What are Buddhist arguments against Vedic validity because of its authorlessness? There has been a rich history of debate between Vedantists and Buddhists.
One main method the Vedantist uses disprove every other sect which doesn't hold Vedas as true, is to first prove that Vedas are authorless, then say that authorless Vedas have to be 100% true because the defects of lies and incomplete knowledge cannot be there in authorless, and therefore that whatever in Vedas must be 100% true and any sect which goes against the Vedas must be false.
These are the two steps

Apourusheyatva (Authorlessness)
Swayam Pramanya (Default Validity)

I have heard that various Buddhist scholars like Dharmakirti etc have tried to refute the claim of authorlessness of Vedas and its validity.
Supposedly one such argument is there in first chapter of Pramanavarttika, which I couldn't find.

The first chapter discusses the structure and types of formal inference and the apoha (exclusion) theory of meaning. Dan Arnold writes that apoha is: &quot;the idea that concepts are more precise or determinate (more contentful) just to the extent that they exclude more from their purview; the scope of cat is narrower than that of mammal just insofar as the former additionally excludes from its range all mammals in the world that are not cats.&quot;[4] In the latter half of this chapter, Dharmakīrti also mounts an attack on Brahmanism, the authority of the Vedas, Brahmins and their use of mantras, and the system of caste (see Eltschinger 2000).[5] He also discusses the role of scripture, which he sees as fallible and yet important for their discussion of “radically inaccessible things” (atyantaparokṣa) such as karma.[6] Dharmakirti critiques the Brahmins thus:
&quot;The unquestioned authority of the Vedas;
the belief in a world-creator;
the quest for purification through ritual bathing;
the arrogant division into castes;
the practice of mortification to atone for sin—
these five are the marks of the crass stupidity of witless men.&quot;

So -- what were Buddhist arguments against Vedic validity because of its authorlessness?
I'm interested in logical syllogism of Dharmakirti and the like -- in response to the authorlessness of Vedas.

Edit -- My question is specific: Vedantists have given a syllogistic argument to prove that the Vedas are authorless, and many eminent scholars of Buddhism like Dharmakirti etc have tried to refute those syllogistic arguments by logic ... what are those arguments? Please don't answer this question in a general or a philosophical way.
This excerpt from DN 13 may answer your question sufficiently.

“Well, of the brahmins who are proficient in the three Vedas,
Vāseṭṭha, is there even a single one who has seen Brahmā with their
own eyes?”
“No, Master Gotama.”
“Well, has even a single one of their teachers seen Brahmā with their
own eyes?”
“No, Master Gotama.”
“Well, has even a single one of their teachers’ teachers seen Brahmā
with their own eyes?”
“No, Master Gotama.”
“Well, has anyone back to the seventh generation of teachers seen
Brahmā with their own eyes?”
“No, Master Gotama.”
“Well, what of the ancient hermits of the brahmins, namely Aṭṭhaka,
Vāmaka, Vāmadeva, Vessāmitta, Yamadaggi, Aṅgīrasa, Bhāradvāja,
Vāseṭṭha, Kassapa, and Bhagu? They were the authors and propagators of
the hymns. Their hymnal was sung and propagated and compiled in
ancient times; and these days, brahmins continue to sing and chant it,
chanting what was chanted and teaching what was taught. Did they say:
‘We know and see where Brahmā is or what way he lies’?”
“No, Master Gotama.”
“So it seems that none of the brahmins have seen Brahmā with their own
eyes, and not even the ancient hermits claimed to know where he is.
Yet the brahmins proficient in the three Vedas say: ‘We teach the path
to the company of that which we neither know nor see. This is the only
straight path, the direct route that leads someone who practices it to
the company of Brahmā.’
What do you think, Vāseṭṭha? This being so, doesn’t their statement
turn out to have no demonstrable basis?”
“Clearly that’s the case, Master Gotama.”
“Good, Vāseṭṭha. For it is impossible that they should teach the path
to that which they neither know nor see.
Suppose there was a queue of blind men, each holding the one in front:
the first one does not see, the middle one does not see, and the last
one does not see. In the same way, it seems to me that the brahmins’
statement turns out to be comparable to a queue of blind men: the
first one does not see, the middle one does not see, and the last one
does not see. Their statement turns out to be a joke—mere words, void
and hollow.
What do you think, Vāseṭṭha? Do the brahmins proficient in the three
Vedas see the sun and moon just as other folk do? And do they pray to
them and beseech them, following their course from where they rise to
where they set with joined palms held in worship?”
“Yes, Master Gotama.”
“What do you think, Vāseṭṭha? Though this is so, are the brahmins
proficient in the three Vedas able to teach the path to the company of
the sun and moon, saying: ‘This is the only straight path, the direct
route that leads someone who practices it to the company of the sun
and moon’?”
“No, Master Gotama.”
“So it seems that even though the brahmins proficient in the three
Vedas see the sun and moon, they are not able to teach the path to the
company of the sun and moon.
But it seems that even though they have not seen Brahmā with their own
eyes, they still claim to teach the path to the company of that which
they neither know nor see.
What do you think, Vāseṭṭha? This being so, doesn’t their statement
turn out to have no demonstrable basis?”
“Clearly that’s the case, Master Gotama.”
“Good, Vāseṭṭha. For it is impossible that they should teach the path
to that which they neither know nor see.