# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:s(X1,h4s_paths_first(s(t_h4s_paths_path(X1,X2),h4s_paths_take(s(t_h4s_nums_num,X4),s(t_h4s_paths_path(X1,X2),X3)))))=s(X1,h4s_paths_first(s(t_h4s_paths_path(X1,X2),X3))),file('i/f/path/first__take', ch4s_paths_firstu_u_take)).
fof(5, axiom,![X2]:![X1]:![X5]:s(X1,h4s_paths_first(s(t_h4s_paths_path(X1,X2),h4s_paths_stoppedu_u_at(s(X1,X5)))))=s(X1,X5),file('i/f/path/first__take', ah4s_paths_firstu_u_thmu_c0)).
fof(6, axiom,![X2]:![X1]:![X5]:![X6]:![X3]:s(X1,h4s_paths_first(s(t_h4s_paths_path(X1,X2),h4s_paths_pcons(s(X1,X5),s(X2,X6),s(t_h4s_paths_path(X1,X2),X3)))))=s(X1,X5),file('i/f/path/first__take', ah4s_paths_firstu_u_thmu_c1)).
fof(7, 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/first__take', ah4s_paths_takeu_u_defu_c0)).
fof(8, axiom,![X1]:![X2]:![X3]:![X7]:s(t_h4s_paths_path(X1,X2),h4s_paths_take(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X7))),s(t_h4s_paths_path(X1,X2),X3)))=s(t_h4s_paths_path(X1,X2),h4s_paths_pcons(s(X1,h4s_paths_first(s(t_h4s_paths_path(X1,X2),X3))),s(X2,h4s_paths_firstu_u_label(s(t_h4s_paths_path(X1,X2),X3))),s(t_h4s_paths_path(X1,X2),h4s_paths_take(s(t_h4s_nums_num,X7),s(t_h4s_paths_path(X1,X2),h4s_paths_tail(s(t_h4s_paths_path(X1,X2),X3))))))),file('i/f/path/first__take', ah4s_paths_takeu_u_defu_c1)).
fof(9, axiom,![X8]:(s(t_h4s_nums_num,X8)=s(t_h4s_nums_num,h4s_nums_0)|?[X7]:s(t_h4s_nums_num,X8)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X7)))),file('i/f/path/first__take', ah4s_arithmetics_numu_u_CASES)).
# SZS output end CNFRefutation
