# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X2),s(t_h4s_integers_int,X1)))=s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,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_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))),s(t_h4s_integers_int,X1))),file('i/f/int_arith/less__to__leq__samer', ch4s_intu_u_ariths_lessu_u_tou_u_lequ_u_samer)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/int_arith/less__to__leq__samer', aHLu_TRUTH)).
fof(6, axiom,![X5]:![X1]:![X2]:s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X2),s(t_h4s_integers_int,X5))),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X1),s(t_h4s_integers_int,X5)))))=s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X2),s(t_h4s_integers_int,X1))),file('i/f/int_arith/less__to__leq__samer', ah4s_integers_INTu_u_LTu_u_RADD)).
fof(7, axiom,![X1]:![X2]:(p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X2),s(t_h4s_integers_int,X1))))<=>~(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X1),s(t_h4s_integers_int,X2)))))),file('i/f/int_arith/less__to__leq__samer', ah4s_integers_intu_u_le0)).
fof(8, axiom,![X1]:![X2]:(~(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X2),s(t_h4s_integers_int,X1)))))<=>p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X1),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,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_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))),file('i/f/int_arith/less__to__leq__samer', ah4s_intu_u_ariths_notu_u_less)).
fof(9, axiom,~(p(s(t_bool,f))),file('i/f/int_arith/less__to__leq__samer', aHLu_FALSITY)).
fof(10, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)|s(t_bool,X4)=s(t_bool,f)),file('i/f/int_arith/less__to__leq__samer', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
