# 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(2, axiom,p(s(t_bool,t)),file('i/f/util_prob/SER__POS', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f0))),file('i/f/util_prob/SER__POS', aHLu_FALSITY)).
fof(11, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)<=>p(s(t_bool,X4))),file('i/f/util_prob/SER__POS', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(12, axiom,![X4]:((p(s(t_bool,X4))=>p(s(t_bool,f0)))<=>s(t_bool,X4)=s(t_bool,f0)),file('i/f/util_prob/SER__POS', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
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(20, 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)).
# SZS output end CNFRefutation
