[LRA proof] Recording & Printing LRA Proofs (#2758)
* [LRA proof] Recording & Printing LRA Proofs
Now we use the ArithProofRecorder to record and later print arithmetic
proofs.
If an LRA lemma can be proven by a single farkas proof, then that is
done. Otherwise, we `trust` the lemma.
I haven't **really** enabled LRA proofs yet, so `--check-proofs` still
is a no-op for LRA.
To test, do
```
lfsccvc4 <(./bin/cvc4 --dump-proofs ../test/regress/regress0/lemmas/mode_cntrl.induction.smt | tail -n +2)
```
where `lfsccvc4` is an alias invoking `lfscc` with all the necessary
signatures. On my machine that is:
```
alias lfsccvc4="/home/aozdemir/repos/LFSC/build/src/lfscc \
/home/aozdemir/repos/CVC4/proofs/signatures/sat.plf \
/home/aozdemir/repos/CVC4/proofs/signatures/smt.plf \
/home/aozdemir/repos/CVC4/proofs/signatures/lrat.plf \
/home/aozdemir/repos/CVC4/proofs/signatures/th_base.plf \
/home/aozdemir/repos/CVC4/proofs/signatures/th_bv.plf \
/home/aozdemir/repos/CVC4/proofs/signatures/th_bv_bitblast.plf \
/home/aozdemir/repos/CVC4/proofs/signatures/th_arrays.plf \
/home/aozdemir/repos/CVC4/proofs/signatures/th_int.plf \
/home/aozdemir/repos/CVC4/proofs/signatures/th_quant.plf \
/home/aozdemir/repos/CVC4/proofs/signatures/th_real.plf \
/home/aozdemir/repos/CVC4/proofs/signatures/th_real.plf"
```
* Added guards to proof recording
Also reverted some small, unintentional changes.
Also had to add printing for STRING_SUBSTR??
* Responding to Yoni's review
* SimpleFarkasProof examples
* Respond to Aina's comments
* Reorder Constraint declarations
* fix build
* Moved friend declaration in Constraint
* Trichotomy example
* Lift getNumChildren invocation in PLUS case
Credits to aina for spotting it.
* Clang-format