# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]: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_complexs_modu(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),X1)))))),file('i/f/complex/MODU__POS', ch4s_complexs_MODUu_u_POS)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/complex/MODU__POS', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/complex/MODU__POS', aHLu_FALSITY)).
fof(6, axiom,![X2]:(s(t_bool,X2)=s(t_bool,t)<=>p(s(t_bool,X2))),file('i/f/complex/MODU__POS', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(7, axiom,![X3]:![X4]:((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,X4))))&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,X3)))))=>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,X4),s(t_h4s_realaxs_real,X3))))))),file('i/f/complex/MODU__POS', ah4s_reals_REALu_u_LEu_u_ADD)).
fof(8, axiom,![X4]: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,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)))))))))),file('i/f/complex/MODU__POS', ah4s_reals_REALu_u_LEu_u_POW2)).
fof(9, axiom,![X4]:(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,X4))))=>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_transcs_sqrt(s(t_h4s_realaxs_real,X4))))))),file('i/f/complex/MODU__POS', ah4s_transcs_SQRTu_u_POSu_u_LE)).
fof(10, 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__POS', ah4s_complexs_modu0)).
fof(11, axiom,![X2]:(s(t_bool,X2)=s(t_bool,t)|s(t_bool,X2)=s(t_bool,f)),file('i/f/complex/MODU__POS', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
