# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:(p(s(t_bool,h4s_paths_firstpu_u_at(s(t_fun(X2,t_bool),X5),s(t_h4s_paths_path(X2,X1),h4s_paths_stoppedu_u_at(s(X2,X3))),s(t_h4s_nums_num,X4))))<=>(s(t_h4s_nums_num,X4)=s(t_h4s_nums_num,h4s_nums_0)&p(s(t_bool,happ(s(t_fun(X2,t_bool),X5),s(X2,X3)))))),file('i/f/path/firstP__at__thm_c0', ch4s_paths_firstPu_u_atu_u_thmu_c0)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/path/firstP__at__thm_c0', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/path/firstP__at__thm_c0', aHLu_FALSITY)).
fof(15, axiom,![X8]:(s(t_bool,X8)=s(t_bool,t)<=>p(s(t_bool,X8))),file('i/f/path/firstP__at__thm_c0', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(23, axiom,![X2]:![X1]:![X20]:![X21]:![X5]:(p(s(t_bool,h4s_paths_firstpu_u_at(s(t_fun(X2,t_bool),X5),s(t_h4s_paths_path(X2,X1),X20),s(t_h4s_nums_num,X21))))<=>(p(s(t_bool,h4s_bools_in(s(t_h4s_nums_num,X21),s(t_fun(t_h4s_nums_num,t_bool),h4s_paths_pl(s(t_h4s_paths_path(X2,X1),X20))))))&(p(s(t_bool,happ(s(t_fun(X2,t_bool),X5),s(X2,h4s_paths_el(s(t_h4s_nums_num,X21),s(t_h4s_paths_path(X2,X1),X20))))))&![X22]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X22),s(t_h4s_nums_num,X21))))=>~(p(s(t_bool,happ(s(t_fun(X2,t_bool),X5),s(X2,h4s_paths_el(s(t_h4s_nums_num,X22),s(t_h4s_paths_path(X2,X1),X20))))))))))),file('i/f/path/firstP__at__thm_c0', ah4s_paths_firstPu_u_atu_u_def)).
fof(24, axiom,![X2]:![X3]:~(p(s(t_bool,h4s_bools_in(s(X2,X3),s(t_fun(X2,t_bool),h4s_predu_u_sets_empty))))),file('i/f/path/firstP__at__thm_c0', ah4s_predu_u_sets_NOTu_u_INu_u_EMPTY)).
fof(25, axiom,![X2]:![X13]:![X3]:![X23]:(p(s(t_bool,h4s_bools_in(s(X2,X3),s(t_fun(X2,t_bool),h4s_predu_u_sets_insert(s(X2,X13),s(t_fun(X2,t_bool),X23))))))<=>(s(X2,X3)=s(X2,X13)|p(s(t_bool,h4s_bools_in(s(X2,X3),s(t_fun(X2,t_bool),X23)))))),file('i/f/path/firstP__at__thm_c0', ah4s_predu_u_sets_INu_u_INSERT)).
fof(26, axiom,![X1]:![X2]:![X3]:s(t_fun(t_h4s_nums_num,t_bool),h4s_paths_pl(s(t_h4s_paths_path(X2,X1),h4s_paths_stoppedu_u_at(s(X2,X3)))))=s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_insert(s(t_h4s_nums_num,h4s_nums_0),s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_empty))),file('i/f/path/firstP__at__thm_c0', ah4s_paths_PLu_u_thmu_c0)).
fof(27, axiom,![X4]:~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/path/firstP__at__thm_c0', ah4s_primu_u_recs_NOTu_u_LESSu_u_0)).
fof(28, axiom,![X2]:![X1]:![X20]:s(X2,h4s_paths_el(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_paths_path(X2,X1),X20)))=s(X2,h4s_paths_first(s(t_h4s_paths_path(X2,X1),X20))),file('i/f/path/firstP__at__thm_c0', ah4s_paths_elu_u_defu_c0)).
fof(29, axiom,![X1]:![X2]:![X3]:s(X2,h4s_paths_first(s(t_h4s_paths_path(X2,X1),h4s_paths_stoppedu_u_at(s(X2,X3)))))=s(X2,X3),file('i/f/path/firstP__at__thm_c0', ah4s_paths_firstu_u_thmu_c0)).
fof(30, axiom,![X8]:(s(t_bool,X8)=s(t_bool,t)|s(t_bool,X8)=s(t_bool,f)),file('i/f/path/firstP__at__thm_c0', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
