# 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),h4s_complexs_complexu_u_exp(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_neg(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_inv(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_exp(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X1))))),file('i/f/complex/COMPLEX__EXP__NEG', ch4s_complexs_COMPLEXu_u_EXPu_u_NEG)).
fof(8, axiom,![X1]:![X8]:((~(s(t_h4s_realaxs_real,X8)=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))&~(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_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_inv(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_scalaru_u_lmul(s(t_h4s_realaxs_real,X8),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_scalaru_u_lmul(s(t_h4s_realaxs_real,h4s_realaxs_inv(s(t_h4s_realaxs_real,X8))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_inv(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X1)))))),file('i/f/complex/COMPLEX__EXP__NEG', ah4s_complexs_COMPLEXu_u_INVu_u_SCALARu_u_LMUL)).
fof(9, axiom,![X7]:s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_inv(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_pairs_u_2c(s(t_h4s_realaxs_real,h4s_transcs_cos(s(t_h4s_realaxs_real,X7))),s(t_h4s_realaxs_real,h4s_transcs_sin(s(t_h4s_realaxs_real,X7)))))))=s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_pairs_u_2c(s(t_h4s_realaxs_real,h4s_transcs_cos(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,X7))))),s(t_h4s_realaxs_real,h4s_transcs_sin(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,X7))))))),file('i/f/complex/COMPLEX__EXP__NEG', ah4s_complexs_COMPLEXu_u_INVu_u_ARG)).
fof(10, axiom,![X1]:s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_exp(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_scalaru_u_lmul(s(t_h4s_realaxs_real,h4s_transcs_exp(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_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_pairs_u_2c(s(t_h4s_realaxs_real,h4s_transcs_cos(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_transcs_sin(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/COMPLEX__EXP__NEG', ah4s_complexs_complexu_u_exp0)).
fof(11, axiom,![X7]:~(s(t_h4s_realaxs_real,h4s_transcs_exp(s(t_h4s_realaxs_real,X7)))=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__EXP__NEG', ah4s_transcs_EXPu_u_NZ)).
fof(12, axiom,![X1]:s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_neg(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_realaxs_realu_u_neg(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/COMPLEX__EXP__NEG', ah4s_complexs_complexu_u_neg0)).
fof(16, axiom,p(s(t_bool,h4s_realaxs_realu_u_lt(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_realu_u_ofu_u_num(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/complex/COMPLEX__EXP__NEG', ah4s_reals_REALu_u_LTu_u_01)).
fof(17, 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))))<=>p(s(t_bool,h4s_realaxs_realu_u_lt(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_complexs_modu(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X1))))))),file('i/f/complex/COMPLEX__EXP__NEG', ah4s_complexs_MODUu_u_NZ)).
fof(19, axiom,![X7]:s(t_h4s_realaxs_real,h4s_transcs_exp(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,X7)))))=s(t_h4s_realaxs_real,h4s_realaxs_inv(s(t_h4s_realaxs_real,h4s_transcs_exp(s(t_h4s_realaxs_real,X7))))),file('i/f/complex/COMPLEX__EXP__NEG', ah4s_transcs_EXPu_u_NEG)).
fof(20, axiom,![X7]:s(t_h4s_realaxs_real,h4s_complexs_modu(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_pairs_u_2c(s(t_h4s_realaxs_real,h4s_transcs_cos(s(t_h4s_realaxs_real,X7))),s(t_h4s_realaxs_real,h4s_transcs_sin(s(t_h4s_realaxs_real,X7)))))))=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(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/complex/COMPLEX__EXP__NEG', ah4s_complexs_MODUu_u_UNIT)).
fof(21, axiom,![X9]:![X5]:![X6]:![X7]:s(X5,h4s_pairs_fst(s(t_h4s_pairs_prod(X5,X9),h4s_pairs_u_2c(s(X5,X7),s(X9,X6)))))=s(X5,X7),file('i/f/complex/COMPLEX__EXP__NEG', ah4s_pairs_FST0)).
fof(22, axiom,![X5]:![X9]:![X6]:![X7]:s(X9,h4s_pairs_snd(s(t_h4s_pairs_prod(X5,X9),h4s_pairs_u_2c(s(X5,X7),s(X9,X6)))))=s(X9,X6),file('i/f/complex/COMPLEX__EXP__NEG', ah4s_pairs_SND0)).
fof(23, 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__EXP__NEG', ah4s_complexs_IM0)).
fof(24, 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__EXP__NEG', ah4s_complexs_RE0)).
# SZS output end CNFRefutation
