ProoVer 2026 Sample Solutions for mrs-proover 0.2.0
=====================================================

Samples run against the official examples from
https://proover-competition.github.io/assets/samples.tgz
(command: `mrs-proover --time 30 --verbose <proof.s>`).

Note: these samples use the current ProoVer/SZS terminology
(`VerifiedGood`/`VerifiedBad`/`Unknown`); an earlier submission used the
older `Verified`/`FailedVerified`/`NotVerified` names, which have been
corrected both here and in the underlying `mrs-proover` code (not just the
sample text) so live competition output matches this terminology too.

Sample: COR000+1 (correct proof)
---------------------------------

% step c [rule=-] -> Some(Sound)
% step s1 [rule=negated_conjecture] -> Some(Sound)
% step a1 [rule=-] -> Some(Sound)
% step f1 [rule=consequence] -> Some(Sound)
% SZS status VerifiedGood

Sample: EVL000+1 (evil proof — deliberately incorrect negated_conjecture step)
--------------------------------------------------------------------------------

% step c [rule=-] -> Some(Sound)
% step s1 [rule=negated_conjecture] -> Some(Unsound("negated_conjecture is not the negation of its parent"))
% step a1 [rule=-] -> Some(Sound)
% step f1 [rule=consequence] -> Some(Sound)
% SZS status VerifiedBad : step s1: negated_conjecture is not the negation of its parent

Sample: TMO000+1 (large synthetic proof — 185 nested Skolemization steps,
designed to stress-test verifier resource limits / timeout handling)
--------------------------------------------------------------------------

% step c [rule=-] -> Some(Sound)
% step neg_c [rule=negated_conjecture] -> Some(Sound)
% step neg_inst [rule=instantiate] -> Some(Sound)
% step a01 [rule=-] -> Some(Sound)
% step sk0 [rule=skolemize] -> Some(Sound)
% step sk1 [rule=skolemize] -> Some(Sound)
...
% step sk184 [rule=skolemize] -> Some(Sound)
% step inst [rule=instantiate] -> Some(Sound)
% step contradiction [rule=consequence] -> Some(Sound)
% SZS status VerifiedGood

(184 individual `skolemize` steps elided above for brevity; each is
checked internally via the dedicated Skolemization structural check
described in the system description, so all 184 steps resolve
immediately without needing an external ATP call — this is why the
large proof does not exhaust the 30s time budget despite its size.)

Notes for the organizer
------------------------

No non-obvious features requiring further explanation. `mrs-proover`
was run with default settings (the full ladder: in-process `mrs`, plus
bundled `eprover`/`vampire` as available). All three outcomes match the
expected classification: a correct proof is `VerifiedGood`, a proof with
a deliberately wrong negated-conjecture step is `VerifiedBad` with a
specific, actionable reason, and a large synthetic proof exercising many
Skolemization steps back-to-back is still `VerifiedGood` well within the
time budget, since Skolemization and negated-conjecture steps are
checked by dedicated internal structural rules rather than external ATP
calls (see "Implementation" in the system description).
