# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:((p(s(t_bool,h4s_seqs_summable(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X1))))&![X2]: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_nums_num,t_h4s_realaxs_real),X1),s(t_h4s_nums_num,X2)))))))=>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,h4s_seqs_suminf(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X1))))))),file('i/f/util_prob/SER__POS', ch4s_utilu_u_probs_SERu_u_POS)).
fof(10, axiom,![X10]:![X11]:((p(s(t_bool,X11))=>p(s(t_bool,X10)))=>((p(s(t_bool,X10))=>p(s(t_bool,X11)))=>s(t_bool,X11)=s(t_bool,X10))),file('i/f/util_prob/SER__POS', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(18, axiom,![X2]:![X1]:((p(s(t_bool,h4s_seqs_summable(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X1))))&![X13]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X13))))=>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_nums_num,t_h4s_realaxs_real),X1),s(t_h4s_nums_num,X13))))))))=>p(s(t_bool,h4s_reals_realu_u_lte(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,h4s_nums_0),s(t_h4s_nums_num,X2))),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X1))),s(t_h4s_realaxs_real,h4s_seqs_suminf(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X1))))))),file('i/f/util_prob/SER__POS', ah4s_seqs_SERu_u_POSu_u_LE)).
fof(23, axiom,![X5]:![X1]:(p(s(t_bool,h4s_seqs_sums(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X1),s(t_h4s_realaxs_real,X5))))=>s(t_h4s_realaxs_real,X5)=s(t_h4s_realaxs_real,h4s_seqs_suminf(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X1)))),file('i/f/util_prob/SER__POS', ah4s_seqs_SUMu_u_UNIQ)).
fof(29, axiom,![X2]:![X1]: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,X2),s(t_h4s_nums_num,h4s_nums_0))),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X1)))=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/util_prob/SER__POS', ah4s_reals_sum0u_c0)).
fof(43, axiom,![X1]:(p(s(t_bool,h4s_seqs_summable(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X1))))<=>?[X22]:p(s(t_bool,h4s_seqs_sums(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X1),s(t_h4s_realaxs_real,X22))))),file('i/f/util_prob/SER__POS', ah4s_seqs_summable0)).
# SZS output end CNFRefutation
