# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/integer/INT__QUOT', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/integer/INT__QUOT', aHLu_FALSITY)).
fof(3, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)|s(t_bool,X1)=s(t_bool,f)),file('i/f/integer/INT__QUOT', aHLu_BOOLu_CASES)).
fof(16, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/integer/INT__QUOT', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(17, axiom,![X9]:![X7]:![X8]:s(X9,h4s_bools_cond(s(t_bool,t),s(X9,X8),s(X9,X7)))=s(X9,X8),file('i/f/integer/INT__QUOT', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(35, axiom,![X22]:![X23]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X23),s(t_h4s_nums_num,X22)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X22),s(t_h4s_nums_num,X23))))),file('i/f/integer/INT__QUOT', ah4s_arithmetics_NOTu_u_LESS)).
fof(38, axiom,![X22]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X22)))),file('i/f/integer/INT__QUOT', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(40, axiom,![X22]:![X23]:(~(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X23),s(t_h4s_nums_num,X22)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X22))),s(t_h4s_nums_num,X23))))),file('i/f/integer/INT__QUOT', ah4s_arithmetics_NOTu_u_LEQ)).
fof(41, axiom,![X22]:![X23]:(~(s(t_h4s_nums_num,X23)=s(t_h4s_nums_num,X22))<=>(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X23))),s(t_h4s_nums_num,X22))))|p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X22))),s(t_h4s_nums_num,X23)))))),file('i/f/integer/INT__QUOT', ah4s_arithmetics_NOTu_u_NUMu_u_EQ)).
fof(46, axiom,![X22]:![X23]:s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X23))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X22)))))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X23),s(t_h4s_nums_num,X22))),file('i/f/integer/INT__QUOT', ah4s_integers_INTu_u_LE)).
fof(47, axiom,![X22]:![X23]: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,X23))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X22)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X23),s(t_h4s_nums_num,X22))),file('i/f/integer/INT__QUOT', ah4s_integers_INTu_u_LT)).
fof(50, axiom,![X22]:s(t_h4s_nums_num,h4s_integers_num(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X22)))))=s(t_h4s_nums_num,X22),file('i/f/integer/INT__QUOT', ah4s_integers_NUMu_u_OFu_u_INT)).
fof(51, axiom,![X25]:![X24]:(~(s(t_h4s_integers_int,X25)=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_quot(s(t_h4s_integers_int,X24),s(t_h4s_integers_int,X25)))=s(t_h4s_integers_int,h4s_bools_cond(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,X25))),s(t_h4s_integers_int,h4s_bools_cond(s(t_bool,h4s_integers_intu_u_le(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,X24))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,h4s_integers_num(s(t_h4s_integers_int,X24))),s(t_h4s_nums_num,h4s_integers_num(s(t_h4s_integers_int,X25))))))),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_div(s(t_h4s_nums_num,h4s_integers_num(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,X24))))),s(t_h4s_nums_num,h4s_integers_num(s(t_h4s_integers_int,X25))))))))))),s(t_h4s_integers_int,h4s_bools_cond(s(t_bool,h4s_integers_intu_u_le(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,X24))),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_div(s(t_h4s_nums_num,h4s_integers_num(s(t_h4s_integers_int,X24))),s(t_h4s_nums_num,h4s_integers_num(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,X25))))))))))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,h4s_integers_num(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,X24))))),s(t_h4s_nums_num,h4s_integers_num(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,X25)))))))))))))),file('i/f/integer/INT__QUOT', ah4s_integers_intu_u_quot0)).
fof(52, conjecture,![X20]:![X21]:(~(s(t_h4s_nums_num,X20)=s(t_h4s_nums_num,h4s_nums_0))=>s(t_h4s_integers_int,h4s_integers_intu_u_quot(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X21))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X20)))))=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,X21),s(t_h4s_nums_num,X20)))))),file('i/f/integer/INT__QUOT', ch4s_integers_INTu_u_QUOT)).
# SZS output end CNFRefutation
