# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/path/exists__thm_c0', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/path/exists__thm_c0', aHLu_FALSITY)).
fof(3, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)|s(t_bool,X1)=s(t_bool,f)),file('i/f/path/exists__thm_c0', aHLu_BOOLu_CASES)).
fof(6, axiom,![X7]:![X8]:((p(s(t_bool,X8))=>p(s(t_bool,X7)))=>((p(s(t_bool,X7))=>p(s(t_bool,X8)))=>s(t_bool,X8)=s(t_bool,X7))),file('i/f/path/exists__thm_c0', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(11, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/path/exists__thm_c0', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(17, axiom,![X16]:![X9]:![X6]:![X17]:![X15]:(p(s(t_bool,h4s_paths_firstpu_u_at(s(t_fun(X9,t_bool),X15),s(t_h4s_paths_path(X9,X16),h4s_paths_stoppedu_u_at(s(X9,X6))),s(t_h4s_nums_num,X17))))<=>(s(t_h4s_nums_num,X17)=s(t_h4s_nums_num,h4s_nums_0)&p(s(t_bool,happ(s(t_fun(X9,t_bool),X15),s(X9,X6)))))),file('i/f/path/exists__thm_c0', ah4s_paths_firstPu_u_atu_u_thmu_c0)).
fof(18, axiom,![X9]:![X16]:![X18]:![X15]:(p(s(t_bool,h4s_paths_exists(s(t_fun(X9,t_bool),X15),s(t_h4s_paths_path(X9,X16),X18))))<=>?[X19]:p(s(t_bool,h4s_paths_firstpu_u_at(s(t_fun(X9,t_bool),X15),s(t_h4s_paths_path(X9,X16),X18),s(t_h4s_nums_num,X19))))),file('i/f/path/exists__thm_c0', ah4s_paths_existsu_u_def)).
fof(19, conjecture,![X16]:![X9]:![X6]:![X15]:s(t_bool,h4s_paths_exists(s(t_fun(X9,t_bool),X15),s(t_h4s_paths_path(X9,X16),h4s_paths_stoppedu_u_at(s(X9,X6)))))=s(t_bool,happ(s(t_fun(X9,t_bool),X15),s(X9,X6))),file('i/f/path/exists__thm_c0', ch4s_paths_existsu_u_thmu_c0)).
# SZS output end CNFRefutation
