# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:s(t_h4s_integers_int,h4s_integers_intu_u_rem(s(t_h4s_integers_int,h4s_integers_intu_u_neg(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,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_bit2(s(t_h4s_nums_num,X1)))))))))=s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,X1))))))))))),file('i/f/integer/INT__REM__REDUCE_c5', ch4s_integers_INTu_u_REMu_u_REDUCEu_c5)).
fof(2, axiom,![X3]:s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X3)))=s(t_h4s_nums_num,X3),file('i/f/integer/INT__REM__REDUCE_c5', ah4s_arithmetics_NUMERALu_u_DEF)).
fof(7, axiom,![X1]:![X2]:(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X2)))=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X1)))<=>s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,X1)),file('i/f/integer/INT__REM__REDUCE_c5', ah4s_integers_INTu_u_INJ)).
fof(29, 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_rem(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,X12))),s(t_h4s_integers_int,X11)))=s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_rem(s(t_h4s_integers_int,X12),s(t_h4s_integers_int,X11)))))&s(t_h4s_integers_int,h4s_integers_intu_u_rem(s(t_h4s_integers_int,X12),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,X11)))))=s(t_h4s_integers_int,h4s_integers_intu_u_rem(s(t_h4s_integers_int,X12),s(t_h4s_integers_int,X11))))),file('i/f/integer/INT__REM__REDUCE_c5', ah4s_integers_INTu_u_REMu_u_CALCULATEu_c1)).
fof(39, axiom,![X1]:![X2]:s(t_h4s_integers_int,h4s_integers_intu_u_rem(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,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_bit2(s(t_h4s_nums_num,X1)))))))))=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,X1))))))))),file('i/f/integer/INT__REM__REDUCE_c5', ah4s_integers_INTu_u_REMu_u_REDUCEu_c3)).
fof(54, 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__REM__REDUCE_c5', ah4s_arithmetics_ONE)).
fof(55, axiom,s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))=s(t_h4s_nums_num,h4s_nums_suc(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/integer/INT__REM__REDUCE_c5', ah4s_arithmetics_TWO)).
fof(56, axiom,![X1]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(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,X1))),file('i/f/integer/INT__REM__REDUCE_c5', ah4s_arithmetics_SUCu_u_ONEu_u_ADD)).
fof(57, axiom,![X1]:s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))))))),file('i/f/integer/INT__REM__REDUCE_c5', ah4s_arithmetics_BIT20)).
fof(59, axiom,![X1]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_bool,f),file('i/f/integer/INT__REM__REDUCE_c5', ah4s_numerals_numeralu_u_lteu_c2)).
fof(60, axiom,![X2]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X2),file('i/f/integer/INT__REM__REDUCE_c5', ah4s_arithmetics_ADDu_u_CLAUSESu_c1)).
fof(61, axiom,![X1]:![X2]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2))),file('i/f/integer/INT__REM__REDUCE_c5', ah4s_arithmetics_ADDu_u_SYM)).
fof(65, axiom,![X1]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X1)))),file('i/f/integer/INT__REM__REDUCE_c5', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(69, axiom,![X1]:![X2]:(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_nums_0)<=>(s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,h4s_nums_0)&s(t_h4s_nums_num,X1)=s(t_h4s_nums_num,h4s_nums_0))),file('i/f/integer/INT__REM__REDUCE_c5', ah4s_arithmetics_ADDu_u_EQu_u_0)).
fof(74, axiom,~(p(s(t_bool,f))),file('i/f/integer/INT__REM__REDUCE_c5', aHLu_FALSITY)).
fof(78, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)<=>p(s(t_bool,X5))),file('i/f/integer/INT__REM__REDUCE_c5', ah4s_bools_EQu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
