# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:((p(s(t_bool,h4s_seqs_summable(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X2))))&![X3]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X3))))=>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,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X2),s(t_h4s_nums_num,X3))))))))=>p(s(t_bool,h4s_realaxs_realu_u_lt(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,X1))),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),X2))))))),file('i/f/seq/SER__POS__LT', ch4s_seqs_SERu_u_POSu_u_LT)).
fof(3, axiom,![X5]:![X6]:(p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X5))))=>p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X5))))),file('i/f/seq/SER__POS__LT', ah4s_reals_REALu_u_LTu_u_IMPu_u_LE)).
fof(4, axiom,![X7]:![X5]:![X6]:((p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X5))))&p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X5),s(t_h4s_realaxs_real,X7)))))=>p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X7))))),file('i/f/seq/SER__POS__LT', ah4s_reals_REALu_u_LTEu_u_TRANS)).
fof(5, axiom,![X5]:![X6]:s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X5)))))=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,X5))),file('i/f/seq/SER__POS__LT', ah4s_reals_REALu_u_LTu_u_ADDR)).
fof(6, axiom,![X1]:![X2]:((p(s(t_bool,h4s_seqs_summable(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X2))))&![X3]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X3))))=>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),X2),s(t_h4s_nums_num,X3))))))))=>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,X1))),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),X2))))))),file('i/f/seq/SER__POS__LT', ah4s_seqs_SERu_u_POSu_u_LE)).
fof(8, axiom,![X1]:![X2]: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,X1),s(t_h4s_nums_num,h4s_nums_0))),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X2)))=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__POS__LT', ah4s_reals_sum0u_c0)).
fof(9, axiom,![X1]:![X3]:![X2]: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,X1),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X3))))),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X2)))=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,X1),s(t_h4s_nums_num,X3))),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X2))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X2),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X3))))))),file('i/f/seq/SER__POS__LT', ah4s_reals_sum0u_c1)).
fof(10, axiom,![X11]:![X1]:![X2]: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,h4s_nums_0),s(t_h4s_nums_num,X1))),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X2))),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,X1),s(t_h4s_nums_num,X11))),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X2)))))=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,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X11))))),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X2))),file('i/f/seq/SER__POS__LT', ah4s_reals_SUMu_u_TWO)).
fof(11, axiom,![X3]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X3),file('i/f/seq/SER__POS__LT', ah4s_arithmetics_ADDu_u_CLAUSESu_c1)).
fof(12, 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__POS__LT', ah4s_reals_REALu_u_ADDu_u_LID)).
fof(13, axiom,![X3]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X3)))))),file('i/f/seq/SER__POS__LT', ah4s_arithmetics_LESSu_u_EQu_u_SUCu_u_REFL)).
fof(14, axiom,![X11]:![X1]:![X3]:((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X1))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X11)))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X11))))),file('i/f/seq/SER__POS__LT', ah4s_arithmetics_LESSu_u_EQu_u_TRANS)).
fof(15, axiom,![X3]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X3)))),file('i/f/seq/SER__POS__LT', ah4s_arithmetics_LESSu_u_EQu_u_REFL)).
fof(16, axiom,![X3]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X3)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X3),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/SER__POS__LT', ah4s_arithmetics_ADD1)).
fof(17, axiom,s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/seq/SER__POS__LT', ah4s_arithmetics_ONE)).
# SZS output end CNFRefutation
