_doubled_factor is_even indices_to_map={2:0} indices_to_quantify=[0,1,2]
apply compose double_add_one multiply output_to_input_map={0:0}
apply compose double_add_one multiply_with_doubled_incr_factor output_to_input_map={0:1}
apply compose product_of_doubles_incr eq output_to_input_map={0:0}
apply forall eq_product_doubled_incr_factors is_odd indices_to_map={2:0} indices_to_quantify=[0,1,2]
apply specialize power_eq_sum_two_powers_match_exp two index_to_specialize=1
apply compose is_pythagorean_triple_zzz gt_zero shared_vars={0:0}
apply compose is_pythagorean_triple_zz gt_zero shared_vars={1:0}
apply compose is_pythagorean_triple_z gt_zero shared_vars={2:0}
apply compose is_pythagorean_triple gt shared_vars={2:0}
apply exists is_pythagorean_triple_gt indices_to_quantify=[0,1,2]
apply forall exists_pythagorean_triple_gt indices_to_quantify=[0]