# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:(![X4]:p(s(t_bool,happ(s(t_fun(t_h4s_paths_path(X1,X2),t_bool),X3),s(t_h4s_paths_path(X1,X2),X4))))<=>(![X5]:p(s(t_bool,happ(s(t_fun(t_h4s_paths_path(X1,X2),t_bool),X3),s(t_h4s_paths_path(X1,X2),h4s_paths_stoppedu_u_at(s(X1,X5))))))&![X5]:![X6]:![X4]:p(s(t_bool,happ(s(t_fun(t_h4s_paths_path(X1,X2),t_bool),X3),s(t_h4s_paths_path(X1,X2),h4s_paths_pcons(s(X1,X5),s(X2,X6),s(t_h4s_paths_path(X1,X2),X4)))))))),file('i/f/path/FORALL__path', ch4s_paths_FORALLu_u_path)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/path/FORALL__path', aHLu_TRUTH)).
fof(8, axiom,![X9]:(s(t_bool,X9)=s(t_bool,t)<=>p(s(t_bool,X9))),file('i/f/path/FORALL__path', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(13, axiom,![X1]:![X2]:![X4]:(?[X5]:s(t_h4s_paths_path(X1,X2),X4)=s(t_h4s_paths_path(X1,X2),h4s_paths_stoppedu_u_at(s(X1,X5)))|?[X5]:?[X6]:?[X18]:s(t_h4s_paths_path(X1,X2),X4)=s(t_h4s_paths_path(X1,X2),h4s_paths_pcons(s(X1,X5),s(X2,X6),s(t_h4s_paths_path(X1,X2),X18)))),file('i/f/path/FORALL__path', ah4s_paths_pathu_u_cases)).
fof(14, axiom,![X9]:(s(t_bool,X9)=s(t_bool,t)|s(t_bool,X9)=s(t_bool,f)),file('i/f/path/FORALL__path', aHLu_BOOLu_CASES)).
fof(15, axiom,~(p(s(t_bool,f))),file('i/f/path/FORALL__path', aHLu_FALSITY)).
# SZS output end CNFRefutation
