# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:s(t_h4s_fracs_frac,h4s_fracs_fracu_u_mul(s(t_h4s_fracs_frac,X1),s(t_h4s_fracs_frac,h4s_fracs_fracu_u_1)))=s(t_h4s_fracs_frac,X1),file('i/f/frac/FRAC__MUL__RID', ch4s_fracs_FRACu_u_MULu_u_RID)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/frac/FRAC__MUL__RID', aHLu_TRUTH)).
fof(5, 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/frac/FRAC__MUL__RID', ah4s_fracs_fracu_u_1u_u_def)).
fof(6, axiom,![X4]:![X5]:s(t_h4s_fracs_frac,h4s_fracs_fracu_u_mul(s(t_h4s_fracs_frac,X5),s(t_h4s_fracs_frac,X4)))=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_mul(s(t_h4s_integers_int,h4s_fracs_fracu_u_nmr(s(t_h4s_fracs_frac,X5))),s(t_h4s_integers_int,h4s_fracs_fracu_u_nmr(s(t_h4s_fracs_frac,X4))))),s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_fracs_fracu_u_dnm(s(t_h4s_fracs_frac,X5))),s(t_h4s_integers_int,h4s_fracs_fracu_u_dnm(s(t_h4s_fracs_frac,X4))))))))),file('i/f/frac/FRAC__MUL__RID', ah4s_fracs_fracu_u_mulu_u_def)).
fof(7, axiom,![X6]: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,X6))),s(t_h4s_integers_int,h4s_fracs_fracu_u_dnm(s(t_h4s_fracs_frac,X6)))))))=s(t_h4s_fracs_frac,X6),file('i/f/frac/FRAC__MUL__RID', ah4s_fracs_FRAC)).
fof(8, axiom,![X7]:![X1]:(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,X7))))=>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,X1),s(t_h4s_integers_int,X7)))))))=s(t_h4s_integers_int,X1)),file('i/f/frac/FRAC__MUL__RID', ah4s_fracs_NMR)).
fof(9, axiom,![X7]:![X1]:(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,X7))))=>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,X1),s(t_h4s_integers_int,X7)))))))=s(t_h4s_integers_int,X7)),file('i/f/frac/FRAC__MUL__RID', ah4s_fracs_DNM)).
fof(12, 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/frac/FRAC__MUL__RID', ah4s_numerals_numeralu_u_ltu_c0)).
fof(13, 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/frac/FRAC__MUL__RID', ah4s_numerals_numeralu_u_distribu_c21)).
fof(14, 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/frac/FRAC__MUL__RID', ah4s_integers_INTu_u_LTu_u_CALCULATEu_c0)).
fof(15, 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/frac/FRAC__MUL__RID', ah4s_integers_INTu_u_MULu_u_RID)).
# SZS output end CNFRefutation
