# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]: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),h4s_topologys_dist(s(t_h4s_topologys_metric(X1),X5))),s(t_h4s_pairs_prod(X1,X1),h4s_pairs_u_2c(s(X1,X4),s(X1,X2))))),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),h4s_topologys_dist(s(t_h4s_topologys_metric(X1),X5))),s(t_h4s_pairs_prod(X1,X1),h4s_pairs_u_2c(s(X1,X4),s(X1,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),X5))),s(t_h4s_pairs_prod(X1,X1),h4s_pairs_u_2c(s(X1,X3),s(X1,X2)))))))))),file('i/f/topology/METRIC__TRIANGLE', ch4s_topologys_METRICu_u_TRIANGLE)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/topology/METRIC__TRIANGLE', aHLu_TRUTH)).
fof(4, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)<=>p(s(t_bool,X6))),file('i/f/topology/METRIC__TRIANGLE', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(5, axiom,![X1]:![X5]:(p(s(t_bool,h4s_topologys_ismet(s(t_fun(t_h4s_pairs_prod(X1,X1),t_h4s_realaxs_real),X5))))<=>(![X4]:![X3]:(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_pairs_prod(X1,X1),t_h4s_realaxs_real),X5),s(t_h4s_pairs_prod(X1,X1),h4s_pairs_u_2c(s(X1,X4),s(X1,X3)))))=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))<=>s(X1,X4)=s(X1,X3))&![X4]:![X3]:![X2]: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),X5),s(t_h4s_pairs_prod(X1,X1),h4s_pairs_u_2c(s(X1,X3),s(X1,X2))))),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),X5),s(t_h4s_pairs_prod(X1,X1),h4s_pairs_u_2c(s(X1,X4),s(X1,X3))))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_pairs_prod(X1,X1),t_h4s_realaxs_real),X5),s(t_h4s_pairs_prod(X1,X1),h4s_pairs_u_2c(s(X1,X4),s(X1,X2)))))))))))),file('i/f/topology/METRIC__TRIANGLE', ah4s_topologys_ismet0)).
fof(7, axiom,![X1]:![X3]:![X4]:![X5]: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),X5))),s(t_h4s_pairs_prod(X1,X1),h4s_pairs_u_2c(s(X1,X4),s(X1,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),X5))),s(t_h4s_pairs_prod(X1,X1),h4s_pairs_u_2c(s(X1,X3),s(X1,X4))))),file('i/f/topology/METRIC__TRIANGLE', ah4s_topologys_METRICu_u_SYM)).
fof(8, axiom,![X1]:![X5]: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),X5)))))),file('i/f/topology/METRIC__TRIANGLE', ah4s_topologys_METRICu_u_ISMET)).
# SZS output end CNFRefutation
