exp1.py: 'evolve' proofs in a Hilbert-style proof system for minimal propositional logic
exp2.py: prove things in minimal propositional sequent calculus (and calculate various statistics about the size of those proofs)

Run:

    # To make exp2.py executable
    chmod +x ./exp2.py

    # To see how the command line interface works
    ./exp2.py --help
    ./exp2.py generate --help
    ./exp2.py stats --help

    # To generate some formulae
    ./exp2.py generate --output formulae.bin --max-depth 3

    # To attempt to prove some formulae and give stats about the size of those proofs
    ./exp2.py stats --input formulae.bin

    # To attempt to evolve a heuristic
    # This example will take a  VERY LONG  time for each generation!
    ./exp2.py evolve --pop-size 100 --num-connectives 3 --num-stmts 1000 --max-depth 5

    # To attempt to evolve a heuristic (more quickly, but not very good)
    ./exp2.py evolve --pop-size 50 --num-connectives 3 --num-stmts 40 --max-depth 4

Example (using old simplistic heuristic, not evolved ones):

    $ ./exp2.py generate --output formulae.bin --max-depth 5 --connectives 1
    generated 10000 statements

    $ ./exp2.py stats --input formulae.bin
    Successes: 4763/10000: 47%
    Timeouts: 0/10000: 0%
    mean: 366.69871929456224
    median: 39
    most_common: [(5, 481), (10, 183), (8, 110)]
    shortest: 4
    longest: 206909
    skewness: 41.36614115870174
    variance: 13868574.485649347
    excess kurtosis: 2102.4202907142203

    $ ./exp2.py stats --input formulae.bin --reverse
    Successes: 4807/10000: 48%
    Timeouts: 0/10000: 0%
    mean: 21.712502600374453
    median: 15
    most_common: [(5, 1018), (10, 367), (13, 219)]
    shortest: 4
    longest: 1548
    skewness: 22.641249523151746
    variance: 1168.119575237977
    excess kurtosis: 881.3525206013211