# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:s(t_h4s_lists_list(X1),h4s_bitstrings_extend(s(X1,X4),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X2))))),s(t_h4s_lists_list(X1),X3)))=s(t_h4s_lists_list(X1),h4s_bitstrings_extend(s(X1,X4),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X2))))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_lists_list(X1),happ(s(t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1)),happ(s(t_fun(X1,t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1))),h4s_lists_cons),s(X1,X4))),s(t_h4s_lists_list(X1),X3))))),file('i/f/bitstring/extend__def__compute_c1', ch4s_bitstrings_extendu_u_defu_u_computeu_c1)).
fof(8, axiom,s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/bitstring/extend__def__compute_c1', ah4s_arithmetics_ONE)).
fof(9, axiom,![X2]:~(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/bitstring/extend__def__compute_c1', ah4s_nums_NOTu_u_SUC)).
fof(16, axiom,s(t_h4s_nums_num,h4s_arithmetics_zero)=s(t_h4s_nums_num,h4s_nums_0),file('i/f/bitstring/extend__def__compute_c1', ah4s_arithmetics_ALTu_u_ZERO)).
fof(23, axiom,![X9]:s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X9)))=s(t_h4s_nums_num,X9),file('i/f/bitstring/extend__def__compute_c1', ah4s_arithmetics_NUMERALu_u_DEF)).
fof(26, axiom,![X1]:![X2]:![X3]:![X4]:s(t_h4s_lists_list(X1),h4s_bitstrings_extend(s(X1,X4),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2))),s(t_h4s_lists_list(X1),X3)))=s(t_h4s_lists_list(X1),h4s_bitstrings_extend(s(X1,X4),s(t_h4s_nums_num,X2),s(t_h4s_lists_list(X1),happ(s(t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1)),happ(s(t_fun(X1,t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1))),h4s_lists_cons),s(X1,X4))),s(t_h4s_lists_list(X1),X3))))),file('i/f/bitstring/extend__def__compute_c1', ah4s_bitstrings_extendu_u_defu_c1)).
fof(36, axiom,![X2]:![X25]:s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X25))),s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X25),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X25),s(t_h4s_nums_num,X2))))))),file('i/f/bitstring/extend__def__compute_c1', ah4s_arithmetics_SUBu_c1)).
fof(37, axiom,![X25]:s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X25)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/bitstring/extend__def__compute_c1', ah4s_arithmetics_SUBu_c0)).
fof(38, axiom,![X25]:s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X25))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))=s(t_h4s_nums_num,X25),file('i/f/bitstring/extend__def__compute_c1', ah4s_arithmetics_SUCu_u_SUB1)).
fof(39, axiom,![X25]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X25)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X25),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),file('i/f/bitstring/extend__def__compute_c1', ah4s_arithmetics_ADD1)).
fof(41, axiom,![X2]:s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))))),file('i/f/bitstring/extend__def__compute_c1', ah4s_arithmetics_BIT10)).
fof(44, axiom,![X2]:![X25]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X25),s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X25))),file('i/f/bitstring/extend__def__compute_c1', ah4s_arithmetics_ADDu_u_COMM)).
fof(47, axiom,![X2]:![X25]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X25))),s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X25),s(t_h4s_nums_num,X2))))),file('i/f/bitstring/extend__def__compute_c1', ah4s_arithmetics_ADDu_c1)).
fof(49, axiom,![X2]:![X25]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X25),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2))))))<=>(s(t_h4s_nums_num,X25)=s(t_h4s_nums_num,X2)|p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X25),s(t_h4s_nums_num,X2)))))),file('i/f/bitstring/extend__def__compute_c1', ah4s_primu_u_recs_LESSu_u_THM)).
fof(53, axiom,p(s(t_bool,t)),file('i/f/bitstring/extend__def__compute_c1', aHLu_TRUTH)).
fof(63, axiom,![X2]:~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/bitstring/extend__def__compute_c1', ah4s_primu_u_recs_NOTu_u_LESSu_u_0)).
fof(72, axiom,![X1]:![X12]:![X13]:s(X1,h4s_bools_cond(s(t_bool,f),s(X1,X13),s(X1,X12)))=s(X1,X12),file('i/f/bitstring/extend__def__compute_c1', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(78, axiom,![X18]:(s(t_bool,X18)=s(t_bool,t)|s(t_bool,X18)=s(t_bool,f)),file('i/f/bitstring/extend__def__compute_c1', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
