Is it to say: "We can have reasonable hope that all will be saved" heretical? Unfortunately, we can hear some lay Catholics (sometimes even a bishop) say that: "We can have reasonable hope that all will be saved". It seems obvious that the statement is untrue, however, is it a heretical statement? And would for example bishop who persists in this error becomes a formal heretic?

We know that the Church condemned the following proposition: 


  If anyone says or thinks that the punishment of demons and of impious
  men is only temporary, and will one day have an end, and that a
  restoration (ἀποκατάστασις) will take place of demons and of impious
  men, let him be anathema.


It seems that corollary of this statement is:

Corollary: Punishments of impious men will never end.

Imagine now that the statement: "We can have reasonable hope that all will be saved" is true. However, if the hope were to be reasonable, then the object of hope should be really possible, namely, it should be really possible that all are saved. But if all were saved, then the previous corollary would really be attributing some property to an empty set and then the condemnation would be vacuously true. But the opposite of the corollary would also be true (because we can attribute anything to an empty set, see a previous link to "Vacuous truth") in that case. Therefore, the case where all are saved seems logically inconsistent if we want to say that condemnation can not be empty.

Edit. My question is not duplicate. I am not searching an answer to a viewpoint on universal salvation, but I explicitly deny that as untrue. I am searching for what kind (degree) of error is to hold universal salvation (or rather, that "we can have reasonable hope that all will be saved").
Doctrinal Universalism
Barron professes the heresy of doctrinal universalism,

The theory that hell is essentially a kind of purgatory in which sins are expiated, so that eventually everyone will be saved. Also called apokatastasis [ἀποκατάστασις], it was condemned by the church in A.D. 543, against the Origenists, who claimed that

the punishment of devils and wicked men is temporary and will eventually cease, that is to say, that devils or the ungodly will be completely restored to their original state

(Denzinger 411).

Balthasar &amp; Barron believe hell is empty.
The Modernist, syncretist, New Theologian Hans Urs Von Balthasar (1905-1988), influenced by the fake mystic Adrienne von Speyr, promoted the heresy that hell is empty. He also wrote the afterword of a book on Tarot cards and the occult.
Barron wrote the preface to the 2nd edition of Balthasar's Dare We Hope That All Men Be Saved.
One cannot hope for the impossible.
The intellectual virtue of faith precedes the virtue of hope, which exists in the will, since the intellect precedes the will (cf. 21st Thomistic thesis). The object of hope cannot contradict reason.
Discussing how faith precedes hope in Summa Theologica II-II q. 17 a. 7 co., St. Thomas Aquinas writes:

the object of hope is a future good, arduous but possible to obtainObiectum enim spei est bonum futurum arduum possibile haberi.

Thus, one cannot hope for impossible things, e.g., that God doesn't exist, that He contradict Himself, that the Church's dogmas change, that 2+2=5, etc.
Religious Indifferentism
Related to his universalist heresy, Barron professes the heresy of religious indifferentism, which holds that no one religion is necessary for salvation. Recently, he told a Jew that Jesus is the &quot;privileged way&quot; of salvation, which implies there are other means of salvation, directly contradicting, e.g., Acts 4:12 (&quot;Neither is there salvation in any other. For there is no other name under heaven given to men, whereby we must be saved.&quot;).
Hell exists, and its punishments are perpetual.
Athanasian Creed (D 40):

those who have done good, will go into life everlasting, but those who have done evil, into eternal fire
qui bona egerunt, ibunt in vitam æternam, qui vero mala, in ignem æternum

The Fourth Lateran Council (1215) defined the dogma that the rejected will receive (D 429):

everlasting punishment with the devil
cum diabolo pœnam perpetuam

Once a soul is damned, there is no hope that it will be saved.
These dogmas are de fide (&quot;of the faith&quot;). Contradicting a de fide truth incurs the censure of heresy; the effects of denying it are:

Mortal sin committed directly against the virtue of faith, and, if the heresy is outwardly professed, excommunication is automatically incurred and membership of the Church forfeited.