
The complete proof:
The Isar proof is in: proofs/isar_proof15.thy
The proof in the natural language form is in: proofs/nl_proof15.tex
The number of steps: 21
The number of axioms used: 2
The list of used axioms:
ax_comp_4123 ax_comp_2134 

The clean proof: 
The Isar proof is in: proofs/isar_proof_optimized15.thy
The proof in the natural language form is in: proofs/nl_proof_optimized15.tex
The number of steps: 13

The list of all axioms considered (given and derived) is in: all_axioms.txt.

Basic time: 2.01 seconds. 
Cleaning time: 0.01 seconds. 
Total time: 2.02 seconds. 

