# 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,happ(s(t_fun(t_h4s_nums_num,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(27, axiom,![X23]:![X24]:(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,X23))))=>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,X24),s(t_h4s_integers_int,X23)))))))=s(t_h4s_integers_int,X24)),file('i/f/rat/RAT__EQ0__NMR', ah4s_fracs_NMR)).
fof(31, axiom,![X25]:![X26]: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,X25))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X26)))))=s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,X25))),s(t_h4s_nums_num,X26))),file('i/f/rat/RAT__EQ0__NMR', ah4s_integers_INTu_u_LTu_u_CALCULATEu_c0)).
fof(32, axiom,![X27]:(s(t_h4s_integers_int,h4s_fracs_fracu_u_nmr(s(t_h4s_fracs_frac,happ(s(t_fun(t_h4s_rats_rat,t_h4s_fracs_frac),h4s_rats_repu_u_rat),s(t_h4s_rats_rat,happ(s(t_fun(t_h4s_fracs_frac,t_h4s_rats_rat),h4s_rats_absu_u_rat),s(t_h4s_fracs_frac,X27)))))))=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,X27)))=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(36, axiom,![X6]: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,X6)))=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(41, axiom,![X25]:s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X25)))))=s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_arithmetics_zero))),s(t_h4s_nums_num,X25))),file('i/f/rat/RAT__EQ0__NMR', ah4s_numerals_numeralu_u_distribu_c21)).
fof(43, axiom,s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0)))=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_numerals_numeralu_u_distribu_c13)).
fof(44, axiom,![X9]:s(t_h4s_integers_int,h4s_rats_ratu_u_nmr(s(t_h4s_rats_rat,X9)))=s(t_h4s_integers_int,h4s_fracs_fracu_u_nmr(s(t_h4s_fracs_frac,happ(s(t_fun(t_h4s_rats_rat,t_h4s_fracs_frac),h4s_rats_repu_u_rat),s(t_h4s_rats_rat,X9))))),file('i/f/rat/RAT__EQ0__NMR', ah4s_rats_ratu_u_nmru_u_def)).
fof(45, axiom,![X29]:![X1]:(s(t_h4s_rats_rat,X1)=s(t_h4s_rats_rat,X29)<=>s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_rats_ratu_u_nmr(s(t_h4s_rats_rat,X1))),s(t_h4s_integers_int,h4s_rats_ratu_u_dnm(s(t_h4s_rats_rat,X29)))))=s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_rats_ratu_u_nmr(s(t_h4s_rats_rat,X29))),s(t_h4s_integers_int,h4s_rats_ratu_u_dnm(s(t_h4s_rats_rat,X1)))))),file('i/f/rat/RAT__EQ0__NMR', ah4s_rats_RATu_u_EQu_u_ALT)).
fof(47, axiom,s(t_h4s_rats_rat,happ(s(t_fun(t_h4s_nums_num,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_ratu_u_0),file('i/f/rat/RAT__EQ0__NMR', ah4s_rats_ratu_u_ofu_u_numu_u_defu_u_computeu_c0)).
fof(48, axiom,s(t_h4s_rats_rat,happ(s(t_fun(t_h4s_nums_num,t_h4s_rats_rat),h4s_rats_ratu_u_ofu_u_num),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_rats_rat,happ(s(t_fun(t_h4s_fracs_frac,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(54, axiom,p(s(t_bool,t)),file('i/f/rat/RAT__EQ0__NMR', aHLu_TRUTH)).
fof(77, 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(81, axiom,![X25]:s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_arithmetics_zero))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X25)))))=s(t_bool,t),file('i/f/rat/RAT__EQ0__NMR', ah4s_numerals_numeralu_u_ltu_c0)).
# SZS output end CNFRefutation
