# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:(~(s(X1,X3)=s(X1,X2))=>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,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))))))))),file('i/f/topology/METRIC__NZ', ch4s_topologys_METRICu_u_NZ)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/topology/METRIC__NZ', aHLu_FALSITY)).
fof(3, 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__NZ', ah4s_reals_REALu_u_LEu_u_ANTISYM)).
fof(5, 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_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X3))))),file('i/f/topology/METRIC__NZ', ah4s_reals_REALu_u_NOTu_u_LE)).
fof(9, axiom,![X7]:(s(t_bool,X7)=s(t_bool,f)<=>~(p(s(t_bool,X7)))),file('i/f/topology/METRIC__NZ', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(57, axiom,![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__NZ', ah4s_topologys_METRICu_u_ZERO)).
fof(61, axiom,![X1]:![X2]:![X3]:![X4]:p(s(t_bool,h4s_reals_realu_u_lte(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,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)))))))),file('i/f/topology/METRIC__NZ', ah4s_topologys_METRICu_u_POS)).
fof(77, axiom,![X7]:(s(t_bool,X7)=s(t_bool,t)|s(t_bool,X7)=s(t_bool,f)),file('i/f/topology/METRIC__NZ', aHLu_BOOLu_CASES)).
fof(78, axiom,(~(p(s(t_bool,f)))<=>p(s(t_bool,t))),file('i/f/topology/METRIC__NZ', ah4s_bools_NOTu_u_CLAUSESu_c2)).
# SZS output end CNFRefutation
