# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:(![X2]:![X3]:![X4]:s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),happ(s(t_fun(t_h4s_realaxs_real,t_fun(t_h4s_nums_num,t_h4s_realaxs_real)),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),t_fun(t_h4s_realaxs_real,t_fun(t_h4s_nums_num,t_h4s_realaxs_real))),X1),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X2))),s(t_h4s_realaxs_real,X3))),s(t_h4s_nums_num,X4)))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_powsers_diffs(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X2),s(t_h4s_nums_num,X4))),s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,X3),s(t_h4s_nums_num,X4)))))=>![X5]:(![X2]:![X3]:![X4]:s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),happ(s(t_fun(t_h4s_realaxs_real,t_fun(t_h4s_nums_num,t_h4s_realaxs_real)),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),t_fun(t_h4s_realaxs_real,t_fun(t_h4s_nums_num,t_h4s_realaxs_real))),X5),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X2))),s(t_h4s_realaxs_real,X3))),s(t_h4s_nums_num,X4)))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,X4))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X2),s(t_h4s_nums_num,X4))),s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,X3),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))=>![X3]:![X6]:![X2]: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,X6))),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),happ(s(t_fun(t_h4s_realaxs_real,t_fun(t_h4s_nums_num,t_h4s_realaxs_real)),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),t_fun(t_h4s_realaxs_real,t_fun(t_h4s_nums_num,t_h4s_realaxs_real))),X5),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X2))),s(t_h4s_realaxs_real,X3)))))=s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(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,X6))),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),happ(s(t_fun(t_h4s_realaxs_real,t_fun(t_h4s_nums_num,t_h4s_realaxs_real)),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),t_fun(t_h4s_realaxs_real,t_fun(t_h4s_nums_num,t_h4s_realaxs_real))),X1),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X2))),s(t_h4s_realaxs_real,X3))))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,X6))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X2),s(t_h4s_nums_num,X6))),s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,X3),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X6),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))))))),file('i/f/powser/DIFFS__LEMMA2', ch4s_powsers_DIFFSu_u_LEMMA2)).
fof(2, axiom,![X7]:![X8]:![X3]:(s(t_h4s_realaxs_real,X3)=s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,X8),s(t_h4s_realaxs_real,X7)))<=>s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X7)))=s(t_h4s_realaxs_real,X8)),file('i/f/powser/DIFFS__LEMMA2', ah4s_reals_REALu_u_EQu_u_SUBu_u_LADD)).
fof(3, axiom,![X1]:(![X2]:![X3]:![X4]:s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),happ(s(t_fun(t_h4s_realaxs_real,t_fun(t_h4s_nums_num,t_h4s_realaxs_real)),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),t_fun(t_h4s_realaxs_real,t_fun(t_h4s_nums_num,t_h4s_realaxs_real))),X1),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X2))),s(t_h4s_realaxs_real,X3))),s(t_h4s_nums_num,X4)))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,X4))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X2),s(t_h4s_nums_num,X4))),s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,X3),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))=>![X5]:(![X2]:![X3]:![X4]:s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),happ(s(t_fun(t_h4s_realaxs_real,t_fun(t_h4s_nums_num,t_h4s_realaxs_real)),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),t_fun(t_h4s_realaxs_real,t_fun(t_h4s_nums_num,t_h4s_realaxs_real))),X5),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X2))),s(t_h4s_realaxs_real,X3))),s(t_h4s_nums_num,X4)))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_powsers_diffs(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X2),s(t_h4s_nums_num,X4))),s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,X3),s(t_h4s_nums_num,X4)))))=>![X3]:![X6]:![X2]: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,X6))),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),happ(s(t_fun(t_h4s_realaxs_real,t_fun(t_h4s_nums_num,t_h4s_realaxs_real)),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),t_fun(t_h4s_realaxs_real,t_fun(t_h4s_nums_num,t_h4s_realaxs_real))),X5),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X2))),s(t_h4s_realaxs_real,X3)))))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(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,X6))),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),happ(s(t_fun(t_h4s_realaxs_real,t_fun(t_h4s_nums_num,t_h4s_realaxs_real)),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),t_fun(t_h4s_realaxs_real,t_fun(t_h4s_nums_num,t_h4s_realaxs_real))),X1),s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X2))),s(t_h4s_realaxs_real,X3))))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,X6))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),X2),s(t_h4s_nums_num,X6))),s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,X3),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X6),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))))))),file('i/f/powser/DIFFS__LEMMA2', ah4s_powsers_DIFFSu_u_LEMMA)).
# SZS output end CNFRefutation
