# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:s(t_h4s_integers_int,h4s_integers_intu_u_mod(s(t_h4s_integers_int,X1),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,X2)))))))))=s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,X1),s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_div(s(t_h4s_integers_int,X1),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,X2))))))))),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,X2))))))))))),file('i/f/integer/INT__MOD__REDUCE_c4', ch4s_integers_INTu_u_MODu_u_REDUCEu_c4)).
fof(11, axiom,![X2]:![X9]:(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,h4s_nums_0)<=>(s(t_h4s_nums_num,X9)=s(t_h4s_nums_num,h4s_nums_0)&s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,h4s_nums_0))),file('i/f/integer/INT__MOD__REDUCE_c4', ah4s_arithmetics_ADDu_u_EQu_u_0)).
fof(13, axiom,![X11]:![X12]:(~(s(t_h4s_integers_int,X11)=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_mod(s(t_h4s_integers_int,X12),s(t_h4s_integers_int,X11)))=s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,X12),s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_div(s(t_h4s_integers_int,X12),s(t_h4s_integers_int,X11))),s(t_h4s_integers_int,X11)))))),file('i/f/integer/INT__MOD__REDUCE_c4', ah4s_integers_intu_u_mod0)).
fof(15, axiom,![X2]:![X9]:(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,X2)))<=>s(t_h4s_nums_num,X9)=s(t_h4s_nums_num,X2)),file('i/f/integer/INT__MOD__REDUCE_c4', ah4s_integers_INTu_u_MODu_u_CALCULATEu_c3)).
fof(16, axiom,![X1]:s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,X1),file('i/f/integer/INT__MOD__REDUCE_c4', ah4s_arithmetics_NUMERALu_u_DEF)).
fof(17, axiom,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_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/integer/INT__MOD__REDUCE_c4', ah4s_arithmetics_ONE)).
fof(21, axiom,![X9]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X9),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_nums_num,X9),file('i/f/integer/INT__MOD__REDUCE_c4', ah4s_arithmetics_MULTu_u_CLAUSESu_c3)).
fof(24, axiom,![X2]:s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))))),file('i/f/integer/INT__MOD__REDUCE_c4', ah4s_arithmetics_BIT10)).
fof(27, axiom,s(t_h4s_nums_num,h4s_arithmetics_zero)=s(t_h4s_nums_num,h4s_nums_0),file('i/f/integer/INT__MOD__REDUCE_c4', ah4s_arithmetics_ALTu_u_ZERO)).
fof(28, axiom,![X9]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/integer/INT__MOD__REDUCE_c4', ah4s_arithmetics_MULTu_u_CLAUSESu_c1)).
fof(34, axiom,![X2]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X2)))),file('i/f/integer/INT__MOD__REDUCE_c4', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(35, axiom,![X2]:![X9]:(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,h4s_nums_0)<=>(s(t_h4s_nums_num,X9)=s(t_h4s_nums_num,h4s_nums_0)|s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,h4s_nums_0))),file('i/f/integer/INT__MOD__REDUCE_c4', ah4s_arithmetics_MULTu_u_EQu_u_0)).
fof(39, axiom,~(p(s(t_bool,f))),file('i/f/integer/INT__MOD__REDUCE_c4', aHLu_FALSITY)).
fof(54, axiom,![X2]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_bool,f),file('i/f/integer/INT__MOD__REDUCE_c4', ah4s_numerals_numeralu_u_lteu_c2)).
fof(55, axiom,![X2]:![X9]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X2)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X9))))),file('i/f/integer/INT__MOD__REDUCE_c4', ah4s_arithmetics_NOTu_u_LESS)).
# SZS output end CNFRefutation
