# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:((p(s(t_bool,h4s_transcs_division(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_pairs_u_2c(s(t_h4s_realaxs_real,X4),s(t_h4s_realaxs_real,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_nums_suc(s(t_h4s_nums_num,X1)))))=s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X2),s(t_h4s_nums_num,X1)))&![X5]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,X1))))=>p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X2),s(t_h4s_nums_num,X5))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X2),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X5)))))))))))=>s(t_h4s_nums_num,h4s_transcs_dsize(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X2)))=s(t_h4s_nums_num,X1)),file('i/f/integral/DIVISION__DSIZE__EQ__ALT', ch4s_integrals_DIVISIONu_u_DSIZEu_u_EQu_u_ALT)).
fof(22, axiom,![X1]:![X2]:![X3]:![X4]:((p(s(t_bool,h4s_transcs_division(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_pairs_u_2c(s(t_h4s_realaxs_real,X4),s(t_h4s_realaxs_real,X3))),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X2))))&p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X2),s(t_h4s_nums_num,X1))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X2),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1)))))))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,h4s_transcs_dsize(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X2))))))),file('i/f/integral/DIVISION__DSIZE__EQ__ALT', ah4s_integrals_DIVISIONu_u_DSIZEu_u_GE)).
fof(28, axiom,![X1]:![X2]:![X3]:![X4]:((p(s(t_bool,h4s_transcs_division(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_pairs_u_2c(s(t_h4s_realaxs_real,X4),s(t_h4s_realaxs_real,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_nums_suc(s(t_h4s_nums_num,X1)))))=s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X2),s(t_h4s_nums_num,X1))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_transcs_dsize(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X2))),s(t_h4s_nums_num,X1))))),file('i/f/integral/DIVISION__DSIZE__EQ__ALT', ah4s_integrals_DIVISIONu_u_DSIZEu_u_LE)).
fof(42, axiom,![X1]:p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1)))))),file('i/f/integral/DIVISION__DSIZE__EQ__ALT', ah4s_primu_u_recs_LESSu_u_SUCu_u_REFL)).
fof(47, axiom,![X1]:![X20]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X20),s(t_h4s_nums_num,X1)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X20))),s(t_h4s_nums_num,X1))),file('i/f/integral/DIVISION__DSIZE__EQ__ALT', ah4s_arithmetics_LESSu_u_EQ)).
fof(53, axiom,![X1]:![X20]:(s(t_h4s_nums_num,X20)=s(t_h4s_nums_num,X1)|(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X20),s(t_h4s_nums_num,X1))))|p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X20)))))),file('i/f/integral/DIVISION__DSIZE__EQ__ALT', ah4s_arithmetics_LESSu_u_LESSu_u_CASES)).
fof(57, axiom,![X1]:![X20]:(~(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X20),s(t_h4s_nums_num,X1)))))<=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X20))))),file('i/f/integral/DIVISION__DSIZE__EQ__ALT', ah4s_arithmetics_NOTu_u_LESSu_u_EQUAL)).
# SZS output end CNFRefutation
