# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:((![X3]:p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X2),s(t_h4s_nums_num,X3))))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X1),s(t_h4s_nums_num,X3))))))&p(s(t_bool,h4s_seqs_summable(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X1)))))=>(p(s(t_bool,h4s_seqs_summable(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X2))))&p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_seqs_suminf(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X2))),s(t_h4s_realaxs_real,h4s_seqs_suminf(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X1)))))))),file('i/f/seq/SER__LE2', ch4s_seqs_SERu_u_LE2)).
fof(6, axiom,![X7]:![X8]:((p(s(t_bool,X8))=>p(s(t_bool,X7)))=>((p(s(t_bool,X7))=>p(s(t_bool,X8)))=>s(t_bool,X8)=s(t_bool,X7))),file('i/f/seq/SER__LE2', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(17, axiom,![X13]:![X14]:![X12]:((p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X12),s(t_h4s_realaxs_real,X14))))&p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X14),s(t_h4s_realaxs_real,X13)))))=>p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X12),s(t_h4s_realaxs_real,X13))))),file('i/f/seq/SER__LE2', ah4s_reals_REALu_u_LEu_u_TRANS)).
fof(25, axiom,![X1]:![X2]:((?[X19]:![X3]:(p(s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X19))))=>p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X2),s(t_h4s_nums_num,X3))))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X1),s(t_h4s_nums_num,X3)))))))&p(s(t_bool,h4s_seqs_summable(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X1)))))=>p(s(t_bool,h4s_seqs_summable(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X2))))),file('i/f/seq/SER__LE2', ah4s_seqs_SERu_u_COMPAR)).
fof(26, axiom,![X1]:![X2]:((![X3]:p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X2),s(t_h4s_nums_num,X3))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X1),s(t_h4s_nums_num,X3))))))&(p(s(t_bool,h4s_seqs_summable(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X2))))&p(s(t_bool,h4s_seqs_summable(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X1))))))=>p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_seqs_suminf(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X2))),s(t_h4s_realaxs_real,h4s_seqs_suminf(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X1))))))),file('i/f/seq/SER__LE2', ah4s_seqs_SERu_u_LE)).
fof(31, axiom,![X12]:p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X12),s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,X12)))))),file('i/f/seq/SER__LE2', ah4s_reals_ABSu_u_LE)).
fof(49, axiom,![X12]:![X2]:(p(s(t_bool,h4s_seqs_sums(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X2),s(t_h4s_realaxs_real,X12))))=>s(t_h4s_realaxs_real,X12)=s(t_h4s_realaxs_real,h4s_seqs_suminf(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X2)))),file('i/f/seq/SER__LE2', ah4s_seqs_SUMu_u_UNIQ)).
fof(50, axiom,![X2]:(p(s(t_bool,h4s_seqs_summable(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X2))))<=>?[X24]:p(s(t_bool,h4s_seqs_sums(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X2),s(t_h4s_realaxs_real,X24))))),file('i/f/seq/SER__LE2', ah4s_seqs_summable0)).
# SZS output end CNFRefutation
