# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,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_seg(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,X4),s(t_h4s_paths_path(X1,X2),X3)))))=s(X1,h4s_paths_el(s(t_h4s_nums_num,X5),s(t_h4s_paths_path(X1,X2),X3)))),file('i/f/path/first__seg', ch4s_paths_firstu_u_seg)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/path/first__seg', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/path/first__seg', aHLu_FALSITY)).
fof(4, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)|s(t_bool,X6)=s(t_bool,f)),file('i/f/path/first__seg', aHLu_BOOLu_CASES)).
fof(22, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)<=>p(s(t_bool,X6))),file('i/f/path/first__seg', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(44, axiom,![X1]:![X2]:![X3]:![X5]:(p(s(t_bool,h4s_bools_in(s(t_h4s_nums_num,X5),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,X5),s(t_h4s_paths_path(X1,X2),X3)))))=s(X1,h4s_paths_el(s(t_h4s_nums_num,X5),s(t_h4s_paths_path(X1,X2),X3)))),file('i/f/path/first__seg', ah4s_paths_firstu_u_drop)).
fof(45, axiom,![X1]:![X2]:![X3]:![X5]:(p(s(t_bool,h4s_bools_in(s(t_h4s_nums_num,X5),s(t_fun(t_h4s_nums_num,t_bool),h4s_paths_pl(s(t_h4s_paths_path(X1,X2),X3))))))=>![X4]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X5))))=>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)))))))),file('i/f/path/first__seg', ah4s_paths_PLu_u_downwardu_u_closed)).
fof(46, axiom,![X1]:![X2]:![X3]:![X5]:s(X1,h4s_paths_first(s(t_h4s_paths_path(X1,X2),h4s_paths_take(s(t_h4s_nums_num,X5),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__seg', ah4s_paths_firstu_u_take)).
fof(47, axiom,![X1]:![X2]:![X3]:![X4]:![X5]:s(t_h4s_paths_path(X1,X2),h4s_paths_seg(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,X4),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,X4),s(t_h4s_nums_num,X5))),s(t_h4s_paths_path(X1,X2),h4s_paths_drop(s(t_h4s_nums_num,X5),s(t_h4s_paths_path(X1,X2),X3))))),file('i/f/path/first__seg', ah4s_paths_segu_u_def)).
fof(48, axiom,![X19]:![X20]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X20),s(t_h4s_nums_num,X19))))<=>(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X20),s(t_h4s_nums_num,X19))))|s(t_h4s_nums_num,X20)=s(t_h4s_nums_num,X19))),file('i/f/path/first__seg', ah4s_arithmetics_LESSu_u_ORu_u_EQ)).
# SZS output end CNFRefutation
