# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:(p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,X4))))=>p(s(t_bool,h4s_topologys_neigh(s(t_h4s_topologys_topology(X1),h4s_topologys_mtop(s(t_h4s_topologys_metric(X1),X3))),s(t_h4s_pairs_prod(t_fun(X1,t_bool),X1),h4s_pairs_u_2c(s(t_fun(X1,t_bool),h4s_topologys_b(s(t_h4s_topologys_metric(X1),X3),s(t_h4s_pairs_prod(X1,t_h4s_realaxs_real),h4s_pairs_u_2c(s(X1,X2),s(t_h4s_realaxs_real,X4))))),s(X1,X2))))))),file('i/f/topology/BALL__NEIGH', ch4s_topologys_BALLu_u_NEIGH)).
fof(25, axiom,![X1]:![X2]:![X19]:![X22]:((p(s(t_bool,happ(s(t_fun(t_fun(X1,t_bool),t_bool),h4s_topologys_open(s(t_h4s_topologys_topology(X1),X19))),s(t_fun(X1,t_bool),X22))))&p(s(t_bool,happ(s(t_fun(X1,t_bool),X22),s(X1,X2)))))=>p(s(t_bool,h4s_topologys_neigh(s(t_h4s_topologys_topology(X1),X19),s(t_h4s_pairs_prod(t_fun(X1,t_bool),X1),h4s_pairs_u_2c(s(t_fun(X1,t_bool),X22),s(X1,X2))))))),file('i/f/topology/BALL__NEIGH', ah4s_topologys_OPENu_u_OWNu_u_NEIGH)).
fof(28, axiom,![X1]:![X2]:![X3]:![X4]:(p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,X4))))=>p(s(t_bool,happ(s(t_fun(t_fun(X1,t_bool),t_bool),h4s_topologys_open(s(t_h4s_topologys_topology(X1),h4s_topologys_mtop(s(t_h4s_topologys_metric(X1),X3))))),s(t_fun(X1,t_bool),h4s_topologys_b(s(t_h4s_topologys_metric(X1),X3),s(t_h4s_pairs_prod(X1,t_h4s_realaxs_real),h4s_pairs_u_2c(s(X1,X2),s(t_h4s_realaxs_real,X4))))))))),file('i/f/topology/BALL__NEIGH', ah4s_topologys_BALLu_u_OPEN)).
fof(29, axiom,![X1]:![X2]:![X3]:![X4]:![X25]:s(t_bool,happ(s(t_fun(X1,t_bool),h4s_topologys_b(s(t_h4s_topologys_metric(X1),X3),s(t_h4s_pairs_prod(X1,t_h4s_realaxs_real),h4s_pairs_u_2c(s(X1,X2),s(t_h4s_realaxs_real,X4))))),s(X1,X25)))=s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_pairs_prod(X1,X1),t_h4s_realaxs_real),h4s_topologys_dist(s(t_h4s_topologys_metric(X1),X3))),s(t_h4s_pairs_prod(X1,X1),h4s_pairs_u_2c(s(X1,X2),s(X1,X25))))),s(t_h4s_realaxs_real,X4))),file('i/f/topology/BALL__NEIGH', ah4s_topologys_ball)).
fof(33, axiom,![X1]:![X2]:![X3]:s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_pairs_prod(X1,X1),t_h4s_realaxs_real),h4s_topologys_dist(s(t_h4s_topologys_metric(X1),X3))),s(t_h4s_pairs_prod(X1,X1),h4s_pairs_u_2c(s(X1,X2),s(X1,X2)))))=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/topology/BALL__NEIGH', ah4s_topologys_METRICu_u_SAME)).
# SZS output end CNFRefutation
