diff --git a/README.md b/README.md
index d719795..182f21a 100644
--- a/README.md
+++ b/README.md
@@ -34,7 +34,7 @@ Overall structure:
 
 ## Generating CNFs
 
-The project includes scripts for generating the CNFs we formalized against.
+The project includes scripts for generating the CNFs we formalized against. These must be run inside the `Lean` subfolder.
 
 #### Convex 6-gon
 For `n` points:
@@ -66,7 +66,7 @@ The **tautology proof** is implied by checking that $F \land (\bigwedge_i \neg C
 As a first step, we will generate the main CNF by running:
 ```
 cd Lean
-lake exe encode hole 6 30 cube_checking/vars.out > cube_checking/6-30.cnf
+lake exe encode hole 6 30 ../cube_checking/vars.out > ../cube_checking/6-30.cnf
 ```
 
 Then, inside the `cube_checking` folder, the **tautology proof** can be verified by running `sh verify_tautology`, which boils down to:
@@ -74,7 +74,7 @@ Then, inside the `cube_checking` folder, the **tautology proof** can be verified
 gcc 6hole-cube.c -o cube_gen
 ./cube_gen 0 vars.out > cubes.icnf
 python3 cube_join.py -f 6-30.cnf -c cubes.icnf --tautcheck -o taut_if_unsat.cnf
-cadical taut_if_unsat.cnf tautology_proof.lrat --lrat
+cadical taut_if_unsat.cnf tautology_proof.lrat --lrat # this should take around 30 seconds
 cake_lpr taut_if_unsat.cnf tautology_proof.lrat
 ```
 Note that this requires:
@@ -90,7 +90,7 @@ For the **UNSAT proof**, given the total amount of computation required to run a
 ```
 ./cube_gen <i> vars.out > .tmp_cube_<i>
 python3 cube_join.py -f 6-30.cnf -c .tmp_cube_<i> -o with_cube_<i>.cnf
-cadical with_cube_<i>.cnf proof_cube_<i>.lrat --lrat
+cadical with_cube_<i>.cnf proof_cube_<i>.lrat --lrat # this should take a few seconds
 cake_lpr with_cube_<i>.cnf proof_cube_<i>.lrat
 ```
 To simplify the process, we have added a bash script `solve_cube.sh`, which can be simply run as (for example, for cube number 42):
@@ -98,8 +98,14 @@ To simplify the process, we have added a bash script `solve_cube.sh`, which can
 ```
 sh solve_cube.sh 42
 ```
+The cubes are indexed from 1 to 312418.
 
-
+To generate the formula + the totality of the cubes for incremental solving, run:
+```
+./cube_gen 0 vars.out > cubes.icnf
+python3 cube_join.py -f 6-30.cnf -c cubes.icnf --inccnf -o full_computation.icnf
+cadical full_computation.icnf # this should take a while :P
+```
 
 ## Authors
 - [Bernardo Subercaseaux](https://bsubercaseaux.github.io/) (Carnegie Mellon University)
diff --git a/cube_checking/cube_join.py b/cube_checking/cube_join.py
index 1b3eb04..44b72e7 100644
--- a/cube_checking/cube_join.py
+++ b/cube_checking/cube_join.py
@@ -6,10 +6,11 @@
     "-f", "--formula", required=True, type=str, help="CNF Formula file"
 )
 argparser.add_argument("-c", "--cubes", required=True, type=str, help="Cube file")
+argparser.add_argument("-o", "--output", required=False, type=str, help="Output file")
 argparser.add_argument(
     "--tautcheck", action="store_true", help="Checks for a tautology"
 )
-argparser.add_argument("-o", "--output", required=False, type=str, help="Output file")
+argparser.add_argument('--inccnf', action="store_true", help="Creates a .icnf file with the formula + cubes")
 
 
 args = argparser.parse_args()
@@ -18,6 +19,7 @@
 cube_file = args.cubes
 output_file = args.output
 tautcheck = args.tautcheck
+icnf = args.inccnf
 
 encoding = modeler.Modeler()
 
@@ -25,7 +27,6 @@ def itokenize(line):
     """
     takes a line as a string, coming from either a `p cnf` or a `p inccnf` file
     returns array of ints without 0
-    
     ignores lines starting with c or p
     """
     if len(line) == 0:
@@ -66,10 +67,11 @@ def itokenize(line):
 
 if tautcheck:
     encoding.serialize(output_file)
+elif icnf:
+    encoding.cube_and_conquer(lambda: cubes, output_file)
 else:
     assert len(cubes) == 1
     cube = cubes[0]
     for lit in cube:
         encoding.add_clause([lit])
     encoding.serialize(output_file)
-    
\ No newline at end of file