# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(![X3]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X1))))=>s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),X2),s(t_h4s_nums_num,X3)))=s(t_h4s_nums_num,h4s_nums_0))<=>s(t_h4s_nums_num,h4s_sumu_u_nums_sum(s(t_h4s_nums_num,X1),s(t_fun(t_h4s_nums_num,t_h4s_nums_num),X2)))=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/sum_num/SUM__ZERO', ch4s_sumu_u_nums_SUMu_u_ZERO)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/sum_num/SUM__ZERO', aHLu_TRUTH)).
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/sum_num/SUM__ZERO', ah4s_arithmetics_ADDu_u_0)).
fof(12, axiom,![X1]:![X3]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X3))),file('i/f/sum_num/SUM__ZERO', ah4s_arithmetics_ADDu_u_SYM)).
fof(14, axiom,![X1]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X1)))),file('i/f/sum_num/SUM__ZERO', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(18, axiom,![X13]:![X1]:![X2]:(![X3]:((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X3))))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X1)))))))=>s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),X2),s(t_h4s_nums_num,X3)))=s(t_h4s_nums_num,h4s_nums_0))<=>s(t_h4s_nums_num,h4s_sumu_u_nums_gsum(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_pairs_u_2c(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X1))),s(t_fun(t_h4s_nums_num,t_h4s_nums_num),X2)))=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/sum_num/SUM__ZERO', ah4s_sumu_u_nums_GSUMu_u_ZERO)).
fof(19, axiom,![X3]:![X2]:s(t_h4s_nums_num,h4s_sumu_u_nums_sum(s(t_h4s_nums_num,X3),s(t_fun(t_h4s_nums_num,t_h4s_nums_num),X2)))=s(t_h4s_nums_num,h4s_sumu_u_nums_gsum(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,X3))),s(t_fun(t_h4s_nums_num,t_h4s_nums_num),X2))),file('i/f/sum_num/SUM__ZERO', ah4s_sumu_u_nums_SUM0)).
fof(22, axiom,~(p(s(t_bool,f0))),file('i/f/sum_num/SUM__ZERO', aHLu_FALSITY)).
fof(25, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)|s(t_bool,X5)=s(t_bool,f0)),file('i/f/sum_num/SUM__ZERO', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
