# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:(p(s(t_bool,h4s_bools_in(s(t_h4s_nums_num,X4),s(t_fun(t_h4s_nums_num,t_bool),h4s_paths_pl(s(t_h4s_paths_path(X1,X2),X3))))))=>s(t_h4s_paths_path(X1,X2),h4s_paths_seg(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X4),s(t_h4s_paths_path(X1,X2),X3)))=s(t_h4s_paths_path(X1,X2),h4s_paths_stoppedu_u_at(s(X1,h4s_paths_el(s(t_h4s_nums_num,X4),s(t_h4s_paths_path(X1,X2),X3)))))),file('i/f/path/singleton__seg', ch4s_paths_singletonu_u_seg)).
fof(4, axiom,![X1]:![X2]:![X3]:s(t_h4s_paths_path(X1,X2),h4s_paths_take(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_paths_path(X1,X2),X3)))=s(t_h4s_paths_path(X1,X2),h4s_paths_stoppedu_u_at(s(X1,h4s_paths_first(s(t_h4s_paths_path(X1,X2),X3))))),file('i/f/path/singleton__seg', ah4s_paths_takeu_u_defu_c0)).
fof(5, axiom,![X1]:![X2]:![X3]:![X4]:(p(s(t_bool,h4s_bools_in(s(t_h4s_nums_num,X4),s(t_fun(t_h4s_nums_num,t_bool),h4s_paths_pl(s(t_h4s_paths_path(X1,X2),X3))))))=>s(X1,h4s_paths_first(s(t_h4s_paths_path(X1,X2),h4s_paths_drop(s(t_h4s_nums_num,X4),s(t_h4s_paths_path(X1,X2),X3)))))=s(X1,h4s_paths_el(s(t_h4s_nums_num,X4),s(t_h4s_paths_path(X1,X2),X3)))),file('i/f/path/singleton__seg', ah4s_paths_firstu_u_drop)).
fof(6, axiom,![X1]:![X2]:![X3]:![X7]:![X4]:s(t_h4s_paths_path(X1,X2),h4s_paths_seg(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X7),s(t_h4s_paths_path(X1,X2),X3)))=s(t_h4s_paths_path(X1,X2),h4s_paths_take(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X4))),s(t_h4s_paths_path(X1,X2),h4s_paths_drop(s(t_h4s_nums_num,X4),s(t_h4s_paths_path(X1,X2),X3))))),file('i/f/path/singleton__seg', ah4s_paths_segu_u_def)).
fof(9, axiom,![X13]:s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X13)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/path/singleton__seg', ah4s_arithmetics_SUBu_u_EQUALu_u_0)).
# SZS output end CNFRefutation
