# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(p(s(t_bool,h4s_integers_intu_u_divides(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_numeral(s(t_h4s_nums_num,X2))))))))<=>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)))))))=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/integer/INT__DIVIDES__REDUCE_c5', ch4s_integers_INTu_u_DIVIDESu_u_REDUCEu_c5)).
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__DIVIDES__REDUCE_c5', ah4s_integers_INTu_u_REMu_u_CALCULATEu_c3)).
fof(28, 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__DIVIDES__REDUCE_c5', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(30, axiom,![X2]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/integer/INT__DIVIDES__REDUCE_c5', ah4s_arithmetics_MULTu_u_CLAUSESu_c1)).
fof(34, axiom,s(t_h4s_nums_num,h4s_arithmetics_zero)=s(t_h4s_nums_num,h4s_nums_0),file('i/f/integer/INT__DIVIDES__REDUCE_c5', ah4s_arithmetics_ALTu_u_ZERO)).
fof(39, 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__DIVIDES__REDUCE_c5', ah4s_arithmetics_NOTu_u_ZEROu_u_LTu_u_ZERO)).
fof(40, axiom,![X5]:s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X5)))=s(t_h4s_nums_num,X5),file('i/f/integer/INT__DIVIDES__REDUCE_c5', ah4s_arithmetics_NUMERALu_u_DEF)).
fof(41, axiom,![X1]:![X2]: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,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__DIVIDES__REDUCE_c5', ah4s_integers_INTu_u_MODu_u_REDUCEu_c3)).
fof(52, axiom,![X1]:![X17]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X1))))=>s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,X17)),file('i/f/integer/INT__DIVIDES__REDUCE_c5', ah4s_arithmetics_LESSu_u_MOD)).
fof(55, axiom,![X1]:s(t_bool,h4s_integers_intu_u_divides(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_bool,f),file('i/f/integer/INT__DIVIDES__REDUCE_c5', ah4s_integers_INTu_u_DIVIDESu_u_REDUCEu_c2)).
fof(62, 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__DIVIDES__REDUCE_c5', ah4s_numerals_numeralu_u_lteu_c2)).
fof(64, axiom,~(p(s(t_bool,f))),file('i/f/integer/INT__DIVIDES__REDUCE_c5', aHLu_FALSITY)).
fof(68, axiom,![X6]:((p(s(t_bool,X6))=>p(s(t_bool,f)))<=>s(t_bool,X6)=s(t_bool,f)),file('i/f/integer/INT__DIVIDES__REDUCE_c5', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(70, axiom,![X6]:(s(t_bool,f)=s(t_bool,X6)<=>~(p(s(t_bool,X6)))),file('i/f/integer/INT__DIVIDES__REDUCE_c5', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(79, axiom,![X11]:![X12]:(p(s(t_bool,h4s_integers_intu_u_divides(s(t_h4s_integers_int,X12),s(t_h4s_integers_int,X11))))<=>((s(t_h4s_integers_int,h4s_integers_intu_u_mod(s(t_h4s_integers_int,X11),s(t_h4s_integers_int,X12)))=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,X12)=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,X12)=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,X11)=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__DIVIDES__REDUCE_c5', ah4s_integers_INTu_u_DIVIDESu_u_MOD0)).
fof(94, axiom,![X1]:![X2]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),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,X2))))),file('i/f/integer/INT__DIVIDES__REDUCE_c5', ah4s_arithmetics_NOTu_u_LESS)).
fof(97, axiom,![X1]:![X2]:s(t_bool,h4s_integers_intu_u_lt(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,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,X2)))))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))),file('i/f/integer/INT__DIVIDES__REDUCE_c5', ah4s_integers_INTu_u_LTu_u_CALCULATEu_c1)).
fof(100, axiom,![X1]:![X2]:(s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,X1)<=>(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),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,X2)))))),file('i/f/integer/INT__DIVIDES__REDUCE_c5', ah4s_arithmetics_EQu_u_LESSu_u_EQ)).
# SZS output end CNFRefutation
