# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:s(t_h4s_realaxs_real,h4s_complexs_modu(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_mul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X1),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X2)))))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_complexs_modu(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X1))),s(t_h4s_realaxs_real,h4s_complexs_modu(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X2))))),file('i/f/complex/MODU__MUL', ch4s_complexs_MODUu_u_MUL)).
fof(14, axiom,![X1]:s(t_h4s_realaxs_real,h4s_complexs_modu(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X1)))=s(t_h4s_realaxs_real,h4s_transcs_sqrt(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,h4s_complexs_re(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X1))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,h4s_complexs_im(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X1))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))),file('i/f/complex/MODU__MUL', ah4s_complexs_modu0)).
fof(15, axiom,![X1]:![X2]:s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_mul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X1),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X2)))=s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_pairs_u_2c(s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_complexs_re(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X1))),s(t_h4s_realaxs_real,h4s_complexs_re(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X2))))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_complexs_im(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X1))),s(t_h4s_realaxs_real,h4s_complexs_im(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X2))))))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_complexs_re(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X1))),s(t_h4s_realaxs_real,h4s_complexs_im(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X2))))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_complexs_im(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X1))),s(t_h4s_realaxs_real,h4s_complexs_re(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X2))))))))),file('i/f/complex/MODU__MUL', ah4s_complexs_complexu_u_mul0)).
fof(16, axiom,![X7]:![X8]:((p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,X8))))&p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,X7)))))=>s(t_h4s_realaxs_real,h4s_transcs_sqrt(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X8),s(t_h4s_realaxs_real,X7)))))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_transcs_sqrt(s(t_h4s_realaxs_real,X8))),s(t_h4s_realaxs_real,h4s_transcs_sqrt(s(t_h4s_realaxs_real,X7)))))),file('i/f/complex/MODU__MUL', ah4s_transcs_SQRTu_u_MUL)).
fof(17, axiom,![X7]:![X8]:((p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,X8))))&p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,X7)))))=>p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X8),s(t_h4s_realaxs_real,X7))))))),file('i/f/complex/MODU__MUL', ah4s_reals_REALu_u_LEu_u_ADD)).
fof(18, axiom,![X8]:p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,X8),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))),file('i/f/complex/MODU__MUL', ah4s_reals_REALu_u_LEu_u_POW2)).
fof(19, axiom,![X15]:![X16]:![X17]:![X18]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X18),s(t_h4s_realaxs_real,X16))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X17),s(t_h4s_realaxs_real,X15))))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X18),s(t_h4s_realaxs_real,X15))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X17),s(t_h4s_realaxs_real,X16))))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,X18),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,X17),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,X16),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,X15),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))),file('i/f/complex/MODU__MUL', ah4s_complexs_COMPLEXu_u_LEMMA1)).
fof(20, axiom,![X1]:s(t_h4s_realaxs_real,h4s_complexs_im(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X1)))=s(t_h4s_realaxs_real,h4s_pairs_snd(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X1))),file('i/f/complex/MODU__MUL', ah4s_complexs_IM0)).
fof(21, axiom,![X1]:s(t_h4s_realaxs_real,h4s_complexs_re(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X1)))=s(t_h4s_realaxs_real,h4s_pairs_fst(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X1))),file('i/f/complex/MODU__MUL', ah4s_complexs_RE0)).
fof(22, axiom,![X19]:![X6]:![X7]:![X8]:s(X6,h4s_pairs_fst(s(t_h4s_pairs_prod(X6,X19),h4s_pairs_u_2c(s(X6,X8),s(X19,X7)))))=s(X6,X8),file('i/f/complex/MODU__MUL', ah4s_pairs_FST0)).
fof(23, axiom,![X6]:![X19]:![X7]:![X8]:s(X19,h4s_pairs_snd(s(t_h4s_pairs_prod(X6,X19),h4s_pairs_u_2c(s(X6,X8),s(X19,X7)))))=s(X19,X7),file('i/f/complex/MODU__MUL', ah4s_pairs_SND0)).
# SZS output end CNFRefutation
