# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:![X6]:(p(s(t_bool,h4s_paths_okpath(s(t_fun(X1,t_fun(X2,t_fun(X1,t_bool))),X6),s(t_h4s_paths_path(X1,X2),h4s_paths_pcons(s(X1,X3),s(X2,X4),s(t_h4s_paths_path(X1,X2),X5))))))<=>(p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X2,t_fun(X1,t_bool)),happ(s(t_fun(X1,t_fun(X2,t_fun(X1,t_bool))),X6),s(X1,X3))),s(X2,X4))),s(X1,h4s_paths_first(s(t_h4s_paths_path(X1,X2),X5))))))&p(s(t_bool,h4s_paths_okpath(s(t_fun(X1,t_fun(X2,t_fun(X1,t_bool))),X6),s(t_h4s_paths_path(X1,X2),X5)))))),file('i/f/path/okpath__thm_c1', ch4s_paths_okpathu_u_thmu_c1)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/path/okpath__thm_c1', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/path/okpath__thm_c1', aHLu_FALSITY)).
fof(11, axiom,![X9]:(s(t_bool,X9)=s(t_bool,t)|s(t_bool,X9)=s(t_bool,f)),file('i/f/path/okpath__thm_c1', aHLu_BOOLu_CASES)).
fof(14, axiom,![X1]:![X2]:![X16]:![X3]:![X17]:![X4]:![X18]:![X5]:(s(t_h4s_paths_path(X1,X2),h4s_paths_pcons(s(X1,X3),s(X2,X4),s(t_h4s_paths_path(X1,X2),X5)))=s(t_h4s_paths_path(X1,X2),h4s_paths_pcons(s(X1,X16),s(X2,X17),s(t_h4s_paths_path(X1,X2),X18)))<=>(s(X1,X3)=s(X1,X16)&(s(X2,X4)=s(X2,X17)&s(t_h4s_paths_path(X1,X2),X5)=s(t_h4s_paths_path(X1,X2),X18)))),file('i/f/path/okpath__thm_c1', ah4s_paths_pconsu_u_11)).
fof(15, axiom,![X1]:![X2]:![X3]:![X6]:(p(s(t_bool,h4s_paths_okpath(s(t_fun(X1,t_fun(X2,t_fun(X1,t_bool))),X6),s(t_h4s_paths_path(X1,X2),X3))))<=>(?[X19]:s(t_h4s_paths_path(X1,X2),X3)=s(t_h4s_paths_path(X1,X2),h4s_paths_stoppedu_u_at(s(X1,X19)))|?[X19]:?[X4]:?[X5]:(s(t_h4s_paths_path(X1,X2),X3)=s(t_h4s_paths_path(X1,X2),h4s_paths_pcons(s(X1,X19),s(X2,X4),s(t_h4s_paths_path(X1,X2),X5)))&(p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X2,t_fun(X1,t_bool)),happ(s(t_fun(X1,t_fun(X2,t_fun(X1,t_bool))),X6),s(X1,X19))),s(X2,X4))),s(X1,h4s_paths_first(s(t_h4s_paths_path(X1,X2),X5))))))&p(s(t_bool,h4s_paths_okpath(s(t_fun(X1,t_fun(X2,t_fun(X1,t_bool))),X6),s(t_h4s_paths_path(X1,X2),X5)))))))),file('i/f/path/okpath__thm_c1', ah4s_paths_okpathu_u_cases)).
fof(16, axiom,![X1]:![X2]:![X16]:![X3]:![X4]:![X5]:~(s(t_h4s_paths_path(X1,X2),h4s_paths_stoppedu_u_at(s(X1,X3)))=s(t_h4s_paths_path(X1,X2),h4s_paths_pcons(s(X1,X16),s(X2,X4),s(t_h4s_paths_path(X1,X2),X5)))),file('i/f/path/okpath__thm_c1', ah4s_paths_stoppedu_u_atu_u_notu_u_pconsu_c0)).
# SZS output end CNFRefutation
