# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:(![X2]:p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),X1),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X2))))))<=>![X3]:(p(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,X3))))=>p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),X1),s(t_h4s_integers_int,X3)))))),file('i/f/int_arith/INT__NUM__FORALL', ch4s_intu_u_ariths_INTu_u_NUMu_u_FORALL)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/int_arith/INT__NUM__FORALL', aHLu_FALSITY)).
fof(19, axiom,![X6]:(s(t_bool,X6)=s(t_bool,f)<=>~(p(s(t_bool,X6)))),file('i/f/int_arith/INT__NUM__FORALL', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(42, axiom,![X2]:![X21]: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,X21))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X2)))))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X21),s(t_h4s_nums_num,X2))),file('i/f/int_arith/INT__NUM__FORALL', ah4s_integers_INTu_u_LE)).
fof(43, axiom,![X22]:(p(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,X22))))=>?[X2]:s(t_h4s_integers_int,X22)=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X2)))),file('i/f/int_arith/INT__NUM__FORALL', ah4s_integers_NUMu_u_POSINTu_u_EXISTS)).
fof(44, axiom,![X2]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X2)))),file('i/f/int_arith/INT__NUM__FORALL', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
# SZS output end CNFRefutation
