# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![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_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_transcs_sin(s(t_h4s_realaxs_real,h4s_complexs_arg(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X1))))))),file('i/f/complex/IM__MODU__ARG', ch4s_complexs_IMu_u_MODUu_u_ARG)).
fof(3, axiom,![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,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))),file('i/f/complex/IM__MODU__ARG', ah4s_reals_REALu_u_MULu_u_LZERO)).
fof(7, axiom,![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_transcs_sin(s(t_h4s_realaxs_real,h4s_complexs_arg(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X1)))))=s(t_h4s_realaxs_real,h4s_reals_u_2f(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_modu(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X1)))))),file('i/f/complex/IM__MODU__ARG', ah4s_complexs_ARGu_u_SIN)).
fof(12, axiom,![X3]:![X4]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X4),s(t_h4s_realaxs_real,X3)))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X4))),file('i/f/complex/IM__MODU__ARG', ah4s_reals_REALu_u_ADDu_u_COMM)).
fof(15, axiom,![X3]:![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,X3),s(t_h4s_realaxs_real,X3)))))=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,X3)=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/complex/IM__MODU__ARG', ah4s_reals_REALu_u_SUMSQ)).
fof(24, axiom,![X3]:![X4]:(~(s(t_h4s_realaxs_real,X3)=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_mul(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,h4s_reals_u_2f(s(t_h4s_realaxs_real,X4),s(t_h4s_realaxs_real,X3)))))=s(t_h4s_realaxs_real,X4)),file('i/f/complex/IM__MODU__ARG', ah4s_reals_REALu_u_DIVu_u_LMUL)).
fof(28, axiom,![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_complexs_modu(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X1)))=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))),file('i/f/complex/IM__MODU__ARG', ah4s_complexs_MODUu_u_ZERO)).
fof(29, axiom,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_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/complex/IM__MODU__ARG', ah4s_complexs_MODUu_u_0)).
fof(45, axiom,![X1]:s(t_h4s_realaxs_real,h4s_reals_pow(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_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,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/IM__MODU__ARG', ah4s_complexs_MODUu_u_POW2)).
fof(46, 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/IM__MODU__ARG', ah4s_reals_POWu_u_2)).
# SZS output end CNFRefutation
