# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:s(t_h4s_options_option(t_h4s_nums_num),h4s_paths_length(s(t_h4s_paths_path(X2,X1),h4s_paths_stoppedu_u_at(s(X2,X3)))))=s(t_h4s_options_option(t_h4s_nums_num),h4s_options_some(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/path/length__thm_c0', ch4s_paths_lengthu_u_thmu_c0)).
fof(8, axiom,![X2]:![X3]:s(X2,h4s_options_the(s(t_h4s_options_option(X2),h4s_options_some(s(X2,X3)))))=s(X2,X3),file('i/f/path/length__thm_c0', ah4s_options_THEu_u_DEF)).
fof(9, axiom,![X2]:s(t_h4s_options_option(t_h4s_lists_list(X2)),h4s_llists_tolist(s(t_h4s_llists_llist(X2),h4s_llists_lnil)))=s(t_h4s_options_option(t_h4s_lists_list(X2)),h4s_options_some(s(t_h4s_lists_list(X2),h4s_lists_nil))),file('i/f/path/length__thm_c0', ah4s_llists_toListu_u_THMu_c0)).
fof(10, axiom,![X2]:![X1]:![X8]:s(t_h4s_options_option(t_h4s_nums_num),h4s_paths_length(s(t_h4s_paths_path(X2,X1),X8)))=s(t_h4s_options_option(t_h4s_nums_num),h4s_bools_cond(s(t_bool,h4s_paths_finite(s(t_h4s_paths_path(X2,X1),X8))),s(t_h4s_options_option(t_h4s_nums_num),h4s_options_some(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(t_h4s_pairs_prod(X1,X2)),h4s_options_the(s(t_h4s_options_option(t_h4s_lists_list(t_h4s_pairs_prod(X1,X2))),h4s_llists_tolist(s(t_h4s_llists_llist(t_h4s_pairs_prod(X1,X2)),h4s_pairs_snd(s(t_h4s_pairs_prod(X2,t_h4s_llists_llist(t_h4s_pairs_prod(X1,X2))),h4s_paths_frompath(s(t_h4s_paths_path(X2,X1),X8))))))))))),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_options_option(t_h4s_nums_num),h4s_options_none))),file('i/f/path/length__thm_c0', ah4s_paths_lengthu_u_def)).
fof(11, axiom,![X9]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X9),file('i/f/path/length__thm_c0', ah4s_arithmetics_ADDu_u_0)).
fof(12, axiom,![X10]:![X9]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X10)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X9))),file('i/f/path/length__thm_c0', ah4s_arithmetics_ADDu_u_SYM)).
fof(13, axiom,![X2]:s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(X2),h4s_lists_nil)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/path/length__thm_c0', ah4s_lists_LENGTH0u_c0)).
fof(14, axiom,![X1]:![X2]:![X3]:s(t_h4s_paths_path(X2,X1),h4s_paths_stoppedu_u_at(s(X2,X3)))=s(t_h4s_paths_path(X2,X1),h4s_paths_topath(s(t_h4s_pairs_prod(X2,t_h4s_llists_llist(t_h4s_pairs_prod(X1,X2))),h4s_pairs_u_2c(s(X2,X3),s(t_h4s_llists_llist(t_h4s_pairs_prod(X1,X2)),h4s_llists_lnil))))),file('i/f/path/length__thm_c0', ah4s_paths_stoppedu_u_atu_u_def)).
fof(15, axiom,![X1]:![X2]:![X3]:s(t_bool,h4s_paths_finite(s(t_h4s_paths_path(X2,X1),h4s_paths_stoppedu_u_at(s(X2,X3)))))=s(t_bool,t),file('i/f/path/length__thm_c0', ah4s_paths_finiteu_u_thmu_c0)).
fof(16, axiom,![X1]:![X2]:![X11]:s(t_h4s_pairs_prod(X2,t_h4s_llists_llist(t_h4s_pairs_prod(X1,X2))),h4s_paths_frompath(s(t_h4s_paths_path(X2,X1),h4s_paths_topath(s(t_h4s_pairs_prod(X2,t_h4s_llists_llist(t_h4s_pairs_prod(X1,X2))),X11)))))=s(t_h4s_pairs_prod(X2,t_h4s_llists_llist(t_h4s_pairs_prod(X1,X2))),X11),file('i/f/path/length__thm_c0', ah4s_paths_pathu_u_repu_u_bijectionsu_u_thmu_c1)).
fof(20, axiom,![X2]:![X6]:![X7]:s(X2,h4s_bools_cond(s(t_bool,t),s(X2,X7),s(X2,X6)))=s(X2,X7),file('i/f/path/length__thm_c0', ah4s_bools_boolu_u_caseu_u_thmu_c0)).
fof(21, axiom,![X2]:![X1]:![X4]:![X3]:s(X1,h4s_pairs_snd(s(t_h4s_pairs_prod(X2,X1),h4s_pairs_u_2c(s(X2,X3),s(X1,X4)))))=s(X1,X4),file('i/f/path/length__thm_c0', ah4s_pairs_SND0)).
# SZS output end CNFRefutation
