# 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_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_bit1(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_bit1(s(t_h4s_nums_num,X1))))))))))),file('i/f/integer/INT__REM__REDUCE_c8', ch4s_integers_INTu_u_REMu_u_REDUCEu_c8)).
fof(13, axiom,![X11]:![X10]:(~(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,X10))),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,X10),s(t_h4s_integers_int,X11)))))&s(t_h4s_integers_int,h4s_integers_intu_u_rem(s(t_h4s_integers_int,X10),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,X10),s(t_h4s_integers_int,X11))))),file('i/f/integer/INT__REM__REDUCE_c8', ah4s_integers_INTu_u_REMu_u_CALCULATEu_c1)).
fof(15, axiom,![X11]:![X10]:(~(s(t_h4s_nums_num,X11)=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_ofu_u_num(s(t_h4s_nums_num,X10))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X11)))))=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,X10),s(t_h4s_nums_num,X11)))))),file('i/f/integer/INT__REM__REDUCE_c8', ah4s_integers_INTu_u_REMu_u_CALCULATEu_c0)).
fof(16, 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_c8', ah4s_integers_INTu_u_REMu_u_CALCULATEu_c3)).
fof(18, axiom,![X7]:s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X7)))=s(t_h4s_nums_num,X7),file('i/f/integer/INT__REM__REDUCE_c8', ah4s_arithmetics_NUMERALu_u_DEF)).
fof(28, axiom,![X1]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit1(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_c8', ah4s_numerals_numeralu_u_lteu_c1)).
fof(29, axiom,s(t_h4s_nums_num,h4s_arithmetics_zero)=s(t_h4s_nums_num,h4s_nums_0),file('i/f/integer/INT__REM__REDUCE_c8', ah4s_arithmetics_ALTu_u_ZERO)).
fof(36, 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_c8', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(41, axiom,~(p(s(t_bool,f))),file('i/f/integer/INT__REM__REDUCE_c8', aHLu_FALSITY)).
fof(42, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)|s(t_bool,X6)=s(t_bool,f)),file('i/f/integer/INT__REM__REDUCE_c8', aHLu_BOOLu_CASES)).
fof(50, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)<=>p(s(t_bool,X6))),file('i/f/integer/INT__REM__REDUCE_c8', ah4s_bools_EQu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
