Merge from LFSC (#26)

* Showing models as coq counter examples in tactic without constructing coq terms

* also read models when calling cvc4 with a file (deactivated because cvc4 crashes)

* Show counter examples with variables in the order they are quantified in the Coq goal

* Circumvent issue with ocamldep

* fix issue with dependencies

* fix issue with dependencies

* Translation and OCaml support for extract, zero_extend, sign_extend

* Show run times of components

* print time on stdout instead

* Tests now work with new version (master) of CVC4

* fix small printing issue

* look for date on mac os x

* proof of valid_check_bbShl: some cases to prove.

* full proof of "left shift checker".

*  full proof of "rigth shift checker".

* Support translation of terms bvlshr, bvshl but LFSC rules do not exists at the moment
Bug fix for bitvector extract (inverted arguments)

* Typo

* More modularity on the format of traces depending on the version of coq

* More straightforward definitions in Int63Native_standard

* Use the Int31 library with coq-8.5

* Use the most efficient operations of Int31

* Improved performance with coq-8.5

* Uniform treatment of sat and smt tactics

* Hopefully solved the problem with universes for the tactic

* Updated the installation instructions

* Holes for unsupported bit blasting rules

* Cherry-picking from smtcoq/smtcoq

* bug fix hole for bitblast

* Predefined arrays are not required anymore

* fix issue with coq bbT and bitof construction from ocaml

* bug fix in smtAtom for uninterpreted functions
fix verit test file

* fix issue with smtlib2 extract parsing

* It looks like we still need the PArray function instances for some examples (see vmcai_bytes.smt2)

* Solver specific reification:
Each solver has a list of supported theories which is passed to Atom.of_coq, this function creates uninterpreted functions / sorts for unsupported features.

* show counter-examples with const_farray instead of const for constant array definitions

* Vernacular commands to debug checkers.
Verit/Lfsc_Checker_Debug will always fail, reporting the first proof step of the certificate that failed be checked

* Update INSTALL.md

* show smtcoq proof when converting

* (Hopefully) repared the universes problems

* Corrected a bug with holes in proofs

* scripts for tests:
create a folder "work" under "lfsc/tests/", locate the benchmarks there.
create a folder "results" under "lfsc/tests/work/" in which you'll find the results of ./cvc4tocoq.

* make sure to give correct path for your benchs...

* Checker for array extensionality modulo symmetry of equality

* fix oversight with bitvectors larger than 63 bits

* some printing functions for smt2 ast

* handle smtlib2 files with more complicated equivalence with (= ... )

* revert: ./cvc4tocoq does not output lfsc proofs...

* bug fix one input was ignored

* Don't show verit translation of LFSC proof if environment variable DONTSHOWVERIT is set
(e.g. put export DONTSHOWVERIT="" in your .bashrc or .bashprofile)

* Also sort names of introduced variables when showing counter-example

* input files for which SMTCoq retuns false.

* input files for which SMTCoq retuns false.

* use debug checker for debug file

* More efficient debug checker

* better approximate number of failing step of certificate in debug checker

* fix mistake in ml4

* very first attempt to support goals in Prop

* bvs: comparison predicates in Prop and their <-> proofs with the ones in bool
farrays: equality predicate in Prop and its <-> proof with the one in bool.

* unit, Bool, Z, Pos: comparison and equality predicates in Prop.

* a typo fixed.

* an example of array equality in  Prop (converted into Bool by hand)...
TODO: enhance the search space of cvc4 tactic.

* first version of cvc4' tactic: "solves" the goals in Prop.
WARNING: supports only bv and array goals and might not be complete
TODO: add support for lia goals

* cvc4' support for lia
WARNING: might not be complete!

* small fix in cvc4' and some variations of examples

* small fix + support for goals in Bool and Bool = true + use of solve tactical
WARNING: does not support UF and INT63 goals in Prop

* cvc4': better arrangement

* cvc4': Prop2Bool by context search...

* cvc4': solve tactial added -> do not modify unsolved goals.

* developer documentation for the smtcoq repo

* cvc4': rudimentary support for uninterpreted function goals in Prop.

* cvc4': support for goals with Leibniz equality...
WARNING: necessary use of "Grab Existential Variables." to instantiate variable types for farrays!

* cvc4': Z.lt adapted + better support from verit...

* cvc4': support for Z.le, Z.ge, Z.gt.

* Try arrays with default value (with a constructor for constant arrays), but extensionality is not provable

* cvc4': support for equality over uninterpreted types

* lfsc demo: goals in Coq's Prop.

* lfsc demo: goals in Bool.

* Fix issue with existential variables generated by prop2bool.
- prop2bool tactic exported by SMTCoq
- remove useless stuff

* update usage and installation instructions

* Update INSTALL.md

* highlighting

* the tactic: bool2prop.

* clean up

* the tactic smt: very first version.

* smt: return unsolved goals in Prop.

* Show when a certificate cannot be checked when running the tactic instead of at Qed

* Tactic improvements
- Handle negation/True/False in prop/bool conversions tactic.
- Remove alias for farray (this caused problem for matching on this type in tactics).
- Tactic `smt` that combines cvc4 and veriT.
- return subgoals in prop

* test change header

* smt: support for negated goals + some reorganization.

* conflicts resolved + some reorganization.

* a way to solve the issue with ambiguous coercions.

* reorganization.

* small change.

* another small change.

* developer documentation of the tactics.

* developer guide: some improvements.

* developer guide: some more improvements.

* developer guide: some more improvements.

* developer guide: some more improvements.

* pass correct environment for conversion + better error messages

* cleaning

* ReflectFacts added.

* re-organizing developers' guide.

* re-organizing developers' guide.

* re-organizing developers' guide.

* removing unused maps.

* headers.

* artifact readme getting started...

* first attempt

* second...

* third...

* 4th...

* 5th...

* 6th...

* 7th...

* 8th...

* 9th...

* 10th...

* 11th...

* 12th...

* 13th...

* 14th...

* 15th...

* 16th...

* 17th...

* Update artifact.md

Use links to lfsc repository like in the paper

* 18th...

* 19th...

* 20th...

* 21st...

* 22nd...

* 23rd...

* 24th...

* 25th...

* 26th...

* 27th...

* 28th...

* Update artifact.md

Small reorganization

* minor edits

* More minor edits

* revised description of tactics

* Final pass

* typo

* name changed: artifact-readme.md

* file added...

* passwd chaged...

* links...

* removal

* performance statement...

* typos...

* the link to the artifact image updated...

* suggestions by Guy...

* aux files removed...

* clean-up...

* clean-up...

* some small changes...

* small fix...

* additional information on newly created files after running cvc4tocoq script...

* some small fix...

* another small fix...

* typo...

* small fix...

* another small fix...

* fix...

* link to the artifact image...

* We do not want to force vm_cast for the Theorem commands

* no_check variants of the tactics

* TODO: a veriT test does not work anymore

* Compiles with both versions of Coq

* Test of the tactics in real conditions

* Comment on this case study

* an example for the FroCoS paper.

* Fix smt tactic that doesn't return cvc4's subgoals

* readme modifications

* readme modifications 2

* small typo in readme.

* small changes in readme.

* small changes in readme.

* typo in readme.

* Sync with https://github.com/LFSC/smtcoq

* Port to Coq 8.6

* README

* README

* INSTALL

* Missing file

* Yves' proposition for installation instructions

* Updated link to CVC4

* Compiles again with native-coq

* Compiles with both versions of Coq

* Command to bypass typechecking when generating a zchaff theorem

* Solved bug on cuts from Hole

* Counter-models for uninterpreted sorts (improves issue #13)

* OCaml version note (#15)

* update .gitignore

* needs OCaml 4.04.0

* Solving merge issues (under progress)

* Make SmtBtype compile

* Compilation of SmtForm under progress

* Make SmtForm compile

* Make SmtCertif compile

* Make SmtTrace compile

* Make SatAtom compile

* Make smtAtom compile

* Make CnfParser compile

* Make Zchaff compile

* Make VeritSyntax compile

* Make VeritParser compile

* Make lfsc/tosmtcoq compile

* Make smtlib2_genconstr compile

* smtCommand under progress

* smtCommands and verit compile again

* lfsc compiles

* ml4 compiles

* Everything compiles

* All ZChaff unit tests and most verit unit tests (but taut5 and un_menteur) go through

* Most LFSC tests ok; some fail due to the problem of verit; a few fail due to an error "Not_found" to investigate

* Authors and headings

* Compiles with native-coq

* Typo

11 files changed, 380 insertions, 39 deletions

diff --git a/examples/Example.v b/examples/Example.v
index 0dba915..c07fb40 100644
--- a/examples/Example.v
+++ b/examples/Example.v
@@ -1,3 +1,15 @@
+(**************************************************************************)
+(*                                                                        *)
+(*     SMTCoq                                                             *)
+(*     Copyright (C) 2011 - 2019                                          *)
+(*                                                                        *)
+(*     See file "AUTHORS" for the list of authors                         *)
+(*                                                                        *)
+(*   This file is distributed under the terms of the CeCILL-C licence     *)
+(*                                                                        *)
+(**************************************************************************)
+
+
 (* [Require Import SMTCoq.SMTCoq.] loads the SMTCoq library.
    If you are using native-coq instead of Coq 8.6, replace it with:
      Require Import SMTCoq.
@@ -5,7 +17,15 @@
 
 Require Import SMTCoq.SMTCoq.
 Require Import Bool.
-Local Open Scope int63_scope.
+
+Local Open Scope Z_scope.
+
+Import BVList.BITVECTOR_LIST.
+Local Open Scope bv_scope.
+
+Import FArray.
+Local Open Scope farray_scope.
+
 
 (* Examples that check ZChaff certificates *)
 
@@ -15,12 +35,21 @@ Check sat.
 
 Zchaff_Checker "hole4.cnf" "hole4.log".
 
-(* Example that checks a VeriT certificate, for logic QF_UF *)
+
+(* Example that checks a VeriT certificate, for logic QF_UFLIA *)
 
 Section Verit.
-  Verit_Checker "euf.smt2" "euf.log".
+  Verit_Checker "lia.smt2" "lia.vtlog".
 End Verit.
 
+
+(* Example that checks a LFSC certificate, for logic QF_UFLIA *)
+
+Section Lfsc.
+  Lfsc_Checker "lia.smt2" "lia.lfsc".
+End Lfsc.
+
+
 (* Examples of the zchaff tactic (requires zchaff in your PATH
    environment variable):
    - with booleans
@@ -33,41 +62,119 @@ Proof.
 Qed.
 
 Goal forall i j k,
-  let a := i == j in
-  let b := j == k in
-  let c := k == i in
+  let a := (i == j)%int in
+  let b := (j == k)%int in
+  let c := (k == i)%int in
   (a || b || c) && ((negb a) || (negb b) || (negb c)) && ((negb a) || b) && ((negb b) || c) && ((negb c) || a) = false.
 Proof.
   zchaff.
 Qed.
 
-(* Examples of the verit tactic (requires verit in your PATH environment
-   variable):
-   - with booleans
-   - in logics QF_UF and QF_LIA *)
+
+(* Examples of the verit tactics (requires verit in your PATH environment
+   variable), which handle
+   - propositional logic
+   - theory of equality
+   - linear integer arithmetic *)
 
 Goal forall a b c, ((a || b || c) && ((negb a) || (negb b) || (negb c)) && ((negb a) || b) && ((negb b) || c) && ((negb c) || a)) = false.
 Proof.
-  verit.
+  verit_bool.
 Qed.
 
-
 Goal forall (a b : Z) (P : Z -> bool) (f : Z -> Z),
-  negb (f a =? b) || negb (P (f a)) || (P b).
+  (negb (Z.eqb (f a) b)) || (negb (P (f a))) || (P b).
 Proof.
-  verit.
+  verit_bool.
 Qed.
 
 Goal forall b1 b2 x1 x2,
-  implb
-  (ifb b1
-    (ifb b2 (2*x1+1 =? 2*x2+1) (2*x1+1 =? 2*x2))
-    (ifb b2 (2*x1 =? 2*x2+1) (2*x1 =? 2*x2)))
-  ((implb b1 b2) && (implb b2 b1) && (x1 =? x2)).
+    implb
+      (ifb b1
+           (ifb b2 (Z.eqb (2*x1+1) (2*x2+1)) (Z.eqb (2*x1+1) (2*x2)))
+           (ifb b2 (Z.eqb (2*x1) (2*x2+1)) (Z.eqb (2*x1) (2*x2))))
+      ((implb b1 b2) && (implb b2 b1) && (Z.eqb x1 x2)).
+Proof.
+  verit_bool.
+Qed.
+
+Goal forall
+    (x y: Z)
+    (f: Z -> Z),
+    x = y + 1 -> f y = f (x - 1).
 Proof.
   verit.
 Qed.
 
+
+(* Examples of the smt tactic (requires verit and cvc4 in your PATH environment
+   variable):
+   - propositional logic
+   - theory of equality
+   - linear integer arithmetic
+   - theory of fixed-sized bit-vectors
+   - theory of arrays *)
+
+Goal forall a b c, ((a || b || c) && ((negb a) || (negb b) || (negb c)) && ((negb a) || b) && ((negb b) || c) && ((negb c) || a)) = false.
+Proof.
+  smt.
+Qed.
+
+Goal forall (a b : Z) (P : Z -> bool) (f : Z -> Z),
+  (negb (Z.eqb (f a) b)) || (negb (P (f a))) || (P b).
+Proof.
+  smt.
+Qed.
+Goal forall b1 b2 x1 x2,
+    implb
+      (ifb b1
+           (ifb b2 (Z.eqb (2*x1+1) (2*x2+1)) (Z.eqb (2*x1+1) (2*x2)))
+           (ifb b2 (Z.eqb (2*x1) (2*x2+1)) (Z.eqb (2*x1) (2*x2))))
+      ((implb b1 b2) && (implb b2 b1) && (Z.eqb x1 x2)).
+Proof.
+  smt.
+Qed.
+
+Goal forall
+    (x y: Z)
+    (f: Z -> Z),
+    x = y + 1 -> f y = f (x - 1).
+Proof.
+  smt.
+Qed.
+
+Goal forall (bv1 bv2 bv3: bitvector 4),
+    bv1 = #b|0|0|0|0|  /\
+    bv2 = #b|1|0|0|0|  /\
+    bv3 = #b|1|1|0|0|  ->
+    bv_ultP bv1 bv2 /\ bv_ultP bv2 bv3.
+Proof.
+  smt.
+Qed.
+
+Goal forall (a b c d: farray Z Z),
+    b[0 <- 4] = c  ->
+    d = b[0 <- 4][1 <- 4]  ->
+    a = d[1 <- b[1]]  ->
+    a = c.
+Proof.
+  smt.
+Qed.
+
+Goal forall (a b: farray Z Z) (v w x y z t: Z)
+            (r s: bitvector 4)
+            (f: Z -> Z)
+            (g: farray Z Z -> Z)
+            (h: bitvector 4 -> Z),
+    a[x <- v] = b /\ a[y <- w] = b ->
+    a[z <- w] = b /\ a[t <- v] = b ->
+    r = s -> v < x + 10 /\ v > x - 5 ->
+    ~ (g a = g b) \/ f (h r) = f (h s).
+Proof.
+  smt.
+Qed.
+
+
 (* Examples of using the conversion tactics *)
 
 Local Open Scope positive_scope.
@@ -231,7 +338,6 @@ Section group.
   Lemma unique_identity e':
     (forall z, op e' z =? z) -> e' =? e.
   Proof. intros pe'. verit_base pe'; vauto. Qed.
-
   Lemma simplification_right x1 x2 y:
       op x1 y =? op x2 y -> x1 =? x2.
   Proof. intro H. verit_base H; vauto. Qed.
diff --git a/examples/InsertionSort.v b/examples/InsertionSort.v
new file mode 100644
index 0000000..fcd5dfc
--- /dev/null
+++ b/examples/InsertionSort.v
@@ -0,0 +1,151 @@
+(**************************************************************************)
+(*                                                                        *)
+(*     SMTCoq                                                             *)
+(*     Copyright (C) 2011 - 2019                                          *)
+(*                                                                        *)
+(*     See file "AUTHORS" for the list of authors                         *)
+(*                                                                        *)
+(*   This file is distributed under the terms of the CeCILL-C licence     *)
+(*                                                                        *)
+(**************************************************************************)
+
+
+(* This example tests the tactics in "real" condition: a part of the
+   proof of correctness of insertion sort. It requires propositional
+   reasoning, uninterpreted functions, and a bit of integer arithmetic.
+
+   Ideally, the proof of each lemma should consists only on
+   induction/destruct followed by a call to [smt]. What we currently
+   lack:
+     - we have to provide all the needed lemmas and unfold all the
+       definitions
+     - it requires too much from uninterpreted functions even when it is
+       not needed
+     - it sometimes fails? (may be realted to the previous item)
+ *)
+
+
+Add Rec LoadPath "../src" as SMTCoq.
+
+Require Import SMTCoq.
+Require Import ZArith List Bool.
+
+
+(* We should really make SMTCoq work with SSReflect! *)
+
+Lemma impl_implb (a b:bool) : (a -> b) <-> (a --> b).
+Proof. auto using (reflect_iff _ _ (ReflectFacts.implyP a b)). Qed.
+
+
+Lemma eq_false b : b = false <-> negb b.
+Proof. case b; intuition. Qed.
+
+
+Section InsertionSort.
+
+  Fixpoint insert (x:Z) (l:list Z) : list Z :=
+    match l with
+    | nil => x::nil
+    | y::ys => if (x <=? y)%Z then x::y::ys else y::(insert x ys)
+    end.
+
+  Fixpoint sort (l:list Z) : list Z :=
+    match l with
+    | nil => nil
+    | x::xs => insert x (sort xs)
+    end.
+
+
+  Section Spec.
+
+    Fixpoint is_sorted (l:list Z) : bool :=
+      match l with
+      | nil => true
+      | x::xs =>
+        match xs with
+        | nil => true
+        | y::_ => (x <=? y)%Z && (is_sorted xs)
+        end
+      end.
+
+    Fixpoint smaller (x:Z) (l:list Z) : bool :=
+      match l with
+      | nil => true
+      | y::ys => (x <=? y)%Z && (smaller x ys)
+      end.
+
+
+    Lemma is_sorted_smaller x y ys :
+      (((x <=? y) && is_sorted (y :: ys)) --> is_sorted (x :: ys)).
+    Proof.
+      destruct ys as [ |z zs].
+      - simpl. smt.
+      - change (is_sorted (y :: z :: zs)) with ((y <=? z)%Z && (is_sorted (z::zs))).
+        change (is_sorted (x :: z :: zs)) with ((x <=? z)%Z && (is_sorted (z::zs))).
+        (* [smt] or [verit] fail? *)
+        assert (H:forall b, (x <=? y) && ((y <=? z) && b) --> (x <=? z) && b) by smt.
+        apply H.
+    Qed.
+
+
+    Lemma is_sorted_cons x xs :
+      (is_sorted (x::xs)) <--> (is_sorted xs && smaller x xs).
+    Proof.
+      induction xs as [ |y ys IHys].
+      - reflexivity.
+      - change (is_sorted (x :: y :: ys)) with ((x <=? y)%Z && (is_sorted (y::ys))).
+        change (smaller x (y :: ys)) with ((x <=? y)%Z && (smaller x ys)).
+        generalize (is_sorted_smaller x y ys). revert IHys. rewrite !impl_implb.
+        (* Idem *)
+        assert (H:forall a b c d, (a <--> b && c) -->
+                                  ((x <=? y) && d --> a) -->
+                                  ((x <=? y) && d <-->
+                                  d && ((x <=? y) && c))) by smt.
+        apply H.
+    Qed.
+
+
+    Lemma insert_keeps_smaller x y ys :
+      smaller y ys --> (y <=? x) --> smaller y (insert x ys).
+    Proof.
+      induction ys as [ |z zs IHzs].
+      - simpl. smt.
+      - simpl. case (x <=? z).
+        + simpl.
+          (* [smt] or [verit] require [Compec (list Z)] but they should not *)
+          assert (H:forall a, (y <=? z) && a --> (y <=? x) --> (y <=? x) && ((y <=? z) && a)) by smt.
+          apply H.
+        + simpl. revert IHzs. rewrite impl_implb.
+          (* Idem *)
+          assert (H:forall a b, (a --> (y <=? x) --> b) --> (y <=? z) && a --> (y <=? x) --> (y <=? z) && b) by smt.
+          apply H.
+    Qed.
+
+
+    Lemma insert_keeps_sorted x l : is_sorted l -> is_sorted (insert x l).
+    Proof.
+      induction l as [ |y ys IHys].
+      - reflexivity.
+      - intro H. simpl. case_eq (x <=? y); intro Heq.
+        + change ((x <=? y)%Z && (is_sorted (y::ys))). rewrite Heq, H. reflexivity.
+        + rewrite eq_false in Heq.
+          rewrite (eqb_prop _ _ (is_sorted_cons _ _)) in H.
+          rewrite (eqb_prop _ _ (is_sorted_cons _ _)).
+          generalize (insert_keeps_smaller x y ys).
+          revert IHys H Heq. rewrite !impl_implb.
+          (* Idem *)
+          assert (H: forall a b c d, (a --> b) --> a && c --> negb (x <=? y) --> (c --> (y <=? x) --> d) --> b && d) by smt.
+          apply H.
+    Qed.
+
+
+    Theorem sort_sorts l : is_sorted (sort l).
+    Proof.
+      induction l as [ |x xs IHxs].
+      - reflexivity.
+      - simpl. now apply insert_keeps_sorted.
+    Qed.
+
+  End Spec.
+
+End InsertionSort.
diff --git a/examples/Non_terminating.v b/examples/Non_terminating.v
index 087301a..7dad08f 100644
--- a/examples/Non_terminating.v
+++ b/examples/Non_terminating.v
@@ -1,3 +1,15 @@
+(**************************************************************************)
+(*                                                                        *)
+(*     SMTCoq                                                             *)
+(*     Copyright (C) 2011 - 2019                                          *)
+(*                                                                        *)
+(*     See file "AUTHORS" for the list of authors                         *)
+(*                                                                        *)
+(*   This file is distributed under the terms of the CeCILL-C licence     *)
+(*                                                                        *)
+(**************************************************************************)
+
+
 Require Import SMTCoq.
 
 Parameter g : Z -> Z.
diff --git a/examples/euf.log b/examples/euf.log
deleted file mode 100644
index 3bccc6a..0000000
--- a/examples/euf.log
+++ /dev/null
@@ -1,8 +0,0 @@
-1:(input (#1:(and #2:(= b a) #3:(= b c) #4:(= c d) #5:(= e c) #6:(= e f) (not #7:(= a f)))))
-2:(and (#2) 1 0)
-3:(and (#3) 1 1)
-4:(and (#5) 1 3)
-5:(and (#6) 1 4)
-6:(and ((not #7)) 1 5)
-7:(eq_transitive ((not #2) (not #3) (not #5) (not #6) #7))
-8:(resolution () 7 2 3 4 5 6)
diff --git a/examples/euf.smt2 b/examples/euf.smt2
deleted file mode 100644
index c151654..0000000
--- a/examples/euf.smt2
+++ /dev/null
@@ -1,11 +0,0 @@
-(set-logic QF_UF)
-(declare-sort U 0)
-(declare-fun a () U)
-(declare-fun b () U)
-(declare-fun c () U)
-(declare-fun d () U)
-(declare-fun e () U)
-(declare-fun f () U)
-(assert (and (= a b) (= b c) (= c d) (= c e) (= e f) (not (= a f))))
-(check-sat)
-(exit)
diff --git a/examples/lia.lfsc b/examples/lia.lfsc
new file mode 100644
index 0000000..1aa900b
--- /dev/null
+++ b/examples/lia.lfsc
@@ -0,0 +1,43 @@
+unsat
+(check
+ ;; Declarations
+(% x (term Int)
+(% A1 (th_holds true)
+(% A0 (th_holds (not (impl (= Int (-_Int x (a_int 3) )  (a_int 7) ) (<=_Int (a_int 10)  x) )))
+(: (holds cln)
+
+ ;; Printing deferred declarations 
+
+
+;; BV const letification
+
+
+
+ ;; Printing the global let map
+(@ let1 false
+
+ ;; Printing aliasing declarations 
+
+
+ ;; Rewrites for Lemmas 
+
+ ;; In the preprocessor we trust 
+(th_let_pf _ (trust_f false) (\ .PA205
+(th_let_pf _ (trust_f (not let1)) (\ .PA227
+
+;; Printing mapping from preprocessed assertions into atoms 
+(decl_atom let1 (\ .v1 (\ .a1
+(satlem _ _ (ast _ _ _ .a1 (\ .l3 (clausify_false (contra _ .l3 .PA227)))) (\ .pb1
+(satlem _ _ (asf _ _ _ .a1 (\ .l2 (clausify_false (contra _ .PA205 .l2)))) (\ .pb4
+ ;; Theory Lemmas 
+
+;; BB atom mapping
+
+
+;; Bit-blasting definitional clauses 
+
+
+ ;; Bit-blasting learned clauses 
+
+(satlem_simplify _ _ _ (R _ _ .pb4 .pb1 .v1) (\ empty empty)))))))))))))))))))
+;;
diff --git a/examples/lia.smt2 b/examples/lia.smt2
new file mode 100644
index 0000000..df290d0
--- /dev/null
+++ b/examples/lia.smt2
@@ -0,0 +1,5 @@
+(set-logic QF_LIA)
+(declare-fun x () Int)
+(assert (not (=> (= (- x 3) 7) (<= 10 x))))
+(check-sat)
+(exit)
diff --git a/examples/lia.vtlog b/examples/lia.vtlog
new file mode 100644
index 0000000..d3a03ee
--- /dev/null
+++ b/examples/lia.vtlog
@@ -0,0 +1,7 @@
+1:(input ((not #1:(=> #2:(= #3:(- x 3) 7) #4:(<= 10 x)))))
+2:(tmp_LA_pre ((not #5:(=> #6:(and #7:(<= #3 7) #8:(<= 7 #3)) #4))) 1)
+3:(not_implies1 (#6) 2)
+4:(and (#8) 3 1)
+5:(not_implies2 ((not #4)) 2)
+6:(la_generic (#4 (not #8)))
+7:(resolution () 6 4 5)
diff --git a/examples/one_equality_switch.v b/examples/one_equality_switch.v
index 3473d08..61fd9c7 100644
--- a/examples/one_equality_switch.v
+++ b/examples/one_equality_switch.v
@@ -1,3 +1,15 @@
+(**************************************************************************)
+(*                                                                        *)
+(*     SMTCoq                                                             *)
+(*     Copyright (C) 2011 - 2019                                          *)
+(*                                                                        *)
+(*     See file "AUTHORS" for the list of authors                         *)
+(*                                                                        *)
+(*   This file is distributed under the terms of the CeCILL-C licence     *)
+(*                                                                        *)
+(**************************************************************************)
+
+
 Require Import SMTCoq.
 Require Import Bool.
 Local Open Scope int63_scope.
diff --git a/examples/switching_input.v b/examples/switching_input.v
index 52261d8..629a3ad 100644
--- a/examples/switching_input.v
+++ b/examples/switching_input.v
@@ -1,3 +1,15 @@
+(**************************************************************************)
+(*                                                                        *)
+(*     SMTCoq                                                             *)
+(*     Copyright (C) 2011 - 2019                                          *)
+(*                                                                        *)
+(*     See file "AUTHORS" for the list of authors                         *)
+(*                                                                        *)
+(*   This file is distributed under the terms of the CeCILL-C licence     *)
+(*                                                                        *)
+(**************************************************************************)
+
+
 Require Import SMTCoq.
 Require Import Bool.
 Local Open Scope int63_scope.
diff --git a/examples/sym_zeq.v b/examples/sym_zeq.v
index b940490..1c4be83 100644
--- a/examples/sym_zeq.v
+++ b/examples/sym_zeq.v
@@ -1,3 +1,15 @@
+(**************************************************************************)
+(*                                                                        *)
+(*     SMTCoq                                                             *)
+(*     Copyright (C) 2011 - 2019                                          *)
+(*                                                                        *)
+(*     See file "AUTHORS" for the list of authors                         *)
+(*                                                                        *)
+(*   This file is distributed under the terms of the CeCILL-C licence     *)
+(*                                                                        *)
+(**************************************************************************)
+
+
 Require Import SMTCoq.
 Require Import Bool.
 Local Open Scope int63_scope.