# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:(![X5]:((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X5))))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2)))))))=>s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X4),s(t_h4s_nums_num,X5)))=s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X3),s(t_h4s_nums_num,X5))))=>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,X1))),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X4)))=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,X1))),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X3)))),file('i/f/real/SUM__EQ', ch4s_reals_SUMu_u_EQ)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/real/SUM__EQ', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f0))),file('i/f/real/SUM__EQ', aHLu_FALSITY)).
fof(4, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)|s(t_bool,X6)=s(t_bool,f0)),file('i/f/real/SUM__EQ', aHLu_BOOLu_CASES)).
fof(7, axiom,![X11]:![X9]:((p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X9),s(t_h4s_realaxs_real,X11))))&p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X11),s(t_h4s_realaxs_real,X9)))))<=>s(t_h4s_realaxs_real,X9)=s(t_h4s_realaxs_real,X11)),file('i/f/real/SUM__EQ', ah4s_reals_REALu_u_LEu_u_ANTISYM)).
fof(9, axiom,![X1]:![X2]:![X3]:![X4]:(![X5]:((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X5))))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2)))))))=>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),X4),s(t_h4s_nums_num,X5))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X3),s(t_h4s_nums_num,X5)))))))=>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,X2),s(t_h4s_nums_num,X1))),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X4))),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,X1))),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X3))))))),file('i/f/real/SUM__EQ', ah4s_reals_SUMu_u_LE)).
# SZS output end CNFRefutation
