# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:s(t_bool,h4s_arithmetics_even(s(t_h4s_nums_num,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_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X1))))),file('i/f/int_arith/INT__NUM__EVEN', ch4s_intu_u_ariths_INTu_u_NUMu_u_EVEN)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/int_arith/INT__NUM__EVEN', aHLu_TRUTH)).
fof(7, axiom,![X1]:(p(s(t_bool,h4s_arithmetics_odd(s(t_h4s_nums_num,X1))))<=>~(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,h4s_arithmetics_zero))))))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X1)))))))),file('i/f/int_arith/INT__NUM__EVEN', ah4s_intu_u_ariths_INTu_u_NUMu_u_ODD)).
fof(8, axiom,![X1]:(p(s(t_bool,h4s_arithmetics_even(s(t_h4s_nums_num,X1))))<=>~(p(s(t_bool,h4s_arithmetics_odd(s(t_h4s_nums_num,X1)))))),file('i/f/int_arith/INT__NUM__EVEN', ah4s_arithmetics_EVENu_u_ODD)).
fof(9, axiom,~(p(s(t_bool,f))),file('i/f/int_arith/INT__NUM__EVEN', aHLu_FALSITY)).
fof(10, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)|s(t_bool,X3)=s(t_bool,f)),file('i/f/int_arith/INT__NUM__EVEN', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
