# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:(p(s(t_bool,h4s_paths_sn(s(t_fun(X1,t_fun(X2,t_fun(X1,t_bool))),X3))))<=>![X4]:(p(s(t_bool,happ(s(t_fun(t_h4s_paths_path(X1,X2),t_bool),h4s_paths_okpath(s(t_fun(X1,t_fun(X2,t_fun(X1,t_bool))),X3))),s(t_h4s_paths_path(X1,X2),X4))))=>p(s(t_bool,h4s_paths_finite(s(t_h4s_paths_path(X1,X2),X4)))))),file('i/f/path/SN__finite__paths__EQ', ch4s_paths_SNu_u_finiteu_u_pathsu_u_EQ)).
fof(37, axiom,![X1]:![X2]:![X4]:![X3]:((p(s(t_bool,h4s_paths_sn(s(t_fun(X1,t_fun(X2,t_fun(X1,t_bool))),X3))))&p(s(t_bool,happ(s(t_fun(t_h4s_paths_path(X1,X2),t_bool),h4s_paths_okpath(s(t_fun(X1,t_fun(X2,t_fun(X1,t_bool))),X3))),s(t_h4s_paths_path(X1,X2),X4)))))=>p(s(t_bool,h4s_paths_finite(s(t_h4s_paths_path(X1,X2),X4))))),file('i/f/path/SN__finite__paths__EQ', ah4s_paths_SNu_u_finiteu_u_paths)).
fof(38, axiom,![X2]:![X1]:![X3]:(![X4]:(p(s(t_bool,happ(s(t_fun(t_h4s_paths_path(X1,X2),t_bool),h4s_paths_okpath(s(t_fun(X1,t_fun(X2,t_fun(X1,t_bool))),X3))),s(t_h4s_paths_path(X1,X2),X4))))=>p(s(t_bool,h4s_paths_finite(s(t_h4s_paths_path(X1,X2),X4)))))=>p(s(t_bool,h4s_paths_sn(s(t_fun(X1,t_fun(X2,t_fun(X1,t_bool))),X3))))),file('i/f/path/SN__finite__paths__EQ', ah4s_paths_finiteu_u_pathsu_u_SN)).
fof(67, axiom,p(s(t_bool,t)),file('i/f/path/SN__finite__paths__EQ', aHLu_TRUTH)).
fof(68, axiom,![X8]:(s(t_bool,X8)=s(t_bool,t)|s(t_bool,X8)=s(t_bool,f)),file('i/f/path/SN__finite__paths__EQ', aHLu_BOOLu_CASES)).
fof(71, axiom,![X8]:(s(t_bool,X8)=s(t_bool,t)<=>p(s(t_bool,X8))),file('i/f/path/SN__finite__paths__EQ', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(76, axiom,(~(p(s(t_bool,f)))<=>p(s(t_bool,t))),file('i/f/path/SN__finite__paths__EQ', ah4s_bools_NOTu_u_CLAUSESu_c2)).
# SZS output end CNFRefutation
