# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/seq/SER__ZERO', aHLu_TRUTH)).
fof(8, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/seq/SER__ZERO', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(9, axiom,![X7]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X7),file('i/f/seq/SER__ZERO', ah4s_arithmetics_ADDu_u_CLAUSESu_c1)).
fof(10, axiom,![X6]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(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,X6)))=s(t_h4s_realaxs_real,X6),file('i/f/seq/SER__ZERO', ah4s_reals_REALu_u_ADDu_u_LID)).
fof(11, axiom,![X6]:s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,X6),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,X6),file('i/f/seq/SER__ZERO', ah4s_reals_REALu_u_SUBu_u_RZERO)).
fof(12, axiom,![X8]:![X4]:s(t_h4s_realaxs_real,h4s_reals_sum(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_pairs_u_2c(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,h4s_nums_0))),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X4)))=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/seq/SER__ZERO', ah4s_reals_sum0u_c0)).
fof(13, axiom,![X8]:![X7]:![X4]:s(t_h4s_realaxs_real,h4s_reals_sum(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_pairs_u_2c(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X7))))),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X4)))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,h4s_reals_sum(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_pairs_u_2c(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X7))),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X4))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X4),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X7))))))),file('i/f/seq/SER__ZERO', ah4s_reals_sum0u_c1)).
fof(14, axiom,![X9]:![X6]:(p(s(t_bool,h4s_seqs_u_2du_2du_3e(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X6),s(t_h4s_realaxs_real,X9))))<=>![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))))=>?[X11]:![X8]:(p(s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X11))))=>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),X6),s(t_h4s_nums_num,X8))),s(t_h4s_realaxs_real,X9))))),s(t_h4s_realaxs_real,X10))))))),file('i/f/seq/SER__ZERO', ah4s_seqs_SEQ)).
fof(15, axiom,![X4]:(p(s(t_bool,h4s_seqs_summable(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X4))))<=>![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))))=>?[X11]:![X7]:![X8]:(p(s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X11))))=>p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,h4s_reals_sum(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_pairs_u_2c(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X8))),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X4))))),s(t_h4s_realaxs_real,X10))))))),file('i/f/seq/SER__ZERO', ah4s_seqs_SERu_u_CAUCHY)).
fof(16, conjecture,![X4]:(p(s(t_bool,h4s_seqs_summable(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X4))))=>p(s(t_bool,h4s_seqs_u_2du_2du_3e(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X4),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))))),file('i/f/seq/SER__ZERO', ch4s_seqs_SERu_u_ZERO)).
# SZS output end CNFRefutation
