# 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/EXISTS__path', ch4s_paths_EXISTSu_u_path)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/path/EXISTS__path', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/path/EXISTS__path', aHLu_FALSITY)).
fof(4, 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__path', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(6, axiom,![X9]:(s(t_bool,X9)=s(t_bool,t)<=>p(s(t_bool,X9))),file('i/f/path/EXISTS__path', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(21, axiom,![X9]:(s(t_bool,X9)=s(t_bool,f)<=>~(p(s(t_bool,X9)))),file('i/f/path/EXISTS__path', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(42, axiom,![X1]:![X18]:![X3]:(?[X5]:(s(X1,X5)=s(X1,X18)&p(s(t_bool,happ(s(t_fun(X1,t_bool),X3),s(X1,X5)))))<=>p(s(t_bool,happ(s(t_fun(X1,t_bool),X3),s(X1,X18))))),file('i/f/path/EXISTS__path', ah4s_bools_UNWINDu_u_THM2)).
fof(44, axiom,![X1]:![X3]:(~(?[X5]:p(s(t_bool,happ(s(t_fun(X1,t_bool),X3),s(X1,X5)))))<=>![X5]:~(p(s(t_bool,happ(s(t_fun(X1,t_bool),X3),s(X1,X5)))))),file('i/f/path/EXISTS__path', ah4s_bools_NOTu_u_EXISTSu_u_THM)).
fof(56, axiom,(p(s(t_bool,f))<=>![X9]:p(s(t_bool,X9))),file('i/f/path/EXISTS__path', ah4s_bools_Fu_u_DEF)).
fof(68, 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]:?[X16]: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),X16)))),file('i/f/path/EXISTS__path', ah4s_paths_pathu_u_cases)).
# SZS output end CNFRefutation
