# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,s(t_h4s_integers_int,h4s_rats_ratu_u_sgn(s(t_h4s_rats_rat,h4s_rats_ratu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/rat/RAT__SGN__0', ch4s_rats_RATu_u_SGNu_u_0)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/rat/RAT__SGN__0', aHLu_TRUTH)).
fof(5, axiom,![X3]:s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,h4s_integers_intu_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,X3)))))))))=s(t_bool,t),file('i/f/rat/RAT__SGN__0', ah4s_integers_INTu_u_LTu_u_REDUCEu_c0)).
fof(6, axiom,![X2]:?[X4]:((p(s(t_bool,X4))<=>s(t_h4s_integers_int,X2)=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))&s(t_h4s_integers_int,h4s_intextensions_sgn(s(t_h4s_integers_int,X2)))=s(t_h4s_integers_int,h4s_bools_cond(s(t_bool,X4),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,h4s_bools_cond(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X2),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_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))))))))),s(t_h4s_integers_int,h4s_integers_intu_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/rat/RAT__SGN__0', ah4s_intExtensions_SGNu_u_def)).
fof(7, axiom,s(t_h4s_fracs_frac,h4s_fracs_fracu_u_0)=s(t_h4s_fracs_frac,h4s_fracs_absu_u_frac(s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,h4s_integers_intu_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/rat/RAT__SGN__0', ah4s_fracs_fracu_u_0u_u_def)).
fof(8, axiom,![X5]:![X6]:(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,X5))))=>s(t_h4s_integers_int,h4s_fracs_fracu_u_nmr(s(t_h4s_fracs_frac,h4s_fracs_absu_u_frac(s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_integers_int,X6),s(t_h4s_integers_int,X5)))))))=s(t_h4s_integers_int,X6)),file('i/f/rat/RAT__SGN__0', ah4s_fracs_NMR)).
fof(9, axiom,s(t_h4s_rats_rat,h4s_rats_ratu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_rats_rat,h4s_rats_absu_u_rat(s(t_h4s_fracs_frac,h4s_fracs_fracu_u_0))),file('i/f/rat/RAT__SGN__0', ah4s_rats_ratu_u_00)).
fof(10, axiom,![X7]:s(t_h4s_integers_int,h4s_fracs_fracu_u_sgn(s(t_h4s_fracs_frac,X7)))=s(t_h4s_integers_int,h4s_intextensions_sgn(s(t_h4s_integers_int,h4s_fracs_fracu_u_nmr(s(t_h4s_fracs_frac,X7))))),file('i/f/rat/RAT__SGN__0', ah4s_fracs_fracu_u_sgnu_u_def)).
fof(11, axiom,![X8]:s(t_h4s_integers_int,h4s_rats_ratu_u_sgn(s(t_h4s_rats_rat,X8)))=s(t_h4s_integers_int,h4s_fracs_fracu_u_sgn(s(t_h4s_fracs_frac,h4s_rats_repu_u_rat(s(t_h4s_rats_rat,X8))))),file('i/f/rat/RAT__SGN__0', ah4s_rats_ratu_u_sgnu_u_def)).
fof(12, axiom,![X7]:s(t_h4s_integers_int,h4s_fracs_fracu_u_sgn(s(t_h4s_fracs_frac,h4s_rats_repu_u_rat(s(t_h4s_rats_rat,h4s_rats_absu_u_rat(s(t_h4s_fracs_frac,X7)))))))=s(t_h4s_integers_int,h4s_fracs_fracu_u_sgn(s(t_h4s_fracs_frac,X7))),file('i/f/rat/RAT__SGN__0', ah4s_rats_RATu_u_SGNu_u_CONG)).
fof(13, axiom,~(p(s(t_bool,f))),file('i/f/rat/RAT__SGN__0', aHLu_FALSITY)).
fof(14, axiom,![X9]:(s(t_bool,X9)=s(t_bool,t)|s(t_bool,X9)=s(t_bool,f)),file('i/f/rat/RAT__SGN__0', aHLu_BOOLu_CASES)).
fof(15, axiom,![X1]:![X10]:![X11]:s(X1,h4s_bools_cond(s(t_bool,t),s(X1,X11),s(X1,X10)))=s(X1,X11),file('i/f/rat/RAT__SGN__0', ah4s_bools_CONDu_u_CLAUSESu_c0)).
# SZS output end CNFRefutation
