# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:(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),X4))),s(t_h4s_pairs_prod(X1,X1),h4s_pairs_u_2c(s(X1,X3),s(X1,X2)))))=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))<=>s(X1,X3)=s(X1,X2)),file('i/f/topology/METRIC__ZERO', ch4s_topologys_METRICu_u_ZERO)).
fof(8, axiom,![X1]:![X4]:p(s(t_bool,h4s_topologys_ismet(s(t_fun(t_h4s_pairs_prod(X1,X1),t_h4s_realaxs_real),h4s_topologys_dist(s(t_h4s_topologys_metric(X1),X4)))))),file('i/f/topology/METRIC__ZERO', ah4s_topologys_METRICu_u_ISMET)).
fof(9, axiom,![X1]:![X4]:(p(s(t_bool,h4s_topologys_ismet(s(t_fun(t_h4s_pairs_prod(X1,X1),t_h4s_realaxs_real),X4))))<=>(![X3]:![X2]:(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_pairs_prod(X1,X1),t_h4s_realaxs_real),X4),s(t_h4s_pairs_prod(X1,X1),h4s_pairs_u_2c(s(X1,X3),s(X1,X2)))))=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))<=>s(X1,X3)=s(X1,X2))&![X3]:![X2]:![X10]:p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_pairs_prod(X1,X1),t_h4s_realaxs_real),X4),s(t_h4s_pairs_prod(X1,X1),h4s_pairs_u_2c(s(X1,X2),s(X1,X10))))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_pairs_prod(X1,X1),t_h4s_realaxs_real),X4),s(t_h4s_pairs_prod(X1,X1),h4s_pairs_u_2c(s(X1,X3),s(X1,X2))))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_pairs_prod(X1,X1),t_h4s_realaxs_real),X4),s(t_h4s_pairs_prod(X1,X1),h4s_pairs_u_2c(s(X1,X3),s(X1,X10)))))))))))),file('i/f/topology/METRIC__ZERO', ah4s_topologys_ismet0)).
# SZS output end CNFRefutation
