# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:s(t_h4s_realaxs_real,h4s_complexs_modu(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_conj(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),X1))),file('i/f/complex/MODU__CONJ', ch4s_complexs_MODUu_u_CONJ)).
fof(6, 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__CONJ', ah4s_complexs_modu0)).
fof(7, axiom,![X5]:![X2]:![X6]:![X4]:s(X2,h4s_pairs_fst(s(t_h4s_pairs_prod(X2,X5),h4s_pairs_u_2c(s(X2,X4),s(X5,X6)))))=s(X2,X4),file('i/f/complex/MODU__CONJ', ah4s_pairs_FST0)).
fof(8, axiom,![X2]:![X5]:![X6]:![X4]:s(X5,h4s_pairs_snd(s(t_h4s_pairs_prod(X2,X5),h4s_pairs_u_2c(s(X2,X4),s(X5,X6)))))=s(X5,X6),file('i/f/complex/MODU__CONJ', ah4s_pairs_SND0)).
fof(9, 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__CONJ', ah4s_complexs_RE0)).
fof(10, 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__CONJ', ah4s_complexs_IM0)).
fof(11, axiom,![X1]:s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_conj(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),h4s_pairs_u_2c(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_realaxs_realu_u_neg(s(t_h4s_realaxs_real,h4s_complexs_im(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X1))))))),file('i/f/complex/MODU__CONJ', ah4s_complexs_conj0)).
fof(12, axiom,![X6]:![X4]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,X4))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,X6)))))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X4),s(t_h4s_realaxs_real,X6))),file('i/f/complex/MODU__CONJ', ah4s_reals_REALu_u_NEGu_u_MUL2)).
fof(13, axiom,![X4]:s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,X4),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,X4),s(t_h4s_realaxs_real,X4))),file('i/f/complex/MODU__CONJ', ah4s_reals_POWu_u_2)).
# SZS output end CNFRefutation
