# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:(p(s(t_bool,h4s_seqs_cauchy(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X1))))=>p(s(t_bool,h4s_netss_bounded(s(t_h4s_pairs_prod(t_h4s_topologys_metric(t_h4s_realaxs_real),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool))),h4s_pairs_u_2c(s(t_h4s_topologys_metric(t_h4s_realaxs_real),h4s_topologys_mr1),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_arithmetics_u_3eu_3d))),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X1))))),file('i/f/seq/SEQ__CBOUNDED', ch4s_seqs_SEQu_u_CBOUNDED)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/seq/SEQ__CBOUNDED', aHLu_TRUTH)).
fof(7, axiom,![X2]:(s(t_bool,X2)=s(t_bool,t)<=>p(s(t_bool,X2))),file('i/f/seq/SEQ__CBOUNDED', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(8, axiom,![X3]:![X4]:![X5]:![X6]:![X1]:(p(s(t_bool,h4s_netss_bounded(s(t_h4s_pairs_prod(t_h4s_topologys_metric(X4),t_fun(X3,t_fun(X3,t_bool))),h4s_pairs_u_2c(s(t_h4s_topologys_metric(X4),X5),s(t_fun(X3,t_fun(X3,t_bool)),X6))),s(t_fun(X3,X4),X1))))<=>?[X7]:?[X8]:?[X9]:(p(s(t_bool,happ(s(t_fun(X3,t_bool),happ(s(t_fun(X3,t_fun(X3,t_bool)),X6),s(X3,X9))),s(X3,X9))))&![X10]:(p(s(t_bool,happ(s(t_fun(X3,t_bool),happ(s(t_fun(X3,t_fun(X3,t_bool)),X6),s(X3,X10))),s(X3,X9))))=>p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_topologys_dist(s(t_h4s_topologys_metric(X4),X5),s(t_h4s_pairs_prod(X4,X4),h4s_pairs_u_2c(s(X4,happ(s(t_fun(X3,X4),X1),s(X3,X10))),s(X4,X8))))),s(t_h4s_realaxs_real,X7))))))),file('i/f/seq/SEQ__CBOUNDED', ah4s_netss_bounded0)).
fof(10, axiom,![X13]:![X8]: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,X8),s(t_h4s_realaxs_real,X13)))))=s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,X13),s(t_h4s_realaxs_real,X8))))),file('i/f/seq/SEQ__CBOUNDED', ah4s_topologys_MR1u_u_DEF)).
fof(11, axiom,![X10]:![X5]:s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_arithmetics_u_3eu_3d),s(t_h4s_nums_num,X10))),s(t_h4s_nums_num,X5)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,X10))),file('i/f/seq/SEQ__CBOUNDED', ah4s_arithmetics_GREATERu_u_EQ)).
fof(12, axiom,![X1]:(p(s(t_bool,h4s_seqs_cauchy(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X1))))<=>![X14]:(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,X14))))=>?[X9]:![X5]:![X10]:((p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_arithmetics_u_3eu_3d),s(t_h4s_nums_num,X5))),s(t_h4s_nums_num,X9))))&p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_arithmetics_u_3eu_3d),s(t_h4s_nums_num,X10))),s(t_h4s_nums_num,X9)))))=>p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X1),s(t_h4s_nums_num,X5))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X1),s(t_h4s_nums_num,X10))))))),s(t_h4s_realaxs_real,X14))))))),file('i/f/seq/SEQ__CBOUNDED', ah4s_seqs_cauchy0)).
fof(13, axiom,![X5]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,X5)))),file('i/f/seq/SEQ__CBOUNDED', ah4s_arithmetics_LESSu_u_EQu_u_REFL)).
fof(14, axiom,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,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))),file('i/f/seq/SEQ__CBOUNDED', ah4s_reals_REALu_u_LTu_u_01)).
# SZS output end CNFRefutation
