# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:(s(t_h4s_rats_rat,X1)=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_rats_ratu_u_nmr(s(t_h4s_rats_rat,X1)))=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__EQ0__NMR', ch4s_rats_RATu_u_EQ0u_u_NMR)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/rat/RAT__EQ0__NMR', aHLu_TRUTH)).
fof(7, axiom,![X3]:s(t_h4s_integers_int,h4s_integers_intu_u_mul(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,X3)))=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__EQ0__NMR', ah4s_integers_INTu_u_MULu_u_LZERO)).
fof(8, axiom,![X5]: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,X5)))))))))=s(t_bool,t),file('i/f/rat/RAT__EQ0__NMR', ah4s_integers_INTu_u_LTu_u_REDUCEu_c0)).
fof(9, 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__EQ0__NMR', ah4s_fracs_fracu_u_0u_u_def)).
fof(10, axiom,![X6]:![X7]:(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,X6))))=>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,X7),s(t_h4s_integers_int,X6)))))))=s(t_h4s_integers_int,X7)),file('i/f/rat/RAT__EQ0__NMR', ah4s_fracs_NMR)).
fof(12, axiom,![X8]:(s(t_h4s_integers_int,h4s_fracs_fracu_u_nmr(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,X8)))))))=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_fracs_fracu_u_nmr(s(t_h4s_fracs_frac,X8)))=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__EQ0__NMR', ah4s_rats_RATu_u_NMREQ0u_u_CONG)).
fof(13, 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__EQ0__NMR', ah4s_rats_ratu_u_00)).
fof(14, axiom,![X9]:![X8]:(p(s(t_bool,h4s_rats_ratu_u_equiv(s(t_h4s_fracs_frac,X8),s(t_h4s_fracs_frac,X9))))<=>s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_fracs_fracu_u_nmr(s(t_h4s_fracs_frac,X8))),s(t_h4s_integers_int,h4s_fracs_fracu_u_dnm(s(t_h4s_fracs_frac,X9)))))=s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_fracs_fracu_u_nmr(s(t_h4s_fracs_frac,X9))),s(t_h4s_integers_int,h4s_fracs_fracu_u_dnm(s(t_h4s_fracs_frac,X8)))))),file('i/f/rat/RAT__EQ0__NMR', ah4s_rats_ratu_u_equivu_u_def)).
fof(15, axiom,![X10]:s(t_h4s_integers_int,h4s_rats_ratu_u_nmr(s(t_h4s_rats_rat,X10)))=s(t_h4s_integers_int,h4s_fracs_fracu_u_nmr(s(t_h4s_fracs_frac,h4s_rats_repu_u_rat(s(t_h4s_rats_rat,X10))))),file('i/f/rat/RAT__EQ0__NMR', ah4s_rats_ratu_u_nmru_u_def)).
fof(16, axiom,![X10]:s(t_h4s_rats_rat,h4s_rats_absu_u_rat(s(t_h4s_fracs_frac,h4s_rats_repu_u_rat(s(t_h4s_rats_rat,X10)))))=s(t_h4s_rats_rat,X10),file('i/f/rat/RAT__EQ0__NMR', ah4s_rats_RAT)).
fof(17, axiom,![X9]:![X8]:(s(t_h4s_rats_rat,h4s_rats_absu_u_rat(s(t_h4s_fracs_frac,X8)))=s(t_h4s_rats_rat,h4s_rats_absu_u_rat(s(t_h4s_fracs_frac,X9)))<=>p(s(t_bool,h4s_rats_ratu_u_equiv(s(t_h4s_fracs_frac,X8),s(t_h4s_fracs_frac,X9))))),file('i/f/rat/RAT__EQ0__NMR', ah4s_rats_RATu_u_ABSu_u_EQUIV)).
fof(18, axiom,~(p(s(t_bool,f))),file('i/f/rat/RAT__EQ0__NMR', aHLu_FALSITY)).
fof(19, axiom,![X11]:(s(t_bool,X11)=s(t_bool,t)|s(t_bool,X11)=s(t_bool,f)),file('i/f/rat/RAT__EQ0__NMR', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
