# 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_bit1(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_c0', ch4s_integers_INTu_u_REMu_u_REDUCEu_c0)).
fof(4, axiom,![X1]:![X5]:(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X5)))=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X1)))<=>s(t_h4s_nums_num,X5)=s(t_h4s_nums_num,X1)),file('i/f/integer/INT__REM__REDUCE_c0', ah4s_integers_INTu_u_INJ)).
fof(6, axiom,![X1]:![X6]:(p(s(t_bool,h4s_integers_intu_u_lt(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,X1))))=>s(t_h4s_integers_int,h4s_integers_intu_u_rem(s(t_h4s_integers_int,X6),s(t_h4s_integers_int,X1)))=s(t_h4s_integers_int,h4s_bools_cond(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X6),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_add(s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,h4s_integers_intu_u_mod(s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,X6),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,h4s_arithmetics_zero))))))))),s(t_h4s_integers_int,X1))),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,h4s_arithmetics_zero))))))))),s(t_h4s_integers_int,h4s_integers_intu_u_mod(s(t_h4s_integers_int,X6),s(t_h4s_integers_int,X1)))))),file('i/f/integer/INT__REM__REDUCE_c0', ah4s_integers_INTu_u_REMu_u_EQu_u_MOD)).
fof(7, axiom,![X4]:s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X4)))=s(t_h4s_nums_num,X4),file('i/f/integer/INT__REM__REDUCE_c0', ah4s_arithmetics_NUMERALu_u_DEF)).
fof(8, axiom,![X2]:![X7]:![X8]:s(X2,h4s_bools_cond(s(t_bool,f),s(X2,X8),s(X2,X7)))=s(X2,X7),file('i/f/integer/INT__REM__REDUCE_c0', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(11, axiom,![X1]:s(t_h4s_integers_int,h4s_integers_intu_u_mod(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_bit1(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_c0', ah4s_integers_INTu_u_MODu_u_REDUCEu_c0)).
fof(12, axiom,![X1]:![X5]:s(t_h4s_integers_int,h4s_integers_intu_u_mod(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,X5))))),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_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X5))),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_c0', ah4s_integers_INTu_u_MODu_u_REDUCEu_c2)).
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_c0', ah4s_arithmetics_ALTu_u_ZERO)).
fof(18, axiom,![X1]:![X5]:s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X5))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X1)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,X1))),file('i/f/integer/INT__REM__REDUCE_c0', ah4s_integers_INTu_u_LT)).
fof(28, axiom,~(p(s(t_bool,f))),file('i/f/integer/INT__REM__REDUCE_c0', aHLu_FALSITY)).
fof(37, axiom,p(s(t_bool,t)),file('i/f/integer/INT__REM__REDUCE_c0', aHLu_TRUTH)).
fof(38, axiom,![X14]:(s(t_bool,X14)=s(t_bool,t)|s(t_bool,X14)=s(t_bool,f)),file('i/f/integer/INT__REM__REDUCE_c0', aHLu_BOOLu_CASES)).
fof(43, axiom,![X14]:(s(t_bool,X14)=s(t_bool,t)<=>p(s(t_bool,X14))),file('i/f/integer/INT__REM__REDUCE_c0', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(55, axiom,![X1]:s(t_h4s_integers_int,h4s_integers_intu_u_div(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_bit1(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_c0', ah4s_integers_INTu_u_DIVu_u_REDUCEu_c0)).
fof(66, axiom,![X1]:(~(s(t_h4s_nums_num,X1)=s(t_h4s_nums_num,h4s_nums_0))<=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X1))))),file('i/f/integer/INT__REM__REDUCE_c0', ah4s_arithmetics_NOTu_u_ZEROu_u_LTu_u_ZERO)).
fof(67, axiom,![X1]:![X5]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X5),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,X5))))),file('i/f/integer/INT__REM__REDUCE_c0', ah4s_arithmetics_NOTu_u_LESS)).
fof(68, axiom,![X1]:s(t_h4s_nums_num,h4s_arithmetics_bit1(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_0))))))),file('i/f/integer/INT__REM__REDUCE_c0', ah4s_arithmetics_BIT10)).
fof(73, 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_c0', ah4s_arithmetics_ONE)).
fof(75, 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_c0', ah4s_numerals_numeralu_u_lteu_c1)).
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_c0', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(80, axiom,![X1]:![X5]:(s(t_h4s_nums_num,X5)=s(t_h4s_nums_num,X1)<=>(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X5),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,X5)))))),file('i/f/integer/INT__REM__REDUCE_c0', ah4s_arithmetics_EQu_u_LESSu_u_EQ)).
# SZS output end CNFRefutation
