# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:(s(t_h4s_rats_rat,h4s_rats_absu_u_rat(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_fracs_fracu_u_nmr(s(t_h4s_fracs_frac,X1))),s(t_h4s_integers_int,h4s_fracs_fracu_u_dnm(s(t_h4s_fracs_frac,X1)))))))))=s(t_h4s_rats_rat,h4s_rats_ratu_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_fracs_fracu_u_nmr(s(t_h4s_fracs_frac,X1)))=s(t_h4s_integers_int,h4s_fracs_fracu_u_dnm(s(t_h4s_fracs_frac,X1)))),file('i/f/rat/RAT__NMRDNM__EQ', ch4s_rats_RATu_u_NMRDNMu_u_EQ)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/rat/RAT__NMRDNM__EQ', aHLu_TRUTH)).
fof(6, axiom,![X5]: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,h4s_fracs_fracu_u_dnm(s(t_h4s_fracs_frac,X5)))))),file('i/f/rat/RAT__NMRDNM__EQ', ah4s_fracs_FRACu_u_DNMPOS)).
fof(7, 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_dnm(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,X6)),file('i/f/rat/RAT__NMRDNM__EQ', ah4s_fracs_DNM)).
fof(8, axiom,![X8]:![X1]:(p(s(t_bool,h4s_rats_ratu_u_equiv(s(t_h4s_fracs_frac,X1),s(t_h4s_fracs_frac,X8))))<=>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,X1))),s(t_h4s_integers_int,h4s_fracs_fracu_u_dnm(s(t_h4s_fracs_frac,X8)))))=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,X1)))))),file('i/f/rat/RAT__NMRDNM__EQ', ah4s_rats_ratu_u_equivu_u_def)).
fof(9, axiom,s(t_h4s_fracs_frac,h4s_fracs_fracu_u_1)=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_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__NMRDNM__EQ', ah4s_fracs_fracu_u_1u_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__NMRDNM__EQ', ah4s_fracs_NMR)).
fof(11, axiom,s(t_h4s_rats_rat,h4s_rats_ratu_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_rats_rat,h4s_rats_absu_u_rat(s(t_h4s_fracs_frac,h4s_fracs_fracu_u_1))),file('i/f/rat/RAT__NMRDNM__EQ', ah4s_rats_ratu_u_10)).
fof(12, axiom,![X8]:![X1]:(s(t_h4s_rats_rat,h4s_rats_absu_u_rat(s(t_h4s_fracs_frac,X1)))=s(t_h4s_rats_rat,h4s_rats_absu_u_rat(s(t_h4s_fracs_frac,X8)))<=>p(s(t_bool,h4s_rats_ratu_u_equiv(s(t_h4s_fracs_frac,X1),s(t_h4s_fracs_frac,X8))))),file('i/f/rat/RAT__NMRDNM__EQ', ah4s_rats_RATu_u_ABSu_u_EQUIV)).
fof(13, 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_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_integers_int,X3)))=s(t_h4s_integers_int,X3),file('i/f/rat/RAT__NMRDNM__EQ', ah4s_integers_INTu_u_MULu_u_LID)).
fof(14, axiom,![X3]:s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,X3),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,X3),file('i/f/rat/RAT__NMRDNM__EQ', ah4s_integers_INTu_u_MULu_u_RID)).
fof(15, axiom,![X9]:![X10]: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,X9))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X10)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X10))),file('i/f/rat/RAT__NMRDNM__EQ', ah4s_integers_INTu_u_LTu_u_CALCULATEu_c0)).
fof(16, axiom,![X9]:s(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,X9)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,X9))),file('i/f/rat/RAT__NMRDNM__EQ', ah4s_numerals_numeralu_u_distribu_c21)).
fof(17, axiom,![X9]:s(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,X9)))))=s(t_bool,t),file('i/f/rat/RAT__NMRDNM__EQ', ah4s_numerals_numeralu_u_ltu_c0)).
fof(18, axiom,~(p(s(t_bool,f))),file('i/f/rat/RAT__NMRDNM__EQ', aHLu_FALSITY)).
fof(19, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)|s(t_bool,X4)=s(t_bool,f)),file('i/f/rat/RAT__NMRDNM__EQ', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
