# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]: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_nums_0))),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_nums_0))),file('i/f/integer/INT__REM__REDUCE_c1', ch4s_integers_INTu_u_REMu_u_REDUCEu_c1)).
fof(13, 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_c1', ah4s_integers_INTu_u_REMu_u_CALCULATEu_c0)).
fof(17, axiom,s(t_h4s_nums_num,h4s_arithmetics_zero)=s(t_h4s_nums_num,h4s_nums_0),file('i/f/integer/INT__REM__REDUCE_c1', ah4s_arithmetics_ALTu_u_ZERO)).
fof(22, 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_c1', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(25, axiom,![X6]:s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X6)))=s(t_h4s_nums_num,X6),file('i/f/integer/INT__REM__REDUCE_c1', ah4s_arithmetics_NUMERALu_u_DEF)).
fof(40, 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_c1', ah4s_numerals_numeralu_u_lteu_c2)).
fof(42, axiom,~(p(s(t_bool,f))),file('i/f/integer/INT__REM__REDUCE_c1', aHLu_FALSITY)).
fof(43, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)|s(t_bool,X5)=s(t_bool,f)),file('i/f/integer/INT__REM__REDUCE_c1', aHLu_BOOLu_CASES)).
fof(51, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)<=>p(s(t_bool,X5))),file('i/f/integer/INT__REM__REDUCE_c1', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(52, axiom,![X5]:((p(s(t_bool,X5))=>p(s(t_bool,f)))<=>s(t_bool,X5)=s(t_bool,f)),file('i/f/integer/INT__REM__REDUCE_c1', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(54, axiom,![X1]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X1))))=>s(t_h4s_nums_num,h4s_arithmetics_mod(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_c1', ah4s_arithmetics_ZEROu_u_MOD)).
fof(56, axiom,![X1]:![X9]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X1)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X9))))),file('i/f/integer/INT__REM__REDUCE_c1', ah4s_arithmetics_NOTu_u_LESS)).
# SZS output end CNFRefutation
