# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:(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_complexs_complexu_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,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)))))))))=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))),file('i/f/complex/COMPLEX__0__THM', ch4s_complexs_COMPLEXu_u_0u_u_THM)).
fof(6, axiom,![X5]:![X4]:(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,X4),s(t_h4s_realaxs_real,X4))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X5),s(t_h4s_realaxs_real,X5)))))=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,X4)=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,X5)=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/complex/COMPLEX__0__THM', ah4s_reals_REALu_u_SUMSQ)).
fof(7, axiom,![X4]:s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_real(s(t_h4s_realaxs_real,X4)))=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,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/complex/COMPLEX__0__THM', ah4s_complexs_complexu_u_ofu_u_real0)).
fof(8, axiom,![X6]:s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_num(s(t_h4s_nums_num,X6)))=s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_real(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,X6))))),file('i/f/complex/COMPLEX__0__THM', ah4s_complexs_complexu_u_ofu_u_num0)).
fof(9, 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/COMPLEX__0__THM', ah4s_reals_POWu_u_2)).
fof(10, 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/COMPLEX__0__THM', ah4s_complexs_RE0)).
fof(11, 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/COMPLEX__0__THM', ah4s_complexs_IM0)).
fof(12, axiom,![X7]:![X2]:![X5]:![X4]:s(X2,h4s_pairs_fst(s(t_h4s_pairs_prod(X2,X7),h4s_pairs_u_2c(s(X2,X4),s(X7,X5)))))=s(X2,X4),file('i/f/complex/COMPLEX__0__THM', ah4s_pairs_FST0)).
fof(13, axiom,![X2]:![X7]:![X5]:![X4]:s(X7,h4s_pairs_snd(s(t_h4s_pairs_prod(X2,X7),h4s_pairs_u_2c(s(X2,X4),s(X7,X5)))))=s(X7,X5),file('i/f/complex/COMPLEX__0__THM', ah4s_pairs_SND0)).
fof(14, axiom,![X2]:![X7]:![X8]:![X9]:(s(t_h4s_pairs_prod(X2,X7),X9)=s(t_h4s_pairs_prod(X2,X7),X8)<=>(s(X2,h4s_pairs_fst(s(t_h4s_pairs_prod(X2,X7),X9)))=s(X2,h4s_pairs_fst(s(t_h4s_pairs_prod(X2,X7),X8)))&s(X7,h4s_pairs_snd(s(t_h4s_pairs_prod(X2,X7),X9)))=s(X7,h4s_pairs_snd(s(t_h4s_pairs_prod(X2,X7),X8))))),file('i/f/complex/COMPLEX__0__THM', ah4s_pairs_PAIRu_u_FSTu_u_SNDu_u_EQ)).
# SZS output end CNFRefutation
