In an episode of "Big Bang Theory",
Kooth Rapali suggets Sheldon Cooper to play Rock, Paper,
Scissors but Sheldon complains about the high probability
of tying so he suggests playing
Rock-paper-scissors-lizard-Spock with the following rules:

- Scissors cut paper
- Paper covers rock
- Rock crushes lizard
- Lizard poisons Spock
- Spock smashes scissors
- Scissors decapitate lizard
- Lizard eats paper
- Paper disproves Spock
- Spock vaporizes rock
- Rock crushes scissors

We suppose that each of them selects one sign in a
completely random way, equally probable for the five
cases.

### What to do

Model the scenario in P-log so that we can conclude any of
the facts,

`winner(kooth)`,

`winner(sheldon)`
or

`tie`, according to the game result. Then,
compute with P-log the following probabilites

- The probability of
`winner(kooth)`.
- The probability of
`winner(kooth)`
conditioned to the observation `play(sheldon)=rock`.
- The probability of a
`tie`.
- The probability that someone marks
`scissors.`

Now suppose that Kooth is sometimes quick enough to see
Sheldon making the "paper" sign. In fact, 2 of each 3
times, she is able to foresee Sheldon's "paper". In that
case, Kooth always marks "scissors". Model this variant
anfourd recompute the probabilities above in this
new situation.

You must deliver three files: two files with the
domains in P-log (the original one and the second
variant) plus a text file listing the obtained results
(and, if possible, explaining their values).

### Installing and using P-log

For installing P-log you will need lparse and smodels
which are analogous tools to gringo and clasp,
respectively. To this aim, follow these instructions

- Download lparse
and smodels
- Compile both tools and place the resulting binaries
in some directory in your path. (You will need
bison/yacc if not installed)

- Download plog
and compile the source with cmake

Finally, for executing plog, type

` plog -t filename.txt`

You can try the following examples included in the
slides: jungle.txt, montyhall.txt, simpson.txt