# 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(X1,X2),X3)))=s(t_h4s_options_option(t_h4s_nums_num),h4s_options_some(s(t_h4s_nums_num,h4s_nums_0)))),file('i/f/path/length__never__zero', ch4s_paths_lengthu_u_neveru_u_zero)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/path/length__never__zero', aHLu_FALSITY)).
fof(12, axiom,![X1]:![X8]:![X7]:(s(t_h4s_options_option(X1),h4s_options_some(s(X1,X7)))=s(t_h4s_options_option(X1),h4s_options_some(s(X1,X8)))<=>s(X1,X7)=s(X1,X8)),file('i/f/path/length__never__zero', ah4s_options_SOMEu_u_11)).
fof(13, axiom,![X2]:![X1]:![X8]:![X7]:![X9]:(s(t_h4s_options_option(X2),h4s_options_optionu_u_map(s(t_fun(X1,X2),X9),s(t_h4s_options_option(X1),X7)))=s(t_h4s_options_option(X2),h4s_options_some(s(X2,X8)))<=>?[X10]:(s(t_h4s_options_option(X1),X7)=s(t_h4s_options_option(X1),h4s_options_some(s(X1,X10)))&s(X2,X8)=s(X2,happ(s(t_fun(X1,X2),X9),s(X1,X10))))),file('i/f/path/length__never__zero', ah4s_options_OPTIONu_u_MAPu_u_EQu_u_SOME)).
fof(14, axiom,![X2]:![X1]:![X7]:s(t_h4s_options_option(t_h4s_nums_num),h4s_paths_length(s(t_h4s_paths_path(X1,X2),h4s_paths_stoppedu_u_at(s(X1,X7)))))=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__never__zero', ah4s_paths_altu_u_lengthu_u_thmu_c0)).
fof(15, axiom,![X11]:~(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_nums_suc),s(t_h4s_nums_num,X11)))=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/path/length__never__zero', ah4s_nums_NOTu_u_SUC)).
fof(16, axiom,![X11]:(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X11)))=s(t_h4s_nums_num,h4s_nums_0)<=>s(t_h4s_nums_num,X11)=s(t_h4s_nums_num,h4s_arithmetics_zero)),file('i/f/path/length__never__zero', ah4s_numerals_numeralu_u_distribu_c17)).
fof(17, axiom,![X11]:(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X11)))=s(t_h4s_nums_num,h4s_arithmetics_zero)<=>p(s(t_bool,f))),file('i/f/path/length__never__zero', ah4s_numerals_numeralu_u_equ_c1)).
fof(18, axiom,![X12]:![X13]:![X7]:![X14]:![X3]:s(t_h4s_options_option(t_h4s_nums_num),h4s_paths_length(s(t_h4s_paths_path(X12,X13),h4s_paths_pcons(s(X12,X7),s(X13,X14),s(t_h4s_paths_path(X12,X13),X3)))))=s(t_h4s_options_option(t_h4s_nums_num),h4s_options_optionu_u_map(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_nums_suc),s(t_h4s_options_option(t_h4s_nums_num),h4s_paths_length(s(t_h4s_paths_path(X12,X13),X3))))),file('i/f/path/length__never__zero', ah4s_paths_altu_u_lengthu_u_thmu_c1)).
fof(19, axiom,![X1]:![X2]:![X3]:(?[X7]:s(t_h4s_paths_path(X1,X2),X3)=s(t_h4s_paths_path(X1,X2),h4s_paths_stoppedu_u_at(s(X1,X7)))|?[X7]:?[X14]:?[X15]:s(t_h4s_paths_path(X1,X2),X3)=s(t_h4s_paths_path(X1,X2),h4s_paths_pcons(s(X1,X7),s(X2,X14),s(t_h4s_paths_path(X1,X2),X15)))),file('i/f/path/length__never__zero', ah4s_paths_pathu_u_cases)).
# SZS output end CNFRefutation
