# 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,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,X2),s(X1,X3))))),file('i/f/topology/METRIC__SYM', ch4s_topologys_METRICu_u_SYM)).
fof(4, axiom,![X1]:![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,X3)))))=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/topology/METRIC__SYM', ah4s_topologys_METRICu_u_SAME)).
fof(5, 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]:![X9]: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,X9))))),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,X9)))))))))))),file('i/f/topology/METRIC__SYM', ah4s_topologys_ismet0)).
fof(6, 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__SYM', ah4s_topologys_METRICu_u_ISMET)).
fof(7, axiom,![X3]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X3),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,X3),file('i/f/topology/METRIC__SYM', ah4s_reals_REALu_u_ADDu_u_RID)).
fof(8, axiom,![X2]:![X3]:((p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X2))))&p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X3)))))<=>s(t_h4s_realaxs_real,X3)=s(t_h4s_realaxs_real,X2)),file('i/f/topology/METRIC__SYM', ah4s_reals_REALu_u_LEu_u_ANTISYM)).
# SZS output end CNFRefutation
