# 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_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_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,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_c7', ch4s_integers_INTu_u_REMu_u_REDUCEu_c7)).
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_c7', ah4s_arithmetics_NUMERALu_u_DEF)).
fof(5, 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_c7', ah4s_integers_INTu_u_INJ)).
fof(19, 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_c7', ah4s_integers_INTu_u_REMu_u_REDUCEu_c3)).
fof(31, axiom,![X14]:![X15]:(~(s(t_h4s_integers_int,X14)=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,X15))),s(t_h4s_integers_int,X14)))=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,X15),s(t_h4s_integers_int,X14)))))&s(t_h4s_integers_int,h4s_integers_intu_u_rem(s(t_h4s_integers_int,X15),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,X14)))))=s(t_h4s_integers_int,h4s_integers_intu_u_rem(s(t_h4s_integers_int,X15),s(t_h4s_integers_int,X14))))),file('i/f/integer/INT__REM__REDUCE_c7', ah4s_integers_INTu_u_REMu_u_CALCULATEu_c1)).
fof(56, 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_c7', ah4s_numerals_numeralu_u_lteu_c2)).
fof(68, axiom,![X7]:(s(t_bool,X7)=s(t_bool,f)<=>~(p(s(t_bool,X7)))),file('i/f/integer/INT__REM__REDUCE_c7', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(78, 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_c7', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
# SZS output end CNFRefutation
