Extended Resolution Signature (#2788)
* Extended Resolution Signature
While extended resolution is a fairly general technique, the paper
"Extended Resolution Simulates DRAT" / the drat2er uses exactly one new
type of rule: definitions of the form
new <=> old v (~l_1 ^ ~l_2 ^ ... ^ ~l_n)
This PR adds axioms supporting this kind of definition, and adds a test
making use of those new axioms. The axioms support the following ideas:
1. Introducing a **fresh** variable, defined in the form above
2. Clausifying that definition to produce proofs of $$ n + 2 $$ new
clauses in the form of two clauses, and a cnf with $$ n $$ clauses
3. An axiom for unrolling the proof of the cnf into proofs of the
original clauses.
* Addressing Yoni's comments
1. Added a new (trivial) test
2. Improved a bunch of documentation
* Update proofs/signatures/er.plf
Co-Authored-By: alex-ozdemir <aozdemir@hmc.edu>
* Removed references to RATs from the signature
There are still a few references in the header comment.
* Aside on continuations
* Scrap the elision annotations