# 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(X1,t_h4s_realaxs_real),happ(s(t_fun(t_fun(X1,t_h4s_realaxs_real),t_fun(X1,t_h4s_realaxs_real)),X2),s(t_fun(X1,t_h4s_realaxs_real),X3))),s(X1,X4)))=s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,happ(s(t_fun(X1,t_h4s_realaxs_real),X3),s(X1,X4)))))=>![X5]:![X3]:![X6]:(p(s(t_bool,h4s_netss_tends(s(t_fun(X1,t_h4s_realaxs_real),X3),s(t_h4s_realaxs_real,X5),s(t_h4s_pairs_prod(t_h4s_topologys_topology(t_h4s_realaxs_real),t_fun(X1,t_fun(X1,t_bool))),h4s_pairs_u_2c(s(t_h4s_topologys_topology(t_h4s_realaxs_real),h4s_topologys_mtop(s(t_h4s_topologys_metric(t_h4s_realaxs_real),h4s_topologys_mr1))),s(t_fun(X1,t_fun(X1,t_bool)),X6))))))=>p(s(t_bool,h4s_netss_tends(s(t_fun(X1,t_h4s_realaxs_real),happ(s(t_fun(t_fun(X1,t_h4s_realaxs_real),t_fun(X1,t_h4s_realaxs_real)),X2),s(t_fun(X1,t_h4s_realaxs_real),X3))),s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,X5))),s(t_h4s_pairs_prod(t_h4s_topologys_topology(t_h4s_realaxs_real),t_fun(X1,t_fun(X1,t_bool))),h4s_pairs_u_2c(s(t_h4s_topologys_topology(t_h4s_realaxs_real),h4s_topologys_mtop(s(t_h4s_topologys_metric(t_h4s_realaxs_real),h4s_topologys_mr1))),s(t_fun(X1,t_fun(X1,t_bool)),X6)))))))),file('i/f/nets/NET__ABS', ch4s_netss_NETu_u_ABS)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/nets/NET__ABS', aHLu_TRUTH)).
fof(5, axiom,![X7]:(s(t_bool,X7)=s(t_bool,t)<=>p(s(t_bool,X7))),file('i/f/nets/NET__ABS', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(6, axiom,![X8]:![X1]:![X5]:![X3]:![X6]:![X9]:(p(s(t_bool,h4s_netss_tends(s(t_fun(X8,X1),X3),s(X1,X5),s(t_h4s_pairs_prod(t_h4s_topologys_topology(X1),t_fun(X8,t_fun(X8,t_bool))),h4s_pairs_u_2c(s(t_h4s_topologys_topology(X1),h4s_topologys_mtop(s(t_h4s_topologys_metric(X1),X9))),s(t_fun(X8,t_fun(X8,t_bool)),X6))))))<=>![X10]:(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,X10))))=>?[X4]:(p(s(t_bool,happ(s(t_fun(X8,t_bool),happ(s(t_fun(X8,t_fun(X8,t_bool)),X6),s(X8,X4))),s(X8,X4))))&![X11]:(p(s(t_bool,happ(s(t_fun(X8,t_bool),happ(s(t_fun(X8,t_fun(X8,t_bool)),X6),s(X8,X11))),s(X8,X4))))=>p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_topologys_dist(s(t_h4s_topologys_metric(X1),X9),s(t_h4s_pairs_prod(X1,X1),h4s_pairs_u_2c(s(X1,happ(s(t_fun(X8,X1),X3),s(X8,X11))),s(X1,X5))))),s(t_h4s_realaxs_real,X10)))))))),file('i/f/nets/NET__ABS', ah4s_netss_MTOPu_u_TENDS)).
fof(7, axiom,![X12]:![X3]:s(t_h4s_realaxs_real,h4s_topologys_dist(s(t_h4s_topologys_metric(t_h4s_realaxs_real),h4s_topologys_mr1),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_pairs_u_2c(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X12)))))=s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,X12),s(t_h4s_realaxs_real,X3))))),file('i/f/nets/NET__ABS', ah4s_topologys_MR1u_u_DEF)).
fof(9, axiom,![X12]:![X3]:p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,X3))),s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,X12))))))),s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X12)))))))),file('i/f/nets/NET__ABS', ah4s_reals_ABSu_u_SUBu_u_ABS)).
fof(10, axiom,![X16]:![X12]:![X3]:((p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X12))))&p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X12),s(t_h4s_realaxs_real,X16)))))=>p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X16))))),file('i/f/nets/NET__ABS', ah4s_reals_REALu_u_LETu_u_TRANS)).
# SZS output end CNFRefutation
