# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))))&~(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),X3),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_nums_0)))=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_sumu_u_nums_sum(s(t_h4s_nums_num,X2),s(t_fun(t_h4s_nums_num,t_h4s_nums_num),X3))),s(t_h4s_nums_num,h4s_sumu_u_nums_sum(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1))),s(t_fun(t_h4s_nums_num,t_h4s_nums_num),X3))))))),file('i/f/sum_num/SUM__MONO', ch4s_sumu_u_nums_SUMu_u_MONO)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/sum_num/SUM__MONO', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f0))),file('i/f/sum_num/SUM__MONO', aHLu_FALSITY)).
fof(4, axiom,![X4]:![X1]:![X2]:![X3]:((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))))&~(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),X3),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X1)))))=s(t_h4s_nums_num,h4s_nums_0)))=>p(s(t_bool,h4s_primu_u_recs_u_3c(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,X4),s(t_h4s_nums_num,X2))),s(t_fun(t_h4s_nums_num,t_h4s_nums_num),X3))),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,X4),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1))))),s(t_fun(t_h4s_nums_num,t_h4s_nums_num),X3))))))),file('i/f/sum_num/SUM__MONO', ah4s_sumu_u_nums_GSUMu_u_MONO)).
fof(5, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)|s(t_bool,X5)=s(t_bool,f0)),file('i/f/sum_num/SUM__MONO', aHLu_BOOLu_CASES)).
fof(8, axiom,![X1]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,X1),file('i/f/sum_num/SUM__MONO', ah4s_arithmetics_ADDu_c0)).
fof(9, axiom,![X2]:![X3]:s(t_h4s_nums_num,h4s_sumu_u_nums_sum(s(t_h4s_nums_num,X2),s(t_fun(t_h4s_nums_num,t_h4s_nums_num),X3)))=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,X2))),s(t_fun(t_h4s_nums_num,t_h4s_nums_num),X3))),file('i/f/sum_num/SUM__MONO', ah4s_sumu_u_nums_SUM0)).
# SZS output end CNFRefutation
