# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:s(t_bool,h4s_paths_exists(s(t_fun(X2,t_bool),X4),s(t_h4s_paths_path(X2,X1),h4s_paths_stoppedu_u_at(s(X2,X3)))))=s(t_bool,happ(s(t_fun(X2,t_bool),X4),s(X2,X3))),file('i/f/path/exists__thm_c0', ch4s_paths_existsu_u_thmu_c0)).
fof(15, axiom,![X13]:![X14]:((p(s(t_bool,X14))=>p(s(t_bool,X13)))=>((p(s(t_bool,X13))=>p(s(t_bool,X14)))=>s(t_bool,X14)=s(t_bool,X13))),file('i/f/path/exists__thm_c0', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(38, axiom,![X2]:![X1]:![X21]:![X4]:(p(s(t_bool,h4s_paths_exists(s(t_fun(X2,t_bool),X4),s(t_h4s_paths_path(X2,X1),X21))))<=>?[X24]:p(s(t_bool,h4s_paths_firstpu_u_at(s(t_fun(X2,t_bool),X4),s(t_h4s_paths_path(X2,X1),X21),s(t_h4s_nums_num,X24))))),file('i/f/path/exists__thm_c0', ah4s_paths_existsu_u_def)).
fof(39, axiom,![X1]:![X2]:![X3]:![X25]:![X4]:(p(s(t_bool,h4s_paths_firstpu_u_at(s(t_fun(X2,t_bool),X4),s(t_h4s_paths_path(X2,X1),h4s_paths_stoppedu_u_at(s(X2,X3))),s(t_h4s_nums_num,X25))))<=>(s(t_h4s_nums_num,X25)=s(t_h4s_nums_num,h4s_nums_0)&p(s(t_bool,happ(s(t_fun(X2,t_bool),X4),s(X2,X3)))))),file('i/f/path/exists__thm_c0', ah4s_paths_firstPu_u_atu_u_thmu_c0)).
fof(40, axiom,![X2]:![X1]:![X21]:![X24]:![X4]:(p(s(t_bool,h4s_paths_firstpu_u_at(s(t_fun(X2,t_bool),X4),s(t_h4s_paths_path(X2,X1),X21),s(t_h4s_nums_num,X24))))<=>(p(s(t_bool,h4s_bools_in(s(t_h4s_nums_num,X24),s(t_fun(t_h4s_nums_num,t_bool),h4s_paths_pl(s(t_h4s_paths_path(X2,X1),X21))))))&(p(s(t_bool,happ(s(t_fun(X2,t_bool),X4),s(X2,h4s_paths_el(s(t_h4s_nums_num,X24),s(t_h4s_paths_path(X2,X1),X21))))))&![X26]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X26),s(t_h4s_nums_num,X24))))=>~(p(s(t_bool,happ(s(t_fun(X2,t_bool),X4),s(X2,h4s_paths_el(s(t_h4s_nums_num,X26),s(t_h4s_paths_path(X2,X1),X21))))))))))),file('i/f/path/exists__thm_c0', ah4s_paths_firstPu_u_atu_u_def)).
# SZS output end CNFRefutation
